Related papers: Directional Heisenberg uncertainty product
It is shown that optimum control of dynamical localization (quantum suppression of classical diffusion) in the context of ultracold atoms in periodically shaken optical lattices subjected to time-periodic forces having equidistant zeros…
In this report we discuss the organization of different levels of nature and the corresponding space-time structures by the consideration of a particular problem of time irreversibility. The fundamental time irreversibility problem consists…
The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the…
In the recent paper [J. Funct. Anal. {\bf 259} (2010)], Naor and Tao introduce a new class of measures with a so-called micro-doubling property and present, via martingale theory and probability methods, a localization theorem for the…
Inspired by the construction of the F{\"o}llmer process, we construct a unit-time flow on the Euclidean space, termed the F{\"o}llmer flow, whose flow map at time 1 pushes forward a standard Gaussian measure onto a general target measure.…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
For the filtering of peaks in periodic signals, we specify polynomial filters that are optimally localized in space. The space localization of functions having an expansion in terms of orthogonal polynomials is thereby measured by a…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc…
We show sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \in \mathbb{N}$. Here we focus on differentiable functions on the Euclidean space in presence of a…
We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…
Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…
Covariant integral quantisation using coherent states for semidirect product groups is studied and applied to the motion of a particle on the circle. In the present case the group is the Euclidean group E$(2)$. We implement the quantisation…
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…