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Convergence properties of model-free two-timescale asymptotic simulations of singularly perturbed hybrid inclusions are developed. A hybrid inclusion combines constrained differential and difference inclusions to capture continuous (flow)…
Bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. These models…
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…
Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous…
An efficient coarse-mesh nodal integral method (NIM), based on cell-centered variables and termed the cell-centered NIM (CCNIM), is developed and applied to solve multi-dimensional, time-dependent, nonlinear Burgers equations, extending the…
Power system voltage regulation is crucial to maintain power quality while integrating intermittent renewable resources in distribution grids. However, the system model on the grid edge is often unknown, making it difficult to model…
This work focuses on the formulation of a four-equation model for simulating unsteady two-phase mixtures with phase transition and strong discontinuities. The main assumption consists in a homogeneous temperature, pressure and velocity…
Coastal communities increasingly face compound floods, where multiple drivers like storm surge, high tide, heavy rainfall, and river discharge occur together or in sequence to produce impacts far greater than any single driver alone.…
In this paper, the physics informed neural networks (PINNs) is employed for the numerical simulation of heat transfer involving a moving source. To reduce the computational effort, a new training method is proposed that uses a continuous…
This study addresses the intricate challenge of decentralized output-feedback control for stochastic non-triangular nonlinear interconnected systems with unknown time-varying sensor sensitivity in a dynamic event-triggered context. The…
A new model of neural networks described by the memristive and diffusive Hindmarsh-Rose equations is proposed. Globally dissipative dynamics is shown with absorbing sets in the state spaces. Through sharp and uniform grouping estimates and…
The work is a continuation of a paper by Iskhakov A.S. and Dinh N.T. "Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations". Part I // arXiv:2008.10509 (2020) [1]. The proposed in [1]…
Event schemas encode knowledge of stereotypical structures of events and their connections. As events unfold, schemas are crucial to act as a scaffolding. Previous work on event schema induction focuses either on atomic events or linear…
We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N tends to…
We study a neural network model in which both neurons and synaptic interactions evolve in time simultaneously. The time evolution of synaptic interactions is described by a Langevin equation including a Hebbian learning term, and a bias…
Conventional deep learning prioritizes unconstrained optimization, yet biological systems operate under strict metabolic constraints. We propose that these physical constraints shape dynamics to function not as limitations, but as a…
Transient and equilibrium synchronizations in complex neuronal networks as a consequence of dynamics induced by having sources placed at specific neurons are investigated. The basic integrate-and-fire neuron is adopted, and the dynamics is…
Phase field models are gradient flows with their energy naturally dissipating in time. In order to preserve this property, many numerical schemes have been well-studied. In this paper we consider a well-known method, namely the exponential…
Accurate single-cell analysis is critical for diagnostics, immunomonitoring, and cell therapy, but coincident events - where multiple cells overlap in a sensing zone - can severely compromise signal fidelity. We present a hybrid framework…
The paper proposes a distributed eventtriggered consensus approach for linear multi-agent systems with guarantees over rate of convergence, resilience to control gain uncertainties, and Pareto optimality of design parameters, namely, the…