An Empirical Study of Finding Approximate Equilibria in Bimatrix Games

While there have been a number of studies about the efficacy of methods to find exact Nash equilibria in bimatrix games, there has been little empirical work on finding approximate Nash equilibria. Here we provide such a study that compares a number of approximation methods and exact methods. In particular, we explore the trade-off between the quality of approximate equilibrium and the required running time to find one. We found that the existing library GAMUT, which has been the de facto standard that has been used to test exact methods, is insufficient as a test bed for approximation methods since many of its games have pure equilibria or other easy-to-find good approximate equilibria. We extend the breadth and depth of our study by including new interesting families of bimatrix games, and studying bimatrix games upto size $2000 \times 2000$. Finally, we provide new close-to-worst-case examples for the best-performing algorithms for finding approximate Nash equilibria

CAD of Stacked Patch Antennas Through Multipurpose Admittance Matrices From FEM and Neural Networks

In this work, a novel computer-aided design methodology for probe-fed, cavity-backed, stacked microstrip patch antennas is proposed. The methodology incorporates the rigor of a numerical technique, such as finite element methods, which, in turn, makes use of a newly developed procedure (multipurpose admittance matrices) to carry out a full-wave analysis in a given structure in spite of certain physical shapes and dimensions not yet being established. With the aid of this technique, we form a training set for a neural network, whose output is the desired response of the antenna according to the value of design parameters. Last, taking advantage of this neural network, we perform a global optimization through a genetic algorithm or simulated annealing to obtain a final design. The proposed methodology is validated through a real design whose numerical results are compared with measurements with good agreement

Эргономика рабочего места служащего

We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions f0; 1gk ! R≥0) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice under set inclusion and are closely related to counting Constraint Satisfaction Problems (CSPs). We identify a sublattice of interesting functional clones and investigate the relationships and properties of the functional clones in this sublattice

Approximating Pairwise Correlations in the Ising Model

In the Ising model, we consider the problem of estimating the covariance of the spins at two specified vertices. In the ferromagnetic case, it is easy to obtain an additive approx- imation to this covariance by repeatedly sampling from the relevant Gibbs distribution. However, we desire a multiplicative approximation, and it is not clear how to achieve this by sampling, given that the covariance can be exponentially small. Our main contribution is a fully polynomial time randomised approximation scheme (FPRAS) for the covariance in the ferromagnetic case. We also show that that the restriction to the ferromagnetic case is essential — there is no FPRAS for multiplicatively estimating the covariance of an antiferromagnetic Ising model unless RP = #P. In fact, we show that even determining the sign of the covariance is #P-hard in the antiferromagnetic case

Advances in medical education and practice: role of massive open online courses

Massive open online courses (MOOCs) are increasingly available in the area of health and medicine. These MOOCs are offered through various commercial and noncommercial online platforms. When offered through reputable institutions, they can provide valuable access to reliable information without the constraints of time, geographical location, or level of education. Most current courses appear introductory in nature. In its drive for quality health care, the National Academy of Medicine has prioritized a focus on known chronic care conditions. Many of these conditions are shared internationally. Among its initiatives, the academy encourages consumer and professional groups, patients, clinicians, health care organizations, and universities to work together to identify evidence-based care processes consistent with best practices, organize major prevention programs to target key associated health risk behaviors, and develop systems to measure and evaluate improvements in the provision of patient- and family-centered health care. Carefully designed and collaboratively developed MOOCs would appear a valuable resource to contribute to these initiatives. Such MOOCs can, 1) increase the health literacy of the public with regard to the prevention and treatment of known chronic care conditions, 2) provide ready access to continuing professional, and interprofessional, education, and 3) explore innovative teaching models for student learning focused on patient- and family-centered care. MOOCs would also appear helpful to facilitate effective communication among international communities of patients and clinicians, including student clinicians, with shared interests. Further, the accumulation of MOOC data through large-scale measurement and analysis, obtained nationally and internationally, has the potential to assist in greater understanding of the risk for diseases and their prevention, with this translating into medical education, and authentic, patient- and family-centered methods for student learning. This paper explores these issues

A 3-player protocol preventing persistence in strategic contention with limited feedback

In this paper, we study contention resolution protocols from a game-theoretic perspective. In a recent work, we considered acknowledgment-based protocols, where a user gets feedback from the channel only when she attempts transmission. In this case she will learn whether her transmission was successful or not. One of the main results of ESA2016 was that no acknowledgment-based protocol can be in equilibrium. In fact, it seems that many natural acknowledgment-based protocols fail to prevent users from unilaterally switching to persistent protocols that always transmit with probability 1. It is therefore natural to ask how powerful a protocol must be so that it can beat persistent deviators. In this paper we consider age-based protocols, which can be described by a sequence of probabilities of transmitting in each time step. Those probabilities are given beforehand and do not change based on the transmission history. We present a 3-player age-based protocol that can prevent users from unilaterally deviating to a persistent protocol in order to decrease their expected transmission time. It is worth noting that the answer to this question does not follow from the results and proof ideas of ESA2016. Our protocol is non-trivial, in the sense that, when all players use it, finite expected transmission time is guaranteed. In fact, we show that this protocol is preferable to any deadline protocol in which, after some fixed time, attempt transmission with probability 1 in every subsequent step. An advantage of our protocol is that it is very simple to describe, and users only need a counter to keep track of time. Whether there exist $n$-player age-based protocols that do not use counters and can prevent persistence is left as an open problem for future research.Comment: arXiv admin note: substantial text overlap with arXiv:1606.0658

Quantum concepts in optical polarization

We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored and their potential applications in quantum technologies are discussed