Related papers: Simulating neuronal dynamics in fractional adaptiv…

We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence…

Event-based neuromorphic systems promise to reduce the energy consumption of deep learning tasks by replacing expensive floating point operations on dense matrices by low power sparse and asynchronous operations on spike events. While these…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…

In this work it is described how to enhance and generalize the equivalent model (arXiv:0802.0421) of integrate-and-fire dynamics in order to treat any complex neuronal networks, especially those exibiting modular structure. It has been…

Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…

Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…

Existing frameworks for gradient-based training of spiking neural networks face a trade-off: discrete-time methods using surrogate gradients support arbitrary neuron models but introduce gradient bias and constrain spike-time resolution,…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…

We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…

Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…

Closed-loop neurotechnology requires the capability to predict the state evolution and its regulation under (possibly) partial measurements. There is evidence that neurophysiological dynamics can be modeled by fractional-order dynamical…

Designing effective neural networks requires tuning architectural elements. This study integrates fractional calculus into neural networks by introducing fractional order derivatives (FDO) as tunable parameters in activation functions,…

This article introduces a framework for measuring the uncertain behaviour of a changing system in terms of the solution of a class of fractional stochastic differential equations (fsDEs). This is accomplished via operational matrices based…

Controlling the False Discovery Rate (FDR) is critical for reproducible variable selection, especially given the prevalence of complex predictive modeling. The recent Split Knockoff method, an extension of the canonical Knockoffs framework,…

The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…

Common wisdom indicates that to implement a Dynamical Memory with spiking neurons two ingredients are necessary: recurrence and a neuron population. Here we shall show that the second requirement is not needed. We shall demonstrate that…

This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced…

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…

Spikes are the currency in central nervous systems for information transmission and processing. They are also believed to play an essential role in low-power consumption of the biological systems, whose efficiency attracts increasing…