Related papers: Algebraic moment closure for population dynamics o…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…
Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…
Moment-closure techniques are commonly used to generate low-dimensional deterministic models to approximate the average dynamics of stochastic systems on networks. The quality of such closures is usually difficult to asses and the…
Moment-closure approximations are an important tool in the analysis of the dynamics on both static and adaptive networks. Here, we provide a broad survey over different approximation schemes by applying each of them to the adaptive voter…
The pervasive presence spatial and size structure in biological populations challenges fundamental assumptions at the heart of continuum models of population dynamics based on mean densities (local or global) only. Individual-based models…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
We present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex, large-scale, nonlinear systems. Building on recently developed equation-free methods, this approach…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
Closure modeling - the statistical modeling of missing dynamics in the natural sciences and engineering - is a growing and active area of research. Existing methods for closure modeling are often computationally prohibitive, lack…
Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clustering, both of which greatly affect epidemic dynamics. To…
We now set up Constraint Closure in a manner consistent with Temporal and Configurational Relationalism. This requires modifying the Dirac Algorithm - which addresses the Constraint Closure Problem facet of the Problem of Time piecemeal -…
We first generalise ideas discussed by Kiss et al. (2015) to prove a theorem for generating exact closures (here expressing joint probabilities in terms of their constituent marginal probabilities) for susceptible-infectious-removed (SIR)…
An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical…
This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with…
We introduce the following discrete time model. Each natural number represents an ecological niche and is assigned a fitness in $(0,1)$. All the sites are updated simultaneously at every discrete time. At any given time the environment may…
We extend the Moran model with single-crossover recombination to include general recombination and mutation. We show that, in the case without resampling, the expectations of products of marginal processes defined via partitions of sites…