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We perform stability analysis of a kinetic bacterial chemotaxis model of bacterial self-organization, assuming that bacteria respond sharply to chemical signals. The resulting discontinuous tumbling kernel represents the key challenge for…
To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit…
A common method for analyzing the effects of molecular noise in chemical reaction networks is to approximate the underlying chemical master equation by a Fokker-Planck equation, and to study the statistics of the associated chemical…
High-dimensional compartmental dynamical systems have been introduced to model brain metabolism. In this article, an approach is proposed to their mathematical analysis. Reductions of these models are obtained by replacing several…
We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken…
While adaptive experimental design has outgrown one-dimensional, staircase-based adaptations, most cognitive experiments still control a single factor and summarize performance with a scalar. We show a validation of a Bayesian, two-axis,…
The analysis of noise-induced escape in populations of bistable elements is challenging, because nonlinearity, coupling, and noise all play essential roles. We show that the interplay of these three factors yields three qualitatively…
Symmetry principles play an important role in geometry, and physics, allowing for the reduction of complicated systems to simpler, more comprehensible models that preserve the system's features of interest. Biological systems are often…
Low-frequency molecular fluctuations in the translational nonequilibrium zone of one-dimensional strong shock waves are characterised for the first time in a kinetic collisional framework in the Mach number range $2\le M\le 10$. Our…
Background: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state…
We study the one-dimensional Fermi gas subject to dissipative reactions. The dynamics is governed by the quantum master equation, where the Hamiltonian describes coherent motion of the particles, while dissipation accounts for irreversible…
In this paper, we propose a robust subspace-constrained quadratic model (SCQM) for learning low-dimensional structure from high-dimensional data. Building upon the subspace-constrained quadratic matrix factorization (SQMF) framework, the…
Structural identification and damage detection can be generalized as the simultaneous estimation of input forces, physical parameters, and dynamical states. Although Kalman-type filters are efficient tools to address this problem, the…
Biological data sets are often high-dimensional, noisy, and governed by complex interactions among sparse signals. This poses major challenges for interpretability and reliable feature selection. Tasks such as identifying motif interactions…
In quorum sensing (QS), bacteria exchange molecular signals to work together. An analytically-tractable model is presented for characterizing QS signal propagation within a population of bacteria and the number of responsive cooperative…
We have developed and implemented a numerical evolution scheme for a class of stochastic problems in which the temporal evolution occurs on widely-separated time scales, and for which the slow evolution can be described in terms of a small…
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…
Microbes are everywhere, including in and on our bodies, and have been shown to play key roles in a variety of prevalent human diseases. Consequently, there has been intense interest in the design of bacteriotherapies or "bugs as drugs,"…
Cells can utilize chemical communication to exchange information and coordinate their behavior in the presence of noise. Communication can reduce noise to shape a collective response, or amplify noise to generate distinct phenotypic…
In this paper we use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-tumble process to the intracellular reaction where the…