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The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…

History and Overview · Mathematics 2013-12-10 Bernhelm Booss-Bavnbek , Philip J. Davis

Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…

Combinatorics · Mathematics 2012-10-26 Khodakhast Bibak

Symbolic Computation and Satisfiability Checking are viewed as individual research areas, but they share common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite these…

The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of…

Computation · Statistics 2023-04-14 Yuan Gao , Weidong Liu , Hansheng Wang , Xiaozhou Wang , Yibo Yan , Riquan Zhang

Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…

Combinatorics · Mathematics 2011-11-10 Terence Tao

Diversity is an important principle in data selection and summarization, facility location, and recommendation systems. Our work focuses on maximizing diversity in data selection, while offering fairness guarantees. In particular, we offer…

Data Structures and Algorithms · Computer Science 2020-10-20 Zafeiria Moumoulidou , Andrew McGregor , Alexandra Meliou

The purpose of the present work is to provide short and supple teaching notes for a $30$ hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the \textit{Rota way}. The themes are organized…

History and Overview · Mathematics 2023-05-03 Andrea Brini , Antonio Teolis

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically…

Social and Information Networks · Computer Science 2013-05-07 Ursula Martin , Alison Pease

The objective of this article is to stimulate discussions in mathematical society about the role of mathematical departments in the life of the community. University community is the center of knowledge and promotes the intellectual…

History and Overview · Mathematics 2010-09-13 Liliana Costa , Evgeny Lakshtanov

Maximum diversity problems arise in many practical settings from facility location to social networks, and constitute an important class of NP-hard problems in combinatorial optimization. There has been a growing interest in these problems…

Optimization and Control · Mathematics 2024-01-25 Francisco Parreño , Ramón Álvarez-Valdés , Rafael Martí

Coded distributed computing introduced by Li et al. in 2015 is an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. In particular, Li et al. show that…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-02-13 Nicholas Woolsey , Rong-Rong Chen , Mingyue Ji

A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not depend on the representation (aka coding)…

Logic · Mathematics 2025-02-05 Sam Sanders

The reproduction and replication of reported scientific results is a hot topic within the academic community. The retraction of numerous studies from a wide range of disciplines, from climate science to bioscience, has drawn the focus of…

Computational Engineering, Finance, and Science · Computer Science 2014-10-15 Tom Crick , Benjamin A. Hall , Samin Ishtiaq , Kenji Takeda

The accelerating global development of quantum technologies strengthens the case for introducing quantum computing concepts before university. Yet in Latin America, there is no consolidated, region wide integration of quantum computing into…

Winner selection by majority, in an election between two candidates, is the only rule compatible with democratic principles. Instead, when the candidates are three or more and the voters rank candidates in order of preference, there are no…

Physics and Society · Physics 2016-04-19 Pierluigi Contucci , Emanuele Panizzi , Federico Ricci-Tersenghi , Alina Sîrbu

One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those…

History and Overview · Mathematics 2024-11-07 Hung Viet Chu , Steven J. Miller , Joshua M. Siktar

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

Logic · Mathematics 2008-03-25 Wesley Calvert , Julia F. Knight

Diversity plays a crucial role in multiple contexts such as team formation, representation of minority groups and generally when allocating resources fairly. Given a community composed by individuals of different types, we study the problem…

Discrete Mathematics · Computer Science 2021-07-13 Sebastian Perez-Salazar , Alfredo Torrico , Victor Verdugo

Sample coordination, where similar instances have similar samples, was proposed by statisticians four decades ago as a way to maximize overlap in repeated surveys. Coordinated sampling had been since used for summarizing massive data sets.…

Databases · Computer Science 2013-08-05 Edith Cohen , Haim Kaplan

Federated learning aims to collaboratively model by integrating multi-source information to obtain a model that can generalize across all client data. Existing methods often leverage knowledge distillation or data augmentation to mitigate…

Computer Vision and Pattern Recognition · Computer Science 2025-04-29 Runhui Zhang , Sijin Zhou , Zhuang Qi
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