Related papers: A function space perspective on stochastic shape e…
We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similarly to the classical lattice growth models the proof makes use of the subadditive ergodic theorem.…
The paper presents a computational stochastic model of virtual cells irradiation, based on Quasi-Markov Chain Monte Carlo method and using biophysical input. The model is based on a stochastic tree of probabilities for each cell of the…
In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure…
This paper presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in geostatistics. We show a general approach to construct stationary models related to a wide class of linear SPDEs,…
In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…
The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to…
Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
Understanding how anatomical shapes evolve in response to developmental covariates and quantifying their spatially varying uncertainties is critical in healthcare research. Existing approaches typically rely on global time-warping…
A simple model of macroevolution is proposed exhibiting both the property of punctuated equilibrium and the dynamics of potentialities for different species to evolve towards increasingly higher complexity. It is based on the phenomenon of…
We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
We present a novel framework for learning system design with neural feature extractors. First, we introduce the feature geometry, which unifies statistical dependence and feature representations in a function space equipped with inner…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
This study elaborates some examples of a simple evolutionary stochastic rate process where the population rate of change depends on the distribution of properties--so different cohorts change at different rates. We investigate the effect on…
We study the biasing relation between dark-matter halos or galaxies and the underlying mass distribution, using cosmological $N$-body simulations in which galaxies are modelled via semi-analytic recipes. The nonlinear, stochastic biasing is…
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been…