Related papers: A neuron inspired model for the time constant of d…

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…

The net of N ``physical'' neurons is considered as a dynamical system. These neurons form a complete graph. The state of any neuron is its electric potential. The potential linearly increases until reaches its maximal value. Then it falls…

Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

Ionic models, the set of ordinary differential equations (ODEs) describing the time evolution of the state of excitable cells, are the cornerstone of modeling in neuro- and cardiac electrophysiology. Modern ionic models can have tens of…

Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…

This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…

We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that…

This paper introduces a biomathematical model designed to describe the internal dynamics of dream formation and spontaneous cognitive processes. The model incorporates neurocognitive factors such as dissatisfaction, acceptance, forgetting,…

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…

The action potential signal of nerve and muscle is produced by voltage sensitive channels that include a specialized device to sense voltage. Gating currents of the voltage sensor are now known to depend on the back-and-forth movements of…

Established recurrent neural networks are well-suited to solve a wide variety of prediction tasks involving discrete sequences. However, they do not perform as well in the task of dynamical system identification, when dealing with…

This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals…

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…

While spiking neural networks (SNNs) provide a biologically inspired and energy-efficient computational framework, their robustness and the dynamic advantages inherent to biological neurons remain significantly underutilized owing to…

In this work we present a novel recurrent neural network architecture designed to model systems characterized by multiple characteristic timescales in their dynamics. The proposed network is composed by several recurrent groups of neurons…

A nonuniform extension of the Glauber model on a one-dimensional lattice with boundaries is investigated. Based on detailed balance, reaction rates are proposed for the system. The static behavior of the system is investigated. It is shown…

Attractor neural networks consider that neural information is stored as stationary states of a dynamical system formed by a large number of interconnected neurons. The attractor property empowers a neural system to encode information…

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…

Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…