Related papers: Comparative Prime Number Theory Problem List

New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…

We introduce a novel sieve for prime numbers based on detecting topological obstructions in a M\"obius-transformed rational metric space. Unlike traditional sieves which rely on divisibility, our method identifies primes as those numbers…

Learning from many real-world datasets is limited by a problem called the class imbalance problem. A dataset is imbalanced when one class (the majority class) has significantly more samples than the other class (the minority class). Such…

This tutorial focuses on efficient methods to predictive monitoring (PM), the problem of detecting at runtime future violations of a given requirement from the current state of a system. While performing model checking at runtime would…

The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1.

Suppose that we wish to estimate a vector $\mathbf{x}$ from a set of binary paired comparisons of the form "$\mathbf{x}$ is closer to $\mathbf{p}$ than to $\mathbf{q}$" for various choices of vectors $\mathbf{p}$ and $\mathbf{q}$. The…

Economic growth, people's health, and urban development face challenges in the post-epidemic era. How to promote high-quality and sustainable urban development, improve citizens' sense of happiness, and solve problems in city management…

We sketch an assortment of problems that were posed -- and not yet solved -- during problem sessions at the conference ``Approximation Theory and Numerical Analysis meet Algebra, Geometry, and Topology'', which was held at the Palazzone…

Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…

Twin prime number problem is mainly the structure of the twin prime numbers and whether there are infinitely many prime twins group. In this paper, by constructing a special cluster number set(see formula(2.3)in the paper), proves that the…

Invited Discussion of "A Unified Framework for De-Duplication and Population Size Estimation", published in Bayesian Analysis. My discussion focuses on two main themes: Providing a more nuanced picture of the costs and benefits of joint…

This preprint contains a detailed Preface to Proceedinngs of the International Conference ``Foundations of Probability and Physics-3'' held in V\"axj\"o, Sweden, 7-12 June 2004; table of contents and round table. The main theme of the round…

The Fourth International Conference on Applied Category Theory took place at the Computer Laboratory of the University of Cambridge on 12--16 July 2021. It was a hybrid event, with physical attendees present in Cambridge and other…

For positive integers $n$ and $k$ such that $k$ is at most $n$, we find an explicit one-to-one correspondence between the following two sets: the set of words consisting of $k$ $R$s, $k$ $U$s, and $n - k$ $D$s, where the first letter of the…

We present an overview of the SciVer shared task, presented at the 2nd Scholarly Document Processing (SDP) workshop at NAACL 2021. In this shared task, systems were provided a scientific claim and a corpus of research abstracts, and asked…

We recount problems, questions and conjectures that arose during a problem session of the Third International Conference on Permutation Patterns, University of Florida, March 7-11, 2005.

Team assembly is a problem that demands trade-offs between multiple fairness criteria and computational optimization. We focus on four criteria: (i) fair distribution of workloads within the team, (ii) fair distribution of skills and…

This paper is meant as a contribution to the often debated subject of how to combine data which appear to be in mutual disagreement. As a practical example, the epsilon-prime/epsilon determinations have been considered.

This special issue is a product of the First Interdisciplinary Symposium on Statistical Challenges and Opportunities in Electronic Commerce Research, which took place on May 22--23, 2005, at the Robert H. Smith School of Business,…

We present new theoretical algorithms that sums the n-ary comparators output in order to get the permutation indices in order to sort a sequence. By analysing the parallel ranking algorithm, we found that the special comparators number of…