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This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…
Given a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann…
Gaussian blur is a commonly-used method to filter image data. This paper introduces the collapsing sum, a new operator on matrices that provides a combinatorial interpretation of Gaussian blur. We study the combinatorial properties of this…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…
We investigate a Maclaurin inequality for vectors and its connection to an Aleksandrov-type inequality for parallelepipeds.
In arXiv:2212.14023 a decomposition of Gaussian measures on finite-dimensional spaces was introduced, which turned out to be a central technical tool to improve currently known bounds on a long standing conjecture in statistical mechanics…
For non-uniformly expanding maps inducing with a general return time to Gibbs Markov maps, we provide sufficient conditions for obtaining higher order asymptotics for the correlation function in the infinite measure setting. Along the way,…
A generalized covariant method of analysis applicable to frames for which time is not orthogonal to space, such as spacetime around a star possessing angular momentum or on a rotating disk, is presented. Important aspects of such an…
Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and…
It is well known that central simple algebras are split by suitable finite Galois extensions of their centers. A counterpart of this result was studied by Juan and Magid in the set up of differential matrix algebras, wherein Picard-Vessiot…
L multiple descriptions of a vector Gaussian source for individual and central receivers are investigated. The sum rate of the descriptions with covariance distortion measure constraints, in a positive semidefinite ordering, is exactly…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
The large-system performance of MAP estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
A new straightforward universal blind detection algorithm for linear Gaussian channel with ISI is given. A new error exponent is derived, which is better than Gallager's random coding error exponent.
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…
Entanglement is fundamental inasmuch because it rephrases the quest for the classical-quantum demarcation line, and it also has potentially enormous practical applications in modern information technology. In this work, employing the…