Cops vs. Gambler

We consider a variation of cop vs.\ robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on $V(G)$ and moves according to this fixed distribution. The cop moves from vertex to adjacent vertex with the goal of minimizing expected capture time. Players move simultaneously. We show that when the gambler's distribution is known, the expected capture time (with best play) on any connected $n$-vertex graph is exactly $n$. We also give bounds on the (generally greater) expected capture time when the gambler's distribution is unknown to the cop.Comment: 6 pages, 0 figure

Locating a robber with multiple probes

We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m\geq n$. The present authors showed that, for all but a few small values of $n$, this bound may be improved to $m\geq n/2$, which is best possible. In this paper we consider the natural extension in which the cop probes a set of $k$ vertices, rather than a single vertex, at each turn. We consider the relationship between the value of $k$ required to ensure victory on the original graph and the length of subdivisions required to ensure victory with $k=1$. We give an asymptotically best-possible linear bound in one direction, but show that in the other direction no subexponential bound holds. We also give a bound on the value of $k$ for which the cop has a winning strategy on any (possibly infinite) connected graph of maximum degree $\Delta$, which is best possible up to a factor of $(1-o(1))$.Comment: 16 pages, 2 figures. Updated to show that Theorem 2 also applies to infinite graphs. Accepted for publication in Discrete Mathematic

Problem gambling: a suitable case for social work?

Problem gambling attracts little attention from health and social care agencies in the UK. Prevalence surveys suggest that 0.6% of the population are problem gamblers and it is suggested that for each of these individuals, 10–17 other people, including children and other family members, are affected. Problem gambling is linked to many individual and social problems including: depression, suicide, significant debt, bankruptcy, family conflict, domestic violence, neglect and maltreatment of children and offending. This makes the issue central to social work territory. Yet, the training of social workers in the UK has consistently neglected issues of addictive behaviour. Whilst some attention has been paid in recent years to substance abuse issues, there has remained a silence in relation to gambling problems. Social workers provide more help for problems relating to addictions than other helping professions. There is good evidence that treatment, and early intervention for gambling problems, including psycho-social and public health approaches, can be very effective. This paper argues that problem gambling should be moved onto the radar of the social work profession, via inclusion on qualifying and post-qualifying training programmes and via research and dissemination of good practice via institutions such as the Social Care Institute for Excellence (SCIE). Keywords: problem gambling; addictive behaviour; socia

Mood and Modality in Beja

version avant révisionTwo intriguing, and crosslinguistically unfrequent, formal means for the expression of modality are discussed in this paper: (i) the cliticization of a nominal copula to finite verb forms, and (ii) the cliticization of a special set of bound object pronouns to finite verb forms. The source and direction of evolution of these constructions are discussed in light of typological data embedded in a more general perspective concerning the commonalities between focus construction and deontic modalit

Spartan Daily, March 8, 1955

Volume 42, Issue 103https://scholarworks.sjsu.edu/spartandaily/12152/thumbnail.jp

Spartan Daily, February 10, 1954

Volume 42, Issue 83https://scholarworks.sjsu.edu/spartandaily/11978/thumbnail.jp

Spartan Daily, February 10, 1954

Volume 42, Issue 83https://scholarworks.sjsu.edu/spartandaily/11978/thumbnail.jp