Related papers: On Matched Metric and Channel Problem
Necessary and sufficient quantitative geometric conditions are given for an unbounded set A in a euclidean space R^n to have the following property with a given c > 0: For every s > 0 and for every s-nearisometry f: A -> R^n there is an…
The degrees of freedom of MIMO interference networks with constant channel coefficients are not known in general. Determining the feasibility of a linear interference alignment solution is a key step toward solving this open problem. Our…
Ar{\i}kan's polar coding technique is based on the idea of synthesizing $n$ channels from the $n$ instances of the physical channel by a simple linear encoding transformation. Each synthesized channel corresponds to a particular input to…
We present a necessary and sufficient condition for a 3 by 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 by 3 matrix can be tested. This test generalizes to a…
As our main result we show that, in order to achieve the randomness assisted message - and entanglement transmission capacities of a finite arbitrarily varying quantum channel it is not necessary that sender and receiver share…
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…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
We clarified the connection between measurements and partitions, and discussed the meaning of semiotics for measurements based on functions. The terms of property and relation quantity were defined by our understanding of partitions and…
We consider the problem of communication over the binary symmetric channel with feedback, where the information sequence is made available in a causal, possibly random, fashion. We develop a real-time variant of the renowned Horstein scheme…
In this paper, we prove the following. First, every square matrix whose entries are multivariable rational functions over a field $\mathbb{F}$ has a Bessmertny\u{i} realization, i.e., is the Schur complement of an affine linear square…
In the article the necessary and sufficient conditions for a representation of Lipschitz function of more than two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome…
The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…
Two non-empty sets $A,B$ of a metric space $(X,d)$ are called parallel if $d(a,B)=d(A,B)=d(A,b)$ for any points $a\in A$ and $b\in B$. Answering a question posed on Mathoverflow, we prove that for a cover $\mathcal C$ of a metrizable space…
We show that for a metric space with an even number of points there is a 1-Lipschitz map to a tree-like space with the same matching number. This result gives the first basic version of an unoriented Kantorovich duality. The study of the…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
We provide a necessary and sufficient condition for existence of Gaussian cubature formulas. It consists of checking whether some overdetermined linear system has a solution and so complements Mysovskikh's theorem which requires computing…
We give sufficient conditions for a finite metric space to be determined by the magnitude function. In particular, a generic finite metric space such that the distances between the points are rationally independent is determined by the…
Parametricity states that polymorphic functions behave the same regardless of how they are instantiated. When developing polymorphic programs, Wadler's free theorems can serve as free specifications, which can turn otherwise partial…
We characterize $n$-rectifiable metric measure spaces as those spaces that admit a countable Borel decomposition so that each piece has positive and finite $n$-densities and one of the following: is an $n$-dimensional Lipschitz…
For a complete Riemannian metric, a pointwise conformal transformation may lead to a complete or incomplete transformed Riemannian metric, depending on the behavior of the conformal factor. We establish conditions on the growth of the…