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 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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 4,260 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) 152 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) 100 Differential geometry (53-XX) 96 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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) 19 Functions of a complex variable (30-XX) 19 Abstract harmonic analysis (43-XX) 18 Commutative algebra (13-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 3,500 Publications have been cited 60,386 times in 51,255 Documents Cited by ▼ Year ▼ On the stability of the linear functional equation. Zbl 0061.26403 Hyers, D. H. 1,278 1941 Neural networks and physical systems with emergent collective computational abilities. Zbl 1369.92007 Hopfield, J. J. 1,188 1982 Equilibrium points in \(n\)-person games. Zbl 0036.01104 Nash, John F. jun. 988 1950 Neurons with graded response have collective computational properties like those of two-state neurons. Zbl 1371.92015 Hopfield, J. J. 861 1984 Community structure in social and biological networks. Zbl 1032.91716 Girvan, M.; Newman, M. E. J. 733 2002 Vertex algebras, Kac-Moody algebras, and the monster. Zbl 0613.17012 Borcherds, Richard E. 578 1986 On the stability of the linear functional equation. JFM 67.0424.01 Hyers, D. H. 545 1941 Complete convergence and the law of large numbers. Zbl 0030.20101 Hsu, P. L.; Robbins, Herbert 524 1947 Nonexpansive nonlinear operators in a Banach space. Zbl 0128.35801 Browder, F. E. 470 1965 Stochastic games. Zbl 0051.35805 Shapley, L. S. 456 1953 Statistical metrics. Zbl 0063.03886 Menger, Karl 455 1942 Fixed-point and minimax theorems in locally convex topological linear spaces. Zbl 0047.35103 Fan, Ky 443 1952 Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Zbl 1355.94013 Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan 422 2016 A central limit theorem and a strong mixing condition. Zbl 0070.13804 Rosenblatt, M. 403 1956 Functorial semantics of algebraic theories. Zbl 0119.25901 Lawvere, F. W. 394 1963 Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137 Han, Jiequn; Jentzen, Arnulf; E, Weinan 383 2018 Bacterial swimming and oxygen transport near contact lines. Zbl 1277.35332 Tuval, Idan; Cisneros, Luis; Dombrowski, Christopher; Wolgemuth, Charles W.; Kessler, John O.; Goldstein, Raymond E. 372 2005 Minimax theorems. Zbl 0050.06501 Fan, Ky 358 1953 A fast marching level set method for monotonically advancing fronts. Zbl 0852.65055 Sethian, J. A. 346 1996 On some exponential sums. Zbl 0032.26102 Weil, André 345 1948 A social equilibrium existence theorem. Zbl 0047.38804 Debreu, Gerard 331 1952 On the contraction of groups and their representations. Zbl 0050.02601 Inönü, E.; Wigner, Eugene P. 331 1953 Optimally sparse representation in general (nonorthogonal) dictionaries via \(\ell^1\) minimization. Zbl 1064.94011 Donoho, David L.; Elad, Michael 318 2003 A class of Markov processes associated with nonlinear parabolic equations. Zbl 0149.13501 McKean, H. P. jun. 305 1966 Systems of conservation equations with a convex extension. Zbl 0229.35061 Friedrichs, K. O.; Lax, P. D. 264 1971 Fixed-point theorems for noncompact mappings in Hilbert space. Zbl 0125.35801 Browder, F. E. 258 1965 Convolution operators on Banach space valued functions. Zbl 0103.33402 Benedek, A.; Calderón, Alberto P.; Panzone, R. 243 1962 Calabi’s conjecture and some new results in algebraic geometry. Zbl 0355.32028 Yau, Shing-Tung 241 1977 Group theoretical discussion of relativistic wave equations. Zbl 0030.42306 Bargmann, V.; Wigner, Eugene P. 234 1948 Finite groups with fixed-point-free automorphisms of prime order. Zbl 0086.25101 Thompson, John G. 230 1959 A characterization of Banach spaces containing \(l^1\). Zbl 0297.46013 Rosenthal, Haskell P. 229 1974 Commutators of singular integral operators. Zbl 0151.16901 Calderón, Alberto P. 221 1965 Nonlinear system theory: another look at dependence. Zbl 1135.62075 Wu, Wei Biao 219 2005 On a generalization of the notion of manifold. Zbl 0074.18103 Satake, Ichirô 210 1956 A new approach to almost periodicity. Zbl 0112.31401 Bochner, Salomon 206 1962 Maximal functions. I: Spherical means. Zbl 0332.42018 Stein, Elias M. 199 1976 Maximum properties and inequalities for the eigenvalues of completely continuous operators. Zbl 0044.11502 Fan, Ky 197 1951 Burrau’s problem of three bodies. Zbl 0158.43206 Szebehely, Victor G. 189 1967 Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. Zbl 1130.62337 Donoho, David L.; Grimes, Carrie 188 2003 The structure of scientific collaboration networks. Zbl 1065.00518 Newman, M. E. J. 182 2001 A nonidentifiability aspect of the problem of competing risks. Zbl 0299.62066 Tsiatis, Anastasios 182 1975 A simple model of global cascades on random networks. Zbl 1022.90001 Watts, Duncan J. 182 2002 Hamiltonian systems and transformations in Hilbert space. Zbl 0002.05701 Koopman, B. O. 177 1931 A nonparametric view of network models and Newman-Girvan and other modularities. Zbl 1359.62411 Bickel, Peter J.; Chen, Aiyou 177 2009 Significance analysis of microarrays applied to the ionizing radiation response. Zbl 1012.92014 Tusher, Virginia Goss; Tibshirani, Robert; Chu, Gilbert 176 2001 The spread of awareness and its impact on epidemic outbreaks. Zbl 1203.91242 Funk, Sebastian; Gilad, Erez; Watkins, Chris; Jansen, Vincent A. A. 173 2009 Approximate entropy as a measure of system complexity. Zbl 0756.60103 Pincus, Steven M. 172 1991 Information contents of distributions. Zbl 0128.14104 Wigner, Eugene P.; Yanase, M. M. 171 1963 A class of bounded pseudo-differential operators. Zbl 0244.35074 Calderon, Alberto P.; Vaillancourt, Remi 169 1972 Cauchy integrals on Lipschitz curves and related operators. Zbl 0373.44003 Calderon, A. P. 165 1977 On a ’monotonicity’ method for the solution of nonlinear equations in Banach spaces. Zbl 0124.07303 Minty, G. J. 164 1963 Decision procedure for indefinite hypergeometric summation. Zbl 0384.40001 Gosper, R. William jun. 163 1978 Statistical significance for genomewide studies. Zbl 1130.62385 Storey, John D.; Tibshirani, Robert 161 2003 Unitary operator bases. Zbl 0090.19006 Schwinger, Julian 158 1960 On sets of integers which contain no three terms in arithmetical progression. Zbl 0060.10302 Behrend, F. A. 157 1946 Global models of growth and competition. Zbl 0272.92016 Gilpin, Michael E.; Ayala, Francisco J. 156 1973 Inequalities between the two kinds of eigenvalues of a linear transformation. Zbl 0032.38701 Weyl, Hermann 154 1949 Synchronization in complex oscillator networks and smart grids. Zbl 1292.94185 Dörfler, Florian; Chertkov, Michael; Bullo, Francesco 153 2013 Vaccination and the theory of games. Zbl 1064.91029 Bauch, Chris T.; Earn, David J. D. 151 2004 On regular rings. Zbl 0015.38802 von Neumann, John 146 1936 Dirichlet spaces. Zbl 0089.08201 Beurling, A.; Deny, Jacques 145 1959 Lyapunov functions for the problem of Lur’e in automatic control. Zbl 0113.07701 Kalman, R. E. 144 1963 Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Zbl 1405.42043 Coifman, R. R.; Lafon, S.; Lee, A. B.; Maggioni, M.; Nadler, B.; Warner, F.; Zucker, S. W. 143 2005 The average distances in random graphs with given expected degrees. Zbl 1064.05137 Chung, Fan; Lu, Linyuan 142 2002 Two theorems in graph theory. Zbl 0086.16202 Berge, Claude 141 1957 Integration of stiff equations. Zbl 0046.13602 Curtiss, C.; Hirschfelder, J. O. 136 1952 Quantum optical implementation of Grover’s algorithm. Zbl 0995.81014 Scully, Marlan O.; Zubairy, M. S. 130 2001 Calculus of twisted vertex operators. Zbl 0579.17010 Lepowsky, J. 129 1985 Randomized algorithms for the low-rank approximation of matrices. Zbl 1215.65080 Liberty, Edo; Woolfe, Franco; Martinsson, Per-Gunnar; Rokhlin, Vladimir; Tygert, Mark 128 2007 Modular invariant representations of infinite-dimensional Lie algebras and superalgebras. Zbl 0652.17010 Kac, Victor G.; Wakimoto, Minoru 126 1988 Sequential Monte Carlo without likelihood. Zbl 1160.65005 Sisson, S. A.; Fan, Y.; Tanaka, Mark M. 126 2007 Solution of the Heawood map-coloring problem. Zbl 0155.51201 Ringel, Gerhard; Youngs, J. W. T. 126 1968 Biregular classification of Fano 3-folds and Fano manifolds of coindex 3. Zbl 0679.14020 Mukai, Shigeru 124 1989 Infinite flag varieties and conjugacy theorems. Zbl 0512.17008 Peterson, Dale H.; Kac, Victor G. 123 1983 Spin and wedge representations of infinite-dimensional Lie algebras and groups. Zbl 0469.22016 Kac, Victor G.; Peterson, Dale H. 123 1981 Continuous mappings of almost automorphic and almost periodic functions. Zbl 0134.30102 Bochner, Salomon 123 1964 Hamiltonian systems and transformations in Hilbert space. JFM 57.1010.02 Koopman, B. O. 122 1931 Effect of inhomogeneity on cosmological models. Zbl 0009.04103 Tolman, Richard C. 122 1934 A natural representation of the Fischer-Griess monster with the modular function J as character. Zbl 0543.20016 Frenkel, I. B.; Lepowsky, J.; Meurman, A. 121 1984 The cutoff phenomenon in finite Markov chains. Zbl 0849.60070 Diaconis, Persi 120 1996 Dirac operators coupled to vector potentials. Zbl 0547.58033 Atiyah, Michael F.; Singer, I. M. 119 1984 Sparse and stable Markowitz portfolios. Zbl 1203.91271 Brodie, Joshua; Daubechies, Ingrid; De Mol, Christine; Giannone, Domenico; Loris, Ignace 119 2009 Kählerian coset spaces of semisimple Lie groups. Zbl 0058.16002 Borel, Armand 116 1954 On finite groups of even order whose 2-Sylow group is a quaternion group. Zbl 0090.01901 Brauer, Richard; Suzuki, Michio 116 1959 Computing geodesic paths on manifolds. Zbl 0908.65049 Kimmel, R.; Sethian, J. A. 115 1998 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 0063.03560 Lin, C. C. 115 1941 On Moulton’s orbits in the restricted problem of three bodies. Zbl 0202.56902 Szebehely, Victor 114 1966 The degree of convergence of sequences of linear positive operators. Zbl 0164.07102 Shisha, O.; Mond, B. 113 1968 A theorem on force-free magnetic fields. Zbl 0081.21703 Woltjer, L. 112 1958 From time series to complex networks: the visibility graph. Zbl 1205.05162 Lacasa, Lucas; Luque, Bartolo; Ballesteros, Fernando; Luque, Jordi; Nuño, Juan Carlos 111 2008 Vertex representations of quantum affine algebras. Zbl 0662.17006 Frenkel, Igor B.; Jing, Naihuan 110 1988 The multivariate \(L_1\)-median and associated data depth. Zbl 1054.62067 Vardi, Yehuda; Zhang, Cun-Hui 110 2000 The independence of the continuum hypothesis. I, II. Zbl 0192.04401 Cohen, Paul Joseph 110 1964 Spectral redemption in clustering sparse networks. Zbl 1359.62252 Krzakala, Florent; Moore, Cristopher; Mossel, Elchanan; Neeman, Joe; Sly, Allan; Zdeborová, Lenka; Zhang, Pan 109 2013 A new technique for the construction of solutions of nonlinear differential equations. Zbl 0104.30503 Moser, Jürgen 108 1961 Gibbs states and the set of solutions of random constraint satisfaction problems. 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Zbl 1456.76009 Nelson, Arif Z.; Kundukad, Binu; Wong, Wai Kuan; Khan, Saif A.; Doyle, Patrick S. 1 2020 ...and 1609 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 59,144 Authors 242 Park, Choonkil 112 Eshaghi Gordji, Madjid 86 Majda, Andrew J. 85 Jung, Soon-Mo 76 Rassias, John Michael 68 Lee, Jung-Rye 68 Wang, Xuejun 65 Zada, Akbar 64 Rassias, Themistocles Michael 62 Dong, Chongying 61 Cao, Jinde 59 Winkler, Michael 54 Cho, Yeol Je 54 Lee, Yang-Hi 53 Bodaghi, Abasalt 50 Bringmann, Kathrin 50 Li, Haisheng 48 Najati, Abbas 47 Browder, Felix Earl 46 Brzdęk, Janusz 44 Kumam, Poom 43 Bellman, Richard Ernest 43 Jing, Naihuan 43 Kim, Hark-Mahn 43 Shang, Pengjian 42 Kac, Victor 42 Kevrekidis, Ioannis George 42 Shah, Kamal 41 Nagurney, Anna 40 Shin, Dong-Yun 40 Stein, Elias Menachem 39 Khan, Mohammed Ali 38 Kutz, J. 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