A Search Game on a Hypergraph with Booby Traps

A set of n boxes, located on the vertices of a hypergraph G, contain known but different rewards. A Searcher opens all the boxes in some hyperedge of G with the objective of collecting the maximum possible total reward. Some of the boxes, however, are booby trapped. If the Searcher opens a booby trapped box, the search ends and she loses all her collected rewards. We assume the number k of booby traps is known, and we model the problem as a zero-sum game between the maximizing Searcher and a minimizing Hider, where the Hider chooses k boxes to booby trap and the Searcher opens all the boxes in some hyperedge. The payoff is the total reward collected by the Searcher. This model could reflect a military operation in which a drone gathers intelligence from guarded locations, and a booby trapped box being opened corresponds to the drone being destroyed or incapacitated. It could also model a machine scheduling problem, in which rewards are obtained from successfully processing jobs but the machine may crash. We solve the game when G is a 1-uniform hypergraph (the hyperedges are all singletons), so the Searcher can open just 1 box. When G is the complete hypergraph (containing all possible hyperedges), we solve the game in a few cases: (1) same reward in each box, (2) k=1, and (3) n=4 and k=2. The solutions to these few cases indicate that a general simple, closed form solution to the game appears unlikely

Searching for Multiple Objects in Multiple Locations

Many practical search problems concern the search for multiple hidden objects or agents, such as earthquake survivors. In such problems, knowing only the list of possible locations, the Searcher needs to find all the hidden objects by visiting these locations one by one. To study this problem, we formulate new game-theoretic models of discrete search between a Hider and a Searcher. The Hider hides $k$ balls in $n$ boxes, and the Searcher opens the boxes one by one with the aim of finding all the balls. Every time the Searcher opens a box she must pay its search cost, and she either finds one of the balls it contains or learns that it is empty. If the Hider is an adversary, an appropriate payoff function may be the expected total search cost paid to find all the balls, while if the Hider is Nature, a more appropriate payoff function may be the difference between the total amount paid and the amount the Searcher would have to pay if she knew the locations of the balls a priori (the regret). We give a full solution to the regret version of this game, and a partial solution to the search cost version. We also consider variations on these games for which the Hider can hide at most one ball in each box. The search cost version of this game has already been solved in previous work, and we give a partial solution in the regret version

DETERMINANTS OF FAST FOOD CONSUMPTION

Replaced with revised version of paper 03/24/03.Food Consumption/Nutrition/Food Safety,

A new integrated design framework for the facility layout problem

This thesis proposes a new integrated design framework for solving facility layout problems (FLP). The most popular existing framework, Muther\u27s Systematic Layout Planning (SLP) does not address the variety of design goals associated with facility layout problems and is highly manual and so time consuming to perform. Furthermore, the SLP framework does not help the designer select a modeling tool to use in developing design alternatives, either by defining what a requisite model would include, or explicitly suggesting ones from literature. With the advancements made in academic research and computational capabilities since the development of the SLP framework, a new framework was needed to better address varying design goals, and assist designers in the selection of appropriate models. The framework proposed here guides the designer through determination of model requirements to meet their design goals by framing the FLP in terms of Design Layers . In addition, it proposes candidate models (or methodologies) to generate analytically derived solutions for design goals such as construction of simple block layouts, or determination of input/output points and flow paths in order to create detailed block layouts. The models and methodologies proposed are shown to rapidly reach good candidate solutions to a wide range of design problems

Dose-Response Effects of Lithium on Spatial Memory in the Black Molly Fish.

Lithium continues to be widely prescribed for the management of bipolar disease, yet cognitive impairment-related side effects promote noncompliance of the treatment regimen. We have introduced a novel animal model, the black molly fish, to study dose-response effects of lithium on short-term (STM) and long-term (LTM) memories. We developed a method utilizing capillary ion analysis (CIA), to measure plasma and brain lithium levels employed in our behavioral studies. We then developed an appropriate testing environment to ascertain learning capacities of these fish. We established that black mollies could adequately perform a forced-choice spontaneous alternation (SA) task used extensively in rodents as an index of spatial STM. Employing this paradigm we designed a dose-response experiment utilizing chronic lithium regimens with a wide range of dosage groups to assess STM in the black molly. Results of the experiment indicated a robust effect in which performances of all dose groups were impaired in different degrees but not dose dependently. Using the same dosing regimen, we tested subjects in a place-learning task to assess dose-response effects of lithium on spatial LTM. A variety of performance measures were analyzed presenting a consistent theme implicating significant impairment with the high dose group. CIA results for the STM and LTM experiments revealed consistent linear relationships between mean plasma and brain lithium levels and lithium dosages. We have immunolocalized a 5-HT1A-like receptor from the caudal midbrain of black mollies, an area structurally homologous to the mammalian raphe nuclei. This autoinhibitory receptor is considered to be involved in the regulation of firing of raphe serotonergic fibers and 5-HT release in terminal projection areas such as the hippocampus and frontal cortex. Downregulation of these receptors initiates excessive serotonin availability that may relieve symptoms of depression yet paradoxically impair cognition. It is unclear whether activity in the presynaptic raphe nuclei or the postsynaptic projection areas is responsible for these phenomena. Because the black molly is not equipped with postsynaptic 5-HT1A receptors it offers a unique opportunity to study the effects of lithium on the presynaptic form of the receptor without compensating effects of the postsynaptic form exhibited in the mammal