Related papers: A hybrid model for large neural network descriptio…

Large-scale neuroscience is generating rich datasets across animals, brain areas and behavioral contexts, yet our modeling efforts remains fragmented across isolated experiments. We argue that understanding behavior requires integrative…

The neural ordinary differential equation (neural ODE) model has attracted increasing attention in time series analysis for its capability to process irregular time steps, i.e., data are not observed over equally-spaced time intervals. In…

In this brief paper, a learning algorithm is developed for Deep Learning NeuroSkin Neural Network to improve their learning properties. Neuroskin is a new type of neural network presented recently by the authors. It is comprised of a…

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting…

Neural networks and other machine learning models compute continuous representations, while humans communicate mostly through discrete symbols. Reconciling these two forms of communication is desirable for generating human-readable…

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…

In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We are specifically concerned with a new agent-based, continuous-in-space,…

Learning dynamical systems is a promising avenue for scientific discoveries. However, capturing the governing dynamics in multiple environments still remains a challenge: model-based approaches rely on the fidelity of assumptions made for a…

Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct…

We consider an idealized network, formed by N neurons individually described by the FitzHugh-Nagumo equations and connected by electrical synapses. The limit for N to infinity of the resulting discrete model is thoroughly investigated, with…

There has been a significant focus on modelling emotion ambiguity in recent years, with advancements made in representing emotions as distributions to capture ambiguity. However, there has been comparatively less effort devoted to the…

Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time…

The simplest model of a smart spatial redistribution of individuals is proposed. A single-species population is considered, to be composed of two discrete subpopulations inhabiting two stations; migration is a transfer between them. The…

Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…

Efficient neural network models that generate brain-like dynamic activity can be a valuable resource for generating synthetic data, analyzing differences in brain transients under conditions such as testing perturbation activity or…

We consider the compilation of a binary neural network's decision function into tractable representations such as Ordered Binary Decision Diagrams (OBDDs) and Sentential Decision Diagrams (SDDs). Obtaining this function as an OBDD/SDD…

We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is…

This work presents an omics-driven modeling pipeline that integrates machine-learning tools to facilitate the dynamic modeling of multiscale biological systems. Random forests and permutation feature importance are proposed to mine omics…

In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…