Locally finite graphs with ends: A topological approach, I. Basic theory

AbstractThis paper is the first of three parts of a comprehensive survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends, assume the role played in finite graphs by paths and cycles. The first two parts of the survey together provide a suitable entry point to this field for new readers; they are available in combined form from the ArXiv [18]. They are complemented by a third part [28], which looks at the theory from an algebraic-topological point of view.The topological approach indicated above has made it possible to extend to locally finite graphs many classical theorems of finite graph theory that do not extend verbatim. While the second part of this survey [19] will concentrate on those applications, this first part explores the new theory as such: it introduces the basic concepts and facts, describes some of the proof techniques that have emerged over the past 10 years (as well as some of the pitfalls these proofs have in stall for the naive explorer), and establishes connections to neighbouring fields such as algebraic topology and infinite matroids. Numerous open problems are suggested

Bases and closures under infinite sums

AbstractMotivated by work of Diestel and Kühn on the cycle spaces of infinite graphs we study the ramifications of allowing infinite sums in a module RM. We show that every generating set in this setup contains a basis if the ground set M is countable, but not necessarily otherwise. Given a family N⊆RM, we determine when the infinite-sum span N of N is closed under infinite sums, i.e.when N=N. We prove that this is the case if R is a field or a finite ring and each element of M lies in the support of only finitely many elements of N. This is, in a sense, best possible. We finally relate closures under infinite sums to topological closures in the product space RM

The Bicycle Boom of the Gay Nineties: A Reassessment

Historians have traditionally seen the bicycle as a transformative agent in turn-of-the-century society, destroying class barriers, stimulating changes in women's clothing, and producing the good roads movement. Closer analysis indicates, however, that these important social changes either occurred independently of the bicycle or that the bicycle was only one of several influential factors. Period bicycling books and magazine articles on the vehicle suggest that the bicycle boom's significance instead lies in the insights it offers into the Victorian mentality — in particular, fascination with decorum, sports, health reform, nature, clubs, and state-of-the-art technology. Within this context, the bicycle emerges as a mirror of existing attitudes, not a catalyst for change. Résumé Les historiens voient généralement dans la bicyclette un facteur de transformation de la société de la Belle Epoque, détruisant les barrières sociales, favorisant la transformation du vêtement féminin et suscitant une action en faveur des bonnes routes. Une analyse plus se.rrée montre toutefois que ces importants changements sociaux se sont produits indépendamment de la bicyclette ou encore que celle-ci compta seulement comme un ëlêvient important parmi d'autres. Les articles de revue et les ouvrages de l'époque consacrés à la bicyclette donnent à penser que l'importance de la popularité de la bicyclette réside plutôt dans ce qu'elle nous fait comprendre de la mentalité victorienne — notamment une certaine fascination pour le décorum, le sport, l'amélioration de l'hygiène, la nature, les clubs et la technologie nouvelle. Dans ce contexte, la bicyclette n'apparaît pas comme un catalyseur qui déclencha le changement, mais comme le miroir des attitudes de l'époque

Chip-Firing and Rotor-Routing on Directed Graphs

We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing open problems.Comment: 34 pages, 11 figures. v2 has additional references, v3 corrects figure 9, v4 corrects several typo

A Stationless Bikeshare Proof of Concept for College Campuses

Bikeshares promote healthy lifestyles and sustainability among commuters, casual riders, and tourists. However, the central pillar of modern systems, the bike station, cannot be easily integrated into a compact college campus. Fixed stations lack the flexibility to meet the needs of college students who make quick, short-distance trips. Additionally, the necessary cost of implementing and maintaining each station prohibits increasing the number of stations for user convenience. Therefore, the team developed a stationless bikeshare based on a smartlock permanently attached to bicycles in the system. The smartlock system design incorporates several innovative approaches to provide usability, security, and reliability that overcome the limitations of a station centered design. A focus group discussion allowed the team to receive feedback on the early lock, system, and website designs, identify improvements and craft a pleasant user experience. The team designed a unique, two-step lock system that is intuitive to operate while mitigating user error. To ensure security, user access is limited through near field ii communications (NFC) technology connected to a mechatronic release system. The said system relied on a NFC module and a servo working through an Arduino microcontroller coded in the Arduino IDE. To track rentals and maintain the system, each bike is fitted with an XBee module to communicate with a scalable ZigBee mesh network. The network allows for bidirectional, real-time communication with a Meteor.js web application, which enables user and administrator functions through an intuitive user interface available on mobile and desktop. The development of an independent smartlock to replace bike stations is essential to meet the needs of the modern college student. With the goal of creating a bikeshare that better serves college students, Team BIKES has laid the framework for a system that is affordable, easily adaptable, and implementable on any university expressing an interest in bringing a bikeshare to its campus