Related papers: Two Proofs of Fine's Theorem
In this paper, within a unified framework of the condition number theory we present the explicit expression of the projected condition number of the equality constrained indefinite least squares problem. By setting specific norms and…
We derive inequalities for $n$ spin-1/2 systems under the assumption that the hidden-variable theoretical joint probability distribution for any pair of commuting observables is equal to the quantum mechanical one. Fine showed that this…
We present theoretical analysis and a suite of tests and procedures for addressing a broad class of redundant and misleading association rules we call \emph{specious rules}. Specious dependencies, also known as \emph{spurious},…
An efficient Bayesian technique for estimation problems in fundamental stellar astronomy is tested on simulated data for a binary observed both astrometrically and spectroscopically. Posterior distributions are computed for the components'…
The theory of Chebyshev (uniform) approximation for univariate polynomial and piecewise polynomial functions has been studied for decades. The optimality conditions are based on the notion of alternating sequence. However, the extension the…
We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of solutions of partial differential equations (PDEs). Our…
Chang's lemma is a useful tool in additive combinatorics and the analysis of Boolean functions. Here we give an elementary proof using entropy. The constant we obtain is tight, and we give a slight improvement in the case where the…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
Using some extensions of a theorem of Heppes on finitely supported discrete probability measures, we address the problems of classification and testing based on projections. In particular, when the support of the distributions is known in…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
Following the renewed interest in the topic [1], we revisit the problem of assigning probabilities to classes of Feynman paths passing through specified space-time regions. We show that by assigning of probabilities to interfering…
We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and…
This paper introduces a new and ubiquitous framework for establishing achievability results in \emph{network information theory} (NIT) problems. The framework uses random binning arguments and is based on a duality between channel and…
The question has been solved whether Bell's inequalities cover all possible kinds of hidden-variable theories. It has been shown that the given nequalities can be hardly derived when the changing space position of photon-pair source…
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…
We present a restricted variable generalization of Warning's Second Theorem (a result giving a lower bound on the number of solutions of a low degree polynomial system over a finite field, assuming one solution exists). This is analogous to…
A long-standing problem in the foundations of quantum mechanics is to identify a physical principle that explains why algebraically maximal violations of Bell inequalities can generally not be achieved in Nature. One recently proposed…
Bell's theorem shows that no hidden-variable model can explain the measurement statistics of a quantum system shared between two parties, thus ruling out a classical (local) understanding of nature. In this work we demonstrate that by…
We give sign conditions on the support and coefficients of a sparse system of d generalized polynomials in d variables that guarantee the existence of at least one positive real root, based on degree theory and Gale duality. In the case of…