Related papers: Variable-free exploration of stochastic models: a …
We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic…
Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and, ultimately, design. Here we propose and illustrate a systematic and powerful approach to…
We propose and illustrate an approach to coarse-graining the dynamics of evolving networks (networks whose connectivity changes dynamically). The approach is based on the equation-free framework: short bursts of detailed network evolution…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…
The data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Developing effective descriptions of the microscopic dynamics of many physical phenomena can both dramatically enhance their computational exploration and lead to a more fundamental understanding of the underlying physics. Previously, an…
We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be…
In order to illustrate the adaptation of traditional continuum numerical techniques to the study of complex network systems, we use the equation-free framework to analyze a dynamically evolving multigraph. This approach is based on coupling…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Biological structure and function depend on complex regulatory interactions between many genes. A wealth of gene expression data is available from high-throughput genome-wide measurement technologies, but effective gene regulatory network…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
Dynamic gene-regulatory networks are complex since the number of potential components involved in the system is very large. Estimating dynamic networks is an important task because they compromise valuable information about interactions…
Cellular regulatory dynamics is driven by large and intricate networks of interactions at the molecular scale, whose sheer size obfuscates understanding. In light of limited experimental data, many parameters of such dynamics are unknown,…
The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
Regulatory networks describe the interactions between molecular or cellular regulators, like transcription factors and genes in gene regulatory networks, kinases and their receptors in signalling networks, or neurons in neural networks. A…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
We present a loss function for neural networks that encompasses an idea of trivial versus non-trivial predictions, such that the network jointly determines its own prediction goals and learns to satisfy them. This permits the network to…