Proceedings of the National Academy of Sciences of the United States of America Short Title: Proc. Natl. Acad. Sci. USA Publisher: National Academy of Sciences, Washington, DC ISSN: 0027-8424; 1091-6490/e Online: https://www.pnas.org/content/by/year Comments: Journal Documents Indexed: 5,093 Publications (since 1915) References Indexed: 865 Publications with 22,167 References. all top 5 Latest Issues 118, No. 10 (2021) 118, No. 9 (2021) 118, No. 6 (2021) 118, No. 4 (2021) 118, No. 3 (2021) 118, No. 2 (2021) 118, No. 1 (2021) 117, No. 52 (2021) 117, No. 51 (2020) 117, No. 50 (2020) 117, No. 49 (2020) 117, No. 48 (2020) 117, No. 47 (2020) 117, No. 46 (2020) 117, No. 44 (2020) 117, No. 42 (2020) 117, No. 41 (2020) 117, No. 40 (2020) 117, No. 39 (2020) 117, No. 38 (2020) 117, No. 37 (2020) 117, No. 36 (2020) 117, No. 35 (2020) 117, No. 34 (2020) 117, No. 33 (2020) 117, No. 32 (2020) 117, No. 31 (2020) 117, No. 30 (2020) 117, No. 29 (2020) 117, No. 28 (2020) 117, No. 27 (2020) 117, No. 26 (2020) 117, No. 25 (2020) 117, No. 24 (2020) 117, No. 23 (2020) 117, No. 22 (2020) 117, No. 21 (2020) 117, No. 20 (2020) 117, No. 19 (2020) 117, No. 18 (2020) 117, No. 12 (2020) 117, No. 11 (2020) 117, No. 10 (2020) 117, No. 9 (2020) 117, No. 8 (2020) 117, No. 7 (2020) 117, No. 6 (2020) 117, No. 5 (2020) 117, No. 4 (2020) 117, No. 3 (2020) 117, No. 2 (2020) 117, No. 1 (2020) 116, No. 52 (2019) 116, No. 51 (2019) 116, No. 50 (2019) 116, No. 48 (2019) 116, No. 47 (2019) 116, No. 46 (2019) 116, No. 45 (2019) 116, No. 44 (2019) 116, No. 43 (2019) 116, No. 42 (2019) 116, No. 40 (2019) 116, No. 39 (2019) 116, No. 38 (2019) 116, No. 37 (2019) 116, No. 36 (2019) 116, No. 34 (2019) 116, No. 32 (2019) 116, No. 31 (2019) 116, No. 30 (2019) 116, No. 29 (2019) 116, No. 28 (2019) 116, No. 23 (2019) 116, No. 21 (2019) 116, No. 20 (2019) 116, No. 19 (2019) 116, No. 18 (2019) 116, No. 17 (2019) 116, No. 16 (2019) 116, No. 14 (2019) 116, No. 13 (2019) 116, No. 12 (2019) 116, No. 10 (2019) 116, No. 8 (2019) 116, No. 7 (2019) 116, No. 6 (2019) 116, No. 5 (2019) 116, No. 4 (2019) 116, No. 3 (2019) 116, No. 2 (2019) 116, No. 1 (2019) 115, No. 51 (2018) 115, No. 46 (2018) 115, No. 44 (2018) 115, No. 43 (2018) 115, No. 42 (2018) 115, No. 41 (2018) 115, No. 40 (2018) 115, No. 39 (2018) ...and 700 more Volumes all top 5 Authors 185 Miller, George Abram 80 Vandiver, Harry Schultz 67 Kasner, Edward 58 Walsh, Joseph Leonard 54 Thomas, Tracy Yerkes 53 Bellman, Richard Ernest 46 Morse, Marston 46 Murnaghan, Francis Dominic 43 de Cicco, John 41 Eisenhart, Luther Pfahler 39 Douglas, Jesse 37 Majda, Andrew J. 36 Bochner, Salomon 35 Bateman, Harry 35 Robbins, Herbert Ellis 34 Michal, Aristotle Demetrius 33 Browder, Felix Earl 33 Wilson, Edwin Bidwell 28 Hille, Einar 28 Moore, Robert Lee 24 Alexander, James Waddell 24 Birkhoff, George David 22 Whyburn, Gordon Thomas 21 Stein, Elias Menachem 21 Veblen, Oswald 20 Epstein, Paul Sophus 19 Kimura, Motoo 19 Lefschetz, Solomon 19 von Neumann, John 19 Whitney, Hassler 19 Wintner, Aurel 18 Albert, Abraham Adrian 18 Kalaba, Robert E. 18 Menger, Karl 18 Pekeris, Chaim Leib 18 Tolman, Richard Chace 17 Courant, Richard 16 Fefferman, Charles Louis 16 Mac Lane, Leslie Saunders 16 Samuelson, Paul Anthony 16 Spencer, Donald Clayton 16 Tamarkin, Jacob David 15 Bell, Eric Temple 15 Birkhoff, Garrett 15 Brauer, Richard 15 Chandrasekhar, Subrahmanyan 14 Barenblatt, Grigory Isaakovich 14 Chorin, Alexandre Joel 14 Karlin, Samuel 14 Kodaira, Kunihiko 14 Levinson, Norman 14 Thomas, Joseph Miller 14 Uhler, Horace Scudder 14 Widder, David Vernon 13 Evans, Griffith Conrad 13 Harish-Chandra 13 Kostant, Bertram 13 Rota, Gian-Carlo 13 Sternberg, Shlomo 13 Stone, Marshall Harvey 12 Eilenberg, Samuel 12 Huntington, Edward Vermilye 12 Sethian, James A. 11 Bagemihl, Frederick 11 Chowla, Sarvadaman 11 Chudnovsky, Gregory V. 11 Seidel, Wladimir 11 Smith, Paul Althaus 10 Cordoba, Diego 10 Kadison, Richard Vincent 10 Luyten, Willem Jacob 10 Nagylaki, Thomas 10 Ono, Ken 10 Rao, Calyampudi Radhakrishna 10 Rosenblatt, Murray 10 Trjitzinsky, Waldemar Joseph 10 Worcester, Jane 9 Chudnovsky, David V. 9 Duffin, Richard James 9 Hirschfelder, Joseph O. 9 Lai, Tze Leung 9 Motzkin, Theodore Samuel 9 Rainich, George Yuri 9 Ritt, Joseph Fels 9 Shapley, Harlow 9 Shiffman, Max 9 Ward, Morgan 9 Whitehead, John Henry Constantine 9 Wiener, Norbert 8 Boas, Ralph Philip jun. 8 Buerger, Martin J. 8 Chern, Shiing-Shen 8 Donoho, David Leigh 8 Eyring, Henry 8 Fubini, Guido 8 Hua, Loo-Keng 8 Igusa, Jun-ichi 8 Jacobson, Nathan 8 Knebelman, Morris Samuel 8 Moore, Charles Napoleon ...and 4,258 more Authors all top 5 Fields 399 Biology and other natural sciences (92-XX) 294 Statistics (62-XX) 166 Fluid mechanics (76-XX) 164 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 159 Probability theory and stochastic processes (60-XX) 150 Number theory (11-XX) 135 Partial differential equations (35-XX) 134 Quantum theory (81-XX) 132 Statistical mechanics, structure of matter (82-XX) 102 Computer science (68-XX) 98 Differential geometry (53-XX) 96 Combinatorics (05-XX) 89 Dynamical systems and ergodic theory (37-XX) 78 Manifolds and cell complexes (57-XX) 70 Numerical analysis (65-XX) 70 Mechanics of deformable solids (74-XX) 66 Group theory and generalizations (20-XX) 65 Operations research, mathematical programming (90-XX) 64 Information and communication theory, circuits (94-XX) 63 Algebraic geometry (14-XX) 61 Functional analysis (46-XX) 55 Nonassociative rings and algebras (17-XX) 50 Topological groups, Lie groups (22-XX) 47 Operator theory (47-XX) 47 Geophysics (86-XX) 44 Global analysis, analysis on manifolds (58-XX) 39 Algebraic topology (55-XX) 34 Ordinary differential equations (34-XX) 34 Harmonic analysis on Euclidean spaces (42-XX) 33 Linear and multilinear algebra; matrix theory (15-XX) 33 Several complex variables and analytic spaces (32-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 28 Systems theory; control (93-XX) 27 Mathematical logic and foundations (03-XX) 27 Associative rings and algebras (16-XX) 25 Mechanics of particles and systems (70-XX) 24 Measure and integration (28-XX) 23 History and biography (01-XX) 21 Convex and discrete geometry (52-XX) 21 General topology (54-XX) 20 Category theory; homological algebra (18-XX) 20 Special functions (33-XX) 19 General and overarching topics; collections (00-XX) 18 Commutative algebra (13-XX) 18 Functions of a complex variable (30-XX) 18 Abstract harmonic analysis (43-XX) 17 Astronomy and astrophysics (85-XX) 16 Approximations and expansions (41-XX) 16 Relativity and gravitational theory (83-XX) 13 Field theory and polynomials (12-XX) 13 Geometry (51-XX) 13 Optics, electromagnetic theory (78-XX) 12 Difference and functional equations (39-XX) 11 Potential theory (31-XX) 10 Real functions (26-XX) 10 Integral transforms, operational calculus (44-XX) 9 Order, lattices, ordered algebraic structures (06-XX) 9 Classical thermodynamics, heat transfer (80-XX) 8 Integral equations (45-XX) 3 Sequences, series, summability (40-XX) 2 \(K\)-theory (19-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 3,458 Publications have been cited 57,393 times in 48,685 Documents Cited by ▼ Year ▼ On the stability of the linear functional equation. Zbl 0061.26403Hyers, D. H. 1,218 1941 Neural networks and physical systems with emergent collective computational abilities. Zbl 1369.92007Hopfield, J. J. 1,143 1982 Equilibrium points in \(n\)-person games. Zbl 0036.01104Nash, John F. jun. 948 1950 Neurons with graded response have collective computational properties like those of two-state neurons. Zbl 1371.92015Hopfield, J. J. 841 1984 Community structure in social and biological networks. Zbl 1032.91716Girvan, M.; Newman, M. E. J. 707 2002 Vertex algebras, Kac-Moody algebras, and the monster. Zbl 0613.17012Borcherds, Richard E. 561 1986 On the stability of the linear functional equation. JFM 67.0424.01Hyers, D. H. 513 1941 Complete convergence and the law of large numbers. Zbl 0030.20101Hsu, P. L.; Robbins, Herbert 501 1947 Nonexpansive nonlinear operators in a Banach space. Zbl 0128.35801Browder, F. E. 446 1965 Stochastic games. Zbl 0051.35805Shapley, L. S. 436 1953 Statistical metrics. Zbl 0063.03886Menger, Karl 432 1942 Fixed-point and minimax theorems in locally convex topological linear spaces. Zbl 0047.35103Fan, Ky 431 1952 Functorial semantics of algebraic theories. Zbl 0119.25901Lawvere, F. W. 387 1963 A central limit theorem and a strong mixing condition. Zbl 0070.13804Rosenblatt, M. 381 1956 Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Zbl 1355.94013Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan 351 2016 Minimax theorems. Zbl 0050.06501Fan, Ky 347 1953 Bacterial swimming and oxygen transport near contact lines. Zbl 1277.35332Tuval, Idan; Cisneros, Luis; Dombrowski, Christopher; Wolgemuth, Charles W.; Kessler, John O.; Goldstein, Raymond E. 337 2005 A fast marching level set method for monotonically advancing fronts. Zbl 0852.65055Sethian, J. A. 333 1996 On some exponential sums. Zbl 0032.26102Weil, André 330 1948 A social equilibrium existence theorem. Zbl 0047.38804Debreu, Gerard 319 1952 On the contraction of groups and their representations. Zbl 0050.02601Inönü, E.; Wigner, Eugene P. 318 1953 Optimally sparse representation in general (nonorthogonal) dictionaries via \(\ell^1\) minimization. Zbl 1064.94011Donoho, David L.; Elad, Michael 301 2003 Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137Han, Jiequn; Jentzen, Arnulf; E, Weinan 292 2018 A class of Markov processes associated with nonlinear parabolic equations. Zbl 0149.13501McKean, H. P. jun. 276 1966 Systems of conservation equations with a convex extension. Zbl 0229.35061Friedrichs, K. O.; Lax, P. D. 256 1971 Fixed-point theorems for noncompact mappings in Hilbert space. Zbl 0125.35801Browder, F. E. 253 1965 Calabi’s conjecture and some new results in algebraic geometry. Zbl 0355.32028Yau, Shing-Tung 231 1977 Group theoretical discussion of relativistic wave equations. Zbl 0030.42306Bargmann, V.; Wigner, Eugene P. 228 1948 Convolution operators on Banach space valued functions. Zbl 0103.33402Benedek, A.; Calderón, Alberto P.; Panzone, R. 227 1962 Finite groups with fixed-point-free automorphisms of prime order. Zbl 0086.25101Thompson, John G. 226 1959 A characterization of Banach spaces containing \(l^1\). Zbl 0297.46013Rosenthal, Haskell P. 225 1974 Commutators of singular integral operators. Zbl 0151.16901Calderón, Alberto P. 212 1965 Nonlinear system theory: another look at dependence. Zbl 1135.62075Wu, Wei Biao 203 2005 On a generalization of the notion of manifold. Zbl 0074.18103Satake, Ichirô 203 1956 A new approach to almost periodicity. Zbl 0112.31401Bochner, Salomon 201 1962 Burrau’s problem of three bodies. Zbl 0158.43206Szebehely, Victor G. 188 1967 Maximum properties and inequalities for the eigenvalues of completely continuous operators. Zbl 0044.11502Fan, Ky 187 1951 Maximal functions. I: Spherical means. Zbl 0332.42018Stein, Elias M. 186 1976 Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. Zbl 1130.62337Donoho, David L.; Grimes, Carrie 180 2003 The structure of scientific collaboration networks. Zbl 1065.00518Newman, M. E. J. 173 2001 A simple model of global cascades on random networks. Zbl 1022.90001Watts, Duncan J. 172 2002 A nonidentifiability aspect of the problem of competing risks. Zbl 0299.62066Tsiatis, Anastasios 171 1975 Significance analysis of microarrays applied to the ionizing radiation response. Zbl 1012.92014Tusher, Virginia Goss; Tibshirani, Robert; Chu, Gilbert 171 2001 Approximate entropy as a measure of system complexity. Zbl 0756.60103Pincus, Steven M. 170 1991 A nonparametric view of network models and Newman-Girvan and other modularities. Zbl 1359.62411Bickel, Peter J.; Chen, Aiyou 163 2009 The spread of awareness and its impact on epidemic outbreaks. Zbl 1203.91242Funk, Sebastian; Gilad, Erez; Watkins, Chris; Jansen, Vincent A. A. 162 2009 Cauchy integrals on Lipschitz curves and related operators. Zbl 0373.44003Calderon, A. P. 160 1977 Decision procedure for indefinite hypergeometric summation. Zbl 0384.40001Gosper, R. William jun. 159 1978 On a ’monotonicity’ method for the solution of nonlinear equations in Banach spaces. Zbl 0124.07303Minty, G. J. 158 1963 A class of bounded pseudo-differential operators. Zbl 0244.35074Calderon, Alberto P.; Vaillancourt, Remi 157 1972 Hamiltonian systems and transformations in Hilbert space. Zbl 0002.05701Koopman, B. O. 156 1931 Global models of growth and competition. Zbl 0272.92016Gilpin, Michael E.; Ayala, Francisco J. 152 1973 Statistical significance for genomewide studies. Zbl 1130.62385Storey, John D.; Tibshirani, Robert 152 2003 Information contents of distributions. Zbl 0128.14104Wigner, Eugene P.; Yanase, M. M. 152 1963 Inequalities between the two kinds of eigenvalues of a linear transformation. Zbl 0032.38701Weyl, Hermann 150 1949 On sets of integers which contain no three terms in arithmetical progression. Zbl 0060.10302Behrend, F. A. 149 1946 Unitary operator bases. Zbl 0090.19006Schwinger, Julian 148 1960 Vaccination and the theory of games. Zbl 1064.91029Bauch, Chris T.; Earn, David J. D. 145 2004 Lyapunov functions for the problem of Lur’e in automatic control. Zbl 0113.07701Kalman, R. E. 143 1963 Synchronization in complex oscillator networks and smart grids. Zbl 1292.94185Dörfler, Florian; Chertkov, Michael; Bullo, Francesco 142 2013 Dirichlet spaces. Zbl 0089.08201Beurling, A.; Deny, Jacques 140 1959 On regular rings. Zbl 0015.38802von Neumann, John 137 1936 Two theorems in graph theory. Zbl 0086.16202Berge, Claude 137 1957 Quantum optical implementation of Grover’s algorithm. Zbl 0995.81014Scully, Marlan O.; Zubairy, M. S. 129 2001 Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Zbl 1405.42043Coifman, R. R.; Lafon, S.; Lee, A. B.; Maggioni, M.; Nadler, B.; Warner, F.; Zucker, S. W. 129 2005 Integration of stiff equations. Zbl 0046.13602Curtiss, C.; Hirschfelder, J. O. 128 1952 The average distances in random graphs with given expected degrees. Zbl 1064.05137Chung, Fan; Lu, Linyuan 127 2002 Infinite flag varieties and conjugacy theorems. Zbl 0512.17008Peterson, Dale H.; Kac, Victor G. 122 1983 Modular invariant representations of infinite-dimensional Lie algebras and superalgebras. Zbl 0652.17010Kac, Victor G.; Wakimoto, Minoru 122 1988 Calculus of twisted vertex operators. Zbl 0579.17010Lepowsky, J. 122 1985 Solution of the Heawood map-coloring problem. Zbl 0155.51201Ringel, Gerhard; Youngs, J. W. T. 122 1968 Continuous mappings of almost automorphic and almost periodic functions. Zbl 0134.30102Bochner, Salomon 120 1964 A natural representation of the Fischer-Griess monster with the modular function J as character. Zbl 0543.20016Frenkel, I. B.; Lepowsky, J.; Meurman, A. 119 1984 Spin and wedge representations of infinite-dimensional Lie algebras and groups. Zbl 0469.22016Kac, Victor G.; Peterson, Dale H. 119 1981 Sequential Monte Carlo without likelihood. Zbl 1160.65005Sisson, S. A.; Fan, Y.; Tanaka, Mark M. 119 2007 Randomized algorithms for the low-rank approximation of matrices. Zbl 1215.65080Liberty, Edo; Woolfe, Franco; Martinsson, Per-Gunnar; Rokhlin, Vladimir; Tygert, Mark 119 2007 Dirac operators coupled to vector potentials. Zbl 0547.58033Atiyah, Michael F.; Singer, I. M. 118 1984 Effect of inhomogeneity on cosmological models. Zbl 0009.04103Tolman, Richard C. 116 1934 On finite groups of even order whose 2-Sylow group is a quaternion group. Zbl 0090.01901Brauer, Richard; Suzuki, Michio 116 1959 Biregular classification of Fano 3-folds and Fano manifolds of coindex 3. Zbl 0679.14020Mukai, Shigeru 114 1989 On Moulton’s orbits in the restricted problem of three bodies. Zbl 0202.56902Szebehely, Victor 113 1966 Hamiltonian systems and transformations in Hilbert space. JFM 57.1010.02Koopman, B. O. 112 1931 Kählerian coset spaces of semisimple Lie groups. Zbl 0058.16002Borel, Armand 112 1954 The cutoff phenomenon in finite Markov chains. Zbl 0849.60070Diaconis, Persi 110 1996 The degree of convergence of sequences of linear positive operators. Zbl 0164.07102Shisha, O.; Mond, B. 110 1968 On the motion of vortices in two dimensions. I: Existence of the Kirchhoff-Routh function. II: Some further investigations on the Kirchhoff-Routh function. Zbl 0063.03560Lin, C. C. 110 1941 Sparse and stable Markowitz portfolios. Zbl 1203.91271Brodie, Joshua; Daubechies, Ingrid; De Mol, Christine; Giannone, Domenico; Loris, Ignace 109 2009 Computing geodesic paths on manifolds. Zbl 0908.65049Kimmel, R.; Sethian, J. A. 108 1998 Vertex representations of quantum affine algebras. Zbl 0662.17006Frenkel, Igor B.; Jing, Naihuan 107 1988 The independence of the continuum hypothesis. I, II. Zbl 0192.04401Cohen, Paul Joseph 107 1964 A new technique for the construction of solutions of nonlinear differential equations. Zbl 0104.30503Moser, Jürgen 107 1961 From time series to complex networks: the visibility graph. Zbl 1205.05162Lacasa, Lucas; Luque, Bartolo; Ballesteros, Fernando; Luque, Jordi; Nuño, Juan Carlos 106 2008 Eigenvalues of the Laplace operator on certain manifolds. Zbl 0124.31202Milnor, John W. 104 1964 On the spectral geometry of spaces with cone-like singularities. Zbl 0411.58003Cheeger, Jeff 103 1979 A theorem on force-free magnetic fields. Zbl 0081.21703Woltjer, L. 102 1958 The multivariate \(L_1\)-median and associated data depth. Zbl 1054.62067Vardi, Yehuda; Zhang, Cun-Hui 101 2000 An analytic generalization of the Rogers-Ramanujan identities for odd moduli. Zbl 0289.10010Andrews, George E. 100 1974 Imprimitivity for representations of locally compact groups. I. Zbl 0035.06901Mackey, George W. 99 1949 Gibbs states and the set of solutions of random constraint satisfaction problems. Zbl 1190.68031Krząkała, Florent; Montanari, Andrea; Ricci-Tersenghi, Federico; Semerjian, Guilhem; Zdeborová, Lenka 98 2007 Spectral redemption in clustering sparse networks. Zbl 1359.62252Krzakala, Florent; Moore, Cristopher; Mossel, Elchanan; Neeman, Joe; Sly, Allan; Zdeborová, Lenka; Zhang, Pan 97 2013 How the growth of ice depends on the fluid dynamics underneath. Zbl 1485.76081Wang, Ziqi; Calzavarini, Enrico; Toschi, Federico 4 2021 A polynomial algorithm for best-subset selection problem. Zbl 1485.68322Zhu, Junxian; Wen, Canhong; Wang, Xueqin 3 2021 Statistical finite elements for misspecified models. Zbl 1485.65104Duffin, Connor; Cripps, Edward; Girolami, Mark 2 2021 Evolutionarily stable strategies in stable and periodically fluctuating populations: the Rosenzweig-MacArthur predator-prey model. Zbl 1485.92087Grunert, Katrin; Holden, Helge; Stenseth, Nils Chr. 2 2021 Infection curves on small-world networks are linear only in the vicinity of the critical point. Zbl 1485.92137Kuśmierz, Łukasz; Toyoizumi, Taro 2 2021 Stochastic dynamics of barrier island elevation. Zbl 1485.86006Vinent, Orencio Durán; Schaffer, Benjamin E.; Rodriguez-Iturbe, Ignacio 1 2021 Probabilistic structure of events controlling the after-storm recovery of coastal dunes. Zbl 1485.86014Rinaldo, Tobia; Ramakrishnan, Kiran Adhithya; Vinent, Orencio Durán 1 2021 On conservation laws in quantum mechanics. Zbl 1485.81005Aharonov, Yakir; Popescu, Sandu; Rohrlich, Daniel 1 2021 True scale-free networks hidden by finite size effects. Zbl 1485.05170Serafino, Matteo; Cimini, Giulio; Caldarelli, Guido 1 2021 The role of double-diffusive convection in basal melting of Antarctic ice shelves. Zbl 1485.86015Rosevear, Madelaine Gamble; Gayen, Bishakhdatta; Galton-Fenzi, Benjamin Keith 1 2021 The inverse variance-flatness relation in stochastic gradient descent is critical for finding flat minima. Zbl 1485.82008Feng, Yu; Tu, Yuhai 1 2021 Probabilistic pragmatics explains gradience and focality in natural language quantification. Zbl 1485.03075van Tiel, Bob; Franke, Michael; Sauerland, Uli 1 2021 Machine learning active-nematic hydrodynamics. Zbl 1485.76005Colen, Jonathan; Han, Ming; Vitelli, Vincenzo 1 2021 Benign overfitting in linear regression. Zbl 1485.62085Bartlett, Peter L.; Long, Philip M.; Tsigler, Alexander 44 2020 The challenges of modeling and forecasting the spread of COVID-19. Zbl 1485.92115Bertozzi, Andrea L.; Franco, Elisa; Sledge, Daniel 14 2020 Mining gold from implicit models to improve likelihood-free inference. Zbl 1461.62043Brehmer, Johann; Louppe, Gilles; Pavez, Juan; Cranmer, Kyle 13 2020 Theoretical issues in deep networks. Zbl 1485.68235Poggio, Tomaso; Banburski, Andrzej; Liao, Qianli 7 2020 The frontier of simulation-based inference. Zbl 1485.62004Cranmer, Kyle; Brehmer, Johann; Louppe, Gilles 7 2020 Shaping the learning landscape in neural networks around wide flat minima. Zbl 1456.92009Baldassi, Carlo; Pittorino, Fabrizio; Zecchina, Riccardo 6 2020 A network-based explanation of why most COVID-19 infection curves are linear. Zbl 1485.92159Thurner, Stefan; Klimek, Peter; Hanel, Rudolf 6 2020 Stable homotopy groups of spheres. Zbl 1485.55017Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli 6 2020 The turning point and end of an expanding epidemic cannot be precisely forecast. Zbl 1485.92118Castro, Mario; Ares, Saúl; Manrubia, Susanna 6 2020 Guided transition waves in multistable mechanical metamaterials. Zbl 1456.74139Jin, Lishuai; Khajehtourian, Romik; Mueller, Jochen; Rafsanjani, Ahmad; Tournat, Vincent; Bertoldi, Katia; Kochmann, Dennis M. 5 2020 Topological data analysis of zebrafish patterns. Zbl 1456.92004Mcguirl, Melissa R.; Volkening, Alexandria; Sandstede, Björn 5 2020 Using machine learning to predict extreme events in complex systems. Zbl 1456.68176Qi, Di; Majda, Andrew J. 4 2020 Veridical data science. Zbl 1456.62321Yu, Bin; Kumbier, Karl 4 2020 Universal inference. Zbl 1485.62020Wasserman, Larry; Ramdas, Aaditya; Balakrishnan, Sivaraman 4 2020 Dimple drainage before the coalescence of a droplet deposited on a smooth substrate. Zbl 1485.76013Duchemin, Laurent; Josserand, Christophe 4 2020 Causal inference in genetic trio studies. Zbl 1485.92072Bates, Stephen; Sesia, Matteo; Candès, Emmanuel 4 2020 Local lockdowns outperform global lockdown on the far side of the COVID-19 epidemic curve. Zbl 1485.92005Karatayev, Vadim A.; Anand, Madhur; Bauch, Chris T. 4 2020 Testing for dependence on tree structures. Zbl 1485.62078Behr, Merle; Ansari, M. Azim; Holmes, Chris 3 2020 Superdiffusive transport of energy in one-dimensional metals. Zbl 1485.82014Bulchandani, Vir B.; Karrasch, Christoph; Moore, Joel E. 3 2020 Deep rotating convection generates the polar hexagon on saturn. Zbl 1485.85023Yadav, Rakesh K.; Bloxham, Jeremy 3 2020 Stochastic reaction networks in dynamic compartment populations. Zbl 1485.92041Duso, Lorenzo; Zechner, Christoph 3 2020 The mysterious story of square ice, piles of cubes, and bijections. Zbl 1485.05009Fischer, Ilse; Konvalinka, Matjaž 3 2020 Prevalence of neural collapse during the terminal phase of deep learning training. Zbl 1489.68237Papyan, Vardan; Han, X. Y.; Donoho, David L. 3 2020 Distance metrics for ranked evolutionary trees. Zbl 1485.92076Kim, Jaehee; Rosenberg, Noah A.; Palacios, Julia A. 3 2020 Evidence that coronavirus superspreading is fat-tailed. Zbl 1485.92168Wong, Felix; Collins, James J. 3 2020 Scaling confirmation of the thermodynamic dislocation theory. Zbl 1485.74003Langer, J. S.; Le, K. C. 3 2020 The unreasonable effectiveness of deep learning in artificial intelligence. Zbl 1485.68237Sejnowski, Terrence J. 3 2020 Fluid interfaces with very sharp tips in viscous flow. Zbl 1485.76034Du Pont, Sylvain Courrech; Eggers, Jens 3 2020 The vortex gas scaling regime of baroclinic turbulence. Zbl 1456.86004Gallet, Basile; Ferrari, Raffaele 2 2020 The grain boundary mobility tensor. Zbl 1456.74029Chen, Kongtao; Han, Jian; Pan, Xiaoqing; Srolovitz, David J. 2 2020 Turning up the heat in turbulent thermal convection. Zbl 1485.76050Doering, Charles R. 2 2020 A nonlinear beam model of photomotile structures. Zbl 1485.74069Korner, Kevin; Kuenstler, Alexa S.; Bhattacharya, Kaushik 2 2020 Airfoil-like mechanics generate thrust on the anterior body of swimming fishes. Zbl 1485.76094Lucas, Kelsey N.; Lauder, George V.; Tytell, Eric D. 2 2020 Quantum Fourier analysis. Zbl 1485.42013Jaffe, Arthur; Jiang, Chunlan; Wu, Jinsong 2 2020 Adaptive social networks promote the wisdom of crowds. Zbl 1485.91176Almaatouq, Abdullah; Noriega-Campero, Alejandro; Pentland, Alex 2 2020 New perspective of fracture mechanics inspired by gap test with crack-parallel compression. Zbl 1485.74083Nguyen, Hoang; Pathirage, Madura; Bažant, Zdeněk P. 2 2020 The role of turbulent fluctuations in aerosol activation and cloud formation. Zbl 1485.86009Prabhakaran, Prasanth; Shawon, Abu Sayeed Md; Shaw, Raymond A. 2 2020 Geometric anomaly detection in data. Zbl 1485.55009Stolz, Bernadette J.; Tanner, Jared; Nanda, Vidit 2 2020 Contrast trees and distribution boosting. Zbl 1485.62033Friedman, Jerome H. 2 2020 Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers. Zbl 1485.11088Beckwith, Olivia; Raum, Martin; Richter, Olav K. 2 2020 The bounded rationality of probability distortion. Zbl 1485.91073Zhang, Hang; Ren, Xiangjuan; Maloney, Laurence T. 2 2020 Overparameterized neural networks implement associative memory. Zbl 1485.68236Radhakrishnan, Adityanarayanan; Belkin, Mikhail; Uhler, Caroline 2 2020 Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene. Zbl 1485.82004Christos, Maine; Sachdev, Subir; Scheurer, Mathias S. 2 2020 Topological weaire-thorpe models of amorphous matter. Zbl 1485.82011Marsal, Quentin; Varjas, Dániel; Grushin, Adolfo G. 2 2020 Multiscale integration of environmental stimuli in plant tropism produces complex behaviors. Zbl 1485.92071Moulton, Derek E.; Oliveri, Hadrien; Goriely, Alain 2 2020 The Nernst effect in Corbino geometry. Zbl 1456.78004Kavokin, A. V.; Altshuler, B. L.; Sharapov, S. G.; Grigoryev, P. S.; Varlamov, A. A. 1 2020 Uncertainty in learning, choice, and visual fixation. Zbl 1456.91041Stojić, Hrvoje; Orquin, Jacob L.; Dayan, Peter; Dolan, Raymond J.; Speekenbrink, Maarten 1 2020 Deterministic and stochastic control of kirigami topology. Zbl 1461.74056Chen, Siheng; Choi, Gary P. T.; Mahadevan, L. 1 2020 Embedded droplet printing in yield-stress fluids. Zbl 1456.76009Nelson, Arif Z.; Kundukad, Binu; Wong, Wai Kuan; Khan, Saif A.; Doyle, Patrick S. 1 2020 Noncollinear phases in Moiré magnets. Zbl 1485.82016Hejazi, Kasra; Luo, Zhu-Xi; Balents, Leon 1 2020 The noise collector for sparse recovery in high dimensions. Zbl 1485.94042Moscoso, Miguel; Novikov, Alexei; Tsogka, Chrysoula 1 2020 Dynamics in a simple evolutionary-epidemiological model for the evolution of an initial asymptomatic infection stage. Zbl 1485.92150Saad-Roy, Chadi M.; Wingreen, Ned S.; Grenfell, Bryan T. 1 2020 P-hacking in clinical trials and how incentives shape the distribution of results across phases. Zbl 1485.62152Adda, Jérôme; Decker, Christian; Ottaviani, Marco 1 2020 Three dimensions of scientific impact. Zbl 1485.62172Siudem, Grzegorz; Żogała-Siudem, Barbara; Gagolewski, Marek 1 2020 Active forces shape the metaphase spindle through a mechanical instability. Zbl 1485.92040Oriola, David; Jülicher, Frank; Brugués, Jan 1 2020 Multiple states and transport properties of double-diffusive convection turbulence. Zbl 1485.76051Yang, Yantao; Chen, Wenyuan; Lohse, Detlef 1 2020 Power-law distribution of degree-degree distance: a better representation of the scale-free property of complex networks. Zbl 1486.90064Zhou, Bin; Meng, Xiangyi; Stanley, H. Eugene 1 2020 Plato’s cube and the natural geometry of fragmentation. Zbl 1485.74086Domokos, Gábor; Jerolmack, Douglas J.; Török, János 1 2020 Predicting the long-term stability of compact multiplanet systems. Zbl 1485.70018Tamayo, Daniel; Cranmer, Miles; Menou, Kristen 1 2020 Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-1/2 fermions. Zbl 1485.82015Cha, Peter; Wentzell, Nils; Kim, Eun-Ah 1 2020 Explaining the low-frequency shear elasticity of confined liquids. Zbl 1485.76015Zaccone, Alessio; Trachenko, Kostya 1 2020 Nonreciprocity as a generic route to traveling states. Zbl 1485.92073You, Zhihong; Baskaran, Aparna; Marchetti, M. Cristina 1 2020 Optimal control of aging in complex networks. Zbl 1485.93030Sun, Eric D.; Michaels, Thomas C. T.; Mahadevan, L. 1 2020 Mathematical model of colorectal cancer initiation. Zbl 1485.92052Paterson, Chay; Clevers, Hans; Bozic, Ivana 1 2020 Stochastic sampling provides a unifying account of visual working memory limits. Zbl 1485.62160Schneegans, Sebastian; Taylor, Robert; Bays, Paul M. 1 2020 Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size. Zbl 1485.81018Gattuso, Hugo; Levine, R. D.; Remacle, F. 1 2020 Elucidating the G” overshoot in soft materials with a yield transition via a time-resolved experimental strain decomposition. Zbl 1485.74014Donley, Gavin J.; Singh, Piyush K.; Rogers, Simon A. 1 2020 Strong spatial embedding of social networks generates nonstandard epidemic dynamics independent of degree distribution and clustering. Zbl 1485.92131Haw, David J.; Pung, Rachael; Riley, Steven 1 2020 Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator. Zbl 1485.82005Pagano, Guido; Bapat, Aniruddha; Monroe, Christopher 1 2020 Generation of thermofield double states and critical ground states with a quantum computer. Zbl 1485.81023Zhu, D.; Johri, S.; Monroe, C. 1 2020 Characterization, stability, and application of domain walls in flexible mechanical metamaterials. Zbl 1485.74006Deng, Bolei; Yu, Siqin; Bertoldi, Katia 1 2020 Reconciling modern machine-learning practice and the classical bias-variance trade-off. Zbl 1433.68325Belkin, Mikhail; Hsu, Daniel; Ma, Siyuan; Mandal, Soumik 75 2019 Learning data-driven discretizations for partial differential equations. Zbl 1431.65195Bar-Sinai, Yohai; Hoyer, Stephan; Hickey, Jason; Brenner, Michael P. 42 2019 Data-driven discovery of coordinates and governing equations. Zbl 1433.68396Champion, Kathleen; Lusch, Bethany; Kutz, Nathan; Brunton, Steven L. 41 2019 Jensen polynomials for the Riemann zeta function and other sequences. Zbl 1431.11105Griffin, Michael; Ono, Ken; Rolen, Larry; Zagier, Don 37 2019 Optimal errors and phase transitions in high-dimensional generalized linear models. Zbl 1416.62421Barbier, Jean; Krzakala, Florent; Macris, Nicolas; Miolane, Léo; Zdeborová, Lenka 36 2019 A modern maximum-likelihood theory for high-dimensional logistic regression. Zbl 1431.62084Sur, Pragya; Candès, Emmanuel J. 33 2019 Nonparametric inference of interaction laws in systems of agents from trajectory data. Zbl 1431.62122Lu, Fei; Zhong, Ming; Tang, Sui; Maggioni, Mauro 23 2019 Uniformly accurate machine learning-based hydrodynamic models for kinetic equations. Zbl 1431.76100Han, Jiequn; Ma, Chao; Ma, Zheng; E, Weinan 20 2019 Definitions, methods, and applications in interpretable machine learning. Zbl 1431.62266Murdoch, W. James; Singh, Chandan; Kumbier, Karl; Abbasi-Asl, Reza; Yu, Bin 20 2019 Turbulent mixing: a perspective. Zbl 1431.76057Sreenivasan, Katepalli R. 20 2019 Inference and uncertainty quantification for noisy matrix completion. Zbl 1431.90117Chen, Yuxin; Fan, Jianqing; Ma, Cong; Yan, Yuling 15 2019 Evolutionary dynamics with game transitions. Zbl 1456.91018Su, Qi; Mcavoy, Alex; Wang, Long; Nowak, Martin A. 15 2019 Sampling can be faster than optimization. Zbl 1433.68397Ma, Yi-An; Chen, Yuansi; Jin, Chi; Flammarion, Nicolas; Jordan, Michael I. 14 2019 Statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change. Zbl 1416.76024Majda, Andrew J.; Moore, M. N. J.; Qi, Di 13 2019 New Laplace and Helmholtz solvers. Zbl 1431.65224Gopal, Abinand; Trefethen, Lloyd N. 10 2019 Almost partition identities. Zbl 1416.05026Andrews, George E.; Ballantine, Cristina 9 2019 ...and 1578 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 55,777 Authors 234 Park, Choonkil 112 Eshaghi Gordji, Madjid 86 Majda, Andrew J. 84 Jung, Soon-Mo 75 Rassias, John Michael 68 Lee, Jung-Rye 63 Rassias, Themistocles Michael 63 Wang, Xuejun 61 Dong, Chongying 60 Cao, Jinde 59 Zada, Akbar 56 Winkler, Michael 53 Cho, Yeol Je 53 Lee, Yang-Hi 50 Bodaghi, Abasalt 49 Bringmann, Kathrin 49 Li, Haisheng 47 Browder, Felix Earl 46 Najati, Abbas 45 Brzdęk, Janusz 44 Kumam, Poom 43 Bellman, Richard Ernest 42 Kim, Hark-Mahn 42 Shang, Pengjian 41 Jing, Naihuan 41 Kac, Victor G. 40 Nagurney, Anna 40 Shah, Kamal 40 Shin, Dong-Yun 39 Kevrekidis, Ioannis George 39 Stein, Elias Menachem 37 N’Guérékata, Gaston Mandata 37 Ono, Ken 36 Brunton, Steven L. 36 Khan, Mohammed Ali 36 Kutz, J. Nathan 36 Nowak, Martin Andreas 35 Saadati, Reza 35 Shumyatsky, Pavel 35 Sung, Soohak 34 Fefferman, Charles Louis 34 Huang, Lihong 34 Volodin, Andrei I. 33 Chung, Jaeyoung 33 El-Fassi, Iz-Iddine 33 Ezzinbi, Khalil 33 Feldman, Marcus W. 33 Karniadakis, George Em 32 Agarwal, Ravi P. 32 Kurths, Jürgen 31 Kabbaj, Samir 31 Kalaba, Robert E. 31 Kim, Gwang Hui 31 Qin, Xiaolong 30 Andrews, George Eyre 30 Ding, Yong 30 Lepowsky, James 30 Wu, Wei Biao 29 Fan, Jianqing 29 Huang, Yi-Zhi 28 Creutzig, Thomas 28 Ebadian, Ali 28 Khodaei, Hamid 28 Wu, Yi 28 Yao, Jen-Chih 27 Coja-Oghlan, Amin 27 Cordoba, Diego 27 Khamsi, Mohamed Amine 27 Popa, Dorian 27 Shen, Aiting 27 Wang, Long 26 Chen, Pingyan 26 Chidume, Charles Ejike 26 Lam, Ching Hung 26 Linshaw, Andrew Ross 26 Lu, Guozhen 26 Sintunavarat, Wutiphol 26 Walsh, Joseph Leonard 25 Hipel, Keith William 25 Hu, Shuhe 25 Kilgour, D. Marc 25 McCrimmon, Kevin 25 Osher, Stanley Joel 25 Park, Wongil 25 Petryshyn, Walter Wolodymyr 25 Xue, Qingying 25 Yau, Stephen Shing-Toung 24 Chang, Shih-Sen 24 Chen, William Yong-Chuan 24 Dolbeault, Jean 24 Marchi, Ezio 24 Mesiar, Radko 24 Moslehian, Mohammad Sal 24 Xiang, Zhaoyin 23 Chang, Ick-Soon 23 Dedecker, Jérôme 23 Ding, Xie Ping 23 Gancedo, Francisco 23 Kang, Shin Min 23 Karlin, Samuel ...and 55,677 more Authors all top 5 Cited in 1,400 Journals 1,072 Journal of Mathematical Analysis and Applications 901 Transactions of the American Mathematical Society 769 Journal of Mathematical Physics 748 Proceedings of the American Mathematical Society 619 Journal of Algebra 577 Advances in Mathematics 572 Journal of Computational Physics 535 Communications in Mathematical Physics 505 Journal of Theoretical Biology 495 Journal of Functional Analysis 448 Theoretical Population Biology 446 Mathematische Annalen 417 Physica A 395 Mathematische Zeitschrift 388 Applied Mathematics and Computation 372 Bulletin of the American Mathematical Society 363 Journal of Statistical Physics 362 Linear Algebra and its Applications 350 Journal of Fluid Mechanics 342 Chaos, Solitons and Fractals 340 Chaos 335 Journal of Differential Equations 293 Physica D 291 Journal of Inequalities and Applications 286 Proceedings of the National Academy of Sciences of the United States of America 274 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 270 Journal of Pure and Applied Algebra 267 Inventiones Mathematicae 258 Mathematical Biosciences 257 Journal of High Energy Physics 237 Journal of Mathematical Biology 231 Bulletin of Mathematical Biology 231 Journal of Physics A: Mathematical and Theoretical 224 Israel Journal of Mathematics 222 Communications in Algebra 222 Neural Computation 221 Journal of Optimization Theory and Applications 214 Statistics & Probability Letters 211 Abstract and Applied Analysis 207 The Annals of Statistics 204 Topology and its Applications 202 Duke Mathematical Journal 202 Communications in Statistics. Theory and Methods 199 International Journal of Theoretical Physics 198 Archive for Rational Mechanics and Analysis 197 Journal of Statistical Mechanics: Theory and Experiment 194 Theoretical Computer Science 190 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 184 Journal of Computational and Applied Mathematics 181 Archiv der Mathematik 180 Discrete Mathematics 179 Advances in Difference Equations 172 Computers & Mathematics with Applications 171 Fuzzy Sets and Systems 169 Computer Methods in Applied Mechanics and Engineering 169 European Journal of Operational Research 169 Journal of Mathematical Sciences (New York) 168 Automatica 166 Bulletin of the American Mathematical Society. New Series 166 Computational Statistics and Data Analysis 163 Journal of Number Theory 163 Fixed Point Theory and Applications 158 Acta Mathematica 157 Journal of Geometry and Physics 156 Annales de l’Institut Fourier 149 Tôhoku Mathematical Journal. Second Series 148 Communications in Nonlinear Science and Numerical Simulation 147 Physical Review, II. Series 146 Neural Networks 146 Quantum Information Processing 145 Games and Economic Behavior 145 Stochastic Processes and their Applications 140 Journal of Economic Theory 139 Information Sciences 137 Journal of Approximation Theory 137 Journal of Soviet Mathematics 133 The Journal of Symbolic Logic 132 Letters in Mathematical Physics 132 Mathematical Notes 132 SIAM Journal on Scientific Computing 131 Acta Mathematica Sinica. English Series 128 Annali di Matematica Pura ed Applicata. Serie Quarta 127 General Relativity and Gravitation 127 Journal of Statistical Planning and Inference 126 Journal of Combinatorial Theory. Series A 126 The Journal of Geometric Analysis 125 Applied and Computational Harmonic Analysis 121 Discrete Applied Mathematics 119 Astrophysics and Space Science 119 Compositio Mathematica 118 Journal of Multivariate Analysis 117 Biological Cybernetics 116 Results in Mathematics 116 Journal of Function Spaces 114 Journal of Scientific Computing 113 Journal d’Analyse Mathématique 112 Probability Theory and Related Fields 112 Journal of Machine Learning Research (JMLR) 111 Bulletin of the Australian Mathematical Society 111 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete ...and 1,300 more Journals all top 5 Cited in 63 Fields 4,995 Biology and other natural sciences (92-XX) 4,267 Partial differential equations (35-XX) 4,151 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4,108 Statistics (62-XX) 3,989 Probability theory and stochastic processes (60-XX) 3,280 Operator theory (47-XX) 3,214 Numerical analysis (65-XX) 3,171 Computer science (68-XX) 2,796 Quantum theory (81-XX) 2,786 Combinatorics (05-XX) 2,626 Functional analysis (46-XX) 2,373 Ordinary differential equations (34-XX) 2,261 Dynamical systems and ergodic theory (37-XX) 2,114 Operations research, mathematical programming (90-XX) 2,109 Fluid mechanics (76-XX) 2,002 Number theory (11-XX) 1,952 Differential geometry (53-XX) 1,924 Nonassociative rings and algebras (17-XX) 1,702 Statistical mechanics, structure of matter (82-XX) 1,559 Harmonic analysis on Euclidean spaces (42-XX) 1,528 Difference and functional equations (39-XX) 1,443 Systems theory; control (93-XX) 1,356 Group theory and generalizations (20-XX) 1,350 Algebraic geometry (14-XX) 1,269 Calculus of variations and optimal control; optimization (49-XX) 1,238 Manifolds and cell complexes (57-XX) 1,201 Global analysis, analysis on manifolds (58-XX) 1,068 Topological groups, Lie groups (22-XX) 1,057 Linear and multilinear algebra; matrix theory (15-XX) 1,013 Mathematical logic and foundations (03-XX) 993 Information and communication theory, circuits (94-XX) 979 General topology (54-XX) 841 Relativity and gravitational theory (83-XX) 837 Associative rings and algebras (16-XX) 827 Several complex variables and analytic spaces (32-XX) 764 Algebraic topology (55-XX) 718 Category theory; homological algebra (18-XX) 695 Mechanics of particles and systems (70-XX) 688 Real functions (26-XX) 639 Mechanics of deformable solids (74-XX) 580 Measure and integration (28-XX) 553 Abstract harmonic analysis (43-XX) 551 Functions of a complex variable (30-XX) 506 Special functions (33-XX) 506 Approximations and expansions (41-XX) 472 Convex and discrete geometry (52-XX) 429 History and biography (01-XX) 365 Commutative algebra (13-XX) 343 Geophysics (86-XX) 341 Integral equations (45-XX) 282 Order, lattices, ordered algebraic structures (06-XX) 222 Potential theory (31-XX) 222 Optics, electromagnetic theory (78-XX) 220 Classical thermodynamics, heat transfer (80-XX) 206 Astronomy and astrophysics (85-XX) 196 Geometry (51-XX) 190 General and overarching topics; collections (00-XX) 184 Integral transforms, operational calculus (44-XX) 134 Field theory and polynomials (12-XX) 130 General algebraic systems (08-XX) 126 \(K\)-theory (19-XX) 107 Sequences, series, summability (40-XX) 11 Mathematics education (97-XX) Citations by Year