Edit Profile (opens in new tab) Tirozzi, Brunello Co-Author Distance Author ID: tirozzi.brunello Published as: Tirozzi, B.; Tirozzi, Brunello Documents Indexed: 98 Publications since 1977, including 2 Books and 3 Additional arXiv Preprints 1 Contribution as Editor Biographic References: 1 Publication Co-Authors: 68 Co-Authors with 92 Joint Publications 1,595 Co-Co-Authors all top 5 Co-Authors 1 single-authored 33 Dobrokhotov, Sergei Yurievich 17 Shcherbina, Mariya 13 Feng, Jianfeng 7 Nazaikinskii, Vladimir E. 6 Albeverio, Sergio A. 6 Reutskiy, Sergiy Yu 4 Bianchi, Daniela 4 Shafarevich, Andreĭ Igorevich 3 Ferraro, Enrico 3 Khrennikov, Andreĭ Yur’evich 3 Klevin, A. I. 3 Rotundo, Giulia 3 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 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 Semenov, E. S. 2 Tudorovskii, T. Ya. 1 Alladio, F. 1 Brown, David 1 Bruschi, Antonella 1 Buratti, P. 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 Lecian, Orchidea Maria 1 Lifits, Sergei 1 Limongiello, Alessandro 1 Marasco, Addolorata 1 Marchetti, Cristina 1 Marie, Helene 1 Mele, Giovanni 1 Micozzi, P. 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 Shcherbina, Masha 1 Sinitsyn, S. O. 1 Tartaglia, Giangaetano 1 Tavani, Flavia 1 Tolchennikov, Anton A. 1 Tudorovskiy, Timur 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) 28 Statistical mechanics, structure of matter (82-XX) 24 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 63 Publications have been cited 498 times in 291 Documents Cited by ▼ Year ▼ Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336 Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B. 48 2008 The central limit theorem and the problem of equivalence of ensembles. Zbl 0391.60095 Dobrushin, R. L.; Tirozzi, Brunello 35 1977 Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014 Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 30 2007 Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 26 2010 \(p\)-adic dynamical systems. Zbl 0974.37018 Albeverio, S.; Khrennikov, A.; Tirozzi, B.; De Smedt, S. 26 1998 The replica-symmetric solution without replica trick for the Hopfield model. Zbl 0835.60092 Pastur, L.; Shcherbina, M.; Tirozzi, B. 24 1994 Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036 Dobrokhotov, 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 1178.35301 Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A. 17 2009 Rigorous solution of the Gardner problem. Zbl 1034.82042 Shcherbina, Mariya; Tirozzi, Brunello 16 2003 Localized solutions of one-dimensional non-linear shallow-water equations with velocity \(c=\sqrt x\). Zbl 1196.35161 Dobrokhotov, S. Yu; Tirozzi, B. 16 2010 Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089 Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya. 13 2006 Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. Zbl 1320.35180 Dobrokhotov, 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 1276.76012 Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B. 12 2013 Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055 Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B. 11 2007 Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: diluted regime. Zbl 1276.05107 Shcherbina, Mariya; Tirozzi, Brunello 11 2012 Infinite differentiability for one-dimensional spin system with long range random interaction. Zbl 0506.58009 Cassandro, M.; Olivieri, E.; Tirozzi, B. 10 1982 On the replica symmetric equations for the Hopfield model. Zbl 0988.82024 Pastur, L.; Shcherbina, M.; Tirozzi, B. 10 1999 The free energy of a class of Hopfield models. Zbl 1097.82551 Shcherbina, M.; Tirozzi, B. 10 1993 Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Zbl 1309.05163 Shcherbina, Mariya; Tirozzi, Brunello 10 2010 \(p\)-adic dynamical systems and neural networks. Zbl 1010.82027 Albeverio, Sergio; Khrennikov, Andrei; Tirozzi, Brunello 9 1999 A quasi Trefftz-type spectral method for initial value problems with moving boundaries. Zbl 0912.65082 Lifits, S. A.; Reutskiy, S. Yu.; Tirozzi, B. 9 1997 Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311 Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskij, T. Ya. 8 2006 Rigorous results for the free energy in the Hopfield model. Zbl 0770.92003 Albeverio, S.; Tirozzi, B.; Zegarlinski, B. 7 1992 Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057 Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B. 7 2016 Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. Zbl 1230.35057 Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B. 6 2011 Quasi Trefftz spectral method for Stokes problem. Zbl 0897.76074 Lifits, S. A.; Reutskiy, S. Yu.; Pontrelli, G.; Tirozzi, B. 6 1997 Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 6 2010 On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 6 2015 Free energies of Boltzmann machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit. Zbl 07382818 Agliari, Elena; Barra, Adriano; Tirozzi, Brunello 6 2019 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 1194.35054 Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B. 5 2008 Fluctuation of the free energy in the Hopfield model. Zbl 0925.82163 Scacciatelli, E.; Tirozzi, B. 5 1992 Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154 Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello 5 2013 Quasi-Trefftz spectral method for separable linear elliptic equations. Zbl 0937.65123 Reutskiy, S. Yu.; Tirozzi, B. 4 1999 Conduction in bundles of demyelinated nerve fibers: computer simulation. Zbl 1105.92325 Reutskiy, S.; Rossoni, E.; Tirozzi, B. 4 2003 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012 Dobrokhotov, S. Yu.; Tirozzi, B.; Tolchennikov, A. A. 4 2014 On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. Zbl 1446.92109 Bianchi, Daniela; Marasco, Addolorata; Limongiello, Alessandro; Marchetti, Cristina; Marie, Helene; Tirozzi, Brunello; Migliore, Michele 4 2012 An introduction to the mathematical theory of neural networks. Zbl 0965.68083 Albeverio, S.; Tirozzi, B. 3 1997 The SLLN for the free-energy of a class of neural networks. Zbl 0840.68099 Feng, Jianfeng; Tirozzi, Brunello 3 1995 Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics. Zbl 1393.82023 Anikin, A. Yu.; Dobrokhotov, S. Yu.; Klevin, A. I.; Tirozzi, B. 3 2017 Learning of \(p\)-adic neural networks. Zbl 1078.82521 Khrennikov, Andrei; Tirozzi, Brunello 3 2000 On the Hamiltonian property of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices. Zbl 1074.76530 Dobrokhotov, S. Yu.; Tirozzi, B. 3 2002 Cauchy–Riemann conditions and localized asymptotic solutions of linearized equations of shallow water theory. Zbl 1100.76506 Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 3 2005 Hugoniót-Maslov chains for singular vortical solutions to quasilinear hyperbolic systems and typhoon trajectory. Zbl 1069.37049 Dobrokhotov, S.; Semenov, E.; Tirozzi, B. 3 2003 Replica symmetry breaking in neural networks with modified pseudo-inverse interactions. Zbl 0775.82003 Dotsenko, V. S.; Tirozzi, B. 3 1991 Forecast of the trajectory of the center of typhoons and the Maslov decomposition. Zbl 1136.86004 Reutskiy, S.; Tirozzi, B. 2 2007 Trefftz spectral method for initial-boundary problems. Zbl 0951.65100 Lifits, Sergei; Reutskiy, Sergei; Tirozzi, Brunello 2 1997 On the critical capacity of the Hopfield model. Zbl 1038.82069 Feng, Jianfeng; Shcherbina, Mariya; Tirozzi, Brunello 2 2001 On the volume of the intersection of a sphere with random half spaces. Zbl 1002.60005 Shcherbina, Maria; Tirozzi, Brunello 2 2002 A perturbative theory of the evolution of the center of typhoons. Zbl 1169.86307 Dobrokhotov, Sergey; Semenov, Evgeny; Tirozzi, Brunello 2 2005 A note on minimum-variance theory and beyond. Zbl 1048.37073 Feng, Jianfeng; Tartaglia, Giangaetano; Tirozzi, Brunello 2 2004 Neural networks and sea time series. Recontruction and extreme-event analysis. Zbl 1094.62121 Tirozzi, Brunello; Puca, Silvia; Pittalis, Stefano; Bruschi, Antonella; Morusci, Sara; Ferraro, Enrico; Corsini, Stefano 2 2006 Modified pseudo-inverse neural networks storing correlated patterns. Zbl 0753.92002 Der, R.; Dotsenko, V. S.; Tirozzi, B. 2 1992 Convergence theorems for the Kohonen feature mapping algorithms with VLRPs. Zbl 0870.60070 Feng, J. F.; Tirozzi, B. 2 1997 Local limit theorem for Gibbs random fields of particles and unbounded spins. Zbl 0415.60091 Campanino, Massimo; Del Grosso, Gabriella; Tirozzi, Brunello 2 1979 The local central limit theorem for a Gibbs random field. Zbl 0421.60091 Campanino, M.; Capocaccia, D.; Tirozzi, B. 2 1979 Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain. Zbl 1354.82032 Dobrokhotov, 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 1329.35246 Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B. 2 2016 The central limit theorem for a class of maps of the interval [0,1]. Zbl 0561.60026 Abundo, M.; Tirozzi, B. 1 1984 Central limit theorems for order parameters of the Gardner problem. Zbl 1213.82051 Shcherbina, M.; Tirozzi, B. 1 2003 Borel summability of the perturbation series in a hierarchical \(\lambda (\nabla \Phi)^ 4\) model. Zbl 0587.60099 Gawȩdzki, K.; Kupiainen, A.; Tirozzi, B. 1 1984 Rigorous results and critical capacity for a short-term memory model. Zbl 0878.60067 Feng, Jianfeng; Tirozzi, B.; Zucchi, R. 1 1996 Optimal movement control models of Langevin and Hamiltonian types. Zbl 1127.93063 Feng, J. F.; Shcherbina, M.; Tirozzi, B.; You, G. Q 1 2007 Generalization and learning error for nonlinear perceptron. Zbl 1168.91512 Shcherbina, M.; Tirozzi, B. 1 2002 Free energies of Boltzmann machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit. Zbl 07382818 Agliari, Elena; Barra, Adriano; Tirozzi, Brunello 6 2019 Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics. Zbl 1393.82023 Anikin, A. Yu.; Dobrokhotov, S. Yu.; Klevin, A. I.; Tirozzi, B. 3 2017 Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057 Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B. 7 2016 Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain. Zbl 1354.82032 Dobrokhotov, 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 1329.35246 Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B. 2 2016 On a homogenization method for differential operators with oscillating coefficients. Zbl 1326.35022 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 6 2015 Asymptotics of shallow water equations on the sphere. Zbl 1311.76012 Dobrokhotov, 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 1320.35180 Dobrokhotov, 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 1276.76012 Dobrokhotov, S. Yu.; Sergeev, S. A.; Tirozzi, B. 12 2013 Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. Zbl 1263.35154 Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello 5 2013 Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: diluted regime. Zbl 1276.05107 Shcherbina, Mariya; Tirozzi, Brunello 11 2012 On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. Zbl 1446.92109 Bianchi, Daniela; Marasco, Addolorata; Limongiello, Alessandro; Marchetti, Cristina; Marie, Helene; Tirozzi, Brunello; Migliore, Michele 4 2012 Asymptotic solutions of the linear shallow-water equations with localized initial data. Zbl 1325.76036 Dobrokhotov, 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 1230.35057 Dobrokhotov, S. Yu.; Nazaĭkinskiĭ, V. E.; Tirozzi, B. 6 2011 Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. Zbl 1387.35404 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 26 2010 Localized solutions of one-dimensional non-linear shallow-water equations with velocity \(c=\sqrt x\). Zbl 1196.35161 Dobrokhotov, S. Yu; Tirozzi, B. 16 2010 Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Zbl 1309.05163 Shcherbina, Mariya; Tirozzi, Brunello 10 2010 Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side. Zbl 1192.35110 Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. 6 2010 Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations. Zbl 1178.35301 Dobrokhotov, S. Yu.; Tirozzi, B.; Vargas, C. A. 17 2009 Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations. Zbl 1180.35336 Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B. 48 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 1194.35054 Bianchi, D.; Dobrokhotov, S. Yu.; Tirozzi, B. 5 2008 Representations of rapidly decaying functions by the Maslov canonical operator. Zbl 1344.58014 Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 30 2007 Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem. Zbl 1146.35055 Dobrokhotov, S. Yu.; Sinitsyn, S. O.; Tirozzi, B. 11 2007 Forecast of the trajectory of the center of typhoons and the Maslov decomposition. Zbl 1136.86004 Reutskiy, S.; Tirozzi, B. 2 2007 Optimal movement control models of Langevin and Hamiltonian types. Zbl 1127.93063 Feng, J. F.; Shcherbina, M.; Tirozzi, B.; You, G. Q 1 2007 Description of tsunami propagation based on the Maslov canonical operator. Zbl 1152.35089 Dobrokhotov, S. Yu.; Sekerzh-Zenkovich, S. Ya.; Tirozzi, B.; Tudorovskii, T. Ya. 13 2006 Description of a tsunami wave propagation on the ground of the Maslov canonical operator. Zbl 1119.76311 Dobrokhotov, 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 1094.62121 Tirozzi, 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 1100.76506 Dobrokhotov, S. Yu.; Tirozzi, B.; Shafarevich, A. I. 3 2005 A perturbative theory of the evolution of the center of typhoons. Zbl 1169.86307 Dobrokhotov, Sergey; Semenov, Evgeny; Tirozzi, Brunello 2 2005 A note on minimum-variance theory and beyond. Zbl 1048.37073 Feng, Jianfeng; Tartaglia, Giangaetano; Tirozzi, Brunello 2 2004 Rigorous solution of the Gardner problem. Zbl 1034.82042 Shcherbina, Mariya; Tirozzi, Brunello 16 2003 Conduction in bundles of demyelinated nerve fibers: computer simulation. Zbl 1105.92325 Reutskiy, S.; Rossoni, E.; Tirozzi, B. 4 2003 Hugoniót-Maslov chains for singular vortical solutions to quasilinear hyperbolic systems and typhoon trajectory. Zbl 1069.37049 Dobrokhotov, S.; Semenov, E.; Tirozzi, B. 3 2003 Central limit theorems for order parameters of the Gardner problem. Zbl 1213.82051 Shcherbina, M.; Tirozzi, B. 1 2003 On the Hamiltonian property of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices. Zbl 1074.76530 Dobrokhotov, S. Yu.; Tirozzi, B. 3 2002 On the volume of the intersection of a sphere with random half spaces. Zbl 1002.60005 Shcherbina, Maria; Tirozzi, Brunello 2 2002 Generalization and learning error for nonlinear perceptron. Zbl 1168.91512 Shcherbina, M.; Tirozzi, B. 1 2002 On the critical capacity of the Hopfield model. Zbl 1038.82069 Feng, Jianfeng; Shcherbina, Mariya; Tirozzi, Brunello 2 2001 Learning of \(p\)-adic neural networks. Zbl 1078.82521 Khrennikov, Andrei; Tirozzi, Brunello 3 2000 On the replica symmetric equations for the Hopfield model. Zbl 0988.82024 Pastur, L.; Shcherbina, M.; Tirozzi, B. 10 1999 \(p\)-adic dynamical systems and neural networks. Zbl 1010.82027 Albeverio, Sergio; Khrennikov, Andrei; Tirozzi, Brunello 9 1999 Quasi-Trefftz spectral method for separable linear elliptic equations. Zbl 0937.65123 Reutskiy, S. Yu.; Tirozzi, B. 4 1999 \(p\)-adic dynamical systems. Zbl 0974.37018 Albeverio, S.; Khrennikov, A.; Tirozzi, B.; De Smedt, S. 26 1998 A quasi Trefftz-type spectral method for initial value problems with moving boundaries. Zbl 0912.65082 Lifits, S. A.; Reutskiy, S. Yu.; Tirozzi, B. 9 1997 Quasi Trefftz spectral method for Stokes problem. Zbl 0897.76074 Lifits, S. A.; Reutskiy, S. Yu.; Pontrelli, G.; Tirozzi, B. 6 1997 An introduction to the mathematical theory of neural networks. Zbl 0965.68083 Albeverio, S.; Tirozzi, B. 3 1997 Trefftz spectral method for initial-boundary problems. Zbl 0951.65100 Lifits, Sergei; Reutskiy, Sergei; Tirozzi, Brunello 2 1997 Convergence theorems for the Kohonen feature mapping algorithms with VLRPs. Zbl 0870.60070 Feng, J. F.; Tirozzi, B. 2 1997 Rigorous results and critical capacity for a short-term memory model. Zbl 0878.60067 Feng, Jianfeng; Tirozzi, B.; Zucchi, R. 1 1996 The SLLN for the free-energy of a class of neural networks. Zbl 0840.68099 Feng, Jianfeng; Tirozzi, Brunello 3 1995 The replica-symmetric solution without replica trick for the Hopfield model. Zbl 0835.60092 Pastur, L.; Shcherbina, M.; Tirozzi, B. 24 1994 The free energy of a class of Hopfield models. Zbl 1097.82551 Shcherbina, M.; Tirozzi, B. 10 1993 Rigorous results for the free energy in the Hopfield model. Zbl 0770.92003 Albeverio, S.; Tirozzi, B.; Zegarlinski, B. 7 1992 Fluctuation of the free energy in the Hopfield model. Zbl 0925.82163 Scacciatelli, E.; Tirozzi, B. 5 1992 Modified pseudo-inverse neural networks storing correlated patterns. Zbl 0753.92002 Der, R.; Dotsenko, V. S.; Tirozzi, B. 2 1992 Replica symmetry breaking in neural networks with modified pseudo-inverse interactions. Zbl 0775.82003 Dotsenko, V. S.; Tirozzi, B. 3 1991 The central limit theorem for a class of maps of the interval [0,1]. Zbl 0561.60026 Abundo, M.; Tirozzi, B. 1 1984 Borel summability of the perturbation series in a hierarchical \(\lambda (\nabla \Phi)^ 4\) model. Zbl 0587.60099 Gawȩdzki, K.; Kupiainen, A.; Tirozzi, B. 1 1984 Infinite differentiability for one-dimensional spin system with long range random interaction. Zbl 0506.58009 Cassandro, M.; Olivieri, E.; Tirozzi, B. 10 1982 Local limit theorem for Gibbs random fields of particles and unbounded spins. Zbl 0415.60091 Campanino, Massimo; Del Grosso, Gabriella; Tirozzi, Brunello 2 1979 The local central limit theorem for a Gibbs random field. Zbl 0421.60091 Campanino, M.; Capocaccia, D.; Tirozzi, B. 2 1979 The central limit theorem and the problem of equivalence of ensembles. Zbl 0391.60095 Dobrushin, R. L.; Tirozzi, Brunello 35 1977 all cited Publications top 5 cited Publications all top 5 Cited by 315 Authors 56 Dobrokhotov, Sergei Yurievich 33 Tirozzi, Brunello 32 Nazaikinskii, Vladimir E. 16 Sergeev, Sergeĭ Alekseevich 15 Shafarevich, Andreĭ Igorevich 12 Tolchennikov, Anton A. 11 Agliari, Elena 10 Khrennikov, Andreĭ Yur’evich 9 Barra, Adriano 9 Minenkov, Dmitrii S. 8 Anikin, A. Yu. 7 Shcherbina, Mariya 6 Fachechi, Alberto 6 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 6 Tsvetkova, Anna V. 5 Allilueva, Anna I. 5 Grushin, V. V. 5 Maslov, Viktor Pavlovich 5 Rozikov, Utkir A. 4 Alemanno, Francesco 4 Feng, Jianfeng 4 Guerra, Francesco 4 Lozhnikov, D. A. 4 Mukhamedov, Farruh Maksutovich 4 Picco, Pierre 4 Sattarov, Iskandar A. 4 Tantari, Daniele 3 Albeverio, Sergio A. 3 Bellomo, Nicola 3 Bovier, Anton 3 Campanino, Massimo 3 Gayrard, Véronique 3 Guionnet, Alice 3 Huang, Jiaoyang 3 Kaneko, Hiroshi 3 Karwowski, Witold 3 Klevin, A. I. 3 Lebowitz, Joel Louis 3 Scacciatelli, E. 3 Volkov, B. I. 3 Yurova, Ekaterina I. 2 Aksenov, Alexander V. 2 Albanese, Linda 2 Barbier, Jean 2 Benatti, Fabio 2 Benaych-Georges, Florent 2 Benfatto, Giuseppe 2 Bianchi, Daniela 2 Borisov, Denis Ivanovich 2 Brezhnev, Yurii V. 2 Bulatov, Vitaliĭ Vasil’evich 2 Capocaccia, D. 2 Cassandro, Marzio 2 Comets, Francis M. 2 De Angelis, Elena 2 Gallavotti, Giovanni M. 2 Genovese, Giuseppe 2 Gramegna, Giovanni 2 Gundlach, Volker Matthias 2 Hu, Chinkun 2 Janžura, Martin 2 Kabanikhin, Sergeĭ Igorevich 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 Mancini, Stefano 2 Marullo, Chiara 2 Medvedev, Sergeĭ Borisovich 2 Mendes, José F. F. 2 Montanari, Andrea 2 Nicolò, Francesco 2 Olivieri, Enzo 2 Pastur, Leonid Andreevich 2 Pelinovsky, Efim 2 Perkins, Will 2 Petrov, P. N. 2 Petrov, Pavel S. 2 Presutti, Errico 2 Rodríguez Bermúdez, Panters 2 Rouleux, Michel 2 Rozanova, Olga S. 2 Shlosman, Senya B. 2 Valiño Alonso, Baldomero 2 Vargas, Carlos A. 2 Yau, Horng-Tzer 2 Yu, Jui-Ling 2 Zhu, Yizhe 2 Zúñiga-Galindo, Wilson A. 1 Abundo, Mario 1 Aihara, Kazuyuki 1 Alvarez, Gustavo Benitez 1 Amari, Shun-ichi 1 Anashin, Vladimir Sergeevich 1 Arora, Sumit 1 Aubin, Benjamin 1 Axelsson, E. Yurova ...and 215 more Authors all top 5 Cited in 82 Serials 43 Russian Journal of Mathematical Physics 31 Mathematical Notes 25 Journal of Statistical Physics 14 Theoretical and Mathematical Physics 10 Communications in Mathematical Physics 9 Journal of Mathematical Physics 9 Probability Theory and Related Fields 8 Mathematical and Computer Modelling 8 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 6 Computers & Mathematics with Applications 5 Doklady Mathematics 5 Proceedings of the Steklov Institute of Mathematics 5 Journal of Physics A: Mathematical and Theoretical 4 Neural Networks 4 Computational Mathematics and Mathematical Physics 4 Journal of Statistical Mechanics: Theory and Experiment 3 Fluid Dynamics 3 Journal of Mathematical Analysis and Applications 3 The Annals of Probability 3 Stochastic Processes and their Applications 2 Biological Cybernetics 2 Chaos, Solitons and Fractals 2 Advances in Mathematics 2 Journal of Differential Equations 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 Engineering Analysis with Boundary Elements 2 Differential Equations 2 Nonlinear Analysis. Real World Applications 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Random Matrices: Theory and Applications 2 The Journal of Mathematical Neuroscience 1 Applicable Analysis 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 Physica A 1 Physics Reports 1 Reports on Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Bulletin of Mathematical Biology 1 Prikladnaya Matematika i Mekhanika 1 The Annals of Statistics 1 Applied Mathematics and Computation 1 Functional Analysis and its Applications 1 Journal of Combinatorial Theory. Series A 1 Journal of Functional Analysis 1 Journal of Soviet Mathematics 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Results in Mathematics 1 Tôhoku 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 Combinatorics, Probability and Computing 1 St. Petersburg Mathematical Journal 1 Journal of Computational Neuroscience 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 Journal of Nonlinear Mathematical Physics 1 Journal of Mathematical Cryptology 1 Journal of Theoretical Biology 1 Journal of Applied Analysis and Computation 1 Evolution Equations and Control Theory 1 JAMM. Journal of Advanced Mathematical Modeling 1 Results in Applied Mathematics 1 Water Waves all top 5 Cited in 43 Fields 105 Partial differential equations (35-XX) 79 Statistical mechanics, structure of matter (82-XX) 72 Probability theory and stochastic processes (60-XX) 57 Fluid mechanics (76-XX) 33 Dynamical systems and ergodic theory (37-XX) 22 Quantum theory (81-XX) 21 Computer science (68-XX) 20 Number theory (11-XX) 19 Biology and other natural sciences (92-XX) 17 Geophysics (86-XX) 14 Combinatorics (05-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 13 Numerical analysis (65-XX) 10 Statistics (62-XX) 9 Differential geometry (53-XX) 7 Operator theory (47-XX) 5 Field theory and polynomials (12-XX) 5 Functional analysis (46-XX) 4 Optics, electromagnetic theory (78-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Measure and integration (28-XX) 3 Ordinary differential equations (34-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Convex and discrete geometry (52-XX) 3 Mechanics of deformable solids (74-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Operations research, mathematical programming (90-XX) 3 Systems theory; control (93-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Integral equations (45-XX) 2 General topology (54-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 2 Information and communication theory, circuits (94-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 Astronomy and astrophysics (85-XX) Citations by Year