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Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a…
Double excitations are crucial to understanding numerous chemical, physical, and biological processes, but accurately predicting them remains a challenge. In this work, we explore the particle-particle random phase approximation (ppRPA) as…
We study the validity of an averaging principle for a slow-fast system of stochastic reaction diffusion equations. We assume here that the coefficients of the fast equation depend on time, so that the classical formulation of the averaging…
Foundation models, including language models, e.g., GPT, and vision models, e.g., CLIP, have significantly advanced numerous biomedical tasks. Despite these advancements, the high inference latency and the "overthinking" issues in model…
Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The…
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic PDE that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges…
We develop a theoretical approach that uses physiochemical kinetics modelling to describe cell population dynamics upon progression of viral infection in cell culture, which results in cell apoptosis (programmed cell death) and necrosis…
The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly…
A preceding paper demonstrated that explicit asymptotic methods generally work much better for extremely stiff reaction networks than has previously been shown in the literature. There we showed that for systems well removed from…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
Mathematical analysis of mass action models of large complex chemical systems is typically only possible if the models are reduced. The most common reduction technique is based on quasi-steady state assumptions. To increase the accuracy of…
Maintaining stability in an uncertain environment is essential for proper functioning of living systems. Robust perfect adaptation (RPA) is a property of a system that generates an output at a fixed level even after fluctuations in input…
We study, from a purely quantitative point of view, the quasi-steady-state assumption for the fundamental mathematical model of the general enzymatic reaction: we re-establish, on a rigorous basis, certain already known results and we…
Oja's algorithm of principal component analysis (PCA) has been one of the methods utilized in practice to reduce dimension. In this paper, we focus on the convergence property of the discrete algorithm. To realize that, we view the…
Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable…
Point processes are an essential tool when we are interested in where in time or space events occur. The basic starting point for point processes is usually the Poisson process. Over the years, Stein's method has been developed with a great…
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 propose a model for cell polarization as a response to an external signal which results in a system of PDEs for different variants of a protein on the cell surface and interior respectively. We study stationary states of this model in…
The classical approach to analyze pharmacokinetic (PK) data in bioequivalence studies aiming to compare two different formulations is to perform noncompartmental analysis (NCA) followed by two one-sided tests (TOST). In this regard the PK…