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The aim of this paper is to propose a novel methodology to deal with micro-structural boundary conditions for the analysis of granular materials. The response of the granular assembly is modelled through the discrete element method (DEM),…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
This note outlines a method for clustering time series based on a statistical model in which volatility shifts at unobserved change-points. The model accommodates some classical stylized features of returns and its relation to GARCH is…
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or $\textit{modal-sets}$, of…
A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…
We propose a clustering procedure to group K populations into subgroups with the same dependence structure. The method is adapted to paired population and can be used with panel data. It relies on the differences between orthogonal…
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form,…
We study the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets. We establish a uniform upper bound on the number of iterations it takes for every orbit of a rational matrix to escape a compact…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
Statistical disclosure limitation (SDL) methods aim to provide analysts general access to a data set while limiting the risk of disclosure of individual records. Many methods in the existing literature are aimed only at the case of…
The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time…
The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual…
The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analysed as a multivariate…
A canonical desideratum for prediction problems is that performance guarantees should hold not just on average over the population, but also for meaningful subpopulations within the overall population. But what constitutes a meaningful…
We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special…
We consider a spatial version of the classical Moran model with seed-banks where the constituent populations have finite sizes. Individuals live in colonies labelled by $\mathbb{Z}^d$, $d\geq 1$, playing the role of a geographic space,…
This paper is devoted to the study of a stochastic epidemiological model which is a variant of the SIR model to which we add an extra factor in the transition rate from susceptible to infected accounting for the inflow of infection due to…
A general stochastic model for susceptible -> infective -> recovered (SIR) epidemics in non homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex…
This contribution shortly outlines and reviews a theoretical and computational approach for a theory of change concerning systems where it is not possible to apply the laws of motion ab initio. The concept of meta-structure relates to the…