相关论文: Preisach models of hysteresis driven by Markovian …

Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…

In this work, we will investigate a Bayesian approach to estimating the parameters of long memory models. Long memory, characterized by the phenomenon of hyperbolic autocorrelation decay in time series, has garnered significant attention.…

This paper investigates the asymptotic behavior of stochastic recursive inclusions in the presence of non-zero, non-diminishing bias, a setting that frequently arises in zeroth-order optimization, stochastic approximation with…

In this work we introduce and investigate the properties of the "relativistic" Hopfield model endowed with temporally correlated patterns. First, we review the "relativistic" Hopfield model and we briefly describe the experimental evidence…

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show…

Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies composing cortical columns is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing $\nu(t)$ scale with the…

We study the aggregation of AR processes and generalized Ornstein-Uhlenbeck (OU) processes. Mixture of spectral densities with random poles are the main tool. In this context, we apply our results for the aggregation of doubly stochastic…

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic…

The ubiquitous effects of the environment on quantum-mechanical systems generally cause temporally correlated fluctuations. This particularly holds for systems of interest for quantum computation where such effects lead to correlated…

We investigate from a computational perspective the efficiency of the Willshaw synaptic update rule in the context of familiarity discrimination, a binary-answer, memory-related task that has been linked through psychophysical experiments…

We investigated a model for the neural integrator based on hysteretic units connected by positive feedback. Hysteresis is assumed to emerge from the intrinsic properties of the cells. We consider the recurrent networks containing either…

The responses of synapses in the neocortex show highly stochastic and nonlinear behavior. The microscopic dynamics underlying this behavior, and its computational consequences during natural patterns of synaptic input, are not explained by…

We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…

We numerically investigate the long-time behavior of the density-density auto-correlation function in driven lattice gases with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo…

Recently Segev et al. (Phys. Rev. E 64,2001, Phys.Rev.Let. 88, 2002) made long-term observations of spontaneous activity of in-vitro cortical networks, which differ from predictions of current models in many features. In this paper we…

We investigate dynamics of recurrent neural networks with correlated noise to analyze the noise's effect. The mechanism of correlated firing has been analyzed in various models, but its functional roles have not been discussed in sufficient…

We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by "controlled" Markov noise. In particular, the faster and slower recursions have non-additive controlled Markov noise…

Contextual memory integration remains a high challenge in the development of language models, particularly in tasks that require maintaining coherence over extended sequences. Traditional approaches, such as self-attention mechanisms and…

In the absence of synaptic coupling, two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams. Recent work has shown that the degree of correlation transfer from input…

Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…