Hide-and-seek games on a network, using combinatorial search paths

This paper introduces a new search paradigm to hide-and-seek games on networks. The Hider locates at any point on any arc. The Searcher adopts a “combinatorial” path when searching the network: a sequence of arcs, each adjacent to the last, and traced out at unit speed. In previous literature the Searcher was allowed “simple motion,” any unit speed path, including ones that turn around inside an arc. The new approach more closely models real problems such as search for improvised explosive devices using vehicles that can only turn around at particular locations on a road. The search game is zero sum, with the time taken to find the Hider as the payoff. Using a lemma giving an upper bound for the expected search time on a semi Eulerian network, we solve the search game on a network Q3 consisting of two nodes connected by three arcs of arbitrary lengths. When two Q3 networks with unit length arcs are linked by two small central arcs incident at the start node, one of these arcs must be traversed at least three times in an optimal search. This property holds for both combinatorial paths and simple motion paths, and the latter makes it a counterexample to a conjecture of Gal, which said that two traversals were always sufficient

Search for an immobile Hider in a known subset of a network

A unit speed Searcher, constrained to start in a given closed set S, wishes to quickly find a point x known to be located in a given closed subset H of a metric network Q. This defines a game G=G(Q,H,S), where the payoff to the maximizing Hider is the time for the Searcher path to reach x. Lengths on Q are defined by a measure λ, which then defines distance as least length of connecting path. For trees Q, we find that the minimax search time (value V of G) is given by V=λ(H)-d_{H}(S)/2, where d_{H}(S) is what we call the `H-diameter of S', and equals the usual diameter d(S) of S in the case H=Q. For the classical case of Gal where the S is a singleton and H=Q, our formula reduces to his result V=λ(Q). If S=H=Q, our formula gives Dagan and Gal's result V=λ(Q)-d(Q)/2. In all other cases, our result is new. Optimal searches consist of minimum length paths covering H which start and end at points of S, traversed equiprobably in either direction

Passage of time

2006 Summer.This collection of work is an expression of my changing body and psyche as a middle-aged woman. For me this is a transformative time of living on the edge between the two halves of my life, young and old. I've chosen to work with the depictions of women's breasts because they are the central icons of femininity; they represent the generative, nurturing aspects of women, as well as their sexual nature. Although identity changes throughout one's life, these times of passage offer opportunities for intense reflection while the body and psyche reconfigure themselves. Changes in the soft tissues of the body occur with time. The breast is one of the more noticeable areas of the body that exhibits these changes. At mid-life, while observing these changes, a woman has the opportunity to consciously let go of socially imposed standards of how she should behave and look, and redefine herself on her own terms. During the process of making molds of many women's breasts, I discovered and wanted to demonstrate how completely unique they are, ranging from the breasts of early adulthood, small and firm, to the weight and distortion that aging brings. Of the range of women who participated in the casting process, one woman was still lactating, other women had nursed their children many years ago, and there were women who have not had children. These castings represent transition away from youth into the unknown, into mysteries yet to unfold. I have chosen to express these ideas through the use of clay, plaster, and bronze. Clay is a fragile substance before firing, soft and malleable like breast tissue. Once fired, the clay castings become more fragile, like dried delicate tissue. Plaster can be used as an intermediary material in the mold-making process or as an end product in sculpture. Fragile plaster castings make way for the strength of bronze. Bronze, like the strength of tempered women is an enduring medium withstanding the passage of time. The wall-mounted breasts represent the underlying unity of women's experiences through time. The small bronze works embody my emotional passages of womanhood, the reconfiguring of self, the release of youth, and the welcoming of wisdom

Genericity in Topological Dynamics

We study genericity of dynamical properties in the space of homeomorphisms of the Cantor set and in the space of subshifts of a suitably large shift space. These rather different settings are related by a Glasner-King type correspondence: genericity in one is equivalent to genericity in the other. By applying symbolic techniques in the shift-space model we derive new results about genericity of dynamical properties for transitive and totally transitive homeomorphisms of the Cantor set. We show that the isomorphism class of the universal odometer is generic in the space of transitive systems. On the other hand, the space of totally transitive systems displays much more varied dynamics. In particular, we show that in this space the isomorphism class of every Cantor system without periodic points is dense, and the following properties are generic: minimality, zero entropy, disjointness from a fixed totally transitive system, weak mixing, strong mixing, and minimal self joinings. The last two stand in striking contrast to the situation in the measure-preserving category. We also prove a correspondence between genericity of dynamical properties in the measure-preserving category and genericity of systems supporting an invariant measure with the same property.Comment: 48 pages, to appear in Ergodic Theory Dynamical Systems. v2: revised exposition, added proof that the universal odometer is generic among transitive Cantor homeomorphism

College Board Exam Places Imprimatur on Women\u27s History

There is a payoff in studying women\u27s history. European History Advanced Placement high school students learned this in May 1978, when they had a chance to demonstrate knowledge of women\u27s history in answering a document-based question dealing with the education of women from the time of the Renaissance to the early eighteenth century. The Advanced Placement examination is divided into three parts: a multiple-choice section testing knowledge of the narrative history of Europe from 1450 to the present (75 minutes); one essay chosen from six topics dealing with major themes (45 minutes); and a required essay based on carefully selected and edited documents which students must read and synthesize (60 minutes). Neither students nor teachers have any advance knowledge of the examination. Essay questions and the required document-based question are a surprise

Appraisal of recordings for use in the teaching of literature in secondary schools.

Thesis (Ed.M.)--Boston University PLEASE NOTE: pages 215-218 are missing from the physical thesis

Reproductive Biology and Speciation in Drosophila pseudoobscura

Sexual selection is an important force driving the evolution of reproductive traits, including sperm morphology and mating behaviour. Divergent sexual selection among populations can eventually lead to errors in spermatogenesis in inter-population hybrids, and subsequently speciation. In Chapter 2, I identify a novel sperm class and how its proportion in the ejaculate is adjusted when Drosophila pseudoobscura males are exposed to competition. In Chapter 3, I assess how competition causes both males and females to adjust their mating behaviour. In Chapter 4, I characterize interspecific hybrid spermatogenic breakdown from two closely-related sub-species. While the genetics of hybrid sterility has been widely studied, the defective spermatogenic phenotypes have largely been ignored. I found that spermatogenic errors are exclusively postmeiotic and partially caused by divergence at the ‘speciation gene’ overdrive. The results of this thesis expand our understanding of the evolution of novel reproductive traits and the evolution of hybrid male sterility