We present an error reconciliation method for Quantum Key Distribution (QKD) that corrects 100% of errors generated in regular binary frames transmitted over a noisy quantum channel regardless the rate. In previous investigation, we introduced novel distillation QKD algorithm whose secret key rate descends linearly with respect to Now, as main achievement this work, demonstrate improved capable...

Abstract The crude Monte Carlo method is computationally expensive. Hence, incorporating model order reduction methods enabling reliability analysis for high‐dimensional problems necessary. However, this strategy may result in an inaccurate estimation of the probability failure rare events two reasons. First, reduction, represented by proper orthogonal decomposition (POD) here, requires respons...

Some problems concerning the additive properties of subsets of R are investigated. From a result of G. G . Lorentz in additive number theory, we show that if P is a nonempty perfect subset of R, then there is a perfect set M with Lebesgue measure zero so that P+M = R. In contrast to this, it is shown that (1) if S is a subset of R is concentrated about a countable set C, then A(S+R) = 0, for ev...

Let G be a directed graph. Its vertex-set will be denoted by X, and its arcs (or ‘directed edges’) are a subset of the Cartesian product X x X. A kernel of G is a subset S of X which is ‘stable’ (independent, i.e.: a vertex in S has no successor in S) and ‘absorbant’ (dominating, i.e. a vertex not in S has a successor in S). This concept has found many applications, for instance in cooperative ...

Golomb and Welch conjectured in 1970 that there only exist perfect Lee codes for radius t = 1 or dimension n = 1, 2. It is admitted that the existence and the construction of quasi-perfect Lee codes have to be studied since they are the best alternative to the perfect codes. In this paper we firstly highlight the relationships between subset sums, Cayley graphs, and Lee linear codes and present...

Let Γ be a graph with vertex set V, and let b nonnegative integers. A subset C of V is called an (a,b)-regular in if every has exactly neighbors V∖C C. In particular, (0,1)-regular sets (1,1)-regular are perfect codes total Γ, respectively. group G said to there exists Cayley which admits as set. this paper we prove that, for any generalized dihedral or order 4p pq some primes p q, nontrivial s...

The core is a set–valued solution concept for cooperative games. In situations where the characteristic function is not monotone the classical definition may not be sufficient. Hence, we propose a subset of the core that is called subcoalition–perfect core. It will be proven that the subcoalition–perfect core coincides with the set of non–negative core allocations. Furthermore, a general mathem...

A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G \ S is adjacent to only one vertex (dv ∈ {1, 2} vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol {3, 6} and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of thei...