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We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we…

We consider a thermodynamically correct framework for electro-energy-reaction-diffusion systems, which feature a monotone entropy functional while conserving the total charge and the total energy. For these systems, we construct a relative…

For strictly entropic Riemann shock solutions of strictly hyperbolic systems of balance laws, we prove that exponential spectral stability implies large-time asymptotic orbital stability. As a preparation, we also prove similar results for…

We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The required stabilizing algebra depends…

We present a technique to characterize differentially expressed genes in terms of their position in a high-dimensional co-expression network. The set-up of Gaussian graphical models is used to construct representations of the co-expression…

In this paper, we derive a periodic model from a one dimensional nonlocal eikonal equation set on the full space modeling dislocation dynamics. Thanks to a gradient entropy estimate, we show that this periodic model converges toward the…

Learning directionality between variables is crucial yet challenging, especially for mechanistic relationships without a priori ordering assumptions. We propose a coefficient of asymmetry to quantify directional asymmetry using Shannon's…

The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…

We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to infinity and the mutation probability goes to 0. A limiting infinite system of differential equations is obtained. We prove the…

Electronic circuits are useful tools for studying potential dynamical behaviors of synthetic genetic networks. The circuit models are complementary to numerical simulations of the networks, especially providing a framework for verification…

Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…

In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…

We use large deviation methods to calculate rates of noise-induced transitions between states in multistable genetic networks. We analyze a synthetic biochemical circuit, the toggle switch, and compare the results to those obtained from a…

One of the outstanding problems in non-equilibrium physics is to precisely understand when and how physically relevant observables in many-body systems equilibrate under unitary time evolution. General equilibration results show that…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion…

Regulatory interactions between genes show a large amount of cross-species variability, even when the underlying functions are conserved: There are many ways to achieve the same function. Here we investigate the ability of regulatory…

In recent times whole-genome gene expression analysis has turned out to be a highly important tool to study the coordinated function of a very large number of genes within their corresponding cellular environment, especially in relation to…

We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems.…

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…