Related papers: Limits and dynamics of randomly connected neuronal…
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…
How the information microscopically processed by individual neurons is integrated and used in organizing the behavior of an animal is a central question in neuroscience. The coherence of neuronal dynamics over different scales has been…
Cortical neurons whose activity is recorded in behavioral experiments has been classified into several types such as stimulus-related neurons, delay-period neurons, and reward-related neurons. Moreover, the population activity of neurons…
This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness…
Networks of strongly-coupled neurons with random connectivity exhibit chaotic, asynchronous fluctuations. In previous work, we showed that when endowed with an additional low-rank connectivity consisting of the outer product of orthogonal…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
The brain is a complex organ characterized by heterogeneous patterns of structural connections supporting unparalleled feats of cognition and a wide range of behaviors. New noninvasive imaging techniques now allow these patterns to be…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative -- or correlated -- activity in neural populations, and in the…
The relation between large-scale brain structure and function is an outstanding open problem in neuroscience. We approach this problem by studying the dynamical regime under which realistic spatio-temporal patterns of brain activity emerge…
The brain is immensely complex, with diverse components and dynamic interactions building upon one another to orchestrate a wide range of functions and behaviors. Understanding patterns of these complex interactions and how they are…
Can multilayer neural networks -- typically constructed as highly complex structures with many nonlinearly activated neurons across layers -- behave in a non-trivial way that yet simplifies away a major part of their complexities? In this…
Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…
A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak…
Understanding how network function constrains neural connectivity is a central challenge in neuroscience. An influential approach is to train neural networks with gradient descent on cognitive tasks and characterize the resulting…
Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…
Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…