Related papers: Parameter Invariance Analysis of Moment Equations …
This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
Homeostasis is a regulatory mechanism that keeps a specific variable close to a set value as other variables fluctuate. The notion of homeostasis can be rigorously formulated when the model of interest is represented as an input-output…
Biochemical reactions with oscillatory behavior play an essential role in synthetic biology at the microscopic scale. Although a robust stability theory for deterministic chemical oscillators in the macroscopic limit exists, the dynamical…
The distributive sequential n-site phosphorylation/dephosphorylation system is an important building block in networks of chemical reactions arising in molecular biology, which has been intensively studied. In the nice paper of Wang and…
Equations of motion that recognize biochemical patterns are described. The equations are partial differential equations in a continuous multiple component system in which adequate initial and boundary conditions are given. The biochemical…
Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medical image analysis with both population trends and random…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
Recently, a variant of the Bohr Hamiltonian was proposed where the mass term is allowed to depend on the beta variable of nuclear deformation. Analytic solutions of this modified Hamiltonian have been obtained using the Davidson and the…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…
We review a dynamical approach to non-equilibrium MD (D-NEMD). We show how, using a proper simulation setup, is possible to treat interesting cases in which the initial condition is a stationary non-equilibrium state produced by a suitable…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years severalmethods for accurately…