The Best Mixing Time for Random Walks on Trees

We characterize the extremal structures for mixing walks on trees that start from the most advantageous vertex. Let $G=(V,E)$ be a tree with stationary distribution $\pi$. For a vertex $v \in V$, let $H(v,\pi)$ denote the expected length of an optimal stopping rule from $v$ to $\pi$. The \emph{best mixing time} for $G$ is $\min_{v \in V} H(v,\pi)$. We show that among all trees with $|V|=n$, the best mixing time is minimized uniquely by the star. For even $n$, the best mixing time is maximized by the uniquely path. Surprising, for odd $n$, the best mixing time is maximized uniquely by a path of length $n-1$ with a single leaf adjacent to one central vertex.Comment: 25 pages, 7 figures, 3 table

Two-Dimensional Pursuit-Evasion in a Compact Domain with Piecewise Analytic Boundary

In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restictive capture condition: a pursuer must become colocated with the evader to win the game. We prove two general results about pursuit-evasion games in topological spaces. First, we show that one pursuer has a winning strategy in any CAT(0) space under this restrictive capture criterion. This complements a result of Alexander, Bishop and Ghrist, who provide a winning strategy for a game with positive capture radius. Second, we consider the game played in a compact domain in Euclidean two-space with piecewise analytic boundary and arbitrary Euler characteristic. We show that three pursuers always have a winning strategy by extending recent work of Bhadauria, Klein, Isler and Suri from polygonal environments to our more general setting.Comment: 21 pages, 6 figure

As newly returned New York Police Commissioner, Bill Bratton’s first task will be to regain the trust of the city’s most heavily policed groups

Last week, Bill Bratton was sworn in as New York City’s police commissioner, as part of the administration of new mayor, Bill de Blasio. David Halle, Andrew A. Beveridge, and Sydney Beveridge, take a closer look at Bill Bratton’s policy success in reducing crime, in both New York and Los Angeles, through the use of the COMPSTAT program and its successors. They write that, now that he has returned to New York, Bratton’s challenge will be to keep crime rates low while reducing the widespread hatred of the police among black residents that has been created by ‘Stop & Frisk’ policies

Does Gaming the System Affect Students' Academic Achievement?

A growing body of evidence suggests that schools use test exemption to game educational accountability systems. However, it is not known whether test exemption affects students' academic progress. Analyzing data from an urban school district in Texas, the authors find that special education students make larger achievement gains when they are tested. Using their most conservative estimates, the effect of being tested is approximately .40 standard deviations in reading and .28 standard deviations in math for grades 3-8. Because special education students are more likely to be minority and poor students and these students are more likely to be exempted than their white and non-poor special education counterparts, the exemption of special education students contributes to the growth of black-white, Hispanic-white, and high-low socioeconomic status achievement gaps

Running records and the automated reconstruction of historical narrative

Die sozialwissenschaftliche Forschung befaßt sich mit dem Studium der Veränderung, obwohl die meisten Wissenschaftler, die quantitative Methoden benutzen - Historiker, Soziologen und auch Wirtschaftswissenschaftler -, bis jetzt nicht in der Lage sind, die Datenquellen voll auszuschöpfen, die erläutern, wie soziale Veränderungen tatsächlich eintreten. Es wird eine Methodologie entwickelt - bekannt als 'laufende Aufzeichungen', die es Forschern erlaubt, nicht nur Datenquellen wie Steuer- und Zensuslisten auszunutzen, die im wesentlichen statisch sind, sondern auch durch Gebrauch des Computers die ungeheure Menge von Material zu nutzen, das die Geschehnisse und Transaktionen des Alltagslebens von weiten Teilen der Bevölkerung festhält - Quellen, die den Prozeß der Veränderung selbst dokumentieren, sowie er sich auf bestehende Strukturen und Institutionen bezieht. (KWübers.)'All social science research is concerned with the study of change, yet most scholars who use quantitative methods - historians, sociologists, and economists alike - have been unable to exploit fully data sources which illuminate how social change actually occurs. We have developed a methodology, known as 'running records' (1), which allows researchers not only to use data sources, such as census schedules and tax lists which are essentially static, but also by exploiting the power of the computer, to utilize the vast of materials which record the events and transactions of everyday life for large populations - sources which document the process of change itself, as it relates to existing structures and institutions.' (author's abstract

'I’m just not sure': the persistence of uncertainty in the information seeking of undergraduate students with dyslexia

As information seeking progresses, it is expected feelings of uncertainty surrounding, for example, the information need, what information will be useful to satisfy the need and how well the need has been satisfied will shift towards confidence and clarity. The six corollaries offered by Kuhlthau outline and explain areas where this shift can happen. However, does it happen for all groups of information-seekers? Undergraduate students with dyslexia often have lower information seeking-related self-efficacy than their peers and this can result in uncertainty persisting throughout information seeking. Retrospective naturalistic think aloud observations were held with 20 undergraduate students with dyslexia. After looking for information for one of their (self-chosen) assignments, participants were invited to explore their thoughts, feelings and actions with the researcher while watching a screen recording of their information seeking session. First, an inductive reflexive Thematic Analysis was conducted which revealed self-efficacy to be a key influence in the information seeking behaviour of undergraduate students with dyslexia. To investigate this further, a dedicated deductive analysis was conducted leveraging Kuhlthau’s six corollaries. The expected shift away from uncertainty towards clarity and confidence was found to be either delayed, disrupted or prevented by participants’ low self-efficacy surrounding selecting and spelling keywords and reading, interpreting and evaluating information online. Uncertainty persisted throughout information seeking and was rarely reduced or resolved. Key areas for additional support during information seeking for this user group are identified, including keyword selection and spelling, accurate reading and interpretation and confident evaluation of online information.Peer Reviewe