Related papers: On the compatibility of binary sequences
We study two operational approaches to quantifying incompatibility that depart significantly from the well known entropic uncertainty relation (EUR) formalism. Both approaches result in incompatibility measures that yield non-zero values…
Fix \epsilon > 0, and let p_1 = 2, p_2 = 3,... be the sequence of all primes. We prove that if (q,a) = 1 then there are infinitely many pairs p_r, p_{r+1} such that p_r \equiv p_{r+1} \equiv a \mod q and p_{r+1} - p_r < \epsilon\log p_r.…
In a recent paper by Harada, Seceleanu, and \c{S}ega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is…
The topic of this paper is the distributed and incremental generation of long executions of concurrent systems, uniformly or more generally with weights associated to elementary actions. Synchronizing sequences of letters on alphabets…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
We consider Bernoulli measures $\mu_p$ on the interval $[0,1]$. For the standard Lebesgue measure the digits $0$ and $1$ in the binary representation of real numbers appear with an equal probability $1/2$. For the Bernoulli measures, the…
A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation,…
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
Let p be any prime, and let a and n be nonnegative integers. Let $r\in Z$ and $f(x)\in Z[x]$. We establish the congruence $$p^{\deg f}\sum_{k=r(mod p^a)}\binom{n}{k}(-1)^k f((k-r)/p^a) =0 (mod p^{\sum_{i=a}^{\infty}[n/p^i]})$$ (motivated by…
The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…
Self-similar sets require a separation condition to admit a nice mathematical structure. The classical open set condition (OSC) is difficult to verify. Zerner proved that there is a positive and finite Hausdorff measure for a weaker…
Topologies $\tau, \sigma$ on a set $X$ are called $\pi$-compatible if $\tau$ is a $\pi$-network for $\sigma$, and vice versa. If topologies $\tau, \sigma$ on a set $X$ are $\pi$-compatible then the families of nowhere dense sets (resp.…
Recently, several works have been carried out in attempt to develop a theory for linear or sublinear elliptic equations involving a general class of nonlocal operators characterized by mild assumptions on the associated Green kernel. In…
We prove that a self similar measure is absolutely continuous providing that it satisfies a condition depending on its Garsia entropy, contraction ratio, and the separation between different points in approximations of the self similar…
Pairwise comparison matrices are increasingly used in settings where some pairs are missing. However, there exist few inconsistency indices for similar incomplete data sets and no reasonable measure has an associated threshold. This paper…
Solomonoff's central result on induction is that the posterior of a universal semimeasure M converges rapidly and with probability 1 to the true sequence generating posterior mu, if the latter is computable. Hence, M is eligible as a…
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…
We provide a new proof of the near-critical scaling relation $\beta=\xi_1\nu$ for Bernoulli percolation on the square lattice already proved by Kesten in 1987. We rely on a novel approach that does not invoke Russo's formula, but rather…
Suppose $a_n$ is a real, nonnegative sequence that does not increase exponentially. For any $p<1$ we contruct a Lebesgue measurable set $E \subseteq \mathbb{R}$ which has measure at least $p$ in any unit interval and which contains no…
A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. We consider the completely positive tensor decomposition problem. A semidefinite algorithm is presented for checking whether a…