Related papers: Some results on fractional vs. expectation thresho…
Talagrand's fundamental result on the entropy numbers is slightly improved. Our proof uses different ideas based on results from greedy approximation.
In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different shorter proof of the main technical lemma that guarantees the existence of a certain kernel. Our proof provides the almost…
We link, by means of a semiclassical approach, the fractional statistics of particles obeying the Haldane exclusion principle to the Tsallis statistics and derive a generalized quantum entropy and its associated statistics.
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The…
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the…
We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…
We study the query complexity of computing a function f:{0,1}^n-->R_+ in expectation. This requires the algorithm on input x to output a nonnegative random variable whose expectation equals f(x), using as few queries to the input x as…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…
Given any finite index quadrilateral $(N, P, Q, M)$ of $II_1$-factors, the notions of interior and exterior angles between $P$ and $Q$ were introduced in \cite{BDLR2017}. We determine the possible values of these angles when the…
This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is given between the…
We consider two-stage recourse models in which the second-stage problem has integer decision variables and uncertainty in the second-stage cost vector, technology matrix, and the right-hand side vector. Such mixed-integer recourse models…
Using the spectral theory on the $S$-spectrum it is possible to define the fractional powers of a large class of vector operators. This possibility leads to new fractional diffusion and evolution problems that are of particular interest for…
We consider a family of quantum conditional entropies based on the concept of quantum $f$-divergences. First, we explicitly formulate conditions under which the notion of quantum conditional entropy is well defined in this way. In…
This article is intended as a compendium and guide to the variety of Bell Inequality derivations that have appeared in the literature in recent years, classifying them into six broad categories, revealing the underlying, often hidden,…
Recently, the authors Khalil, R., Al Horani, M., Yousef. A. and Sababheh, M., in " A new Denition Of Fractional Derivative, J. Comput. Appl. Math. 264. pp. 6570, 2014. " introduced a new simple well-behaved definition of the fractional…
In this paper we investigate the problem of learning an unknown bounded function. We be emphasize special cases where it is possible to provide very simple (in terms of computation) estimates enjoying in addition the property of being…