Related papers: Generalization of the event-based Carnevale-Hines …
The bio-inspired integrate-fire-reset mechanism of spiking neurons constitutes the foundation for efficient processing in Spiking Neural Networks (SNNs). Recent progress in large models demands that spiking neurons support highly parallel…
Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…
How do neuronal populations encode time-dependent stimuli in their population firing rate? To address this question, I consider the quasi-renewal equation and the event-based expansion, two theoretical approximations proposed recently, and…
This paper proposes a framework for the biological learning mechanism as a general learning system. The proposal is as follows. The bursting and tonic modes of firing patterns found in many neuron types in the brain correspond to two…
Maxwell's equations are the fundamental equations for understanding electric and magnetic field interactions and play a crucial role in designing and optimizing sensor systems like capacitive touch sensors, which are widely prevalent in…
The Network of Noisy Leaky Integrate and Fire (NNLIF) model describes the behavior of a neural network at mesoscopic level. It is one of the simplest self-contained mean-field models considered for that purpose. Even so, to study the…
An inverse procedure is proposed and tested which aims at recovering the a priori unknown functional and structural information from global signals of living brains activity. To this end we consider a Leaky-Integrate and Fire (LIF) model…
Recent advances in neuromorphic signal processing have introduced time encoding machines as a promising alternative to conventional uniform sampling for low-power communication receivers. In this paradigm, analog signals are converted into…
We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprise two modules, each of which contains two components. We model each component using a…
Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are…
The functional significance of correlations between action potentials of neurons is still a matter of vivid debates. In particular it is presently unclear how much synchrony is caused by afferent synchronized events and how much is…
Callaway's dual relaxation times model, which takes into account the normal and resistive scatterings of phonon, is used to describe the heat conduction in materials like graphene. For steady-state problems, the Callaway model is usually…
The classical phase-field modeling approaches for multiphase problems represent each phase using a regularized characteristic function, which necessarily introduces a simplex constraint for the phase-field variables. Additionally, the…
Limitations in processing capabilities and memory of today's computers make spiking neuron-based (human) whole-brain simulations inevitably characterized by a compromise between bio-plausibility and computational cost. It translates into…
Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here…
We propose TRACIE, a novel temporal reasoning dataset that evaluates the degree to which systems understand implicit events -- events that are not mentioned explicitly in natural language text but can be inferred from it. This introduces a…
This paper develops a novel deep learning approach for solving evolutionary equations, which integrates sequential learning strategies with an enhanced hard constraint strategy featuring trainable parameters, addressing the low…
We propose a Multivariate Spatio-Temporal Neural Hawkes Process for modeling complex multivariate event data with spatio-temporal dynamics. The proposed model extends continuous-time neural Hawkes processes by integrating spatial…
We introduce and study an extension of the classical elapsed time equation in the context of neuron populations that are described by the elapsed time since the last discharge, i.e., the refractory period. In this extension we incorporate…
Kinetics of a balanced network of neurons with a sparse grid of synaptic links is well representable by the stochastic dynamics of a generic neuron subject to an effective shot noise. The rate of delta-pulses of the noise is determined…