Related papers: Workflow description to dynamically model \beta-ar…

Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…

Building biological models by inferring functional dependencies from experimental data is an im- portant issue in Molecular Biology. To relieve the biologist from this traditionally manual process, various approaches have been proposed to…

A neural network system in an animal brain contains many modules and generates adaptive behavior by integrating the outputs from the modules. The mathematical modeling of such large systems to elucidate the mechanism of rapidly finding…

Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living…

Many networks are important because they are substrates for dynamical systems, and their pattern of functional connectivity can itself be dynamic -- they can functionally reorganize, even if their underlying anatomical structure remains…

Cell signaling networks are complex and often incompletely characterized, making it difficult to obtain a comprehensive picture of the mechanisms they encode. Mathematical modeling of these networks provides important clues, but the models…

Dynamic analysis of structures subjected to earthquake excitation is a time-consuming process, particularly in the case of extremely small time step required, or in the presence of high geometric and material nonlinearity. Performing…

We present a statistical framework for generating predicted dynamic networks based on the observed evolution of social relationships in a population. The framework includes a novel and flexible procedure to sample dynamic networks given a…

Neural circuits are able to perform computations under very diverse conditions and requirements. The required computations impose clear constraints on their fine-tuning: a rapid and maximally informative response to stimuli in general…

Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

The use of recurrent neural networks to represent the dynamics of unstable systems is difficult due to the need to properly initialize their internal states, which in most of the cases do not have any physical meaning, consequent to the…

Network inference approaches are now widely used in biological applications to probe regulatory relationships between molecular components such as genes or proteins. Many methods have been proposed for this setting, but the connections and…

Dynamic positron emission tomography (PET) images can reveal the distribution of tracers in the organism and the dynamic processes involved in biochemical reactions, and it is widely used in clinical practice. Despite the high effectiveness…

Inferring the mechanisms underlying physiological and pathological processes in the brain from recorded electrical activity is challenging. Bayesian model selection and dynamic causal modelling aim to identify likely biophysical models to…

Recent studies have shown that functional brain brainwork is dynamic even during rest. A common approach to modeling the brain network in whole brain resting-state fMRI is to compute the correlation between anatomical regions via sliding…

Mathematical models of stem cell differentiation are commonly based upon the concept of subsequent cell fate decisions, each controlled by a gene regulatory network. These networks exhibit a multistable behavior and cause the system to…

We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two…