Related papers: Remarks on a Bailey pair with one free parameter
The static dependency pair method is a method for proving the termination of higher-order rewrite systems a la Nipkow. It combines the dependency pair method introduced for first-order rewrite systems with the notion of strong computability…
We give a simple proof of the fact that there exist measures on the real line of discrete support, whose Fourier Transform is also a measure of discrete support, yet this Fourier pair cannot be constructed by repeatedly applying the Poisson…
In this note we produce generalized versions of the classical inequalities of Hardy and of Hilbert and we establish their equivalence. Our methods rely on the H^1-BMOA duality. We produce a class of examples to establish that the…
An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.
Pair-copula constructions are flexible dependence models that use bivariate copulas as building blocks. In this paper, we use generalized additive models to extend them by allowing covariates effects. Borrowing ideas from a traditionally…
After making some general remarks, I consider two examples that illustrate the use of Bayesian Probability Theory. The first is a simple one, the physicist's favorite "toy," that provides a forum for a discussion of the key conceptual issue…
This note has been updated (April, 2020) to respond to "Towards Clarifying the Theory of the Deconfounder" by Yixin Wang, David M. Blei (arXiv:2003.04948). This original note, posted in January, 2020, is meant to complement our previous…
We prove dual theorems to theorems proved by author in \cite {5}. Beginning with Section 10, we introduce and study so-called "twin numbers of the second kind" and a postulate for them. We give two proofs of the infinity of these numbers…
For binary experimental data, we discuss randomization-based inferential procedures that do not need to invoke any modeling assumptions. We also introduce methods for likelihood and Bayesian inference based solely on the physical…
We extend to the multivariate non-commutative context the descriptions of a "once-stripped" probability measure in terms of Jacobi parameters, orthogonal polynomials, and the moment generating function. The corresponding map Phi on states…
A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the…
We obtain some Bailey pairs associated with indefinite quadratic forms with the $\beta_n$ connected to a finite sum. A new general identity is given, which provides identities for $q$-hypergeometric series, including mock theta functions.
The existence of $q$-ary linear complementary pairs (LCPs) of codes with $q> 2$ has been completely characterized so far. This paper gives a characterization for the existence of binary LCPs of codes. As a result, we solve an open problem…
This article introduces the bpcs R package (Bayesian Paired Comparison in Stan) and the statistical models implemented in the package. This package aims to facilitate the use of Bayesian models for paired comparison data in behavioral…
This document seeks to prove there are infinitely many primes whose difference is 2, referred to as twin prime pairs. This proof's methodology involves constructing a function that approximates the number of positive integers, less than a…
Path pairs are a modification of parallelogram polyominoes that provide yet another combinatorial interpretation of the Catalan numbers. More generally, the number of path pairs of length $n$ and distance $\delta$ corresponds to the…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage from local to global one needs a connected fiber hypothesis…
We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.
We study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel method to estimate the mutual information between the two random variables. The…