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

Power adjustment and scheduling in OFDMA femtocell networks

Densely-deployed femtocell networks are used to enhance wireless coverage in public spaces like office buildings, subways, and academic buildings. These networks can increase throughput for users, but edge users can suffer from co-channel interference, leading to service outages. This paper introduces a distributed algorithm for network configuration, called Radius Reduction and Scheduling (RRS), to improve the performance and fairness of the network. RRS determines cell sizes using a Voronoi-Laguerre framework, then schedules users using a scheduling algorithm that includes vacancy requests to increase fairness in dense femtocell networks. We prove that our algorithm always terminate in a finite time, producing a configuration that guarantees user or area coverage. Simulation results show a decrease in outage probability of up to 50%, as well as an increase in Jain's fairness index of almost 200%

Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case

We present a calculation of the perturbative quark-to-quark transverse parton distribution function at next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate for the first time that such a definition works beyond the first non-trivial order. We extract from our calculation the coefficient functions relevant for a next-to-next-to-next-to-leading logarithmic $Q_T$ resummation in a large class of processes at hadron colliders.Comment: 4 pages, 1 figure, revised version, accepted for publication in PR

Low cloud investigations for project FIRE: Island studies of cloud properties, surface radiation, and boundary layer dynamics. A simulation of the reflectivity over a stratocumulus cloud deck by the Monte Carlo method

The radiation field over a broken stratocumulus cloud deck is simulated by the Monte Carlo method. We conducted four experiments to investigate the main factor for the observed shortwave reflectively over the FIRE flight 2 leg 5, in which reflectivity decreases almost linearly from the cloud center to cloud edge while the cloud top height and the brightness temperature remain almost constant through out the clouds. From our results, the geometry effect, however, did not contribute significantly to what has been observed. We found that the variation of the volume extinction coefficient as a function of its relative position in the cloud affects the reflectivity efficiently. Additional check of the brightness temperature of each experiment also confirms this conclusion. The cloud microphysical data showed some interesting features. We found that the cloud droplet spectrum is nearly log-normal distributed when the clouds were solid. However, whether the shift of cloud droplet spectrum toward the larger end is not certain. The decrease of number density from cloud center to cloud edges seems to have more significant effects on the optical properties

Criticality in the approach to failure in amorphous solids

Failure of amorphous solids is fundamental to various phenomena, including landslides and earthquakes. Recent experiments indicate that highly plastic regions form elongated structures that are especially apparent near the maximal shear stress $\Sigma_{\max}$ where failure occurs. This observation suggested that $\Sigma_{\max}$ acts as a critical point where the length scale of those structures diverges, possibly causing macroscopic transient shear bands. Here we argue instead that the entire solid phase ($\Sigma<\Sigma_{\max}$) is critical, that plasticity always involves system-spanning events, and that their magnitude diverges at $\Sigma_{\max}$ independently of the presence of shear bands. We relate the statistics and fractal properties of these rearrangements to an exponent $\theta$ that captures the stability of the material, which is observed to vary continuously with stress, and we confirm our predictions in elastoplastic models.Comment: 6 pages, 5 figure

Renormalization-Group Improved Prediction for Higgs Production at Hadron Colliders

We use renormalization-group methods in effective field theory to improve the theoretical prediction for the cross section for Higgs-boson production at hadron colliders. In addition to soft-gluon resummation at NNNLL, we also resum enhanced contributions of the form (C_A\pi\alpha_s)^n, which arise in the analytic continuation of the gluon form factor to time-like momentum transfer. This resummation is achieved by evaluating the matching corrections arising at the Higgs-boson mass scale at a time-like renormalization point \mu^2<0, followed by renormalization-group evolution to \mu^2>0. We match our resummed result to NNLO fixed-order perturbation theory and give numerical predictions for the total production cross section as a function of the Higgs-boson mass. Resummation effects are significant even at NNLO, where our improved predictions for the cross sections at the Tevatron and the LHC exceed the fixed-order predictions by about 13% and 8%, respectively, for m_H=120 GeV. We also discuss the application of our technique to other time-like processes such as Drell-Yan production, e^+ e^- --> hadrons, and hadronic decays of the Higgs boson.Comment: 35 pages, 6 figures; v2: update to MSTW2008 PDFs, detailed comparison with moment-space formalism; v3: typo in equation (A.3) correcte