Related papers: Poincar\'e type inequalities for compact degenerat…

This work is devoted to the problem of synchronization of two Morris-Lecar neuron models. The Morris-Lecar model is a second-order system of differential equations, which describes an uneasy relationship between the membrane potential and…

Dunkl processes are multidimensional Markov processes defined through the use of Dunkl operators. These processes have discontinuities, and they can be separated into their continuous (radial) part, and their discontinuous (jump) part.…

Ever since the advent of the neuron doctrine more than a century ago, information processing in the brain is widely believed to mainly follow the forward pre to post-synaptic neurons direction. Challenging this prevalent view, in this…

The growing interest in brain-inspired computational models arises from the remarkable problem-solving efficiency of the human brain. Action recognition, a complex task in computational neuroscience, has received significant attention due…

The nervous system, more specifically, the brain, is capable of solving complex problems simply and efficiently, far surpassing modern computers. In this regard, neuromorphic engineering is a research field that focuses on mimicking the…

In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium…

We investigate the use of a certain class of functional inequalities known as weak Poincar\'e inequalities to bound convergence of Markov chains to equilibrium. We show that this enables the straightforward and transparent derivation of…

We develop a theory of weak Poincar\'e inequalities to characterize convergence rates of ergodic Markov chains. Motivated by the application of Markov chains in the context of algorithms, we develop a relevant set of tools which enable the…

Neurons in cortical circuits exhibit coordinated spiking activity, and can produce correlated synchronous spikes during behavior and cognition. We recently developed a method for estimating the dynamics of correlated ensemble activity by…

We study a random walk model in which the jumping probability to a site is dependent on the number of previous visits to the site, as a model of the mobility with memory. To this end we introduce two parameters called the memory parameter…

While feed-forward neurons in pre-trained language models (PLMs) can encode knowledge, past research targeted a small subset of neurons that heavily influence outputs. This leaves the broader role of neuron activations unclear, limiting…

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds…

Excitation-inhibition (E-I) balance is ubiquitously observed in the cortex. Recent studies suggest an intriguing link between balance on fast timescales, tight balance, and efficient information coding with spikes. We further this…

The characterization of coordinated activity in neuronal populations has received renewed interest in the light of advancing experimental techniques which allow recordings from multiple units simultaneously. Across both in vitro and in vivo…

The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the…

We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate.…

The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances raises the question how these models relate to each other. In particular it is hard to distinguish between…

Ever since the last two decades of the past century pioneering studies in the field of statistical physics had focused their efforts on developing models of neural networks that could display memory storage and retrieval. Though many…

We prove an equivalence between weighted Poincare inequalities and the existence of weak solutions to a Neumann problem related to a degenerate p- Laplacian. The Poincare inequalities are formulated in the context of degenerate Sobolev…

Neurons are spatially extended cells; different parts of a neuron have specific voltage dynamics. Important types of neurons even generate different spikes in different parts of the cell. Neurons' inputs are also often spatially…