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It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
In the present work, we formulate a necessary condition for functionals with Lagrangians depending on fractional derivatives of differentiable functions to possess an extremum. The Euler-Lagrange equation we obtained generalizes previously…
Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals…
We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible we illustrate the general ideas using the Laplacian with…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
In this paper we address the problem of feature selection when the data is functional, we study several statistical procedures including classification, regression and principal components. One advantage of the blinding procedure is that it…
We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…
Elicitable functionals and (strictly) consistent scoring functions are of interest due to their utility of determining (uniquely) optimal forecasts, and thus the ability to effectively backtest predictions. However, in practice, assuming…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
We consider the dynamical properties of transcendental entire functions and their compositions. We give several conditions under which Fatou set of a transcendental entire function $f$ coincide with that of $f\circ g,$ where $g$ is another…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given…