Connectivity and equilibrium in random games

We study how the structure of the interaction graph of a game affects the existence of pure Nash equilibria. In particular, for a fixed interaction graph, we are interested in whether there are pure Nash equilibria arising when random utility tables are assigned to the players. We provide conditions for the structure of the graph under which equilibria are likely to exist and complementary conditions which make the existence of equilibria highly unlikely. Our results have immediate implications for many deterministic graphs and generalize known results for random games on the complete graph. In particular, our results imply that the probability that bounded degree graphs have pure Nash equilibria is exponentially small in the size of the graph and yield a simple algorithm that finds small nonexistence certificates for a large family of graphs. Then we show that in any strongly connected graph of n vertices with expansion $(1+\Omega(1))\log_2(n)$ the distribution of the number of equilibria approaches the Poisson distribution with parameter 1, asymptotically as $n \to +\infty$.Comment: Published in at http://dx.doi.org/10.1214/10-AAP715 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Searches for the Higgs Boson in CMS

The CMS potential for the Higgs boson discovery is discussed in the framework of the Standard Model (SM) and its Minimal Supersymmetric extension (MSSM)

Stretching Method-Based Operational Modal Analysis of An Old Masonry Lighthouse.

We present in this paper a structural health monitoring study of the Egyptian lighthouse of Rethymnon in Crete, Greece. Using structural vibration data collected on a limited number of sensors during a 3-month period, we illustrate the potential of the stretching method for monitoring variations in the natural frequencies of the structure. The stretching method compares two signals, the current that refers to the actual state of the structure, with the reference one that characterizes the structure at a reference healthy condition. For the structure under study, an 8-day time interval is used for the reference quantity while the current quantity is computed using a time window of 24 h. Our results indicate that frequency shifts of 1% can be detected with high accuracy allowing for early damage assessment. We also provide a simple numerical model that is calibrated to match the natural frequencies estimated using the stretching method. The model is used to produce possible damage scenarios that correspond to 1% shift in the first natural frequencies. Although simple in nature, this model seems to deliver a realistic response of the structure. This is shown by comparing the response at the top of the structure to the actual measurement during a small earthquake. This is a preliminary study indicating the potential of the stretching method for structural health monitoring of historical monuments. The results are very promising. Further analysis is necessary requiring the deployment of the instrumentation (possibly with additional instruments) for a longer period of time

Computer-aided verification in mechanism design

In mechanism design, the gold standard solution concepts are dominant strategy incentive compatibility and Bayesian incentive compatibility. These solution concepts relieve the (possibly unsophisticated) bidders from the need to engage in complicated strategizing. While incentive properties are simple to state, their proofs are specific to the mechanism and can be quite complex. This raises two concerns. From a practical perspective, checking a complex proof can be a tedious process, often requiring experts knowledgeable in mechanism design. Furthermore, from a modeling perspective, if unsophisticated agents are unconvinced of incentive properties, they may strategize in unpredictable ways. To address both concerns, we explore techniques from computer-aided verification to construct formal proofs of incentive properties. Because formal proofs can be automatically checked, agents do not need to manually check the properties, or even understand the proof. To demonstrate, we present the verification of a sophisticated mechanism: the generic reduction from Bayesian incentive compatible mechanism design to algorithm design given by Hartline, Kleinberg, and Malekian. This mechanism presents new challenges for formal verification, including essential use of randomness from both the execution of the mechanism and from the prior type distributions. As an immediate consequence, our work also formalizes Bayesian incentive compatibility for the entire family of mechanisms derived via this reduction. Finally, as an intermediate step in our formalization, we provide the first formal verification of incentive compatibility for the celebrated Vickrey-Clarke-Groves mechanism

A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, thus eliminating some of the difficulties involved in following the known indirect reduction.Comment: 21 page

Efficiency in Multi-objective Games

In a multi-objective game, each agent individually evaluates each overall action-profile on multiple objectives. I generalize the price of anarchy to multi-objective games and provide a polynomial-time algorithm to assess it. This work asserts that policies on tobacco promote a higher economic efficiency

Race/Ethnicity, Gender, Weight Status, and Colorectal Cancer Screening

Background. The literature on colorectal cancer (CRC) screening is contradictory regarding the impact of weight status on CRC screening. This study was intended to determine if CRC screening rates among 2005 National Health Interview Survey (NHIS) respondent racial/ethnic and gender subgroups were influenced by weight status. Methods. Univariable and multivariable logistic regression analyses were performed to determine if CRC screening use differed significantly among obese, overweight, and normal-weight individuals in race/ethnic and gender subgroups. Results. Multivariable analyses showed that CRC screening rates did not differ significantly for individuals within these subgroups who were obese or overweight as compared to their normal-weight peers. Conclusion. Weight status does not contribute to disparities in CRC screening in race/ethnicity and gender subgroups

Two successful natural pregnancies in a patient with severe uterine prolapse: A case report

<p>Abstract</p> <p>Introduction</p> <p>Uterine prolapse is a common gynecologic condition that is rare during or before pregnancy. We report an exceptional case of two pregnancies in a totally prolapsed uterus.</p> <p>Case presentation</p> <p>A 36-year-old Caucasian woman with a history of uterine prolapse presented with pregnancy. A vaginal pessary was applied to keep her uterus inside the pelvis after manual reposition. The pessary was removed at the 24th week. The gravid uterus persisted in the abdominal cavity because of its increased volume.</p> <p>Conclusion</p> <p>Our case shows that pregnancy during uterine prolapse is possible and that careful assessment is required to prevent complications during delivery. According to our experience, an elective caesarean section near term could be the safest mode of delivery.</p