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We report on both analytical and numerical results concerning stochastic Hopfield--like neural automata exhibiting the following (biologically inspired) features: (1) Neurons and synapses evolve in time as in contact with respective baths…
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…
We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
The dynamics of spatially-structured networks of $N$ interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is known, a general question has remained unanswered: does…
The plasticity of the conduction delay between neurons plays a fundamental role in learning. However, the exact underlying mechanisms in the brain for this modulation is still an open problem. Understanding the precise adjustment of…
Neuromorphic computing has recently gained momentum with the emergence of various neuromorphic processors. As the field advances, there is an increasing focus on developing training methods that can effectively leverage the unique…
Neuronal oscillations are closely related to the symptoms of Parkinson's disease (PD). In this study, we explore how random fluctuations (or "stochastic inputs") affect these oscillations in brain states, which reflect the collective…
In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system,…
We study the evolution of dynamic fluctuations averaged over different space lengths and time scales to characterize spatially and temporally heterogeneous behavior of TIP4P/2005 water in liquid and supercooled states. Analysing a million…
We consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph with average connectivity $<k>$ scaling as a power law with the number of neurons in…
Neurons regulate the distribution of signaling components across an extended tree-like cellular structure using both local and global feedback control. This is hypothesized to allow homeostatic control of the electrical activity of a neuron…
Spiking neural networks (SNNs) exhibit superior energy efficiency but suffer from limited performance. In this paper, we consider SNNs as ensembles of temporal subnetworks that share architectures and weights, and highlight a crucial issue…
We show that the unavoidable increase in neuronal response latency to ongoing stimulation serves as a nonuniform gradual stretching of neuronal circuit delay loops and emerges as an essential mechanism in the formation of various types of…
We consider dynamics of the empirical measure of vertex neighborhood states of Markov interacting jump processes on sparse random graphs, in a suitable asymptotic limit as the graph size goes to infinity. Under the assumption of a certain…
There have been suggestions that heat caused by cerebral metabolic activity may constrain mammalian brain evolution, architecture, and function. This article investigates physical limits on brain wiring and corresponding changes in brain…
Homeostatic plasticity is a stabilizing mechanism commonly observed in real neural systems that allows neurons to maintain their activity around a functional operating point. This phenomenon can be used in neuromorphic systems to compensate…
We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at differentctime scales. Using…
A coarse-grained computational model is used to investigate the effect of a fluctuating fluid membrane on the dynamics of patchy-particle assembly into virus capsid-like cores. Results from simulations for a broad range of parameters are…
The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro.…
We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a continuous limit for the macroscopic behavior of the system, the…