相关论文: Memory Uncertainty Relation and Harmonic Memory in…

Competitive neural networks are often used to model the dynamics of perceptual bistability. Switching between percepts can occur through fluctuations and/or a slow adaptive process. Here, we analyze switching statistics in competitive…

We study the effect of parameter fluctuations on synchronization of a coupled chaotic system. The fluctuations to the parameter can be random or it can be a periodic modulation. For random fluctuations we introduce a new quantity, the…

Spike generation in neurons produces a temporal point process, whose statistics is governed by intrinsic phenomena and the external incoming inputs to be coded. In particular, spike-evoked adaptation currents support a slow temporal process…

Noise is an inherent part of neuronal dynamics, and thus of the brain. It can be observed in neuronal activity at different spatiotemporal scales, including in neuronal membrane potentials, local field potentials, electroencephalography,…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

The extension of deep learning towards temporal data processing is gaining an increasing research interest. In this paper we investigate the properties of state dynamics developed in successive levels of deep recurrent neural networks…

Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, they are often treated as black-box models and as such it is difficult to understand what exactly they learn as well as…

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…

Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermite rank. From a statistical point of view, however, we argue…

We study emerging phenomena in binary neural networks where, with a probability c synaptic intensities are chosen according with a Hebbian prescription, and with probability (1-c) there is an extra random contribution to synaptic weights.…

Memory consistency models define the order in which accesses to shared memory in a concurrent system may be observed to occur. Such models are a necessity since program order is not a reliable indicator of execution order, due to…

Chaos and Noise are ubiquitous in the Brain. Inspired by the chaotic firing of neurons and the constructive role of noise in neuronal models, we for the first time connect chaos, noise and learning. In this paper, we demonstrate Stochastic…

Neural networks encode information through their collective spiking activity in response to external stimuli. This population response is noisy and strongly correlated, with complex interplay between correlations induced by the stimulus,…

Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent…

The classic paradigms for learning and memory recall focus on strengths of synaptic couplings and how these can be modulated to encode memories. In a previous paper [A. K. Behera, M. Rao, S. Sastry, and S. Vaikuntanathan, Physical Review X…

We show that in the generic situation where a biological network, e.g. a protein interaction network, is in fact a subnetwork embedded in a larger "bulk" network, the presence of the bulk causes not just extrinsic noise but also memory…

Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information…

Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…

We investigate a nonlinear dynamical system which ``remembers'' preselected values of a system parameter. The deterministic version of the system can encode many parameter values during a transient period, but in the limit of long times,…

In this work we study the detection of weak stimuli by spiking neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present…