Related papers: On Matched Metric and Channel Problem
A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.
Quantum channels depending on a number of classical control parameters are considered. Assuming the stochastic fluctuations of the control parameters in the small errors limit it is shown that the channel fidelity is equal to the average…
Using the quasi-Maxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, expressed in terms of the gravitational and gravitomagnetic fields…
We consider fundamental limits for communicating over a compound channel when the state of the channel needs to be masked. Our model is closely related to an area of study known as covert communication that is a setting in which the…
This paper introduces a quantitative generalization of the ``more capable'' comparison of broadcast channels, which is termed ``more capable with advantage''. Some basic properties are demonstrated (including tensorization on product…
In this paper we study the following problem: for a given bounded positive function $f$ on a filtered probability space can we find another function (a multiplier) $m$, $0\le m\le 1$, such that the function $mf$ is not ``too small'' but its…
Capacity analysis for channels with side information at the receiver has been an active area of interest. This problem is well investigated for the case of finite alphabet channels. However, the results are not easily generalizable to the…
In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…
In this paper, we show that an arbitrary separable state can be the output of a certain entanglement-breaking channel corresponding exactly to the input of a maximally entangled state. A necessary and sufficient separability criterion and…
On the set $\mathcal M$ of mean functions the symmetric mean of $M$ with respect to mean $M_0$ can be defined in several ways. The first one is related to the group structure on $\mathcal M$ and the second one is defined trough Gauss'…
The mutual information is bounded from above by a decreasing affine function of the square of the distance between the input distribution and the set of all capacity-achieving input distributions $\Pi_{\mathcal{A}}$, on small enough…
In this article we provide a combinatorial sufficient (and conjecturally, necessary) condition (called $\alpha$-symmetry) for the mating of two postcritically finite polynomials in $\mathcal{S}_1$ to be obstructed. To do this, we study the…
Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information…
The study proves the existence of an algorithm to receive all elements of a class of binary matrices without obtaining redundant elements, e. g. without obtaining binary matrices that do not belong to the class. This makes it possible to…
The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable…
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…
We present a simple, dimension-independent criterion which guarantees that some quantum channel $\Phi$ is divisible, i.e. that there exists a non-trivial factorization $\Phi=\Phi_1\Phi_2$. The idea is to first define an "elementary" channel…
Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given.
We consider the problem of communicating over a channel for which no mathematical model is specified. We present achievable rates as a function of the channel input and output known a-posteriori for discrete and continuous channels, as well…
The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance.…