Related papers: Remarks on a Bailey pair with one free parameter
In software testing, the large size of the input domain makes exhaustively testing the inputs a daunting and often impossible task. Pair-wise testing is a popular approach to combinatorial testing problems. This paper reviews Pair-wise…
The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.
Given an infinite subset $\mathcal A \subseteq\mathbb N$, let $A$ denote its smallest $N$ elements. There is a rich and growing literature on the question of whether for typical $\alpha\in[0,1]$, the pair correlations of the set $\alpha A…
Generalizing work of Marin [12], we construct in a unified way all the "braids and ties'' algebras available in literature and new ones.
A new method for the experimental study of bin-bin correlations is proposed. It is shown that this method is able to reveal important additional information on bin-bin correlations, beyond that of factorial-correlator measurements.
We show that the sum of two free random variables can have a free Poisson law without any of them having a free Poisson law.
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…
We present a novel, scalable and Bayesian approach to modelling the occurrence of pairs of symbols (i,j) drawn from a large vocabulary. Observed pairs are assumed to be generated by a simple popularity based selection process followed by…
A series of examples of computational models is provided, where the model aim is to interpret numerical results in terms of internal states of agents minds. Two opposite strategies or research can be distinguished in the literature. First…
Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…
In this paper, we provide proofs of two ${}_5\psi_5$ summation formulas of Bailey using a ${}_5\phi_4$ identity of Carlitz. We show that in the limiting case, the two ${}_5\psi_5$ identities give rise to two ${}_3\psi_3$ summation formulas…
A principled approach to cyclicality and intransitivity in paired comparison data is developed. The proposed methodology enables more precise estimation of the underlying preference profile and facilitates the identification of all cyclic…
In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.
Instead of developing a customized typed lambda-calculus for each theory, we attempt to design a general parametric calculus that permits to express the proofs of any theory. This way, the problem of expressing proofs in the lambda-calculus…
We study correlations in a bipartite, Fermionic, free state in terms of perturbations induced by one party on the other. In particular, we show that all so conditioned free states can be modelled by an auxiliary Fermionic system and a…
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…
We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauss' 2-F-1 summation and elementary series manipulations to give a simple proof of Dougall's 2-H-2…