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We define a counting function that is related to the binomial coefficients. An explicit formula for this function is proved. In some particular cases, simpler explicit formuls are derived. We also derive a formula for the number of…
We will provide algorithmic implementation with proofs of existence and uniqueness for the Absolute and Alternating Ostrowski Numeration Systems.
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
We demonstrate a practical possibility of loss compensation in measured photocounting statistics in the presence of dark counts and background radiation noise. It is shown that satisfactory results are obtained even in the case of low…
This paper studies the counting problem in random dynamical systems. We noticed that the nature of counting in the random setting is completely different than that of the deterministic systems in the sense that non-exponential growth is…
This article gives a formula for associated Stirling numbers of the second kind based on the moment of a sum of independent random variables having a beta distribution. From this formula we deduce, using probabilistic approaches, lower and…
This is an introduction to some of the most probabilistic aspects of free probability theory.
The paper is an introduction to intuitionistic mathematics.
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…
Grover's quantum algorithm for an unstructured search problem and the Count algorithm by Brassard et al. are generalized to the case when the initial state is arbitrarily and maximally entangled. This ansatz might be relevant with quantum…
In this article we will be dedicated some algorithms of addition, subtraction, multiplication and division of two positive integers using Zeckendorf form. Such results find application in coding theory.
Two contributions to the discussion of Fearnhead P. and D. Prangle (2012). Constructing summary statistics for approximate Bayesian computation: Semi-automatic approx- imate Bayesian computation, J. Roy. Statist. Soc. B, 74 (3).
Many real-world scenarios require the random selection of one or more individuals from a pool of eligible candidates. One example of especial social relevance refers to the legal system, in which the jurors and judges are commonly picked…
The past two decades have witnessed a surge of new research in the analysis of randomized experiments. The emergence of this literature may seem surprising given the widespread use and long history of experiments as the "gold standard" in…
Computations in the cohomology of finite groups.
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
We present a zero-crossings counting problem that is a generalization of the Bernstein-Vazirani problem. The goal of this problem is to count the number of zero-crossings (or sign changes) in a special type of sequence S, whose definition…
Assignment of weights to multiple authors of a paper is a challenging task due to its dependence on the conventions that may be different among different fields of research and research groups. In this paper, we describe a scheme for…
We present fully polynomial-time (deterministic or randomised) approximation schemes for Holant problems, defined by a non-negative constraint function satisfying a generalised second order recurrence modulo a couple of exceptional cases.…