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A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…

Optimization and Control · Mathematics 2021-06-15 Giacomo Albi , Stefano Almi , Marco Morandotti , Francesco Solombrino

Mean-field models provide a link between microscopic neuronal activity and macroscopic brain dynamics. Their derivation depends on simplifying assumptions, such as all-to-all connectivity, limiting their biological realism. To overcome…

Neurons and Cognition · Quantitative Biology 2025-09-05 Martin Breyton , Viktor Sip , Marmaduke Woodman , Meysam Hashemi , Spase Petkoski , Viktor Jirsa

We consider a threshold-crossing spiking process as a simple model for the activity within a population of neurons. Assuming that these neurons are driven by a common fluctuating input with Gaussian statistics, we evaluate the…

Neurons and Cognition · Quantitative Biology 2009-06-11 Yoram Burak , Sam Lewallen , Haim Sompolinsky

The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…

Probability · Mathematics 2025-05-27 James MacLaurin , Pedro Vilanova

Dynamical systems driven by strong external signals are ubiquituous in nature and engineering. Here we study "echo state networks", networks of a large number of randomly connected nodes, which represent a simple model of a neural network,…

Chaotic Dynamics · Physics 2013-11-07 Marc Massar , Serge Massar

We consider a network of randomly coupled rate-based neurons influenced by external and internal noise. We derive a second-order stochastic mean-field model for the network dynamics and use it to analyze the stability and bifurcations in…

Chaotic Dynamics · Physics 2015-12-14 Vladimir Klinshov , Igor Franovic

Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity.…

Neurons and Cognition · Quantitative Biology 2009-05-15 Michael A. Buice , Jack D. Cowan , Carson C. Chow

Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how…

Neurons and Cognition · Quantitative Biology 2020-03-13 Yajing Zheng , Shanshan Jia , Zhaofei Yu , Tiejun Huang , Jian K. Liu , Yonghong Tian

A mean field feedback artificial neural network algorithm is developed and explored for the set covering problem. A convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function. An approximate…

Neural and Evolutionary Computing · Computer Science 2007-05-23 Mattias Ohlsson , Carsten Peterson , Bo Söderberg

Travelling waves of neural firing activity are observed in brain tissue as a part of various sensory, motor and cognitive processes. They represent an object of major interest in the study of excitable networks, with analysis conducted in…

Neurons and Cognition · Quantitative Biology 2025-11-10 Henry D. J. Kerr , Peter Ashwin , Kyle C. A. Wedgwood

Computational models of cortical activity provide insight into the mechanisms of higher-order processing in the human brain including planning, perception and the control of movement. Activity in the cortex is ongoing even in the absence of…

Neurons and Cognition · Quantitative Biology 2023-07-07 Lysea Haggie , Thor Besier , Angus McMorland

Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for…

Physics and Society · Physics 2015-03-17 James P. Gleeson , Sergey Melnik , Jonathan A. Ward , Mason A. Porter , Peter J. Mucha

Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…

Disordered Systems and Neural Networks · Physics 2019-08-13 David Dahmen , Markus Diesmann , Moritz Helias

A statistical theory of the mean field is developed. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction, obtained after the…

Nuclear Theory · Physics 2009-10-30 R. Caracciolo , A. De Pace , H. Feshbach , A. Molinari

The response time of physical computational elements is finite, and neurons are no exception. In hierarchical models of cortical networks each layer thus introduces a response lag. This inherent property of physical dynamical systems…

Neurons and Cognition · Quantitative Biology 2021-10-28 Paul Haider , Benjamin Ellenberger , Laura Kriener , Jakob Jordan , Walter Senn , Mihai A. Petrovici

We study finite-size fluctuations in a network of spiking deterministic neurons coupled with non-uniform synaptic coupling. We generalize a previously developed theory of finite size effects for uniform globally coupled neurons. In the…

Neurons and Cognition · Quantitative Biology 2019-01-02 Siwei Qiu , Carson Chow

Mesoscopic models of finite-size neuronal populations are crucial to understand the dynamics of neural networks in the brain, especially their fluctuations and response to stimuli. However, current theories to derive such models are based…

Neurons and Cognition · Quantitative Biology 2026-01-26 Nils E. Greven , Jonas Ranft , Tilo Schwalger

A spin version of dynamical mean-field theory is extended for magnetically ordered states in the Heisenberg model. The self-consistency equations are solved with high numerical accuracy by means of the continuous-time quantum Monte Carlo…

Strongly Correlated Electrons · Physics 2013-08-02 Junya Otsuki , Yoshio Kuramoto

Research has shown that neurons within the brain are selective to certain stimuli. For example, the fusiform face area (FFA) region is known by neuroscientists to selectively activate when people see faces over non-face objects. However,…

Computer Vision and Pattern Recognition · Computer Science 2021-03-24 Edward Kim , Maryam Daniali , Jocelyn Rego , Garrett T. Kenyon

We propose and analyse a procedure for using a standard activity-based neuron network model and firing data to compute the effective connection strengths between neurons in a network. We assume a Heaviside response function, that the…

Dynamical Systems · Mathematics 2025-02-12 Maren Bråthen Kristoffersen , Bjørn Fredrik Nielsen , Susanne Solem