Related papers: Population dynamics method with a multi-canonical …
We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution---a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an…
We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the Bolker-Pacala-Dieckmann-Law model. Under the…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…
While distributed parameter estimation has been extensively studied in the literature, little has been achieved in terms of robust analysis and tuning methods in the presence of disturbances. However, disturbances such as measurement noise…
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past…
Population dynamics with complex biological interactions, accounting for uncertainty quantification, is critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the…
In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools…
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of…
We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…
Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
We consider numerical schemes for computing the linear response of steady-state averages of stochastic dynamics with respect to a perturbation of the drift part of the stochastic differential equation. The schemes are based on Girsanov's…
Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying…
Periodic dynamical systems, distinguished by their repetitive behavior over time, are prevalent across various engineering disciplines. In numerous applications, particularly within industrial contexts, the implementation of model…
Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…
We analyze a class of nonlinear partial differential equations (PDEs) defined on $\mathbb{R}^d \times \mathcal{P}_2(\mathbb{R}^d),$ where $\mathcal{P}_2(\mathbb{R}^d)$ is the Wasserstein space of probability measures on $\mathbb{R}^d$ with…
This work delves into presenting a probabilistic method for analyzing linear process data with weakly dependent innovations, focusing on detecting change-points in the mean and estimating its spectral density. We develop a test for…
An operational description of the controlled Markov dynamics of quantum-mechanical system is introduced. The feedback control strategies with regard to the dynamical reduction of quantum states in the course of quantum real-time…