Edit Profile (opens in new tab) Tirozzi, Brunello Compute Distance To: Compute Author ID: tirozzi.brunello Published as: Tirozzi, B.; Tirozzi, Brunello Documents Indexed: 94 Publications since 1977, including 2 Books 1 Contribution as Editor Biographic References: 1 Publication Co-Authors: 56 Co-Authors with 79 Joint Publications 1,356 Co-Co-Authors all top 5 Co-Authors 1 single-authored 32 Dobrokhotov, Sergei Yurievich 17 Shcherbina, Mariya 10 Feng, Jianfeng 7 Nazaikinskii, Vladimir E. 6 Albeverio, Sergio A. 4 Bianchi, Daniela 4 Reutskiy, Sergiy Yu 4 Shafarevich, Andreĭ Igorevich 3 Ferraro, Enrico 3 Khrennikov, Andreĭ Yur’evich 3 Klevin, A. I. 3 Rotundo, Giulia 3 Sergeev, Sergeĭ Alekseevich 2 Abundo, Mario 2 Agliari, Elena 2 Anikin, A. Yu. 2 Barra, Adriano 2 Campanino, Massimo 2 Lifits, S. A. 2 Minenkov, Dmitrii S. 2 Pastur, Leonid Andreevich 2 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 2 Semenov, E. S. 2 Tudorovskii, T. Ya. 1 Brown, David 1 Bruschi, Antonella 1 Calogero, Raffaele A. 1 Capocaccia, D. 1 Cardinali, Alessandro 1 Cassandro, Marzio 1 Corsini, Stefano 1 De Smedt, Stany 1 Del Grosso, Gabriella 1 Dobrushin, Roland L’vovich 1 Doria, Serena 1 Dorotheyev, E. A. 1 Gawȩdzki, Krzysztof 1 Grushin, V. V. 1 Krüger, Norbert 1 Kupiainen, Antti 1 Lifits, Sergei 1 Limongiello, Alessandro 1 Marasco, Addolorata 1 Marchetti, Cristina 1 Marie, Helene 1 Mele, Giovanni 1 Migliore, Michele 1 Minasyan, V. B. 1 Morusci, Sara 1 Nekrasov, R. V. 1 Olivieri, Enzo 1 Pittalis, Stefano 1 Pontrelli, Giuseppe 1 Puca, Silvia 1 Rossoni, Enrico 1 Scacciatelli, E. 1 Semënov, Evgeniĭ Mikhaĭlovich 1 Sinitsyn, S. O. 1 Tartaglia, Giangaetano 1 Tavani, Flavia 1 Tolchennikov, Anton A. 1 Vargas, Carlos A. 1 Wei, Gang 1 You, Gongqiang 1 Zegarlinski, Boguslaw 1 Zucchi, R. all top 5 Serials 14 Russian Journal of Mathematical Physics 6 Communications in Mathematical Physics 6 Mathematical and Computer Modelling 6 Journal of Physics A: Mathematical and General 4 Journal of Mathematical Physics 4 Journal of Statistical Physics 4 Theoretical and Mathematical Physics 4 Doklady Mathematics 4 Markov Processes and Related Fields 3 Computers & Mathematics with Applications 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Helvetica Physica Acta 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Doklady Akademii Nauk 2 Computer Assisted Mechanics and Engineering Sciences 2 Communications on Pure and Applied Analysis 1 International Journal of Modern Physics B 1 Biological Cybernetics 1 Journal of Engineering Mathematics 1 Prikladnaya Matematika i Mekhanika 1 Bollettino della Unione Matemàtica Italiana. Serie VI. C. Analisi Funzionale e Applicazioni 1 Bollettino della Unione Matemàtica Italiana. Serie VI. A 1 Bollettino della Unione Matemàtica Italiana. Serie VI. B 1 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 Journal of Computational Neuroscience 1 International Journal of Theoretical and Applied Finance 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of Statistical Mechanics: Theory and Experiment 1 Series on Advances in Mathematics for Applied Sciences 1 Modeling and Simulation in Science, Engineering and Technology all top 5 Fields 30 Partial differential equations (35-XX) 27 Statistical mechanics, structure of matter (82-XX) 23 Fluid mechanics (76-XX) 22 Biology and other natural sciences (92-XX) 19 Probability theory and stochastic processes (60-XX) 11 Computer science (68-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Geophysics (86-XX) 6 Numerical analysis (65-XX) 5 Statistics (62-XX) 5 Quantum theory (81-XX) 4 Systems theory; control (93-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 2 Convex and discrete geometry (52-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 61 Publications have been cited 443 times in 240 Documents Cited by ▼ Year ▼ Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B. 46 2008 The central limit theorem and the problem of equivalence of ensembles. Zbl 0391.60095Dobrushin, R. L.; Tirozzi, Brunello 33 1977 Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 28 2007 The replica-symmetric solution without replica trick for the Hopfield model. Zbl 0835.60092Pastur, L.; Shcherbina, M.; Tirozzi, B. 22 1994 Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 22 2010 \(p\)-adic dynamical systems. Zbl 0974.37018Albeverio, S.; Khrennikov, A.; Tirozzi, B.; De Smedt, S. 21 1998 Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tirozzi, B. 17 2011 Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations. Zbl 1178.35301Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A. 16 2009 Localized solutions of one-dimensional non-linear shallow-water equations with velocity \(c=\sqrt x\). Zbl 1196.35161Dobrokhotov, S. Yu; Tirozzi, B. 13 2010 Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. Zbl 1320.35180Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 13 2013 Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya. 12 2006 Rigorous solution of the Gardner problem. Zbl 1034.82042Shcherbina, Mariya; Tirozzi, Brunello 11 2003 Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B. 10 2007 The free energy of a class of Hopfield models. Zbl 1097.82551Shcherbina, M.; Tirozzi, B. 10 1993 Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients. Zbl 1276.76012Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B. 10 2013 Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: diluted regime. Zbl 1276.05107Shcherbina, Mariya; Tirozzi, Brunello 10 2012 On the replica symmetric equations for the Hopfield model. Zbl 0988.82024Pastur, L.; Shcherbina, M.; Tirozzi, B. 9 1999 Infinite differentiability for one-dimensional spin system with long range random interaction. Zbl 0506.58009Cassandro, M.; Olivieri, E.; Tirozzi, B. 9 1982 A quasi Trefftz-type spectral method for initial value problems with moving boundaries. Zbl 0912.65082Lifits, S. A.; Reutskiy, S. Yu.; Tirozzi, B. 8 1997 Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskij, T. Ya. 8 2006 Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Zbl 1309.05163Shcherbina, Mariya; Tirozzi, Brunello 8 2010 Rigorous results for the free energy in the Hopfield model. Zbl 0770.92003Albeverio, S.; Tirozzi, B.; Zegarlinski, B. 7 1992 Quasi Trefftz spectral method for Stokes problem. Zbl 0897.76074Lifits, S. A.; Reutskiy, S. Yu.; Pontrelli, G.; Tirozzi, B. 6 1997 \(p\)-adic dynamical systems and neural networks. Zbl 1010.82027Albeverio, Sergio; Khrennikov, Andrei; Tirozzi, Brunello 6 1999 Fluctuation of the free energy in the Hopfield model. Zbl 0925.82163Scacciatelli, E.; Tirozzi, B. 5 1992 Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 5 2010 Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. Zbl 1230.35057Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B. 5 2011 Quasi-Trefftz spectral method for separable linear elliptic equations. Zbl 0937.65123Reutskiy, S. Yu.; Tirozzi, B. 4 1999 Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B. 4 2016 Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello 4 2013 Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. II: Taking into account a source on the right-hand side and a weak dispersion. Zbl 1194.35054Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B. 4 2008 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. 4 2014 An introduction to the mathematical theory of neural networks. Zbl 0965.68083Albeverio, S.; Tirozzi, B. 3 1997 The SLLN for the free-energy of a class of neural networks. Zbl 0840.68099Feng, Jianfeng; Tirozzi, Brunello 3 1995 Conduction in bundles of demyelinated nerve fibers: computer simulation. Zbl 1105.92325Reutskiy, S.; Rossoni, E.; Tirozzi, B. 3 2003 Cauchy–Riemann conditions and localized asymptotic solutions of linearized equations of shallow water theory. Zbl 1100.76506Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 3 2005 On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 3 2015 Replica symmetry breaking in neural networks with modified pseudo-inverse interactions. Zbl 0775.82003Dotsenko, V. S.; Tirozzi, B. 2 1991 On the volume of the intersection of a sphere with random half spaces. Zbl 1002.60005Shcherbina, Maria; Tirozzi, Brunello 2 2002 Trefftz spectral method for initial-boundary problems. Zbl 0951.65100Lifits, Sergei; Reutskiy, Sergei; Tirozzi, Brunello 2 1997 Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics. Zbl 1393.82023Anikin, A. Yu.; Dobrokhotov, S. Yu.; Klevin, A. I.; Tirozzi, B. 2 2017 Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain. Zbl 1354.82032Dobrokhotov, S. Yu.; Cardinali, A.; Klevin, A. I.; Tirozzi, Brunello 2 2016 Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. Zbl 1329.35246Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B. 2 2016 Neural networks and sea time series. Recontruction and extreme-event analysis. Zbl 1094.62121Tirozzi, Brunello; Puca, Silvia; Pittalis, Stefano; Bruschi, Antonella; Morusci, Sara; Ferraro, Enrico; Corsini, Stefano 2 2006 On the critical capacity of the Hopfield model. Zbl 1038.82069Feng, Jianfeng; Shcherbina, Mariya; Tirozzi, Brunello 2 2001 On the Hamiltonian property of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices. Zbl 1074.76530Dobrokhotov, S. Yu.; Tirozzi, B. 2 2002 Convergence theorems for the Kohonen feature mapping algorithms with VLRPs. Zbl 0870.60070Feng, J. F.; Tirozzi, B. 2 1997 A note on minimum-variance theory and beyond. Zbl 1048.37073Feng, Jianfeng; Tartaglia, Giangaetano; Tirozzi, Brunello 2 2004 Forecast of the trajectory of the center of typhoons and the Maslov decomposition. Zbl 1136.86004Reutskiy, S.; Tirozzi, B. 2 2007 Hugoniót-Maslov chains for singular vortical solutions to quasilinear hyperbolic systems and typhoon trajectory. Zbl 1069.37049Dobrokhotov, S.; Semenov, E.; Tirozzi, B. 2 2003 A perturbative theory of the evolution of the center of typhoons. Zbl 1169.86307Dobrokhotov, Sergey; Semenov, Evgeny; Tirozzi, Brunello 2 2005 Optimal movement control models of Langevin and Hamiltonian types. Zbl 1127.93063Feng, J. F.; Shcherbina, M.; Tirozzi, B.; You, G. Q 1 2007 Modified pseudo-inverse neural networks storing correlated patterns. Zbl 0753.92002Der, R.; Dotsenko, V. S.; Tirozzi, B. 1 1992 Borel summability of the perturbation series in a hierarchical \(\lambda (\nabla \Phi)^ 4\) model. Zbl 0587.60099Gawȩdzki, K.; Kupiainen, A.; Tirozzi, B. 1 1984 Generalization and learning error for nonlinear perceptron. Zbl 1168.91512Shcherbina, M.; Tirozzi, B. 1 2002 Local limit theorem for Gibbs random fields of particles and unbounded spins. Zbl 0415.60091Campanino, Massimo; Del Grosso, Gabriella; Tirozzi, Brunello 1 1979 The central limit theorem for a class of maps of the interval [0,1]. Zbl 0561.60026Abundo, M.; Tirozzi, B. 1 1984 Learning of \(p\)-adic neural networks. Zbl 1078.82521Khrennikov, Andrei; Tirozzi, Brunello 1 2000 Rigorous results and critical capacity for a short-term memory model. Zbl 0878.60067Feng, Jianfeng; Tirozzi, B.; Zucchi, R. 1 1996 Free energies of Boltzmann machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit. Zbl 07382818Agliari, Elena; Barra, Adriano; Tirozzi, Brunello 1 2019 On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. Zbl 1446.92109Bianchi, Daniela; Marasco, Addolorata; Limongiello, Alessandro; Marchetti, Cristina; Marie, Helene; Tirozzi, Brunello; Migliore, Michele 1 2012 Free energies of Boltzmann machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit. Zbl 07382818Agliari, Elena; Barra, Adriano; Tirozzi, Brunello 1 2019 Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics. Zbl 1393.82023Anikin, A. Yu.; Dobrokhotov, S. Yu.; Klevin, A. I.; Tirozzi, B. 2 2017 Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B. 4 2016 Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain. Zbl 1354.82032Dobrokhotov, S. Yu.; Cardinali, A.; Klevin, A. I.; Tirozzi, Brunello 2 2016 Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. Zbl 1329.35246Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B. 2 2016 On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 3 2015 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. 4 2014 Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. Zbl 1320.35180Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 13 2013 Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients. Zbl 1276.76012Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B. 10 2013 Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello 4 2013 Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: diluted regime. Zbl 1276.05107Shcherbina, Mariya; Tirozzi, Brunello 10 2012 On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. Zbl 1446.92109Bianchi, Daniela; Marasco, Addolorata; Limongiello, Alessandro; Marchetti, Cristina; Marie, Helene; Tirozzi, Brunello; Migliore, Michele 1 2012 Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036Dobrokhotov, S. Yu.; Nekrasov, R. V.; Tirozzi, B. 17 2011 Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. Zbl 1230.35057Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B. 5 2011 Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 22 2010 Localized solutions of one-dimensional non-linear shallow-water equations with velocity \(c=\sqrt x\). Zbl 1196.35161Dobrokhotov, S. Yu; Tirozzi, B. 13 2010 Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Zbl 1309.05163Shcherbina, Mariya; Tirozzi, Brunello 8 2010 Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 5 2010 Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations. Zbl 1178.35301Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A. 16 2009 Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B. 46 2008 Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. II: Taking into account a source on the right-hand side and a weak dispersion. Zbl 1194.35054Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B. 4 2008 Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 28 2007 Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B. 10 2007 Forecast of the trajectory of the center of typhoons and the Maslov decomposition. Zbl 1136.86004Reutskiy, S.; Tirozzi, B. 2 2007 Optimal movement control models of Langevin and Hamiltonian types. Zbl 1127.93063Feng, J. F.; Shcherbina, M.; Tirozzi, B.; You, G. Q 1 2007 Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya. 12 2006 Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskij, T. Ya. 8 2006 Neural networks and sea time series. Recontruction and extreme-event analysis. Zbl 1094.62121Tirozzi, Brunello; Puca, Silvia; Pittalis, Stefano; Bruschi, Antonella; Morusci, Sara; Ferraro, Enrico; Corsini, Stefano 2 2006 Cauchy–Riemann conditions and localized asymptotic solutions of linearized equations of shallow water theory. Zbl 1100.76506Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 3 2005 A perturbative theory of the evolution of the center of typhoons. Zbl 1169.86307Dobrokhotov, Sergey; Semenov, Evgeny; Tirozzi, Brunello 2 2005 A note on minimum-variance theory and beyond. Zbl 1048.37073Feng, Jianfeng; Tartaglia, Giangaetano; Tirozzi, Brunello 2 2004 Rigorous solution of the Gardner problem. Zbl 1034.82042Shcherbina, Mariya; Tirozzi, Brunello 11 2003 Conduction in bundles of demyelinated nerve fibers: computer simulation. Zbl 1105.92325Reutskiy, S.; Rossoni, E.; Tirozzi, B. 3 2003 Hugoniót-Maslov chains for singular vortical solutions to quasilinear hyperbolic systems and typhoon trajectory. Zbl 1069.37049Dobrokhotov, S.; Semenov, E.; Tirozzi, B. 2 2003 On the volume of the intersection of a sphere with random half spaces. Zbl 1002.60005Shcherbina, Maria; Tirozzi, Brunello 2 2002 On the Hamiltonian property of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices. Zbl 1074.76530Dobrokhotov, S. Yu.; Tirozzi, B. 2 2002 Generalization and learning error for nonlinear perceptron. Zbl 1168.91512Shcherbina, M.; Tirozzi, B. 1 2002 On the critical capacity of the Hopfield model. Zbl 1038.82069Feng, Jianfeng; Shcherbina, Mariya; Tirozzi, Brunello 2 2001 Learning of \(p\)-adic neural networks. Zbl 1078.82521Khrennikov, Andrei; Tirozzi, Brunello 1 2000 On the replica symmetric equations for the Hopfield model. Zbl 0988.82024Pastur, L.; Shcherbina, M.; Tirozzi, B. 9 1999 \(p\)-adic dynamical systems and neural networks. Zbl 1010.82027Albeverio, Sergio; Khrennikov, Andrei; Tirozzi, Brunello 6 1999 Quasi-Trefftz spectral method for separable linear elliptic equations. Zbl 0937.65123Reutskiy, S. Yu.; Tirozzi, B. 4 1999 \(p\)-adic dynamical systems. Zbl 0974.37018Albeverio, S.; Khrennikov, A.; Tirozzi, B.; De Smedt, S. 21 1998 A quasi Trefftz-type spectral method for initial value problems with moving boundaries. Zbl 0912.65082Lifits, S. A.; Reutskiy, S. Yu.; Tirozzi, B. 8 1997 Quasi Trefftz spectral method for Stokes problem. Zbl 0897.76074Lifits, S. A.; Reutskiy, S. Yu.; Pontrelli, G.; Tirozzi, B. 6 1997 An introduction to the mathematical theory of neural networks. Zbl 0965.68083Albeverio, S.; Tirozzi, B. 3 1997 Trefftz spectral method for initial-boundary problems. Zbl 0951.65100Lifits, Sergei; Reutskiy, Sergei; Tirozzi, Brunello 2 1997 Convergence theorems for the Kohonen feature mapping algorithms with VLRPs. Zbl 0870.60070Feng, J. F.; Tirozzi, B. 2 1997 Rigorous results and critical capacity for a short-term memory model. Zbl 0878.60067Feng, Jianfeng; Tirozzi, B.; Zucchi, R. 1 1996 The SLLN for the free-energy of a class of neural networks. Zbl 0840.68099Feng, Jianfeng; Tirozzi, Brunello 3 1995 The replica-symmetric solution without replica trick for the Hopfield model. Zbl 0835.60092Pastur, L.; Shcherbina, M.; Tirozzi, B. 22 1994 The free energy of a class of Hopfield models. Zbl 1097.82551Shcherbina, M.; Tirozzi, B. 10 1993 Rigorous results for the free energy in the Hopfield model. Zbl 0770.92003Albeverio, S.; Tirozzi, B.; Zegarlinski, B. 7 1992 Fluctuation of the free energy in the Hopfield model. Zbl 0925.82163Scacciatelli, E.; Tirozzi, B. 5 1992 Modified pseudo-inverse neural networks storing correlated patterns. Zbl 0753.92002Der, R.; Dotsenko, V. S.; Tirozzi, B. 1 1992 Replica symmetry breaking in neural networks with modified pseudo-inverse interactions. Zbl 0775.82003Dotsenko, V. S.; Tirozzi, B. 2 1991 Borel summability of the perturbation series in a hierarchical \(\lambda (\nabla \Phi)^ 4\) model. Zbl 0587.60099Gawȩdzki, K.; Kupiainen, A.; Tirozzi, B. 1 1984 The central limit theorem for a class of maps of the interval [0,1]. Zbl 0561.60026Abundo, M.; Tirozzi, B. 1 1984 Infinite differentiability for one-dimensional spin system with long range random interaction. Zbl 0506.58009Cassandro, M.; Olivieri, E.; Tirozzi, B. 9 1982 Local limit theorem for Gibbs random fields of particles and unbounded spins. Zbl 0415.60091Campanino, Massimo; Del Grosso, Gabriella; Tirozzi, Brunello 1 1979 The central limit theorem and the problem of equivalence of ensembles. Zbl 0391.60095Dobrushin, R. L.; Tirozzi, Brunello 33 1977 all cited Publications top 5 cited Publications all top 5 Cited by 251 Authors 51 Dobrokhotov, Sergei Yurievich 29 Nazaikinskii, Vladimir E. 29 Tirozzi, Brunello 14 Sergeev, Sergeĭ Alekseevich 14 Shafarevich, Andreĭ Igorevich 12 Tolchennikov, Anton A. 9 Khrennikov, Andreĭ Yur’evich 8 Agliari, Elena 8 Barra, Adriano 7 Minenkov, Dmitrii S. 6 Anikin, A. Yu. 6 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 6 Shcherbina, Mariya 6 Tsvetkova, Anna V. 5 Grushin, V. V. 5 Maslov, Viktor Pavlovich 5 Rozikov, Utkir A. 4 Allilueva, Anna I. 4 Fachechi, Alberto 4 Guerra, Francesco 4 Lozhnikov, D. A. 4 Picco, Pierre 4 Sattarov, Iskandar A. 3 Albeverio, Sergio A. 3 Bovier, Anton 3 Campanino, Massimo 3 Gayrard, Véronique 3 Huang, Jiaoyang 3 Kaneko, Hiroshi 3 Lebowitz, Joel Louis 3 Mukhamedov, Farruh Maksutovich 3 Scacciatelli, E. 3 Tantari, Daniele 3 Volkov, B. I. 3 Yurova, Ekaterina I. 2 Alemanno, Francesco 2 Benaych-Georges, Florent 2 Benfatto, Giuseppe 2 Bianchi, Daniela 2 Brezhnev, Yurii V. 2 Bulatov, Vitaliĭ Vasil’evich 2 Capocaccia, D. 2 Cassandro, Marzio 2 Comets, Francis M. 2 Feng, Jianfeng 2 Gallavotti, Giovanni M. 2 Genovese, Giuseppe 2 Guionnet, Alice 2 Gundlach, Volker Matthias 2 Hu, Chinkun 2 Janžura, Martin 2 Kabanikhin, Sergeĭ Igorevich 2 Karwowski, Witold 2 Klevin, A. I. 2 Kozyrev, Sergeĭ Vladimirovich 2 Krivorotko, Olga I. 2 Künsch, Hans Rudolf 2 Landon, Benjamin A. 2 Löwe, Matthias 2 Makrakis, George N. 2 Male, Camille 2 Medvedev, Sergeĭ Borisovich 2 Montanari, Andrea 2 Nicolò, Francesco 2 Olivieri, Enzo 2 Pastur, Leonid Andreevich 2 Petrov, P. N. 2 Petrov, Pavel S. 2 Presutti, Errico 2 Rodríguez Bermúdez, Panters 2 Rozanova, Olga S. 2 Shlosman, Senya B. 2 Valiño Alonso, Baldomero 2 Vargas, Carlos A. 2 Yau, Horng-Tzer 2 Yu, Jui-Ling 1 Abundo, Mario 1 Aihara, Kazuyuki 1 Alvarez, Gustavo Benitez 1 Amari, Shun-ichi 1 Anashin, Vladimir Sergeevich 1 Arora, Sumit 1 Axelsson, E. Yurova 1 Barbier, Jean 1 Beccaria, Matteo 1 Berend, Daniel 1 Berry, Hugues 1 Boldrighini, Carlo 1 Bordenave, Charles 1 Boutillier, Cédric 1 Bradley, Patrick Erik 1 Buckel, Maxwell 1 Calderoni, Paola 1 Calogero, Raffaele A. 1 Cancrini, Nicoletta 1 Chen, Dongqing 1 Cheng, Yu-Chen 1 Chirkunov, Yuriĭ Aleksandrovich 1 Christov, Christo Ivanov 1 Christov, Ivan C. ...and 151 more Authors all top 5 Cited in 71 Serials 40 Russian Journal of Mathematical Physics 29 Mathematical Notes 22 Journal of Statistical Physics 11 Theoretical and Mathematical Physics 9 Communications in Mathematical Physics 9 Probability Theory and Related Fields 8 Journal of Mathematical Physics 8 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 5 Mathematical and Computer Modelling 5 Doklady Mathematics 5 Proceedings of the Steklov Institute of Mathematics 4 Computational Mathematics and Mathematical Physics 3 Computers & Mathematics with Applications 3 Neural Networks 3 Stochastic Processes and their Applications 3 Journal of Statistical Mechanics: Theory and Experiment 2 Fluid Dynamics 2 Journal of Mathematical Analysis and Applications 2 Chaos, Solitons and Fractals 2 Advances in Mathematics 2 The Annals of Probability 2 Journal of Number Theory 2 Kybernetika 2 Ergodic Theory and Dynamical Systems 2 Physica D 2 Journal of Theoretical Probability 2 Annales de l’Institut Henri Poincaré. Physique Théorique 2 Indagationes Mathematicae. New Series 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Nonlinear Analysis. Real World Applications 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 The Journal of Mathematical Neuroscience 1 Applicable Analysis 1 Biological Cybernetics 1 International Journal of Theoretical Physics 1 Journal of Applied Mathematics and Mechanics 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Mathematical Methods in the Applied Sciences 1 Physics Reports 1 Reports on Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Prikladnaya Matematika i Mekhanika 1 The Annals of Statistics 1 Journal of Combinatorial Theory. Series A 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Results in Mathematics 1 Tohoku Mathematical Journal. Second Series 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Acta Mathematicae Applicatae Sinica. English Series 1 Neural Computation 1 The Annals of Applied Probability 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 SIAM Journal on Applied Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 St. Petersburg Mathematical Journal 1 Engineering Analysis with Boundary Elements 1 Discrete and Continuous Dynamical Systems 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Chaos 1 New Journal of Physics 1 Annales Henri Poincaré 1 Differential Equations 1 Journal of Mathematical Cryptology 1 Random Matrices: Theory and Applications 1 Journal of Applied Analysis and Computation 1 Evolution Equations and Control Theory 1 JAMM. Journal of Advanced Mathematical Modeling 1 Water Waves all top 5 Cited in 43 Fields 89 Partial differential equations (35-XX) 64 Statistical mechanics, structure of matter (82-XX) 62 Probability theory and stochastic processes (60-XX) 51 Fluid mechanics (76-XX) 30 Dynamical systems and ergodic theory (37-XX) 17 Number theory (11-XX) 17 Quantum theory (81-XX) 15 Biology and other natural sciences (92-XX) 14 Computer science (68-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 12 Geophysics (86-XX) 11 Combinatorics (05-XX) 9 Statistics (62-XX) 9 Numerical analysis (65-XX) 8 Differential geometry (53-XX) 5 Operator theory (47-XX) 4 Field theory and polynomials (12-XX) 4 Functional analysis (46-XX) 3 Measure and integration (28-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Convex and discrete geometry (52-XX) 3 Optics, electromagnetic theory (78-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Special functions (33-XX) 2 Ordinary differential equations (34-XX) 2 Difference and functional equations (39-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year