## 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
 Documents Indexed: 5,093 Publications (since 1915) References Indexed: 865 Publications with 22,167 References.
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### 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 4,238 more Authors
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### 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) 94 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) 64 Operations research, mathematical programming (90-XX) 64 Information and communication theory, circuits (94-XX) 63 Algebraic geometry (14-XX) 62 Group theory and generalizations (20-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) 38 Algebraic topology (55-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) 33 Ordinary differential equations (34-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 28 Systems theory; control (93-XX) 27 Mathematical logic and foundations (03-XX) 26 Associative rings and algebras (16-XX) 24 Measure and integration (28-XX) 24 Mechanics of particles and systems (70-XX) 23 History and biography (01-XX) 21 Convex and discrete geometry (52-XX) 20 Special functions (33-XX) 19 General and overarching topics; collections (00-XX) 19 Category theory; homological algebra (18-XX) 18 Commutative algebra (13-XX) 18 Abstract harmonic analysis (43-XX) 18 General topology (54-XX) 17 Functions of a complex variable (30-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 Classical thermodynamics, heat transfer (80-XX) 8 Integral equations (45-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 3 Sequences, series, summability (40-XX) 2 $$K$$-theory (19-XX)

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A nonidentifiability aspect of the problem of competing risks. Zbl 0299.62066
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Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. Zbl 1130.62337
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Significance analysis of microarrays applied to the ionizing radiation response. Zbl 1012.92014
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A simple model of global cascades on random networks. Zbl 1022.90001
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The structure of scientific collaboration networks. Zbl 1065.00518
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Decision procedure for indefinite hypergeometric summation. Zbl 0384.40001
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The spread of awareness and its impact on epidemic outbreaks. Zbl 1203.91242
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A nonparametric view of network models and Newman-Girvan and other modularities. Zbl 1359.62411
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Cauchy integrals on Lipschitz curves and related operators. Zbl 0373.44003
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Global models of growth and competition. Zbl 0272.92016
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Statistical significance for genomewide studies. Zbl 1130.62385
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Lyapunov functions for the problem of Lur’e in automatic control. Zbl 0113.07701
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A class of bounded pseudo-differential operators. Zbl 0244.35074
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On sets of integers which contain no three terms in arithmetical progression. Zbl 0060.10302
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Vaccination and the theory of games. Zbl 1064.91029
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Quantum optical implementation of Grover’s algorithm. Zbl 0995.81014
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Synchronization in complex oscillator networks and smart grids. Zbl 1292.94185
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1964
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1971
A theorem on force-free magnetic fields. Zbl 0081.21703
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Gibbs states and the set of solutions of random constraint satisfaction problems. Zbl 1190.68031
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2007
Infection curves on small-world networks are linear only in the vicinity of the critical point. Zbl 1485.92137
Kuśmierz, Łukasz; Toyoizumi, Taro
2021
Stochastic dynamics of barrier island elevation. Zbl 1485.86006
Vinent, Orencio Durán; Schaffer, Benjamin E.; Rodriguez-Iturbe, Ignacio
2021
Probabilistic structure of events controlling the after-storm recovery of coastal dunes. Zbl 1485.86014
Rinaldo, Tobia; Ramakrishnan, Kiran Adhithya; Vinent, Orencio Durán
2021
The role of double-diffusive convection in basal melting of Antarctic ice shelves. Zbl 1485.86015
Rosevear, Madelaine Gamble; Gayen, Bishakhdatta; Galton-Fenzi, Benjamin Keith
2021
Probabilistic pragmatics explains gradience and focality in natural language quantification. Zbl 1485.03075
van Tiel, Bob; Franke, Michael; Sauerland, Uli
2021
How the growth of ice depends on the fluid dynamics underneath. Zbl 1485.76081
Wang, Ziqi; Calzavarini, Enrico; Toschi, Federico
2021
Benign overfitting in linear regression. Zbl 1485.62085
Bartlett, Peter L.; Long, Philip M.; Tsigler, Alexander
2020
Mining gold from implicit models to improve likelihood-free inference. Zbl 1461.62043
Brehmer, Johann; Louppe, Gilles; Pavez, Juan; Cranmer, Kyle
2020
Shaping the learning landscape in neural networks around wide flat minima. Zbl 1456.92009
Baldassi, Carlo; Pittorino, Fabrizio; Zecchina, Riccardo
2020
Guided transition waves in multistable mechanical metamaterials. Zbl 1456.74139
Jin, Lishuai; Khajehtourian, Romik; Mueller, Jochen; Rafsanjani, Ahmad; Tournat, Vincent; Bertoldi, Katia; Kochmann, Dennis M.
2020
Veridical data science. Zbl 1456.62321
Yu, Bin; Kumbier, Karl
2020
Topological data analysis of zebrafish patterns. Zbl 1456.92004
Mcguirl, Melissa R.; Volkening, Alexandria; Sandstede, Björn
2020
Theoretical issues in deep networks. Zbl 1485.68235
Poggio, Tomaso; Banburski, Andrzej; Liao, Qianli
2020
Using machine learning to predict extreme events in complex systems. Zbl 1456.68176
Qi, Di; Majda, Andrew J.
2020
Stochastic reaction networks in dynamic compartment populations. Zbl 1485.92041
Duso, Lorenzo; Zechner, Christoph
2020
A network-based explanation of why most COVID-19 infection curves are linear. Zbl 1485.92159
Thurner, Stefan; Klimek, Peter; Hanel, Rudolf
2020
Local lockdowns outperform global lockdown on the far side of the COVID-19 epidemic curve. Zbl 1485.92005
2020
The turning point and end of an expanding epidemic cannot be precisely forecast. Zbl 1485.92118
Castro, Mario; Ares, Saúl; Manrubia, Susanna
2020
The frontier of simulation-based inference. Zbl 1485.62004
Cranmer, Kyle; Brehmer, Johann; Louppe, Gilles
2020
Fluid interfaces with very sharp tips in viscous flow. Zbl 1485.76034
Du Pont, Sylvain Courrech; Eggers, Jens
2020
The vortex gas scaling regime of baroclinic turbulence. Zbl 1456.86004
Gallet, Basile; Ferrari, Raffaele
2020
Deterministic and stochastic control of kirigami topology. Zbl 1461.74056
Chen, Siheng; Choi, Gary P. T.; Mahadevan, L.
2020
The grain boundary mobility tensor. Zbl 1456.74029
Chen, Kongtao; Han, Jian; Pan, Xiaoqing; Srolovitz, David J.
2020
A nonlinear beam model of photomotile structures. Zbl 1485.74069
Korner, Kevin; Kuenstler, Alexa S.; Bhattacharya, Kaushik
2020
Testing for dependence on tree structures. Zbl 1485.62078
Behr, Merle; Ansari, M. Azim; Holmes, Chris
2020
Airfoil-like mechanics generate thrust on the anterior body of swimming fishes. Zbl 1485.76094
Lucas, Kelsey N.; Lauder, George V.; Tytell, Eric D.
2020
Quantum Fourier analysis. Zbl 1485.42013
Jaffe, Arthur; Jiang, Chunlan; Wu, Jinsong
2020
P-hacking in clinical trials and how incentives shape the distribution of results across phases. Zbl 1485.62152
Adda, Jérôme; Decker, Christian; Ottaviani, Marco
2020
Three dimensions of scientific impact. Zbl 1485.62172
Siudem, Grzegorz; Żogała-Siudem, Barbara; Gagolewski, Marek
2020
Deep rotating convection generates the polar hexagon on saturn. Zbl 1485.85023
2020
The role of turbulent fluctuations in aerosol activation and cloud formation. Zbl 1485.86009
Prabhakaran, Prasanth; Shawon, Abu Sayeed Md; Shaw, Raymond A.
2020
Predicting the long-term stability of compact multiplanet systems. Zbl 1485.70018
Tamayo, Daniel; Cranmer, Miles; Menou, Kristen
2020
Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-1/2 fermions. Zbl 1485.82015
Cha, Peter; Wentzell, Nils; Kim, Eun-Ah
2020
Explaining the low-frequency shear elasticity of confined liquids. Zbl 1485.76015
Zaccone, Alessio; Trachenko, Kostya
2020
Dimple drainage before the coalescence of a droplet deposited on a smooth substrate. Zbl 1485.76013
Duchemin, Laurent; Josserand, Christophe
2020
Stochastic sampling provides a unifying account of visual working memory limits. Zbl 1485.62160
Schneegans, Sebastian; Taylor, Robert; Bays, Paul M.
2020
Elucidating the G” overshoot in soft materials with a yield transition via a time-resolved experimental strain decomposition. Zbl 1485.74014
Donley, Gavin J.; Singh, Piyush K.; Rogers, Simon A.
2020
The bounded rationality of probability distortion. Zbl 1485.91073
Zhang, Hang; Ren, Xiangjuan; Maloney, Laurence T.
2020
The mysterious story of square ice, piles of cubes, and bijections. Zbl 1485.05009
2020
Stable homotopy groups of spheres. Zbl 1485.55017
Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli
2020
Overparameterized neural networks implement associative memory. Zbl 1485.68236
2020
Evidence that coronavirus superspreading is fat-tailed. Zbl 1485.92168
Wong, Felix; Collins, James J.
2020
Topological weaire-thorpe models of amorphous matter. Zbl 1485.82011
Marsal, Quentin; Varjas, Dániel; Grushin, Adolfo G.
2020
Multiscale integration of environmental stimuli in plant tropism produces complex behaviors. Zbl 1485.92071
Moulton, Derek E.; Oliveri, Hadrien; Goriely, Alain
2020
Reconciling modern machine-learning practice and the classical bias-variance trade-off. Zbl 1433.68325
Belkin, Mikhail; Hsu, Daniel; Ma, Siyuan; Mandal, Soumik
2019
Data-driven discovery of coordinates and governing equations. Zbl 1433.68396
Champion, Kathleen; Lusch, Bethany; Kutz, Nathan; Brunton, Steven L.
2019
Learning data-driven discretizations for partial differential equations. Zbl 1431.65195
Bar-Sinai, Yohai; Hoyer, Stephan; Hickey, Jason; Brenner, Michael P.
2019
Jensen polynomials for the Riemann zeta function and other sequences. Zbl 1431.11105
Griffin, Michael; Ono, Ken; Rolen, Larry; Zagier, Don
2019
Optimal errors and phase transitions in high-dimensional generalized linear models. Zbl 1416.62421
Barbier, Jean; Krzakala, Florent; Macris, Nicolas; Miolane, Léo; Zdeborová, Lenka
2019
A modern maximum-likelihood theory for high-dimensional logistic regression. Zbl 1431.62084
Sur, Pragya; Candès, Emmanuel J.
2019
Uniformly accurate machine learning-based hydrodynamic models for kinetic equations. Zbl 1431.76100
Han, Jiequn; Ma, Chao; Ma, Zheng; E, Weinan
2019
Nonparametric inference of interaction laws in systems of agents from trajectory data. Zbl 1431.62122
Lu, Fei; Zhong, Ming; Tang, Sui; Maggioni, Mauro
2019
Inference and uncertainty quantification for noisy matrix completion. Zbl 1431.90117
Chen, Yuxin; Fan, Jianqing; Ma, Cong; Yan, Yuling
2019
Turbulent mixing: a perspective. Zbl 1431.76057
Sreenivasan, Katepalli R.
2019
Evolutionary dynamics with game transitions. Zbl 1456.91018
Su, Qi; Mcavoy, Alex; Wang, Long; Nowak, Martin A.
2019
Statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change. Zbl 1416.76024
Majda, Andrew J.; Moore, M. N. J.; Qi, Di
2019
Definitions, methods, and applications in interpretable machine learning. Zbl 1431.62266
Murdoch, W. James; Singh, Chandan; Kumbier, Karl; Abbasi-Asl, Reza; Yu, Bin
2019
New Laplace and Helmholtz solvers. Zbl 1431.65224
Gopal, Abinand; Trefethen, Lloyd N.
2019
Sampling can be faster than optimization. Zbl 1433.68397
Ma, Yi-An; Chen, Yuansi; Jin, Chi; Flammarion, Nicolas; Jordan, Michael I.
2019
On a two-truths phenomenon in spectral graph clustering. Zbl 1431.62269
Priebe, Carey E.; Park, Youngser; Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Tang, Minh; Athreya, Avanti; Cape, Joshua; Bridgeford, Eric
2019
Fast scrambling on sparse graphs. Zbl 1416.81038
Bentsen, Gregory; Gu, Yingfei; Lucas, Andrew
2019
The harmonic mean $$p$$-value for combining dependent tests. Zbl 1416.62303
Wilson, Daniel J.
2019
Markovian approaches to modeling intracellular reaction processes with molecular memory. Zbl 1431.92045
Zhang, Jiajun; Zhou, Tianshou
2019
Universal behavior of cascading failures in interdependent networks. Zbl 1431.90032
Duan, Dongli; Lv, Changchun; Si, Shubin; Wang, Zhen; Li, Daqing; Gao, Jianxi; Havlin, Shlomo; Stanley, H. Eugene; Boccaletti, Stefano
2019
Supernova, nuclear synthesis, fluid instabilities, and interfacial mixing. Zbl 1431.85002
Abarzhi, Snezhana I.; Bhowmick, Aklant K.; Naveh, Annie; Pandian, Arun; Swisher, Nora C.; Stellingwerf, Robert F.; Arnett, W. David
2019
Subdiffusive and superdiffusive transport in plane steady viscous flows. Zbl 1431.76119
Zaks, Michael A.; Nepomnyashchy, Alexander
2019
Deep learning in turbulent convection networks. Zbl 1431.76063
Fonda, Enrico; Pandey, Ambrish; Schumacher, Jörg; Sreenivasan, Katepalli R.
2019
Bootstrapping variables in algebraic circuits. Zbl 1433.68151
Agrawal, Manindra; Ghosh, Sumanta; Saxena, Nitin
2019
A formula for the value of a stochastic game. Zbl 1456.91008
Attia, Luc; Oliu-Barton, Miquel
2019
Almost partition identities. Zbl 1416.05026
Andrews, George E.; Ballantine, Cristina
2019
Geometry and arithmetic of crystallographic sphere packings. Zbl 1422.52009
Kontorovich, Alex; Nakamura, Kei
2019
The Ramsey property implies no mad families. Zbl 1431.03063
Schrittesser, David; Törnquist, Asger
2019
Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics. Zbl 1431.76162
Zhou, Shenggao; Weiß, R. Gregor; Cheng, Li-Tien; Dzubiella, Joachim; Mccammon, J. Andrew; Li, Bo
2019
New progress on the zeta function: from old conjectures to a major breakthrough. Zbl 1431.11104
Bombieri, Enrico
2019
Bubble pinch-off in turbulence. Zbl 1456.76131
Ruth, Daniel J.; Mostert, Wouter; Perrard, Stéphane; Deike, Luc
2019
Generalized network dismantling. Zbl 1418.90060
Ren, Xiao-Long; Gleinig, Niels; Helbing, Dirk; Antulov-Fantulin, Nino
2019
Adaptive, locally linear models of complex dynamics. Zbl 1416.37066
Costa, Antonio C.; Ahamed, Tosif; Stephens, Greg J.
2019
Newcomb-Benford law and the detection of frauds in international trade. Zbl 1418.91308
Cerioli, Andrea; Barabesi, Lucio; Cerasa, Andrea; Menegatti, Mario; Perrotta, Domenico
2019
The importance of better models in stochastic optimization. Zbl 1431.90098
Asi, Hilal; Duchi, John C.
2019
Message passing on networks with loops. Zbl 1431.94214
Cantwell, George T.; Newman, M. E. J.
2019
Characteristic disruptions of an excitable carbon cycle. Zbl 1431.86010
Rothman, Daniel H.
2019
Learning to predict the cosmological structure formation. Zbl 1431.83191
He, Siyu; Li, Yin; Feng, Yu; Ho, Shirley; Ravanbakhsh, Siamak; Chen, Wei; Póczos, Barnabás
2019
Disconnection description of triple-junction motion. Zbl 1431.74039
Thomas, Spencer L.; Wei, Chaozhen; Han, Jian; Xiang, Yang; Srolovitz, David J.
2019
Counterexamples in scale calculus. Zbl 1431.58006
Filippenko, Benjamin; Zhou, Zhengyi; Wehrheim, Katrin
2019
Learning stable and predictive structures in kinetic systems. Zbl 1456.70002
Pfister, Niklas; Bauer, Stefan; Peters, Jonas
2019
Reflective prolate-spheroidal operators and the KP/KdV equations. Zbl 1462.35330
Casper, W. Riley; Grünbaum, F. Alberto; Yakimov, Milen; Zurrián, Ignacio
2019
A mathematical theory of semantic development in deep neural networks. Zbl 1416.92018
Saxe, Andrew M.; McClelland, James L.; Ganguli, Surya
2019
Geometrically incompatible confinement of solids. Zbl 1416.74069
Davidovitch, Benny; Sun, Yiwei; Grason, Gregory M.
2019
Hydrodynamics of random-organizing hyperuniform fluids. Zbl 1431.76041
Lei, Qun-Li; Ni, Ran
2019
Thermalization and possible signatures of quantum chaos in complex crystalline materials. Zbl 1431.82034
Zhang, Jiecheng; Kountz, Erik D.; Behnia, Kamran; Kapitulnik, Aharon
2019
Building more accurate decision trees with the additive tree. Zbl 1431.62264
Luna, José Marcio; Gennatas, Efstathios D.; Ungar, Lyle H.; Eaton, Eric; Diffenderfer, Eric S.; Jensen, Shane T.; Simone, Charles B. II; Friedman, Jerome H.; Solberg, Timothy D.; Valdes, Gilmer
2019
On the bounded generation of arithmetic $$\mathrm{SL}_2$$. Zbl 1432.11029
Jordan, Bruce W.; Zaytman, Yevgeny
2019
Interface dynamics: mechanisms of stabilization and destabilization and structure of flow fields. Zbl 1431.76054
Abarzhi, Snezhana I.; Ilyin, Daniil V.; Goddard, William A. III; Anisimov, Sergei I.
2019
Network analysis predicts failure of materials and structures. Zbl 1431.74013
Moretti, Paolo; Zaiser, Michael
2019
Forecasting failure locations in 2-dimensional disordered lattices. Zbl 1431.74038
Berthier, Estelle; Porter, Mason A.; Daniels, Karen E.
2019
Second-order induction in prediction problems. Zbl 1431.91053
Argenziano, Rossella; Gilboa, Itzhak
2019
On the Bayesian interpretation of the harmonic mean $$p$$-value. Zbl 1431.62238
Held, Leonhard
2019
Topological descriptions of protein folding. Zbl 1431.57003
Flapan, Erica; He, Adam; Wong, Helen
2019
Detecting different topologies immanent in scale-free networks with the same degree distribution. Zbl 1418.90063
Tsiotas, Dimitrios
2019
Solving matrix equations in one step with cross-point resistive arrays. Zbl 1416.65577
Sun, Zhong; Pedretti, Giacomo; Ambrosi, Elia; Bricalli, Alessandro; Wang, Wei; Ielmini, Daniele
2019
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### Cited by 50,901 Authors

 220 Park, Choonkil 110 Eshaghi Gordji, Madjid 85 Majda, Andrew J. 82 Jung, Soon-Mo 73 Rassias, John Michael 62 Lee, Jung-Rye 60 Dong, Chongying 56 Cao, Jinde 55 Zada, Akbar 54 Wang, Xuejun 53 Cho, Yeol Je 53 Lee, Yang-Hi 50 Winkler, Michael 48 Rassias, Themistocles Michael 47 Bringmann, Kathrin 47 Browder, Felix Earl 46 Bodaghi, Abasalt 43 Bellman, Richard Ernest 43 Kumam, Poom 42 Brzdęk, Janusz 42 Najati, Abbas 41 Kac, Victor G. 41 Li, Haisheng 41 Shang, Pengjian 40 Jing, Naihuan 39 Kim, Hark-Mahn 39 Nagurney, Anna 38 Shin, Dong-Yun 38 Stein, Elias Menachem 37 Shah, Kamal 36 N’Guérékata, Gaston Mandata 35 Nowak, Martin Andreas 34 Fefferman, Charles Louis 34 Kevrekidis, Ioannis George 34 Khan, Mohammed Ali 34 Saadati, Reza 34 Shumyatsky, Pavel 34 Sung, Soohak 34 Volodin, Andrei I. 33 Brunton, Steven L. 33 Huang, Lihong 33 Ono, Ken 33 Wu, Wei Biao 32 Chung, Jaeyoung 32 Ezzinbi, Khalil 32 Feldman, Marcus W. 32 Kutz, J. Nathan 31 Agarwal, Ravi P. 31 El-Fassi, Iz-Iddine 31 Kalaba, Robert E. 31 Qin, Xiaolong 30 Ding, Yong 30 Kim, Gwang Hui 30 Kurths, Jürgen 29 Karniadakis, George Em 29 Lepowsky, James 28 Ebadian, Ali 28 Khodaei, Hamid 28 Yao, Jen-Chih 27 Andrews, George Eyre 27 Kabbaj, Samir 27 Khamsi, Mohamed Amine 27 Wu, Yi 26 Chidume, Charles Ejike 26 Cordoba, Diego 26 Huang, Yi-Zhi 26 Walsh, Joseph Leonard 25 Chen, Pingyan 25 Fan, Jianqing 25 Hipel, Keith William 25 Hu, Shuhe 25 McCrimmon, Kevin 25 Park, Wongil 25 Petryshyn, Walter Wolodymyr 25 Popa, Dorian 25 Shen, Aiting 25 Sintunavarat, Wutiphol 25 Xue, Qingying 24 Chen, William Yong-Chuan 24 Coja-Oghlan, Amin 24 Dolbeault, Jean 24 Kilgour, D. Marc 24 Linshaw, Andrew Ross 24 Marchi, Ezio 23 Chang, Shih-Sen 23 Creutzig, Thomas 23 Karlin, Samuel 23 Lam, Ching Hung 23 Lu, Guozhen 23 Mesiar, Radko 23 Osher, Stanley Joel 23 Tanimoto, Jun 22 Bae, Jae-Hyeong 22 Chang, Ick-Soon 22 Ding, Xie Ping 22 Gancedo, Francisco 22 Kang, Shin Min 22 Khukhro, Evgeniĭ I. 22 Mezić, Igor 22 Moslehian, Mohammad Sal ...and 50,801 more Authors
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### Cited in 1,361 Journals

 1,041 Journal of Mathematical Analysis and Applications 885 Transactions of the American Mathematical Society 740 Journal of Mathematical Physics 730 Proceedings of the American Mathematical Society 607 Journal of Algebra 544 Advances in Mathematics 512 Communications in Mathematical Physics 477 Journal of Functional Analysis 475 Journal of Theoretical Biology 474 Journal of Computational Physics 445 Mathematische Annalen 443 Theoretical Population Biology 391 Physica A 382 Mathematische Zeitschrift 372 Bulletin of the American Mathematical Society 365 Applied Mathematics and Computation 357 Journal of Statistical Physics 352 Linear Algebra and its Applications 338 Chaos 323 Chaos, Solitons and Fractals 305 Journal of Differential Equations 293 Journal of Fluid Mechanics 286 Proceedings of the National Academy of Sciences of the United States of America 283 Journal of Inequalities and Applications 265 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 261 Inventiones Mathematicae 255 Physica D 252 Journal of Pure and Applied Algebra 251 Mathematical Biosciences 223 Israel Journal of Mathematics 221 Journal of Mathematical Biology 220 Neural Computation 219 Bulletin of Mathematical Biology 216 Journal of Optimization Theory and Applications 213 Communications in Algebra 207 Statistics & Probability Letters 207 Abstract and Applied Analysis 201 Duke Mathematical Journal 195 International Journal of Theoretical Physics 192 Archive for Rational Mechanics and Analysis 192 Topology and its Applications 190 The Annals of Statistics 189 Communications in Statistics. Theory and Methods 188 Theoretical Computer Science 187 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 184 Journal of High Energy Physics 180 Archiv der Mathematik 179 Advances in Difference Equations 175 Discrete Mathematics 172 Journal of Computational and Applied Mathematics 168 Fuzzy Sets and Systems 165 Journal of Statistical Mechanics: Theory and Experiment 164 Journal of Mathematical Sciences (New York) 163 Bulletin of the American Mathematical Society. New Series 163 Fixed Point Theory and Applications 162 Computers & Mathematics with Applications 158 Acta Mathematica 156 Computational Statistics and Data Analysis 155 Journal of Number Theory 154 European Journal of Operational Research 152 Journal of Geometry and Physics 152 Annales de l’Institut Fourier 148 Tôhoku Mathematical Journal. Second Series 147 Physical Review, II. Series 145 Automatica 140 Games and Economic Behavior 137 Journal of Soviet Mathematics 136 Journal of Approximation Theory 135 Journal of Economic Theory 134 Computer Methods in Applied Mechanics and Engineering 134 Information Sciences 133 Neural Networks 132 Mathematical Notes 132 Stochastic Processes and their Applications 128 The Journal of Symbolic Logic 127 General Relativity and Gravitation 127 Annali di Matematica Pura ed Applicata. Serie Quarta 127 Acta Mathematica Sinica. English Series 124 Letters in Mathematical Physics 123 Journal of Statistical Planning and Inference 121 Journal of Combinatorial Theory. Series A 119 Astrophysics and Space Science 119 Compositio Mathematica 119 Applied and Computational Harmonic Analysis 118 Communications in Nonlinear Science and Numerical Simulation 117 Biological Cybernetics 117 The Journal of Geometric Analysis 115 Discrete Applied Mathematics 114 SIAM Journal on Scientific Computing 113 Journal of Multivariate Analysis 112 Journal d’Analyse Mathématique 111 Results in Mathematics 110 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 109 Bulletin of the Australian Mathematical Society 108 Journal of Mathematical Economics 108 Journal of Function Spaces 106 Applied Mathematics Letters 106 Journal of Scientific Computing 105 The Ramanujan Journal 105 Proceedings of the Japan Academy ...and 1,261 more Journals
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### Cited in 63 Fields

 4,613 Biology and other natural sciences (92-XX) 3,811 Partial differential equations (35-XX) 3,782 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3,673 Statistics (62-XX) 3,594 Probability theory and stochastic processes (60-XX) 3,067 Operator theory (47-XX) 2,876 Numerical analysis (65-XX) 2,732 Computer science (68-XX) 2,499 Combinatorics (05-XX) 2,477 Functional analysis (46-XX) 2,426 Quantum theory (81-XX) 2,198 Ordinary differential equations (34-XX) 2,073 Dynamical systems and ergodic theory (37-XX) 1,939 Operations research, mathematical programming (90-XX) 1,847 Fluid mechanics (76-XX) 1,821 Differential geometry (53-XX) 1,816 Number theory (11-XX) 1,804 Nonassociative rings and algebras (17-XX) 1,563 Statistical mechanics, structure of matter (82-XX) 1,440 Harmonic analysis on Euclidean spaces (42-XX) 1,435 Difference and functional equations (39-XX) 1,308 Systems theory; control (93-XX) 1,276 Group theory and generalizations (20-XX) 1,244 Algebraic geometry (14-XX) 1,179 Calculus of variations and optimal control; optimization (49-XX) 1,129 Global analysis, analysis on manifolds (58-XX) 1,114 Manifolds and cell complexes (57-XX) 1,016 Topological groups, Lie groups (22-XX) 964 Linear and multilinear algebra; matrix theory (15-XX) 938 Mathematical logic and foundations (03-XX) 920 General topology (54-XX) 907 Information and communication theory, circuits (94-XX) 783 Associative rings and algebras (16-XX) 771 Relativity and gravitational theory (83-XX) 765 Several complex variables and analytic spaces (32-XX) 703 Algebraic topology (55-XX) 649 Category theory; homological algebra (18-XX) 636 Mechanics of particles and systems (70-XX) 615 Real functions (26-XX) 575 Mechanics of deformable solids (74-XX) 542 Measure and integration (28-XX) 524 Abstract harmonic analysis (43-XX) 517 Functions of a complex variable (30-XX) 478 Approximations and expansions (41-XX) 468 Special functions (33-XX) 432 Convex and discrete geometry (52-XX) 407 History and biography (01-XX) 332 Commutative algebra (13-XX) 318 Integral equations (45-XX) 302 Geophysics (86-XX) 258 Order, lattices, ordered algebraic structures (06-XX) 207 Potential theory (31-XX) 195 Optics, electromagnetic theory (78-XX) 195 Astronomy and astrophysics (85-XX) 186 Classical thermodynamics, heat transfer (80-XX) 178 Geometry (51-XX) 169 Integral transforms, operational calculus (44-XX) 162 General and overarching topics; collections (00-XX) 130 Field theory and polynomials (12-XX) 119 General algebraic systems (08-XX) 110 $$K$$-theory (19-XX) 98 Sequences, series, summability (40-XX) 12 Mathematics education (97-XX)