Related papers: Stable developmental patterns of gene expression w…
We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of…
The advent of new experimental genomic technologies and the massive increase of DNA sequence information is helping researchers better understand how our genes work. Recently, experiments on mRNA abundance (gene expression) have revealed…
Classical adaptive control proves total-system stability for control of linear plants, but only for plants meeting very restrictive assumptions. Approximate Dynamic Programming (ADP) has the potential, in principle, to ensure stability…
In this paper, we use a variety of mathematical techniques to explore existence, local stability, and global stability of equilibria in abstract models of mitochondrial metabolism. The class of models constructed is defined by the…
We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeable networks. Conditional on latent (unobserved) variables, the edges of the network are generated by their finite growth history…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
This article treats global uniform exponential stability (GUES) of discrete-time switched linear systems under restricted switching. Given admissible minimum and maximum dwell times, we provide sufficient conditions on the subsystems under…
Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…
Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the…
How can a microorganism adapt to a variety of environmental conditions despite there exists a limited number of signal transduction machineries? We show that for any growing cells whose gene expression is under stochastic fluctuations,…
Regime shifts in biology, ecology, and other complex systems are often interpreted through stability landscapes and early warning signals that implicitly assume dynamics without memory effects. Yet many real systems exhibit these effects,…
Recently, the stability of graph filters has been studied as one of the key theoretical properties driving the highly successful graph convolutional neural networks (GCNs). The stability of a graph filter characterizes the effect of…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
Genetic regulation is a key component in development, but a clear understanding of the structure and dynamics of genetic networks is not yet at hand. In this work we investigate these properties within an artificial genome model originally…
We study transient sequential dynamics of evolving dynamical networks, i.e., those having active nodes and links and activity-dependent topology. We show that such networks can generate sequences of metastable cluster states where each…
Localized persistent neural activity can encode delayed estimates of continuous variables. Common experiments require that subjects store and report the feature value (e.g., orientation) of a particular cue (e.g., oriented bar on a screen)…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…