Recent zbMATH articles in MSC 68https://zbmath.org/atom/cc/682021-11-25T18:46:10.358925ZWerkzeugBook review of: M. Hudec, Fuzziness in information systems. How to deal with crisp and fuzzy data in selection, classification, and summarizationhttps://zbmath.org/1472.000392021-11-25T18:46:10.358925Z"Vujošević, Mirko"https://zbmath.org/authors/?q=ai:vujosevic.mirkoReview of [Zbl 1467.68001].On logic embeddings and Gödel's Godhttps://zbmath.org/1472.030132021-11-25T18:46:10.358925Z"Benzmüller, Christoph"https://zbmath.org/authors/?q=ai:benzmuller.christoph-e"Paleo, Bruno Woltzenlogel"https://zbmath.org/authors/?q=ai:woltzenlogel-paleo.brunoSummary: We have applied an elegant and flexible logic embedding approach to verify and automate a prominent philosophical argument: the ontological argument for the existence of God. In our ongoing computer-assisted study, higher-order automated reasoning tools have made some interesting observations, some of which were previously unknown.
For the entire collection see [Zbl 1327.68013].Rules with parameters in modal logic. II.https://zbmath.org/1472.030162021-11-25T18:46:10.358925Z"Jeřábek, Emil"https://zbmath.org/authors/?q=ai:jerabek.emilThis paper deals with the computational complexity of admissibility and unifiability with parameters in transitive modal logics. It is a continuation of the author's paper [ibid. 166, No. 9, 881--933 (2015; Zbl 1408.03015)], which the author strongly suggests to read. Thus we confine ourselves to quote from the present paper's Abstract: ''We completely classify the complexity of unifiability or inadmissibility in any clx (i.e., cluster-extensible) logic as being complete for one of \(\Sigma^{\mathrm{exp}}_{2}\), NEXP, coNEXP, PSPACE or \(\Pi^{p}_{2}\). [\dots] Our upper bounds are specific to clx logics, but we also include similar results for logics of bounded depth and width. In contrast, our lower bounds are very general: they apply each to a class of all transitive logics whose frames allow occurrence of certain finite subframes. [\dots] We prove PSCACE-hardness of derivability for a broad class of transitive logics that include all logics with a disjunctive property.''Deciding the Bernays-Schoenfinkel fragment over bounded difference constraints by simple clause learning over theorieshttps://zbmath.org/1472.030242021-11-25T18:46:10.358925Z"Bromberger, Martin"https://zbmath.org/authors/?q=ai:bromberger.martin"Fiori, Alberto"https://zbmath.org/authors/?q=ai:fiori.alberto"Weidenbach, Christoph"https://zbmath.org/authors/?q=ai:weidenbach.christophSummary: Simple clause learning over theories SCL(T) is a decision procedure for the Bernays-Schoenfinkel fragment over bounded difference constraints BS(BD). The BS(BD) fragment consists of clauses built from first-order literals without function symbols together with simple bounds or difference constraints, where for the latter it is required that the variables of the difference constraint are bounded from below and above. The SCL(T) calculus builds model assumptions over a fixed finite set of fresh constants. The model assumptions consist of ground foreground first-order and ground background theory literals. The model assumptions guide inferences on the original clauses with variables. We prove that all clauses generated this way are non-redundant. As a consequence, expensive testing for tautologies and forward subsumption is completely obsolete and termination with respect to a fixed finite set of constants is a consequence. We prove SCL(T) to be sound and refutationally complete for the combination of the Bernays Schoenfinkel fragment with any compact theory. Refutational completeness is obtained by enlarging the set of considered constants. For the case of BS(BD) we prove an abstract finite model property such that the size of a sufficiently large set of constants can be fixed a priori.
For the entire collection see [Zbl 1471.68017].Compositional satisfiability solving in separation logichttps://zbmath.org/1472.030252021-11-25T18:46:10.358925Z"Le, Quang Loc"https://zbmath.org/authors/?q=ai:le.quang-locSummary: We introduce a novel decision procedure to the satisfiability problem in array separation logic combined with general inductively defined predicates and arithmetic. Our proposal differentiates itself from existing works by solving satisfiability through compositional reasoning. First, following Fermat's method of infinite descent, it infers for every inductive definition a ``base'' that precisely characterises the satisfiability. It then utilises the base to derive such a base for any formula where these inductive predicates reside in. Especially, we identify an expressive decidable fragment for the compositionality. We have implemented the proposal in a tool and evaluated it over challenging problems. The experimental results show that the compositional satisfiability solving is efficient and our tool is effective and efficient when compared with existing solvers.
For the entire collection see [Zbl 1471.68017].First-order definitions of subgraph isomorphism through the adjacency and order relationshttps://zbmath.org/1472.030262021-11-25T18:46:10.358925Z"Grigoryan, Oleg"https://zbmath.org/authors/?q=ai:grigoryan.oleg"Makarov, Mikhail"https://zbmath.org/authors/?q=ai:makarov.mikhail-v"Zhukovskii, Maksim"https://zbmath.org/authors/?q=ai:zhukovskii.maximGiven a graph \(F\), let \(\mathcal S(F)\) be the graphical property of having \(F\) as a (not necessarily induced) subgraph. If \(\sim\) is the vertex adjacency relation symbol, let \(\Sigma = \{ \sim, < \}\) be the signature for linearly ordered finite graphs. A first-order sentence \(\varphi\) of signature \(\Sigma\) defines \(\mathcal S(F)\) if, for any graph \(G\), and any linear ordering of \(G\)'s vertices, if \(G'\) is \(G\) expanded by that linear ordering, then \(G' \models \varphi\) iff \(G\) has \(F\) as a (not necessarily induced) subgraph. Let \(D_< (F)\) be the minimum quantifier depth of any \(\Sigma\)-sentence defining \(\mathcal S(F)\) and let \(W_< (F)\) be the minimum number of variables of any \(\Sigma\)-sentence defining \(\mathcal S(F)\).
The primary result of this paper is that if \(F\) is a tree of \(\ell\) vertices, then \(D_< (F) \leq \ell/2 + \lceil \log_2 (\ell + 2) \rceil - 1\); they also observe that \(W_< (F) \leq \ell/2 + 2\). In addition, using Fraïsse-Ehrenfeucht games, \(D_<(F)\) is computed for each graph \(F\) of order less than \(5\).
There are some typos, so readers should take care.Solovay reducibility and continuityhttps://zbmath.org/1472.030412021-11-25T18:46:10.358925Z"Kumabe, Masahiro"https://zbmath.org/authors/?q=ai:kumabe.masahiro"Miyabe, Kenshi"https://zbmath.org/authors/?q=ai:miyabe.kenshi"Mizusawa, Yuki"https://zbmath.org/authors/?q=ai:mizusawa.yuki"Suzuki, Toshio"https://zbmath.org/authors/?q=ai:suzuki.toshioSolovay reducibility is introduced by Solovay to investigate left-c.e. random reals. In the paper under review, the author gives a characterization of Solovay reducibility from the analytical point of view. I.e., roughly speaking, for left-c.e. reals \(\alpha\) and \(\beta\), \(\alpha\) is Solovay reducible to \(\beta\) if and only if there is a partial computable Lipschitz function \(f:[s,\beta]\to \mathbb{R}\), where \(s\) is a rational point, so that there is an increasing sequence rationals \(\{r_n\}_{n}\) from \([s, \beta]\) with \(r_n\to \beta\) for which \(f(r_n)\to \alpha\) and \(\forall nf(r_n)\leq \alpha\). They also introduce a weaker reducibility, called quasi-Solovay reducibility, and found its characerterization via Hölder continuity.Restricted stacks as functionshttps://zbmath.org/1472.050042021-11-25T18:46:10.358925Z"Berlow, Katalin"https://zbmath.org/authors/?q=ai:berlow.katalinSummary: The stack sort algorithm has been the subject of extensive study over the years. In this paper we explore a generalized version of this algorithm where instead of avoiding a single decrease, the stack avoids a set \(T\) of permutations. We let \(s_T\) denote this map. We classify for which sets \(T\) the map \(s_T\) is bijective. A corollary to this answers a question of \textit{J.-L. Baril} et al. [Inf. Process. Lett. 171, Article ID 106138, 9 p. (2021; Zbl 07360091)] about stack sort composed with \(s_{\{ \sigma , \tau \}}\), known as the \((\sigma, \tau)\)-machine. This fully classifies for which \(\sigma\) and \(\tau\) the preimage of the identity under the \((\sigma, \tau)\)-machine is counted by the Catalan numbers. We also prove that the number of preimages of a permutation under the map \(s_T\) is bounded by the Catalan numbers, with a shift of indices. For \(T\) of size 1, we classify exactly when this bound is sharp. We also explore the periodic points and maximum number of preimages of various \(s_T\) for \(T\) containing two length 3 permutations.Codes, cubes, and graphical designshttps://zbmath.org/1472.050302021-11-25T18:46:10.358925Z"Babecki, Catherine"https://zbmath.org/authors/?q=ai:babecki.catherineSummary: Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical design. We show that even in highly structured graphs, graphical designs are distinct from the related concepts of extremal designs, maximum stable sets in distance graphs, and \(t\)-designs on association schemes.Maximal strongly connected cliques in directed graphs: algorithms and boundshttps://zbmath.org/1472.050612021-11-25T18:46:10.358925Z"Conte, Alessio"https://zbmath.org/authors/?q=ai:conte.alessio"Kanté, Mamadou Moustapha"https://zbmath.org/authors/?q=ai:kante.mamadou-moustapha"Uno, Takeaki"https://zbmath.org/authors/?q=ai:uno.takeaki"Wasa, Kunihiro"https://zbmath.org/authors/?q=ai:wasa.kunihiroSummary: Finding communities in the form of cohesive subgraphs is a fundamental problem in network analysis. In domains that model networks as undirected graphs, communities are generally associated with dense subgraphs, and many community models have been proposed. Maximal cliques are arguably the most widely studied among such models, with early works dating back to the '60s, and a continuous stream of research up to the present. In domains that model networks as directed graphs, several approaches for community detection have been proposed, but there seems to be no clear model of cohesive subgraph, i.e., of what a community should look like. We extend the fundamental model of clique to directed graphs, adding the natural constraint of strong connectivity within the clique.
We consider in this paper the problem of listing all maximal strongly connected cliques in a directed graph. We first investigate the combinatorial properties of strongly connected cliques and use them to prove that every \(n\)-vertex directed graph has at most \(3^{n / 3}\) maximal strongly connected cliques. We then exploit these properties to produce the first algorithms with polynomial delay for enumerating maximal strongly connected cliques: a first algorithm with polynomial delay and exponential space usage, and a second one, based on reverse-search, with higher (still polynomial) delay but which uses linear space.On the complexity of a linear ordering of weighted directed acyclic graphshttps://zbmath.org/1472.050652021-11-25T18:46:10.358925Z"Shchekalev, M. I."https://zbmath.org/authors/?q=ai:shchekalev.m-i"Bokov, G. V."https://zbmath.org/authors/?q=ai:bokov.grigoriy-v"Kudryavtsev, V. B."https://zbmath.org/authors/?q=ai:kudryavtsev.valerii-borisovichSummary: We consider weighted directed acyclic graphs to whose edges nonnegative integers as weights are assigned. The complexity of a linear ordering of vertices is examined for these graphs in the order of topological sorting. An accurate estimate for the Shannon function of the complexity of the linear ordering problem for weighted directed acyclic graphs is obtained.Efficiently enumerating minimal triangulationshttps://zbmath.org/1472.050702021-11-25T18:46:10.358925Z"Carmeli, Nofar"https://zbmath.org/authors/?q=ai:carmeli.nofar"Kenig, Batya"https://zbmath.org/authors/?q=ai:kenig.batya"Kimelfeld, Benny"https://zbmath.org/authors/?q=ai:kimelfeld.benny"Kröll, Markus"https://zbmath.org/authors/?q=ai:kroll.markusSummary: We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where ``proper'' means that the tree decomposition cannot be improved by removing or splitting a bag. The algorithm can incorporate any method for (ordinary, single result) triangulation or tree decomposition, and can serve as an anytime algorithm to improve such a method. We describe an extensive experimental study of an implementation on real data from different fields. Our experiments show that the algorithm improves upon central quality measures over the underlying tree decompositions, and is able to produce a large number of high-quality decompositions.Efficient enumeration of maximal induced bicliqueshttps://zbmath.org/1472.050712021-11-25T18:46:10.358925Z"Hermelin, Danny"https://zbmath.org/authors/?q=ai:hermelin.danny"Manoussakis, George"https://zbmath.org/authors/?q=ai:manoussakis.georgeSummary: Given a graph \(G\) of order \(n\), we consider the problem of enumerating all its maximal induced bicliques. We first propose an algorithm running in time \(\mathcal{O} ( n 3^{n / 3} )\). As the maximum number of maximal induced bicliques of a graph with \(n\) vertices is \(\Theta ( 3^{n / 3} )\), the algorithm is worst-case output size optimal. Then, we prove new bounds on the maximum number of maximal induced bicliques of graphs with respect to their maximum degree \(\Delta\) and degeneracy \(k\), and propose a near-optimal algorithm with enumeration time \(\mathcal{O} ( n k ( \Delta + k ) 3^{\frac{ \Delta + k}{ 3}} )\). Then, we provide output sensitive algorithms for this problem with enumeration time depending only on the maximum degree of the input graph. Since we need to store the bicliques in these algorithms, the space complexity may be exponential. Thus, we show how to modify them so they only require polynomial space, but with a slight time complexity increase.Efficient enumeration of dominating sets for sparse graphshttps://zbmath.org/1472.050732021-11-25T18:46:10.358925Z"Kurita, Kazuhiro"https://zbmath.org/authors/?q=ai:kurita.kazuhiro"Wasa, Kunihiro"https://zbmath.org/authors/?q=ai:wasa.kunihiro"Arimura, Hiroki"https://zbmath.org/authors/?q=ai:arimura.hiroki"Uno, Takeaki"https://zbmath.org/authors/?q=ai:uno.takeakiSummary: A dominating set \(D\) of a graph \(G\) is a set of vertices such that any vertex in \(G\) is in \(D\) or its neighbor is in \(D\). Enumeration of minimal dominating sets in a graph is one of the central problems in enumeration study since enumeration of minimal dominating sets corresponds to the enumeration of minimal hypergraph transversals. The output-polynomial time enumeration of minimal hypergraph transversals is an interesting open problem. On the other hand, enumeration of dominating sets including non-minimal ones has not been received much attention. In this paper, we address enumeration problems for dominating sets from sparse graphs which are degenerate graphs and graphs with large girth, and we propose two algorithms for solving the problems. The first algorithm enumerates all the dominating sets for a \(k\)-degenerate graph in \(O \left( k\right)\) time per solution using \(O \left( n + m\right)\) space, where \(n\) and \(m\) are respectively the number of vertices and edges in an input graph. That is, the algorithm is optimal for graphs with constant degeneracy such as trees, planar graphs, \(H\)-minor free graphs with some fixed \(H\). The second algorithm enumerates all the dominating sets in constant time per solution for input graphs with girth at least nine.Compact cactus representations of all non-trivial min-cutshttps://zbmath.org/1472.050852021-11-25T18:46:10.358925Z"Lo, On-Hei S."https://zbmath.org/authors/?q=ai:lo.on-hei-solomon"Schmidt, Jens M."https://zbmath.org/authors/?q=ai:schmidt.jens-m"Thorup, Mikkel"https://zbmath.org/authors/?q=ai:thorup.mikkelSummary: Recently, \textit{K.-I. Kawarabayashi} and \textit{M. Thorup} [J. ACM 66, No. 1, Article No. 4, 50 p. (2019; Zbl 1426.68217)] presented the first deterministic edge-connectivity recognition algorithm in near-linear time. A crucial step in their algorithm uses the existence of vertex subsets of a simple graph \(G\) on \(n\) vertices whose contractions leave a multigraph with \(\widetilde{O} ( n / \delta )\) vertices and \(\widetilde{O} ( n )\) edges that preserves all non-trivial min-cuts of \(G\), where \(\delta\) is the minimum degree of \(G\) and \(\widetilde{O}\) hides logarithmic factors.
We present a simple argument that improves this contraction-based sparsifier by eliminating the poly-logarithmic factors, that is, we show a contraction-based sparsification that leaves \(O ( n / \delta )\) vertices and \(O ( n )\) edges, preserves all non-trivial min-cuts and can be computed in near-linear time \(\widetilde{O} ( m )\), where \(m\) is the number of edges of \(G\). We also obtain that every simple graph has \(O ( ( n / \delta )^2 )\) non-trivial min-cuts.
Our approach allows to represent all non-trivial min-cuts of a graph by a cactus representation, whose cactus graph has \(O ( n / \delta )\) vertices. Moreover, this cactus representation can be derived directly from the standard cactus representation of all min-cuts in linear time. We apply this compact structure to show that all min-cuts can be explicitly listed in \(\widetilde{O} ( m ) + O ( n^2 / \delta )\) time for every simple graph, which improves the previous best time bound \(O ( n m )\) given by \textit{D. Gusfield} and \textit{D. Naor} [Algorithmica 10, No. 1, 64--89 (1993; Zbl 0781.90087)].Correction to: ``Properties of a \(q\)-analogue of zero forcing''https://zbmath.org/1472.051112021-11-25T18:46:10.358925Z"Butler, Steve"https://zbmath.org/authors/?q=ai:butler.steve"Erickson, Craig"https://zbmath.org/authors/?q=ai:erickson.craig"Fallat, Shaun"https://zbmath.org/authors/?q=ai:fallat.shaun-m"Hall, H. Tracy"https://zbmath.org/authors/?q=ai:hall.h-tracy"Kroschel, Brenda"https://zbmath.org/authors/?q=ai:kroschel.brenda-k"Lin, Jephian C.-H."https://zbmath.org/authors/?q=ai:lin.jephian-chin-hung"Shader, Bryan"https://zbmath.org/authors/?q=ai:shader.bryan-l"Warnberg, Nathan"https://zbmath.org/authors/?q=ai:warnberg.nathan"Yang, Boting"https://zbmath.org/authors/?q=ai:yang.botingFrom the text: The LaTeX control sequence \(\setminus\)\(\deg\) is interpreted differently in the authors' and the publisher's LaTeX setting. The authors' intention is deg, as the degree of a vertex on a graph; however, it becomes a circle, as the degree for temperature, in the publisher's environment. As a consequence, the mistakes occur whenever the macro \(\setminus\)\(\deg\) is used. The original article [the authors, ibid. 36, No. 5, 1401--1419 (2020; Zbl 1458.05166)] has been corrected.On problems of \(\mathcal{CF}\)-connected graphs for \({K}_{{m,n}} \)https://zbmath.org/1472.051152021-11-25T18:46:10.358925Z"Staš, Michal"https://zbmath.org/authors/?q=ai:stas.michal"Valiska, Juraj"https://zbmath.org/authors/?q=ai:valiska.jurajSummary: A connected graph \(G\) is \(\mathcal{CF} \)-connected if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of \(G\). We conjecture that a complete bipartite graph \(K_{m,n}\) is \(\mathcal{CF} \)-connected if and only if it does not contain a subgraph of \(K_{3,6}\) or \(K_{4,4}\). We establish the validity of this conjecture for all complete bipartite graphs \(K_{m,n}\) for any \(m,n\) with \(\min \{m,n\}\leq 6\), and conditionally for \(m,n\geq 7\) on the assumption of Zarankiewicz's conjecture that \(\operatorname{cr}(K_{m,n})=\left\lfloor \frac{m}{2} \right \rfloor \left \lfloor \frac{m-1}{2} \right \rfloor \left \lfloor \frac{n}{2} \right \rfloor \left \lfloor \frac{n-1}{2} \right \rfloor \).Sampling hypergraphs with given degreeshttps://zbmath.org/1472.051172021-11-25T18:46:10.358925Z"Dyer, Martin"https://zbmath.org/authors/?q=ai:dyer.martin-e"Greenhill, Catherine"https://zbmath.org/authors/?q=ai:greenhill.catherine-s"Kleer, Pieter"https://zbmath.org/authors/?q=ai:kleer.pieter"Ross, James"https://zbmath.org/authors/?q=ai:ross.james-lance|ross.james-e|ross.james-b"Stougie, Leen"https://zbmath.org/authors/?q=ai:stougie.leenSummary: There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm \(\mathcal{A}\) for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm \(\mathcal{A} \), and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a positive constant.Complexity and characterization aspects of edge-related domination for graphshttps://zbmath.org/1472.051212021-11-25T18:46:10.358925Z"Pan, Zhuo"https://zbmath.org/authors/?q=ai:pan.zhuo"Li, Xianyue"https://zbmath.org/authors/?q=ai:li.xianyue"Xu, Shou-Jun"https://zbmath.org/authors/?q=ai:xu.shoujunLet \(G=(V,E)\) be a connected graph. A subset \(F\) of \(E\) is an edge dominating set (resp. a total edge dominating set) if every edge in \(E \setminus F\) (resp. in \(E\)) is adjacent to at least one edge in \(F\). The minimum cardinality of an edge dominating set (resp. a total edge dominating set) of \(G\) is the edge domination number (resp. total edge domination number) of \(G\), denoted by \(\gamma^\prime(G)\) (resp. \(\gamma_t^\prime(G)\)). A semitotal edge dominating set is an edge dominating set \(S\) such that, for every edge \(e\) in \(S\), there exists such an edge \(e^\prime\) in \(S\) that \(e\) either is adjacent to \(e^\prime\) or shares a common neighbor edge with \(e^\prime\). The semitotal edge domination number, denoted by \(\gamma_{st}^\prime (G)\), is the minimum cardinality of a semitotal edge dominating set of \(G\). It is obvious from definitions that \(\gamma'(G)\le \gamma_{st}^\prime (G) \le \gamma_t^\prime(G)\).
In this paper, the authors first prove that the problem of deciding whether \(\gamma^\prime(G) = \gamma_{st}^\prime (G)\) is NP-hard in planar bipartite graphs with maximum degree 4, and then prove that the problem of deciding whether \(\gamma^\prime(G) = \gamma_{t}^\prime (G)\) is NP-hard in planar graphs with maximum degree 4, respectively. Furthermore, they characterize trees with equal edge domination and semitotal edge domination numbers.A general stochastic matching model on multigraphshttps://zbmath.org/1472.051232021-11-25T18:46:10.358925Z"Begeot, Jocelyn"https://zbmath.org/authors/?q=ai:begeot.jocelyn"Marcovici, Irène"https://zbmath.org/authors/?q=ai:marcovici.irene"Moyal, Pascal"https://zbmath.org/authors/?q=ai:moyal.pascal"Rahme, Youssef"https://zbmath.org/authors/?q=ai:rahme.youssefSummary: We extend the general stochastic matching model on graphs introduced in \textit{J. Mairesse} and \textit{P. Moyal} [J. Appl. Probab. 53, No. 4, 1064--1077 (2016; Zbl 1356.60147)], to matching models on multigraphs, that is, graphs with self-loops. The evolution of the model can be described by a discrete time Markov chain whose positive recurrence is investigated. Necessary and sufficient stability conditions are provided, together with the explicit form of the stationary probability in the case where the matching policy is `First Come, First Matched'.On null 3-hypergraphshttps://zbmath.org/1472.051292021-11-25T18:46:10.358925Z"Frosini, Andrea"https://zbmath.org/authors/?q=ai:frosini.andrea"Kocay, William L."https://zbmath.org/authors/?q=ai:kocay.william-l"Palma, Giulia"https://zbmath.org/authors/?q=ai:palma.giulia"Tarsissi, Lama"https://zbmath.org/authors/?q=ai:tarsissi.lamaSummary: Given a 3-uniform hypergraph \(H\) consisting of a set \(V\) of vertices, and \(T \subseteq \binom{V}{3}\) triples, a null labelling is an assignment of \(\pm 1\) to the triples such that each vertex is contained in an equal number of triples labelled \(+ 1\) and \(- 1\). Thus, the signed degree of each vertex is zero. A necessary condition for a null labelling is that the degree of every vertex of \(H\) is even. The Null Labelling Problem is to determine whether \(H\) has a null labelling. It is proved that this problem is NP-complete. Computer enumerations suggest that most hypergraphs which satisfy the necessary condition do have a null labelling. Some constructions are given which produce hypergraphs satisfying the necessary condition, but which do not have a null labelling. A self complementary 3-hypergraph with this property is also constructed.Exact \(p\)-adic computation in Magmahttps://zbmath.org/1472.110042021-11-25T18:46:10.358925Z"Doris, Christopher"https://zbmath.org/authors/?q=ai:doris.christopherSummary: We describe a new arithmetic system for the Magma computer algebra system for working with \(p\)-adic numbers exactly, in the sense that numbers are represented lazily to infinite \(p\)-adic precision. This is the first highly featured such implementation. This has the benefits of increasing user-friendliness and speeding up some computations, as well as forcibly producing provable results. We give theoretical and practical justification for its design and describe some use cases. The intention is that this article will be of benefit to anyone wanting to implement similar functionality in other languages.On the minimal Hamming weight of a multi-base representationhttps://zbmath.org/1472.110452021-11-25T18:46:10.358925Z"Krenn, Daniel"https://zbmath.org/authors/?q=ai:krenn.daniel"Suppakitpaisarn, Vorapong"https://zbmath.org/authors/?q=ai:suppakitpaisarn.vorapong"Wagner, Stephan"https://zbmath.org/authors/?q=ai:wagner.stephan-gSummary: Given a finite set of bases \(b_1, b_2, \ldots, b_r\) (integers greater than 1), a multi-base representation of an integer \(n\) is a sum with summands \(db_1^{\alpha_1} b_2^{\alpha_2} \cdots b_r^{\alpha_r}\), where the \(\alpha_j\) are nonnegative integers and the digits \(d\) are taken from a fixed finite set. We consider multi-base representations with at least two bases that are multiplicatively independent. Our main result states that the order of magnitude of the minimal Hamming weight of an integer \(n\), i.e., the minimal number of nonzero summands in a representation of \(n\), is \(\log n /(\log \log n)\). This is independent of the number of bases, the bases themselves, and the digit set.
For the proof, the existing upper bound for prime bases is generalized to multiplicatively independent bases; for the required analysis of the natural greedy algorithm, an auxiliary result in Diophantine approximation is derived. The lower bound follows by a counting argument and alternatively by using communication complexity; thereby improving the existing bounds and closing the gap in the order of magnitude. This implies also that the greedy algorithm terminates after \(\mathcal{O}(\log n / \log \log n)\) steps, and that this bound is sharp.Connection and duplication formulas for the Boas-Buck-Appell polynomialshttps://zbmath.org/1472.110852021-11-25T18:46:10.358925Z"Nahid, Tabinda"https://zbmath.org/authors/?q=ai:nahid.tabinda"Khan, Subuhi"https://zbmath.org/authors/?q=ai:khan.subuhiSummary: The present paper conduct to introduce the connection and duplication formulas associated with the Boas-Buck-Appell polynomials. Examples providing the analogues results for certain members related to the Boas-Buck-Appell polynomials are considered.On multiplicative automatic sequenceshttps://zbmath.org/1472.110882021-11-25T18:46:10.358925Z"Konieczny, Jakub"https://zbmath.org/authors/?q=ai:konieczny.jakubA sequence \(a:\mathbb{N}\to\mathbb{C}\) is \textit{multiplicative} if \(a(mn) = a(m)a(n)\) for any coprime \(m, n\). If such a relation holds for all \(m,n\), it is said to be \textit{completely multiplicative}. Automatic sequences were first introduced by Cobham and then largely disseminated by the work of Allouche and Shallit. In this paper, the author proves that if \(a:\mathbb{N}\to\mathbb{C}\) is an automatic multiplicative sequence then there exists a threshold \(p_*\) and sequence \(\chi\) which is either a Dirichlet character or identically zero such that \(a(n) = \chi(n)\) for all \(n\) not divisible any prime \(p < p_*\). This answers a question of Bell, Bruin and Coons: classification of completely multiplicative automatic sequences was known but the question remained open for sequences which are multiplicative but not completely. As mentionned by the author, a similar result was obtained independently by \textit{O. Klurman} and \textit{P. Kurlberg} [Bull. Lond. Math. Soc. 52, No. 1, 185--188 (2020; Zbl 1457.11023)].Analysis of generalized continued fraction algorithms over polynomialshttps://zbmath.org/1472.112072021-11-25T18:46:10.358925Z"Berthé, Valérie"https://zbmath.org/authors/?q=ai:berthe.valerie"Nakada, Hitoshi"https://zbmath.org/authors/?q=ai:nakada.hitoshi"Natsui, Rie"https://zbmath.org/authors/?q=ai:natsui.rie"Vallée, Brigitte"https://zbmath.org/authors/?q=ai:vallee.brigitteIts well knew that the greatest common divisor (gcd) computation for univariate polynomials is a basic operation in computer algebra and Euclid's algorithm completely solves the problem of gcd computation for two entries. However, there does not exist a canonical generalization of Euclid's algorithm when working with at least three entries. Three generalized Euclidean algorithms for polynomials with coefficients in a finite field, inspired by classical multidimensional continued fraction maps, namely the Jacobi-Perron, the Brun, and the fully subtractive maps were chosen and compared in this paper. The two-dimensional versions of the Jacobi-Perron, the Brun, and the fully subtractive algorithms are associated with continued fraction maps. A unified framework for these algorithms and their associated continued fraction maps are provided. The convergence of the continued fraction maps was discussed. The bivariate generating functions are the main tool of the study. This enables in particular to exhibit asymptotic Gaussian laws. The various costs for the gcd algorithms, including the number of iterations and two versions of the bit-complexity, corresponding to two representations of polynomials analyzed in the paper. The associated two-dimensional continued fraction maps are studied and the invariance and the ergodicity of the Haar measure are proved. The authors obtain corresponding estimates for the costs of truncated trajectories under the action of these continued fraction maps and are compared the two models (gcd algorithms and their associated continued fraction maps).Irreducibility and deterministic \(r\)-th root finding over finite fieldshttps://zbmath.org/1472.112972021-11-25T18:46:10.358925Z"Bhargava, Vishwas"https://zbmath.org/authors/?q=ai:bhargava.vishwas"Ivanyos, Gábor"https://zbmath.org/authors/?q=ai:ivanyos.gabor"Mittal, Rajat"https://zbmath.org/authors/?q=ai:mittal.rajat"Saxena, Nitin"https://zbmath.org/authors/?q=ai:saxena.nitinA reduction of integer factorization to modular tetrationhttps://zbmath.org/1472.113122021-11-25T18:46:10.358925Z"Hittmeir, Markus"https://zbmath.org/authors/?q=ai:hittmeir.markusDeterministic integer factorization with oracles for Euler's totient functionhttps://zbmath.org/1472.113142021-11-25T18:46:10.358925Z"Hittmeir, Markus"https://zbmath.org/authors/?q=ai:hittmeir.markus"Pomykała, Jacek"https://zbmath.org/authors/?q=ai:pomykala.jacek-mSummary: In this paper, we construct deterministic factorization algorithms for natural numbers \(N\) under the assumption that the prime power decomposition of Euler's totient function \(\phi (N)\) is known. Their runtime complexities depend on the number \(\omega (N)\) of distinct prime divisors of \(N\), and we present efficient methods for relatively small values of \(\omega (N)\) as well as for its large values. One of our main goals is to establish an asymptotic expression with explicit remainder term \(O(x/A)\) for the number of positive integers \(N \leq x\) composed of \(s\) distinct prime factors that can be factored nontrivially in deterministic time \(t = t(x)\), provided that the prime power decomposition of \(\phi(N)\) is known. We obtain it for \(A = A(x) = x^{1-\varepsilon}\), where \(\varepsilon = \varepsilon(s) > 0\) is sufficiently small and \(t = t(x)\) is a polynomial in \(\log x\) of degree \(d = d(\varepsilon)\). An analogous bound is deduced under the assumption of the oracle providing the decomposition of orders of elements in \(\mathbb{Z}_N^\ast\).Calculating the power residue symbol and ibeta. Applications of computing the group structure of the principal units of a \(\mathfrak{p}\)-adic number field completionhttps://zbmath.org/1472.113172021-11-25T18:46:10.358925Z"de Boer, Koen"https://zbmath.org/authors/?q=ai:de-boer.koen"Pagano, Carlo"https://zbmath.org/authors/?q=ai:pagano.carloThe nearest-colattice algorithm: time-approximation tradeoff for approx-CVPhttps://zbmath.org/1472.113182021-11-25T18:46:10.358925Z"Espitau, Thomas"https://zbmath.org/authors/?q=ai:espitau.thomas"Kirchner, Paul"https://zbmath.org/authors/?q=ai:kirchner.paulSummary: We exhibit a hierarchy of polynomial time algorithms solving approximate variants of the closest vector problem (CVP). Our first contribution is a heuristic algorithm achieving the same distance tradeoff as HSVP algorithms, namely \(\approx\beta^{n/(2\beta)}\text{covol}(\Lambda)^{1/n}\) for a random lattice \(\Lambda\) of rank \(n\). Compared to the so-called Kannan's embedding technique, our algorithm allows the use of precomputations and can be used for efficient batch CVP instances. This implies that some attacks on lattice-based signatures lead to very cheap forgeries, after a precomputation. Our second contribution is a proven reduction from approximating the closest vector with a factor \(\approx n^{3/2}\beta^{3n/(2\beta)}\) to the shortest vector problem (SVP) in dimension \(\beta\).
For the entire collection see [Zbl 1452.11005].Reductions between short vector problems and simultaneous approximationhttps://zbmath.org/1472.113202021-11-25T18:46:10.358925Z"Martin, Daniel E."https://zbmath.org/authors/?q=ai:martin.daniel-eSummary: \textit{J. C. Lagarias} [SIAM J. Comput. 14, 196--209 (1985; Zbl 0563.10025)] showed that solving the approximate shortest vector problem also solves the problem of finding good simultaneous Diophantine approximations. Here we provide a deterministic, dimension-preserving reduction in the reverse direction. It has polynomial time and space complexity, and it is gap-preserving under the appropriate norms. We also give an alternative to the Lagarias [loc. cit.] algorithm by first reducing his version of simultaneous approximation to one with no explicit range in which a solution is sought.
For the entire collection see [Zbl 1452.11005].Refined analysis to the extended tower number field sievehttps://zbmath.org/1472.113232021-11-25T18:46:10.358925Z"Zhu, Yuqing"https://zbmath.org/authors/?q=ai:zhu.yuqing"Wen, Jiejing"https://zbmath.org/authors/?q=ai:wen.jiejing"Zhuang, Jincheng"https://zbmath.org/authors/?q=ai:zhuang.jincheng"Lv, Chang"https://zbmath.org/authors/?q=ai:lv.chang"Lin, Dongdai"https://zbmath.org/authors/?q=ai:lin.dongdaiSummary: The hardness of discrete logarithm problem over finite fields is the security foundation of many cryptographic protocols. When the characteristic of the finite field is medium or large, the state-of-art algorithms for solving the corresponding problem are the number field sieve and its variants. In 2016, \textit{T. Kim} and \textit{R. Barbulescu} [Crypto 2016, Lect. Notes Comput. Sci. 9814, 543--571 (2016; Zbl 1384.94075)] presented the extended tower number field sieve, which achieves a new complexity in the medium prime case and imposes a new estimation of the security of concrete parameters in certain cryptosystems such as pairing-based cryptosystems. In this paper, a refined analysis to this algorithm is given as follows.
\begin{itemize}
\item[--] Firstly, a uniform formula is given for the total complexity of the extended tower number field sieve. For a given polynomial selection method, this formula can directly give the complexity in this case.
\item[--] Then, a method is proposed to improve the computation in the smoothing phase by exploring subfield structures when the extension degree is composite.
\item[--] At last, the complexity of the descent phase is analyzed when sieving over degree-one polynomials and high-degree polynomials respectively and it is shown still negligible compared to the improved smoothing phase.
\end{itemize}New bounds and an efficient algorithm for sparse difference resultantshttps://zbmath.org/1472.120052021-11-25T18:46:10.358925Z"Yuan, Chun-Ming"https://zbmath.org/authors/?q=ai:yuan.chunming"Zhang, Zhi-Yong"https://zbmath.org/authors/?q=ai:zhang.zhiyongSummary: The sparse difference resultant introduced in [\textit{Wei Li} et al., J. Symb. Comput. 68, Part 1, 169--203 (2015; Zbl 1328.65266)] is a basic concept in difference elimination theory. In this paper, we show that the sparse difference resultant of a generic Laurent transformally essential system can be computed via the sparse resultant of a simple algebraic system arising from the difference system. Moreover, new order bounds of sparse difference resultant are found. Then we propose an efficient algorithm to compute sparse difference resultant which is the quotient of two determinants whose elements are the coefficients of the polynomials in the algebraic system. The complexity of the algorithm is analyzed and experimental results show the efficiency of the algorithm.Ideals modulo a primehttps://zbmath.org/1472.130432021-11-25T18:46:10.358925Z"Abbott, John"https://zbmath.org/authors/?q=ai:abbott.john-a"Bigatti, Anna Maria"https://zbmath.org/authors/?q=ai:bigatti.anna-maria"Robbiano, Lorenzo"https://zbmath.org/authors/?q=ai:robbiano.lorenzoThe present paper deals with the problem of reducing an ideal modulo \(p\), i.e. relating an ideal \(I\) in the polynomial ring \(\mathbb{Q}[x_1,\dots,x_n]\) to a corresponding ideal in \(\mathbb{F}_p[x_1,\dots,x_n]\) where \(p\) is a prime number.
The authors define a notion of \(\sigma\)-good prime, where \(\sigma\) is a term ordering and relate it to other similar notions in the literature. Furthermore, the paper introduces a new invariant called universal denominator, which is independent of the term ordering and allows to show that all but finitely many primes are good for \(I\) (see Definiton 2.4).
The methods in the paper make it easy to detect bad primes, a key feature in modular methods (Theorem 4.1 and Corollary 4.2).
The paper includes practical applications to modular computations of Gröbner bases and also includes examples of computations using the computer algebra systems \verb|CoCoA| and \verb|SINGULAR|.Saturations of subalgebras, SAGBI bases, and U-invariantshttps://zbmath.org/1472.130442021-11-25T18:46:10.358925Z"Bigatti, Anna Maria"https://zbmath.org/authors/?q=ai:bigatti.anna-maria"Robbiano, Lorenzo"https://zbmath.org/authors/?q=ai:robbiano.lorenzoLet \(R=K[x_1,\dots ,x_n]\) and \(F\) be a (not necessarily finite) subset of \(R\). Then the subalgebra of \(R\) generated by \(F\) is denoted \(K[F]\). Similar to the notion of Grobner bases for ideals of \(R\), we can define the notion of SAGBI Gröbner basis for \(K[F]\) (see e.g. the paper of the second author and \textit{M. Sweedler} [Lect. Notes Math. 1430, 61--87 (1990; Zbl 0725.13013)] which is regarded as a pioneer work).
Let \(S\) be a \(K\)-subalgebra of the polynomial ring \(R\) , and let \(0 \ne g\in S\). We denote the set \(\bigcup_{i=0}^\infty \{ f \in R \ | \ g^i f \in S\}\) by \(S : g^\infty\).
The problem that the authors address in this paper is as follows: Given polynomials \(g_1,\dots, g_r \in R\), let \(S= K[g_1,\dots, g_r]\) and \(0\ne g \in S\). The problem is to compute a set of generators for \(S : g^\infty\). In the first part of the paper, an algorithm has been presented to compute a set of generators for \(S : g^\infty\) which terminates if and only if it is finitely generated.
In the second part of the paper, the authors consider the case that \(S\) is graded. They show that two operations of computing a SAGBI basis for \(S\) and a set of generators for \(S : g^\infty\) commute and this leads to nice algorithms for computing with \(S : g^\infty\).A comparison of unrestricted dynamic Gröbner basis algorithmshttps://zbmath.org/1472.130452021-11-25T18:46:10.358925Z"Langeloh, Gabriel Mattos"https://zbmath.org/authors/?q=ai:langeloh.gabriel-mattosA Gröbner Basis algorithm is dynamic when it may change the monomial ordering during the computation. Dynamic Gröbner Basis algorithms often yield smaller output bases and ocasionally faster running times than the traditional ones.
The present paper proposes three new dynamic unrestricted Gröbner Basis algorithms based on the concept of neighbourhoods for monomial orders. These algorithms are experimentally compared to other dynamic algorithms. The results show that the proposed algorithms produce small bases containing polynomials of low degree, with little overhead.Coisotropic hypersurfaces in Grassmannianshttps://zbmath.org/1472.130462021-11-25T18:46:10.358925Z"Kohn, Kathlén"https://zbmath.org/authors/?q=ai:kohn.kathlenThis paper studies the so-called higher associated hypersurfaces of a projective variety via the notion of coisotropy. For a \(k\)-dimensional projective variety \(X\) in \(\mathbb{P}^n\), the \(i\)-th associated hypersurface of \(X\) consists of (the Zariski closure of) all \((n-k-1+i)\)-dimensional linear spaces in \(\mathbb{P}^n\) that meet \(X\) at a smooth point non-transversely, which is a subvariety of a Grassmannian. Historically, the cases \(i = 0\) and \(i=1\) have been studied as the Chow and Hurwitz form of \(X\), respectively.
A main result of this paper is a new and direct proof of a characterization (due originally to Gel'fand, Kapranov and Zelevinsky) of such hypersurfaces in the Grassmannian. Namely, a hypersurface in the Grassmannian is the associated hypersurface of some (irreducible) projective variety iff it is coisotropic, i.e. every normal space at a smooth point of the hypersurface is spanned by rank 1 homomorphisms. Since the notion of coisotropy does not depend on the underlying projective variety, this provides an intrinsic description of all higher associated hypersurfaces (hence the term coisotropic hypersurfaces).
In addition, many other results on coisotropic hypersurfaces are given: e.g. the coisotropic hypersurfaces of the projective dual of \(X\) are the reverse of those of \(X\), and the degrees of these are precisely the polar degrees of \(X\). It is also shown that hyperdeterminants are precisely the coisotropic hypersurfaces associated to Segre varieties. Finally, equations for the Cayley variety of all coisotropic forms of a given degree are given, inside Grassmannians of lines. The author has also written a Macaulay2 package to explicitly realize computation of coisotropic hypersurfaces.Syzygies of the apolar ideals of the determinant and permanenthttps://zbmath.org/1472.140582021-11-25T18:46:10.358925Z"Alper, Jarod"https://zbmath.org/authors/?q=ai:alper.jarod"Rowlands, Rowan"https://zbmath.org/authors/?q=ai:rowlands.rowanGiven a polynomial \(f\in \mathbb K[y_1,\ldots,y_k]\) one defines its apolar ideal \(f^{\bot}\) as \[f^{\bot}=\{g\in\mathbb K[y_1,\ldots,y_k] : \partial g(f)=0\}.\] Recall that to a monomial \(y^{\alpha}=y_1^{\alpha_1}\ldots y_k^{\alpha_k}\) one associates a differential operator \[\frac{\partial}{\partial y^{\alpha}}=\frac{\partial}{\partial y_1^{\alpha_1}\cdots\partial y_k^{\alpha_k}}\] and extends this definition linearly to all polynomials.
Thus for \(g=\sum c_{\alpha}y^{\alpha}\) one associates a differential operator \[\partial g= \sum c_{\alpha}\frac{\partial}{\partial y^{\alpha}}.\] The authors of the paper under review are interested in apolar ideals of two specific polynomials \(\mathrm{def}_n\) and \(\mathrm{perm}_n\) which are elements of the ring \(\mathbb K[x_{11},\ldots, x_{1n},x_{21},\ldots,x_{nn}]\) defines as \[\mathrm{def}_n=\sum_{\sigma\in S_n} \mathrm{sgn}(\sigma) x_{1\sigma(1)}\ldots x_{n\sigma(n)}\] and \[\mathrm{perm}_n=\sum_{\sigma\in S_n} x_{1\sigma(1)}\ldots x_{n\sigma(n)}.\] [\textit{S. M. Shafiei}, J. Commut. Algebra 7, No. 1, 89--123 (2015; Zbl 1364.13024)] showed that the ideals \((\mathrm{def}_n)^{\bot}\) and \((\mathrm{perm}_n)^{\bot}\) are generated by quadrics. She provided an explicit minimal set of generators. The authors extend this study to the first syzygies. They show that the first syzygies of \((\mathrm{def}_n)^{\bot}\) are linear except in characteristic two, where both polynomials and hence their apolar ideals coincide. Thus \((\mathrm{def}_n)^{\bot}\) satisfies at lest the \(N_3\) property of \textit{M. L. Green} [J. Differ. Geom. 19, 125--167, 168--171 (1984; Zbl 0559.14008)].
On the other hand syzygies of \((\mathrm{perm}_n)^{\bot}\) require also quadratic generators, in arbitrary characteristic. Thus one can distinguish both polynomials by properties of their minimal graded free resolution.
The paper is clearly written and all arguments are kept pretty effective, even if some of them are quite involved.Computing the equisingularity type of a pseudo-irreducible polynomialhttps://zbmath.org/1472.140692021-11-25T18:46:10.358925Z"Poteaux, Adrien"https://zbmath.org/authors/?q=ai:poteaux.adrien"Weimann, Martin"https://zbmath.org/authors/?q=ai:weimann.martinIn the paper under review, the authors characterize a class of germs of plane curve singularities, containing irreducible ones, whose equisingularity type can be computed in an expected quasi-linear time with respect to the discriminant valuation of a Weierstrass equation.Merge decompositions, two-sided Krohn-Rhodes, and aperiodic pointlikeshttps://zbmath.org/1472.201292021-11-25T18:46:10.358925Z"van Gool, Samuel J."https://zbmath.org/authors/?q=ai:van-gool.samuel-j"Steinberg, Benjamin"https://zbmath.org/authors/?q=ai:steinberg.benjaminSummary: This paper provides short proofs of two fundamental theorems of finite semigroup theory whose previous proofs were significantly longer, namely the two-sided Krohn-Rhodes decomposition theorem and Henckell's aperiodic pointlike theorem. We use a new algebraic technique that we call the merge decomposition. A prototypical application of this technique decomposes a semigroup \(T\) into a two-sided semidirect product whose components are built from two subsemigroups \(T_{1}\), \(T_{2}\), which together generate \(T\), and the subsemigroup generated by their setwise product \(T_{1}T_{2}\). In this sense we decompose \(T\) by merging the subsemigroups \(T_{1}\) and \(T_{2}\). More generally, our technique merges semigroup homomorphisms from free semigroups.The relationship between word complexity and computational complexity in subshiftshttps://zbmath.org/1472.370172021-11-25T18:46:10.358925Z"Pavlov, Ronnie"https://zbmath.org/authors/?q=ai:pavlov.ronnie"Vanier, Pascal"https://zbmath.org/authors/?q=ai:vanier.pascalGiven a finite set \(A\), a subshift over \(A\) is a subset of \(A^\mathbb{Z}\) which is closed in the product topology and invariant under the shift map \(\sigma\) defined by \((\sigma x)(n)=x(n+1)\). The word complexity function \(c_n(X)\) of a subshift \(X\) is defined by \(c_n(X)=|{\mathcal L}_n(X)|\), where \({\mathcal L}_n(X)\) is the set of all words of length \(n\), i.e., \(c_n(X)\) is the number of all words with length \(n\) appearing in some \(x\in X\).
The Turing spectrum of a subshift \(X\), denoted by \(\mathrm{Sp} (X)\), is the set \(\{\mathbf{d} | \exists x\in X, \mathrm{deg}_T (x) = \mathbf{d}\}\) of all Turing degrees of all points of \(X\). \par The authors study the relationship between the word complexity function of a subshift and the Turing spectrum of the subshift. In particular, it is proved that a Turing spectrum can be realized via a subshift of linear complexity if and only if it consists of the union of a finite set and a finite number of cones, that a Turing spectrum can be realized via a subshift of exponential complexity if and only if it contains a cone, and that every Turing spectrum which either contains degree \(\mathbf 0\) or is a union of cones is realizable by subshifts with a wide range of ``intermediate'' complexity growth rates between linear and exponential.An alphabetical approach to Nivat's conjecturehttps://zbmath.org/1472.370522021-11-25T18:46:10.358925Z"Colle, Cleber F."https://zbmath.org/authors/?q=ai:colle.cleber-f"Garibaldi, Eduardo"https://zbmath.org/authors/?q=ai:garibaldi.eduardoStability and memory-loss go hand-in-hand: three results in dynamics and computationhttps://zbmath.org/1472.370882021-11-25T18:46:10.358925Z"Manjunath, G."https://zbmath.org/authors/?q=ai:manjunath.gSummary: The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and computation is a driven dynamical system that responds to a temporal input. Surprisingly, we find memory-loss a feature of driven systems to forget their internal states helps provide unambiguous answers to the following fundamental stability questions that have been unanswered for decades: what is necessary and sufficient so that slightly different inputs still lead to mostly similar responses? How does changing the driven system's parameters affect stability? What is the mathematical definition of the edge-of-criticality? We anticipate our results to be timely in understanding and designing biologically inspired computers that are entering an era of dedicated hardware implementations for neuromorphic computing and state-of-the-art reservoir computing applications.A projected primal-dual gradient optimal control method for deep reinforcement learninghttps://zbmath.org/1472.490422021-11-25T18:46:10.358925Z"Gottschalk, Simon"https://zbmath.org/authors/?q=ai:gottschalk.simon"Burger, Michael"https://zbmath.org/authors/?q=ai:burger.michael"Gerdts, Matthias"https://zbmath.org/authors/?q=ai:gerdts.matthiasSummary: In this contribution, we start with a policy-based Reinforcement Learning ansatz using neural networks. The underlying Markov Decision Process consists of a transition probability representing the dynamical system and a policy realized by a neural network mapping the current state to parameters of a distribution. Therefrom, the next control can be sampled. In this setting, the neural network is replaced by an ODE, which is based on a recently discussed interpretation of neural networks. The resulting infinite optimization problem is transformed into an optimization problem similar to the well-known optimal control problems. Afterwards, the necessary optimality conditions are established and from this a new numerical algorithm is derived. The operating principle is shown with two examples. It is applied to a simple example, where a moving point is steered through an obstacle course to a desired end position in a 2D plane. The second example shows the applicability to more complex problems. There, the aim is to control the finger tip of a human arm model with five degrees of freedom and 29 Hill's muscle models to a desired end position.On parametrizations of loxodromes on time-like rotational surfaces in Minkowski space-timehttps://zbmath.org/1472.530162021-11-25T18:46:10.358925Z"Babaarslan, Murat"https://zbmath.org/authors/?q=ai:babaarslan.murat"Gümüş, Murat"https://zbmath.org/authors/?q=ai:gumus.muratConvenient pretopologies on \(\mathbb{Z}^2\)https://zbmath.org/1472.540322021-11-25T18:46:10.358925Z"Šlapal, J."https://zbmath.org/authors/?q=ai:slapal.josefThis is an excellent, ground-breaking paper in digital topology, that includes complete basic definitions of key terms and a number of important results in terms of Jordan curves in the digital plane \(\mathbb{Z}^2\). This paper focuses on pretopologies on the digital plane \(\mathbb{Z}^2\) convenient for studying and processing digital images. It introduces a natural graph on the vertex sets \(\mathbb{Z}^2\), whose cycles are eligible for Jordan curves in the digital plane and solves the problem of finding those cycles that are Jordan curves.
Let \(2^X\) denote the collection of subsets in a nonvoid set \(X\) and the empty set is denoted by \(\emptyset\). Recall that a topology \(p\) on a nonvoid set \(X\) is the Kuratowski closure operator on \(p:2^X\to 2^X\) that satisfies the following axioms:
\begin{enumerate}
\item[(i)] \(p\emptyset = \emptyset\),
\item[(ii)] \(A\subseteq pA\ \mbox{for all}\ A\subseteq X\),
\item[(iii)] \(p(A\cup B) = pA \cup pB\ \mbox{for all}\ A,B\subseteq X\),
\item[(iv)] \(ppA = pA\ \mbox{for all}\ A\subseteq X\).
\end{enumerate}
The pair \((X,p)\) is a pretopological space, provided \(p\) satisfies axioms (i)--(iii), but not necessarily axiom (iv). Also recall that a \emph{digital simple closed curve} in a pretopological space \((\mathbb{Z}^2,p)\) is a nonempty subset \(C\subseteq \mathbb{Z}^2\) such that there are exactly two points of \(C\) adjacent to \(x\) in the connectedness graph of \(p\), for every \(x\in C\). A digital simple closed curve \(C\) in \((\mathbb{Z}^2,p)\) is a digital Jordan curve, provided \(C\) separates the space into precisely two components.
For a planar digital image, let \(A_4\) denote the 4-adjaceny graph on \(\mathbb{Z}^2, (x,y)\in \mathbb{Z}^2\); we have
\[
A_4(x,y) = \left\{\left(x+i,y+j\right): i,j\in \left\{-1,0,1\right\}, ij=0,i+j\neq 0\right\}.
\]
It is observed (and demonstrated) that the basic pretopologies possess a rich variety of Jordan curves useful in structuring the digital plane \(\mathbb{Z}^2\). This paper introduces \(sd\)-pretopology (Definition 3.2) as well as Alexandroff pretopologies \(u\) and \(v\) on \(\mathbb{Z}^2\), leading to a number of important companion results, e.g.,
Theorem 4.4, p. 49
Let \(D\) be a simple closed curve in \((\mathbb{Z}^2,u)\) having more than four points and such that every pair of different points \(z_1,z_2\in D\) with both coordinates even satisfies \(A_4(z_1)\cap A_4(z_2)\subseteq D\). Then \(D\) is a Jordan curve in \((\mathbb{Z}^2,u)\).
Theorem 4.5, p. 50
Let \(D\) be a simple closed curve in \((\mathbb{Z}^2,u)\) such that, for every point \(z\in D\) with both coordinates odd, \(A_4(z)\cap D\neq \emptyset\). Then \(D\) is a Jordan curve in \((\mathbb{Z}^2,v)\).Cohomology with local coefficients and knotted manifoldshttps://zbmath.org/1472.570042021-11-25T18:46:10.358925Z"Ellis, Graham"https://zbmath.org/authors/?q=ai:ellis.graham-j"Killeen, Kelvin"https://zbmath.org/authors/?q=ai:killeen.kelvinThis paper shows how classical ideas used on knot theory can be encoded in a way that makes it possible to use a computer to calculate ambient isotopy invariants of continuous embeddings \(N \ \hookrightarrow \ M\). The authors describe an algorithm for computing the homology and cohomology of a finite connected CW-complex \(X\) with coefficients in a \({\mathbb Z}\pi_{1}(X)\) module \(A\) when \(A\) is finitely generated over \(\mathbb Z\). As examples of the effectiveness of the algorithm, which is implemented in the Groups, Algorithms, and Programming system GAP (\url{http://www.gap-system.org}) and in HAP -- the homological homological algebra programming system (\url{http://hamilton.nuigalway.ie/}) built on GAP -- the authors give two illustrations of the technique. The first shows that degree 2 homology distinguishes the homotopy types of the complements of the spun Hopf link and Satoh's tube map of the welded Hopf links. The second example shows that the system distinguishes between the homeomorphism types of the complements of the granny knot and the reef knot. The details of the implementations are given in the paper. In order to make the computations manageable, a CW complex \(X\) is represented by a regular CW complex \(Y\) -- that is one whose attaching maps restrict to homeomorphisms on cell boundaries -- together with a simple homotopy equivalence \(Y \simeq X\). The paper contains many useful diagrams to illustrate the constructions used. Timings for the execution of the various codes are given based on execution on a standard GNU/Linux box. Note that GAP/HAP has a substantial number of built-in routines so that the algorithms illustrated in the paper are quite short.Statistical programming with R. A detailed and clear, exciting and practice tested introductionhttps://zbmath.org/1472.620022021-11-25T18:46:10.358925Z"Obszelka, Daniel"https://zbmath.org/authors/?q=ai:obszelka.daniel"Baierl, Andreas"https://zbmath.org/authors/?q=ai:baierl.andreasPublisher's description: Dieses Buch gibt eine umfassende, didaktisch erprobte Einführung in die statistische Programmiersprache R. Es vermittelt fundierte Kenntnisse zum sicheren und effizienten Einsatz von R zur Datenaufbereitung, Datenanalyse, Visualisierung, Berichterstellung und Simulation. Sein didaktisches Konzept wurde im Rahmen der mit dem Teaching Award der Universität Wien ausgezeichneten Lehrveranstaltung ``Statistisches Programmieren'' entwickelt. Das Buch ist somit sowohl als Lehrbuch in Lehrveranstaltungen als auch zum Selbststudium und als Nachschlagewerk für R-Profis bestens geeignet.A note on support vector machines with polynomial kernelshttps://zbmath.org/1472.620052021-11-25T18:46:10.358925Z"Tong, Hongzhi"https://zbmath.org/authors/?q=ai:tong.hongzhiSummary: We present a better theoretical foundation of support vector machines with polynomial kernels. The sample error is estimated under Tsybakov's noise assumption. In bounding the approximation error, we take advantage of a geometric noise assumption that was introduced to analyze gaussian kernels. Compared with the previous literature, the error analysis in this note does not require any regularity of the marginal distribution or smoothness of Bayes' rule. We thus establish the learning rates for polynomial kernels for a wide class of distributions.Design-unbiased statistical learning in survey samplinghttps://zbmath.org/1472.620212021-11-25T18:46:10.358925Z"Sande, Luis Sanguiao"https://zbmath.org/authors/?q=ai:sande.luis-sanguiao"Zhang, Li-Chun"https://zbmath.org/authors/?q=ai:zhang.lichunSummary: Design-consistent model-assisted estimation has become the standard practice in survey sampling. However, design consistency remains to be established for many machine-learning techniques that can potentially be very powerful assisting models. We propose a subsampling Rao-Blackwell method, and develop a statistical learning theory for \textit{exactly} design-unbiased estimation with the help of linear or non-linear prediction models. Our approach makes use of classic ideas from Statistical Science as well as the rapidly growing field of Machine Learning. Provided rich auxiliary information, it can yield considerable efficiency gains over standard linear model-assisted methods, while ensuring valid estimation for the given target population, which is robust against potential mis-specifications of the assisting model, even if the design consistency of following the standard recipe for plug-in model-assisted estimator cannot be established.Estimating leverage scores via rank revealing methods and randomizationhttps://zbmath.org/1472.620822021-11-25T18:46:10.358925Z"Sobczyk, Aleksandros"https://zbmath.org/authors/?q=ai:sobczyk.aleksandros"Gallopoulos, Efstratios"https://zbmath.org/authors/?q=ai:gallopoulos.efstratiosStacking with dynamic weights on base modelshttps://zbmath.org/1472.621002021-11-25T18:46:10.358925Z"Mookherjee, Biswaroop"https://zbmath.org/authors/?q=ai:mookherjee.biswaroop"Halder, Abhishek"https://zbmath.org/authors/?q=ai:halder.abhishekSummary: Stacking is used to combine models based on different techniques using a second-level model to come up with higher accuracy. The second-level model essentially uses the values predicted by different base-level models as independent variables, while the dependent variable remains the observed one. Though fit of the base-level models differ at various parts of the data, the second-level model uses same set of weights on base-level models on the whole data. We have derived two methods where we replace the second-level model by a linear combination of base model outputs where the weights vary. In our methods, we select a part of the data based on some predefined condition of proximity for classification of a new observation. Then, weights are assigned on different base models considering their accuracy in that part of the data. In one method, all points in the neighbourhood get equal importance, while in the other method, points get importance based on proximity. The algorithms apply same principle on each of the new observations which get their neighbourhoods in different parts of the data; thus, weights vary. The new ensemble methods are tried on different datasets from different fields and found to give better results than conventional stacking.
For the entire collection see [Zbl 1466.91004].Robust clustering method in the presence of scattered observationshttps://zbmath.org/1472.621012021-11-25T18:46:10.358925Z"Notsu, Akifumi"https://zbmath.org/authors/?q=ai:notsu.akifumi"Eguchi, Shinto"https://zbmath.org/authors/?q=ai:eguchi.shintoSummary: Contamination of scattered observations, which are either featureless or unlike the other observations, frequently degrades the performance of standard methods such as \(K\)-means and model-based clustering. In this letter, we propose a robust clustering method in the presence of scattered observations called Gamma-clust. Gamma-clust is based on a robust estimation for cluster centers using gamma-divergence. It provides a proper solution for clustering in which the distributions for clustered data are nonnormal, such as \textit{t}-distributions with different variance-covariance matrices and degrees of freedom. As demonstrated in a simulation study and data analysis, Gamma-clust is more flexible and provides superior results compared to the robustified \(K\)-means and model-based clustering.On the trade-off between number of examples and precision of supervision in machine learning problemshttps://zbmath.org/1472.621092021-11-25T18:46:10.358925Z"Gnecco, Giorgio"https://zbmath.org/authors/?q=ai:gnecco.giorgio"Nutarelli, Federico"https://zbmath.org/authors/?q=ai:nutarelli.federicoSummary: We investigate linear regression problems for which one is given the additional possibility of controlling the conditional variance of the output given the input, by varying the computational time dedicated to supervise each example. For a given upper bound on the total computational time for supervision, we optimize the trade-off between the number of examples and their precision (the reciprocal of the conditional variance of the output), by formulating and solving suitable optimization problems, based on large-sample approximations of the outputs of the classical ordinary least squares and weighted least squares regression algorithms. Considering a specific functional form for that precision, we prove that there are cases in which ``many but bad'' examples provide a smaller generalization error than ``few but good'' ones, but also that the converse can occur, depending on the ``returns to scale'' of the precision with respect to the computational time assigned to supervise each example. Hence, the results of this study highlight that increasing the size of the dataset is not always beneficial, if one has the possibility to collect a smaller number of more reliable examples. We conclude presenting numerical results validating the theory, and discussing extensions of the proposed framework to other optimization problems.Joint outlier detection and variable selection using discrete optimizationhttps://zbmath.org/1472.621102021-11-25T18:46:10.358925Z"Jammal, Mahdi"https://zbmath.org/authors/?q=ai:jammal.mahdi"Canu, Stephane"https://zbmath.org/authors/?q=ai:canu.stephane"Abdallah, Maher"https://zbmath.org/authors/?q=ai:abdallah.maherSummary: In regression, the quality of estimators is known to be very sensitive to the presence of spurious variables and outliers. Unfortunately, this is a frequent situation when dealing with real data. To handle outlier proneness and achieve variable selection, we propose a robust method performing the outright rejection of discordant observations together with the selection of relevant variables. A natural way to define the corresponding optimization problem is to use the \(\ell_0\) norm and recast it as a mixed integer optimization problem. To retrieve this global solution more efficiently, we suggest the use of additional constraints as well as a clever initialization. To this end, an efficient and scalable non-convex proximal alternate algorithm is introduced. An empirical comparison between the \(\ell_0\) norm approach and its \(\ell_1\) relaxation is presented as well. Results on both synthetic and real data sets provided that the mixed integer programming approach and its discrete first order warm start provide high quality solutions.Significance-based community detection in weighted networkshttps://zbmath.org/1472.621232021-11-25T18:46:10.358925Z"Palowitch, John"https://zbmath.org/authors/?q=ai:palowitch.john"Bhamidi, Shankar"https://zbmath.org/authors/?q=ai:bhamidi.shankar"Nobel, Andrew B."https://zbmath.org/authors/?q=ai:nobel.andrew-bSummary: Community detection is the process of grouping strongly connected nodes in a network. Many community detection methods for un-weighted networks have a theoretical basis in a null model. Communities discovered by these methods therefore have interpretations in terms of statistical significance. In this paper, we introduce a null for weighted networks called the continuous configuration model. First, we propose a community extraction algorithm for weighted networks which incorporates iterative hypothesis testing under the null. We prove a central limit theorem for edge-weight sums and asymptotic consistency of the algorithm under a weighted stochastic block model. We then incorporate the algorithm in a community detection method called CCME. To benchmark the method, we provide a simulation framework involving the null to plant ``background'' nodes in weighted networks with communities. We show that the empirical performance of CCME on these simulations is competitive with existing methods,
particularly
when overlapping communities and background nodes are present. To further validate the method, we present two real-world networks with potential background nodes and analyze them with CCME, yielding results that reveal macro-features of the corresponding systems.Sequential tests for large-scale learninghttps://zbmath.org/1472.621292021-11-25T18:46:10.358925Z"Korattikara, Anoop"https://zbmath.org/authors/?q=ai:korattikara.anoop"Chen, Yutian"https://zbmath.org/authors/?q=ai:chen.yutian"Welling, Max"https://zbmath.org/authors/?q=ai:welling.maxSummary: We argue that when faced with big data sets, learning and inference algorithms should compute updates using only subsets of data items. We introduce algorithms that use sequential hypothesis tests to adaptively select such a subset of data points. The statistical properties of this subsampling process can be used to control the efficiency and accuracy of learning or inference. In the context of learning by optimization, we test for the probability that the update direction is no more than 90 degrees in the wrong direction. In the context of posterior inference using Markov chain Monte Carlo, we test for the probability that our decision to accept or reject a sample is wrong. We experimentally evaluate our algorithms on a number of models and data sets.Nonlinear autoregressive sieve bootstrap based on extreme learning machineshttps://zbmath.org/1472.621352021-11-25T18:46:10.358925Z"La Rocca, Michelle"https://zbmath.org/authors/?q=ai:la-rocca.michelle"Perna, Cira"https://zbmath.org/authors/?q=ai:perna.ciraSummary: The aim of the paper is to propose and discuss a sieve bootstrap scheme based on extreme learning machines for non linear time series. The procedure is fully nonparametric in its spirit and retains the conceptual simplicity of the residual bootstrap. Using extreme learning machines in the resampling scheme can dramatically reduce the computational burden of the bootstrap procedure, with performances comparable to the NN-Sieve bootstrap and computing time similar to the ARSieve bootstrap. A Monte Carlo simulation experiment has been implemented, in order to evaluate the performance of the proposed procedure and to compare it with the NN-Sieve bootstrap. The distributions of the bootstrap variance estimators appear to be consistent, delivering good results both in terms of accuracy and bias, for either linear and nonlinear statistics (such as the mean and the median) and smooth functions of means (such as the variance and the covariance).Estimation error analysis of deep learning on the regression problem on the variable exponent Besov spacehttps://zbmath.org/1472.621442021-11-25T18:46:10.358925Z"Tsuji, Kazuma"https://zbmath.org/authors/?q=ai:tsuji.kazuma"Suzuki, Taiji"https://zbmath.org/authors/?q=ai:suzuki.taijiSummary: Deep learning has achieved notable success in various fields, including image and speech recognition. One of the factors in the successful performance of deep learning is its high feature extraction ability. In this study, we focus on the adaptivity of deep learning; consequently, we treat the variable exponent Besov space, which has a different smoothness depending on the input location \(x\). In other words, the difficulty of the estimation is not uniform within the domain. We analyze the general approximation error of the variable exponent Besov space and the approximation and estimation errors of deep learning. We note that the improvement based on adaptivity is remarkable when the region upon which the target function has less smoothness is small and the dimension is large. Moreover, the superiority to linear estimators is shown with respect to the convergence rate of the estimation error.Moment conditions selection based on adaptive penalized empirical likelihoodhttps://zbmath.org/1472.621752021-11-25T18:46:10.358925Z"Song, Yunquan"https://zbmath.org/authors/?q=ai:song.yunquanSummary: Empirical likelihood is a very popular method and has been widely used in the fields of artificial intelligence (AI) and data mining as tablets and mobile application and social media dominate the technology landscape. This paper proposes an empirical likelihood shrinkage method to efficiently estimate unknown parameters and select correct moment conditions simultaneously, when the model is defined by moment restrictions in which some are possibly misspecified. We show that our method enjoys oracle-like properties; that is, it consistently selects the correct moment conditions and at the same time its estimator is as efficient as the empirical likelihood estimator obtained by all correct moment conditions. Moreover, unlike the GMM, our proposed method allows us to carry out confidence regions for the parameters included in the model without estimating the covariances of the estimators. For empirical implementation, we provide some data-driven procedures for selecting the tuning parameter of the
penalty function. The simulation results show that the method works remarkably well in terms of correct moment selection and the finite sample properties of the estimators. Also, a real-life example is carried out to illustrate the new methodology.Solving Bayesian inverse problems from the perspective of deep generative networkshttps://zbmath.org/1472.650092021-11-25T18:46:10.358925Z"Hou, Thomas Y."https://zbmath.org/authors/?q=ai:hou.thomas-yizhao"Lam, Ka Chun"https://zbmath.org/authors/?q=ai:lam.ka-chun"Zhang, Pengchuan"https://zbmath.org/authors/?q=ai:zhang.pengchuan"Zhang, Shumao"https://zbmath.org/authors/?q=ai:zhang.shumaoSummary: Deep generative networks have achieved great success in high dimensional density approximation, especially for applications in natural images and language. In this paper, we investigate their approximation capability in capturing the posterior distribution in Bayesian inverse problems by learning a transport map. Because only the unnormalized density of the posterior is available, training methods that learn from posterior samples, such as variational autoencoders and generative adversarial networks, are not applicable in our setting. We propose a class of network training methods that can be combined with sample-based Bayesian inference algorithms, such as various MCMC algorithms, ensemble Kalman filter and Stein variational gradient descent. Our experiment results show the pros and cons of deep generative networks in Bayesian inverse problems. They also reveal the potential of our proposed methodology in capturing high dimensional probability distributions.Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applicationshttps://zbmath.org/1472.650642021-11-25T18:46:10.358925Z"Tan, Bing"https://zbmath.org/authors/?q=ai:tan.bing.1"Qin, Xiaolong"https://zbmath.org/authors/?q=ai:qin.xiaolong"Yao, Jen-Chih"https://zbmath.org/authors/?q=ai:yao.jen-chihSummary: In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.Efficient nonnegative matrix factorization by DC programming and DCAhttps://zbmath.org/1472.650702021-11-25T18:46:10.358925Z"Le Thi, Hoai An"https://zbmath.org/authors/?q=ai:le-thi-hoai-an."Vo, Xuan Thanh"https://zbmath.org/authors/?q=ai:vo.xuan-thanh"Dinh, Tao Pham"https://zbmath.org/authors/?q=ai:pham-dinh-tao.Summary: In this letter, we consider the nonnegative matrix factorization (NMF) problem and several NMF variants. Two approaches based on DC (difference of convex functions) programming and DCA (DC algorithm) are developed. The first approach follows the alternating framework that requires solving, at each iteration, two nonnegativity-constrained least squares subproblems for which DCA-based schemes are investigated. The convergence property of the proposed algorithm is carefully studied. We show that with suitable DC decompositions, our algorithm generates most of the standard methods for the NMF problem. The second approach directly applies DCA on the whole NMF problem. Two algorithms -- one computing all variables and one deploying a variable selection strategy -- are proposed. The proposed methods are then adapted to solve various NMF variants, including the nonnegative factorization, the smooth regularization NMF, the sparse regularization NMF, the multilayer NMF, the convex/convex-hull NMF, and the symmetric NMF. We also show that our algorithms include several existing methods for these NMF variants as special versions. The efficiency of the proposed approaches is empirically demonstrated on both real-world and synthetic data sets. It turns out that our algorithms compete favorably with five state-of-the-art alternating nonnegative least squares algorithms.Data-driven algorithm selection and tuning in optimization and signal processinghttps://zbmath.org/1472.650742021-11-25T18:46:10.358925Z"De Loera, Jesús A."https://zbmath.org/authors/?q=ai:de-loera.jesus-a"Haddock, Jamie"https://zbmath.org/authors/?q=ai:haddock.jamie"Ma, Anna"https://zbmath.org/authors/?q=ai:ma.anna"Needell, Deanna"https://zbmath.org/authors/?q=ai:needell.deannaSummary: Machine learning algorithms typically rely on optimization subroutines and are well known to provide very effective outcomes for many types of problems. Here, we flip the reliance and ask the reverse question: can machine learning algorithms lead to more effective outcomes for optimization problems? Our goal is to train machine learning methods to automatically improve the performance of optimization and signal processing algorithms. As a proof of concept, we use our approach to improve two popular data processing subroutines in data science: stochastic gradient descent and greedy methods in compressed sensing. We provide experimental results that demonstrate the answer is ``yes'', machine learning algorithms do lead to more effective outcomes for optimization problems, and show the future potential for this research direction. In addition to our experimental work, we prove relevant \textit{Probably Approximately Correct} (PAC) learning theorems for our problems of interest. More precisely, we show that there exists a learning algorithm that, with high probability, will select the algorithm that optimizes the average performance on an input set of problem instances with a given distribution.Nonisometric surface registration via conformal Laplace-Beltrami basis pursuithttps://zbmath.org/1472.650762021-11-25T18:46:10.358925Z"Schonsheck, Stefan C."https://zbmath.org/authors/?q=ai:schonsheck.stefan-c"Bronstein, Michael M."https://zbmath.org/authors/?q=ai:bronstein.michael-m"Lai, Rongjie"https://zbmath.org/authors/?q=ai:lai.rongjieSummary: Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to compute correspondence between surfaces which are intrinsically less similar. In this paper, we propose a variational model to align the Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via conformal deformations. This method enables us to compute geometrically meaningful point-to-point maps between non-isometric shapes. Our model is based on a novel basis pursuit scheme whereby we simultaneously compute a conformal deformation of a 'target shape' and its deformed LB eigensystem. We solve the model using a proximal alternating minimization algorithm hybridized with the augmented Lagrangian method which produces accurate correspondences given only a few landmark points. We also propose a re-initialization scheme to overcome some of the difficulties caused by the non-convexity of the variational problem. Intensive numerical experiments illustrate the effectiveness and robustness of the proposed method to handle non-isometric surfaces with large deformation with respect to both noises on the underlying manifolds and errors within the given landmarks or feature functions.Efficient approximation of solutions of parametric linear transport equations by ReLU DNNshttps://zbmath.org/1472.651342021-11-25T18:46:10.358925Z"Laakmann, Fabian"https://zbmath.org/authors/?q=ai:laakmann.fabian"Petersen, Philipp"https://zbmath.org/authors/?q=ai:petersen.philipp-cSummary: We demonstrate that deep neural networks with the ReLU activation function can efficiently approximate the solutions of various types of parametric linear transport equations. For non-smooth initial conditions, the solutions of these PDEs are high-dimensional and non-smooth. Therefore, approximation of these functions suffers from a curse of dimension. We demonstrate that through their inherent compositionality deep neural networks can resolve the characteristic flow underlying the transport equations and thereby allow approximation rates independent of the parameter dimension.Machine learning in medicine -- a complete overview. With the help from Henny I. Cleophas-Allershttps://zbmath.org/1472.680012021-11-25T18:46:10.358925Z"Cleophas, Ton J."https://zbmath.org/authors/?q=ai:cleophas.ton-j"Zwinderman, Aeilko H."https://zbmath.org/authors/?q=ai:zwinderman.aeilko-hPublisher's description: Adequate health and health care is no longer possible without proper data supervision from modern machine learning methodologies like cluster models, neural networks, and other data mining methodologies. The current book is the first publication of a complete overview of machine learning methodologies for the medical and health sector, and it was written as a training companion, and as a must-read, not only for physicians and students, but also for any one involved in the process and progress of health and health care.
In this second edition the authors have removed the textual errors from the first edition. Also, the improved tables from the first edition, have been replaced with the original tables from the software programs as applied. This is, because, unlike the former, the latter were without error, and readers were better familiar with them.
The main purpose of the first edition [\textit{T. J. Cleophas} and \textit{A. H. Zwinderman}, Machine learning in medicine -- a complete overview. Cham: Springer (2015)] was, to provide stepwise analyses of the novel methods from data examples, but background information and clinical relevance information may have been somewhat lacking. Therefore, each chapter now contains a section entitled ``Background Information''.
Machine learning may be more informative, and may provide better sensitivity of testing than traditional analytic methods may do. In the second edition a place has been given for the use of machine learning not only to the analysis of observational clinical data, but also to that of controlled clinical trials.Unlike the first edition, the second edition has drawings in full color providing a helpful extra dimension to the data analysis.
Several machine learning methodologies not yet covered in the first edition, but increasingly important today, have been included in this updated edition, for example, negative binomial and Poisson regressions, sparse canonical analysis, Firth's bias adjusted logistic analysis, omics research, eigenvalues and eigenvectors.Thinking programs. Logical modeling and reasoning about languages, data, computations, and executionshttps://zbmath.org/1472.680022021-11-25T18:46:10.358925Z"Schreiner, Wolfgang"https://zbmath.org/authors/?q=ai:schreiner.wolfgangPublisher's description: This book describes some basic principles that allow developers of computer programs (computer scientists, software engineers, programmers) to clearly \textit{think} about the artifacts they deal with in their daily work: data types, programming languages, programs written in these languages that compute from given inputs wanted outputs, and programs that describe continuously executing systems. The core message is that clear thinking about programs can be expressed in a single universal language, the formal language of \textit{logic}. Apart from its universal elegance and expressiveness, this ``logical'' approach to the formal modeling of and reasoning about computer programs has another advantage: due to advances in computational logic (automated theorem proving, satisfiability solving, model checking), nowadays much of this process can be supported by \textit{software}. This book therefore accompanies its theoretical elaborations by practical demonstrations of various systems and tools that are based on respectively make use of the presented logical underpinnings.Statistical model checking and time-bounded reachability analysis for hybrid Petri nets with multiple stochastic variableshttps://zbmath.org/1472.680032021-11-25T18:46:10.358925Z"Pilch, Carina"https://zbmath.org/authors/?q=ai:pilch.carina(no abstract)On software implementation of Kuznyechik on Intel CPUshttps://zbmath.org/1472.680042021-11-25T18:46:10.358925Z"Rybkin, A. S."https://zbmath.org/authors/?q=ai:rybkin.andrey-sSummary: In this paper we investigate high speed software performance issues of the Kuznyechik block cipher on Intel CPUs. We consider general block cipher implementation methods, including byte slicing technique, available speedup possibilities on Intel architecture, and evaluate their efficiency when applied to Kuznyechik. The contributions of each element of the algorithm into its overall complexity are investigated in dependence on the optimization method used. Practical implementation results are given, and potential speed-ups are discussed.Introduction to the special issue on logic rules and reasoning: selected papers from the 2nd international joint conference on rules and reasoning (RuleML+RR 2018)https://zbmath.org/1472.680052021-11-25T18:46:10.358925Z"Benzmüller, Christoph"https://zbmath.org/authors/?q=ai:benzmuller.christoph-e"Parent, Xavier"https://zbmath.org/authors/?q=ai:parent.xavier"Ricca, Francesco"https://zbmath.org/authors/?q=ai:ricca.francesco(no abstract)Special issue on algorithmic theory of dynamic networks and its applications -- prefacehttps://zbmath.org/1472.680062021-11-25T18:46:10.358925Z"Bonomi, Silvia"https://zbmath.org/authors/?q=ai:bonomi.silvia"Di Luna, Giuseppe A."https://zbmath.org/authors/?q=ai:di-luna.giuseppe-antonio"Michail, Othon"https://zbmath.org/authors/?q=ai:michail.othon"Querzoni, Leonardo"https://zbmath.org/authors/?q=ai:querzoni.leonardoFrom the text: A key aspect of many modern distributed systems is their highly dynamic nature. New technologies such as wireless
sensors networks, software defined networks, and networks of smart devices are effectively creating topologies that continuously change, either by exogenous factors (such as the mobility of the devices or the highly unreliable nature of the links) or by endogenous factors (this it the example of software defined networks where the topology can be swiftly modified at runtime by a program). This new landscape is in stark contrast with the previous distributed computing vision where the
dynamic aspect was brought by the presence of sporadic and sparse failure events.
This special issue on Algorithmic Theory of Dynamic Networks and its Applications belongs to this line of activities. It has two purposes, the first is to collect high-quality content on the hot areas; the second is to foster the growth of the newborn community. To this end the special issue has invited contributions from key persons of the community, while being also open to spontaneous submissions.Agent-based optimizationhttps://zbmath.org/1472.680072021-11-25T18:46:10.358925Z"Czarnowski, Ireneusz"https://zbmath.org/authors/?q=ai:czarnowski.ireneusz"Jȩdrzejowicz, Piotr"https://zbmath.org/authors/?q=ai:jedrzejowicz.piotr"Kacprzyk, Janusz"https://zbmath.org/authors/?q=ai:kacprzyk.januszPublisher's description: This volume presents a collection of original research works by leading specialists focusing on novel and promising approaches in which the multi-agent system paradigm is used to support, enhance or replace traditional approaches to solving difficult optimization problems. The editors have invited several well-known specialists to present their solutions, tools, and models falling under the common denominator of the agent-based optimization. The book consists of eight chapters covering examples of application of the multi-agent paradigm and respective customized tools to solve difficult optimization problems arising in different areas such as machine learning, scheduling, transportation and, more generally, distributed and cooperative problem solving.
The articles of this volume will be reviewed individually.Soft computing techniques in engineering, health, mathematical and social scienceshttps://zbmath.org/1472.680082021-11-25T18:46:10.358925Z"Debnath, Pradip"https://zbmath.org/authors/?q=ai:debnath.pradip"Mohiuddine, S. A."https://zbmath.org/authors/?q=ai:mohiuddine.syed-adbul|mohiuddine.syed-abdulPublisher's description: Soft computing techniques are no longer limited to the arena of computer science. The discipline has an exponentially growing demand in other branches of science and engineering and even into health and social science. This book contains theory and applications of soft computing in engineering, health, and social and applied sciences. Different soft computing techniques such as artificial neural networks, fuzzy systems, evolutionary algorithms and hybrid systems are discussed. It also contains important chapters in machine learning and clustering. This book presents a survey of the existing knowledge and also the current state of art development through original new contributions from the researchers. This book may be used as a one-stop reference book for a broad range of readers worldwide interested in soft computing. In each chapter, the preliminaries have been presented first and then the advanced discussion takes place. Learners and researchers from a wide variety of backgrounds will find several useful tools and techniques to develop their soft computing skills. This book is meant for graduate students, faculty and researchers willing to expand their knowledge in any branch of soft computing. The readers of this book will require minimum prerequisites of undergraduate studies in computation and mathematics.
The articles of mathematical interest will be reviewed individually.Beyond the worst-case analysis of algorithmshttps://zbmath.org/1472.680092021-11-25T18:46:10.358925Z"Roughgarden, Tim"https://zbmath.org/authors/?q=ai:roughgarden.timPublisher's description: There are no silver bullets in algorithm design, and no single algorithmic idea is powerful and flexible enough to solve every computational problem. Nor are there silver bullets in algorithm analysis, as the most enlightening method for analyzing an algorithm often depends on the problem and the application. However, typical algorithms courses rely almost entirely on a single analysis framework, that of worst-case analysis, wherein an algorithm is assessed by its worst performance on any input of a given size. The purpose of this book is to popularize several alternatives to worst-case analysis and their most notable algorithmic applications, from clustering to linear programming to neural network training. Forty leading researchers have contributed introductions to different facets of this field, emphasizing the most important models and results, many of which can be taught in lectures to beginning graduate students in theoretical computer science and machine learning.
The articles of this volume will be reviewed individually.Special issue: Developments in language theory (DLT 2019). Prefacehttps://zbmath.org/1472.680102021-11-25T18:46:10.358925Z"Skrzypczak, Michał"https://zbmath.org/authors/?q=ai:skrzypczak.michal"Hofman, Piotr"https://zbmath.org/authors/?q=ai:hofman.piotrFrom the text: This special issue of the Fundamenta Informaticae contains five papers, which are revised and extended versions of the papers selected from the 23rd International Conference on Developments in Language Theory, DLT 2019, hosted by the University of Warsaw, Poland from 5 till 9 August 2019.A full operational semantics for asynchronous relational networkshttps://zbmath.org/1472.680112021-11-25T18:46:10.358925Z"Vissani, Ignacio"https://zbmath.org/authors/?q=ai:vissani.ignacio"Pombo, Carlos Gustavo Lopez"https://zbmath.org/authors/?q=ai:lopez-pombo.carlos-gustavo"Ţuţu, Ionuţ"https://zbmath.org/authors/?q=ai:tutu.ionut"Fiadeiro, José Luiz"https://zbmath.org/authors/?q=ai:fiadeiro.jose-luizSummary: Service-oriented computing is a new paradigm where applications run over global computational networks and are formed by services discovered and bound at run-time through the intervention of a middleware. Asynchronous Relational Nets (ARNs) were presented by Fiadeiro and Lopes with the aim of formalising the elements of an interface theory for service-oriented software designs. The semantics of ARNs was originally given in terms of sequences of sets of actions corresponding to the behaviour of the service. Later, they were given an institution-based semantics where signatures are ARNs and models are morphisms into ground networks, that have no dependencies on external services.
In this work, we propose a full operational semantics capable of reflecting the dynamic nature of service execution by making explicit the reconfigurations that take place at run-time as the result of the discovery and binding of required services. This provides us a refined view of the execution of ARNs based upon which a specialized variant of linear temporal logic can be used to express, and even to verify through standard model-checking techniques, properties concerning the behaviour of ARNs that are more complex than those considered before.
For the entire collection see [Zbl 1327.68013].Netter: probabilistic, stateful network modelshttps://zbmath.org/1472.680122021-11-25T18:46:10.358925Z"Zhang, Han"https://zbmath.org/authors/?q=ai:zhang.han"Zhang, Chi"https://zbmath.org/authors/?q=ai:zhang.chi"Azevedo de Amorim, Arthur"https://zbmath.org/authors/?q=ai:azevedo-de-amorim.arthur"Agarwal, Yuvraj"https://zbmath.org/authors/?q=ai:agarwal.yuvraj"Fredrikson, Matt"https://zbmath.org/authors/?q=ai:fredrikson.matthew"Jia, Limin"https://zbmath.org/authors/?q=ai:jia.liminSummary: We study the problem of using probabilistic network models to formally analyze their quantitative properties, such as the effect of different load-balancing strategies on the long-term traffic on a server farm. Compared to prior work, we explore a different design space in terms of tradeoffs between model expressiveness and analysis scalability, which we realize in a language we call \textit{Netter}. Netter code is compiled to probabilistic automata, undergoing optimization passes to reduce the state space of the generated models, thus helping verification scale. We evaluate Netter on several case studies, including a probabilistic load balancer, a routing scheme reminiscent of MPLS, and a network defense mechanism against link-flooding attacks. Our results show that Netter can analyze quantitative properties of interesting routing schemes that prior work hadn't addressed, for networks of small size (4--9 nodes and a few different types of flows). Moreover, when specialized to simpler, stateless networks, Netter can parallel the performance of previous state-of-the-art tools, scaling up to millions of nodes.
For the entire collection see [Zbl 1471.68017].Optimization of a probabilistic interruption mechanism for cognitive radio networks with prioritized secondary usershttps://zbmath.org/1472.680132021-11-25T18:46:10.358925Z"Zhao, Yuan"https://zbmath.org/authors/?q=ai:zhao.yuan"Yue, Wuyi"https://zbmath.org/authors/?q=ai:yue.wuyiSummary: In this paper, taking the various transmission needs of network users in cognitive radio networks into consideration, we analyze the system performance of cognitive radio networks by considering prioritized secondary users (SUs). The SUs are divided into SUs with higher priority (named SU1) and SUs with lower priority (named SU2). Unlike the preemptive and non-preemptive mechanisms proposed in conventional cognitive radio networks with prioritized SUs, in this paper, we propose a probabilistic interruption mechanism to balance the performance between the two types of SUs. We assume that if an SU1 packet arrives and finds the channel is being occupied by an SU2 packet, this SU1 packet will interrupt the SU2 packet's transmission with a probability (referred to as an interrupting index). In order to adapt to the digital nature of communication networks, based on the system actions of different types of packets, we build a discrete-time Markov chain model to derive the formulas for some important system performance measures. To assess the influence of the interrupting index on the system performance, we demonstrate the numerical results of different performance measures with respect to the interrupting index. Finally, from the perspective of the SU1 packets, we build an optimal function to obtain the optimal interrupting index under different parameter settings.A separation of \(n\)-consensus and \((n+1)\)-consensus based on process schedulinghttps://zbmath.org/1472.680142021-11-25T18:46:10.358925Z"Delporte-Gallet, Carole"https://zbmath.org/authors/?q=ai:delporte-gallet.carole"Fauconnier, Hugues"https://zbmath.org/authors/?q=ai:fauconnier.hugues"Toueg, Sam"https://zbmath.org/authors/?q=ai:toueg.samSummary: A fundamental research theme in distributed computing is the comparison of systems in terms of their ability to solve basic problems such as consensus that cannot be solved in completely asynchronous systems. In particular, in a seminal work
[``Wait-free synchronization'', ACM Trans. Program. Lang. Syst. 13, No. 1, 124--149 (1991; \url{doi:10.1145/114005.102808})], \textit{M. Herlihy}
compares shared-memory systems in terms of the shared objects that they have: he proved that there are shared objects that are powerful enough to solve consensus for \(n\) processes, but are too weak to solve consensus for \(n+1\) processes; such objects are placed at level \(n\) of a \textit{wait-free hierarchy}.
As in [loc. cit.],
we compare shared-memory systems with respect to their ability to solve consensus for \(n\) processes. But instead of comparing systems defined by the shared objects that they have, we compare read-write systems defined by the set of \textit{process schedules} that can occur in these systems. Defining systems this way can capture many types of systems, e.g., systems whose synchrony ranges from fully synchronous to completely
asynchronous, several systems with failure detectors, and ``obstruction-free'' systems. In this paper, we consider read-write systems defined in terms of sets of process schedules, and investigate the following fundamental question: Is there a system of \(n+1\) processes such that consensus can be solved for every subset of \(n\) processes in the system, but consensus cannot be solved for the \(n+1\) processes of the system? We show that the answer to the above question is ``yes'', and so these systems can be classified into hierarchy akin to Herlihy's hierarchy.
For the entire collection see [Zbl 1325.68023].Target counting with Presburger constraints and its application in sensor networkshttps://zbmath.org/1472.680152021-11-25T18:46:10.358925Z"Linker, Sven"https://zbmath.org/authors/?q=ai:linker.sven"Sevegnani, Michele"https://zbmath.org/authors/?q=ai:sevegnani.micheleSummary: One of the applications popularized by the emergence of wireless sensor networks is target counting: the computational task of determining the total number of targets located in an area by aggregating the individual counts of each sensor. The complexity of this task lies in the fact that sensing ranges may overlap, and therefore, targets may be overcounted as, in this setting, they are assumed to be indistinguishable from each other. In the literature, this problem has been proven to be unsolvable, hence the existence of several estimation algorithms. However, the main limitation currently affecting these algorithms is that no \textit{assurance} regarding the precision of a solution can be given. We present a novel algorithm for target counting based on exhaustive enumeration of target distributions using linear Presburger constraints. We improve on current approaches since the estimated counts obtained by our algorithm are by construction guaranteed to be consistent with the counts of each sensor. We further extend our algorithm to allow for weighted topologies and sensing errors for applicability in real-world deployments. We evaluate our approach through an extensive collection of synthetic and real-life configurations.Security analysis of systems with simple trajectories of functioning within the base role DP-modelhttps://zbmath.org/1472.680162021-11-25T18:46:10.358925Z"Devyanin, P. N."https://zbmath.org/authors/?q=ai:devyanin.p-nSummary: In the paper, we consider computer systems with only simple trajectories of functioning and with the any number of the cooperated user sessions that do not get access owning to each other by using the information flows by memory to essences functionally associated with the user sessions. For these systems, the conditions for transfering access rights and realizing information flows by memory are formulated and proved within the base role DP-model.Security analysis of systems with simple trajectories functioning within framework of the base role DP-modelhttps://zbmath.org/1472.680172021-11-25T18:46:10.358925Z"Devyanin, P. N."https://zbmath.org/authors/?q=ai:devyanin.p-nSummary: Conditions for transferring access rights and realizing memory information flows in computer systems are formulated and proved within framework of base role DP-model. Thus only simple trajectories of system functioning are examined when the any number of user sessions are cooperated and they do not get owning access to each other with the use of memory information flows to essences functionally associated with the user sessions.Integrating security policies with computer systems by means of AOP with application to Apache FTP serverhttps://zbmath.org/1472.680182021-11-25T18:46:10.358925Z"Stefantsov, D. A."https://zbmath.org/authors/?q=ai:stefantsov.d-a"Filimonov, A. Y."https://zbmath.org/authors/?q=ai:filimonov.a-ySummary: Recommendations for integrating security policies with computer systems by means of aspect oriented programming are given. It is shown how to integrate the role-based access control policy with the Apache FTP Server by following this recommendations.A theoretical foundation for programming languages aggregationhttps://zbmath.org/1472.680192021-11-25T18:46:10.358925Z"Ciobâcă, Ştefan"https://zbmath.org/authors/?q=ai:ciobaca.stefan"Lucanu, Dorel"https://zbmath.org/authors/?q=ai:lucanu.dorel"Rusu, Vlad"https://zbmath.org/authors/?q=ai:rusu.vlad"Roşu, Grigore"https://zbmath.org/authors/?q=ai:rosu.grigoreSummary: Programming languages should be formally specified in order to reason about programs written in them. We show that, given two formally specified programming languages, it is possible to construct the formal semantics of an aggregated language, in which programs consist of pairs of programs from the initial languages. The construction is based on algebraic techniques and it can be used to reduce relational properties (such as equivalence of programs) to reachability properties (in the aggregated language).
For the entire collection see [Zbl 1327.68013].A synchronous effects logic for temporal verification of pure Esterelhttps://zbmath.org/1472.680202021-11-25T18:46:10.358925Z"Song, Yahui"https://zbmath.org/authors/?q=ai:song.yahui"Chin, Wei-Ngan"https://zbmath.org/authors/?q=ai:chin.wei-nganSummary: Esterel is an imperative synchronous language that has found success in many safety-critical applications. Its precise semantics makes it natural for programming and reasoning. Existing techniques tackle either one of its main challenges: correctness checking or temporal verification. To resolve the issues simultaneously, we propose a new solution via a Hoare-style forward verifier and a term rewriting system (TRS) on \textit{Synced Effects}. The first contribution is, by deploying a novel effects logic, the verifier computes the deterministic program behaviour via construction rules at the source level, defining program evaluation syntactically. As a second contribution, by avoiding the complex translation from LTL formulas to Esterel programs, our purely algebraic TRS efficiently checks temporal properties described by expressive Synced Effects. To demonstrate our method's feasibility, we prototype this logic; prove its correctness; provide experimental results, and a number of case studies.
For the entire collection see [Zbl 1471.68017].Description, implementation, and evaluation of a generic design for tabled CLPhttps://zbmath.org/1472.680212021-11-25T18:46:10.358925Z"Arias, Joaquín"https://zbmath.org/authors/?q=ai:arias.joaquin"Carro, Manuel"https://zbmath.org/authors/?q=ai:carro.manuelSummary: Logic programming with tabling and constraints (TCLP, \textit{tabled constraint logic programming}) has been shown to be more expressive and in some cases more efficient than LP, CLP, or LP + tabling. Previous designs of TCLP systems did not fully use entailment to determine call/answer subsumption and did not provide a simple and well-documented interface to facilitate the integration of constraint solvers in existing tabling systems. We study the role of projection and entailment in the termination, soundness, and completeness of TCLP systems and present the design and an experimental evaluation of Mod TCLP, a framework that eases the integration of additional constraint solvers. Mod TCLP views constraint solvers as clients of the tabling system, which is generic w.r.t. the solver and only requires a clear interface from the latter. We validate our design by integrating four constraint solvers: a previously existing constraint solver for difference constraints, written in C; the standard versions of Holzbaur's \(\mathrm{CLP}(\mathbb{Q})\) and \(\mathrm{CLP}(\mathbb{R})\), written in Prolog; and a new constraint solver for equations over finite lattices. We evaluate the performance of our framework in several benchmarks using the aforementioned solvers. Mod TCLP is developed in Ciao Prolog, a robust, mature, next-generation Prolog system.selp: a single-shot epistemic logic program solverhttps://zbmath.org/1472.680222021-11-25T18:46:10.358925Z"Bichler, Manuel"https://zbmath.org/authors/?q=ai:bichler.manuel"Morak, Michael"https://zbmath.org/authors/?q=ai:morak.michael"Woltran, Stefan"https://zbmath.org/authors/?q=ai:woltran.stefanSummary: Epistemic logic programs (ELPs) are an extension of answer set programming (ASP) with epistemic operators that allow for a form of meta-reasoning, that is, reasoning over multiple possible worlds. Existing ELP solving approaches generally rely on making multiple calls to an ASP solver in order to evaluate the ELP. However, in this paper, we show that there also exists a direct translation from ELPs into non-ground ASP with bounded arity. The resulting ASP program can thus be solved in a single shot. We then implement this encoding method, using recently proposed techniques to handle large, non-ground ASP rules, into the prototype ELP solving system ``selp,'' which we present in this paper. This solver exhibits competitive performance on a set of ELP benchmark instances.Boosting answer set optimization with weighted comparator networkshttps://zbmath.org/1472.680232021-11-25T18:46:10.358925Z"Bomanson, Jori"https://zbmath.org/authors/?q=ai:bomanson.jori"Janhunen, Tomi"https://zbmath.org/authors/?q=ai:janhunen.tomiSummary: Answer set programming (ASP) is a paradigm for modeling knowledge-intensive domains and solving challenging reasoning problems. In ASP solving, a typical strategy is to preprocess problem instances by rewriting complex rules into simpler ones. Normalization is a rewriting process that removes extended rule types altogether in favor of normal rules. Recently, such techniques led to optimization rewriting in ASP, where the goal is to boost answer set optimization by refactoring the optimization criteria of interest. In this paper, we present a novel, general, and effective technique for optimization rewriting based on comparator networks which are specific kinds of circuits for reordering the elements of vectors. The idea is to connect an ASP encoding of a comparator network to the literals being optimized and to redistribute the weights of these literals over the structure of the network. The encoding captures information about the weight of an answer set in auxiliary atoms in a structured way that is proven to yield exponential improvements during branch-and-bound optimization on an infinite family of example programs. The used comparator network can be tuned freely, for example, to find the best size for a given benchmark class. Experiments show accelerated optimization performance on several benchmark problems.Optimizing answer set computation via heuristic-based decompositionhttps://zbmath.org/1472.680242021-11-25T18:46:10.358925Z"Calimeri, Francesco"https://zbmath.org/authors/?q=ai:calimeri.francesco"Perri, Simona"https://zbmath.org/authors/?q=ai:perri.simona"Zangari, Jessica"https://zbmath.org/authors/?q=ai:zangari.jessicaSummary: Answer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and non-monotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are computed by an ASP system. Different, semantically equivalent, programs can be defined for the same problem; however, performance of systems evaluating them might significantly vary. We propose an approach for automatically transforming an input logic program into an equivalent one that can be evaluated more efficiently. One can make use of existing tree-decomposition techniques for rewriting selected rules into a set of multiple ones; the idea is to guide and adaptively apply them on the basis of proper new heuristics, to obtain a smart rewriting algorithm to be integrated into an ASP system. The method is rather general: it can be adapted to any system and implement different preference policies. Furthermore, we define a set of new heuristics tailored at optimizing grounding, one of the main phases of the ASP computation; we use them in order to implement the approach into the ASP system \textit{DLV}, in particular into its grounding subsystem \(\mathscr{I}\)-\textit{DLV}, and carry out an extensive experimental activity for assessing the impact of the proposal.Foundations of logic programming in hybridised logicshttps://zbmath.org/1472.680252021-11-25T18:46:10.358925Z"Găină, Daniel"https://zbmath.org/authors/?q=ai:gaina.danielSummary: The present paper sets the foundation of logic programming in hybridised logics. The basic logic programming semantic concepts such as query and solutions, and the fundamental results such as the existence of initial models and Herbrand's theorem, are developed over a very general hybrid logical system. We employ the hybridisation process proposed by Diaconescu over an arbitrary logical system captured as an institution to define the logic programming framework.
For the entire collection see [Zbl 1327.68013].The Seventh Answer Set Programming Competition: design and resultshttps://zbmath.org/1472.680262021-11-25T18:46:10.358925Z"Gebser, Martin"https://zbmath.org/authors/?q=ai:gebser.martin"Maratea, Marco"https://zbmath.org/authors/?q=ai:maratea.marco"Ricca, Francesco"https://zbmath.org/authors/?q=ai:ricca.francescoSummary: Answer Set Programming (ASP) is a prominent knowledge representation language with roots in logic programming and non-monotonic reasoning. Biennial ASP competitions are organized in order to furnish challenging benchmark collections and assess the advancement of the state of the art in ASP solving. In this paper, we report on the design and results of the Seventh ASP Competition, jointly organized by the University of Calabria (Italy), the University of Genova (Italy), and the University of Potsdam (Germany), in affiliation with the 14th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR 2017).Inlining external sources in answer set programshttps://zbmath.org/1472.680272021-11-25T18:46:10.358925Z"Redl, Christoph"https://zbmath.org/authors/?q=ai:redl.christophSummary: HEX-programs are an extension of answer set programs (ASP) with external sources. To this end, \textit{external atoms} provide a bidirectional interface between the program and an external source. The traditional evaluation algorithm for HEX-programs is based on guessing truth values of external atoms and verifying them by explicit calls of the external source. The approach was optimized by techniques that reduce the number of necessary verification calls or speed them up, but the remaining external calls are still expensive. In this paper, we present an alternative evaluation approach based on \textit{inlining} of external atoms, motivated by existing but less general approaches for specialized formalisms such as DL-programs. External atoms are then compiled away such that no verification calls are necessary. The approach is implemented in the \textsf{dlvhex} reasoner. Experiments show a significant performance gain. Besides performance improvements, we further exploit inlining for extending previous (semantic) characterizations of program equivalence from ASP to HEX-programs, including those of \textit{strong equivalence, uniform equivalence}, and \(\langle\mathcal{H},\mathcal{B}\rangle\)-\textit{equivalence}. Finally, based on these equivalence criteria, we characterize also inconsistency of programs w.r.t. extensions. Since well-known ASP extensions (such as constraint ASP) are special cases of HEX, the results are interesting beyond the particular formalism.Backjumping is exception handlinghttps://zbmath.org/1472.680282021-11-25T18:46:10.358925Z"Robbins, Ed"https://zbmath.org/authors/?q=ai:robbins.edward-henry|robbins.edward-l"King, Andy"https://zbmath.org/authors/?q=ai:king.andy"Howe, Jacob M."https://zbmath.org/authors/?q=ai:howe.jacob-mSummary: ISO Prolog provides catch and throw to realize the control flow of exception handling. This pearl demonstrates that catch and throw are inconspicuously amenable to the implementation of backjumping. In fact, they have precisely the semantics required: rewinding the search to a specific point and carrying of a preserved term to that point. The utility of these properties is demonstrated through an implementation of graph coloring with backjumping and a backjumping SAT solver that applies conflict-driven clause learning.Omission-based abstraction for answer set programshttps://zbmath.org/1472.680292021-11-25T18:46:10.358925Z"Saribatur, Zeynep G."https://zbmath.org/authors/?q=ai:saribatur.zeynep-gozen"Eiter, Thomas"https://zbmath.org/authors/?q=ai:eiter.thomasSummary: Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We introduce a method to automatically abstract ASP programs that preserves their structure by reducing the vocabulary while ensuring an over-approximation (i.e., each original answer set maps to some abstract answer set). This allows for generating partial answer set candidates that can help with approximation of reasoning. Computing the abstract answer sets is intuitively easier due to a smaller search space, at the cost of encountering spurious answer sets. Faithful (non-spurious) abstractions may be used to represent projected answer sets and to guide solvers in answer set construction. For dealing with spurious answer sets, we employ an ASP debugging approach to help with abstraction refinement, which determines atoms as badly omitted and adds them back in the abstraction. As a show case, we apply abstraction to explain unsatisfiability of ASP programs in terms of blocker sets, which are the sets of atoms such that abstraction to them preserves unsatisfiability. Their usefulness is demonstrated by experimental results.Erratum to: ``Omission-based abstraction for answer set programs''https://zbmath.org/1472.680302021-11-25T18:46:10.358925Z"Saribatur, Zeynep G."https://zbmath.org/authors/?q=ai:saribatur.zeynep-gozen"Eiter, Thomas"https://zbmath.org/authors/?q=ai:eiter.thomasErratum to the authors' paper [ibid. 21, No. 2, 145--195 (2021; Zbl 1472.68029)].The use of erratic behavior templates in debugging parallel programs by the automated validity verification methodhttps://zbmath.org/1472.680312021-11-25T18:46:10.358925Z"Vlasenko, A. Yu."https://zbmath.org/authors/?q=ai:vlasenko.a-yu"Gudov, A. M."https://zbmath.org/authors/?q=ai:gudov.a-mSummary: A modification of the method of automated validity verification used in debugging parallel programs for computers with distributed memory is proposed. A feature of the proposed approach is the use of text erratic behavior templates that make it possible to control the checks performed during the analysis of a running parallel application. A tool implementing the proposed approach to detecting logical errors in parallel programs using the Message Passing Interface is described.A self-certifying compilation framework for WebAssemblyhttps://zbmath.org/1472.680322021-11-25T18:46:10.358925Z"Namjoshi, Kedar S."https://zbmath.org/authors/?q=ai:namjoshi.kedar-s"Xue, Anton"https://zbmath.org/authors/?q=ai:xue.antonSummary: A \textit{self-certifying} compiler is designed to generate a correctness proof for each optimization performed during compilation. The generated proofs are checked automatically by an independent proof validator. The outcome is formally verified compilation, achieved \textit{without} formally verifying the compiler. This paper describes the design and implementation of a self-certifying compilation framework for WebAssembly, a new intermediate language supported by all major browsers.
For the entire collection see [Zbl 1471.68017].A transformational approach to resource analysis with typed-norms inferencehttps://zbmath.org/1472.680332021-11-25T18:46:10.358925Z"Albert, Elvira"https://zbmath.org/authors/?q=ai:albert.elvira"Genaim, Samir"https://zbmath.org/authors/?q=ai:genaim.samir"Gutiérrez, Raúl"https://zbmath.org/authors/?q=ai:gutierrez.raul"Martin-Martin, Enrique"https://zbmath.org/authors/?q=ai:martin-martin.enriqueSummary: In order to automatically infer the resource consumption of programs, analyzers track how \textit{data sizes} change along program's execution. Typically, analyzers measure the sizes of data by applying \textit{norms} which are mappings from data to natural numbers that represent the sizes of the corresponding data. When norms are defined by taking type information into account, they are named \textit{typed-norms}. This article presents a transformational approach to resource analysis with typed-norms that are inferred by a data-flow analysis. The analysis is based on a transformation of the program into an \textit{intermediate abstract program} in which each variable is abstracted with respect to all considered norms which are valid for its type. We also present the data-flow analysis to automatically infer the required, useful, typed-norms from programs. Our analysis is formalized on a simple rule-based representation to which programs written in different programming paradigms (e.g., functional, logic, and imperative) can be automatically translated. Experimental results on standard benchmarks used by other type-based analyzers show that our approach is both efficient and accurate in practice.An institutional foundation for the \(\mathbb {K}\) semantic frameworkhttps://zbmath.org/1472.680342021-11-25T18:46:10.358925Z"Chiriţă, Claudia Elena"https://zbmath.org/authors/?q=ai:chirita.claudia-elena"Şerbănuţă, Traian Florin"https://zbmath.org/authors/?q=ai:serbanuta.traian-florinSummary: We advance an institutional formalisation of the logical systems that underlie the \(\mathbb {K}\) semantic framework and are used to capture both structural properties of program configurations through pattern matching, and changes of configurations through reachability rules. By defining encodings of matching and reachability logic into the institution of first-order logic, we set the foundation for integrating \(\mathbb {K}\) into logic graphs of heterogeneous institution-based specification languages such as \textsc{HetCasl}. This will further enable the use of the \(\mathbb {K}\) tool with other existing formal specification and verification tools associated with \textsc{Hets}.
For the entire collection see [Zbl 1327.68013].Incremental and modular context-sensitive analysishttps://zbmath.org/1472.680352021-11-25T18:46:10.358925Z"Garcia-Contreras, Isabel"https://zbmath.org/authors/?q=ai:garcia-contreras.isabel"Morales, José F."https://zbmath.org/authors/?q=ai:morales.jose-francisco"Hermenegildo, Manuel V."https://zbmath.org/authors/?q=ai:hermenegildo.manuel-vSummary: Context-sensitive global analysis of large code bases can be expensive, which can make its use impractical during software development. However, there are many situations in which modifications are small and isolated within a few components, and it is desirable to reuse as much as possible previous analysis results. This has been achieved to date through incremental global analysis fixpoint algorithms that achieve cost reductions at fine levels of granularity, such as changes in program lines. However, these fine-grained techniques are neither directly applicable to modular programs nor are they designed to take advantage of modular structures. This paper describes, implements, and evaluates an algorithm that performs efficient context-sensitive analysis incrementally on modular partitions of programs. The experimental results show that the proposed modular algorithm shows significant improvements, in both time and memory consumption, when compared to existing non-modular, fine-grain incremental analysis techniques. Furthermore, thanks to the proposed intermodular propagation of analysis information, our algorithm also outperforms traditional modular analysis even when analyzing from scratch.Algebra-based synthesis of loops and their invariants (invited paper)https://zbmath.org/1472.680362021-11-25T18:46:10.358925Z"Humenberger, Andreas"https://zbmath.org/authors/?q=ai:humenberger.andreas"Kovács, Laura"https://zbmath.org/authors/?q=ai:kovacs.laura-ildikoSummary: Provably correct software is one of the key challenges in our software-driven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction. In this paper we overview some of our results for both of these scenarios when analysing programs with loops. The class of loops we consider can be modelled by a system of linear recurrence equations with constant coefficients, called C-finite recurrences. We first describe an algorithmic approach for synthesising all polynomial equality invariants of such non-deterministic numeric single-path loops. By reverse engineering invariant synthesis, we then describe an automated method for synthesising program loops satisfying a given set of polynomial loop invariants. Our results have applications towards proving partial correctness of programs, compiler optimisation and generating number sequences from algebraic relations.
For the entire collection see [Zbl 1471.68017].Approximate bit dependency analysis to identify program synthesis problems as infeasiblehttps://zbmath.org/1472.680372021-11-25T18:46:10.358925Z"Kamp, Marius"https://zbmath.org/authors/?q=ai:kamp.marius"Philippsen, Michael"https://zbmath.org/authors/?q=ai:philippsen.michaelSummary: Bit-vector-based program synthesis is an important building block of state-of-the-art techniques in computer programming. Some of these techniques do not only rely on a synthesizer's ability to return an appropriate program if it exists but also require a synthesizer to detect if there is no such program at all in the entire search space (i.e., the problem is infeasible), which is a computationally demanding task.
In this paper, we propose an approach to quickly identify some synthesis problems as infeasible. We observe that a specification function encodes dependencies between input and output bits that a correct program must satisfy. To exploit this fact, we present approximate analyses of essential bits and use them in two novel algorithms to check if a synthesis problem is infeasible. Our experiments show that adding our technique to applications of bit vector synthesis can save up to 33\% of their time.
For the entire collection see [Zbl 1471.68017].On subexponentials, synthetic connectives, and multi-level delimited controlhttps://zbmath.org/1472.680382021-11-25T18:46:10.358925Z"Liang, Chuck"https://zbmath.org/authors/?q=ai:liang.chuck"Miller, Dale"https://zbmath.org/authors/?q=ai:miller.dale-aSummary: We construct a partially-ordered hierarchy of delimited control operators similar to those of the CPS hierarchy of
\textit{O. Danvy} and \textit{A. Filinski} [``Abstracting control'', in: Proceedings of the 1990 ACM conference on LISP and functional programming, LFP'90. New York, NY: Association for Computing Machinery (ACM). 151--160 (1990; \url{doi:10.1145/91556.91622})].
However, instead of relying on nested CPS translations, these operators are directly interpreted in linear logic extended with subexponentials (i.e., multiple pairs of ! and ?). We construct an independent proof theory for a fragment of this logic based on the principle of focusing. It is then shown that the new constraints placed on the permutation of cuts correspond to multiple levels of delimited control.
For the entire collection see [Zbl 1326.68013].Twinning automata and regular expressions for string static analysishttps://zbmath.org/1472.680392021-11-25T18:46:10.358925Z"Negrini, Luca"https://zbmath.org/authors/?q=ai:negrini.luca"Arceri, Vincenzo"https://zbmath.org/authors/?q=ai:arceri.vincenzo"Ferrara, Pietro"https://zbmath.org/authors/?q=ai:ferrara.pietro"Cortesi, Agostino"https://zbmath.org/authors/?q=ai:cortesi.agostinoSummary: In this paper we formalize \textsc{Tarsis}, a new abstract domain based on the abstract interpretation theory that approximates string values through finite state automata. The main novelty of \textsc{Tarsis} is that it works over an alphabet of strings instead of single characters. On the one hand, such an approach requires a more complex and refined definition of the widening operator, and the abstract semantics of string operators. On the other hand, it is in position to obtain strictly more precise results than state-of-the-art approaches. We implemented a prototype of \textsc{Tarsis}, and we applied it to some case studies taken from some of the most popular Java libraries manipulating string values. The experimental results confirm that \textsc{Tarsis} is in position to obtain strictly more precise results than existing analyses.
For the entire collection see [Zbl 1471.68017].Automated repair of heap-manipulating programs using deductive synthesishttps://zbmath.org/1472.680402021-11-25T18:46:10.358925Z"Nguyen, Thanh-Toan"https://zbmath.org/authors/?q=ai:nguyen.thanh-toan"Ta, Quang-Trung"https://zbmath.org/authors/?q=ai:ta.quang-trung"Sergey, Ilya"https://zbmath.org/authors/?q=ai:sergey.ilya"Chin, Wei-Ngan"https://zbmath.org/authors/?q=ai:chin.wei-nganSummary: We propose a novel method to automatically repairing buggy heap-manipulating programs using constraint solving and deductive synthesis. Given an input program \texttt{C} and its formal specification in the form of a Hoare triple: \(\{\mathcal{P}\}\) \texttt{C} \(\{\mathcal{Q}\}\), we use a separation-logic-based verifier to verify if program \texttt{C} is correct w.r.t. its specifications. If program \texttt{C} is found buggy, we then repair it in the following steps. First, we rely on the verification results to collect a list of suspicious statements of the buggy program. For each suspicious statement, we temporarily replace it with a template patch representing the desired statements. The template patch is also formally specified using a pair of unknown pre- and postcondition. Next, we use the verifier to analyze the temporarily patched program to collect constraints related to the pre- and postcondition of the template patch. Then, these constraints are solved by our constraint solving technique to discover the suitable specifications of the template patch. Subsequently, these specifications can be used to synthesize program statements of the template patch, consequently creating a candidate program. Finally, if the candidate program is validated, it is returned as the repaired program. We demonstrate the effectiveness of our approach by evaluating our implementation and a state-of-the-art approach on a benchmark of 231 buggy programs. The experimental results show that our tool successfully repairs 223 buggy programs and considerably outperforms the compared tool.
For the entire collection see [Zbl 1471.68017].Property-based testing for Spark Streaminghttps://zbmath.org/1472.680412021-11-25T18:46:10.358925Z"Riesco, A."https://zbmath.org/authors/?q=ai:riesco.adrian"Rodríguez-Hortalá, J."https://zbmath.org/authors/?q=ai:rodriguez-hortala.juanSummary: Stream processing has reached the mainstream in the last years, as a new generation of open-source distributed stream processing systems, designed for scaling horizontally on commodity hardware, has brought the capability for processing high-volume and high-velocity data streams to companies of all sizes. In this work, we propose a combination of temporal logic and property-based testing (PBT) for dealing with the challenges of testing programs that employ this programming model. We formalize our approach in a discrete time temporal logic for finite words, with some additions to improve the expressiveness of properties, which includes timeouts for temporal operators and a binding operator for letters. In particular, we focus on testing Spark Streaming programs written with the Spark API for the functional language Scala, using the PBT library ScalaCheck. For that we add temporal logic operators to a set of new ScalaCheck generators and properties, as part of our testing library sscheck.Generative program analysis and beyond: the power of domain-specific languages (invited paper)https://zbmath.org/1472.680422021-11-25T18:46:10.358925Z"Steffen, Bernhard"https://zbmath.org/authors/?q=ai:steffen.bernhard"Murtovi, Alnis"https://zbmath.org/authors/?q=ai:murtovi.alnisSummary: In this paper we position Linear Time Temporal Logic (LTL), structural operational semantics (SOS), and a graphical generalization of BNF as central DSLs for program analysis and verification tasks in order to illustrate the impact of language to the mindset: (1) Specifying program analyses in LTL changes the classical algorithmic `HOW' thinking into a property-oriented `WHAT' thinking that allows one to logically combine analysis goals and eases proofs. (2) Playing with the original store component in SOS configurations allows one to elegantly realize variants of abstract program interpretations, and to align different aspects, like e.g., the symbolic values of variables and path conditions. (3) Specializing languages by refining their BNF-like meta models has the power to lift certain verification tasks from the program to the programming language level. We will illustrate the advantages of the change of mindset imposed by these three DSLs, as well as the fact that these advantages come at low price due to available adequate generator technology.
For the entire collection see [Zbl 1471.68017].Multidimensional range selectionhttps://zbmath.org/1472.680432021-11-25T18:46:10.358925Z"Chan, Timothy M."https://zbmath.org/authors/?q=ai:chan.timothy-m-y"Zhou, Gelin"https://zbmath.org/authors/?q=ai:zhou.gelinSummary: We study the problem of supporting (orthogonal) \textit{range selection} queries over a set of \(n\) points in constant-dimensional space. Under the standard word-RAM model with word size \(w = \varOmega (\lg n)\), we present data structures that occupy \(O(n \cdot (\lg n / \lg \lg n)^{d - 1})\) words of space and support \(d\)-dimensional range selection queries using \(O((\lg n / \lg \lg n)^d)\) query time. This improves the best known data structure by a factor of \(\lg \lg n\) in query time. To develop our data structures, we generalize the ``parallel counting'' technique of
\textit{G. S. Brodal} et al. [Theor. Comput. Sci. 412, No. 24, 2588--2601 (2011; Zbl 1220.68052)]
for one-dimensional range selection to higher dimensions.
As a byproduct, we design data structures to support \(d\)-dimensional range counting queries within \(O(n \cdot (\lg n / \lg w + 1)^{d - 2})\) words of space and \(O((\lg n / \lg w + 1)^{d - 1})\) query time, for any word size \(w = \varOmega (\lg n)\). This improves the best known result of
\textit{J. JaJa} et al. [Lect. Notes Comput. Sci. 3341, 558--568 (2004; Zbl 1116.68629)]
when \(\lg w\gg \lg \lg n\).
For the entire collection see [Zbl 1326.68015].Optimal search trees with 2-way comparisonshttps://zbmath.org/1472.680442021-11-25T18:46:10.358925Z"Chrobak, Marek"https://zbmath.org/authors/?q=ai:chrobak.marek"Golin, Mordecai"https://zbmath.org/authors/?q=ai:golin.mordecai-j"Munro, J. Ian"https://zbmath.org/authors/?q=ai:munro.j-ian"Young, Neal E."https://zbmath.org/authors/?q=ai:young.neal-eSummary: In 1971, Knuth gave an \(O(n^2)\)-time algorithm for the classic problem of finding an optimal binary search tree. Knuth's algorithm works only for search trees based on 3-way comparisons, but most modern computers support only 2-way comparisons (\(<\), \(\leq \), \(=\), \(\geq \), and \(>\)). Until this paper, the problem of finding an optimal search tree using 2-way comparisons remained open -- poly-time algorithms were known only for restricted variants. We solve the general case, giving (i) an \(O(n^4)\)-time algorithm and (ii) an \(O(n\log n)\)-time additive-3 approximation algorithm. For finding optimal \textit{binary split trees}, we (iii) obtain a linear speedup and (iv) prove some previous work incorrect.
For the entire collection see [Zbl 1326.68015].On the succinct representation of unlabeled permutationshttps://zbmath.org/1472.680452021-11-25T18:46:10.358925Z"El-Zein, Hicham"https://zbmath.org/authors/?q=ai:el-zein.hicham"Munro, J. Ian"https://zbmath.org/authors/?q=ai:munro.j-ian"Yang, Siwei"https://zbmath.org/authors/?q=ai:yang.siweiSummary: We investigate the problem of succinctly representing an arbitrary unlabeled permutation \(\pi \), so that \(\pi ^k(i)\) can be computed quickly for any \(i\) and any integer power \(k\). We consider the problem in several scenarios: {\parindent=0.5 cm \begin{itemize}\item[--] Labeling schemes where we assign labels to elements and the query is to be answered by just examining the labels of the queried elements: we show that a label space of \(\sum_{i=1}^n \lfloor \frac{n}{i} \rfloor \cdot i\) is necessary and sufficient. In other words, \(2\lg n\) bits of space are necessary and sufficient for representing each of the labels. \item[--] Succinct data structures for the problem where we assign labels to the \(n\) elements from the label set \(\{1,\ldots, cn\}\) where \(c\geq 1\): we show that \(\varTheta (\sqrt{n})\) bits are necessary and sufficient to represent the permutation. Moreover, we support queries in such a structure in \(O\)(1) time in the standard word-RAM model. \item[--] Succinct data structures for the problem where we assign labels to the \(n\) elements
from the label set \(\{1,\ldots, cn^{1+\epsilon}\}\) where \(c\) is a constant and \(0 < \epsilon < 1\): we show that \(\varTheta (n^{{(1-\epsilon)}/{2}})\) bits are necessary and sufficient to represent the permutation. We can also support queries in such a structure in \(O(1)\) time in the standard word-RAM model.
\end{itemize}}
For the entire collection see [Zbl 1326.68015].EERTREE: an efficient data structure for processing palindromes in stringshttps://zbmath.org/1472.680462021-11-25T18:46:10.358925Z"Rubinchik, Mikhail"https://zbmath.org/authors/?q=ai:rubinchik.mikhail"Shur, Arseny M."https://zbmath.org/authors/?q=ai:shur.arseny-mSummary: We propose a new linear-size data structure which provides a fast access to all palindromic substrings of a string or a set of strings. This structure inherits some ideas from the construction of both the suffix trie and suffix tree. Using this structure, we present simple and efficient solutions for a number of problems involving palindromes.
For the entire collection see [Zbl 1331.68018].Rank and select operations on a wordhttps://zbmath.org/1472.680472021-11-25T18:46:10.358925Z"Zhang, Meng"https://zbmath.org/authors/?q=ai:zhang.meng"Zhang, Yi"https://zbmath.org/authors/?q=ai:zhang.yi.10Summary: Given a bit-vector \(t\), operation \(\mathtt{rank}_1(t, i)\) returns the number of occurrences of 1-bits in the prefix of \(t\) ending at position \(i\). Operation \(\mathtt{select}_1(t, c)\), \(c\geq 1\) returns the position of the \(c\)-th 1-bit in \(t\). These operations are building blocks for succinct data structures. We present algorithms of and on an arbitrary word that run in \(O(\log^\ast w)\) time and use constant space by basic operations on words, where \(w\) is the word size in bits of the word RAM model. The method improves the current known \(O(\log\log w)\) method of counting the number of 1-bits in a word. We also give and algorithms taking constant running time and space for bit-vectors of length not greater than \(w/(\lceil\lg w-\lg\lg w\rceil+1)\).Making big data smallhttps://zbmath.org/1472.680482021-11-25T18:46:10.358925Z"Fan, Wenfei"https://zbmath.org/authors/?q=ai:fan.wenfeiSummary: Big data analytics is often prohibitively costly and is typically conducted by parallel processing with a cluster of machines. Is big data analytics beyond the reach of small companies that can only afford limited resources? This paper tackles this question by presenting Boundedly EvAlable SQL (BEAS), a system for querying big relations with constrained resources. The idea is to make big data small. To answer a query posed on a dataset, it often suffices to access a small fraction of the data no matter how big the dataset is. In the light of this, BEAS answers queries on big data by identifying and fetching a small set of the data needed. Under available resources, it computes exact answers whenever possible and otherwise approximate answers with accuracy guarantees. Underlying BEAS are principled approaches of bounded evaluation and data-driven approximation, the focus of this paper.Private information retrieval protocolhttps://zbmath.org/1472.680492021-11-25T18:46:10.358925Z"Afanas'eva, A. V."https://zbmath.org/authors/?q=ai:afanaseva.a-v"Balakirskiĭ, V. B."https://zbmath.org/authors/?q=ai:balakirsky.vladimir-b"Bezzateev, S. V."https://zbmath.org/authors/?q=ai:bezzateev.sergei-vSummary: A new computationally efficient private information retrieval protocol is proposed. It is based on coset properties of Galois groups of the field \(\mathrm{GF}(q)\) finite extensions. The proposed protocol has communication complexity slightly worse than the best known schemes based on locally decodable codes and it may be constructed for any system parameters (as opposed to codes). In comparison with similar solutions based on polynomials the computational complexity of our method is smaller which is important especially for servers processing multiple requests from multiple users.Action-centered information retrievalhttps://zbmath.org/1472.680502021-11-25T18:46:10.358925Z"Balduccini, Marcello"https://zbmath.org/authors/?q=ai:balduccini.marcello"Leblanc, Emily C."https://zbmath.org/authors/?q=ai:leblanc.emily-cSummary: Information retrieval (IR) aims at retrieving documents that are most relevant to a query provided by a user. Traditional techniques rely mostly on syntactic methods. In some cases, however, links at a deeper semantic level must be considered. In this paper, we explore a type of IR task in which documents describe sequences of events, and queries are about the state of the world after such events. In this context, successfully matching documents and query requires considering the events' possibly implicit uncertain effects and side effects. We begin by analyzing the problem, then propose an action language-based formalization, and finally automate the corresponding IR task using answer set programming.A patent retrieval query expansion method based on semantic dictionaryhttps://zbmath.org/1472.680512021-11-25T18:46:10.358925Z"Xu, Kan"https://zbmath.org/authors/?q=ai:xu.kan"Feng, Jiaojiao"https://zbmath.org/authors/?q=ai:feng.jiaojiao"Wang, Kaiqiao"https://zbmath.org/authors/?q=ai:wang.kaiqiao"Lin, Hongfei"https://zbmath.org/authors/?q=ai:lin.hongfei"Lin, Yuan"https://zbmath.org/authors/?q=ai:lin.yuanSummary: The query expansion can select expanded words to add to the original query based on semantic relationships and terms co-occurrence relationships to better understand the user's query intent. This paper proposes a method of using semantic dictionary WordNet as an external resource for query expansion to improve patent retrieval. LambdaMART method was used to be combined with different query expansion to improve the performance of patent retrieval. Experiments on TREC datasets showed that the learning to rank model, which used WordNet to modify expanded term weights, has better performance and improves the performance of patent retrieval.On a family of universal hash functionshttps://zbmath.org/1472.680522021-11-25T18:46:10.358925Z"Nesterenko, A. Yu."https://zbmath.org/authors/?q=ai:nesterenko.aleksey-yuSummary: We construct a new family of compressing mappings by means of superposition of several bijective mappings and mappings with specified properties. All functions in this family are proved to be universal hash functions. Concrete examples of functions from the family which are suitable for cryptographic applications are supplied.Authentication in trusted subsystem model using commutative encryptionhttps://zbmath.org/1472.680532021-11-25T18:46:10.358925Z"Pautov, P. A."https://zbmath.org/authors/?q=ai:pautov.p-aSummary: The paper considers the peculiarities of authentication in multi-tier environment and corresponding security problems. The authentication protocol for multi-tier system based on commutative encryption is provided. Also, some specific commutative encryption algorithms are considered.Networks of picture processors as problem solvershttps://zbmath.org/1472.680542021-11-25T18:46:10.358925Z"Bordihn, Henning"https://zbmath.org/authors/?q=ai:bordihn.henning"Bottoni, Paolo"https://zbmath.org/authors/?q=ai:bottoni.paolo"Labella, Anna"https://zbmath.org/authors/?q=ai:labella.anna"Mitrana, Victor"https://zbmath.org/authors/?q=ai:mitrana.victorSummary: We propose a solution based on networks of picture processors to the problem of picture pattern matching. The network solving the problem can be informally described as follows: it consists of two subnetworks, one of them extracts at each step, simultaneously, all subpictures of identical (progressively decreasing) size from the input picture and sends them to the other subnetwork which checks whether any of the received pictures is identical to the pattern. We present an efficient solution based on networks with evolutionary processors only, for patterns with at most three rows or columns. Afterward, we present a solution based on networks containing both evolutionary and hiding processors running in \(\mathcal O(n+m+kl)\) computational (processing and communication) steps, for any size \((n,m)\) of the input picture and \((k,l)\) of the pattern. From the proofs of these results, we infer that any \((k,l)\)-local language with \(1\leq k\leq 3\) can be decided in \(\mathcal O(n+m+l)\) computational steps by networks with evolutionary processors only, while any \((k,l)\)-local language with arbitrary \(k\), \(l\) can be decided in \(\mathcal O(n+m+kl)\) computational steps by networks containing both evolutionary and hiding processors.A theory of sequence indexing and working memory in recurrent neural networkshttps://zbmath.org/1472.680552021-11-25T18:46:10.358925Z"Frady, E. Paxon"https://zbmath.org/authors/?q=ai:frady.e-paxon"Kleyko, Denis"https://zbmath.org/authors/?q=ai:kleyko.denis"Sommer, Friedrich T."https://zbmath.org/authors/?q=ai:sommer.friedrich-tobiasSummary: To accommodate structured approaches of neural computation, we propose a class of recurrent neural networks for indexing and storing sequences of symbols or analog data vectors. These networks with randomized input weights and orthogonal recurrent weights implement coding principles previously described in vector symbolic architectures (VSA) and leverage properties of reservoir computing. In general, the storage in reservoir computing is lossy, and crosstalk noise limits the retrieval accuracy and information capacity. A novel theory to optimize memory performance in such networks is presented and compared with simulation experiments. The theory describes linear readout of analog data and readout with winner-take-all error correction of symbolic data as proposed in VSA models. We find that diverse VSA models from the literature have universal performance properties, which are superior to what previous analyses predicted. Further, we propose novel VSA models with the statistically optimal Wiener filter in the readout that exhibit much higher information capacity, in particular for storing analog data.
The theory we present also applies to memory buffers, networks with gradual forgetting, which can operate on infinite data streams without memory overflow. Interestingly, we find that different forgetting mechanisms, such as attenuating recurrent weights or neural nonlinearities, produce very similar behavior if the forgetting time constants are matched. Such models exhibit extensive capacity when their forgetting time constant is optimized for given noise conditions and network size. These results enable the design of new types of VSA models for the online processing of data streams.Solving constraint-satisfaction problems with distributed neocortical-like neuronal networkshttps://zbmath.org/1472.680562021-11-25T18:46:10.358925Z"Rutishauser, Ueli"https://zbmath.org/authors/?q=ai:rutishauser.ueli"Slotine, Jean-Jacques"https://zbmath.org/authors/?q=ai:slotine.jean-jacques-e"Douglas, Rodney J."https://zbmath.org/authors/?q=ai:douglas.rodney-jSummary: Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSP's planar four-color graph coloring, maximum independent set, and sudoku on this substrate and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of nonsaturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by nonlinear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation and offer insight into the computational role of dual inhibitory mechanisms in neural circuits.Formal semantics and verification of network-based biocomputation circuitshttps://zbmath.org/1472.680572021-11-25T18:46:10.358925Z"Aluf-Medina, Michelle"https://zbmath.org/authors/?q=ai:aluf-medina.michelle"Korten, Till"https://zbmath.org/authors/?q=ai:korten.till"Raviv, Avraham"https://zbmath.org/authors/?q=ai:raviv.avraham"Nicolau, Dan V. jun."https://zbmath.org/authors/?q=ai:nicolau.dan-v-jun"Kugler, Hillel"https://zbmath.org/authors/?q=ai:kugler.hillelSummary: Network-Based Biocomputation Circuits (NBCs) offer a new paradigm for solving complex computational problems by utilizing biological agents that operate in parallel to explore manufactured planar devices. The approach can also have future applications in diagnostics and medicine by combining NBCs computational power with the ability to interface with biological material. To realize this potential, devices should be designed in a way that ensures their correctness and robust operation. For this purpose, formal methods and tools can offer significant advantages by allowing investigation of design limitations and detection of errors before manufacturing and experimentation. Here we define a computational model for NBCs by providing formal semantics to NBC circuits. We present a formal verification-based approach and prototype tool that can assist in the design of NBCs by enabling verification of a given design's correctness. Our tool allows verification of the correctness of NBC designs for several NP-Complete problems, including the Subset Sum, Exact Cover and Satisfiability problems and can be extended to other NBC implementations. Our approach is based on defining transition systems for NBCs and using temporal logic for specifying and proving properties of the design using model checking. Our formal model can also serve as a starting point for computational complexity studies of the power and limitations of NBC systems.
For the entire collection see [Zbl 1471.68017].Computing with spikes: the advantage of fine-grained timinghttps://zbmath.org/1472.680582021-11-25T18:46:10.358925Z"Verzi, Stephen J."https://zbmath.org/authors/?q=ai:verzi.stephen-j"Rothganger, Fredrick"https://zbmath.org/authors/?q=ai:rothganger.fredrick-h"Parekh, Ojas D."https://zbmath.org/authors/?q=ai:parekh.ojas-d"Quach, Tu-Thach"https://zbmath.org/authors/?q=ai:quach.tu-thach"Miner, Nadine E."https://zbmath.org/authors/?q=ai:miner.nadine-e"Vineyard, Craig M."https://zbmath.org/authors/?q=ai:vineyard.craig-m"James, Conrad D."https://zbmath.org/authors/?q=ai:james.conrad-d"Aimone, James B."https://zbmath.org/authors/?q=ai:aimone.james-bSummary: Neural-inspired spike-based computing machines often claim to achieve considerable advantages in terms of energy and time efficiency by using spikes for computation and communication. However, fundamental questions about spike-based computation remain unanswered. For instance, how much advantage do spike-based approaches have over conventional methods, and under what circumstances does spike-based computing provide a comparative advantage? Simply implementing existing algorithms using spikes as the medium of computation and communication is not guaranteed to yield an advantage. Here, we demonstrate that spike-based communication and computation within algorithms can increase throughput, and they can decrease energy cost in some cases. We present several spiking algorithms, including sorting a set of numbers in ascending/descending order, as well as finding the maximum or minimum or median of a set of numbers. We also provide an example application: a spiking median-filtering approach for image processing providing a low-energy, parallel implementation. The algorithms and analyses presented here demonstrate that spiking algorithms can provide performance advantages and offer efficient computation of fundamental operations useful in more complex algorithms.A substrate-independent framework to characterize reservoir computershttps://zbmath.org/1472.680592021-11-25T18:46:10.358925Z"Dale, Matthew"https://zbmath.org/authors/?q=ai:dale.matthew"Miller, Julian F."https://zbmath.org/authors/?q=ai:miller.julian-f"Stepney, Susan"https://zbmath.org/authors/?q=ai:stepney.susan"Trefzer, Martin A."https://zbmath.org/authors/?q=ai:trefzer.martin-aSummary: The reservoir computing (RC) framework states that any nonlinear, input-driven dynamical system (the \textit{reservoir}) exhibiting properties such as a fading memory and input separability can be trained to perform computational tasks. This broad inclusion of systems has led to many new physical substrates for RC. Properties essential for reservoirs to compute are tuned through reconfiguration of the substrate, such as change in virtual topology or physical morphology. As a result, each substrate possesses a unique `quality' -- obtained through reconfiguration -- to realize different reservoirs for different tasks. Here we describe an experimental framework to characterize the quality of potentially \textit{any} substrate for RC. Our framework reveals that a definition of quality is not only useful to compare substrates, but can help map the non-trivial relationship between properties and task performance. In the wider context, the framework offers a greater understanding as to what makes a dynamical system compute, helping improve the design of future substrates for RC.Quantum bit commitment with application in quantum zero-knowledge proof (extended abstract)https://zbmath.org/1472.680602021-11-25T18:46:10.358925Z"Yan, Jun"https://zbmath.org/authors/?q=ai:yan.jun"Weng, Jian"https://zbmath.org/authors/?q=ai:weng.jian"Lin, Dongdai"https://zbmath.org/authors/?q=ai:lin.dongdai"Quan, Yujuan"https://zbmath.org/authors/?q=ai:quan.yujuanSummary: In this work, we study formalization and construction of non-interactive statistically binding quantum bit commitment scheme (QBC), as well as its application in quantum zero-knowledge (QZK) proof. We explore the fully quantum model, where both computation and communication could be quantum. While most of the proofs here are straightforward based on previous works, we have two technical contributions. First, we show how to use reversibility of quantum computation to construct non-interactive QBC. Second, we identify new issue caused by quantum binding in security analysis and give our idea to circumvent it, which may be found useful elsewhere.
For the entire collection see [Zbl 1326.68015].Choice is hardhttps://zbmath.org/1472.680612021-11-25T18:46:10.358925Z"Arkin, Esther M."https://zbmath.org/authors/?q=ai:arkin.esther-m"Banik, Aritra"https://zbmath.org/authors/?q=ai:banik.aritra"Carmi, Paz"https://zbmath.org/authors/?q=ai:carmi.paz"Citovsky, Gui"https://zbmath.org/authors/?q=ai:citovsky.gui"Katz, Matthew J."https://zbmath.org/authors/?q=ai:katz.matthew-j"Mitchell, Joseph S. B."https://zbmath.org/authors/?q=ai:mitchell.joseph-s-b"Simakov, Marina"https://zbmath.org/authors/?q=ai:simakov.marinaSummary: Let \(P=\{C_1,C_2,\ldots, C_n\}\) be a set of color classes, where each color class \(C_i\) consists of a pair of objects. We focus on two problems in which the objects are points on the line. In the first problem (\textit{rainbow minmax gap}), given \(P\), one needs to select exactly one point from each color class, such that the maximum distance between a pair of consecutive selected points is minimized. This problem was studied by Consuegra and Narasimhan, who left the question of its complexity unresolved. We prove that it is NP-hard. For our proof we obtain the following auxiliary result. A 3-SAT formula is an LSAT formula if each clause (viewed as a set of literals) intersects at most one other clause, and, moreover, if two clauses intersect, then they have exactly one literal in common. We prove that the problem of deciding whether an LSAT formula is satisfiable or not is NP-complete. We present two additional applications of the LSAT result, namely, to \textit{rainbow piercing} and \textit{rainbow covering}.
In the second problem (\textit{covering color classes with intervals}), given \(P\), one needs to find a minimum-cardinality set \(\mathcal {I}\) of intervals, such that exactly one point from each color class is covered by an interval in \(\mathcal {I}\). Motivated by a problem in storage systems, this problem has received significant attention. Here, we settle the complexity question by proving that it is NP-hard.
For the entire collection see [Zbl 1326.68015].General caching is hard: even with small pageshttps://zbmath.org/1472.680622021-11-25T18:46:10.358925Z"Folwarczný, Lukáš"https://zbmath.org/authors/?q=ai:folwarczny.lukas"Sgall, Jiří"https://zbmath.org/authors/?q=ai:sgall.jiriSummary: \textit{Caching} (also known as \textit{paging}) is a classical problem concerning page replacement policies in two-level memory systems. \textit{General caching} is the variant with pages of different sizes and fault costs. The strong NP-hardness of its two important cases, the \textit{fault model} (each page has unit fault cost) and the \textit{bit model} (each page has the same fault cost as size) has been established. We prove that this already holds when page sizes are bounded by a small constant: The bit and fault models are strongly NP-complete even when page sizes are limited to \(\{1, 2, 3\}\).
Considering only the decision versions of the problems, general caching is equivalent to the \textit{unsplittable flow on a path problem} and therefore our results also improve the hardness results about this problem.
For the entire collection see [Zbl 1326.68015].NP-completeness of special string editing problemshttps://zbmath.org/1472.680632021-11-25T18:46:10.358925Z"Martynov, S. S."https://zbmath.org/authors/?q=ai:martynov.s-sSummary: We establish the NP-completeness of the string editing problems with respect to a language defined by restrictions on subwords of its words. The editing operation consists in a replacement of the substrings belonging to a specified block code, by the words of another block code.The projection games conjecture and the hardness of approximation of Super-SAT and related problemshttps://zbmath.org/1472.680642021-11-25T18:46:10.358925Z"Mukhopadhyay, Priyanka"https://zbmath.org/authors/?q=ai:mukhopadhyay.priyankaSummary: The Super-SAT (SSAT) problem was introduced in
[\textit{I. Dinur} et al., Combinatorica 23, No. 2, 205--243 (2003; Zbl 1049.68072);
Theor. Comput. Sci. 285, No. 1, 55--71 (2002; Zbl 1016.68041)]
to prove the NP-hardness of approximation of two popular lattice problems -- Shortest Vector Problem and Closest Vector Problem. SSAT is conjectured to be NP-hard to approximate to within a factor of \(n^c\) (\(c\) is positive constant, \(n\) is the size of the SSAT instance). In this paper we prove this conjecture assuming the Projection Games Conjecture (PGC)
[\textit{D. Moshkovitz}, Lect. Notes Comput. Sci. 7408, 276--287 (2012; Zbl 1336.68104)].
This implies hardness of approximation of these lattice problems within polynomial factors, assuming PGC. We also reduce SSAT to the Nearest Codeword Problem and Learning Halfspace Problem
[\textit{S. Arora} et al., J. Comput. Syst. Sci. 54, No. 2, 317--331 (1997; Zbl 0877.68067)].
This proves that both these problems are NP-hard to approximate within a factor of \(N^{c'/\log\log n}\) (\(c'\) is positive constant, \(N\) is the size of the instances of the respective problems). Assuming PGC these problems are proved to be NP-hard to approximate within polynomial factors.Give me another one!https://zbmath.org/1472.680652021-11-25T18:46:10.358925Z"Behrisch, Mike"https://zbmath.org/authors/?q=ai:behrisch.mike"Hermann, Miki"https://zbmath.org/authors/?q=ai:hermann.miki"Mengel, Stefan"https://zbmath.org/authors/?q=ai:mengel.stefan"Salzer, Gernot"https://zbmath.org/authors/?q=ai:salzer.gernotSummary: We investigate the complexity of an optimization problem in Boolean propositional logic related to information theory: Given a conjunctive formula over a set of relations, find a satisfying assignment with minimal Hamming distance to a given assignment that satisfies the formula (\textsf{NearestOtherSolution}, \textsf{NOSol}).
We present a complete classification with respect to the relations admitted in the formula. We give polynomial-time algorithms for several classes of constraint languages. For all other cases we prove hardness or completeness regarding poly-APX, NPO, or equivalence to a well-known hard optimization problem.
For the entire collection see [Zbl 1326.68015].Corrigendum to: ``On the complexity of finding first-order critical points in constrained nonlinear optimization''https://zbmath.org/1472.680662021-11-25T18:46:10.358925Z"Cartis, C."https://zbmath.org/authors/?q=ai:cartis.coralia"Gould, N. I. M."https://zbmath.org/authors/?q=ai:gould.nicholas-ian-mark|gould.nick-i-m"Toint, Ph. L."https://zbmath.org/authors/?q=ai:toint.philippe-lSummary: In a recent paper [the authors, ibid. 144, No. 1--2 (A), 93--106 (2014; Zbl 1301.68154)], the evaluation complexity of an algorithm to find an approximate first-order critical point for the general smooth constrained optimization problem was examined. Unfortunately, the proof of Lemma 3.5 in that paper uses a result from an earlier paper in an incorrect way, and indeed the result of the lemma is false. The purpose of this corrigendum is to provide a modification of the previous analysis that allows us to restore the complexity bound for a different, scaled measure of first-order criticality.Game values and computational complexity: an analysis via black-white combinatorial gameshttps://zbmath.org/1472.680672021-11-25T18:46:10.358925Z"Fenner, Stephen A."https://zbmath.org/authors/?q=ai:fenner.stephen-a"Grier, Daniel"https://zbmath.org/authors/?q=ai:grier.daniel"Messner, Jochen"https://zbmath.org/authors/?q=ai:messner.jochen"Schaeffer, Luke"https://zbmath.org/authors/?q=ai:schaeffer.luke"Thierauf, Thomas"https://zbmath.org/authors/?q=ai:thierauf.thomasSummary: A black-white combinatorial game is a two-person game in which the pieces are colored either black or white. The players alternate moving or taking elements of a specific color designated to them before the game begins. A player loses the game if there is no legal move available for his color on his turn.
We first show that some black-white versions of combinatorial games can only assume combinatorial game values that are numbers, which indicates that the game has many nice properties making it easier to solve. Indeed, numeric games have only previously been shown to be hard for \textsf{NP}. We exhibit a language of natural numeric games (specifically, black-white poset games) that is \textsf{PSPACE}-complete, closing the gap in complexity for the first time between these numeric games and the large collection of combinatorial games that are known to be \textsf{PSPACE}-complete.
In this vein, we also show that the game of Col played on general graphs is also \textsf{PSPACE}-complete despite the
fact that it can only assume two very simple game values. This is interesting because its natural black-white variant is numeric but only complete for \(\mathsf P^{\mathsf{NP}[\log]}\). Finally, we show that the problem of determining the winner of black-white \textsc{Graph Nim} is in \textsf{P} using a flow-based technique.
For the entire collection see [Zbl 1326.68015].Word equations in non-deterministic linear spacehttps://zbmath.org/1472.680682021-11-25T18:46:10.358925Z"Jeż, Artur"https://zbmath.org/authors/?q=ai:jez.arturSummary: Satisfiability of word equations problem is: Given two sequences consisting of letters and variables decide whether there is a substitution for the variables that turns this equation into true equality. The exact computational complexity of this problem remains unknown, with the best lower and upper bounds being, respectively, \textsf{NP} and \textsf{PSPACE}. Recently, the novel technique of recompression was applied to this problem, simplifying the known proofs and lowering the space complexity to (non-deterministic) \(\mathcal{O}(n\log n)\). In this paper we show that satisfiability of word equations is in non-deterministic linear space, thus the language of satisfiable word equations is context-sensitive. We use the known recompression-based algorithm and additionally employ Huffman coding for letters. The proof, however, uses analysis of how the fragments of the equation depend on each other as well as a new strategy for non-deterministic choices of the algorithm.Effectiveness of structural restrictions for hybrid CSPshttps://zbmath.org/1472.680692021-11-25T18:46:10.358925Z"Kolmogorov, Vladimir"https://zbmath.org/authors/?q=ai:kolmogorov.vladimir"Rolínek, Michal"https://zbmath.org/authors/?q=ai:rolinek.michal"Takhanov, Rustem"https://zbmath.org/authors/?q=ai:takhanov.rustemSummary: Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism \({\mathbf {R}\rightarrow \boldsymbol{\Gamma}}\) between two relational structures, e.g. between two directed graphs. Analyzing its complexity has been a prominent research direction, especially for the \textit{fixed template CSPs} where the right side \(\boldsymbol{\Gamma}\) is fixed and the left side \(\mathbf {R}\) is unconstrained.
Far fewer results are known for the \textit{hybrid} setting that restricts both sides simultaneously. It assumes that \(\mathbf {R}\) belongs to a certain class of relational structures (called a \textit{structural restriction} in this paper). We study which structural restrictions are \textit{effective}, i.e. there exists a fixed template \(\boldsymbol{\Gamma}\) (from a certain class of languages) for which the problem is tractable when \(\mathbf {R}\) is restricted, and NP-hard otherwise. We provide
a characterization for structural restrictions that are \textit{closed under inverse homomorphisms}. The criterion is based on the \textit{chromatic number} of a relational structure defined in this paper; it generalizes the standard chromatic number of a graph.
As our main tool, we use the algebraic machinery developed for fixed template CSPs. To apply it to our case, we introduce a new construction called a ``lifted language''. We also give a characterization for structural restrictions corresponding to minor-closed families of graphs, extend results to certain Valued CSPs (namely conservative valued languages), and state implications for (valued) CSPs with ordered variables and for the maximum weight independent set problem on some restricted families of graphs.
For the entire collection see [Zbl 1326.68015].A new approximate min-max theorem with applications in cryptographyhttps://zbmath.org/1472.680702021-11-25T18:46:10.358925Z"Skórski, Maciej"https://zbmath.org/authors/?q=ai:skorski.maciejSummary: We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max theorem and convex approximation techniques, offering quantitative improvements over the standard way of using min-max theorems as well as more concise and elegant proofs.
For the entire collection see [Zbl 1326.68015].On structural parameterizations of the matching cut problemhttps://zbmath.org/1472.680712021-11-25T18:46:10.358925Z"Aravind, N. R."https://zbmath.org/authors/?q=ai:aravind.n-r"Kalyanasundaram, Subrahmanyam"https://zbmath.org/authors/?q=ai:kalyanasundaram.subrahmanyam"Kare, Anjeneya Swami"https://zbmath.org/authors/?q=ai:kare.anjeneya-swamiSummary: In an undirected graph, a matching cut is a partition of vertices into two sets such that the edges across the sets induce a matching. The Matching Cut problem is the problem of deciding whether a given graph has a matching cut. The Matching Cut problem can be expressed using a monadic second-order logic (MSOL) formula and hence is solvable in linear time for graphs with bounded tree-width. However, this approach leads to a running time of \(f(\phi,t)n^{O(1)}\), where \(\phi\) is the length of the MSOL formula, \(t\) is the tree-width of the graph and \(n\) is the number of vertices of the graph.
In [Theor. Comput. Sci. 609, Part 2, 328--335 (2016; Zbl 1331.68109)], \textit{D. Kratsch} and \textit{V. B. Le}
asked to give a single exponential algorithm for the Matching Cut problem with tree-width alone as the parameter. We answer this question by giving a \(2^{O(t)}n^{O(1)}\) time algorithm. We also show the tractability of the Matching Cut problem when parameterized by neighborhood diversity and other structural parameters.
For the entire collection see [Zbl 1378.68013].Algorithmic learning for steganography: proper learning of \(k\)-term DNF formulas from positive sampleshttps://zbmath.org/1472.680722021-11-25T18:46:10.358925Z"Ernst, Matthias"https://zbmath.org/authors/?q=ai:ernst.matthias"Liśkiewicz, Maciej"https://zbmath.org/authors/?q=ai:liskiewicz.maciej"Reischuk, Rüdiger"https://zbmath.org/authors/?q=ai:reischuk.rudigerSummary: Proper learning from positive samples is a basic ingredient for designing secure steganographic systems for unknown covertext channels. In addition, security requirements imply that the hypothesis should not contain false positives. We present such a learner for \(k\)-term DNF formulas for the uniform distribution and a generalization to \(q\)-bounded distributions. We briefly also describe how these results can be used to design a secure stegosystem.
For the entire collection see [Zbl 1326.68015].Intrinsic complexity of partial learninghttps://zbmath.org/1472.680732021-11-25T18:46:10.358925Z"Jain, Sanjay"https://zbmath.org/authors/?q=ai:jain.sanjay"Kinber, Efim"https://zbmath.org/authors/?q=ai:kinber.efim-bSummary: A partial learner in the limit
[\textit{D. Osherson} et al., Systems that learn: an introduction to learning theory for cognitive and computer scientists. Cambridge: MIT Press (1986)],
given a representation of the target language (a text), outputs a sequence of conjectures, where one correct conjecture appears infinitely many times and other conjectures each appear a finite number of times. Following
[\textit{R. Freivalds} et al., Inf. Comput. 123, No. 1, 64--71 (1995; Zbl 1096.68635);
the first author and \textit{A. Sharma}, J. Comput. Syst. Sci. 52, No. 3, 393--402 (1996; Zbl 0858.68052)],
we define intrinsic complexity of partial learning, based on reducibilities between learning problems. Although the whole class of recursively enumerable languages is partially learnable
(see [Osherson et al., loc. cit.])
and, thus, belongs to the complete learnability degree, we discovered a rich structure of incomplete degrees, reflecting different types of learning strategies (based, to some extent, on topological structures of the target language classes). We also exhibit examples of complete classes that illuminate the character of the strategies for partial learning of the hardest classes.
For the entire collection see [Zbl 1346.68016].Corrigendum to: ``Simple matrix grammars and their leftmost variants''https://zbmath.org/1472.680742021-11-25T18:46:10.358925Z"Meduna, Alexander"https://zbmath.org/authors/?q=ai:meduna.alexander"Soukup, Ondřej"https://zbmath.org/authors/?q=ai:soukup.ondrejCorrigendum to the authors' paper [ibid. 27, No. 3, 359--373 (2016; Zbl 1344.68111)].On constructing minimal deterministic finite automaton recognizing a prefix-code of a given cardinalityhttps://zbmath.org/1472.680752021-11-25T18:46:10.358925Z"Akishev, I. R."https://zbmath.org/authors/?q=ai:akishev.i-r"Dvorkin, M. È."https://zbmath.org/authors/?q=ai:dvorkin.m-eSummary: The article considers constructing minimal deterministic finite automaton recognizing a prefix-code of a given cardinality over the alphabet \(\{0,1\}\). The considered problem is proved to be equivalent to the problem of finding the shortest addition-chain ending with a given number. Several interesting properties of the desired minimal finite automaton are proved, and the identical problem concerning Moore automata is discussed.On constructing minimal deterministic finite automaton recognizing a prefix-code of given cardinalityhttps://zbmath.org/1472.680762021-11-25T18:46:10.358925Z"Akishev, I. R."https://zbmath.org/authors/?q=ai:akishev.i-r"Dvorkin, M. È."https://zbmath.org/authors/?q=ai:dvorkin.m-eSummary: The article considers the problem of constructing minimal deterministic finite automaton recognizing a prefix-code of a given cardinality over the alphabet \(\{0,1\}\). The considered problem is proved to be equivalent to the problem of finding the shortest addition-chain ending with a given number. Several interesting properties of the desired minimal finite automaton are proved, and the identical problem concerning Moore automata is discussed.Solving parallel equations over \(\omega \)-languageshttps://zbmath.org/1472.680772021-11-25T18:46:10.358925Z"Bushkov, V. G."https://zbmath.org/authors/?q=ai:bushkov.v-g"Evtushenko, N. V."https://zbmath.org/authors/?q=ai:evtushenko.n-vSummary: The paper is devoted to the problem of solving equations over \(\omega \)-languages. Similar to formal languages, a solvable equation over \(\omega \)-languages has the largest solution and the formula of the largest solution is similar to that for formal languages.Solving inequalities over finite state machines in the reactive systems designhttps://zbmath.org/1472.680782021-11-25T18:46:10.358925Z"Chebotarëv, A. N."https://zbmath.org/authors/?q=ai:chebotarev.anatoli-nSummary: The problem of solving inequalities over finite state machines (FSMs) is considered. This problem arises in compositional approach to the design of reactive systems. The problem is formulated and solved at the level of FSMs specifications in the logical language \(L\). We show how to compute the maximal solution to the inequality with respect to the operation of synchronous composition of FSMs.On one FSM class with a polynomial number of states in observable formhttps://zbmath.org/1472.680792021-11-25T18:46:10.358925Z"Gromov, Maxim L."https://zbmath.org/authors/?q=ai:gromov.maksim-leonidovich"Kondratyeva, Ol'ga V."https://zbmath.org/authors/?q=ai:kondratyeva.olga-vSummary: This work is devoted to the description of some property of a finite state machine (FSM), which allows one to speak about polynomial number of states in observable form of a FSM. The observable form is an essential part of the vast variety of methods for testing and optimization of systems, based on FSM model.On representation of context-free languages by diagonals of linear languageshttps://zbmath.org/1472.680802021-11-25T18:46:10.358925Z"Safonov, K. V."https://zbmath.org/authors/?q=ai:safonov.konstantin-v"Kalugin-Balashov, D. A."https://zbmath.org/authors/?q=ai:kalugin-balashov.d-aSummary: A sufficient condition for a symbolic equation system to determine a context-free language closely connected with a linear language by the simple procedure of diagonalization is presented.Layers of a finite automatonhttps://zbmath.org/1472.680812021-11-25T18:46:10.358925Z"Smirnov, V. G."https://zbmath.org/authors/?q=ai:smirnov.v-gSummary: Layers of automaton are defined, their properties are investigated and conditions for a state of automata to belong to a layer are found. A notion of \(t\)-unrollment of initial automaton graph is introduced as an oriented graph with marked edges; this notion is used for reduction the enumeration of preimages of the output sequence segment to the construction of graph of solutions for a system of \(k\)-valued logic equations. An algorithm for the construction of such graph with complexity proportional to the number of vertices of \(t\)-unrollment is designed. The complexity may depend on \(t\) polynomially or exponentially.Reconfigurable finite state machines with shared memoryhttps://zbmath.org/1472.680822021-11-25T18:46:10.358925Z"Tren'kaev, V. N."https://zbmath.org/authors/?q=ai:trenkaev.v-nSummary: The paper presents a structure of reconfigurable finite state machine (FSM) consisting of the output/next state logic of two basic FSMs, the control unit, and the state register. The state register is shared by two basic FSMs. One of the basic FSMs has a fixed behavior, and another -- a changeable behavior. The reconfigurable FSM is proven to model the joint behavior of two basic FSMs.A reduction theorem for randomized distributed algorithms under weak adversarieshttps://zbmath.org/1472.680832021-11-25T18:46:10.358925Z"Bertrand, Nathalie"https://zbmath.org/authors/?q=ai:bertrand.nathalie"Lazić, Marijana"https://zbmath.org/authors/?q=ai:lazic.marijana"Widder, Josef"https://zbmath.org/authors/?q=ai:widder.josefSummary: Weak adversaries are a way to model the uncertainty due to asynchrony in randomized distributed algorithms. They are a standard notion in correctness proofs for distributed algorithms, and express the property that the adversary (scheduler), which has to decide which messages to deliver to which process, has no means of inferring the outcome of random choices, and the content of the messages.
In this paper, we introduce a model for randomized distributed algorithms that allows us to formalize the notion of weak adversaries. It applies to randomized distributed algorithms that proceed in rounds and are tolerant to process failures. For this wide class of algorithms, we prove that for verification purposes, the class of weak adversaries can be restricted to simple ones, so-called round-rigid adversaries, that keep the processes tightly synchronized. As recently a verification method for round-rigid adversaries has been introduced, our new reduction theorem paves the way to the parameterized verification of randomized distributed algorithms under the more realistic weak adversaries.
For the entire collection see [Zbl 1471.68017].Regular form of deterministic FSMs specifications in the language Lhttps://zbmath.org/1472.680842021-11-25T18:46:10.358925Z"Chebotarev, A. N."https://zbmath.org/authors/?q=ai:chebotarev.anatoli-nSummary: Some forms for representation of deterministic FSMs specification in the language L are investigated. The use of such forms in constructing specifications decreases the possibility of errors.Proving the existence of fair paths in infinite-state systemshttps://zbmath.org/1472.680852021-11-25T18:46:10.358925Z"Cimatti, Alessandro"https://zbmath.org/authors/?q=ai:cimatti.alessandro"Griggio, Alberto"https://zbmath.org/authors/?q=ai:griggio.alberto"Magnago, Enrico"https://zbmath.org/authors/?q=ai:magnago.enricoSummary: In finite-state systems, true existential properties admit witnesses in form of lasso-shaped fair paths. When dealing with the infinite-state case (e.g. software non-termination, model checking of hybrid automata) this is no longer the case. In this paper, we propose a compositional approach for proving the existence of fair paths of infinite-state systems. First, we describe a formal approach to prove the existence of a non-empty under-approximation of the original system that only contains fair paths. Second, we define an automated procedure that, given a set of hints (in form of basic components), searches for a suitable composition proving the existence of a fair path. We experimentally evaluate the approach on examples taken from both software and hybrid systems, showing its wide applicability and expressiveness.
For the entire collection see [Zbl 1471.68017].Erratum to: ``Solving Horn clauses on inductive data types without induction''https://zbmath.org/1472.680862021-11-25T18:46:10.358925Z"De Angelis, Emanuele"https://zbmath.org/authors/?q=ai:de-angelis.emanuele"Fioravanti, Fabio"https://zbmath.org/authors/?q=ai:fioravanti.fabio"Pettorossi, Alberto"https://zbmath.org/authors/?q=ai:pettorossi.alberto"Proietti, Maurizio"https://zbmath.org/authors/?q=ai:proietti.maurizioSome misprints in a few lines in the authors' paper [ibid. 18, No. 3--4, 452--469 (2018; Zbl 1451.68172)] are corrected.Verification of concurrent programs using Petri net unfoldingshttps://zbmath.org/1472.680872021-11-25T18:46:10.358925Z"Dietsch, Daniel"https://zbmath.org/authors/?q=ai:dietsch.daniel"Heizmann, Matthias"https://zbmath.org/authors/?q=ai:heizmann.matthias"Klumpp, Dominik"https://zbmath.org/authors/?q=ai:klumpp.dominik"Naouar, Mehdi"https://zbmath.org/authors/?q=ai:naouar.mehdi"Podelski, Andreas"https://zbmath.org/authors/?q=ai:podelski.andreas"Schätzle, Claus"https://zbmath.org/authors/?q=ai:schatzle.clausSummary: Given a verification problem for a concurrent program (with a fixed number of threads) over infinite data domains, we can construct a model checking problem for an abstraction of the concurrent program through a Petri net (a problem which can be solved using McMillan's unfoldings technique). We present a method of abstraction refinement which translates Floyd/Hoare-style proofs for sample traces into additional synchronization constraints for the Petri net.
For the entire collection see [Zbl 1471.68017].Model checking algorithms for hyperproperties (invited paper)https://zbmath.org/1472.680882021-11-25T18:46:10.358925Z"Finkbeiner, Bernd"https://zbmath.org/authors/?q=ai:finkbeiner.berndSummary: Hyperproperties generalize trace properties by expressing relations between multiple computations. Hyperpropertes include policies from information-flow security, like observational determinism or noninterference, and many other system properties including promptness and knowledge. In this paper, we give an overview on the model checking problem for temporal hyperlogics. Our starting point is the model checking algorithm for HyperLTL, a reduction to Büchi automata emptiness. This basic construction can be extended with propositional quantification, resulting in an algorithm for HyperQPTL. It can also be extended with branching time, resulting in an algorithm for HyperCTL*. However, it is not possible to have both extensions at the same time: the model checking problem of HyperQCTL* is undecidable. An attractive compromise is offered by MPL[\textit{E}], i.e., monadic path logic extended with the equal-level predicate. The expressiveness of MPL[\textit{E}] falls strictly between that of HyperCTL* and HyperQCTL*. MPL[\textit{E}] subsumes both HyperCTL* and HyperKCTL*, the extension of HyperCTL* with the knowledge operator. We show that the model checking problem for MPL[\textit{E}] is still decidable.
For the entire collection see [Zbl 1471.68017].Compositional model checking for multi-propertieshttps://zbmath.org/1472.680892021-11-25T18:46:10.358925Z"Goudsmid, Ohad"https://zbmath.org/authors/?q=ai:goudsmid.ohad"Grumberg, Orna"https://zbmath.org/authors/?q=ai:grumberg.orna"Sheinvald, Sarai"https://zbmath.org/authors/?q=ai:sheinvald.saraiSummary: \textit{Hyperproperties} lift conventional trace properties in a way that describes how a system behaves in its entirety, and not just based on its individual traces. We generalize this notion to \textit{multi-properties}, which describe the behavior of not just a single system, but of a set of systems, which we call a \textit{multi-model}. We demonstrate the usefulness of our setting with practical examples. We show that model-checking multi-properties is equivalent to model-checking hyperproperties. However, our framework has the immediate advantage of being \textit{compositional}. We introduce sound and complete compositional proof rules for model-checking multi-properties, based on over- and under-approximations of the systems in the multi-model. We then describe methods of computing such approximations. The first is abstraction-refinement based, in which a coarse initial abstraction is continuously refined using counterexamples, until a suitable approximation is found. The second, tailored for models with finite traces, finds suitable approximations via the \(L^*\) learning algorithm. Our methods can produce much smaller models than the original ones, and can therefore be used for accelerating model-checking for both multi-properties and hyperproperties.
For the entire collection see [Zbl 1471.68017].Decomposing data structure commutativity proofs with \(mn\)-differencinghttps://zbmath.org/1472.680902021-11-25T18:46:10.358925Z"Koskinen, Eric"https://zbmath.org/authors/?q=ai:koskinen.eric"Bansal, Kshitij"https://zbmath.org/authors/?q=ai:bansal.kshitijSummary: Commutativity of data structure methods is of ongoing interest in contexts such as parallelizing compilers, transactional memory, speculative execution and software scalability. Despite this interest, we lack effective theories and techniques to aid commutativity verification.
In this paper, we introduce a novel decomposition to improve the task of verifying method-pair commutativity conditions from data structure implementations. The key enabling insight -- called \(mn\)-differencing -- defines the precision necessary for an abstraction to be fine-grained enough so that commutativity of method implementations in the abstract domain entails commutativity in the concrete domain, yet can be less precise than what is needed for full-functional correctness. We incorporate this decomposition into a proof rule, as well as an automata-theoretic reduction for commutativity verification. Finally, we discuss our simple proof-of-concept implementation and experimental results showing that \(mn\)-differencing leads to more scalable commutativity verification of some simple examples.
For the entire collection see [Zbl 1471.68017].A design of GPU-based quantitative model checkinghttps://zbmath.org/1472.680912021-11-25T18:46:10.358925Z"Kwon, YoungMin"https://zbmath.org/authors/?q=ai:kwon.youngmin"Kim, Eunhee"https://zbmath.org/authors/?q=ai:kim.eunheeSummary: In this paper, we implement a GPU-based quantitative model checker and compare its performance with a CPU-based one. Linear Temporal Logic for Control (LTLC) is a quantitative variation of LTL to describe properties of a linear system and LTLC-Checker is an implementation of its model checking algorithm. In practice, its long and unpredictable execution time has been a concern in applying the technique to real-time applications such as automatic control systems. In this paper, we design an LTLC model checker using a GPGPU programming technique. The resulting model checker is not only faster than the CPU-based one especially when the problem is not simple, but it has less variation in the execution time as well. Furthermore, multiple counterexamples can be found together when the CPU-based checker can find only one.
For the entire collection see [Zbl 1471.68017].Concurrent correctness in vector spacehttps://zbmath.org/1472.680922021-11-25T18:46:10.358925Z"Peterson, Christina"https://zbmath.org/authors/?q=ai:peterson.christina-l"Cook, Victor"https://zbmath.org/authors/?q=ai:cook.victor"Dechev, Damian"https://zbmath.org/authors/?q=ai:dechev.damianSummary: Correctness verification of a concurrent history is challenging and has been proven to be an NP-complete problem. The reason that verifying correctness cannot be solved in polynomial time is a consequence of the way correctness is defined. Traditional correctness conditions require a concurrent history to be equivalent to a legal sequential history. The worst case number of legal sequential histories for a concurrent history is \(O(n!)\) with respect to \(n\) methods invoked. Existing correctness verification tools improve the time complexity by either reducing the size of the possible legal sequential histories or improving the efficiency of generating the possible legal sequential histories. Further improvements to the time complexity of correctness verification can be achieved by changing the way correctness of concurrent programs is defined. In this paper, we present the first methodology to recast the correctness conditions in literature to be defined in vector space. The concurrent histories are represented as a set of method call vectors, and correctness is defined as properties over the set of vectors. The challenge with defining correctness in vector space is accounting for method call ordering and data structure semantics. We solve this challenge by incorporating a priority assignment scheme to the values of the method call vectors. Using our new definitions of concurrent correctness, we design a dynamic analysis tool that checks the vector space correctness of concurrent data structures in \(O(n^2)\) with respect to \(n\) method calls, a significant improvement over \(O(n!)\) time required to analyze legal sequential histories. We showcase our dynamic analysis tool by using it to check the vector space correctness of a variety of queues, stacks, and hashmaps.
For the entire collection see [Zbl 1471.68017].Unbounded procedure summaries from bounded environmentshttps://zbmath.org/1472.680932021-11-25T18:46:10.358925Z"Pick, Lauren"https://zbmath.org/authors/?q=ai:pick.lauren"Fedyukovich, Grigory"https://zbmath.org/authors/?q=ai:fedyukovich.grigory"Gupta, Aarti"https://zbmath.org/authors/?q=ai:gupta.aartiSummary: Modular approaches to verifying interprocedural programs involve learning summaries for individual procedures rather than verifying a monolithic program. Modern approaches based on use of Satisfiability Modulo Theory (SMT) solvers have made much progress in this direction. However, it is still challenging to handle mutual recursion and to derive adequate procedure summaries using scalable methods. We propose a novel modular verification algorithm that addresses these challenges by learning lemmas about the relationships among procedure summaries and by using \textit{bounded environments} in SMT queries. We have implemented our algorithm in a tool called \textsc{Clover} and report on a detailed evaluation that shows that it outperforms existing automated tools on benchmark programs with mutual recursion while being competitive on standard benchmarks.
For the entire collection see [Zbl 1471.68017].Eliminating message counters in synchronous threshold automatahttps://zbmath.org/1472.680942021-11-25T18:46:10.358925Z"Stoilkovska, Ilina"https://zbmath.org/authors/?q=ai:stoilkovska.ilina"Konnov, Igor"https://zbmath.org/authors/?q=ai:konnov.igor-v"Widder, Josef"https://zbmath.org/authors/?q=ai:widder.josef"Zuleger, Florian"https://zbmath.org/authors/?q=ai:zuleger.florianSummary: In previous work, we introduced synchronous threshold automata for the verification of synchronous fault-tolerant distributed algorithms, and presented a verification method based on bounded model checking. Modeling a distributed algorithm by a threshold automaton requires to correctly deal with the semantics for sending and receiving messages based on the fault assumption. This step was done manually so far, and required human ingenuity. Motivated by similar results for asynchronous threshold automata, in this paper we show that one can start from a faithful model of the distributed algorithm that includes the sending and receiving of messages, and then automatically obtain a threshold automaton by applying quantifier elimination on the receive message counters. In this way, we obtain a fully automated verification pipeline. We present an experimental evaluation, discovering a bug in our previous manual encoding. Interestingly, while quantifier elimination in general produces larger threshold automata than the manual encoding, the verification times are comparable and even faster in several cases, allowing us to verify benchmarks that could not be handled before.
For the entire collection see [Zbl 1471.68017].Runtime abstract interpretation for numerical accuracy and robustnesshttps://zbmath.org/1472.680952021-11-25T18:46:10.358925Z"Védrine, Franck"https://zbmath.org/authors/?q=ai:vedrine.franck"Jacquemin, Maxime"https://zbmath.org/authors/?q=ai:jacquemin.maxime"Kosmatov, Nikolai"https://zbmath.org/authors/?q=ai:kosmatov.nikolai"Signoles, Julien"https://zbmath.org/authors/?q=ai:signoles.julienSummary: Verification of numerical accuracy properties in modern software remains an important and challenging task. One of its difficulties is related to unstable tests, where the execution can take different branches for real and floating-point numbers. This paper presents a new verification technique for numerical properties, named Runtime Abstract Interpretation (RAI), that, given an annotated source code, embeds into it an abstract analyzer in order to analyze the program behavior at runtime. RAI is a hybrid technique combining abstract interpretation and runtime verification that aims at being sound as the former while taking benefit from the concrete run to gain greater precision from the latter when necessary. It solves the problem of unstable tests by surrounding an unstable test by two carefully defined program points, forming a so-called split-merge section, for which it separately analyzes different executions and merges the computed domains at the end of the section. Our implementation of this technique in a toolchain called \textsf{FLDBox} relies on two basic tools, \textsf{FLDCompiler}, that performs a source-to-source transformation of the given program and defines the split-merge sections, and an instrumentation library \textsf{FLDLib} that provides necessary primitives to explore relevant (partial) executions of each section and propagate accuracy properties. Initial experiments show that the proposed technique can efficiently and soundly analyze numerical accuracy for industrial programs on thin numerical scenarios.
For the entire collection see [Zbl 1471.68017].Syntax-guided synthesis for lemma generation in hardware model checkinghttps://zbmath.org/1472.680962021-11-25T18:46:10.358925Z"Zhang, Hongce"https://zbmath.org/authors/?q=ai:zhang.hongce"Gupta, Aarti"https://zbmath.org/authors/?q=ai:gupta.aarti"Malik, Sharad"https://zbmath.org/authors/?q=ai:malik.sharadSummary: In this work we propose to use Syntax-Guided Synthesis (SyGuS) for lemma generation in a word-level IC3/PDR framework for bit-vector problems. Hardware model checking is moving from bit-level to word-level problems, and it is expected that model checkers can benefit when such high-level information is available. However, for bit-vectors, it is challenging to find a good word-level interpolation strategy for lemma generation, which hinders the use of word-level IC3/PDR algorithms.
Our SyGuS-based procedure, \textsf{SyGuS}-\(\mathcal{A}\)\textsf{PDR}, is tightly integrated with an existing word-level IC3/PDR framework \(\mathcal{A}\)\textsf{PDR}. It includes a predefined grammar template and term production rules for generating candidate lemmas, and does not rely on any extra human inputs. Our experiments on benchmarks from the hardware model checking competition show that \textsf{SyGuS}-\(\mathcal{A}\)\textsf{PDR} can outperform state-of-the-art Constrained Horn Clause (CHC) solvers, including those that implement bit-level IC3/PDR. We also show that \textsf{SyGuS}-\(\mathcal{A}\)\textsf{PDR} and these CHC solvers can solve many instances faster than other leading word-level hardware model checkers that are not CHC-based. As a by-product of our work, we provide a translator \texttt{Btor2CHC} that enables the use of CHC solvers for general hardware model checking problems, and contribute representative bit-vector benchmarks to the CHC-solver community.
For the entire collection see [Zbl 1471.68017].What Is a derived signature morphism?https://zbmath.org/1472.680972021-11-25T18:46:10.358925Z"Mossakowski, Till"https://zbmath.org/authors/?q=ai:mossakowski.till"Krumnack, Ulf"https://zbmath.org/authors/?q=ai:krumnack.ulf"Maibaum, Tom"https://zbmath.org/authors/?q=ai:maibaum.thomas-s-eSummary: The notion of signature morphism is basic to the theory of institutions. It provides a powerful primitive for the study of specifications, their modularity and their relations in an abstract setting. The notion of derived signature morphism generalises signature morphisms to more complex constructions, where symbols may be mapped not only to symbols, but to arbitrary terms. The purpose of this work is to study derived signature morphisms in an institution-independent way. We will recall and generalize two known approaches to derived signature morphisms, introduce a third one, and discuss their pros and cons. We especially study the existence of colimits of derived signature morphisms. The motivation is to give an independent semantics to the notion of derived signature morphism, query and substitution in the context of the Distributed Ontology, Modeling and Specification Language DOL.
For the entire collection see [Zbl 1327.68013].Coalgebraic semantics of heavy-weighted automatahttps://zbmath.org/1472.680982021-11-25T18:46:10.358925Z"Fortin, Marie"https://zbmath.org/authors/?q=ai:fortin.marie-josee"Bonsangue, Marcello M."https://zbmath.org/authors/?q=ai:bonsangue.marcello-maria"Rutten, Jan"https://zbmath.org/authors/?q=ai:rutten.jan-j-m-mSummary: In this paper we study heavy-weighted automata, a generalization of weighted automata in which the weights of the transitions can be formal power series. As for ordinary weighted automata, the behaviour of heavy-weighted automata is expressed in terms of formal power series. We propose several equivalent definitions for their semantics, including a system of behavioural differential equations (following the approach of coinductive calculus), or an embedding into a coalgebra for the functor \(S\times (-)^A\), for which the set of formal power series is a final coalgebra. Using techniques based on bisimulations and coinductive calculus, we study how ordinary weighted automata can be transformed into more compact heavy-weighted ones.
For the entire collection see [Zbl 1327.68013].On the homomorphisms of strongly connected finite automata into substitution automatahttps://zbmath.org/1472.680992021-11-25T18:46:10.358925Z"Kruglov, I. A."https://zbmath.org/authors/?q=ai:kruglov.igor-aleksandrovichSummary: An approach to a description of homomorphisms of strongly connected finite automata into substitution automata is suggested. This approach is based on special homomorphisms such that their composition with homomorphism of an automaton considered into substitution automaton preserves the group of an image. By means of this approach for strongly connected automata a criterion is given for the existence of nontrivial substitutional homomorphic image wish commutative partial transition functions.Frame of an automatonhttps://zbmath.org/1472.681002021-11-25T18:46:10.358925Z"Saliĭ, V. N."https://zbmath.org/authors/?q=ai:salii.viacheslav-nSummary: The frame of an automaton is the partially ordered set of its strongly connected subsets together with the relation of inverse attainability. Some properties of frames are established related to basic algebraic constructions such as subautomata, homomorphisms, and congruences.On the frame of an automatonhttps://zbmath.org/1472.681012021-11-25T18:46:10.358925Z"Saliĭ, V. N."https://zbmath.org/authors/?q=ai:salii.viacheslav-nSummary: The frame of an automaton is the partially ordered set of its strongly connected subsets together with the relation of inverse attainability. Some properties of frames are established related to basic algebraic constructions such as subautomata, homomorphisms, and congruences.Analysis of non-linear automata with delay 2 over a finite ringhttps://zbmath.org/1472.681022021-11-25T18:46:10.358925Z"Skobelev, V. V."https://zbmath.org/authors/?q=ai:skobelev.vladimir-vladimirovich|skobelev.volodymyr-v"Skobelev, V. G."https://zbmath.org/authors/?q=ai:skobelev.vladimir-gSummary: For invertible one-dimensional automata with delay 2 over the ring \(\mathbf{Z}_{p^k}=(\mathbb{Z}_{p^k},\oplus,\circ)\), the structure of the transition graph is investigated, the sets of equivalent states are characterized, the problems of the parametric identification and of the initial state identification are solved, the sets of fixed points of mappings realized by initial automata are characterized.Random number generation using decimal cellular automatahttps://zbmath.org/1472.681032021-11-25T18:46:10.358925Z"Bhattacharjee, Kamalika"https://zbmath.org/authors/?q=ai:bhattacharjee.kamalika"Das, Sukanta"https://zbmath.org/authors/?q=ai:das.sukantaSummary: This paper illustrates the potentiality of decimal CAs as source of pseudo-randomness. Some desirable properties for a CA to be a good source of pseudo-randomness are identified. As the rule space is huge, greedy strategies are taken to select CAs satisfying these properties. Finally, two heuristic algorithms are given to synthesize such CAs. As application of pseudo-randomness, two schemes are reported to develop pseudo-random number generators (PRNGs) using these CAs. To generate a number from a configuration, we have used the concept of window. It is observed that, our PRNGs are at least as good as the best known PRNGs existing in literature.High-speed pseudorandom sequence generators based on cellular automatahttps://zbmath.org/1472.681042021-11-25T18:46:10.358925Z"Sukhinin, B. M."https://zbmath.org/authors/?q=ai:sukhinin.b-mSummary: We investigate a number of properties of uniform two-dimensional Boolean cellular automata and propose a new method for pseudorandom sequences generation based on such automata. Generated sequences show good statistical properties. Moreover, hardware implementation of the method on a typical FPGA has very high performance of up to 25 Gbps at 100 MHz frequency.High-speed pseudorandom sequence generators based on cellular automatahttps://zbmath.org/1472.681052021-11-25T18:46:10.358925Z"Sukhinin, B. M."https://zbmath.org/authors/?q=ai:sukhinin.b-mSummary: We investigate a number of properties of uniform two-dimensional Boolean cellular automata and propose a new method for pseudorandom sequences generation based on such automata. Generated sequences show good statistical properties. Moreover, hardware implementation of proposed methods on a typical FPGA has very high performance of up to 25 Gbps at 100 MHz frequency.Symbolic computation using cellular automata-based hyperdimensional computinghttps://zbmath.org/1472.681062021-11-25T18:46:10.358925Z"Yilmaz, Ozgur"https://zbmath.org/authors/?q=ai:yilmaz.ozgurSummary: This letter introduces a novel framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation. A cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells, and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir. The proposed framework is shown to be capable of long-term memory, and it requires orders of magnitude less computation compared to echo state networks. As the focus of the letter, we suggest that binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way for concept building and symbolic processing. To demonstrate the capability of the proposed system, we make analogies directly on image data by asking,
What is the automobile of air?Multi-parametric classification of automaton Markov models based on the sequences they generatehttps://zbmath.org/1472.681072021-11-25T18:46:10.358925Z"Nurutdinova, A. R."https://zbmath.org/authors/?q=ai:nurutdinova.a-r"Shalagin, S. V."https://zbmath.org/authors/?q=ai:shalagin.sergei-viktorovichSummary: This article is devoted to multi-parametric classification of automaton Markov models (AMMs) on the base of output sequences with the use of discriminant analysis. The AMMs under consideration are specified by means of stochastic matrices belonging to subclasses defined a priori. A set of claasification features is introduced to distinguish AMMs specified by matrices from different subclasses. The features are related to the frequency characteristics of sequences generated by AMMs. A method is suggested for determining the minimal length of the sequence need to calculate the features with a required accuracy.Minimizing the maximum moving cost of interval coveragehttps://zbmath.org/1472.681082021-11-25T18:46:10.358925Z"Wang, Haitao"https://zbmath.org/authors/?q=ai:wang.haitao"Zhang, Xiao"https://zbmath.org/authors/?q=ai:zhang.xiaoSummary: In this paper, we study an interval coverage problem. We are given \(n\) intervals of the same length on a line \(L\) and a line segment \(B\) on \(L\). Each interval has a nonnegative weight. The goal is to move the intervals along \(L\) such that every point of \(B\) is covered by at least one interval and the maximum moving cost of all intervals is minimized, where the moving cost of each interval is its moving distance times its weight. Algorithms for the ``unweighted'' version of this problem have been given before. In this paper, we present a first-known algorithm for this weighted version and our algorithm runs in \(O(n^2\log n\log \log n)\) time. The problem has applications in mobile sensor barrier coverage.
For the entire collection see [Zbl 1326.68015].Colored non-crossing Euclidean Steiner foresthttps://zbmath.org/1472.681092021-11-25T18:46:10.358925Z"Bereg, Sergey"https://zbmath.org/authors/?q=ai:bereg.sergey-n"Fleszar, Krzysztof"https://zbmath.org/authors/?q=ai:fleszar.krzysztof"Kindermann, Philipp"https://zbmath.org/authors/?q=ai:kindermann.philipp"Pupyrev, Sergey"https://zbmath.org/authors/?q=ai:pupyrev.sergey"Spoerhase, Joachim"https://zbmath.org/authors/?q=ai:spoerhase.joachim"Wolff, Alexander"https://zbmath.org/authors/?q=ai:wolff.alexanderSummary: Given a set of \(k\)-colored points in the plane, we consider the problem of finding \(k\) trees such that each tree connects all points of one color class, no two trees cross, and the total edge length of the trees is minimized. For \(k = 1\), this is the well-known Euclidean Steiner tree problem. For general \(k\), a \(k\rho \)-approximation algorithm is known, where \(\rho \leq 1.21\) is the Steiner ratio.
We present a PTAS for \(k=2\), a \((5/3+\varepsilon)\)-approximation for \(k=3\), and two approximation algorithms for general \(k\), with ratios \(O(\sqrt{n} \log k)\) and \(k+\varepsilon \).
For the entire collection see [Zbl 1326.68015].Minimum degree up to local complementation: bounds, parameterized complexity, and exact algorithmshttps://zbmath.org/1472.681102021-11-25T18:46:10.358925Z"Cattanéo, David"https://zbmath.org/authors/?q=ai:cattaneo.david"Perdrix, Simon"https://zbmath.org/authors/?q=ai:perdrix.simonSummary: The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any \(n\), there exist graphs of order \(n\) which have a local minimum degree at least \(0.189n\), or at least \(0.110n\) when restricted to bipartite graphs. Regarding the upper bound, we show that the local minimum degree is at most \(\frac{3}{8}n+o(n)\) for general graphs and \(\frac{n}{4}+o(n)\) for bipartite graphs, improving the known \(\frac{n}{2}\) upper bound. We also prove that the local minimum degree is smaller than half of the vertex cover number (up to a logarithmic term). The local minimum degree problem is NP-Complete and hard to approximate. We show that this problem, even when restricted to bipartite graphs, is in W[2] and FPT-equivalent to the \textsc{EvenSet} problem, whose W[1]-hardness is a long standing open question. Finally, we show that the local minimum degree is computed by a \(\mathcal O^*(1.938^n)\)-algorithm, and a \(\mathcal O^*(1.466^n)\)-algorithm for the
bipartite graphs.
For the entire collection see [Zbl 1326.68015].An improved algorithm for the Steiner tree problem with bounded edge-lengthhttps://zbmath.org/1472.681112021-11-25T18:46:10.358925Z"Chen, Chi-Yeh"https://zbmath.org/authors/?q=ai:chen.chi-yeh"Hsieh, Sun-Yuan"https://zbmath.org/authors/?q=ai:hsieh.sun-yuanSummary: This work firstly studies the Steiner tree problem with bounded edge-length \(d\) in which \(d\) is the ratio of the maximum edge cost to the minimum edge cost. This work analyzes the algorithm of
\textit{J. Byrka} et al. [J. ACM 60, No. 1, Article No. 6, 33 p. (2013; Zbl 1281.68234)]
and shows that the approximation ratio of \(\frac{d\ln 4}{d+\ln 4-1}+\epsilon\) for general graphs and approximation ratio of \(\frac{73\cdot d}{60\cdot d+13}+\epsilon\) for quasi-bipartite graphs. The algorithm implies approximation ratio of \(1.162+\epsilon\) for the problem on complete graphs with edge distances 1 and 2. This finding represents an improvement upon the previous best approximation ratio of 1.25. This work then presents a combinatorial two-phase heuristic for the general Steiner tree in greedy strategy that achieves an approximation ratio of 1.4295.Sliding token on bipartite permutation graphshttps://zbmath.org/1472.681122021-11-25T18:46:10.358925Z"Fox-Epstein, Eli"https://zbmath.org/authors/?q=ai:fox-epstein.eli"Hoang, Duc A."https://zbmath.org/authors/?q=ai:hoang.duc-a"Otachi, Yota"https://zbmath.org/authors/?q=ai:otachi.yota"Uehara, Ryuhei"https://zbmath.org/authors/?q=ai:uehara.ryuheiSummary: \textsc{Sliding Token} is a natural reconfiguration problem in which vertices of independent sets are iteratively replaced by neighbors. We develop techniques that may be useful in answering the conjecture that \textsc{Sliding Token} is polynomial-time decidable on bipartite graphs. Along the way, we give efficient algorithms for \textsc{Sliding Token} on bipartite permutation and bipartite distance-hereditary graphs.
For the entire collection see [Zbl 1326.68015].Complexity of stabilityhttps://zbmath.org/1472.681132021-11-25T18:46:10.358925Z"Frei, Fabian"https://zbmath.org/authors/?q=ai:frei.fabian"Hemaspaandra, Edith"https://zbmath.org/authors/?q=ai:hemaspaandra.edith"Rothe, Jörg"https://zbmath.org/authors/?q=ai:rothe.jorg-matthiasSummary: Graph parameters such as the clique number and the chromatic number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the chromatic number of a graph can be applied in solving practical tasks as diverse as pattern matching, scheduling jobs to machines, allocating registers in compiler optimization, and even solving Sudoku puzzles. Typically, however, the underlying graphs are subject to (often minor) changes. To make these applications of graph parameters robust, it is important to know which graphs are stable in the sense that adding or deleting single edges or vertices does not change them. We initiate the study of stability of graphs in terms of their computational complexity. We show for various central graph parameters that deciding the stability of a given graph is complete for \(\Theta_2^{\mathrm{P}}\), a well-known complexity class in the second level of the polynomial hierarchy.Provable efficiency of contraction hierarchies with randomized preprocessinghttps://zbmath.org/1472.681142021-11-25T18:46:10.358925Z"Funke, Stefan"https://zbmath.org/authors/?q=ai:funke.stefan"Storandt, Sabine"https://zbmath.org/authors/?q=ai:storandt.sabineSummary: We present a new way of analyzing Contraction Hierarchies (CH), a widely used speed-up technique for shortest path computations in road networks. In previous work, preprocessing and query times of deterministically constructed CH on road networks with \(n\) nodes were shown to be polynomial in \(n\) as well as the highway dimension \(h\) of the network and its diameter \(D\). While \(h\) is conjectured to be polylogarithmic for road networks, a tight bound remains an open problem. We rely on the empirically justifiable assumption of the road network exhibiting small growth. We introduce a method to construct randomized Contraction Hierarchies on road networks as well as a probabilistic query routine. Our analysis reveals that randomized CH lead to sublinear search space sizes in the order of \(\sqrt{n} \log \sqrt{n}\), auxiliary data in the order of \(n \log^2 \sqrt{n}\), and correct query results with high probability after a polynomial time preprocessing phase.
For the entire collection see [Zbl 1326.68015].On hardness of the joint crossing numberhttps://zbmath.org/1472.681152021-11-25T18:46:10.358925Z"Hliněný, Petr"https://zbmath.org/authors/?q=ai:hlineny.petr"Salazar, Gelasio"https://zbmath.org/authors/?q=ai:salazar.gelasioSummary: The Joint Crossing Number problem asks for a simultaneous embedding of two disjoint graphs into one surface such that the number of edge crossings (between the two graphs) is minimized. It was introduced by
\textit{S. Negami} in [J. Graph Theory 36, No. 1, 8--23 (2001; Zbl 0971.05037)]
in connection with diagonal flips in triangulations of surfaces, and subsequently investigated in a general form for small-genus surfaces. We prove that all of the commonly considered variants of this problem are NP-hard already in the orientable surface of genus 6, by a reduction from a special variant of the anchored crossing number problem of
\textit{S. Cabello} and \textit{B. Mohar} [SIAM J. Comput. 42, No. 5, 1803--1829 (2013; Zbl 1282.05033)].
For the entire collection see [Zbl 1326.68015].Polynomial anonymous dynamic distributed computing without a unique leaderhttps://zbmath.org/1472.681162021-11-25T18:46:10.358925Z"Kowalski, Dariusz R."https://zbmath.org/authors/?q=ai:kowalski.dariusz-r"Mosteiro, Miguel A."https://zbmath.org/authors/?q=ai:mosteiro.miguel-aSummary: Counting the number of nodes in Anonymous Dynamic Networks is enticing from an algorithmic perspective: an important computation in a restricted platform with promising applications. Starting with
\textit{O. Michail} et al. [Lect. Notes Comput. Sci. 8255, 281--295 (2013; Zbl 06350181)],
a flurry of papers sped up the running time guarantees from doubly-exponential to polynomial
[the authors, LIPIcs -- Leibniz Int. Proc. Inform. 107, Article 156, 14 p. (2018; Zbl 07376083); J. ACM 67, No. 2, Article No. 11, 17 p. (2020; Zbl 07273082)].
There is a common theme across all those works: a distinguished node is assumed to be present, because Counting cannot be solved deterministically without at least one. In the present work we study challenging questions that naturally follow: how to efficiently count with more than one distinguished node, or how to count without any distinguished node. More importantly, what is the minimal information needed about these distinguished nodes and what is the best we can aim for (count precision, stochastic guarantees, etc.) without any. We present negative and positive results to answer these questions. To the best of our knowledge, this is the first work that addresses them.Coloring temporal graphshttps://zbmath.org/1472.681172021-11-25T18:46:10.358925Z"Marino, Andrea"https://zbmath.org/authors/?q=ai:marino.andrea"Silva, Ana"https://zbmath.org/authors/?q=ai:silva.ana-carolina|silva.ana-maria-f|silva.ana-t-c|silva.ana-lSummary: A \textit{temporal graph} is a pair \((G,\lambda)\) where \(G\) is a simple graph and \(\lambda\) is a function assigning to each edge time labels telling at which snapshots each edge is active. As recently defined by
\textit{G. B. Mertzios} et al. [J. Comput. Syst. Sci. 120, 97--115 (2021; Zbl 07365382)],
a \textit{temporal coloring} of \((G,\lambda)\) is a sequence of colorings of the vertices of the snapshots such that each edge is properly colored at least once. We first focus on \textit{t-persistent} and \textit{t-occurrent} temporal graphs. The former (resp. the latter) are temporal graphs where each edge of \(G\) stays active for at least \(t\) consecutive (resp. not-necessarily consecutive) snapshots. We study which values of \(t\) make the problem polynomial-time solvable. We also investigate the complexity of the problem when restricted to temporal graphs \((G,\lambda)\) such that \(G\) has bounded treewidth.Retracted article: ``A distance vector similarity metric for complex networks''https://zbmath.org/1472.681182021-11-25T18:46:10.358925Z"Meghanathan, Natarajan"https://zbmath.org/authors/?q=ai:meghanathan.natarajanFrom the text: The editor-in-chief and publisher have retracted this article in agreement with the author. The article was simultaneously submitted to and published online in Computing and in
[J. King Saud Univ. -- Comput. Inf. Sci., \url{doi:10.1016/j.jksuci.2017.06.007}].
The online version of this article contains the full text of the retracted article as electronic supplementary material.Improved distance sensitivity oracles with subcubic preprocessing timehttps://zbmath.org/1472.681192021-11-25T18:46:10.358925Z"Ren, Hanlin"https://zbmath.org/authors/?q=ai:ren.hanlinSummary: We consider the problem of building \textit{distance sensitivity oracles} (DSOs). Given a directed graph \(G=(V,E)\) with edge weights in \(\{1,2,\dots,M\}\), we need to preprocess it into a data structure, and answer the following queries: given vertices \(u,v\in V\) and a failed vertex or edge \(f\in(V\cup E)\), output the length of the shortest path from \(u\) to \(v\) that does not go through \(f\).
Our main result is a simple DSO with \(\tilde{O}(n^{2.7233}M)\) preprocessing time and \(O(1)\) query time. Moreover, if the input graph is undirected, the preprocessing time can be improved to \(\tilde{O}( n^{2.6865}M)\). The preprocessing algorithm is randomized with correct probability \(\geq 1-1/n^C\), for a constant \(C\) that can be made arbitrarily large. This improves the previous best DSO with \(\tilde{O}(n^{2.8729}M)\) preprocessing time and \(\operatorname{polylog}(n)\) query time
[\textit{S. Chechik} and \textit{S. Cohen}, in: Proceedings of the 52nd annual ACM SIGACT symposium on theory of computing, STOC'20. New York, NY: Association for Computing Machinery (ACM). 1375--1388 (2020; Zbl 07298335)].The network-untangling problem: from interactions to activity timelineshttps://zbmath.org/1472.681202021-11-25T18:46:10.358925Z"Rozenshtein, Polina"https://zbmath.org/authors/?q=ai:rozenshtein.polina"Tatti, Nikolaj"https://zbmath.org/authors/?q=ai:tatti.nikolaj"Gionis, Aristides"https://zbmath.org/authors/?q=ai:gionis.aristidesSummary: In this paper we study a problem of determining when entities are active based on their interactions with each other. We consider a set of entities \(V\) and a sequence of time-stamped edges \(E\) among the entities. Each edge \((u,v,t)\in E\) denotes an interaction between entities \(u\) and \(v\) at time \(t\). We assume an activity model where each entity is active during at most \(k\) time intervals. An interaction \((u, v, t)\) can be \textit{explained} if at least one of \(u\) or \(v\) are active at time \(t\). Our goal is to reconstruct the \textit{activity intervals} for all entities in the network, so as to explain the observed interactions. This problem, the \textit{network-untangling problem}, can be applied to discover event timelines from complex entity interactions. We provide two formulations of the network-untangling problem: (i) minimizing the total interval length over all entities (sum version), and (ii) minimizing the maximum interval length (max version). We study separately the two problems for \(k=1\) and \(k>1\) activity intervals per entity. For the case \(k=1\), we show that the sum problem is \textbf{NP}-hard, while the max problem can be solved optimally in linear time. For the sum problem we provide efficient algorithms motivated by realistic assumptions. For the case of \(k>1\), we show that both formulations are inapproximable. However, we propose efficient algorithms based on alternative optimization. We complement our study with an evaluation on synthetic and real-world datasets, which demonstrates the validity of our concepts and the good performance of our algorithms.Waypoint routing on bounded treewidth graphshttps://zbmath.org/1472.681212021-11-25T18:46:10.358925Z"Schierreich, Šimon"https://zbmath.org/authors/?q=ai:schierreich.simon"Suchý, Ondřej"https://zbmath.org/authors/?q=ai:suchy.ondrejSummary: In the \textsc{Waypoint Routing Problem} one is given an undirected capacitated and weighted graph \(G\), a source-destination pair \(s,t\in V(G)\) and a set \(W\subseteq V(G)\), of \textit{waypoints}. The task is to find a walk which starts at the source vertex \(s\), visits, in any order, all waypoints, ends at the destination vertex \(t\), respects edge capacities, that is, traverses each edge at most as many times as is its capacity, and minimizes the cost computed as the sum of costs of traversed edges with multiplicities. We study the problem for graphs of bounded treewidth and present a new algorithm for the problem working in \(2^{\mathcal{O}(\mathrm{tw})}\cdot n\) time, significantly improving upon the previously known algorithms. We also show that this running time is optimal for the problem under Exponential Time Hypothesis.On mapping graphs of parallel programs onto graphs of distributed computer systems by recurrent neural networkshttps://zbmath.org/1472.681222021-11-25T18:46:10.358925Z"Tarkov, M. S."https://zbmath.org/authors/?q=ai:tarkov.mikhail-sSummary: A problem of mapping graphs of parallel programs onto graphs of distributed computer systems by recurrent neural networks is formulated. The network parameters providing the absence of incorrect solutions are experimentally determined. By introduction of a penalty coefficient into the Lyapunov function for the program graph edges non-coincided with the edges of the computer system, the optimal solutions are computed for mapping the ``line'' program graph onto a two-dimensional torus. To increase the optimal solution probability a method of the mapping decomposition is proposed. The method essence is a reduction of the solution matrix to a block-diagonal shape. For exclusion of incorrect solutions in mapping the line onto three-dimensional torus, a recurrent Wang network is used because it is converged more rapidly than the Hopfield network.Generating random hyperbolic graphs in subquadratic timehttps://zbmath.org/1472.681232021-11-25T18:46:10.358925Z"von Looz, Moritz"https://zbmath.org/authors/?q=ai:von-looz.moritz"Meyerhenke, Henning"https://zbmath.org/authors/?q=ai:meyerhenke.henning"Prutkin, Roman"https://zbmath.org/authors/?q=ai:prutkin.romanSummary: Complex networks have become increasingly popular for modeling various real-world phenomena. Realistic generative network models are important in this context as they simplify complex network research regarding data sharing, reproducibility, and scalability studies. \textit{Random hyperbolic graphs} are a very promising family of geometric graphs with unit-disk neighborhood in the hyperbolic plane. Previous work provided empirical and theoretical evidence that this generative graph model creates networks with many realistic features.
In this work, we provide the first generation algorithm for random hyperbolic graphs with subquadratic running time. We prove a time complexity of \(O((n^{3/2}+m) \log n)\) with high probability for the generation process. This running time is confirmed by experimental data with our implementation. The acceleration stems primarily from the reduction of pairwise distance computations through a polar quadtree, which we adapt to hyperbolic space for this purpose and
which
can be of independent interest. In practice we improve the running time of a previous implementation (which allows more general neighborhoods than the unit disk) by at least two orders of magnitude this way. Networks with billions of edges can now be generated in a few minutes.
For the entire collection see [Zbl 1326.68015].On a generalization of Nemhauser and Trotter's local optimization theoremhttps://zbmath.org/1472.681242021-11-25T18:46:10.358925Z"Xiao, Mingyu"https://zbmath.org/authors/?q=ai:xiao.mingyuSummary: The Nemhauser and Trotter's theorem applies to the famous \textsc{Vertex Cover} problem and can obtain a 2-approximation solution and a problem kernel of 2\(k\) vertices. This theorem is a famous theorem in combinatorial optimization and has been extensively studied. One way to generalize this theorem is to extend the result to the \textsc{Bounded-Degree Vertex Deletion} problem. For a fixed integer \(d\geq 0\), \textsc{Bounded-Degree Vertex Deletion} asks to delete at most \(k\) vertices of the input graph to make the maximum degree of the remaining graph at most \(d\). \textsc{Vertex Cover} is a special case that \(d=0\). Fellows, Guo, Moser and Niedermeier proved a generalized theorem that implies an \(O(k)\)-vertex kernel for \textsc{Bounded-Degree Vertex Deletion} for \(d=0\) and 1, and for any \(\varepsilon >0\), an \(O(k^{1+\varepsilon})\)-vertex kernel for each \(d\geq 2\). In fact, it is still left as an open problem whether \textsc{Bounded-Degree Vertex Deletion} parameterized by \(k\) admits a linear-vertex
kernel for each \(d\geq 3\). In this paper, we refine the generalized Nemhauser and Trotter's theorem. Our result implies a linear-vertex kernel for \textsc{Bounded-Degree Vertex Deletion} parameterized by \(k\) for each \(d\geq 0\).
For the entire collection see [Zbl 1326.68015].End vertices of graph searches on bipartite graphshttps://zbmath.org/1472.681252021-11-25T18:46:10.358925Z"Zou, Meibiao"https://zbmath.org/authors/?q=ai:zou.meibiao"Wang, Zhifeng"https://zbmath.org/authors/?q=ai:wang.zhifeng"Wang, Jianxin"https://zbmath.org/authors/?q=ai:wang.jianxin"Cao, Yixin"https://zbmath.org/authors/?q=ai:cao.yixinSummary: For a graph search algorithm, the end vertex problem is concerned with which vertices of a graph can be the last visited by this algorithm. We show that for both lexicographic depth-first search and maximum cardinality search, the end vertex problem is NP-complete on bipartite graphs, even if the maximum degree of the graph is bounded.Avoiding abelian powers cyclicallyhttps://zbmath.org/1472.681262021-11-25T18:46:10.358925Z"Peltomäki, Jarkko"https://zbmath.org/authors/?q=ai:salo.ville-o"Whiteland, Markus A."https://zbmath.org/authors/?q=ai:whiteland.markus-aSummary: We study a new notion of cyclic avoidance of abelian powers. A finite word \(w\) avoids abelian \(N\)-powers cyclically if for each abelian \(N\)-power of period \(m\) occurring in the infinite word \(w^\omega\), we have \(m\geq |w|\). Let \(\mathcal{A}(k)\) be the least integer \(N\) such that for all \(n\) there exists a word of length \(n\) over a \(k\)-letter alphabet that avoids abelian \(N\)-powers cyclically. Let \(\mathcal{A}_\infty(k)\) be the least integer \(N\) such that there exist arbitrarily long words over a \(k\)-letter alphabet that avoid abelian \(N\)-powers cyclically.
We prove that \(5\leq\mathcal{A}(2)\leq 8\), \(3\leq\mathcal{A}(3)\leq 4\), \(2\leq\mathcal{A}(4)\leq 3\), and \(\mathcal{A}(k)=2\) for \(k\geq 5\). Moreover, we show that \(\mathcal{A}_\infty(2)=4\), \(\mathcal{A}_\infty(3)=3\), and \(\mathcal{A}_\infty(4)=2\).Machine learning: deepest learning as statistical data assimilation problemshttps://zbmath.org/1472.681272021-11-25T18:46:10.358925Z"Abarbanel, Henry D. I."https://zbmath.org/authors/?q=ai:abarbanel.henry-d-i"Rozdeba, Paul J."https://zbmath.org/authors/?q=ai:rozdeba.paul-j"Shirman, Sasha"https://zbmath.org/authors/?q=ai:shirman.sashaSummary: We formulate an equivalence between machine learning and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in a feedforward artificial network setting is the analog of time in the data assimilation setting. This connection has been noted in the machine learning literature. We add a perspective that expands on how methods from statistical physics and aspects of Lagrangian and Hamiltonian dynamics play a role in how networks can be trained and designed. Within the discussion of this equivalence, we show that adding more layers (making the network deeper) is analogous to adding temporal resolution in a data assimilation framework. Extending this equivalence to recurrent networks is also discussed.
We explore how one can find a candidate for the global minimum of the cost functions in the machine learning context using a method from data assimilation. Calculations on simple models from both sides of the equivalence are reported.
Also discussed is a framework in which the time or layer label is taken to be continuous, providing a differential equation, the Euler-Lagrange equation and its boundary conditions, as a necessary condition for a minimum of the cost function. This shows that the problem being solved is a two-point boundary value problem familiar in the discussion of variational methods. The use of continuous layers is denoted ``deepest learning.''
These problems respect a symplectic symmetry in continuous layer phase space. Both Lagrangian versions and Hamiltonian versions of these problems are presented. Their well-studied implementation in a discrete time/layer, while respecting the symplectic structure, is addressed. The Hamiltonian version provides a direct rationale for backpropagation as a solution method for a certain two-point boundary value problem.Dynamics of learning in MLP: natural gradient and singularity revisitedhttps://zbmath.org/1472.681282021-11-25T18:46:10.358925Z"Amari, Shun-ichi"https://zbmath.org/authors/?q=ai:amari.shun-ichi"Ozeki, Tomoko"https://zbmath.org/authors/?q=ai:ozeki.tomoko"Karakida, Ryo"https://zbmath.org/authors/?q=ai:karakida.ryo"Yoshida, Yuki"https://zbmath.org/authors/?q=ai:yoshida.yuki"Okada, Masato"https://zbmath.org/authors/?q=ai:okada.masatoSummary: The dynamics of supervised learning play a main role in deep learning, which takes place in the parameter space of a multilayer perceptron (MLP). We review the history of supervised stochastic gradient learning, focusing on its singular structure and natural gradient. The parameter space includes singular regions in which parameters are not identifiable. One of our results is a full exploration of the dynamical behaviors of stochastic gradient learning in an elementary singular network. The bad news is its pathological nature, in which part of the singular region becomes an attractor and another part a repulser at the same time, forming a Milnor attractor. A learning trajectory is attracted by the attractor region, staying in it for a long time, before it escapes the singular region through the repulser region. This is typical of plateau phenomena in learning. We demonstrate the strange topology of a singular region by introducing blow-down coordinates, which are useful for analyzing the natural gradient dynamics. We confirm that the natural gradient dynamics are free of critical slowdown. The second main result is the good news: the interactions of elementary singular networks eliminate the attractor part and the Milnor-type attractors disappear. This explains why large-scale networks do not suffer from serious critical slowdowns due to singularities. We finally show that the unit-wise natural gradient is effective for learning in spite of its low computational cost.Transfer learning by mapping and revising boosted relational dependency networkshttps://zbmath.org/1472.681292021-11-25T18:46:10.358925Z"Azevedo Santos, Rodrigo"https://zbmath.org/authors/?q=ai:azevedo-santos.rodrigo"Paes, Aline"https://zbmath.org/authors/?q=ai:paes.aline"Zaverucha, Gerson"https://zbmath.org/authors/?q=ai:zaverucha.gersonTransfer learning methods have been employed increasingly often, but most of them do not take into account relationships between entities. The paper under review addresses transfer learning in the context of the area known as statistical relational learning (SRL). It presents an algorithm called TreeBoostler, which transfers the SRL state-of-the-art Boosted Relational Dependency Networks learned in the source domain to the target domain. It is based on the predicate mapping algorithm proposed by \textit{L. Mihalkova} et al. to transfer clauses in Markov logic networks [``Mapping and revising Markov logic networks for transfer learning'', in: Proceedings of the 22nd national conference on artificial intelligence Vol. 1, AAAI'07. Palo Alto: AAAI Press. 608--614 (2007)], and consists of two phases: first, it transfers the source boosted trees structure to the target domain by finding an adequate predicate mapping, then it revises those trees by pruning and expanding nodes. The authors have experimentally validated that the revision phase improves the performance of the transfer process, though, at the same time, it increases its computational costs because it introduces another search. They have also compared the TreeBoostler on seven publicly available datasets with three baseline methods that learn from scratch. The results of those comparisons show that the TreeBoostler learns more accurate models than the baselines, no matter whether with minimal target data or with an increasing amount of them.A simple label switching algorithm for semisupervised structural SVMshttps://zbmath.org/1472.681302021-11-25T18:46:10.358925Z"Balamurugan, Palaniappan"https://zbmath.org/authors/?q=ai:balamurugan.palaniappan"Shevade, Shirish"https://zbmath.org/authors/?q=ai:shevade.shirish-krishnaj"Sundararajan, S."https://zbmath.org/authors/?q=ai:sundararajan.sSummary: In structured output learning, obtaining labeled data for real-world applications is usually costly, while unlabeled examples are available in abundance. Semisupervised structured classification deals with a small number of labeled examples and a large number of unlabeled structured data. In this work, we consider semisupervised structural support vector machines with domain constraints. The optimization problem, which in general is not convex, contains the loss terms associated with the labeled and unlabeled examples, along with the domain constraints. We propose a simple optimization approach that alternates between solving a supervised learning problem and a constraint matching problem. Solving the constraint matching problem is difficult for structured prediction, and we propose an efficient and effective label switching method to solve it. The alternating optimization is carried out within a deterministic annealing framework, which helps in effective constraint matching and avoiding poor
local minima, which are not very useful. The algorithm is simple and easy to implement. Further, it is suitable for any structured output learning problem where exact inference is available. Experiments on benchmark sequence labeling data sets and a natural language parsing data set show that the proposed approach, though simple, achieves comparable generalization performance.A homotopy training algorithm for fully connected neural networkshttps://zbmath.org/1472.681312021-11-25T18:46:10.358925Z"Chen, Qipin"https://zbmath.org/authors/?q=ai:chen.qipin"Hao, Wenrui"https://zbmath.org/authors/?q=ai:hao.wenruiSummary: In this paper, we present a homotopy training algorithm (HTA) to solve optimization problems arising from fully connected neural networks with complicated structures. The HTA dynamically builds the neural network starting from a simplified version and ending with the fully connected network via adding layers and nodes adaptively. Therefore, the corresponding optimization problem is easy to solve at the beginning and connects to the original model via a continuous path guided by the HTA, which provides a high probability of obtaining a global minimum. By gradually increasing the complexity of the model along the continuous path, the HTA provides a rather good solution to the original loss function. This is confirmed by various numerical results including VGG models on CIFAR-10. For example, on the VGG13 model with batch normalization, HTA reduces the error rate by 11.86\% on the test dataset compared with the traditional method. Moreover, the HTA also allows us to find the optimal structure for a fully connected neural network by building the neutral network adaptively.Learning data manifolds with a cutting plane methodhttps://zbmath.org/1472.681322021-11-25T18:46:10.358925Z"Chung, Sueyeon"https://zbmath.org/authors/?q=ai:chung.sueyeon"Cohen, Uri"https://zbmath.org/authors/?q=ai:cohen.uri"Sompolinsky, Haim"https://zbmath.org/authors/?q=ai:sompolinsky.haim"Lee, Daniel D."https://zbmath.org/authors/?q=ai:lee.daniel-dSummary: We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely on sampling large numbers of training examples from these manifolds. Instead, we propose an iterative algorithm, \(M_{CP}\), based on a cutting plane approach that efficiently solves a quadratic semi-infinite programming problem to find the maximum margin solution. We provide a proof of convergence as well as a polynomial bound on the number of iterations required for a desired tolerance in the objective function. The efficiency and performance of \(M_{CP}\) are demonstrated in high-dimensional simulations and on image manifolds generated from the ImageNet data set. Our results indicate that \(M_{CP}\) is able to rapidly learn good classifiers and shows superior generalization performance compared with conventional maximum margin methods using data augmentation methods.Mining explainable local and global subgraph patterns with surprising densitieshttps://zbmath.org/1472.681332021-11-25T18:46:10.358925Z"Deng, Junning"https://zbmath.org/authors/?q=ai:deng.junning"Kang, Bo"https://zbmath.org/authors/?q=ai:kang.bo"Lijffijt, Jefrey"https://zbmath.org/authors/?q=ai:lijffijt.jefrey"De Bie, Tijl"https://zbmath.org/authors/?q=ai:de-bie.tijlSummary: The connectivity structure of graphs is typically related to the attributes of the vertices. In social networks for example, the probability of a friendship between any pair of people depends on a range of attributes, such as their age, residence location, workplace, and hobbies. The high-level structure of a graph can thus possibly be described well by means of patterns of the form `the subgroup of all individuals with certain properties X are often (or rarely) friends with individuals in another subgroup defined by properties Y', ideally relative to their expected connectivity. Such rules present potentially actionable and generalizable insight into the graph. Prior work has already considered the search for dense subgraphs (`communities') with homogeneous attributes. The first contribution in this paper is to generalize this type of pattern to densities between a \textit{pair of subgroups}, as well as between \textit{all pairs from a set of subgroups that partition the vertices}. Second, we develop a novel information-theoretic approach for quantifying the subjective interestingness of such patterns, by contrasting them with prior information an analyst may have about the graph's connectivity. We demonstrate empirically that in the special case of dense subgraphs, this approach yields results that are superior to the state-of-the-art. Finally, we propose algorithms for efficiently finding interesting patterns of these different types.Online direct density-ratio estimation applied to inlier-based outlier detectionhttps://zbmath.org/1472.681342021-11-25T18:46:10.358925Z"du Plessis, Marthinus Christoffel"https://zbmath.org/authors/?q=ai:du-plessis.marthinus-christoffel"Shiino, Hiroaki"https://zbmath.org/authors/?q=ai:shiino.hiroaki"Sugiyama, Masashi"https://zbmath.org/authors/?q=ai:sugiyama.masashiSummary: Many machine learning problems, such as nonstationarity adaptation, outlier detection, dimensionality reduction, and conditional density estimation, can be effectively solved by using the ratio of probability densities. Since the naive two-step procedure of first estimating the probability densities and then taking their ratio performs poorly, methods to directly estimate the density ratio from two sets of samples without density estimation have been extensively studied recently. However, these methods are batch algorithms that use the whole data set to estimate the density ratio, and they are inefficient in the online setup, where training samples are provided sequentially and solutions are updated incrementally without storing previous samples. In this letter, we propose two online density-ratio estimators based on the adaptive regularization of weight vectors. Through experiments on inlier-based outlier detection, we demonstrate the usefulness of the proposed methods.Temporal causal inference with time laghttps://zbmath.org/1472.681352021-11-25T18:46:10.358925Z"Du, Sizhen"https://zbmath.org/authors/?q=ai:du.sizhen"Song, Guojie"https://zbmath.org/authors/?q=ai:song.guojie"Han, Lei"https://zbmath.org/authors/?q=ai:han.lei"Hong, Haikun"https://zbmath.org/authors/?q=ai:hong.haikunSummary: Accurate causal inference among time series helps to better understand the interactive scheme behind the temporal variables. For time series analysis, an unavoidable issue is the existence of time lag among different temporal variables. That is, past evidence would take some time to cause a future effect instead of an immediate response. To model this process, existing approaches commonly adopt a prefixed time window to define the lag. However, in many real-world applications, this parameter may vary among different time series, and it is hard to be predefined with a fixed value. In this letter, we propose to learn the causal relations as well as the lag among different time series simultaneously from data. Specifically, we develop a probabilistic decomposed slab-and-spike (DSS) model to perform the inference by applying a pair of decomposed spike-and-slab variables for the model coefficients, where the first variable is used to estimate the causal relationship and the second one captures the lag information among different temporal variables. For parameter inference, we propose an efficient expectation propagation (EP) algorithm to solve the DSS model. Experimental results conducted on both synthetic and real-world problems demonstrate the effectiveness of the proposed method. The revealed time lag can be well validated by the domain knowledge within the real-world applications.Machine learning from a continuous viewpoint. Ihttps://zbmath.org/1472.681362021-11-25T18:46:10.358925Z"E, Weinan"https://zbmath.org/authors/?q=ai:e.weinan"Ma, Chao"https://zbmath.org/authors/?q=ai:ma.chao"Wu, Lei"https://zbmath.org/authors/?q=ai:wu.lei.1|wu.lei.2|wu.lei.3|wu.lei.4Summary: We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models and algorithms, such as the random feature model, the two-layer neural network model and the residual neural network model, can all be recovered (in a scaled form) as particular discretizations of different continuous formulations. We also present examples of new models, such as the flow-based random feature model, and new algorithms, such as the smoothed particle method and spectral method, that arise naturally from this continuous formulation. We discuss how the issues of generalization error and implicit regularization can be studied under this framework.Robust support vector machines for classification with nonconvex and smooth losseshttps://zbmath.org/1472.681372021-11-25T18:46:10.358925Z"Feng, Yunlong"https://zbmath.org/authors/?q=ai:feng.yunlong"Yang, Yuning"https://zbmath.org/authors/?q=ai:yang.yuning"Huang, Xiaolin"https://zbmath.org/authors/?q=ai:huang.xiaolin"Mehrkanoon, Siamak"https://zbmath.org/authors/?q=ai:mehrkanoon.siamak"Suykens, Johan A. K."https://zbmath.org/authors/?q=ai:suykens.johan-a-kSummary: This letter addresses the robustness problem when learning a large margin classifier in the presence of label noise. In our study, we achieve this purpose by proposing robustified large margin support vector machines. The robustness of the proposed robust support vector classifiers (RSVC), which is interpreted from a weighted viewpoint in this work, is due to the use of nonconvex classification losses. Besides the robustness, we also show that the proposed RSCV is simultaneously smooth, which again benefits from using smooth classification losses. The idea of proposing RSVC comes from M-estimation in statistics since the proposed robust and smooth classification losses can be taken as one-sided cost functions in robust statistics. Its Fisher consistency property and generalization ability are also investigated. Besides the robustness and smoothness, another nice property of RSVC lies in the fact that its solution can be obtained by solving weighted squared hinge loss-based support vector machine problems iteratively. We further show that in each iteration, it is a quadratic programming problem in its dual space and can be solved by using state-of-the-art methods. We thus propose an iteratively reweighted type algorithm and provide a constructive proof of its convergence to a stationary point. Effectiveness of the proposed classifiers is verified on both artificial and real data sets.Neural simpletrons: learning in the limit of few labels with directed generative networkshttps://zbmath.org/1472.681382021-11-25T18:46:10.358925Z"Forster, Dennis"https://zbmath.org/authors/?q=ai:forster.dennis"Sheikh, Abdul-Saboor"https://zbmath.org/authors/?q=ai:sheikh.abdul-saboor"Lücke, Jörg"https://zbmath.org/authors/?q=ai:lucke.jorgSummary: We explore classifier training for data sets with very few labels. We investigate this task using a neural network for nonnegative data. The network is derived from a hierarchical normalized Poisson mixture model with one observed and two hidden layers. With the single objective of likelihood optimization, both labeled and unlabeled data are naturally incorporated into learning. The neural activation and learning equations resulting from our derivation are concise and local. As a consequence, the network can be scaled using standard deep learning tools for parallelized GPU implementation. Using standard benchmarks for nonnegative data, such as text document representations, MNIST, and NIST SD19, we study the classification performance when very few labels are used for training. In different settings, the network's performance is compared to standard and recently suggested semisupervised classifiers. While other recent approaches are more competitive for many labels or fully labeled data sets, we find that the network studied here can be applied to numbers of few labels where no other system has been reported to operate so far.Local Procrustes for manifold embedding: a measure of embedding quality and embedding algorithmshttps://zbmath.org/1472.681392021-11-25T18:46:10.358925Z"Goldberg, Yair"https://zbmath.org/authors/?q=ai:goldberg.yair"Ritov, Ya'acov"https://zbmath.org/authors/?q=ai:ritov.yaacovSummary: We present the Procrustes measure, a novel measure based on Procrustes rotation that enables quantitative comparison of the output of manifold-based embedding algorithms such as LLE
[\textit{S. T. Roweis} and \textit{L. K. Saul}, ``Nonlinear dimensionality reduction by locally linear embedding'', Science 290, No. 5500, 2323--2326 (2000; \url{doi:10.1126/science.290.5500.2323})]
and Isomap
[\textit{J. B. Tenenbaum} et al., ``A global geometric framework for nonlinear dimensionality reduction'', Science 290, No. 5500, 2319--2323 (2000; \url{doi:10.1126/science.290.5500.2319})]. The measure also serves as a natural tool when choosing dimension-reduction parameters. We also present two novel dimension-reduction techniques that attempt to minimize the suggested measure, and compare the results of these techniques to the results of existing algorithms. Finally, we suggest a simple iterative method that can be used to improve the output of existing algorithms.Adaptive learning algorithm convergence in passive and reactive environmentshttps://zbmath.org/1472.681402021-11-25T18:46:10.358925Z"Golden, Richard M."https://zbmath.org/authors/?q=ai:golden.richard-mSummary: Although the number of artificial neural network and machine learning architectures is growing at an exponential pace, more attention needs to be paid to theoretical guarantees of asymptotic convergence for novel, nonlinear, high-dimensional adaptive learning algorithms. When properly understood, such guarantees can guide the algorithm development and evaluation process and provide theoretical validation for a particular algorithm design. For many decades, the machine learning community has widely recognized the importance of stochastic approximation theory as a powerful tool for identifying explicit convergence conditions for adaptive learning machines. However, the verification of such conditions is challenging for multidisciplinary researchers not working in the area of stochastic approximation theory. For this reason, this letter presents a new stochastic approximation theorem for both passive and reactive learning environments with assumptions that are easily verifiable. The theorem is widely applicable to the analysis and design of important machine learning algorithms including deep learning algorithms with multiple strict local minimizers, Monte Carlo expectation-maximization algorithms, contrastive divergence learning in Markov fields, and policy gradient reinforcement learning.Sketching information divergenceshttps://zbmath.org/1472.681412021-11-25T18:46:10.358925Z"Guha, Sudipto"https://zbmath.org/authors/?q=ai:guha.sudipto"Indyk, Piotr"https://zbmath.org/authors/?q=ai:indyk.piotr"McGregor, Andrew"https://zbmath.org/authors/?q=ai:mcgregor.andrewSummary: When comparing discrete probability distributions, natural measures of similarity are not \(\ell _{p }\) distances but rather are information divergences such as Kullback-Leibler and Hellinger. This paper considers some of the issues related to constructing small-space sketches of distributions in the data-stream model, a concept related to dimensionality reduction, such that these measures can be approximated from the sketches. Related problems for \(\ell _{p }\) distances are reasonably well understood via a series of results by
\textit{W. B. Johnson} and \textit{J. Lindenstrauss} [Contemp. Math. 26, 189--206 (1984; Zbl 0539.46017)],
\textit{N. Alon} et al. [J. Comput. Syst. Sci. 58, No. 1, 137--147 (1999; Zbl 0938.68153)],
the second author and \textit{D. Woodruff} [in: Proceedings of the 37th annual ACM symposium on theory of computing, STOC'05. New York, NY: Association for Computing Machinery (ACM). 202--208 (2005; Zbl 1192.68364)],
and
\textit{B. Brinkman} and \textit{M. Charikar} [``On the impossibility of dimension reduction in \(\ell_1\)'', in: Proceedings of the 44th annual IEEE symposium on foundations of computer science, FOCS'03. Los Alamitos, CA: IEEE Computer Society. 514--523 (2003; \url{doi:10.1109/SFCS.2003.1238224})].
In contrast, almost no analogous results are known to date about constructing sketches for the information divergences used in statistics and learning theory.
Our main result is an impossibility result that shows that no small-space sketches exist for the multiplicative approximation of any commonly used \(f\)-divergences and Bregman divergences with the notable exceptions of \(\ell _{1}\) and \(\ell _{2}\) where small-space sketches exist. We then present data-stream algorithms for the additive approximation of a wide range of information divergences. Throughout, our emphasis is on providing general characterizations.Dynamic neural Turing machine with continuous and discrete addressing schemeshttps://zbmath.org/1472.681422021-11-25T18:46:10.358925Z"Gulcehre, Caglar"https://zbmath.org/authors/?q=ai:gulcehre.caglar"Chandar, Sarath"https://zbmath.org/authors/?q=ai:chandar.sarath"Cho, Kyunghyun"https://zbmath.org/authors/?q=ai:cho.kyunghyun"Bengio, Yoshua"https://zbmath.org/authors/?q=ai:bengio.yoshuaSummary: We extend the neural Turing machine (NTM) model into a dynamic neural Turing machine (D-NTM) by introducing trainable address vectors. This addressing scheme maintains for each memory cell two separate vectors, content and address vectors. This allows the D-NTM to learn a wide variety of location-based addressing strategies, including both linear and nonlinear ones. We implement the D-NTM with both continuous and discrete read and write mechanisms. We investigate the mechanisms and effects of learning to read and write into a memory through experiments on Facebook bAbI tasks using both a feedforward and GRU controller. We provide extensive analysis of our model and compare different variations of neural Turing machines on this task. We show that our model outperforms long short-term memory and NTM variants. We provide further experimental results on the sequential \(p\)MNIST, Stanford Natural Language Inference, associative recall, and copy tasks.A survey of community detection methods in multilayer networkshttps://zbmath.org/1472.681432021-11-25T18:46:10.358925Z"Huang, Xinyu"https://zbmath.org/authors/?q=ai:huang.xinyu"Chen, Dongming"https://zbmath.org/authors/?q=ai:chen.dongming"Ren, Tao"https://zbmath.org/authors/?q=ai:ren.tao"Wang, Dongqi"https://zbmath.org/authors/?q=ai:wang.dongqiSummary: Community detection is one of the most popular researches in a variety of complex systems, ranging from biology to sociology. In recent years, there's an increasing focus on the rapid development of more complicated networks, namely multilayer networks. Communities in a single-layer network are groups of nodes that are more strongly connected among themselves than the others, while in multilayer networks, a group of well-connected nodes are shared in multiple layers. Most traditional algorithms can rarely perform well on a multilayer network without modifications. Thus, in this paper, we offer overall comparisons of existing works and analyze several representative algorithms, providing a comprehensive understanding of community detection methods in multilayer networks. The comparison results indicate that the promoting of algorithm efficiency and the extending for general multilayer networks are also expected in the forthcoming studies.Semi-supervised graph clustering: a kernel approachhttps://zbmath.org/1472.681442021-11-25T18:46:10.358925Z"Kulis, Brian"https://zbmath.org/authors/?q=ai:kulis.brian"Basu, Sugato"https://zbmath.org/authors/?q=ai:basu.sugato"Dhillon, Inderjit"https://zbmath.org/authors/?q=ai:dhillon.inderjit-s"Mooney, Raymond"https://zbmath.org/authors/?q=ai:mooney.raymond-jSummary: Semi-supervised clustering algorithms aim to improve clustering results using limited supervision. The supervision is generally given as pairwise constraints; such constraints are natural for graphs, yet most semi-supervised clustering algorithms are designed for data represented as vectors. In this paper, we unify vector-based and graph-based approaches. We first show that a recently-proposed objective function for semi-supervised clustering based on Hidden Markov Random Fields, with squared Euclidean distance and a certain class of constraint penalty functions, can be expressed as a special case of the weighted kernel \(k\)-means objective
[the third author et al., ``Kernel \(k\)-means, spectral clustering and normalized cuts'', in: Proceedings of the 10th ACM SIGKDD international conference on knowledge discovery and data mining, KDD'04. New York, NY: Association for Computing Machinery (ACM). 551--556 (2004; \url{doi:10.1145/1014052.1014118}).
A recent theoretical connection between weighted kernel \(k\)-means and several graph clustering objectives enables us to perform semi-supervised clustering of data given either as vectors or as a graph. For graph data, this result leads to algorithms for optimizing several new semi-supervised graph clustering objectives. For vector data, the kernel approach also enables us to find clusters with non-linear boundaries in the input data space. Furthermore, we show that recent work on spectral learning
[\textit{S. D. Kamvar} et al., ``Spectral learning'', in: Proceedings of the 18th international joint conference on artificial intelligence, IJCAI'03. s.l., CA: International Joint Conferences on Artificial Intelligence Organization. 561--566 (2003)]
may be viewed as a special case of our formulation. We empirically show that our algorithm is able to outperform current state-of-the-art semi-supervised algorithms on both vector-based and graph-based data sets.Mahalanobis distance informed by clusteringhttps://zbmath.org/1472.681452021-11-25T18:46:10.358925Z"Lahav, Almog"https://zbmath.org/authors/?q=ai:lahav.almog"Talmon, Ronen"https://zbmath.org/authors/?q=ai:talmon.ronen"Kluger, Yuval"https://zbmath.org/authors/?q=ai:kluger.yuvalSummary: A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of meaningfulness is more prominent (e.g. the Euclidean distance between images). In this paper, we propose to exploit a property of high-dimensional data that is usually ignored, which is the structure stemming from the relationships between the coordinates. Specifically, we show that organizing similar coordinates in clusters can be exploited for the construction of the Mahalanobis distance between samples. When the observable samples are generated by a nonlinear transformation of hidden variables, the Mahalanobis distance allows the recovery of the Euclidean distances in the hidden space. We illustrate the advantage of our approach on a synthetic example where the discovery of clusters of correlated coordinates improves the estimation of the principal directions of the samples. Our method was applied to real data of gene expression for lung adenocarcinomas (lung cancer). By using the proposed metric we found a partition of subjects to risk groups with a good separation between their Kaplan-Meier survival plot.Active learning using hint informationhttps://zbmath.org/1472.681462021-11-25T18:46:10.358925Z"Li, Chun-Liang"https://zbmath.org/authors/?q=ai:li.chun-liang"Ferng, Chun-Sung"https://zbmath.org/authors/?q=ai:ferng.chun-sung"Lin, Hsuan-Tien"https://zbmath.org/authors/?q=ai:lin.hsuan-tienSummary: The abundance of real-world data and limited labeling budget calls for active learning, an important learning paradigm for reducing human labeling efforts. Many recently developed active learning algorithms consider both uncertainty and representativeness when making querying decisions. However, exploiting representativeness with uncertainty concurrently usually requires tackling sophisticated and challenging learning tasks, such as clustering. In this letter, we propose a new active learning framework, called hinted sampling, which takes both uncertainty and representativeness into account in a simpler way. We design a novel active learning algorithm within the hinted sampling framework with an extended support vector machine. Experimental results validate that the novel active learning algorithm can result in a better and more stable performance than that achieved by state-of-the-art algorithms. We also show that the hinted sampling framework allows improving another active learning algorithm designed from the transductive support vector machine.A fast algorithm for learning overcomplete dictionary for sparse representation based on proximal operatorshttps://zbmath.org/1472.681472021-11-25T18:46:10.358925Z"Li, Zhenni"https://zbmath.org/authors/?q=ai:li.zhenni"Ding, Shuxue"https://zbmath.org/authors/?q=ai:ding.shuxue"Li, Yujie"https://zbmath.org/authors/?q=ai:li.yujieSummary: We present a fast, efficient algorithm for learning an overcomplete dictionary for sparse representation of signals. The whole problem is considered as a minimization of the approximation error function with a coherence penalty for the dictionary atoms and with the sparsity regularization of the coefficient matrix. Because the problem is nonconvex and nonsmooth, this minimization problem cannot be solved efficiently by an ordinary optimization method. We propose a decomposition scheme and an alternating optimization that can turn the problem into a set of minimizations of piecewise quadratic and univariate subproblems, each of which is a single variable vector problem, of either one dictionary atom or one coefficient vector. Although the subproblems are still nonsmooth, remarkably they become much simpler so that we can find a closed-form solution by introducing a proximal operator. This leads to an efficient algorithm for sparse representation. To our knowledge, applying the proximal operator to the problem with an incoherence term and obtaining the optimal dictionary atoms in closed form with a proximal operator technique have not previously been studied. The main advantages of the proposed algorithm are that, as suggested by our analysis and simulation study, it has lower computational complexity and a higher convergence rate than state-of-the-art algorithms. In addition, for real applications, it shows good performance and significant reductions in computational time.Manifold learning with bi-stochastic kernelshttps://zbmath.org/1472.681482021-11-25T18:46:10.358925Z"Marshall, Nicholas F."https://zbmath.org/authors/?q=ai:marshall.nicholas-f"Coifman, Ronald R."https://zbmath.org/authors/?q=ai:coifman.ronald-raphaelSummary: In this paper we answer the following question: what is the infinitesimal generator of the diffusion process defined by a kernel that is normalized such that it is bi-stochastic with respect to a specified measure? More precisely, under the assumption that data is sampled from a Riemannian manifold we determine how the resulting infinitesimal generator depends on the potentially non-uniform distribution of the sample points, and the specified measure for the bi-stochastic normalization. In a special case, we demonstrate a connection to the heat kernel. We consider both the case where only a single data set is given, and the case where a data set and a reference set are given. The spectral theory of the constructed operators is studied, and Nyström extension formulas for the gradients of the eigenfunctions are computed. Applications to discrete point sets and manifold learning are discussed.An online policy gradient algorithm for Markov decision processes with continuous states and actionshttps://zbmath.org/1472.681492021-11-25T18:46:10.358925Z"Ma, Yao"https://zbmath.org/authors/?q=ai:ma.yao"Zhao, Tingting"https://zbmath.org/authors/?q=ai:zhao.tingting"Hatano, Kohei"https://zbmath.org/authors/?q=ai:hatano.kohei"Sugiyama, Masashi"https://zbmath.org/authors/?q=ai:sugiyama.masashiSummary: We consider the learning problem under an online Markov decision process (MDP) aimed at learning the time-dependent decision-making policy of an agent that minimizes the regret -- the difference from the best fixed policy. The difficulty of online MDP learning is that the reward function changes over time. In this letter, we show that a simple online policy gradient algorithm achieves regret \(O(\sqrt{T})\) for \(T\) steps under a certain concavity assumption and \(O(\log T)\) under a strong concavity assumption. To the best of our knowledge, this is the first work to present an online MDP algorithm that can handle continuous state, action, and parameter spaces with guarantee. We also illustrate the behavior of the proposed online policy gradient method through experiments.For real: a thorough look at numeric attributes in subgroup discoveryhttps://zbmath.org/1472.681502021-11-25T18:46:10.358925Z"Meeng, Marvin"https://zbmath.org/authors/?q=ai:meeng.marvin"Knobbe, Arno"https://zbmath.org/authors/?q=ai:knobbe.arno-jSummary: Subgroup discovery (SD) is an exploratory pattern mining paradigm that comes into its own when dealing with large real-world data, which typically involves many attributes, of a mixture of data types. Essential is the ability to deal with numeric attributes, whether they concern the target (a regression setting) or the description attributes (by which subgroups are identified). Various specific algorithms have been proposed in the literature for both cases, but a systematic review of the available options is missing. This paper presents a generic framework that can be instantiated in various ways in order to create different strategies for dealing with numeric data. The bulk of the work in this paper describes an experimental comparison of a considerable range of numeric strategies in SD, where these strategies are organised according to four central dimensions. These experiments are furthermore repeated for both the classification task (target is nominal) and regression task (target is numeric), and the strategies are compared based on the quality of the top subgroup, and the quality and redundancy of the top-\(k\) result set. Results of three search strategies are compared: traditional beam search, complete search, and a variant of diverse subgroup set discovery called cover-based subgroup selection. Although there are various subtleties in the outcome of the experiments, the following general conclusions can be drawn: it is often best to determine numeric thresholds dynamically (locally), in a fine-grained manner, with binary splits, while considering multiple candidate thresholds per attribute.A block successive lower-bound maximization algorithm for the maximum pseudo-likelihood estimation of fully visible Boltzmann machineshttps://zbmath.org/1472.681512021-11-25T18:46:10.358925Z"Nguyen, Hien D."https://zbmath.org/authors/?q=ai:nguyen.hien-d-t"Wood, Ian A."https://zbmath.org/authors/?q=ai:wood.ian-aSummary: Maximum pseudo-likelihood estimation (MPLE) is an attractive method for training fully visible Boltzmann machines (FVBMs) due to its computational scalability and the desirable statistical properties of the MPLE. No published algorithms for MPLE have been proven to be convergent or monotonic. In this note, we present an algorithm for the MPLE of FVBMs based on the block successive lower-bound maximization (BSLM) principle. We show that the BSLM algorithm monotonically increases the pseudo-likelihood values and that the sequence of BSLM estimates converges to the unique global maximizer of the pseudo-likelihood function. The relationship between the BSLM algorithm and the gradient ascent (GA) algorithm for MPLE of FVBMs is also discussed, and a convergence criterion for the GA algorithm is given.Hybrid ASP-based approach to pattern mininghttps://zbmath.org/1472.681522021-11-25T18:46:10.358925Z"Paramonov, Sergey"https://zbmath.org/authors/?q=ai:paramonov.sergey"Stepanova, Daria"https://zbmath.org/authors/?q=ai:stepanova.daria-a"Miettinen, Pauli"https://zbmath.org/authors/?q=ai:miettinen.pauliSummary: Detecting small sets of relevant patterns from a given data set is a central challenge in data mining. The relevance of a pattern is based on user-provided criteria; typically, all patterns that satisfy certain criteria are considered relevant. Rule-based languages like answer set programming (ASP) seem well suited for specifying such criteria in a form of constraints. Although progress has been made, on the one hand, on solving individual mining problems and, on the other hand, developing generic mining systems, the existing methods focus either on scalability or on generality. In this paper, we make steps toward combining local (frequency, size, and cost) and global (various condensed representations like maximal, closed, and skyline) constraints in a generic and efficient way. We present a hybrid approach for itemset, sequence, and graph mining which exploits dedicated highly optimized mining systems to detect frequent patterns and then filters the results using declarative ASP. To further demonstrate the generic nature of our hybrid framework, we apply it to a problem of approximately tiling a database. Experiments on real-world data sets show the effectiveness of the proposed method and computational gains for itemset, sequence, and graph mining, as well as approximate tiling.A Hebbian/anti-Hebbian neural network for linear subspace learning: a derivation from multidimensional scaling of streaming datahttps://zbmath.org/1472.681532021-11-25T18:46:10.358925Z"Pehlevan, Cengiz"https://zbmath.org/authors/?q=ai:pehlevan.cengiz"Hu, Tao"https://zbmath.org/authors/?q=ai:hu.tao"Chklovskii, Dmitri B."https://zbmath.org/authors/?q=ai:chklovskii.dmitri-bSummary: Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis, by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost function, these rules are nonlocal and hence biologically implausible. At the same time, biologically plausible local rules have been postulated rather than derived from a principled cost function. Here, to bridge this gap, we derive a biologically plausible network for subspace learning on streaming data by minimizing a principled cost function. In a departure from previous work, where cost was quantified by the representation, or reconstruction, error, we adopt a multidimensional scaling cost function for streaming data. The resulting algorithm relies only on biologically plausible Hebbian and anti-Hebbian local learning rules. In a stochastic setting, synaptic weights converge to a stationary state, which projects the input data onto the principal subspace. If the data are generated by a nonstationary distribution, the network can track the principal subspace. Thus, our result makes a step toward an algorithmic theory of neural computation.Feature ranking for multi-target regressionhttps://zbmath.org/1472.681542021-11-25T18:46:10.358925Z"Petković, Matej"https://zbmath.org/authors/?q=ai:petkovic.matej"Kocev, Dragi"https://zbmath.org/authors/?q=ai:kocev.dragi"Džeroski, Sašo"https://zbmath.org/authors/?q=ai:dzeroski.sasoThis paper considers multi-task regression (MTR) where the goal is to learn a model that predicts several target variables simultaneously. In particular the authors address the task of feature ranking to score the importance of descriptive attributes. While there is several work on feature ranking in single-task regression, this paper presents one of the first feature ranking methods for MTR. It introduces two methods for feature ranking: one based on an ensemble of predictive clustering trees and one as an extension of RReliefF. Extensive experimental results are reported to justify the effectiveness of the proposed methods.Indefinite proximity learning: a reviewhttps://zbmath.org/1472.681552021-11-25T18:46:10.358925Z"Schleif, Frank-Michael"https://zbmath.org/authors/?q=ai:schleif.frank-michael"Tino, Peter"https://zbmath.org/authors/?q=ai:tino.peterSummary: Efficient learning of a data analysis task strongly depends on the data representation. Most methods rely on (symmetric) similarity or dissimilarity representations by means of metric inner products or distances, providing easy access to powerful mathematical formalisms like kernel or branch-and-bound approaches. Similarities and dissimilarities are, however, often naturally obtained by nonmetric proximity measures that cannot easily be handled by classical learning algorithms. Major efforts have been undertaken to provide approaches that can either directly be used for such data or to make standard methods available for these types of data. We provide a comprehensive survey for the field of learning with nonmetric proximities. First, we introduce the formalism used in nonmetric spaces and motivate specific treatments for nonmetric proximity data. Second, we provide a systematization of the various approaches. For each category of approaches, we provide a comparative discussion of the individual algorithms and address complexity issues and generalization properties. In a summarizing section, we provide a larger experimental study for the majority of the algorithms on standard data sets. We also address the problem of large-scale proximity learning, which is often overlooked in this context and of major importance to make the method relevant in practice. The algorithms we discuss are in general applicable for proximity-based clustering, one-class classification, classification, regression, and embedding approaches. In the experimental part, we focus on classification tasks.Efficient feature selection using shrinkage estimatorshttps://zbmath.org/1472.681562021-11-25T18:46:10.358925Z"Sechidis, Konstantinos"https://zbmath.org/authors/?q=ai:sechidis.konstantinos"Azzimonti, Laura"https://zbmath.org/authors/?q=ai:azzimonti.laura"Pocock, Adam"https://zbmath.org/authors/?q=ai:pocock.adam"Corani, Giorgio"https://zbmath.org/authors/?q=ai:corani.giorgio"Weatherall, James"https://zbmath.org/authors/?q=ai:weatherall.james-owen|weatherall.james-wez"Brown, Gavin"https://zbmath.org/authors/?q=ai:brown.gavin.3Summary: Information theoretic feature selection methods quantify the importance of each feature by estimating mutual information terms to capture: the relevancy, the redundancy and the complementarity. These terms are commonly estimated by maximum likelihood, while an under-explored area of research is how to use shrinkage methods instead. Our work suggests a novel shrinkage method for data-efficient estimation of information theoretic terms. The small sample behaviour makes it particularly suitable for estimation of discrete distributions with large number of categories (bins). Using our novel estimators we derive a framework for generating feature selection criteria that capture any high-order feature interaction for redundancy and complementarity. We perform a thorough empirical study across datasets from diverse sources and using various evaluation measures. Our first finding is that our shrinkage based methods achieve better results, while they keep the same computational cost as the simple maximum likelihood based methods. Furthermore, under our framework we derive efficient novel high-order criteria that outperform state-of-the-art methods in various tasks.Correction to: ``Efficient feature selection using shrinkage estimators''https://zbmath.org/1472.681572021-11-25T18:46:10.358925Z"Sechidis, Konstantinos"https://zbmath.org/authors/?q=ai:sechidis.konstantinos"Azzimonti, Laura"https://zbmath.org/authors/?q=ai:azzimonti.laura"Pocock, Adam"https://zbmath.org/authors/?q=ai:pocock.adam"Corani, Giorgio"https://zbmath.org/authors/?q=ai:corani.giorgio"Weatherall, James"https://zbmath.org/authors/?q=ai:weatherall.james-owen|weatherall.james-wez"Brown, Gavin"https://zbmath.org/authors/?q=ai:brown.gavin.3From the text: There was a mistake in the proof of the optimal shrinkage intensity for our estimator presented in Section 3.1 of our paper [ibid. 108, No. 8--9, 1261--1286 (2019; Zbl 1472.68156)]. The main theorem still holds, and the shrinkage intensity presented in the corrected version is the optimal in the sense of minimizing the mean squared error (MSE). In this document, apart from correcting the proof for the optimal shrinkage intensity, we provide empirical verification on the correctness via simulations.A comparative study of pairwise learning methods based on kernel ridge regressionhttps://zbmath.org/1472.681582021-11-25T18:46:10.358925Z"Stock, Michiel"https://zbmath.org/authors/?q=ai:stock.michiel"Pahikkala, Tapio"https://zbmath.org/authors/?q=ai:pahikkala.tapio"Airola, Antti"https://zbmath.org/authors/?q=ai:airola.antti"De Baets, Bernard"https://zbmath.org/authors/?q=ai:de-baets.bernard"Waegeman, Willem"https://zbmath.org/authors/?q=ai:waegeman.willemSummary: Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction, or network inference problems. During the past decade, kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their behavior has been underexplored in the machine learning literature. In this work we review and unify kernel-based algorithms that are commonly used in different pairwise learning settings, ranging from matrix filtering to zero-shot learning. To this end, we focus on closed-form efficient instantiations of Kronecker kernel ridge regression. We show that independent task kernel ridge regression, two-step kernel ridge regression, and a linear matrix filter arise naturally as a special case of Kronecker kernel ridge regression, implying that all these methods implicitly minimize a squared loss. In addition, we analyze universality, consistency, and spectral filtering properties. Our theoretical results provide valuable insights into assessing the advantages and limitations of existing pairwise learning methods.Why does large batch training result in poor generalization? A comprehensive explanation and a better strategy from the viewpoint of stochastic optimizationhttps://zbmath.org/1472.681592021-11-25T18:46:10.358925Z"Takase, Tomoumi"https://zbmath.org/authors/?q=ai:takase.tomoumi"Oyama, Satoshi"https://zbmath.org/authors/?q=ai:oyama.satoshi"Kurihara, Masahito"https://zbmath.org/authors/?q=ai:kurihara.masahitoSummary: We present a comprehensive framework of search methods, such as simulated annealing and batch training, for solving nonconvex optimization problems. These methods search a wider range by gradually decreasing the randomness added to the standard gradient descent method. The formulation that we define on the basis of this framework can be directly applied to neural network training. This produces an effective approach that gradually increases batch size during training. We also explain why large batch training degrades generalization performance, which previous studies have not clarified.A novel parameter estimation method for Boltzmann machineshttps://zbmath.org/1472.681602021-11-25T18:46:10.358925Z"Takenouchi, Takashi"https://zbmath.org/authors/?q=ai:takenouchi.takashiSummary: We propose a novel estimator for a specific class of probabilistic models on discrete spaces such as the Boltzmann machine. The proposed estimator is derived from minimization of a convex risk function and can be constructed without calculating the normalization constant, whose computational cost is exponential order. We investigate statistical properties of the proposed estimator such as consistency and asymptotic normality in the framework of the estimating function. Small experiments show that the proposed estimator can attain comparable performance to the maximum likelihood expectation at a much lower computational cost and is applicable to high-dimensional data.A mathematical motivation for complex-valued convolutional networkshttps://zbmath.org/1472.681612021-11-25T18:46:10.358925Z"Tygert, Mark"https://zbmath.org/authors/?q=ai:tygert.mark"Bruna, Joan"https://zbmath.org/authors/?q=ai:bruna.joan"Chintala, Soumith"https://zbmath.org/authors/?q=ai:chintala.soumith"LeCun, Yann"https://zbmath.org/authors/?q=ai:lecun.yann"Piantino, Serkan"https://zbmath.org/authors/?q=ai:piantino.serkan"Szlam, Arthur"https://zbmath.org/authors/?q=ai:szlam.arthur-dSummary: A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors, followed by (2) taking the absolute value of every entry of the resulting vectors, followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as data-driven multiscale windowed power spectra, data-driven multiscale windowed absolute spectra, data-driven multiwavelet absolute values, or (in their most general configuration) data-driven nonlinear multiwavelet packets. Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (e.g., logistic or tanh) nonlinearities, or max pooling, for example, do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.Subsampled Hessian Newton methods for supervised learninghttps://zbmath.org/1472.681622021-11-25T18:46:10.358925Z"Wang, Chien-Chih"https://zbmath.org/authors/?q=ai:wang.chien-chih"Huang, Chun-Heng"https://zbmath.org/authors/?q=ai:huang.chun-heng"Lin, Chih-Jen"https://zbmath.org/authors/?q=ai:lin.chih-jenSummary: Newton methods can be applied in many supervised learning approaches. However, for large-scale data, the use of the whole Hessian matrix can be time-consuming. Recently, subsampled Newton methods have been proposed to reduce the computational time by using only a subset of data for calculating an approximation of the Hessian matrix. Unfortunately, we find that in some situations, the running speed is worse than the standard Newton method because cheaper but less accurate search directions are used. In this work, we propose some novel techniques to improve the existing subsampled Hessian Newton method. The main idea is to solve a two-dimensional subproblem per iteration to adjust the search direction to better minimize the second-order approximation of the function value. We prove the theoretical convergence of the proposed method. Experiments on logistic regression, linear SVM, maximum entropy, and deep networks indicate that our techniques significantly reduce the running time of the subsampled Hessian Newton method. The resulting algorithm becomes a compelling alternative to the standard Newton method for large-scale data classification.Cross-domain metric and multiple kernel learning based on information theoryhttps://zbmath.org/1472.681632021-11-25T18:46:10.358925Z"Wang, Wei"https://zbmath.org/authors/?q=ai:wang.wei.30"Wang, Hao"https://zbmath.org/authors/?q=ai:wang.hao.9"Zhang, Chen"https://zbmath.org/authors/?q=ai:zhang.chen"Gao, Yang"https://zbmath.org/authors/?q=ai:gao.yangSummary: Learning an appropriate distance metric plays a substantial role in the success of many learning machines. Conventional metric learning algorithms have limited utility when the training and test samples are drawn from related but different domains (i.e., source domain and target domain). In this letter, we propose two novel metric learning algorithms for domain adaptation in an information-theoretic setting, allowing for discriminating power transfer and standard learning machine propagation across two domains. In the first one, a cross-domain Mahalanobis distance is learned by combining three goals: reducing the distribution difference between different domains, preserving the geometry of target domain data, and aligning the geometry of source domain data with label information. Furthermore, we devote our efforts to solving complex domain adaptation problems and go beyond linear cross-domain metric learning by extending the first method to a multiple kernel learning framework. A convex combination of multiple kernels and a linear transformation are adaptively learned in a single optimization, which greatly benefits the exploration of prior knowledge and the description of data characteristics. Comprehensive experiments in three real-world applications (face recognition, text classification, and object categorization) verify that the proposed methods outperform state-of-the-art metric learning and domain adaptation methods.Convex coupled matrix and tensor completionhttps://zbmath.org/1472.681642021-11-25T18:46:10.358925Z"Wimalawarne, Kishan"https://zbmath.org/authors/?q=ai:wimalawarne.kishan"Yamada, Makoto"https://zbmath.org/authors/?q=ai:yamada.makoto"Mamitsuka, Hiroshi"https://zbmath.org/authors/?q=ai:mamitsuka.hiroshiSummary: We propose a set of convex low-rank inducing norms for coupled matrices and tensors (hereafter referred to as coupled tensors), in which information is shared between the matrices and tensors through common modes. More specifically, we first propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, propose a completion model regularized using these norms to impute coupled tensors. A key advantage of the proposed norms is that they are convex and can be used to find a globally optimal solution, whereas existing methods for coupled learning are nonconvex. We also analyze the excess risk bounds of the completion model regularized using our proposed norms and show that they can exploit the low-rankness of coupled tensors, leading to better bounds compared to those obtained using uncoupled norms. Through synthetic and real-data experiments, we show that the proposed completion model compares favorably with existing ones.High-dimensional model recovery from random sketched data by exploring intrinsic sparsityhttps://zbmath.org/1472.681652021-11-25T18:46:10.358925Z"Yang, Tianbao"https://zbmath.org/authors/?q=ai:yang.tianbao"Zhang, Lijun"https://zbmath.org/authors/?q=ai:zhang.lijun"Lin, Qihang"https://zbmath.org/authors/?q=ai:lin.qihang"Zhu, Shenghuo"https://zbmath.org/authors/?q=ai:zhu.shenghuo"Jin, Rong"https://zbmath.org/authors/?q=ai:jin.rongThis paper proposes randomized reduction methods to solve large-scale and high-dimensional machine learning problems, which can greatly speed up the modeling process by reducing either the dimensionality or the scale of the data. Furthermore, the authors theoretically show that the developed methods can recover well the optimal models built from the original data. This model recovery is achieved by using the intrinsic sparsity of optimal solutions and does not rely on any stringent assumption. Empirical results are also included to support both the method and the theory.Bayesian differential programming for robust systems identification under uncertaintyhttps://zbmath.org/1472.681662021-11-25T18:46:10.358925Z"Yang, Yibo"https://zbmath.org/authors/?q=ai:yang.yibo"Bhouri, Mohamed Aziz"https://zbmath.org/authors/?q=ai:bhouri.mohamed-aziz"Perdikaris, Paris"https://zbmath.org/authors/?q=ai:perdikaris.paris-gSummary: This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator-prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at \url{https://bit.ly/34FOJMj}.Bandit-based task assignment for heterogeneous crowdsourcinghttps://zbmath.org/1472.681672021-11-25T18:46:10.358925Z"Zhang, Hao"https://zbmath.org/authors/?q=ai:zhang.hao|zhang.hao.3|zhang.hao.2|zhang.hao.1|zhang.hao.4"Ma, Yao"https://zbmath.org/authors/?q=ai:ma.yao"Sugiyama, Masashi"https://zbmath.org/authors/?q=ai:sugiyama.masashiSummary: We consider a task assignment problem in crowdsourcing, which is aimed at collecting as many reliable labels as possible within a limited budget. A challenge in this scenario is how to cope with the diversity of tasks and the task-dependent reliability of workers; for example, a worker may be good at recognizing the names of sports teams but not be familiar with cosmetics brands. We refer to this practical setting as heterogeneous crowdsourcing. In this letter, we propose a contextual bandit formulation for task assignment in heterogeneous crowdsourcing that is able to deal with the exploration-exploitation trade-off in worker selection. We also theoretically investigate the regret bounds for the proposed method and demonstrate its practical usefulness experimentally.Adaptive structure concept factorization for multiview clusteringhttps://zbmath.org/1472.681682021-11-25T18:46:10.358925Z"Zhan, Kun"https://zbmath.org/authors/?q=ai:zhan.kun"Shi, Jinhui"https://zbmath.org/authors/?q=ai:shi.jinhui"Wang, Jing"https://zbmath.org/authors/?q=ai:wang.jing|wang.jing.15|wang.jing.13|wang.jing.17|wang.jing.3|wang.jing.11|wang.jing.16|wang.jing.2|wang.jing.6|wang.jing.5|wang.jing.1|wang.jing.14"Wang, Haibo"https://zbmath.org/authors/?q=ai:wang.haibo"Xie, Yuange"https://zbmath.org/authors/?q=ai:xie.yuangeSummary: Most existing multiview clustering methods require that graph matrices in different views are computed beforehand and that each graph is obtained independently. However, this requirement ignores the correlation between multiple views. In this letter, we tackle the problem of multiview clustering by jointly optimizing the graph matrix to make full use of the data correlation between views. With the interview correlation, a concept factorization-based multiview clustering method is developed for data integration, and the adaptive method correlates the affinity weights of all views. This method differs from nonnegative matrix factorization-based clustering methods in that it can be applicable to data sets containing negative values. Experiments are conducted to demonstrate the effectiveness of the proposed method in comparison with state-of-the-art approaches in terms of accuracy, normalized mutual information, and purity.Joint concept correlation and feature-concept relevance learning for multilabel classificationhttps://zbmath.org/1472.681692021-11-25T18:46:10.358925Z"Zhao, Xiaowei"https://zbmath.org/authors/?q=ai:zhao.xiaowei"Ma, Zhigang"https://zbmath.org/authors/?q=ai:ma.zhigang"Li, Zhi"https://zbmath.org/authors/?q=ai:li.zhi.1|li.zhi"Li, Zhihui"https://zbmath.org/authors/?q=ai:li.zhihuiSummary: In recent years, multilabel classification has attracted significant attention in multimedia annotation. However, most of the multilabel classification methods focus only on the inherent correlations existing among multiple labels and concepts and ignore the relevance between features and the target concepts. To obtain more robust multilabel classification results, we propose a new multilabel classification method aiming to capture the correlations among multiple concepts by leveraging hypergraph that is proved to be beneficial for relational learning. Moreover, we consider mining feature-concept relevance, which is often overlooked by many multilabel learning algorithms. To better show the feature-concept relevance, we impose a sparsity constraint on the proposed method. We compare the proposed method with several other multilabel classification methods and evaluate the classification performance by mean average precision on several data sets. The experimental results show that the proposed method outperforms the state-of-the-art methods.Multi-instance dimensionality reduction via sparsity and orthogonalityhttps://zbmath.org/1472.681702021-11-25T18:46:10.358925Z"Zhu, Hong"https://zbmath.org/authors/?q=ai:zhu.hong"Liao, Li-Zhi"https://zbmath.org/authors/?q=ai:liao.li-zhi"Ng, Michael K."https://zbmath.org/authors/?q=ai:ng.michael-kSummary: We study a multi-instance (MI) learning dimensionality-reduction algorithm through sparsity and orthogonality, which is especially useful for high-dimensional MI data sets. We develop a novel algorithm to handle both sparsity and orthogonality constraints that existing methods do not handle well simultaneously. Our main idea is to formulate an optimization problem where the sparse term appears in the objective function and the orthogonality term is formed as a constraint. The resulting optimization problem can be solved by using approximate augmented Lagrangian iterations as the outer loop and inertial proximal alternating linearized minimization (iPALM) iterations as the inner loop. The main advantage of this method is that both sparsity and orthogonality can be satisfied in the proposed algorithm. We show the global convergence of the proposed iterative algorithm. We also demonstrate that the proposed algorithm can achieve high sparsity and orthogonality requirements, which are very important for dimensionality reduction. Experimental results on both synthetic and real data sets show that the proposed algorithm can obtain learning performance comparable to that of other tested MI learning algorithms.Control of chaotic systems by deep reinforcement learninghttps://zbmath.org/1472.681712021-11-25T18:46:10.358925Z"Bucci, M. A."https://zbmath.org/authors/?q=ai:bucci.michele-alessandro"Semeraro, O."https://zbmath.org/authors/?q=ai:semeraro.onofrio"Allauzen, A."https://zbmath.org/authors/?q=ai:allauzen.alexandre"Wisniewski, G."https://zbmath.org/authors/?q=ai:wisniewski.grzegorz"Cordier, L."https://zbmath.org/authors/?q=ai:cordier.laurent"Mathelin, L."https://zbmath.org/authors/?q=ai:mathelin.lionelSummary: Deep reinforcement learning (DRL) is applied to control a nonlinear, chaotic system governed by the one-dimensional Kuramoto-Sivashinsky (KS) equation. DRL uses reinforcement learning principles for the determination of optimal control solutions and deep neural networks for approximating the value function and the control policy. Recent applications have shown that DRL may achieve superhuman performance in complex cognitive tasks. In this work, we show that using restricted localized actuation, partial knowledge of the state based on limited sensor measurements and model-free DRL controllers, it is possible to stabilize the dynamics of the KS system around its unstable fixed solutions, here considered as target states. The robustness of the controllers is tested by considering several trajectories in the phase space emanating from different initial conditions; we show that DRL is always capable of driving and stabilizing the dynamics around target states. The possibility of controlling the KS system in the chaotic regime by using a DRL strategy solely relying on local measurements suggests the extension of the application of RL methods to the control of more complex systems such as drag reduction in bluff-body wakes or the enhancement/diminution of turbulent mixing.Shallow neural networks for fluid flow reconstruction with limited sensorshttps://zbmath.org/1472.681722021-11-25T18:46:10.358925Z"Erichson, N. Benjamin"https://zbmath.org/authors/?q=ai:erichson.n-benjamin"Mathelin, Lionel"https://zbmath.org/authors/?q=ai:mathelin.lionel"Yao, Zhewei"https://zbmath.org/authors/?q=ai:yao.zhewei"Brunton, Steven L."https://zbmath.org/authors/?q=ai:brunton.steven-l"Mahoney, Michael W."https://zbmath.org/authors/?q=ai:mahoney.michael-w"Kutz, J. Nathan"https://zbmath.org/authors/?q=ai:kutz.j-nathanSummary: In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such fluid flow reconstruction. Our approach learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data. No prior knowledge is assumed to be available, and the estimation method is purely data-driven. We demonstrate the performance on three examples in fluid mechanics and oceanography, showing that this modern data-driven approach outperforms traditional modal approximation techniques which are commonly used for flow reconstruction. Not only does the proposed method show superior performance characteristics, it can also produce a comparable level of performance to traditional methods in the area, using significantly fewer sensors. Thus, the mathematical architecture is ideal for emerging global monitoring technologies where measurement data are often limited.A survey of deep network techniques all classifiers can adopthttps://zbmath.org/1472.681732021-11-25T18:46:10.358925Z"Ghods, Alireza"https://zbmath.org/authors/?q=ai:ghods.alireza"Cook, Diane J."https://zbmath.org/authors/?q=ai:cook.diane-jSummary: Deep neural networks (DNNs) have introduced novel and useful tools to the machine learning community. Other types of classifiers can potentially make use of these tools as well to improve their performance and generality. This paper reviews the current state of the art for deep learning classifier technologies that are being used outside of deep neural networks. Non-neural network classifiers can employ many components found in DNN architectures. In this paper, we review the feature learning, optimization, and regularization methods that form a core of deep network technologies. We then survey non-neural network learning algorithms that make innovative use of these methods to improve classification performance. Because many opportunities and challenges still exist, we discuss directions that can be pursued to expand the area of deep learning for a variety of classification algorithms.Deep neural networks for waves assisted by the Wiener-Hopf methodhttps://zbmath.org/1472.681742021-11-25T18:46:10.358925Z"Huang, Xun"https://zbmath.org/authors/?q=ai:huang.xunSummary: In this work, the classical Wiener-Hopf method is incorporated into the emerging deep neural networks for the study of certain wave problems. The essential idea is to use the first-principle-based analytical method to efficiently produce a large volume of datasets that would supervise the learning of data-hungry deep neural networks, and to further explain the working mechanisms on underneath. To demonstrate such a combinational research strategy, a deep feed-forward network is first used to approximate the forward propagation model of a duct acoustic problem, which can find important aerospace applications in aeroengine noise tests. Next, a convolutional type U-net is developed to learn spatial derivatives in wave equations, which could help to promote computational paradigm in mathematical physics and engineering applications. A couple of extensions of the U-net architecture are proposed to further impose possible physical constraints. Finally, after giving the implementation details, the performance of the neural networks are studied by comparing with analytical solutions from the Wiener-Hopf method. Overall, the Wiener-Hopf method is used here from a totally new perspective and such a combinational research strategy shall represent the key achievement of this work.Locally adaptive activation functions with slope recovery for deep and physics-informed neural networkshttps://zbmath.org/1472.681752021-11-25T18:46:10.358925Z"Jagtap, Ameya D."https://zbmath.org/authors/?q=ai:jagtap.ameya-d"Kawaguchi, Kenji"https://zbmath.org/authors/?q=ai:kawaguchi.kenji"Karniadakis, George Em"https://zbmath.org/authors/?q=ai:karniadakis.george-emSummary: We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based \textit{slope recovery} term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix-vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.Distributed Newton methods for deep neural networkshttps://zbmath.org/1472.681762021-11-25T18:46:10.358925Z"Wang, Chien-Chih"https://zbmath.org/authors/?q=ai:wang.chien-chih"Tan, Kent Loong"https://zbmath.org/authors/?q=ai:tan.kent-loong"Chen, Chun-Ting"https://zbmath.org/authors/?q=ai:chen.chun-ting"Lin, Yu-Hsiang"https://zbmath.org/authors/?q=ai:lin.yu-hsiang"Keerthi, S. Sathiya"https://zbmath.org/authors/?q=ai:keerthi.s-sathiya"Mahajan, Dhruv"https://zbmath.org/authors/?q=ai:mahajan.dhruv"Sundararajan, S."https://zbmath.org/authors/?q=ai:sundararajan.s"Lin, Chih-Jen"https://zbmath.org/authors/?q=ai:lin.chih-jenSummary: Deep learning involves a difficult nonconvex optimization problem with a large number of weights between any two adjacent layers of a deep structure. To handle large data sets or complicated networks, distributed training is needed, but the calculation of function, gradient, and Hessian is expensive. In particular, the communication and the synchronization cost may become a bottleneck. In this letter, we focus on situations where the model is distributedly stored and propose a novel distributed Newton method for training deep neural networks. By variable and feature-wise data partitions and some careful designs, we are able to explicitly use the Jacobian matrix for matrix-vector products in the Newton method. Some techniques are incorporated to reduce the running time as well as memory consumption. First, to reduce the communication cost, we propose a diagonalization method such that an approximate Newton direction can be obtained without communication between machines. Second, we consider subsampled Gauss-Newton matrices for reducing the running time as well as the communication cost. Third, to reduce the synchronization cost, we terminate the process of finding an approximate Newton direction even though some nodes have not finished their tasks. Details of some implementation issues in distributed environments are thoroughly investigated. Experiments demonstrate that the proposed method is effective for the distributed training of deep neural networks. Compared with stochastic gradient methods, it is more robust and may give better test accuracy.Deep semisupervised zero-shot learning with maximum mean discrepancyhttps://zbmath.org/1472.681772021-11-25T18:46:10.358925Z"Zhang, Lingling"https://zbmath.org/authors/?q=ai:zhang.lingling"Liu, Jun"https://zbmath.org/authors/?q=ai:liu.jun.5|liu.jun.3|liu.jun.4|liu.jun.1|liu.jun|liu.jun.2"Luo, Minnan"https://zbmath.org/authors/?q=ai:luo.minnan"Chang, Xiaojun"https://zbmath.org/authors/?q=ai:chang.xiaojun"Zheng, Qinghua"https://zbmath.org/authors/?q=ai:zheng.qinghuaSummary: Due to the difficulty of collecting labeled images for hundreds of thousands of visual categories, zero-shot learning, where unseen categories do not have any labeled images in training stage, has attracted more attention. In the past, many studies focused on transferring knowledge from seen to unseen categories by projecting all category labels into a semantic space. However, the label embeddings could not adequately express the semantics of categories. Furthermore, the common semantics of seen and unseen instances cannot be captured accurately because the distribution of these instances may be quite different. For these issues, we propose a novel deep semisupervised method by jointly considering the heterogeneity gap between different modalities and the correlation among unimodal instances. This method replaces the original labels with the corresponding textual descriptions to better capture the category semantics. This method also overcomes the problem of distribution difference by minimizing the maximum mean discrepancy between seen and unseen instance distributions. Extensive experimental results on two benchmark data sets, CU200-Birds and Oxford Flowers-102, indicate that our method achieves significant improvements over previous methods.The ASP system DLV2https://zbmath.org/1472.681782021-11-25T18:46:10.358925Z"Alviano, Mario"https://zbmath.org/authors/?q=ai:alviano.mario"Calimeri, Francesco"https://zbmath.org/authors/?q=ai:calimeri.francesco"Dodaro, Carmine"https://zbmath.org/authors/?q=ai:dodaro.carmine"Fuscà, Davide"https://zbmath.org/authors/?q=ai:fusca.davide"Leone, Nicola"https://zbmath.org/authors/?q=ai:leone.nicola"Perri, Simona"https://zbmath.org/authors/?q=ai:perri.simona"Ricca, Francesco"https://zbmath.org/authors/?q=ai:ricca.francesco"Veltri, Pierfrancesco"https://zbmath.org/authors/?q=ai:veltri.pierfrancesco"Zangari, Jessica"https://zbmath.org/authors/?q=ai:zangari.jessicaSummary: We introduce DLV2, a new answer set programming (ASP) system. DVL2 combines \(\mathcal {I}\)-DLV, a fully-compliant ASP-Core-2 grounder, with the well-assessed solver WASP. Input programs may be enriched by annotations and directives that customize heuristics of the system and extend its solving capabilities. An empirical analysis conducted on benchmarks from past ASP competitions shows that DLV2 outperforms the old DVL system and is close to the state-of-the-art ASP system Clingo.
For the entire collection see [Zbl 1367.68005].Technical note. Efficiently coupling the \(\mathscr{I}\)-DLV grounder with ASP solvershttps://zbmath.org/1472.681792021-11-25T18:46:10.358925Z"Calimeri, Francesco"https://zbmath.org/authors/?q=ai:calimeri.francesco"Dodaro, Carmine"https://zbmath.org/authors/?q=ai:dodaro.carmine"Fuscà, Davide"https://zbmath.org/authors/?q=ai:fusca.davide"Perri, Simona"https://zbmath.org/authors/?q=ai:perri.simona"Zangari, Jessica"https://zbmath.org/authors/?q=ai:zangari.jessicaSummary: We present \(\mathscr{I}\)-\textsc{dlv}\(+ \mathscr{MS}\), a new answer set programming (ASP) system that integrates an efficient grounder, namely \(\mathscr{I}\)-\textsc{dlv}, with an automatic selector that inductively chooses a solver: depending on some inherent features of the instantiation produced by \(\mathscr{I}\)-\textsc{dlv}, machine learning techniques guide the selection of the most appropriate solver. The system participated in the latest (7th) ASP competition, winning the regular track, category \textit{SP} (i.e., one processor allowed).ASP-Core-2 input language formathttps://zbmath.org/1472.681802021-11-25T18:46:10.358925Z"Calimeri, Francesco"https://zbmath.org/authors/?q=ai:calimeri.francesco"Faber, Wolfgang"https://zbmath.org/authors/?q=ai:faber.wolfgang"Gebser, Martin"https://zbmath.org/authors/?q=ai:gebser.martin"Ianni, Giovambattista"https://zbmath.org/authors/?q=ai:ianni.giovambattista"Kaminski, Roland"https://zbmath.org/authors/?q=ai:kaminski.roland"Krennwallner, Thomas"https://zbmath.org/authors/?q=ai:krennwallner.thomas"Leone, Nicola"https://zbmath.org/authors/?q=ai:leone.nicola"Maratea, Marco"https://zbmath.org/authors/?q=ai:maratea.marco"Ricca, Francesco"https://zbmath.org/authors/?q=ai:ricca.francesco"Schaub, Torsten"https://zbmath.org/authors/?q=ai:schaub.torsten-hSummary: Standardization of solver input languages has been a main driver for the growth of several areas within knowledge representation and reasoning, fostering the exploitation in actual applications. In this document, we present the \textsf{ASP-Core-2} standard input language for Answer Set Programming, which has been adopted in ASP Competition events since 2013.Why simheuristics? Benefits, limitations, and best practices when combining metaheuristics with simulationhttps://zbmath.org/1472.681812021-11-25T18:46:10.358925Z"Chica, Manuel"https://zbmath.org/authors/?q=ai:chica.manuel"Juan, Angel A."https://zbmath.org/authors/?q=ai:juan.angel-a"Bayliss, Christopher"https://zbmath.org/authors/?q=ai:bayliss.christopher"Cordón, Oscar"https://zbmath.org/authors/?q=ai:cordon.oscar"Kelton, W. David"https://zbmath.org/authors/?q=ai:kelton.w-davidSummary: Many decision-making processes in our society involve NP-hard optimization problems. The largescale, dynamism, and uncertainty of these problems constrain the potential use of stand-alone optimization methods. The same applies for isolated simulation models, which do not have the potential to find optimal solutions in a combinatorial environment. This paper discusses the utilization of modelling and solving approaches based on the integration of simulation with metaheuristics. These `simheuristic' algorithms, which constitute a natural extension of both metaheuristics and simulation techniques, should be used as a `first-resort' method when addressing large-scale and NP-hard optimization problems under uncertainty -- which is a frequent case in real-life applications. We outline the benefits and limitations of simheuristic algorithms, provide numerical experiments that validate our arguments, review some recent publications, and outline the best practices to consider during their design and implementation stages.plasp 3: towards effective ASP planninghttps://zbmath.org/1472.681822021-11-25T18:46:10.358925Z"Dimopoulos, Yannis"https://zbmath.org/authors/?q=ai:dimopoulos.yannis"Gebser, Martin"https://zbmath.org/authors/?q=ai:gebser.martin"Lühne, Patrick"https://zbmath.org/authors/?q=ai:luhne.patrick"Romero, Javier"https://zbmath.org/authors/?q=ai:romero.javier"Schaub, Torsten"https://zbmath.org/authors/?q=ai:schaub.torsten-hSummary: We describe the new version of the Planning Domain Definition Language (PDDL)-to-Answer Set Programming (ASP) translator \textit{plasp}. First, it widens the range of accepted PDDL features. Second, it contains novel planning encodings, some inspired by Satisfiability Testing (SAT) planning and others exploiting ASP features such as well-foundedness. All of them are designed for handling multivalued fluents in order to capture both PDDL as well as SAS planning formats. Third, enabled by multishot ASP solving, it offers advanced planning algorithms also borrowed from SAT planning. As a result, \textit{plasp} provides us with an ASP-based framework for studying a variety of planning techniques in a uniform setting. Finally, we demonstrate in an empirical analysis that these techniques have a significant impact on the performance of ASP planning.The external interface for extending WASPhttps://zbmath.org/1472.681832021-11-25T18:46:10.358925Z"Dodaro, Carmine"https://zbmath.org/authors/?q=ai:dodaro.carmine"Ricca, Francesco"https://zbmath.org/authors/?q=ai:ricca.francescoSummary: Answer set programming (ASP) is a successful declarative formalism for knowledge representation and reasoning. The evaluation of ASP programs is nowadays based on the conflict-driven clause learning (CDCL) backtracking search algorithm. Recent work suggested that the performance of CDCL-based implementations can be considerably improved on specific benchmarks by extending their solving capabilities with custom heuristics and propagators. However, embedding such algorithms into existing systems requires expert knowledge of the internals of ASP implementations. The development of effective solver extensions can be made easier by providing suitable programming interfaces. In this paper, we present the interface for extending the CDCL-based ASP solver wasp. The interface is both \textit{general}, that is, it can be used for providing either new branching heuristics or propagators, and \textit{external}, that is, the implementation of new algorithms requires no internal modifications of WASP. Moreover, we review the applications of the interface witnessing it can be successfully used to extend wasp for solving effectively hard instances of both real-world and synthetic problems.Incremental search for conflict and unit instances of quantified formulas with E-matchinghttps://zbmath.org/1472.681842021-11-25T18:46:10.358925Z"Hoenicke, Jochen"https://zbmath.org/authors/?q=ai:hoenicke.jochen"Schindler, Tanja"https://zbmath.org/authors/?q=ai:schindler.tanja-iSummary: We present a new method to find conflicting instances of quantified formulas in the context of SMT solving. Our method splits the search for such instances in two parts. In the first part, E-matching is used to find candidate instances of the quantified formulas. In principle, any existing incremental E-matching technique can be used. The incrementality avoids duplicating work for each small change of the E-graph. Together with the candidate instance, E-matching also provides an existing node in the E-graph corresponding to each term in this instance. In the second part, these nodes are used to evaluate the candidate instance, i.e., without creating new terms. The evaluation can be done in constant time per instance. Our method detects conflicting instances and unit-propagating instances (clauses that propagate new literals). This makes our method suitable for a tight integration with the DPLL\(( \mathcal{T})\) framework, very much in the style of an additional theory solver.
For the entire collection see [Zbl 1471.68017].On preprocessing for weighted MaxSAThttps://zbmath.org/1472.681852021-11-25T18:46:10.358925Z"Paxian, Tobias"https://zbmath.org/authors/?q=ai:paxian.tobias"Raiola, Pascal"https://zbmath.org/authors/?q=ai:raiola.pascal"Becker, Bernd"https://zbmath.org/authors/?q=ai:becker.berndSummary: Modern competitive solvers employ various preprocessing techniques to efficiently tackle complex problems. This work introduces two preprocessing techniques to improve solving weighted partial MaxSAT problems: \textit{Generalized Boolean Multilevel Optimization (GBMO)} and \textit{Trimming MaxSAT (TrimMaxSAT)}.
GBMO refines and extends Boolean Multilevel Optimization (BMO), thereby splitting instances due to their distribution of weights into multiple less complex subproblems, which are solved one after the other to obtain the overall solution.
The second technique, TrimMaxSAT, finds unsatisfiable soft clauses and removes them from the instance. This reduces the complexity of the MaxSAT instance and works especially well in combination with GBMO. The proposed algorithm works incrementally in a binary search fashion, testing the satisfiability of every soft clause. Furthermore, as a by-product, typically an initial weight close to the maximum is found, which is in turn advantageous w.r.t. the size of e.g. the Dynamic Polynomial Watchdog (DPW) encoding.
Both techniques can be used by all MaxSAT solvers, though our focus lies on Pseudo Boolean constraint based MaxSAT solvers. Experimental results show the effectiveness of both techniques on a large set of benchmarks from a hardware security application and from the 2019 MaxSAT Evaluation. In particular for the hardest of the application benchmarks, the solver Pacose with GBMO and TrimMaxSAT performs best compared to the MaxSAT Evaluation solvers of 2019. For the benchmarks of the 2019 MaxSAT Evaluation, we show that with the proposed techniques the top solver combination solves significantly more instances.
For the entire collection see [Zbl 1471.68017].Solving advanced argumentation problems with answer set programminghttps://zbmath.org/1472.681862021-11-25T18:46:10.358925Z"Brewka, Gerhard"https://zbmath.org/authors/?q=ai:brewka.gerhard"Diller, Martin"https://zbmath.org/authors/?q=ai:diller.martin"Heissenberger, Georg"https://zbmath.org/authors/?q=ai:heissenberger.georg"Linsbichler, Thomas"https://zbmath.org/authors/?q=ai:linsbichler.thomas"Woltran, Stefan"https://zbmath.org/authors/?q=ai:woltran.stefanSummary: Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labeled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from ADFs and GRAPPA to ASP. More specifically, we provide reductions for the five main ADF semantics of admissible, complete, preferred, grounded, and stable interpretations, and exemplify how these reductions need to be adapted for GRAPPA for the admissible, complete, and preferred semantics.A logic-based framework leveraging neural networks for studying the evolution of neurological disordershttps://zbmath.org/1472.681872021-11-25T18:46:10.358925Z"Calimeri, Francesco"https://zbmath.org/authors/?q=ai:calimeri.francesco"Cauteruccio, Francesco"https://zbmath.org/authors/?q=ai:cauteruccio.francesco"Cinelli, Luca"https://zbmath.org/authors/?q=ai:cinelli.luca"Marzullo, Aldo"https://zbmath.org/authors/?q=ai:marzullo.aldo"Stamile, Claudio"https://zbmath.org/authors/?q=ai:stamile.claudio"Terracina, Giorgio"https://zbmath.org/authors/?q=ai:terracina.giorgio"Durand-Dubief, Françoise"https://zbmath.org/authors/?q=ai:durand-dubief.francoise"Sappey-Marinier, Dominique"https://zbmath.org/authors/?q=ai:sappey-marinier.dominiqueSummary: Deductive formalisms have been strongly developed in recent years; among them, answer set programming (ASP) gained some momentum and has been lately fruitfully employed in many real-world scenarios. Nonetheless, in spite of a large number of success stories in relevant application areas, and even in industrial contexts, deductive reasoning cannot be considered the ultimate, comprehensive solution to artificial intelligence; indeed, in several contexts, other approaches result to be more useful. Typical bioinformatics tasks, for instance classification, are currently carried out mostly by machine learning (ML)-based solutions.
In this paper, we focus on the relatively new problem of analyzing the \textit{evolution} of neurological disorders. In this context, ML approaches already demonstrated to be a viable solution for classification tasks; here, we show how ASP can play a relevant role in the brain evolution simulation task. In particular, we propose a general and extensible framework to support physiciansCharacterizing boundedness in chase variantshttps://zbmath.org/1472.681882021-11-25T18:46:10.358925Z"Delivorias, Stathis"https://zbmath.org/authors/?q=ai:delivorias.stathis"Leclère, Michel"https://zbmath.org/authors/?q=ai:leclere.michel"Mugnier, Marie-Laure"https://zbmath.org/authors/?q=ai:mugnier.marie-laure"Ulliana, Federico"https://zbmath.org/authors/?q=ai:ulliana.federicoSummary: Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the \(k\)-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of \(k\)-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.A comparative study of some central notions of \(\mathit{ASPIC}^+\) and \textit{DeLP}https://zbmath.org/1472.681892021-11-25T18:46:10.358925Z"García, Alejandro J."https://zbmath.org/authors/?q=ai:garcia.alejandro-javier"Prakken, Henry"https://zbmath.org/authors/?q=ai:prakken.henry"Simari, Guillermo R."https://zbmath.org/authors/?q=ai:simari.guillermo-ricardoSummary: This paper formally compares some central notions from two well-known formalisms for rule-based argumentation, \textit{DeLP} and \(\mathit{ASPIC}^+\). The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out that \textit{DeLP}'s definitions are intuitively appealing but that they may not fully comply with Caminada and Amgoud's rationality postulates of strict closure and indirect consistency. For some special cases, the \textit{DeLP} definitions are shown to fare better than \(\mathit{ASPIC}^+\). Next, it is argued that there are reasons to consider a variant of \textit{DeLP} with grounded semantics, since in some examples its current notion of warrant arguably has counterintuitive consequences and may lead to sets of warranted arguments that are not admissible. Finally, under some minimality and consistency assumptions on \(\mathit{ASPIC}^+\) arguments, a one-to-many correspondence between \(\mathit{ASPIC}^+\) arguments and \textit{DeLP} arguments is identified in such a way that if the \textit{DeLP} warranting procedure is changed to grounded semantics, then 's \textit{DeLP} notion of warrant and \(\mathit{ASPIC}^+\)'s notion of justification are equivalent. This result is proven for three alternative definitions of attack.Restricted chase termination for existential rules: a hierarchical approach and experimentationhttps://zbmath.org/1472.681902021-11-25T18:46:10.358925Z"Karimi, Arash"https://zbmath.org/authors/?q=ai:karimi.arash"Zhang, Heng"https://zbmath.org/authors/?q=ai:zhang.heng"You, Jia-Huai"https://zbmath.org/authors/?q=ai:you.jia-huaiSummary: The chase procedure for existential rules is an indispensable tool for several database applications, where its termination guarantees the decidability of these tasks. Most previous studies have focused on the skolem chase variant and its termination analysis. It is known that the restricted chase variant is a more powerful tool in termination analysis provided a database is given. But all-instance termination presents a challenge since the critical database and similar techniques do not work. In this paper, we develop a novel technique to characterize the activeness of all possible cycles of a certain length for the restricted chase, which leads to the formulation of a framework of parameterized classes of the finite restricted chase, called \(k\)-\textsf{safe}\((\Phi)\) rule sets. This approach applies to any class of finite skolem chase identified with a condition of acyclicity. More generally, we show that the approach can be applied to the hierarchy of \textit{bounded rule sets} previously only defined for the skolem chase. Experiments on a collection of ontologies from the web show the applicability of the proposed methods on real-world ontologies.Rethinking defeasible reasoning: a scalable approachhttps://zbmath.org/1472.681912021-11-25T18:46:10.358925Z"Maher, Michael J."https://zbmath.org/authors/?q=ai:maher.michael-j"Tachmazidis, Ilias"https://zbmath.org/authors/?q=ai:tachmazidis.ilias"Antoniou, Grigoris"https://zbmath.org/authors/?q=ai:antoniou.grigoris"Wade, Stephen"https://zbmath.org/authors/?q=ai:wade.stephen"Cheng, Long"https://zbmath.org/authors/?q=ai:cheng.longSummary: Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks, and social media. Analytics in terms of defeasible reasoning -- for example, for decision making -- could provide richer knowledge of the underlying domain. Traditionally, defeasible reasoning has focused on complex knowledge structures over small to medium amounts of data, but recent research efforts have attempted to parallelize the reasoning process over theories with large numbers of facts. Such work has shown that traditional defeasible logics come with overheads that limit scalability. In this work, we design a new logic for defeasible reasoning, thus ensuring scalability by design. We establish several properties of the logic, including its relation to existing defeasible logics. Our experimental results indicate that our approach is indeed scalable and defeasible reasoning can be applied to billions of facts.A hybrid of tense logic \(\mathrm{S}4_\mathrm{T}\) and multi-agent logic with interacting agentshttps://zbmath.org/1472.681922021-11-25T18:46:10.358925Z"Rybakov, Vladimir V."https://zbmath.org/authors/?q=ai:rybakov.vladimir-vladimirovich"Babenyshev, Sergej V."https://zbmath.org/authors/?q=ai:babenyshev.sergej-vSummary: In this paper we introduce a temporal multi-agent logic \(\mathrm{S}4_\mathrm{T}^{\mathcal{IA}}\), which implements interacting agents. Logic \(\mathrm{S}4_\mathrm{T}^{\mathcal{IA}}\) is defined semantically as the set of all formulas of the appropriate propositional language that are valid in special Kripke models. The models are based on S4-like time frames, i.e., with reflexive and transitive time-accessibility relations. Agents knowledge-accessibility relations \(R_i\), defined independently for each individual agent, are S5-relations on \(R\)-time clusters, and interaction of the agents consists of passing knowledge along arbitrary paths of such relations. The key result of the paper is an algorithm for checking satisfiability and recognizing theorems of \(\mathrm{S}4_\mathrm{T}^{\mathcal{IA}}\). We also prove the effective finite model property for the logic \(\mathrm{S}4_\mathrm{T}^{\mathcal{IA}}\).Logical inference on the base of optimal subset of mixed diagnostic tests for intelligent systemshttps://zbmath.org/1472.681932021-11-25T18:46:10.358925Z"Yankovskaya, A. E."https://zbmath.org/authors/?q=ai:yankovskaya.anna-e"Gedike, A. I."https://zbmath.org/authors/?q=ai:gedike.a-iSummary: It is proposed to realize logical inference in intelligent systems on the base of mixed diagnostic tests (MDT) consisting of an optimal combination of unconditional and conditional components. For this purpose the tree of MDT is constructed on the base an optimal subset (OS) of unconditional irredundant diagnostic tests (UIDT). The criteria of considering the sequence for UIDT as well as features involved in each of them are stated, which results in enumeration reduction and, as a rule, allows MDT construction from not all UIDT in an UIDT OS. Logical inference is performed along all MDT in the process of MDT tree construction. Matrix model of data and knowledge representation, the algorithm of MDT tree construction and logical inference regarding the object under investigation are given. At the present time logical inference on the base of MDT is realized in intelligent software tool IMSLOG.Probabilistic DL reasoning with pinpointing formulas: a Prolog-based approachhttps://zbmath.org/1472.681942021-11-25T18:46:10.358925Z"Zese, Riccardo"https://zbmath.org/authors/?q=ai:zese.riccardo"Cota, Giuseppe"https://zbmath.org/authors/?q=ai:cota.giuseppe"Lamma, Evelina"https://zbmath.org/authors/?q=ai:lamma.evelina"Bellodi, Elena"https://zbmath.org/authors/?q=ai:bellodi.elena"Riguzzi, Fabrizio"https://zbmath.org/authors/?q=ai:riguzzi.fabrizioSummary: When modeling real-world domains, we have to deal with information that is incomplete or that comes from sources with different trust levels. This motivates the need for managing uncertainty in the Semantic Web. To this purpose, we introduced a probabilistic semantics, named DISPONTE, in order to combine description logics (DLs) with probability theory. The probability of a query can be then computed from the set of its explanations by building a Binary Decision Diagram (BDD). The set of explanations can be found using the \textit{tableau algorithm}, which has to handle non-determinism. Prolog, with its efficient handling of non-determinism, is suitable for implementing the tableau algorithm. TRILL and \(\mathrm{TRILL}^{P}\) are systems offering a Prolog implementation of the tableau algorithm. \(\mathrm{TRILL}^{P}\) builds a \textit{pinpointing formula} that compactly represents the set of explanations and can be directly translated into a BDD. Both reasoners were shown to outperform state-of-the-art DL reasoners. In this paper, we present an improvement of \(\mathrm{TRILL}^{P}\), named TORNADO, in which the BDD is directly built during the construction of the tableau, further speeding up the overall inference process. An experimental comparison shows the effectiveness of TORNADO. All systems can be tried online in the TRILL on SWISH web application at \url{http://trill.ml.unife.it/}.Semantic DMN: formalizing and reasoning about decisions in the presence of background knowledgehttps://zbmath.org/1472.681952021-11-25T18:46:10.358925Z"Calvanese, Diego"https://zbmath.org/authors/?q=ai:calvanese.diego"Montali, Marco"https://zbmath.org/authors/?q=ai:montali.marco"Dumas, Marlon"https://zbmath.org/authors/?q=ai:dumas.marlon"Maggi, Fabrizio M."https://zbmath.org/authors/?q=ai:maggi.fabrizio-mSummary: The Decision Model and Notation (DMN) is a recent Object Management Group standard for the elicitation and representation of decision models and for managing their interconnection with business processes. DMN builds on the notion of decision tables and their combination into more complex decision requirements graphs (DRGs), which bridge between business process models and decision logic models. DRGs may rely on additional, external business knowledge models, whose functioning is not part of the standard. In this work, we consider one of the most important types of business knowledge, namely, background knowledge that conceptually accounts for the structural aspects of the domain of interest, and propose \textit{decision knowledge bases} (DKBs), which semantically combine DRGs modeled in DMN, and domain knowledge captured by means of first-order logic with datatypes. We provide a logic-based semantics for such an integration, and formalize different DMN reasoning tasks for DKBs. We then consider background knowledge formulated as a description logic (DL) ontology with datatypes, and show how the main verification tasks for DMN in this enriched setting can be formalized as standard DL reasoning services and actually carried out in \textsc{ExpTime}. We discuss the effectiveness of our framework on a case study in maritime security.Use case analysis based on formal methods: an empirical studyhttps://zbmath.org/1472.681962021-11-25T18:46:10.358925Z"Oliveira, Marcos"https://zbmath.org/authors/?q=ai:oliveira.marcos-william-da-silva"Ribeiro, Leila"https://zbmath.org/authors/?q=ai:ribeiro.leila"Cota, Érika"https://zbmath.org/authors/?q=ai:cota.erika"Duarte, Lucio Mauro"https://zbmath.org/authors/?q=ai:duarte.lucio-mauro"Nunes, Ingrid"https://zbmath.org/authors/?q=ai:nunes.ingrid"Reis, Filipe"https://zbmath.org/authors/?q=ai:reis.filipeSummary: Use cases (UC) are a popular way of describing system behavior and represent important artifacts for system design, analysis, and evolution. Hence, UC quality impacts the overall system quality and defect rates. However, they are presented in natural language, which is usually the cause of issues related to imprecision, ambiguity, and incompleteness. We present the results of an empirical study on the formalization of UCs as graph transformation models (GTs) with the goal of running tool-supported analyses on them and revealing possible errors (treated as open issues). We describe initial steps for a translation from a UC to a GT, how to use an existing tool to analyze the produced GT, and present some diagnostic feedback based on the results of these analyses and the possible level of severity of the detected problems. To evaluate the effectiveness of the translation and of the analyses in identifying problems in UCs, we applied our approach on a set of real UC descriptions obtained from a software developer company and measured the results using a well-known metric. The final results demonstrate that this approach can reveal real problems that could otherwise go undetected and, thus, help improve the quality of the UCs.
For the entire collection see [Zbl 1327.68013].FRS: a simple knowledge graph embedding model for entity predictionhttps://zbmath.org/1472.681972021-11-25T18:46:10.358925Z"Wang, Lifang"https://zbmath.org/authors/?q=ai:wang.lifang"Lu, Xinyu"https://zbmath.org/authors/?q=ai:lu.xinyu"Jiang, Zejun"https://zbmath.org/authors/?q=ai:jiang.zejun"Zhang, Zhikai"https://zbmath.org/authors/?q=ai:zhang.zhikai"Li, Ronghan"https://zbmath.org/authors/?q=ai:li.ronghan"Zhao, Meng"https://zbmath.org/authors/?q=ai:zhao.meng"Chen, Daqing"https://zbmath.org/authors/?q=ai:chen.daqingSummary: Entity prediction is the task of predicting a missing entity that has a specific relation-ship with another given entity. Researchers usually use knowledge graphs embedding (KGE) methods to embed triples into continuous vectors for computation and perform the tasks of entity prediction. However, KGE models tend to use simple operations to refactor entities and relationships, resulting in insufficient interaction of components of knowledge graphs (KGs), thus limiting the performance of the entity prediction model. In this paper, we propose a new entity prediction model called FRS (Feature Refactoring Scoring) to alleviate the problem of insufficient interaction and solve information incom-pleteness problems in the KGs. Different from the traditional KGE methods of directly using simple operations, the FRS model innovatively provides the procedure of feature processing in the entity prediction tasks, realizing the alignment of entities and relationships in the same feature space and improving the performance of entity prediction model. Although FRS is a simple three-layer network, we find that our own model outperforms state-of-the-art KGC methods in FB15K and WN18. Through extensive experiments on FRS, we discover several insights. For example, the effect of embedding size and negative candidate sampling probability on experimental results is in reverse.A new safety assessment method of type-2 prediction sets based on credibility degree of datahttps://zbmath.org/1472.681982021-11-25T18:46:10.358925Z"Wang, Xiaoxia"https://zbmath.org/authors/?q=ai:wang.xiaoxia"Yang, Fengbao"https://zbmath.org/authors/?q=ai:yang.fengbao"Zhu, Boxiu"https://zbmath.org/authors/?q=ai:zhu.boxiuSummary: In this paper, a safety assessment method of type-2 prediction sets based on credibility degree is proposed. The aim is to solve the misjudgment problem for lacking the credibility of data in safety assessment. Firstly, define the type-2 prediction sets and its relevant concepts on the basis of possibility distribution and credibility distribution, and subsequently propose the calculation method of similarity measure and its center between type-2 prediction set would be proposed subsequently. Secondly, two operations need to be conducted respectively. One is establishing joint distribution of disparate data based on the assessment requirements and safety rating scale of disparate data. The other is using weighted fusion method to fuse the disparate data on the distribution of type-2. Finally, compute the similarity measure between the fusion distribution and its safety rating scale distribution, determine the center of mass position in the joint plane scale and determine safe level. The experiment results show that the method proposed in this paper used in tailings dam of safety determination is effective to reduce the granularity of evaluation results to avoid the misjudgment problems, and also facilitates the accurate judge of dam safety level.Application of granular computing in rough rule extractionhttps://zbmath.org/1472.681992021-11-25T18:46:10.358925Z"Yan, Hongcan"https://zbmath.org/authors/?q=ai:yan.hongcan"Wang, Huifang"https://zbmath.org/authors/?q=ai:wang.huifang"Guo, Shasha"https://zbmath.org/authors/?q=ai:guo.shashaSummary: Rule extraction is a hot research topic in data mining, especially in the fields of decision support system, artificial intelligence, recommendation system, etc., where attribute reduction and minimal rule set extraction are the key links. Most importantly, the efficiency of extraction is determined by its application. The rough set model and granular computing theory are applied to the decision rule reduction, and granular computing model based on concept lattice is built. The decision table is granulated by granulation function; the grain of membership and the concept granular set construction algorithm generate the initial concept granular set. Therefore, attribute reduction can be realized by the distinguish operator of concept granule, and decision rule extraction can be achieved by visualization of stable concept granule lattice. Moreover we discuss the effect of selecting graining function threshold to generate the concept granule. Finally, the effectiveness and efficiency of the algorithm is proved by empirical research, and the method is easier to be applied to computer programming.Partially consistent reduction based on discernibility information tree in interval-valued fuzzy ordered information systems with decisionhttps://zbmath.org/1472.682002021-11-25T18:46:10.358925Z"Zhang, Jia"https://zbmath.org/authors/?q=ai:zhang.jia"Zhang, Xiaoyan"https://zbmath.org/authors/?q=ai:zhang.xiaoyan.3Summary: Attribute reduction is a hot issue in the field of rough set research in recent years, among which identifiable matrix is one of the most commonly used methods for attribute reduction. However, the elements of identifiable attribute set in identifiable matrix are interlaced and repeated, which brings a lot of inconvenience for reduction. Therefore, a novel method based on discernibility information tree (\textit{DIT}) proposed by Jiang to overcome the above issues. On this basis, this paper constructs the discernibility information tree (\textit{DIT}\(^\succeq\)) under the dominance relation and generalizes it to the interval-valued fuzzy ordered information system with decision (\textit{IVFOIS}\(_d\)). Furthermore, combining the discernibility information tree of \textit{IVFOIS}\(_d\) with the partially consistent function, a complete partially consistent reduction algorithm based on \textit{DIT}\(^\succeq\) is presented. At the same time, some related properties and the complexity of the algorithm are studied. Finally, the effectiveness and accuracy of the \textit{DIT}\(^\succeq\)-based reduction method are domonstrated by a concrete example.Learning 3D shape completion under weak supervisionhttps://zbmath.org/1472.682012021-11-25T18:46:10.358925Z"Stutz, David"https://zbmath.org/authors/?q=ai:stutz.david"Geiger, Andreas"https://zbmath.org/authors/?q=ai:geiger.andreasSummary: We address the problem of 3D shape completion from sparse and noisy point clouds, a fundamental problem in computer vision and robotics. Recent approaches are either data-driven or learning-based: Data-driven approaches rely on a shape model whose parameters are optimized to fit the observations; Learning-based approaches, in contrast, avoid the expensive optimization step by learning to directly predict complete shapes from incomplete observations in a fully-supervised setting. However, full supervision is often not available in practice. In this work, we propose a weakly-supervised learning-based approach to 3D shape completion which neither requires slow optimization nor direct supervision. While we also learn a shape prior on synthetic data, we amortize, i.e., \textit{learn}, maximum likelihood fitting using deep neural networks resulting in efficient shape completion without sacrificing accuracy. On synthetic benchmarks based on ShapeNet
[\textit{A. X. Chang} et al., ``ShapeNet: an information-rich 3D model repository'', Preprint, \url{arXiv:1512.03012}]
and ModelNet
[\textit{Z. Wu} et al., ``3D ShapeNets: a deep representation for volumetric shapes'', in: Proceedings of IEEE conference on computer vision and pattern recognition, CVPR'15. Los Alamitos, CA: IEEE Computer Society. 1912--1920 (2015; \url{doi:10.1109/CVPR.2015.7298801})]
as well as on real robotics data from KITTI
[the second author et al., ``Are we ready for autonomous driving? The KITTI vision benchmark suite'', in: Proceedings of IEEE conference on computer vision and pattern recognition, CVPR'12. Los Alamitos, CA: IEEE Computer Society. 3354--3361 (2012; \url{doi:10.1109/CVPR.2012.6248074})]
and Kinect
[\textit{B. Yang} et al., ``Dense 3D object reconstruction from a single depth view'', IEEE Trans. Pattern Anal. Mach. Intell. 41, No. 12, 2820--2834 (2019; \url{doi:10.1109/TPAMI.2018.2868195})]
we demonstrate that the proposed amortized maximum likelihood approach is able to compete with the fully supervised baseline of
\textit{A. Dai} et al. [``Shape completion using 3D-encoder-predictor CNNs and shape synthesis'', in: Proceedings of IEEE conference on computer vision and pattern recognition, CVPR'17. Los Alamitos, CA: IEEE Computer Society. 6545--6554 (2017; \url{doi:10.1109/CVPR.2017.693})]
and outperforms the data-driven approach of
\textit{F. Engelmann} et al. [``Joint object pose estimation and shape reconstruction in urban street scenes using 3D shape priors'', Lect. Notes Comput. Sci. 9796, 219--230 (2016; \url{doi:10.1007/978-3-319-45886-1_18})],
while requiring less supervision and being significantly faster.Competitive local routing with constraintshttps://zbmath.org/1472.682022021-11-25T18:46:10.358925Z"Bose, Prosenjit"https://zbmath.org/authors/?q=ai:bose.prosenjit-k"Fagerberg, Rolf"https://zbmath.org/authors/?q=ai:fagerberg.rolf"van Renssen, André"https://zbmath.org/authors/?q=ai:van-renssen.andre"Verdonschot, Sander"https://zbmath.org/authors/?q=ai:verdonschot.sanderSummary: Let \(P\) be a set of \(n\) vertices in the plane and \(S\) a set of non-crossing line segments between vertices in \(P\), called constraints. Two vertices are visible if the straight line segment connecting them does not properly intersect any constraints. The constrained \(\theta_m\)-graph is constructed by partitioning the plane around each vertex into \(m\) disjoint cones with aperture \(\theta = 2\pi /m\), and adding an edge to the `closest' visible vertex in each cone. We consider how to route on the constrained \(\theta_6\)-graph. We first show that no deterministic 1-local routing algorithm is \(o(\sqrt{n})\)-competitive on all pairs of vertices of the constrained \(\theta_6\)-graph. After that, we show how to route between any two visible vertices using only 1-local information, while guaranteeing that the returned path has length at most 2 times the Euclidean distance between the source and destination. To the best of our knowledge, this is the first local routing algorithm in the
constrained setting with guarantees on the path length.
For the entire collection see [Zbl 1326.68015].Model-based classification of trajectorieshttps://zbmath.org/1472.682032021-11-25T18:46:10.358925Z"Buchin, Maike"https://zbmath.org/authors/?q=ai:buchin.maike"Sijben, Stef"https://zbmath.org/authors/?q=ai:sijben.stefSummary: We present algorithms for classifying trajectories based on a movement model parameterized by a single parameter, like the Brownian bridge movement model. Classification is the problem of assigning trajectories to classes of similar movement characteristics. For instance, the set of trajectories might be the subtrajectories resulting from segmenting a trajectory, thus identifying movement phases. We give an efficient algorithm to compute the optimal classification for a discrete set of parameter values. We also show that classification is NP-hard if the parameter values are allowed to vary continuously and present an algorithm that solves the problem in polynomial time under mild assumptions on the input.
For the entire collection see [Zbl 1326.68015].Size-dependent tile self-assembly: constant-height rectangles and stabilityhttps://zbmath.org/1472.682042021-11-25T18:46:10.358925Z"Fekete, Sándor P."https://zbmath.org/authors/?q=ai:fekete.sandor-p"Schweller, Robert T."https://zbmath.org/authors/?q=ai:schweller.robert-t"Winslow, Andrew"https://zbmath.org/authors/?q=ai:winslow.andrewSummary: We introduce a new model of algorithmic tile self-assembly called \textit{size-dependent assembly}. In previous models, supertiles are stable when the total strength of the bonds between any two halves exceeds some constant temperature. In this model, this constant temperature requirement is replaced by an nondecreasing \textit{temperature function} \(\tau : \mathbb {N} \rightarrow \mathbb {N}\) that depends on the size of the smaller of the two halves. This generalization allows supertiles to become unstable and break apart, and captures the increased forces that large structures may place on the bonds holding them together.
We demonstrate the power of this model in two ways. First, we give fixed tile sets that assemble constant-height rectangles and squares of arbitrary input size given an appropriate temperature function. Second, we prove that deciding whether a supertile is stable is coNP-complete. Both results contrast with known results for fixed temperature.
For the entire collection see [Zbl 1326.68015].The VC-dimension of visibility on the boundary of a simple polygonhttps://zbmath.org/1472.682052021-11-25T18:46:10.358925Z"Gibson, Matt"https://zbmath.org/authors/?q=ai:gibson.matthew-r"Krohn, Erik"https://zbmath.org/authors/?q=ai:krohn.erik-a"Wang, Qing"https://zbmath.org/authors/?q=ai:wang.qing.4|wang.qing.1|wang.qing.2|wang.qing.3Summary: In this paper, we prove that the VC-Dimension of visibility on the boundary of a simple polygon is exactly 6. Our result is the first tight bound for any variant of the VC-Dimension problem regarding simple polygons. Our upper bound proof is based off several structural lemmas which may be of independent interest to researchers studying geometric visibility.
For the entire collection see [Zbl 1326.68015].Linear-time algorithms for the farthest-segment Voronoi diagram and related tree structureshttps://zbmath.org/1472.682062021-11-25T18:46:10.358925Z"Khramtcova, Elena"https://zbmath.org/authors/?q=ai:khramtcova.elena"Papadopoulou, Evanthia"https://zbmath.org/authors/?q=ai:papadopoulou.evanthiaSummary: We present linear-time algorithms to construct tree-like Voronoi diagrams with disconnected regions after the sequence of their faces along an enclosing boundary (or at infinity) is known. We focus on the farthest-segment Voronoi diagram, however, our techniques are also applicable to constructing the order-\((k{+}1)\) subdivision within an order-\(k\) Voronoi region of segments and updating a nearest-neighbor Voronoi diagram of segments after deletion of one site. Although tree-structured, these diagrams illustrate properties surprisingly different from their counterparts for points. The sequence of their faces along the relevant boundary forms a Davenport-Schinzel sequence of order \(\geq 2\). Once this sequence is known, we show how to compute the corresponding Voronoi diagram in linear time, expected or deterministic, augmenting the existing linear-time frameworks for points in convex position with the ability to handle non-point sites and multiple Voronoi faces.
For the entire collection see [Zbl 1326.68015].The 2-center problem in a simple polygonhttps://zbmath.org/1472.682072021-11-25T18:46:10.358925Z"Oh, Eunjin"https://zbmath.org/authors/?q=ai:oh.eunjin"De Carufel, Jean-Lou"https://zbmath.org/authors/?q=ai:de-carufel.jean-lou"Ahn, Hee-Kap"https://zbmath.org/authors/?q=ai:ahn.hee-kapSummary: The geodesic \(k\)-center problem in a simple polygon with \(n\) vertices consists in the following. Find \(k\) points, called \textit{centers}, in the polygon to minimize the maximum geodesic distance from any point of the polygon to its closest center. In this paper, we focus on the case where \(k=2\) and present an exact algorithm that returns an optimal geodesic 2-center in \(O(n^2\log ^2 n)\) time.
For the entire collection see [Zbl 1326.68015].An optimal algorithm for tiling the plane with a translated polyominohttps://zbmath.org/1472.682082021-11-25T18:46:10.358925Z"Winslow, Andrew"https://zbmath.org/authors/?q=ai:winslow.andrewSummary: We give a \(O(n)\)-time algorithm for determining whether translations of a polyomino with \(n\) edges can tile the plane. The algorithm is also a \(O(n)\)-time algorithm for enumerating all regular tilings, and we prove that at most \(\varTheta (n)\) such tilings exist.
For the entire collection see [Zbl 1326.68015].Geometric matching algorithms for two realistic terrainshttps://zbmath.org/1472.682092021-11-25T18:46:10.358925Z"Yoon, Sang Duk"https://zbmath.org/authors/?q=ai:yoon.sang-duk"Kim, Min-Gyu"https://zbmath.org/authors/?q=ai:kim.mingyu"Son, Wanbin"https://zbmath.org/authors/?q=ai:son.wanbin"Ahn, Hee-Kap"https://zbmath.org/authors/?q=ai:ahn.hee-kapSummary: We consider a geometric matching of two realistic terrains, each of which is modeled as a piecewise-linear bivariate function. For two realistic terrains \(f\) and \(g\) where the domain of \(g\) is relatively larger than that of \(f\), we seek to find a translated copy \(f'\) of \(f\) such that the domain of \(f'\) is a sub-domain of \(g\) and the \(L_\infty \) or the \(L_1\) distance of \(f'\) and \(g\) restricted to the domain of \(f'\) is minimized. In this paper, we show a tight bound on the number of different combinatorial structures that \(f\) and \(g\) can have under translation in their projections on the \(xy\)-plane. We give a deterministic algorithm and a randomized algorithm that compute an optimal translation of \(f\) with respect to \(g\) under \(L_\infty \) metric. We also give a deterministic algorithm that computes an optimal translation of \(f\) with respect to \(g\) under \(L_1\) metric.
For the entire collection see [Zbl 1326.68015].On image restoration from random sampling noisy frequency data with regularizationhttps://zbmath.org/1472.682102021-11-25T18:46:10.358925Z"Liu, Xiaoman"https://zbmath.org/authors/?q=ai:liu.xiaoman"Liu, Jijun"https://zbmath.org/authors/?q=ai:liu.jijunSummary: Consider the image restoration using random sampling noisy frequency data by total variation regularization. By exploring image sparsity property under wavelet expansion, we establish an optimization model with two regularizing terms specifying image sparsity and edge preservation on the restored image. The choice strategy for the regularizing parameters is rigorously set up together with corresponding error estimate on the restored image. The cost functional with data-fitting in the frequency domain is minimized using the Bregman iteration scheme. By deriving the gradient of the cost functional explicitly, the minimizer of the cost functional at each Bregman step is also generated by an inner iteration process with Tikhonov regularization, which is implemented stably and efficiently due to the special structure of the regularizing iterative matrix. Numerical tests are given to show the validity of the proposed scheme.Cam-based HDR color and tone reproduction for enhanced stereoscopic display viewinghttps://zbmath.org/1472.682112021-11-25T18:46:10.358925Z"Song, Inho"https://zbmath.org/authors/?q=ai:song.inho"Kwon, Hyuk-Ju"https://zbmath.org/authors/?q=ai:kwon.hyuk-ju"Kim, Tae-Kyu"https://zbmath.org/authors/?q=ai:kim.tae-kyu"Wei, Qun"https://zbmath.org/authors/?q=ai:wei.qun"Lee, Sung-Hak"https://zbmath.org/authors/?q=ai:lee.sung-hakSummary: Brightness degradation occcurs in almost all stereoscopic displays (three-dimensional (3D) displays). When the brightness of the display is lowered in 3D mode, the lightness, hue, and chroma of the color attributes are the same, but the colorfulness becomes lower than in the two-dimensional (2D) mode. In this paper, we propose a color appearance model-based (CAM-based) high dynamic range (HDR) color and tone reproduction method that compensates for the loss of colorfulness and the change of visual contrast due to the brightness reduction of the 3D display. As a result of applying the proposed method, it is confirmed that an HDR image is reproduced in 3D mode, the tone mapping is processed appropriately in 3D viewing condition and the colorfulness if improved to that of 2D mode.The secretary problem with a choice functionhttps://zbmath.org/1472.682122021-11-25T18:46:10.358925Z"Kawase, Yasushi"https://zbmath.org/authors/?q=ai:kawase.yasushiSummary: In the classical secretary problem, a decision-maker is willing to hire the best secretary out of \(n\) applicants that arrive in a random order, and the goal is to maximize the probability of choosing the best applicant. In this paper, we introduce the secretary problem with a choice function. The choice function represents the preference of the decision-maker. In this problem, the decision-maker hires some applicants, and the goal is to maximize the probability of choosing the best set of applicants defined by the choice function. We see that the secretary problem with a path-independent choice function generalizes secretary version of the stable matching problem, the maximum weight bipartite matching problem, and the maximum weight base problem in a matroid. When the choice function is path-independent, we provide an algorithm that succeeds with probability at least \(1/e^k\) where \(k\) is the maximum size of the choice, and prove that this is the best possible. Moreover, for the non-path-independent case, we prove that the success probability goes to arbitrary small for any algorithm even if the maximum size of the choice is 2.
For the entire collection see [Zbl 1326.68015].Randomized minmax regret for combinatorial optimization under uncertaintyhttps://zbmath.org/1472.682132021-11-25T18:46:10.358925Z"Mastin, Andrew"https://zbmath.org/authors/?q=ai:mastin.andrew"Jaillet, Patrick"https://zbmath.org/authors/?q=ai:jaillet.patrick"Chin, Sang"https://zbmath.org/authors/?q=ai:chin.sangSummary: The minmax regret problem for combinatorial optimization under uncertainty can be viewed as a zero-sum game played between an optimizing player and an adversary, where the optimizing player selects a solution and the adversary selects costs with the intention of maximizing the regret of the player. The conventional minmax regret model considers only deterministic solutions/strategies, and minmax regret versions of most polynomial solvable problems are NP-hard. In this paper, we consider a randomized model where the optimizing player selects a probability distribution (corresponding to a mixed strategy) over solutions and the adversary selects costs with knowledge of the player's distribution, but not its realization. We show that under this randomized model, the minmax regret version of any polynomial solvable combinatorial problem becomes polynomial solvable. This holds true for both interval and discrete scenario representations of uncertainty. Using the randomized model, we show new proofs
of existing approximation algorithms for the deterministic model based on primal-dual approaches. We also determine integrality gaps of minmax regret formulations, giving tight bounds on the limits of performance gains from randomization. Finally, we prove that minmax regret problems are NP-hard under general convex uncertainty.
For the entire collection see [Zbl 1326.68015].On the minimum cost range assignment problemhttps://zbmath.org/1472.682142021-11-25T18:46:10.358925Z"Carmi, Paz"https://zbmath.org/authors/?q=ai:carmi.paz"Chaitman-Yerushalmi, Lilach"https://zbmath.org/authors/?q=ai:chaitman-yerushalmi.lilachSummary: We study the problem of assigning transmission ranges to radio stations placed in a \(d\)-dimensional (\(d\)-D) Euclidean space in order to achieve a strongly connected communication network with minimum total cost, where the cost of transmitting in range \(r\) is proportional to \(r^\alpha \). While this problem can be solved optimally in 1D, in higher dimensions it is known to be NP-hard for any \(\alpha \geq 1\).
For the 1D version of the problem and \(\alpha \geq 1\), we propose a new approach that achieves an exact \(O(n^2)\)-time algorithm. This improves the running time of the best known algorithm by a factor of \(n\). Moreover, we show that this new technique can be utilized for achieving a polynomial-time algorithm for finding the minimum cost range assignment in 1D whose induced communication graph is a \(t\)-spanner, for any \(t \geq 1\).
In higher dimensions, finding the optimal range assignment is NP-hard; however, it can be approximated within a constant factor. The best known
approximation ratio is for the case \(\alpha =1\), where the approximation ratio is 1.5. We show a new approximation algorithm that breaks the 1.5 ratio.
For the entire collection see [Zbl 1326.68015].A \(4+\epsilon\) approximation for \(k\)-connected subgraphshttps://zbmath.org/1472.682152021-11-25T18:46:10.358925Z"Nutov, Zeev"https://zbmath.org/authors/?q=ai:nutov.zeevSummary: We obtain approximation ratio \(4+\frac{2}{\ell}\approx 4+\frac{4\lg k}{\lg n-\lg k}\) for the (undirected) \(k\)-\textsc{Connected Subgraph} problem, where \(\ell=\lfloor\frac{\lg n-\lg k+1}{2\lg k+1} \rfloor\) is the largest integer such that \(2^{\ell-1}k^{2\ell+1}\leq n\). For large values of \(n\) this improves the ratio 6 of
\textit{J. Cheriyan} and \textit{L. A. Végh} [SIAM J. Comput. 43, No. 4, 1342--1362 (2014; Zbl 1303.05097)]
when \(n\geq k^3\) (the case \(\ell=1)\). Our result implies an fpt-approximation ratio \(4+\epsilon\) that matches (up to the ``\(+\epsilon\)'' term) the best known ratio 4 for \(k=6,7\) for both the general and the easier augmentation versions of the problem. Similar results are shown for the problem of covering an arbitrary symmetric crossing supermodular biset function.Approximation algorithms in the successive hitting set modelhttps://zbmath.org/1472.682162021-11-25T18:46:10.358925Z"Storandt, Sabine"https://zbmath.org/authors/?q=ai:storandt.sabineSummary: We introduce the successive Hitting Set model, where the set system is not given in advance but a set generator produces the sets that contain a specific element from the universe on demand. Despite incomplete knowledge about the set system, we show that several approximation algorithms for the conventional Hitting Set problem can be adopted to perform well in this model. We describe, and experimentally investigate, several scenarios where the new model is beneficial compared to the conventional one.
For the entire collection see [Zbl 1326.68015].Run generation revisited: what goes up may or may not come downhttps://zbmath.org/1472.682172021-11-25T18:46:10.358925Z"Bender, Michael A."https://zbmath.org/authors/?q=ai:bender.michael-a"McCauley, Samuel"https://zbmath.org/authors/?q=ai:mccauley.samuel"McGregor, Andrew"https://zbmath.org/authors/?q=ai:mcgregor.andrew"Singh, Shikha"https://zbmath.org/authors/?q=ai:singh.shikha"Vu, Hoa T."https://zbmath.org/authors/?q=ai:vu.hoa-tSummary: We revisit the classic problem of run generation. Run generation is the first phase of external-memory sorting, where the objective is to scan through the data, reorder elements using a small buffer of size \(M\), and output runs (contiguously sorted chunks of elements) that are as long as possible.
We develop algorithms for minimizing the total number of runs (or equivalently, maximizing the average run length) when the runs are allowed to be sorted or reverse sorted. We study the problem in the online setting, both with and without resource augmentation, and in the offline setting.
First, we analyze alternating-up-down replacement selection (runs alternate between sorted and reverse sorted), which was studied by Knuth as far back as 1963. We show that this simple policy is asymptotically optimal.
Next, we give online algorithms having smaller competitive ratios with resource augmentation. We demonstrate that performance can also be improved with a small amount of foresight. Lastly, we
present algorithms tailored for ``nearly sorted'' inputs which are guaranteed to have sufficiently long optimal runs.
For the entire collection see [Zbl 1326.68015].Streaming verification in data analysishttps://zbmath.org/1472.682182021-11-25T18:46:10.358925Z"Daruki, Samira"https://zbmath.org/authors/?q=ai:daruki.samira"Thaler, Justin"https://zbmath.org/authors/?q=ai:thaler.justin"Venkatasubramanian, Suresh"https://zbmath.org/authors/?q=ai:venkatasubramanian.sureshSummary: Streaming interactive proofs (SIPs) are a framework to reason about outsourced computation, where a data owner (the verifier) outsources a computation to the cloud (the prover), but wishes to verify the correctness of the solution provided by the cloud service. In this paper, we present streaming interactive proofs for problems in data analysis. We present protocols for clustering and shape fitting problems, as well as an improved protocol for rectangular matrix multiplication. The latter can in turn be used to verify \(k\) \textit{eigenvectors} of a (streamed) \(n \times n\) matrix.
In general, our solutions use polylogarithmic rounds of communication and polylogarithmic total communication and verifier space. For special cases (when optimality certificates can be verified easily), we present constant round protocols with similar costs. For rectangular matrix multiplication and eigenvector verification, our protocols work in the more restricted annotated data streaming model, and use sublinear (but not polylogarithmic) communication.
For the entire collection see [Zbl 1326.68015].Serving online requests with mobile servershttps://zbmath.org/1472.682192021-11-25T18:46:10.358925Z"Ghodselahi, Abdolhamid"https://zbmath.org/authors/?q=ai:ghodselahi.abdolhamid"Kuhn, Fabian"https://zbmath.org/authors/?q=ai:kuhn.fabianSummary: We study an online problem in which mobile servers have to be moved in order to efficiently serve at set of online requests. More formally, there is a set of \(n\) nodes and a set of \(k\) mobile servers that are placed at some of the nodes. Each node can potentially host several servers and the servers can be moved between the nodes. There are requests \(1,2,\ldots \) that are adversarially issued at nodes one at a time, where a request issued at time \(t\) needs to be served at all times \(t' \geq t\). The cost for serving the requests is a function of the number of servers and requests at the different nodes. The requirements on how to serve the requests are governed by two parameters \(\alpha \geq 1\) and \(\beta \geq 0\). An algorithm needs to guarantee that at all times, the total service cost remains within a multiplicative factor \(\alpha \) and an additive term \(\beta \) of the current optimal service cost.
We consider online algorithms for two different minimization objectives. We first
consider the natural problem of minimizing the total number of server movements. We show that in this case for every \(k\), the competitive ratio of every deterministic online algorithm needs to be at least \(\varOmega (n)\). Given this negative result, we then extend the minimization objective to also include the current service cost. We give almost tight bounds on the competitive ratio of the online problem where one needs to minimize the sum of the total number of movements and the current service cost. In particular, we show that at the cost of an additional additive term which is roughly linear in \(k\), it is possible to achieve a multiplicative competitive ratio of \(1+\varepsilon \) for every constant \(\varepsilon >0\).
For the entire collection see [Zbl 1326.68015].All-around near-optimal solutions for the online bin packing problemhttps://zbmath.org/1472.682202021-11-25T18:46:10.358925Z"Kamali, Shahin"https://zbmath.org/authors/?q=ai:kamali.shahin"López-Ortiz, Alejandro"https://zbmath.org/authors/?q=ai:lopez-ortiz.alejandroSummary: In this paper, we present algorithms with optimal average-case and close-to-best known worst-case performance for the classic online bin packing problem. It has long been observed that known bin packing algorithms with optimal average-case performance are not optimal in the worst-case. In particular, First Fit and Best Fit have optimal asymptotic average-case ratio of 1 but a worst-case competitive ratio of 1.7. The competitive ratio can be improved to 1.691 using the Harmonic algorithm. Further variations of this algorithm can push down the competitive ratio to 1.588. However, these algorithms have poor performance on average; in particular, Harmonic algorithm has average-case ratio of 1.27. In this paper, first we introduce a simple algorithm which we term Harmonic Match. This algorithm performs as well as Best Fit on average, i.e., it has an average-case ratio of 1. Moreover, the competitive ratio of the algorithm is as good as Harmonic, i.e., it converges to 1.691 which is an improvement
over
Best Fit and First Fit. We also introduce a different algorithm, termed as Refined Harmonic Match, which achieves an improved competitive ratio of 1.636 while maintaining the good average-case performance of Harmonic Match and Best Fit. Our experimental evaluations show that our proposed algorithms have comparable average-case performance with Best Fit and First Fit, and this holds also for sequences that follow distributions other than the uniform distribution.
For the entire collection see [Zbl 1326.68015].Online pairwise learning algorithmshttps://zbmath.org/1472.682212021-11-25T18:46:10.358925Z"Ying, Yiming"https://zbmath.org/authors/?q=ai:ying.yiming"Zhou, Ding-Xuan"https://zbmath.org/authors/?q=ai:zhou.dingxuanSummary: Pairwise learning usually refers to a learning task that involves a loss function depending on pairs of examples, among which the most notable ones are bipartite ranking, metric learning, and AUC maximization. In this letter we study an online algorithm for pairwise learning with a least-square loss function in an unconstrained setting of a reproducing kernel Hilbert space (RKHS) that we refer to as the Online Pairwise lEaRning Algorithm (OPERA). In contrast to existing works (Kar, Sriperumbudur, Jain, and Karnick, 2013; Wang, Khardon, Pechyony, and Jones, 2012), which require that the iterates are restricted to a bounded domain or the loss function is strongly convex, OPERA is associated with a non-strongly convex objective function and learns the target function in an unconstrained RKHS. Specifically, we establish a general theorem that guarantees the almost sure convergence for the last iterate of OPERA without any assumptions on the underlying distribution. Explicit convergence rates are derived under the condition of polynomially decaying step sizes. We also establish an interesting property for a family of widely used kernels in the setting of pairwise learning and illustrate the convergence results using such kernels. Our methodology mainly depends on the characterization of RKHSs using its associated integral operators and probability inequalities for random variables with values in a Hilbert space.Toehold DNA languages are regular (extended abstract)https://zbmath.org/1472.682222021-11-25T18:46:10.358925Z"Brandt, Sebastian"https://zbmath.org/authors/?q=ai:brandt.sebastian-f"Mattia, Nicolas"https://zbmath.org/authors/?q=ai:mattia.nicolas"Seidel, Jochen"https://zbmath.org/authors/?q=ai:seidel.jochen"Wattenhofer, Roger"https://zbmath.org/authors/?q=ai:wattenhofer.roger-pSummary: We explore a method of designing algorithms using two types of DNA strands, namely rule strands (rules) and input strands. Rules are fixed in advance, and their task is to bind with the input strands in order to produce an output. We present algorithms for divisibility and primality testing as well as for square root computation. We measure the complexity of our algorithms in terms of the necessary rule strands. Our three algorithms utilize a super-constant amount of complex rules.
Can one solve interesting problems using only few -- or at least simple -- rule strands? Our main result proves that restricting oneself to a constant number of rule strands is equivalent to deciding regular languages. More precisely, we show that an algorithm (possibly using infinitely many rule strands of arbitrary length) can merely decide regular languages if the structure of the rules themselves is simple, i.e., if the rule strands constitute a regular language.
For the entire collection see [Zbl 1326.68015].Subpolynomial trace reconstruction for random strings and arbitrary deletion probabilityhttps://zbmath.org/1472.682232021-11-25T18:46:10.358925Z"Holden, Nina"https://zbmath.org/authors/?q=ai:holden.nina"Pemantle, Robin"https://zbmath.org/authors/?q=ai:pemantle.robin"Peres, Yuval"https://zbmath.org/authors/?q=ai:peres.yuval"Zhai, Alex"https://zbmath.org/authors/?q=ai:zhai.alexSummary: The insertion-deletion channel takes as input a bit string \(\mathbf x \in \{0,1\}^n\), and outputs a string where bits have been deleted and inserted independently at random. The trace reconstruction problem is to recover \(\mathbf x\) from many independent outputs (called ``traces'') of the insertion-deletion channel applied to \(\mathbf x\). We show that if \(\mathbf x\) is chosen uniformly at random, then \((O(\log^{1/3} n))\) traces suffice to reconstruct \(\mathbf x\) with high probability. For the deletion channel with deletion probability \(q < 1/2\) the earlier upper bound was \(\exp(O(\log^{1/2}n))\). The case of \(q \geq 1/2\) or the case where insertions are allowed has not been previously analyzed, and therefore the earlier upper bound was as for worst-case strings, i.e., \(\exp(O(n^{1/3}))\). We also show that our reconstruction algorithm runs in \(n^{1+o(1)}\) time.
A key ingredient in our proof is a delicate two-step alignment procedure where we estimate the location in each trace corresponding to a given bit of \(\mathbf x\). The alignment is done by viewing the strings as random walks and comparing the increments in the walk associated with the input string and the trace, respectively.An in-place framework for exact and approximate shortest unique substring querieshttps://zbmath.org/1472.682242021-11-25T18:46:10.358925Z"Hon, Wing-Kai"https://zbmath.org/authors/?q=ai:hon.wing-kai"Thankachan, Sharma V."https://zbmath.org/authors/?q=ai:thankachan.sharma-v"Xu, Bojian"https://zbmath.org/authors/?q=ai:xu.bojianSummary: We revisit the exact shortest unique substring (SUS) finding problem, and propose its approximate version where mismatches are allowed, due to its applications in subfields such as computational biology. We design a generic in-place framework that fits to solve both the exact and approximate \(k\)-mismatch SUS finding, using the minimum \(2n\) memory words plus \(n\) bytes space, where \(n\) is the input string size. By using the in-place framework, we can find the exact and approximate \(k\)-mismatch SUS for every string position using a total of \(O(n)\) and \(O(n^2)\) time, respectively, regardless of the value of \(k\). Our framework does not involve any compressed or succinct data structures and thus is practical and easy to implement.
For the entire collection see [Zbl 1326.68015].Palindromic trees for a sliding window and its applicationshttps://zbmath.org/1472.682252021-11-25T18:46:10.358925Z"Mieno, Takuya"https://zbmath.org/authors/?q=ai:mieno.takuya"Watanabe, Kiichi"https://zbmath.org/authors/?q=ai:watanabe.kiichi"Nakashima, Yuto"https://zbmath.org/authors/?q=ai:nakashima.yuto"Inenaga, Shunsuke"https://zbmath.org/authors/?q=ai:inenaga.shunsuke"Bannai, Hideo"https://zbmath.org/authors/?q=ai:bannai.hideo"Takeda, Masayuki"https://zbmath.org/authors/?q=ai:takeda.masayukiSummary: The palindromic tree (a.k.a. eertree) for a string \(S\) of length \(n\) is a tree-like data structure that represents the set of all distinct palindromic substrings of \(S\), using \(O(n)\) space [\textit{M. Rubinchik} and \textit{A. M. Shur}, Eur. J. Comb. 68, 249--265 (2018; Zbl 1374.68131)]. It is known that, when \(S\) is over an alphabet of size \(\sigma\) and is given in an online manner, then the palindromic tree of \(S\) can be constructed in \(O(n\log\sigma)\) time with \(O(n)\) space. In this paper, we consider the sliding window version of the problem: For a sliding window of length at most \(d\), we present two versions of an algorithm which maintains the palindromic tree of size \(O(d)\) for every sliding window \(S [i . . j]\) over \(S\), where \(1\leq j-i+1\leq d\). The first version works in \(O(n\log\sigma')\) time with \(O(d)\) space where \(\sigma'\leq d\) is the maximum number of distinct characters in the windows, and the second one works in \(O(n+d\sigma)\) time with \((d+2)\sigma+O(d)\) space. We also show how our algorithms can be applied to efficient computation of minimal unique palindromic substrings (MUPS) and minimal absent palindromic words (MAPW) for a sliding window.Inferring strings from full abelian periodshttps://zbmath.org/1472.682262021-11-25T18:46:10.358925Z"Nishida, Makoto"https://zbmath.org/authors/?q=ai:nishida.makoto"I., Tomohiro"https://zbmath.org/authors/?q=ai:i.tomohiro"Inenaga, Shunsuke"https://zbmath.org/authors/?q=ai:inenaga.shunsuke"Bannai, Hideo"https://zbmath.org/authors/?q=ai:bannai.hideo"Takeda, Masayuki"https://zbmath.org/authors/?q=ai:takeda.masayukiSummary: Strings \(u\), \(v\) are said to be \textit{abelian equivalent} if \(u\) is a permutation of the characters appearing in \(v\). A string \(w\) is said to have a \textit{full abelian period}\(p\) if \(w = w_1 \cdots w_k\), where all \(w_i\)'s are of length \(p\) each and are all abelian equivalent. This paper studies reverse-engineering problems on full abelian periods. Given a positive integer \(n\) and a set \(D\) of divisors of \(n\), we show how to compute in \(O(n)\) time the lexicographically smallest string of length \(n\) which has all elements of \(D\) as its full abelian periods and has the minimum number of full abelian periods not in \(D\). Moreover, we give an algorithm to enumerate all such strings in amortized constant time per output after \(O(n)\)-time preprocessing. Also, we show how to enumerate the strings which have all elements of \(D\) as its full abelian periods in amortized constant time per output after \(O(n)\)-time preprocessing.
For the entire collection see [Zbl 1326.68015].An algorithm for the sequence alignment with gap penalty problem using multiway divide-and-conquer and matrix transpositionhttps://zbmath.org/1472.682272021-11-25T18:46:10.358925Z"Shubham"https://zbmath.org/authors/?q=ai:shubham.k"Prakash, Surya"https://zbmath.org/authors/?q=ai:prakash.surya"Ganapathi, Pramod"https://zbmath.org/authors/?q=ai:ganapathi.pramodSummary: We present a cache-efficient parallel algorithm for the sequence alignment with gap penalty problem for shared-memory machines using multiway divide-and-conquer and not-in-place matrix transposition.
Our \(r\)-way divide-and-conquer algorithm, for a fixed natural number \(r\geq 2\), performs \(\Theta(n^3)\) work, achieves \(\Theta(n^{\log_r(2r-1)})\) span, and incurs \(\mathcal{O}\left(n^3/(BM)+(n^2/B)\log\sqrt{M}\right)\) serial cache misses for \(n>\gamma M\), and incurs \(\mathcal{O}\left((n^2/B)\log(n/\sqrt{M})\right)\) serial cache misses for \(\alpha\sqrt{M}<n\leq\gamma M\), where, \(M\) is the cache size, \(B\) is the cache line size, and \(\alpha\) and \(\gamma\) are constants.Mathematical methods for the analysis of recursive algorithmshttps://zbmath.org/1472.682282021-11-25T18:46:10.358925Z"Bykova, Valentina V."https://zbmath.org/authors/?q=ai:bykova.valentina-vladimirovnaSummary: We prove a theorem that defines asymptotic estimates for the solution of a recurrent relation. This recurrent relation typically describes time complexity functions for recursive algorithms with an additive reduction of the dimension of a given problem. The presented results together with a known main theorem on recurrent relations give a tool for the analysis of the complexity of two most typical recursive schemes.Recognition method of algorithms classes on the basis of asymptotics for the elasticity of complexity functionshttps://zbmath.org/1472.682292021-11-25T18:46:10.358925Z"Bykova, Valentina V."https://zbmath.org/authors/?q=ai:bykova.valentina-vladimirovnaSummary: We offer a new indication to recognize the algorithms classes which is based on the asymptotic behavior of the elasticity of complexity functions. The present day analogy for functions of complexity algorithms and produced functions is used, the rate of which is traditionally evaluated by elasticity in econometrics. The theorem that states the characterization of elasticity for rapid, polynomial, subexponential, exponential and hyperexponential algorithms has been proved. The principal advantage of the suggested indication is that it allows the simplicity of computation caused by the well-known properties of elasticity.Algorithms using ROBDD as a base for Boolean constraintshttps://zbmath.org/1472.682302021-11-25T18:46:10.358925Z"Ignat'ev, A. S."https://zbmath.org/authors/?q=ai:ignatev.a-s"Semenov, A. A."https://zbmath.org/authors/?q=ai:semenov.aleksandr-anatolevichSummary: In the paper, we study algorithmic properties of ROBDD considered in the role of Boolean constraints in the hybrid (SAT+ROBDD) logical derivation. We suggest ROBDD-analogs for the basic algorithmic procedures used in DPLL-derivation such as variable assignment, unit clause, clause learning, and the techniques of delayed computations. A new algorithm intended for ROBDD reordering is proposed. Computational complexity of all the considered algorithms is provided.A complexity analysis of algorithm of parallel search of the ``gold'' collisionhttps://zbmath.org/1472.682312021-11-25T18:46:10.358925Z"Pil'shchikov, D. V."https://zbmath.org/authors/?q=ai:pilshchikov.d-vSummary: The paper refines known estimates of time and memory complexities of Oorschot and Wiener algorithm for the ``gold'' collision searching. We use results related to the computation of characteristics of time-memory-data tradeoff method with distinguished points. Probabilistic approximations of the algorithm characteristics by random variables depending on the number of particles and the total number of particles in a subcritical Galton-Watson process are described. The limits of expectations of these random variables are found.The benefit of recombination in noisy evolutionary searchhttps://zbmath.org/1472.682322021-11-25T18:46:10.358925Z"Friedrich, Tobias"https://zbmath.org/authors/?q=ai:friedrich.tobias"Kötzing, Timo"https://zbmath.org/authors/?q=ai:kotzing.timo"Krejca, Martin S."https://zbmath.org/authors/?q=ai:krejca.martin-s"Sutton, Andrew M."https://zbmath.org/authors/?q=ai:sutton.andrew-mSummary: Practical optimization problems frequently include uncertainty about the quality measure, for example due to noisy evaluations. Thus, they do not allow for a straightforward application of traditional optimization techniques. In these settings meta-heuristics are a popular choice for deriving good optimization algorithms, most notably evolutionary algorithms which mimic evolution in nature. Empirical evidence suggests that genetic recombination is useful in uncertain environments because it can stabilize a noisy fitness signal. With this paper, we want to support this claim with mathematical rigor.
The setting we consider is that of noisy optimization. We study a simple noisy fitness function that is derived by adding Gaussian noise to a monotone function. First, we show that a classical evolutionary algorithm that does not employ sexual recombination (the \(( \mu +1) \)-EA) cannot handle the noise efficiently, regardless of the population size. Then we show that an evolutionary algorithm
which
does employ sexual recombination (the Compact Genetic Algorithm, short: cGA) can handle the noise using a graceful scaling of the population.
For the entire collection see [Zbl 1326.68015].A deep energy method for finite deformation hyperelasticityhttps://zbmath.org/1472.742132021-11-25T18:46:10.358925Z"Nguyen-Thanh, Vien Minh"https://zbmath.org/authors/?q=ai:nguyen-thanh.vien-minh"Zhuang, Xiaoying"https://zbmath.org/authors/?q=ai:zhuang.xiaoying"Rabczuk, Timon"https://zbmath.org/authors/?q=ai:rabczuk.timonSummary: We present a deep energy method for finite deformation hyperelasticitiy using deep neural networks (DNNs). The method avoids entirely a discretization such as FEM. Instead, the potential energy as a loss function of the system is directly minimized. To train the DNNs, a backpropagation dealing with the gradient loss is computed and then the minimization is performed by a standard optimizer. The learning process will yield the neural network's parameters (weights and biases). Once the network is trained, a numerical solution can be obtained much faster compared to a classical approach based on finite elements for instance. The presented approach is very simple to implement and requires only a few lines of code within the open-source machine learning framework such as Tensorflow or Pytorch. Finally, we demonstrate the performance of our DNNs based solution for several benchmark problems, which shows comparable computational efficiency such as FEM solutions.Quantum information capsule and information delocalization by entanglement in multiple-qubit systemshttps://zbmath.org/1472.810452021-11-25T18:46:10.358925Z"Yamaguchi, Koji"https://zbmath.org/authors/?q=ai:yamaguchi.koji"Watamura, Naoki"https://zbmath.org/authors/?q=ai:watamura.naoki"Hotta, Masahiro"https://zbmath.org/authors/?q=ai:hotta.masahiroSummary: Where do entangled multiple-qubit systems store information? For information injected into a qubit, this question is nontrivial and interesting since the entanglement delocalizes the information. So far, a common picture is that of a qubit and its purification partner sharing the information quantum mechanically. Here, we introduce a new picture of a single qubit in the correlation space, referred to as quantum information capsule (QIC), confining the information perfectly. This picture is applicable for the entangled multiple-qubit system in an arbitrary state. Unlike the partner picture, in the QIC picture, by swapping the single-body state, leaving other subsystems untouched, the whole information can be retrieved out of the system. After the swapping process, no information remains in the system.Readout of a weakly coupled qubit through the use of an auxiliary modehttps://zbmath.org/1472.810562021-11-25T18:46:10.358925Z"Troiani, Filippo"https://zbmath.org/authors/?q=ai:troiani.filippoSummary: The dispersive coupling between a qubit and a cavity mode is widely used for performing non-destructive readout of the qubit state. In this approach, it is typically required that the dispersive strong coupling regime is achieved. Here we show that the use of an auxiliary cavity mode reduces by orders of magnitude the required value of the dispersive coupling, for a given decay rate of the cavity mode. The analysis is performed within the input-output formalism, in terms of the photon scattering matrix elements and of the signal-to-noise ratio. We derive simple analytical expressions for the optimal parameters and recover the standard single-mode result as a limiting case. The present results can also be applied to the qubit readout based on longitudinal cavity-qubit interactions, and to any sensing scheme where the cavity frequency is used as a probe to estimate some physical parameter of interest.Autonomous quantum machines and finite-sized clockshttps://zbmath.org/1472.810582021-11-25T18:46:10.358925Z"Woods, Mischa P."https://zbmath.org/authors/?q=ai:woods.mischa-p"Silva, Ralph"https://zbmath.org/authors/?q=ai:silva.ralph-s"Oppenheim, Jonathan"https://zbmath.org/authors/?q=ai:oppenheim.jonathanThe article provides for an important contribution to quantum technologies, being of key interest to those researching on quantum technologies, in general, and for those researching in particular in quantum control, quantum robotics, quantum artificial intelligence and nanotechnology.
The main focus of the article regards the possibility of building a fully quantum machine as an autonomous quantum device which interacts with its surroundings. In this way rather than an external control of a quantum device, one allows the system to operate without an external controller.
In order to develop such a quantum device, the authors show that one needs to consider finite-dimensional clock, however, they highlight that finite clocks can only accurately record time at discrete intervals and, also, any attempt to use the clock for time measurement or using it as a control system disturbs the clock reducing its performance with use, the authors work overcomes these two points by working with a finite-sized quantum clock and showing that one can use such a clock in the context of autonomous quantum devices, in particular, they address how unitary operations and time-dependent interaction Hamiltonians which are externally controlled in current quantum computation can be turned into operations performed by an autonomous device, they also address the backreaction on the quantum clock and derive the analytic bounds on the errors developed in the clock and in the target system, showing that the disturbance in the quantum clock can be made exponentially small in the clock's dimension, so that backreaction on the quantum clock can be made negligible allowing for an operative development of an autonomous quantum machine which may work for a given length of time before becoming too degraded.
The article is organized in two parts, the first is comprised of sections 1 to 6 which give a complete overview of the article's main work, with main conclusions provided in section 6. The second part of the article, from sections 7 onward, deal with the complete formal work and mathematical proofs supporting the authors findings.
For researchers working in Quantum AI (QAI), quantum robotics and automata theory and even Quantum Artificial Life (QALife) this article is of key importance since it supplies for a foundational basis on which future work may be developed around quantum automation solutions, which can draw upon this article's main findings and proposal. The work is also of key importance for nanotechnology, in particular nanorobotics where quantum dynamics enter into play.Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learninghttps://zbmath.org/1472.810892021-11-25T18:46:10.358925Z"Zhou, Zijian"https://zbmath.org/authors/?q=ai:zhou.zijian"Yan, Zhenya"https://zbmath.org/authors/?q=ai:yan.zhenyaSummary: In this paper, we investigate the logarithmic nonlinear Schrödinger (LNLS) equation with the parity-time \((\mathcal{PT})\)-symmetric harmonic potential, which is an important physical model in many fields such as nuclear physics, quantum optics, magma transport phenomena, and effective quantum gravity. Three types of initial value conditions and periodic boundary conditions are chosen to solve the LNLS equation with \(\mathcal{PT}\)-symmetric harmonic potential via the physics-informed neural networks (PINNs) deep learning method, and these obtained results are compared with ones deduced from the Fourier spectral method. Moreover, we also investigate the effectiveness of the PINNs deep learning for the LNLS equation with \(\mathcal{PT}\) symmetric potential by choosing the distinct space widths or distinct optimized steps. Finally, we use the PINNs deep learning method to effectively tackle the data-driven discovery of the LNLS equation with \(\mathcal{PT} \)-symmetric harmonic potential such that the coefficients of dispersion and nonlinear terms or the amplitudes of \(\mathcal{PT}\)-symmetric harmonic potential can be approximately found.Configurational complexity of nonautonomous discrete one-soliton and rogue waves in Ablowitz-Ladik-Hirota waveguidehttps://zbmath.org/1472.811062021-11-25T18:46:10.358925Z"Thakur, Pooja"https://zbmath.org/authors/?q=ai:thakur.pooja"Gleiser, Marcelo"https://zbmath.org/authors/?q=ai:gleiser.marcelo"Kumar, Anil"https://zbmath.org/authors/?q=ai:kumar.anil"Gupta, Rama"https://zbmath.org/authors/?q=ai:gupta.ramaSummary: We compute the configurational complexity (CC) for discrete soliton and rogue waves traveling along an Ablowitz-Ladik-Hirota (ALH) waveguide and modeled by a discrete nonlinear Schrödinger equation. We show that for a specific range of the soliton transverse direction \(\kappa\) propagating along the parametric time \(\zeta(t)\), CC reaches an evolving series of global minima. These minima represent maximum compressibility of information in the momentum modes along the Ablowitz-Ladik-Hirota waveguide. Computing the CC for rogue waves as a function of background amplitude modulation \(\mu\), we show that it displays two essential features: a maximum representing the optimal value for the rogue wave inception (the ``gradient catastrophe'') and saturation representing the rogue wave dispersion into constituent wave modes. We show that saturation is achieved earlier for higher values of modulation amplitude as the discrete rogue wave evolves along time \(\zeta(t)\).GANs for generating EFT modelshttps://zbmath.org/1472.811552021-11-25T18:46:10.358925Z"Erbin, Harold"https://zbmath.org/authors/?q=ai:erbin.harold"Krippendorf, Sven"https://zbmath.org/authors/?q=ai:krippendorf.svenSummary: We initiate a way of generating effective field theories (EFT) models by the computer, satisfying both experimental and theoretical constraints. We use Generative Adversarial Networks (GAN) and display generated instances which go beyond the examples known to the machine during training. As a starting point, we apply this idea to the generation of supersymmetric field theories with a single field. We find cases where the number of minima in the generated scalar potential is different from values found in the training data. We comment on potential further applications of this framework.Revisiting the simulation of quantum Turing machines by quantum circuitshttps://zbmath.org/1472.812792021-11-25T18:46:10.358925Z"Molina, Abel"https://zbmath.org/authors/?q=ai:molina.abel"Watrous, John"https://zbmath.org/authors/?q=ai:watrous.johnSummary: \textit{A. C.-C. Yao}'s publication [``Quantum circuit complexity'', in: Proceedings of the 34th annual IEEE symposium on foundations of computer science, FOCS'93. Los Alamitos, CA: IEEE Computer Society. 352--361 (1993; \url{doi:10.1109/SFCS.1993.366852})],
proved that quantum Turing machines and quantum circuits are polynomially equivalent computational models: \(t \geq n\) steps of a quantum Turing machine running on an input of length \(n\) can be simulated by a uniformly generated family of quantum circuits with size quadratic in \(t\), and a polynomial-time uniformly generated family of quantum circuits can be simulated by a quantum Turing machine running in polynomial time. We revisit the simulation of quantum Turing machines with uniformly generated quantum circuits, which is the more challenging of the two simulation tasks, and present a variation on the simulation method employed by Yao together with an analysis of it. This analysis reveals that the simulation of quantum Turing machines can be performed by quantum circuits having depth linear in \(t\), rather than quadratic depth, and can be extended to variants of quantum Turing machines, such as ones having multi-dimensional tapes. Our analysis is based on an extension of method described by
\textit{P. Arrighi} et al. [J. Comput. Syst. Sci. 77, No. 2, 372--378 (2011; Zbl 1210.81067)],
that allows for the localization of causal unitary evolutions.Spin texture and Berry phase for heavy-mass holes confined in SiGe mixed-alloy two-dimensional system: intersubband interaction via the coexistence of Rashba and Dresselhaus spin-orbit interactionshttps://zbmath.org/1472.813172021-11-25T18:46:10.358925Z"Tojo, Tatsuki"https://zbmath.org/authors/?q=ai:tojo.tatsuki"Takeda, Kyozaburo"https://zbmath.org/authors/?q=ai:takeda.kyozaburoSummary: By extending the \(\boldsymbol{k} \cdot \boldsymbol{p}\) approach, we study the spin texture and Berry phase of heavy-mass holes (HHs) confined in the SiGe two-dimensional (2D) quantum well system, focusing on the intersubband interaction via the coexistence of the Rashba and Dresselhaus spin-orbit interactions (SOIs). The coexistence of both SOIs generates spin-stabilized(+)/destabilized(-) HHs. The strong intersubband interaction causes \textit{quasi}-degenerate states resembling the 2D massive Dirac fermion. Consequently, the Berry phases of HHs have unique energy dependence understood by counting the \textit{quasi}-degenerate points with the signs of the Berry phases. Thermal averaging of the Berry phase demonstrates that HH\(+/-\) has a peculiar plateau of \(+\pi/-\pi\) at less than 30 K and then changes its sign at approximately 200 K.Complexity of the Einstein-Born-Infeld-massive black holeshttps://zbmath.org/1472.830472021-11-25T18:46:10.358925Z"Bahrami-Asl, B."https://zbmath.org/authors/?q=ai:bahrami-asl.b"Hendi, S. H."https://zbmath.org/authors/?q=ai:hendi.seyed-hosseinSummary: Motivated by interesting correspondence between computational complexity in a CFT and the action evaluated on a WDW patch in the bulk, we study the complexity of the Einstein-massive black holes in the presence of BI nonlinear electrodynamics. The upper limit of Lloyd's bound according to the WDW patch is investigated and it is found that there are some physical intervals for massive parameters in which Lloyd's bound is held.Testing the complexity conjecture in regular black holes geometryhttps://zbmath.org/1472.830502021-11-25T18:46:10.358925Z"El Moumni, H."https://zbmath.org/authors/?q=ai:el-moumni.hasan"Masmar, K."https://zbmath.org/authors/?q=ai:masmar.karimaSummary: Motived by the new complexity conjecture [\textit{A. R. Brown} et al., ``Holographic complexity equals bulk action?'', Phys. Rev. Lett. 116, No. 19, Article ID 191301, 5 p. (2016; \url{doi:10.1103/PhysRevLett.116.191301})] suggesting that the fastest computer in nature are the black holes. We study the action growth rate for a variety of four-dimensional regular black holes such as Hayward, Bardeen and the new class proposed in [\textit{Z. Y. Fan} and \textit{X. Wang}, ``Construction of regular black holes in general relativity'', Phys. Rev. D (3) 94, No. 12, Article ID 124027, 9 p. (2016; \url{doi:10.1103/PhysRevD.94.124027})]. Generally, we show that action growth rates of the Wheeler-De Witt patch are finite for such black hole configurations at the late time approach and satisfy the Lloyd bound on the rate of quantum computation. Also, the case of three dimensions space is investigated. In each regular black hole configuration, we found that the form of the Lloyd bound formula remains unaltered but the energy is modified due to the effect of the nonlinear electrodynamics where some extra-therm have appeared in the total growth action.Seismic stratum segmentation using an encoder-decoder convolutional neural networkhttps://zbmath.org/1472.860132021-11-25T18:46:10.358925Z"Wang, Detao"https://zbmath.org/authors/?q=ai:wang.detao"Chen, Guoxiong"https://zbmath.org/authors/?q=ai:chen.guoxiongSummary: As an essential step in reservoir characterization, seismic stratigraphic interpretation is often dependent on the development of powerful computer-based interpretation tools that can simulate the intelligence of experienced interpreters. With the success of machine/deep learning applications in many aspects of geoscience in recent decades, geophysicists have become more dedicated to exploring seismic big data in a smarter and more sophisticated way to better image subsurface reservoirs/structures. In this paper, a specific U-shaped fully convolutional network (U-Net) is established for automatic seismic stratigraphic interpretation. Specifically, this task is formulated as a semantic segmentation problem by identifying strata at the pixel level and classifying each pixel in the image into a specific stratum category. An experiment using the Netherlands F3 seismic dataset suggests that, compared with previously established deep learning models requiring a large number of training sets, the proposed U-Net method can achieve high evaluation indicators and better stratum segmentations in the case of a limited training set. During the test, the proposed U-Net model outperforms the Bayesian neural network (BNN) model for seismic stratum segmentation with regard to the training time, prediction speed, and segmentation accuracy. These results indicate the great potential of using U-Net-based deep learning for intelligent seismic stratigraphic interpretation.A coarse-to-fine approach for intelligent logging lithology identification with extremely randomized treeshttps://zbmath.org/1472.860442021-11-25T18:46:10.358925Z"Xie, Yunxin"https://zbmath.org/authors/?q=ai:xie.yunxin"Zhu, Chenyang"https://zbmath.org/authors/?q=ai:zhu.chenyang"Hu, Runshan"https://zbmath.org/authors/?q=ai:hu.runshan"Zhu, Zhengwei"https://zbmath.org/authors/?q=ai:zhu.zhengweiSummary: Lithology identification is vital for reservoir exploration and petroleum engineering. Recently, there has been growing interest in using an intelligent logging approach for lithology classification. Machine learning has emerged as a powerful tool in inferring lithology types with the logging curves. However, well logs are susceptible to logging parameter manual entry, borehole conditions and tool calibrations. Most studies in the field of lithology classification with machine learning approaches have focused only on improving the prediction accuracy of classifiers. Also, a model trained in one location is not reusable in a new location due to different data distributions. In this paper, a unified framework is provided for training a multi-class lithology classification model for a data set with outlier data. In this paper, a coarse-to-fine framework that combines outlier detection, multi-class classification with an extremely randomized tree-based classifier is proposed to solve these issues. An unsupervised learning approach is used to detect the outliers in the data set. Then a coarse-to-fine inference procedure is used to infer the lithology class with an extremely randomized tree classifier. Two real-world data sets of well-logging are used to demonstrate the effectiveness of the proposed framework. Comparisons are conducted with some baseline machine learning classifiers, namely random forest, gradient tree boosting, and xgboosting. Results show that the proposed framework has higher prediction accuracy in sandstones compared with other approaches.A simheuristic algorithm for time-dependent waste collection management with stochastic travel timeshttps://zbmath.org/1472.900132021-11-25T18:46:10.358925Z"Gruler, Aljoscha"https://zbmath.org/authors/?q=ai:gruler.aljoscha"Perez-Navarro, Antoni"https://zbmath.org/authors/?q=ai:perez-navarro.antoni"Calvet, Laura"https://zbmath.org/authors/?q=ai:calvet.laura"Juan, Angel A."https://zbmath.org/authors/?q=ai:juan.angel-aSummary: A major operational task in city logistics is related to waste collection. Due to large problem sizes and numerous constraints, the optimization of real-life waste collection problems on a daily basis requires the use of metaheuristic solving frameworks to generate near-optimal collection routes in low computation times. This paper presents a simheuristic algorithm for the time-dependent waste collection problem with stochastic travel times. By combining Monte Carlo simulation with a biased randomized iterated local search metaheuristic, time-varying and stochastic travel speeds between different network nodes are accounted for. The algorithm is tested using real instances in a medium-sized city in Spain.Complex systems: features, similarity and connectivityhttps://zbmath.org/1472.900202021-11-25T18:46:10.358925Z"Comin, Cesar H."https://zbmath.org/authors/?q=ai:comin.cesar-henrique"Peron, Thomas"https://zbmath.org/authors/?q=ai:peron.thomas-k-dm"Silva, Filipi N."https://zbmath.org/authors/?q=ai:silva.filipi-nascimento"Amancio, Diego R."https://zbmath.org/authors/?q=ai:amancio.diego-r"Rodrigues, Francisco A."https://zbmath.org/authors/?q=ai:rodrigues.francisco-aparecido"Costa, Luciano da F."https://zbmath.org/authors/?q=ai:costa.luciano-da-fontoura|da-f-costa.lucianoSummary: The increasing interest in complex networks research has been motivated by intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of concepts and methods deriving from many areas, from statistical physics to sociology, which are often used in an independent way. Yet, for this same reason, it would be desirable to integrate these various aspects into a more coherent and organic framework, which would imply in several benefits normally allowed by the systematization in science, including the identification of new types of problems and the cross-fertilization between fields. More specifically, the identification of the main areas to which the concepts frequently used in complex networks can be applied paves the way to adopting and applying a larger set of concepts and methods deriving from those respective areas. Among the several areas that have been used in complex networks research, pattern recognition, optimization, linear algebra, and time series analysis seem to play a particularly basic and recurrent role. In the present manuscript, we propose a systematic way to integrate the concepts from these diverse areas regarding complex networks research. In order to do so, we start by grouping the multidisciplinary concepts into three main groups of representations, namely features, similarity, and network connectivity. Then we show that several of the analysis and modeling approaches to complex networks can be thought as a composition of maps between these three groups, with emphasis on nine main types of mappings, which are presented and illustrated. For instance, we argue that many models used to generate networks can be understood as a mapping from features to similarity, and then to network connectivity concepts. Such a systematization of principles and approaches also provides an opportunity to review some of the most closely related works in the literature, which is also developed in this article.Correction to: ``Online failure diagnosis in interdependent networks''https://zbmath.org/1472.900232021-11-25T18:46:10.358925Z"Shiri, Davood"https://zbmath.org/authors/?q=ai:shiri.davood"Akbari, Vahid"https://zbmath.org/authors/?q=ai:akbari.vahidCorrects the license information of the authors' paper [ibid. 2, No. 1, Paper No. 10, 15 p. (2021; Zbl 1457.90031)] to CC-BY-4.0.Design, analysis and performance evaluation of parallel algorithms for solving triangular linear systems on multicore platformshttps://zbmath.org/1472.900692021-11-25T18:46:10.358925Z"Belmabrouk, Mounira"https://zbmath.org/authors/?q=ai:belmabrouk.mounira"Marrakchi, Mounir"https://zbmath.org/authors/?q=ai:marrakchi.mounirSummary: In this paper, we focus on the schedulings of 2-steps graph with constant task cost obtained when parallelizing algorithm solving a triangular linear system. We present three scheduling approaches having the same least theoretical execution time. The first is designed through solving a 0-1 integer problem by Mixed Integer Programming (MIP), the second is based on the Critical Path Algorithm (CPA) and the third is a particular Column-Oriented Scheduling (COS). The MIP approach experiments were carried out and confirmed that the makespan values of the MIP scheduling coincide with those of the corresponding lower bound already reached. Experimental results of the last two approaches detailing both makespans and efficiencies are presented and show that their practical performances differ though they are theoretically identical. We compare also these results to those of the appropriate procedure into so-called PLASMA library (Parallel Linear Algebra for Scalable Multi-core Architectures).Integer and constraint programming approaches for providing optimality to the bandwidth multicoloring problemhttps://zbmath.org/1472.900702021-11-25T18:46:10.358925Z"Dias, Bruno"https://zbmath.org/authors/?q=ai:dias.bruno-h"de Freitas, Rosiane"https://zbmath.org/authors/?q=ai:de-freitas.rosiane"Maculan, Nelson"https://zbmath.org/authors/?q=ai:maculan.nelson-f"Michelon, Philippe"https://zbmath.org/authors/?q=ai:michelon.philippe-yves-paulSummary: In this paper, constraint and integer programming techniques are applied to solving bandwidth coloring problems, in the sense of proving optimality or finding better feasible solutions for benchmark instances from the literature. The Bandwidth Coloring Problem (BCP) is a generalization of the classic vertex coloring problem (VCP), where, given a graph, its vertices must be colored such that not only adjacent ones do not share the same color, but also their colors must be separated by a minimum given value. BCP is further generalized to the Bandwidth Multicoloring Problem (BMCP), where each vertex can receive more than one different color, also subject to separation constraints. BMCP is used to model the Minimum Span Channel Assignment Problem (MS-CAP), which arises in the planning of telecommunication networks. Research on algorithmic strategies to solve these problems focus mainly on heuristic approaches and the performance of such methods is tested on artificial and real scenarios benchmarks, such as GEOM, Philadelphia and Helsinki sets. We achieve optimal solutions or provide better upper bounds for these well-known instances, We also compare the effects of multicoloring demands on the performance of each exact solution approach, based on empirical analysis.Erratum to: ``An abstract model for branching and its application to mixed integer programming''https://zbmath.org/1472.900732021-11-25T18:46:10.358925Z"Le Bodic, Pierre"https://zbmath.org/authors/?q=ai:le-bodic.pierre"Nemhauser, George"https://zbmath.org/authors/?q=ai:nemhauser.george-lFrom the text: In the original version of the article [the authors, ibid. 166, No. 1-2 (A), 369--405 (2017; Zbl 1386.90087)], the format of Table 1 was incorrect. The original article has been revised to provide the correct table.An iterative vertex enumeration method for objective space based vector optimization algorithmshttps://zbmath.org/1472.901212021-11-25T18:46:10.358925Z"Kaya, İrfan Caner"https://zbmath.org/authors/?q=ai:kaya.irfan-caner"Ulus, Firdevs"https://zbmath.org/authors/?q=ai:ulus.firdevsSummary: An application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex vector optimization algorithms whose aim is to generate (an approximation of) the Pareto frontier. In such algorithms, VEP, which is defined in the objective space, is solved in each iteration and it has a special structure. Namely, the recession cone of the polyhedron to be generated is the ordering cone. We consider and give a detailed description of a vertex enumeration procedure, which iterates by calling a modified ``double description (DD) method'' that works for such unbounded polyhedrons. We employ this procedure as a function of an existing objective space based vector optimization algorithm (Algorithm 1); and test the performance of it for randomly generated linear multiobjective optimization problems. We compare the efficiency of this procedure with another existing DD method as well as with the current vertex enumeration subroutine of Algorithm 1. We observe that the modified procedure excels the others especially as the dimension of the vertex enumeration problem (the number of objectives of the corresponding multiobjective problem) increases.A neurodynamic approach to nonlinear optimization problems with affine equality and convex inequality constraintshttps://zbmath.org/1472.901282021-11-25T18:46:10.358925Z"Liu, Na"https://zbmath.org/authors/?q=ai:liu.na"Qin, Sitian"https://zbmath.org/authors/?q=ai:qin.sitianThe paper deals with the weakest possible conditions that optimization problems can be treated by using a recurrent neural network. Convex, generalized convex as well as nonlinear nonconvex problems are considered. The Introduction gives a good overview of the existing results in the literature, followed by four remarks showing that the network used in this paper is really new. Chapter 2 recalls needed definitions. Chapter 3 gives the optimization problem P (finite-dimensional space, convex inequalities, linear equalities with full row rank, the objective function is not necessarily convex or smooth), where some conditions must be fulfilled: Slater conditions, boundedness of the feasible domain, regularity and Lipschitz property of the objective function. Furthermore, the recurrent neural network to solve P is presented being a nonautonomous differential inclusion. Two figures support the mathematical presentation. Chapter 4 gives the theoretical analysis starting with the definition of a critical point of P and the state solution of the network together with its convergence behavior as for instance that the state of neural network enters the feasible region in finite time and remains thereafter, about the distance to the set of critical points and about relations to Kuhn-Tucker points of P and finally, if the objective function is pseudoconvex, then the state of the network is globally convergent to an optimal solution of P. Chapter 5 starts with the definition of a slow solution of a (common) differential inclusion and it is shown, that a solution of the network (with special initial point) is just its slow solution and is unique, if the objective function is convex Five test examples with remarks and figures supplement the paper.Hybrid cell selection-based heuristic for capacitated multi-facility Weber problem with continuous fixed costshttps://zbmath.org/1472.901542021-11-25T18:46:10.358925Z"Jamil, Nur Shifa Farah Ain"https://zbmath.org/authors/?q=ai:jamil.nur-shifa-farah-ain"Abdul-Rahman, Syariza"https://zbmath.org/authors/?q=ai:abdul-rahman.syariza"Luis, Martino"https://zbmath.org/authors/?q=ai:luis.martino"Benjamin, Aida Mauziah"https://zbmath.org/authors/?q=ai:benjamin.aida-mauziahSummary: Location-allocation problem (LAP) has attracted much attention in facility location field. The LAP in continuous plane is well-known as Weber problem. This paper assessed this problem by considering capacity constraints and fixed costs as each facility has different setup cost and capacity limit to serve customers. Previous studies considered profitable areas by dividing continuous space into a discrete number of equal cells to identify optimal locations from a smaller set of promising locations. Unfortunately, it may lead to avoid choosing good locations because unprofitable areas are still considered while locating the facilities. Hence, this allows a significant increment in the transportation costs. Thus, this paper intelligently selected profitable area through a hybridization of enhanced Cell Selection-based Heuristic (CSBH) and Furthest Distance Rule (FDR) to minimize total transportation and fixed costs. The CSBH divides customer distribution into smaller set of promising locations and intelligently selected profitable area to increase possibility of finding better locations, while FDR aims to forbid the new locations of the facilities to be close to the previously selected locations. Numerical experiments tested on well-known benchmark datasets showed that the results of hybrid heuristic outperformed single CSBH and FDR, while producing competitive results when compared with previously published results, apart from significantly improving total transportation cost. The new hybrid heuristic is simple yet effective in solving LAP.German conference on bioinformatics 2012, GCB'12, September 19--22, 2012, Jena, Germany. Selected papers based on the presentations at the conference.https://zbmath.org/1472.920012021-11-25T18:46:10.358925Z"Böcker, Sebastian"https://zbmath.org/authors/?q=ai:bocker.sebastian"Hufsky, Franziska"https://zbmath.org/authors/?q=ai:hufsky.franziska"Scheubert, Kerstin"https://zbmath.org/authors/?q=ai:scheubert.kerstin"Schleicher, Jana"https://zbmath.org/authors/?q=ai:schleicher.jana"Schuster, Stefan"https://zbmath.org/authors/?q=ai:schuster.stefanThe articles of mathematical interest will be reviewed individually.
Indexed articles:
\textit{Hoppe, Andreas; Holzhütter, Hermann-Georg}, ModeScore: a method to infer changed activity of metabolic function from transcript profiles, 1-11, electronic only [Zbl 1472.92113]
\textit{Ludwig, Marcus; Hufsky, Franziska; Elshamy, Samy; Böcker, Sebastian}, Finding characteristic substructures for metabolite classes, 23-38, electronic only [Zbl 1472.92320]
\textit{D'Addario, Marianna; Kriege, Nils; Rahmann, Sven}, Designing q-unique DNA sequences with integer linear programs and Euler tours in de Bruijn graphs, 82-92, electronic only [Zbl 1472.92162]
\textit{Schäfer, Tim; May, Patrick; Koch, Ina}, Computation and visualization of protein topology graphs including ligand information, 108-118, electronic only [Zbl 1472.92168]
\textit{Esmaielbeiki, Reyhaneh; Nebel, Jean-Christophe}, Unbiased protein interface prediction based on ligand diversity quantification, 119-130, electronic only [Zbl 1472.92163]Predictive coding for dynamic visual processing: development of functional hierarchy in a multiple spatiotemporal scales RNN modelhttps://zbmath.org/1472.920132021-11-25T18:46:10.358925Z"Choi, Minkyu"https://zbmath.org/authors/?q=ai:choi.minkyu"Tani, Jun"https://zbmath.org/authors/?q=ai:tani.junSummary: This letter proposes a novel predictive coding type neural network model, the predictive multiple spatiotemporal scales recurrent neural network (P-MSTRNN). The P-MSTRNN learns to predict visually perceived human whole-body cyclic movement patterns by exploiting multiscale spatiotemporal constraints imposed on network dynamics by using differently sized receptive fields as well as different time constant values for each layer. After learning, the network can imitate target movement patterns by inferring or recognizing corresponding intentions by means of the regression of prediction error. Results show that the network can develop a functional hierarchy by developing a different type of dynamic structure at each layer. The letter examines how model performance during pattern generation, as well as predictive imitation, varies depending on the stage of learning. The number of limit cycle attractors corresponding to target movement patterns increases as learning proceeds. Transient dynamics developing early in the learning process successfully perform pattern generation and predictive imitation tasks. The letter concludes that exploitation of transient dynamics facilitates successful task performance during early learning periods.Competitive STDP learning of overlapping spatial patternshttps://zbmath.org/1472.920272021-11-25T18:46:10.358925Z"Krunglevicius, Dalius"https://zbmath.org/authors/?q=ai:krunglevicius.daliusSummary: Spike-timing-dependent plasticity (STDP) is a set of Hebbian learning rules firmly based on biological evidence. It has been demonstrated that one of the STDP learning rules is suited for learning spatiotemporal patterns. When multiple neurons are organized in a simple competitive spiking neural network, this network is capable of learning multiple distinct patterns. If patterns overlap significantly (i.e., patterns are mutually inclusive), however, competition would not preclude trained neuron's responding to a new pattern and adjusting synaptic weights accordingly.
This letter presents a simple neural network that combines vertical inhibition and Euclidean distance-dependent synaptic strength factor. This approach helps to solve the problem of pattern size-dependent parameter optimality and significantly reduces the probability of a neuron's forgetting an already learned pattern. For demonstration purposes, the network was trained for the first ten letters of the Braille alphabet.Sequence classification using third-order momentshttps://zbmath.org/1472.920432021-11-25T18:46:10.358925Z"Troelsgaard, Rasmus"https://zbmath.org/authors/?q=ai:troelsgaard.rasmus"Hansen, Lars Kai"https://zbmath.org/authors/?q=ai:hansen.lars-kaiSummary: Model-based classification of sequence data using a set of hidden Markov models is a well-known technique. The involved score function, which is often based on the class-conditional likelihood, can, however, be computationally demanding, especially for long data sequences. Inspired by recent theoretical advances in spectral learning of hidden Markov models, we propose a score function based on third-order moments. In particular, we propose to use the Kullback-Leibler divergence between theoretical and empirical third-order moments for classification of sequence data with discrete observations. The proposed method provides lower computational complexity at classification time than the usual likelihood-based methods. In order to demonstrate the properties of the proposed method, we perform classification of both simulated data and empirical data from a human activity recognition study.SuperSpike: supervised learning in multilayer spiking neural networkshttps://zbmath.org/1472.920482021-11-25T18:46:10.358925Z"Zenke, Friedemann"https://zbmath.org/authors/?q=ai:zenke.friedemann"Ganguli, Surya"https://zbmath.org/authors/?q=ai:ganguli.suryaSummary: A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in silico. Here we revisit the problem of supervised learning in temporally coding multilayer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three-factor learning rule capable of training multilayer networks of deterministic integrate-and-fire neurons to perform nonlinear computations on spatiotemporal spike patterns. Second, inspired by recent results on feedback alignment, we compare the performance of our learning rule under different credit assignment strategies for propagating output errors to hidden units. Specifically, we test uniform, symmetric, and random feedback, finding that simpler tasks can be solved with any type of feedback, while more complex tasks require symmetric feedback. In summary, our results open the door to obtaining a better scientific understanding of learning and computation in spiking neural networks by advancing our ability to train them to solve nonlinear problems involving transformations between different spatiotemporal spike time patterns.The design principles of discrete Turing patterning systemshttps://zbmath.org/1472.920562021-11-25T18:46:10.358925Z"Leyshon, Thomas"https://zbmath.org/authors/?q=ai:leyshon.thomas"Tonello, Elisa"https://zbmath.org/authors/?q=ai:tonello.elisa"Schnoerr, David"https://zbmath.org/authors/?q=ai:schnoerr.david"Siebert, Heike"https://zbmath.org/authors/?q=ai:siebert.heike"Stumpf, Michael P. H."https://zbmath.org/authors/?q=ai:stumpf.michael-p-hSummary: The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-species networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find these Turing pattern topologies to be substantially more robust to changes in the parameters of the model. We also find that diffusion-driven instabilities are substantially weaker predictors for Turing patterns in our discrete modelling framework in comparison to the continuous case, in the sense that the presence of an instability does not guarantee a pattern emerging in simulations. We show that a more refined criterion constitutes a stronger predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought.Machine-learned regression assessment of the HIV epidemiological development in Asian regionhttps://zbmath.org/1472.921982021-11-25T18:46:10.358925Z"Bhardwaj, Rashmi"https://zbmath.org/authors/?q=ai:bhardwaj.rashmi"Bangia, Aashima"https://zbmath.org/authors/?q=ai:bangia.aashimaSummary: The World Health Organization (WHO) expresses vital populated areas as the ones that would be vulnerable towards and at most risk at acquiring HIV. Strategies refer to at most-risk populations as ``men who have sex with men, transgender people, people who inject drugs and sex workers. At most-risk populated regions get inexplicably influenced by HIV.'' Exposed inhabitants are recognized through aiming a particular social demographic feature for the region. Perception of the crucial populated regions related to epidemical jargon as demarcated through the Joint United Nations Programme on UNAIDS that renders towards ``concentrated epidemic'' is the one where it would spread promptly among populated areas generally, which stands \(>5\%\) prevalent. ``Generalized epidemic'' is the one which gets self-sustained inside regions with populations via heterosexually spreading it. The aim of this study is to contribute towards the analytical preview of mechanism for global epidemiological spread in Asian region, including the influence of its treatment and prevention schemes on epidemiological trends for over a decade.
According to UNAIDS data, an estimation of around \(1.8\) million first-hand HIV infections have been transmitted universally in 2017, which characterized a \(14\%\) waning from \(2.1\) million newfound contagions in the year 2015 also \(22\%\) decline since \(2.3\) million new contaminations in the year 2012. Sub-Saharan Africa led the approach with \(25\%\) decline in newly infected population from 2012 to 2017, which is declining from \(1.6\) to \(1.2\) million. Though most of the regions have observed a decline in new annual infections since 2012, growths occur in Latin America from \(86,000\) towards a lakh plus Caribbean having ranges of \(12,000-15,000\). The number of newly discovered infections remained at level at eastern side of Europe and Central Asian regions.
Thus, it is need of our generation for understanding the elementary mechanism of infection spread with progression of the epidemic. It effects various immune cells, particularly \(CD^{4+}T\) cells, macrophages, and microglial cells. HIV-\(1\) accesses macrophages plus \(CD^{4+}T\) cells, which is possible because of interface of the virion-sachet glycoproteins within \(CD^{4+}\) molecule on the targeted ones. Virions then pass on a disease to several cellular targets disseminating inside the whole body. Mathematical modeling development of the viral dynamics for HIV has been developed towards studying spread and treatment. Model for this virus infection has three variables: T accounts for the amount of uninfected target cells, I refers to the number of infected cells, and \(V\) refers to the amount of virus particles in the blood cells. The nonlinearity of the HIV epidemiology is studied using intelligent analysis. Further, machine-learned regressions consisting of L\(1\)-norm, logistic, Poisson, etc. with the uncertainty of prediction help to understand the virion behavior in a better way. It is observed that if the state variables undergo alterations, then the viral dynamics changes the behavior gradually.
For the entire collection see [Zbl 1461.92002].Grammars of organic chemistryhttps://zbmath.org/1472.923252021-11-25T18:46:10.358925Z"Matyszczak, Grzegorz"https://zbmath.org/authors/?q=ai:matyszczak.grzegorzSummary: Automata theory has been used in the subject of organic chemistry. The alphabet of the language of all organic compounds has been proposed and discussed, furthermore, universal system of notation has been presented that allows writing certain organic compound as a string. Deterministic finite-state automaton have been constructed to decide whether the organic compound can be synthesized in the esterification reaction. Then deterministic finite-state automaton for more synthetically useful organic reaction, which is the Radziszewski reaction, has been presented as well as a discussion of problems that arise while constructing finite-state automata for more complex organic reactions. A proof that the grammar of organic compounds language is not regular has been made based on the contrapositive of the Pumping Lemma. The algebraic structure of organic chemistry has been briefly discussed. Directions of further investigations that would allow more applications of automata theory in chemistry are outlined, especially in chemical informatics and organic synthesis planning.Application of a robust hybrid algorithm (neural networks-AGDC) for the determination of kinetic parameters and discrimination among reaction mechanismshttps://zbmath.org/1472.923532021-11-25T18:46:10.358925Z"González-Hernández, J. L."https://zbmath.org/authors/?q=ai:gonzalez-hernandez.j-l"Canedo, M. Mar"https://zbmath.org/authors/?q=ai:canedo.m-mar"Encinar, Sonsoles"https://zbmath.org/authors/?q=ai:encinar.sonsolesSummary: In this paper a hybrid algorithm (HA) is applied to determine the kinetic parameters and the discrimination between mechanisms responsible for the development of a chemical reaction. The HA used is formed by a combination of two complementary algorithms that are applied sequentially: the method ``soft-modelling'' of artificial neural networks (ANN) and the mathematical optimization algorithm, AGDC. The consecutively application of these methods means a great advantage due to the ANN methodology which is a treatment that does not (need to) use initial estimates of the parameters to determine. Initially the soft-modelling ANN methodology is applied and the obtained results are used as initial estimates in the second method (AGDC) that uses these values because it is a gradient optimization method.
The hybrid algorithm (ANN-AGDC) is applied to determine the individual rate constants that correspond to three different reaction models in which the several different species, the reactions between the species and the rate constants are involved. First, the ``soft-modelling'' ANN methodology is applied because it is not necessary to have initial estimates of the rate constants and after, the values obtained for the kinetic constants, are used as initial estimates for the application of the second method of the HA, the AGDC algorithm.
The results of the application of the HA let us to establish the most probable reaction mechanism responsible of the experimental kinetic data, since the methodology has the capacity of discrimination between the different models that are theoretically applicable to the chemical reaction. This robust algorithm HA, provides the rate constants of the stages reactions of the global mechanism and further, it is able to discriminate between several different possible models that represent a great very valuable advantage in the field of modelling in chemical kinetics.Adaptive tuning of network traffic policing mechanisms for DDoS attack mitigation systemshttps://zbmath.org/1472.930872021-11-25T18:46:10.358925Z"Karpowicz, Michał P."https://zbmath.org/authors/?q=ai:karpowicz.michal-pSummary: Distributed denial-of-service (DDoS) attacks are responsible for shutting down servers, denying access to critical sectors of the economy, and generating substantial downtime costs and reputation harm. Only in 2020, over ten million DDoS attacks were observed worldwide. Commonly, open-loop network traffic rate policing is used to mitigate them. That is how network devices are currently designed. This paper shows how to extend the state-of-the-art design by introducing the adaptive closed-loop tuning of policing mechanisms. As demonstrated experimentally, open-loop policing based on the celebrated token-bucket mechanism generates a steady-state control error. In contrast, the robust self-tuning controller eliminates that control error while adjusting the bitrate limiting operations to the severe and hardware-specific network operating conditions during a DDoS attack. The study shows the controller's implementation details and discusses the critical difficulties encountered in its technical development. Furthermore, it illustrates how the control error variance depends on the commanded traffic rate limit and explains why the self-tuning controller's anti-windup filter may fail to bring the control signal back to the set of admissible control values. All experiments presented in this paper were conducted using real data from the Polish nation-wide cybersecurity system FLDX managed by the NASK National Research Institute.Using temporary logics and model checkers for dynamic control abnormal deviations of the systemhttps://zbmath.org/1472.931142021-11-25T18:46:10.358925Z"Prokop'ev, S. E."https://zbmath.org/authors/?q=ai:prokopev.s-eSummary: We propose to apply the temporary logics and model checkers for dynamic control of ``abnormal'' deviations of a system by approximating its ``normal'' features with the temporary logic formulas. Also, we propose an exhaustive blind search algorithm for discovering regularities which can be expressed with the help of the temporal logics.A reinforcement learning neural network for robotic manipulator controlhttps://zbmath.org/1472.931262021-11-25T18:46:10.358925Z"Hu, Yazhou"https://zbmath.org/authors/?q=ai:hu.yazhou"Si, Bailu"https://zbmath.org/authors/?q=ai:si.bailuSummary: We propose a neural network model for reinforcement learning to control a robotic manipulator with unknown parameters and dead zones. The model is composed of three networks. The state of the robotic manipulator is predicted by the state network of the model, the action policy is learned by the action network, and the performance index of the action policy is estimated by a critic network. The three networks work together to optimize the performance index based on the reinforcement learning control scheme. The convergence of the learning methods is analyzed. Application of the proposed model on a simulated two-link robotic manipulator demonstrates the effectiveness and the stability of the model.A machine-learning approach to synthesize virtual sensors for parameter-varying systemshttps://zbmath.org/1472.931812021-11-25T18:46:10.358925Z"Masti, Daniele"https://zbmath.org/authors/?q=ai:masti.daniele"Bernardini, Daniele"https://zbmath.org/authors/?q=ai:bernardini.daniele"Bemporad, Alberto"https://zbmath.org/authors/?q=ai:bemporad.albertoSummary: This paper introduces a novel model-free approach to synthesize virtual sensors for the estimation of dynamical quantities that are unmeasurable at runtime but are available for design purposes on test benches. After collecting a dataset of measurements of such quantities, together with other variables that are also available during on-line operations, the virtual sensor is obtained using machine learning techniques by training a predictor whose inputs are the measured variables and the features extracted by a bank of linear observers fed with the same measures. The approach is applicable to infer the value of quantities such as physical states and other time-varying parameters that affect the dynamics of the system. The proposed virtual sensor architecture -- whose structure can be related to the multiple model adaptive estimation framework -- is conceived to keep computational and memory requirements as low as possible, so that it can be efficiently implemented in embedded hardware platforms.
The effectiveness of the approach is shown in different numerical examples, involving the estimation of the scheduling parameter of a nonlinear parameter-varying system, the reconstruction of the mode of a switching linear system, and the estimation of the state of charge (SoC) of a lithium-ion battery.A nonlocal Weickert type PDE applied to multi-frame super-resolutionhttps://zbmath.org/1472.940022021-11-25T18:46:10.358925Z"Ait Bella, Fatimzehrae"https://zbmath.org/authors/?q=ai:ait-bella.fatimzehrae"Hadri, Aissam"https://zbmath.org/authors/?q=ai:hadri.aissam"Hakim, Abdelilah"https://zbmath.org/authors/?q=ai:hakim.abdelilah"Laghrib, Amine"https://zbmath.org/authors/?q=ai:laghrib.amineSummary: In this paper, we propose a nonlocal Weickert type PDE for the multiframe super-resolution task. The proposed PDE can not only preserve singularities and edges while smoothing, but also can keep safe the texture much better. This PDE is based on the nonlocal setting of the anisotropic diffusion behavior by constructing a nonlocal term of Weickert type, which is known by its coherence enhancing diffusion tensor properties. A mathematical study concerning the well-posedness of the nonlocal PDE is also investigated with an appropriate choice of the functional space. This PDE has demonstrated its efficiency by combining the diffusion process of Perona-Malik in the flat regions and the anisotropic diffusion of the Weickert model near strong edges, as well as the ability of the non-local term to preserve the texture. The elaborated experimental results give a great insight into the effectiveness of the proposed nonlocal PDE compared to some PDEs, visually and quantitatively.Image encryption using adaptive multiband signal decompositionhttps://zbmath.org/1472.940032021-11-25T18:46:10.358925Z"Alkishriwo, Osama A. S."https://zbmath.org/authors/?q=ai:alkishriwo.osama-a-sSummary: Due to the rapid growth of multimedia transmission over the internet, the challenges of image security have become an important research topic. In this paper, an Adaptive Multiband Signal Decomposition (AMSD) is proposed and its application for image encryption is explored. Like the conventional multiband wavelet transform, the AMSD can decompose the original image into multiband subimages. The perfect reconstruction of the original image from the decomposed multibands is achieved. In addition, a novel image encryption algorithm based on the adaptive multiband image decomposition with three dimensional discrete chaotic maps is developed and its performance is evaluated using common security analysis methods. Simulation results show that the proposed encryption algorithm has great degree of security and can resist various typical attacks.Shearlets as feature extractor for semantic edge detection: the model-based and data-driven realmhttps://zbmath.org/1472.940042021-11-25T18:46:10.358925Z"Andrade-Loarca, Héctor"https://zbmath.org/authors/?q=ai:andrade-loarca.hector"Kutyniok, Gitta"https://zbmath.org/authors/?q=ai:kutyniok.gitta"Öktem, Ozan"https://zbmath.org/authors/?q=ai:oktem.ozanSummary: Semantic edge detection has recently gained a lot of attention as an image-processing task, mainly because of its wide range of real-world applications. This is based on the fact that edges in images contain most of the semantic information. Semantic edge detection involves two tasks, namely pure edge detection and edge classification. Those are in fact fundamentally distinct in terms of the level of abstraction that each task requires. This fact is known as the distracted supervision paradox and limits the possible performance of a supervised model in semantic edge detection. In this work, we will present a novel hybrid method that is based on a combination of the model-based concept of shearlets, which provides probably optimally sparse approximations of a model class of images, and the data-driven method of a suitably designed convolutional neural network. We show that it avoids the distracted supervision paradox and achieves high performance in semantic edge detection. In addition, our approach requires significantly fewer parameters than a pure data-driven approach. Finally, we present several applications such as tomographic reconstruction and show that our approach significantly outperforms former methods, thereby also indicating the value of such hybrid methods for biomedical imaging.Variational approach for rigid co-registration of optical/SAR satellite images in agricultural areashttps://zbmath.org/1472.940072021-11-25T18:46:10.358925Z"Hnatushenko, Volodymyr"https://zbmath.org/authors/?q=ai:hnatushenko.volodymyr-v"Kogut, Peter"https://zbmath.org/authors/?q=ai:kogut.peter-i"Uvarov, Mykola"https://zbmath.org/authors/?q=ai:uvarov.mykola-vSummary: In this paper the problem of Synthetic Aperture Radar (SAR) and optical satellite images co-registration is considered. Because of the distinct natures of SAR and optical images, there exist huge radiometric and geometric differences between such images. As a result, the traditional registration approaches are no longer applicable in this case and it makes the registration process challenging. Mostly motivated by the crop field monitoring problem, we propose a new variational approach to the co-registration of SAR and optical images. The core idea of our approach is to involve into consideration a constrained optimization problem on the set of affine transformations for which the cost functional is the \(L^p\)-cross-correlation between sustainable parts of two fattened skeletons for the selectively smoothed SAR image and the luma component of an optical image, respectively.
We discuss the consistency of the proposed statement of this problem, propose the scheme for its regularization, derive the corresponding optimality system, and describe in detail the algorithm for the practical implementation of co-registration procedure. To evaluate the performance of the proposed approach, we illustrate its crucial steps with the help of several numerical experiments and real satellite images.Enhanced HDR image synthesis using local luminance and activity-adaptive multi-layer tone combinationhttps://zbmath.org/1472.940082021-11-25T18:46:10.358925Z"Kim, Tae-Kyu"https://zbmath.org/authors/?q=ai:kim.tae-kyu"Lee, Sung-Hak"https://zbmath.org/authors/?q=ai:lee.sung-hak"Song, Inho"https://zbmath.org/authors/?q=ai:song.inho"Wei, Qun"https://zbmath.org/authors/?q=ai:wei.qunSummary: High dynamic range (HDR) imaging is the process of compressing a HDR image into a low dynamic range (LDR) image for LDR displays. In most cases, detail preservation takes precedence over tone mapping because the dynamic range differs significantly between the input and output images. But there are disadvantages of color distortion and noise amplification at the object boundary. In this paper, the separated detail signal is combined with the base signal after an adaptive Kalman filter is applied according to local standard deviation. As well, the image is mixed by calculating the appropriate contrast extension factor using the local standard deviation. We confirmed that the proposed method enhances the image quality by checking the noise reduction in the dim surround region and reducing color degradation in the bright region.Image classification method with multi-scale featureshttps://zbmath.org/1472.940122021-11-25T18:46:10.358925Z"Lu, Peng"https://zbmath.org/authors/?q=ai:lu.peng"Zou, Peiqi"https://zbmath.org/authors/?q=ai:zou.peiqi"Zou, Guoliang"https://zbmath.org/authors/?q=ai:zou.guoliang"Zheng, Zongsheng"https://zbmath.org/authors/?q=ai:zheng.zongsheng"Liang, Sheng"https://zbmath.org/authors/?q=ai:liang.shengSummary: The study of complex image classification involves extracting features of different scales of a mixed-grained data set. However, the ouput feature of convolutional neural network is fixed and cannot fully satisfy the classification requirements of the image. This problem has a certain impact on feature extraction. In this paper, we propose a new multi-scale model based on multi-scale feature with support vector machine (MS-SVM) algorithm for adaptive and robust complex objects classification, also we aggregate localization features and high-level semantics features for this purpose. A multi-scale feature space is established for weighting the extracted multi-scale features. The experimental results show that the proposed method was able to achieve accuracies of 97.2\% on the MalayaKew (MK) leaf dataset, and has a strong generalization in the common datasets.Image mosaic based on structural similarity and fuzzy reasoninghttps://zbmath.org/1472.940132021-11-25T18:46:10.358925Z"Niu, Guochen"https://zbmath.org/authors/?q=ai:niu.guochen"Wang, Licheng"https://zbmath.org/authors/?q=ai:wang.lichengSummary: Aiming at the facts that the internal structure of the aircraft fuel tank is complex and the adjacent images are difficult to be matched, an image mosaic based on structural similarity and fuzzy reasoning is proposed. The feature points are detected according to the speed-up robust features (SURF) algorithm. The major matching point pairs are found by structural similarity calculation and the model parameters of the optimal homography matrix are obtained to proceed to the next step. After image registration, image fusion is performed by using the weighted average method where the weights are obtained by fuzzy reasoning. Experiments show that the image mosaic method based on structural similarity and fuzzy reasoning is better than the traditional method, and the detailed information of images could have good effects on panorama fusion.A multi-scale UAV image matching method applied to large-scale landslide reconstructionhttps://zbmath.org/1472.940152021-11-25T18:46:10.358925Z"Ren, Chaofeng"https://zbmath.org/authors/?q=ai:ren.chaofeng"Zhi, Xiaodong"https://zbmath.org/authors/?q=ai:zhi.xiaodong"Pu, Yuchi"https://zbmath.org/authors/?q=ai:pu.yuchi"Zhang, Fuqiang"https://zbmath.org/authors/?q=ai:zhang.fuqiangSummary: Three-dimensional (3D) sparse reconstruction of landslide topography based on unmanned aerial vehicle (UAV) images has been widely used for landslide monitoring and geomorphological analysis. In order to solve the isolated island phenomenon caused by multi-scale image matching, which means that there is no connection between the images of different scales, we herein propose a method that selects UAV image pairs based on image retrieval. In this method, sparse reconstruction was obtained via the sequential structure-from-motion (SfM) pipeline. First, principal component analysis (PCA) was used to reduce high-dimensional features to low-dimensional features to improve the efficiency of retrieval vocabulary construction. Second, by calculating the query depth threshold and discarding the invalid image pairs, we improved the efficiency of image matching. Third, the connected network of the dataset was constructed based on the initial matching of image pairs. The lost multi-scale image pairs were identified and matched through the image query between the connection components, which further improved the integrity of image matching. Our experimental results show that, compared with the traditional image retrieval method, the efficiency of the proposed method is improved by 25.9\%.An effective subgradient method for simultaneous restoration and segmentation of blurred imageshttps://zbmath.org/1472.940162021-11-25T18:46:10.358925Z"Serezhnikova, T. I."https://zbmath.org/authors/?q=ai:serezhnikova.t-iSummary: The segmentation of blurred and noise images is of great importance. There have been several recent works to link the problems of image segmentation and image reconstruction. Here we describe the universal subgradient method for simultaneous restoration and segmentation of blurred and noise images. Our method is based on the universal subgradient construction. Our universal subgradient contains both the brightness function and the brightness function gradient. In the paper we demonstrate that our method is effective for simultaneous restorations and segmentations of blurred images.
For the entire collection see [Zbl 1467.34001].Multi-source remote sensing image classification based on two-channel densely connected convolutional networkshttps://zbmath.org/1472.940172021-11-25T18:46:10.358925Z"Song, Haifeng"https://zbmath.org/authors/?q=ai:song.haifeng"Yang, Weiwei"https://zbmath.org/authors/?q=ai:yang.weiwei"Dai, Songsong"https://zbmath.org/authors/?q=ai:dai.songsong"Yuan, Haiyan"https://zbmath.org/authors/?q=ai:yuan.haiyanSummary: Remote sensing image classification exploiting multiple sensors is a very challenging problem: The traditional methods based on the medium- or low-resolution remote sensing images always provide low accuracy and poor automation level because the potential of multi-source remote sensing data are not fully utilized and the low-level features are not effectively organized. The recent method based on deep learning can efficiently improve the classification accuracy, but as the depth of deep neural network increases, the network is prone to be overfitting. In order to address these problems, a novel Two-channel Densely Connected Convolutional Networks (TDCC) is proposed to automatically classify the ground surfaces based on deep learning and multi-source remote sensing data. The main contributions of this paper includes the following aspects: First, the multi-source remote sensing data consisting of hyperspectral image (HSI) and Light Detection and Ranging (LiDAR) are pre-processed and re-sampled, and then the hyperspectral data and LiDAR data are input into the feature extraction channel, respectively. Secondly, two-channel densely connected convolutional networks for feature extraction were proposed to automatically extract the spatial-spectral feature of HSI and LiDAR. Thirdly, a feature fusion network is designed to fuse the hyperspectral image features and LiDAR features. The fused features were classified and the output result is the category of the corresponding pixel. The experiments were conducted on popular dataset, the results demonstrate that the competitive performance of the TDCC with respect to classification performance compared with other state-of-the-art classification methods in terms of the OA, AA and Kappa, and it is more suitable for the classification of complex ground surfaces.A method for segmentation of color images and contour detectionhttps://zbmath.org/1472.940182021-11-25T18:46:10.358925Z"Spasova, Gergana"https://zbmath.org/authors/?q=ai:spasova.gerganaThis article focuses on segmenting color images of water sources and detecting contours of the water sources. Based on the observation that, on the blue channel, the water area in the image is darker, a threshold algorithm identifying the blue pixels is presented to solve the problem. The algorithm has been tested on four images of different sizes and resolutions to show its effectiveness. To show the practicality of the algorithm, it is expected to do experiments on more color images and also check the effects of selected thresholds on results.
For the entire collection see [Zbl 1445.53003].Multilevel thresholding using a modified ant lion optimizer with opposition-based learning for color image segmentationhttps://zbmath.org/1472.940192021-11-25T18:46:10.358925Z"Wang, Shikai"https://zbmath.org/authors/?q=ai:wang.shikai"Sun, Kangjian"https://zbmath.org/authors/?q=ai:sun.kangjian"Zhang, Wanying"https://zbmath.org/authors/?q=ai:zhang.wanying"Jia, Heming"https://zbmath.org/authors/?q=ai:jia.hemingSummary: Multilevel thresholding has important research value in image segmentation and can effectively solve region analysis problems of complex images. In this paper, Otsu and Kapur's entropy are adopted among thresholding segmentation methods. They are used as the objective functions. When the number of threshold increases, the time complexity increases exponentially. In order to overcome this drawback, a modified ant lion optimizer algorithm based on opposition-based learning (MALO) is proposed to determine the optimum threshold values by the maximization of the objective functions. By introducing the opposition-based learning strategy, the search accuracy and convergence performance are increased. In addition to IEEE CEC 2017 benchmark functions validation, 11 state-of-the-art algorithms are selected for comparison. A series of experiments are conducted to evaluate the segmentation performance of the algorithm. The evaluation metrics include: fitness value, peak signal-to-noise ratio, structural similarity index, feature similarity index, and computational time. The experimental data are analyzed and discussed in details. The experimental results significantly demonstrate that the proposed method is superior over others, which can be considered as a powerful and efficient thresholding technique.Design of an alternative NTRU encryption with high secure and efficienthttps://zbmath.org/1472.940442021-11-25T18:46:10.358925Z"Abo-Alsood, Hadeel Hadi"https://zbmath.org/authors/?q=ai:abo-alsood.hadeel-hadi"Yassein, Hassan Rashed"https://zbmath.org/authors/?q=ai:yassein.hassan-rashedSummary: With the need to store a huge amount of personal information, Computer hardware has become extremely vital nowadays. However, some challenges follow this expansion; for instance, solving the problem of maintaining security challenges by using high-security algorithms. As a result, a high-security cryptosystem with low computation power is needed. One of the lattice-based cryptosystems that meet these requirements is NTRU. Since the NTRU cryptosystem proposal, many variants were proposed by researchers using different algebraic structures. In this paper, we design a new cryptosystem variant of NTRU, called BOTRU, which is a high-performing system based on bi-octonion subalgebra and it has good resistance to some well-known attacks, such as a brute force attack. The creation of two public keys in the system proposed has differentiated it from NTRU and NTRU like cryptosystems. Some arithmetic operations are used for comparing the efficiency of BOTRU with the OTRU cryptosystem. Based on arithmetic assessment, the comparison reveals that the BOTRU has a higher speed than the OTRU.Big prime field FFT on the GPUhttps://zbmath.org/1472.940462021-11-25T18:46:10.358925Z"Chen, Liangyu"https://zbmath.org/authors/?q=ai:chen.liangyu"Covanov, Svyatoslav"https://zbmath.org/authors/?q=ai:covanov.svyatoslav"Mohajerani, Davood"https://zbmath.org/authors/?q=ai:mohajerani.davood"Moreno Maza, Marc"https://zbmath.org/authors/?q=ai:moreno-maza.marcSeedless fruit is the sweetest: random number generation, revisitedhttps://zbmath.org/1472.940482021-11-25T18:46:10.358925Z"Coretti, Sandro"https://zbmath.org/authors/?q=ai:coretti.sandro"Dodis, Yevgeniy"https://zbmath.org/authors/?q=ai:dodis.yevgeniy"Karthikeyan, Harish"https://zbmath.org/authors/?q=ai:karthikeyan.harish"Tessaro, Stefano"https://zbmath.org/authors/?q=ai:tessaro.stefanoSummary: The need for high-quality randomness in cryptography makes random-number generation one of its most fundamental tasks.
A recent important line of work (initiated by \textit{Y. Dodis} et al. [``Security analysis of pseudo-random number generators with input: /dev/random is not robust'', in: Proceedings of the 2013 ACM SIGSAC conference on computer \& communications security, CCS'13, Berlin, Germany, November 4--8, 2013. 647--658 (2013; \url{doi:10.1145/2508859.2516653})]) focuses on the notion of robustness for pseudorandom number generators (PRNGs) with inputs. These are primitives that use various sources to accumulate sufficient entropy into a state, from which pseudorandom bits are extracted. Robustness ensures that PRNGs remain secure even under state compromise and adversarial control of entropy sources. However, the achievability of robustness inherently depends on a seed, or, alternatively, on an ideal primitive (e.g., a random oracle), independent of the source of entropy. Both assumptions are problematic: seed generation requires randomness to start with, and it is arguable whether the seed or the ideal primitive can be kept independent of the source.
This paper resolves this dilemma by putting forward new notions of robustness which enable both (1) seedless PRNGs and (2) primitive-dependent adversarial sources of entropy. To bypass obvious impossibility results, we make a realistic compromise by requiring that the source produce sufficient entropy even given its evaluations of the underlying primitive. We also provide natural, practical, and provably secure constructions based on hash-function designs from compression functions, block ciphers, and permutations. Our constructions can be instantiated with minimal changes to industry-standard hash functions SHA-2 and SHA-3, or key derivation function HKDF, and can be downgraded to (online) seedless randomness extractors, which are of independent interest.
On the way we consider both a computational variant of robustness, where attackers only make a bounded number of queries to the ideal primitive, as well as a new information-theoretic variant, which dispenses with this assumption to a certain extent, at the price of requiring a high rate of injected weak randomness (as it is, e.g., plausible on Intel's on-chip RNG). The latter notion enables applications such as everlasting security. Finally, we show that the CBC extractor, used by Intel's on-chip RNG, is provably insecure in our model.
For the entire collection see [Zbl 1428.94004].An algorithm for checking the existence of subquasigroupshttps://zbmath.org/1472.940502021-11-25T18:46:10.358925Z"Galatenko, Alekseĭ Vladimirovich"https://zbmath.org/authors/?q=ai:galatenko.aleksei-vladimirovich"Pankrat'ev, Anton Evgen'evich"https://zbmath.org/authors/?q=ai:pankratev.anton-evgenevich"Staroverov, Vladimir Mikhaĭlovich"https://zbmath.org/authors/?q=ai:staroverov.vladimir-mikhailovichSummary: Quasigroup-based cryptoalgorithms are being actively studied in the framework of theoretic projects; besides that, a number of quasigroup-based algorithms took part in NIST contests for selection of cryptographic standards. From the viewpoint of security it is highly desirable to use quasigroups without proper subquasigroups (otherwise transformations can degrade). We propose algorithms that take a quasigroup specified by the Cayley table as the input and decide whether there exist proper subquasigroups or subquasigroups of the order at least 2. Temporal complexity of the algorithms is optimized at the cost of increased spatial complexity. We prove bounds on time and memory and analyze the efficiency of software implementations applied to quasigroups of a large order. The results were reported at the XVIII International Conference ``Algebra, Number Theory and Discrete Geometry: modern problems, applications and problems of history''.Symmetric cryptoalgorithms in the residue number systemhttps://zbmath.org/1472.940532021-11-25T18:46:10.358925Z"Kasianchuk, M. M."https://zbmath.org/authors/?q=ai:kasianchuk.m-m"Yakymenko, I. Z."https://zbmath.org/authors/?q=ai:yakymenko.i-z"Nykolaychuk, Ya. M."https://zbmath.org/authors/?q=ai:nykolaychuk.ya-mSummary: This paper presents theoretical backgrounds of the symmetric encryption based on the residue number system. The peculiarities of this approach are that in the case of restoring a decimal number based on its residuals using the Chinese remainder theorem, multiplication occurs by arbitrarily chosen coefficients (keys). It is established that cryptostability of the developed methods is determined by the number of modules and their bit size. In addition, the described methods are found to allow to almost indefinitely increase the block of plain text for encryption, which eliminates the necessity to use different encryption modes.Construction of RNG using random automata and ``one-way'' functionshttps://zbmath.org/1472.940602021-11-25T18:46:10.358925Z"Popov, V. O."https://zbmath.org/authors/?q=ai:popov.vladimir-olegovich"Smyshlyaev, S. V."https://zbmath.org/authors/?q=ai:smyshlyaev.stanislav-vSummary: We consider a number of practical issues related to requirements for pseudorandom number generators used for cryptographic software needs. They extend further than general requirements of (practical) indistinguishability of output sequence from the sequence of independent uniformly distributed random variables. We formulate these additional requirements and present a general construction of RNG for usage in cryptographic software that is proposed to meet all of them.Injective trapdoor functions via derandomization: how strong is Rudich's black-box barrier?https://zbmath.org/1472.940612021-11-25T18:46:10.358925Z"Rotem, Lior"https://zbmath.org/authors/?q=ai:rotem.lior"Segev, Gil"https://zbmath.org/authors/?q=ai:segev.gilSummary: We present a cryptographic primitive \(\mathcal{P}\) satisfying the following properties:
\par i) \textit{S. Rudich}'s seminal impossibility result [Limits on the provable consequences of one-way functions. EECS Department, University of California, Berkeley (PhD Thesis) (1988)] shows that \(\mathcal{P}\) cannot be used in a black-box manner to construct an injective one-way function.
\par i) \(\mathcal{P}\) can be used in a non-black-box manner to construct an injective one-way function assuming the existence of a hitting-set generator that fools deterministic circuits (such a generator is known to exist based on the worst-case assumption that \(\mathrm{E}=\mathrm{DTIME}(2^{O(n)})\) has a function of deterministic circuit complexity \(2^{\Omega(n)})\). The non-black box aspect of our construction only requires a bound on the size of \(\mathcal{P}\)'s implementation.
\par ii) Augmenting \(\mathcal{P}\) with a trapdoor algorithm enables a non-black-box construction of an injective trapdoor function (once again, assuming the existence of a hitting-set generator that fools deterministic circuits), while Rudich's impossibility result [loc. cit.] still holds.
The primitive \(\mathcal{P}\) and its augmented variant can be constructed based on any injective one-way function and on any injective trapdoor function, respectively, and they are thus unconditionally essential for the existence of such functions. Moreover, \(\mathcal{P}\) can also be constructed based on various known primitives that are secure against related-key attacks (e.g., pseudorandom functions), thus enabling to base the strong structural guarantees of injective one-way functions on the strong security guarantees of such primitives. Our application of derandomization techniques is inspired mainly by the work of \textit{B. Barak} et al. [Lect. Notes Comput. Sci. 2729, 299--315 (2003; Zbl 1122.94347)], which on one hand relies on any one-way function, but on the other hand only results in a non-interactive perfectly binding commitment scheme (offering significantly weaker structural guarantees compared to injective one-way functions) and does not seem to enable an extension to public-key primitives. The key observation underlying our approach is that Rudich's impossibility result [loc. cit.] applies not only to one-way functions as the underlying primitive, but in fact to a variety of ``unstructured'' primitives. We put forward a condition for identifying such primitives, and then subtly tailor the properties of our primitives such that they are both sufficiently unstructured in order to satisfy this condition, and sufficiently structured in order to yield injective one-way and trapdoor functions. This circumvents the basic approach underlying Rudich's long-standing evidence for the difficulty of constructing injective one-way functions (and, in particular, injective trapdoor functions) based on seemingly weaker or unstructured assumptions.Proposing an MILP-based method for the experimental verification of difference-based trails: application to SPECK, SIMECKhttps://zbmath.org/1472.940622021-11-25T18:46:10.358925Z"Sadeghi, Sadegh"https://zbmath.org/authors/?q=ai:sadeghi.sadegh"Rijmen, Vincent"https://zbmath.org/authors/?q=ai:rijmen.vincent"Bagheri, Nasour"https://zbmath.org/authors/?q=ai:bagheri.nasourSummary: Searching for the right pairs of inputs in difference-based distinguishers is an important task for the experimental verification of the distinguishers in symmetric-key ciphers. In this paper, we develop an MILP-based approach to verify the possibility of difference-based distinguishers and extract the right pairs. We apply the proposed method to some published difference-based trails (Related-Key Differentials (RKD), Rotational-XOR (RX)) of block ciphers \texttt{SIMECK}, and \texttt{SPECK}. As a result, we show that some of the reported RX-trails of \texttt{SIMECK} and \texttt{SPECK} are incompatible, i.e. there are no right pairs that follow the expected propagation of the differences for the trail. Also, for compatible trails, the proposed approach can efficiently speed up the search process of finding the exact value of a weak key from the target weak key space. For example, in one of the reported 14-round RX trails of \texttt{SPECK}, the probability of a key pair to be a weak key is \(2^{-94.91}\) when the whole key space is \(2^{96}\); our method can find a key pair for it in a comparatively short time. It is worth noting that it was impossible to find this key pair using a traditional search. As another result, we apply the proposed method to \texttt{SPECK} block cipher, to construct longer related-key differential trails of \texttt{SPECK} which we could reach 15, 16, 17, and 19 rounds for \texttt{SPECK32/64}, \texttt{SPECK48/96}, \texttt{SPECK64/128}, and \texttt{SPECK128/256}, respectively. It should be compared with the best previous results which are 12, 15, 15, and 20 rounds, respectively, that both attacks work for a certain weak key class. It should be also considered as an improvement over the reported result of rotational-XOR cryptanalysis on \texttt{SPECK}.Constructing keyed strong S-Box using an enhanced quadratic maphttps://zbmath.org/1472.940642021-11-25T18:46:10.358925Z"Si, Yuanyuan"https://zbmath.org/authors/?q=ai:si.yuanyuan"Liu, Hongjun"https://zbmath.org/authors/?q=ai:liu.hongjun"Chen, Yuehui"https://zbmath.org/authors/?q=ai:chen.yuehuiA novel lightweight block encryption algorithm based on combined chaotic S-boxhttps://zbmath.org/1472.940652021-11-25T18:46:10.358925Z"Tong, Xiaojun"https://zbmath.org/authors/?q=ai:tong.xiaojun"Liu, Xudong"https://zbmath.org/authors/?q=ai:liu.xudong"Liu, Jing"https://zbmath.org/authors/?q=ai:liu.jing.1|liu.jing"Zhang, Miao"https://zbmath.org/authors/?q=ai:zhang.miao"Wang, Zhu"https://zbmath.org/authors/?q=ai:wang.zhuZakrevskij's cipher based on reconfigurable FSMhttps://zbmath.org/1472.940662021-11-25T18:46:10.358925Z"Tren'kaev, V. N."https://zbmath.org/authors/?q=ai:trenkaev.v-nSummary: The paper presents Zakrevskij's cipher realization based on reconfigurable finite state machine (FSM). The reconfigurable FSM generates a ciphering automaton according to a key. The cipher system can resist the brute-force attack and has key length which is acceptable in practice. The cipher system is shown can not resist the chosen-plaintext attack when a cryptanalyst knows the initial state of the ciphering automaton and has many copies of the cipher machine.On digital circuit optimization using automata equationshttps://zbmath.org/1472.941012021-11-25T18:46:10.358925Z"Kushik, Natal'y G."https://zbmath.org/authors/?q=ai:kushik.nataly-g"Rekun, Mariya V."https://zbmath.org/authors/?q=ai:rekun.mariya-vSummary: The paper is devoted to combinational circuit optimization based on automata equation solving. We show how the flexibility of a component circuit can be calculated when using behavioral functions and propose a technique for checking whether some output functions can be simplified. For example, we show how to chek whether there exists an output function that can equal to 0 or to 1 or whether two output functions can be equal up to the inversion. The proposed technique is illustrated by a simple example.