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The conditional diffusion model has been demonstrated as an efficient tool for learning robot policies, owing to its advancement to accurately model the conditional distribution of policies. The intricate nature of real-world scenarios,…

The unscented Kalman filter is a nonlinear estimation algorithm commonly used in navigation applications. The prediction of the mean and covariance matrix is crucial to the stable behavior of the filter. This prediction is done by…

We investigate the statistical properties of translation invariant random fields (including point processes) on Euclidean spaces (or lattices) under constraints on their spectrum or structure function. An important class of models that…

A compatible point-shift $F$ maps, in a translation invariant way, each point of a stationary point process $\Phi$ to some point of $\Phi$. It is fully determined by its associated point-map, $f$, which gives the image of the origin by $F$.…

As the variety of systems displaying scale invariant characteristics are matched only by their number, it is becoming increasingly important to understand their fundamental and universal elements. Much work has attempted to apply 2nd order…

In work started in [17] and continued in this paper our objective is to study selectors of multivalued functions which have interesting dynamical properties, such as possessing absolutely continuous invariant measures. We specify the graph…

A distributional equation as a criterion for invariant measures of Markov processes associated to L\'evy-type operators is established. This is obtained via a characterization of infinitesimally invariant measures of the associated…

Let us consider a pair signal-observation ((xn,yn),n 0) where the unobserved signal (xn) is a Markov chain and the observed component is such that, given the whole sequence (xn), the random variables (yn) are independent and the conditional…

The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require…

Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…

Unfolding problems often arise in the context of statistical data analysis. Such problematics occur when the probability distribution of a physical quantity is to be measured, but it is randomized (smeared) by some well understood process,…

This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from…

Diffusion models generate samples by incrementally reversing a process that turns data into noise. We show that when the step size goes to zero, the reversed process is invariant to the distribution of these increments. This reveals a…

We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…

We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…

We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…

This paper presents a framework for intrinsic point of interest discovery from trajectory databases. Intrinsic points of interest are regions of a geospatial area innately defined by the spatial and temporal aspects of trajectory data, and…

In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman-Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function.…

In extending the conventional dynamic models, we consider a simple model to account for the environment fluctuations of particle atoms in a protein system and derive the elastic incoherent structure factor (EISF) and the incoherent…

We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…