Related papers: An inequality for the entropy numbers and its appl…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…
Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with…
Entropies must correspond to mean values for them to be measurable. The Shannon entropy corresponds to the weighted arithmetic mean, whereas the Renyi entropy corresponds to the exponential mean. These means refer to code lengths, which are…
We give a necessary and sufficient condition for transport-entropy inequalities in dimension one. As an application, we construct a new example of a probability distribution verifying Talagrand's T2 inequality and not the logarithmic…
The definition of $k^{th}$-order empirical entropy of strings is extended to node labelled binary trees. A suitable binary encoding of tree straight-line programs (that have been used for grammar-based tree compression before) is shown to…
This paper is concerned with non-parametric estimation of the entropy in ranked set sampling. Theoretical properties of the proposed estimator are studied. The proposed estimator is compared with the rival estimator in simple random…
This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov-Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…
A quadratic inequality is formulated in the paper. An estimate on the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations.
For a family of stochastic differential equations, we investigate the asymptotic behaviors of its corresponding Picard's iteration, establishing convergence results in terms of relative entropy. Our convergence results complement the…
In this work, we show that Bell's inequality violation of arise from the fact that the condition imposed upon the development of inequality is not respected when it is applied in the idealized experiment. Such a condition is that the…
We establish a general class of entropy inequalities that take the concise form of Gaussian comparisons. The main result unifies many classical and recent results, including the Shannon-Stam inequality, the Brunn-Minkowski inequality, the…
We prove Carl's type inequalities for the error of approximation of compact sets K by deep and shallow neural networks. This in turn gives lower bounds on how well we can approximate the functions in K when requiring the approximants to…
This paper aims at characterizing the approximability of bounded sets in the range of nonlinear operators in Banach spaces by finite-dimensional linear varieties. In particular, the class of operators we consider includes the endpoint maps…
Under Poincar\'e-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on improved concentration inequalities on high-dimensional…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Using martingale methods, we provide bounds for the entropy of a probability measure on $\mathbb {R}^d$ with the right-hand side given in a certain integral form. As a corollary, in the one-dimensional case, we obtain a weighted log-Sobolev…
We use rigorous non-equilibrium thermodynamic arguments to prove (i) the residual entropy of any system is bounded below by the experimentally (calorimetrically) determined absolute temperature entropy, which itself is bounded below by the…