A Continuation Method for Nash Equilibria in Structured Games

Structured game representations have recently attracted interest as models for multi-agent artificial intelligence scenarios, with rational behavior most commonly characterized by Nash equilibria. This paper presents efficient, exact algorithms for computing Nash equilibria in structured game representations, including both graphical games and multi-agent influence diagrams (MAIDs). The algorithms are derived from a continuation method for normal-form and extensive-form games due to Govindan and Wilson; they follow a trajectory through a space of perturbed games and their equilibria, exploiting game structure through fast computation of the Jacobian of the payoff function. They are theoretically guaranteed to find at least one equilibrium of the game, and may find more. Our approach provides the first efficient algorithm for computing exact equilibria in graphical games with arbitrary topology, and the first algorithm to exploit fine-grained structural properties of MAIDs. Experimental results are presented demonstrating the effectiveness of the algorithms and comparing them to predecessors. The running time of the graphical game algorithm is similar to, and often better than, the running time of previous approximate algorithms. The algorithm for MAIDs can effectively solve games that are much larger than those solvable by previous methods

One loop renormalization for the axial Ward-Takahashi identity in Domain-wall QCD

We calculate one-loop correction to the axial Ward-Takahashi identity given by Furman and Shamir in domain-wall QCD. It is shown perturbatively that the renormalized axial Ward-Takahashi identity is satisfied without fine tuning and the ``conserved'' axial current receives no renormalization, giving $Z_A=1$. This fact will simplify the calculation of the pion decay constant in numerical simulations since the decay constant defined by this current needs no lattice renormalization factor.Comment: 16 pages, 3 axodraw.sty figure

A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.Comment: Published in at http://dx.doi.org/10.1214/12-STS406 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Improved position measurement of nano electromechanical systems using cross correlations

We consider position measurements using the cross-correlated output of two tunnel junction position detectors. Using a fully quantum treatment, we calculate the equation of motion for the density matrix of the coupled detector-detector-mechanical oscillator system. After discussing the presence of a bound on the peak-to-background ratio in a position measurement using a single detector, we show how one can use detector cross correlations to overcome this bound. We analyze two different possible experimental realizations of the cross correlation measurement and show that in both cases the maximum cross-correlated output is obtained when using twin detectors and applying equal bias to each tunnel junction. Furthermore, we show how the double-detector setup can be exploited to drastically reduce the added displacement noise of the oscillator.Comment: 9 pages, 1 figure; v2: new Sec.

Synthesis and Thermal Behavior of Poly(Methyl Acrylate) Attached to Silica by Surface-Initiated ATRP

The modification of the surface of an object dictates the response of the object to an external environment.1 Surface-modified materials and nanoparticles have attracted immense interest due to the various desirable electronic, optical and magnetic properties they possess.2 Silica is widely used as an inorganic filler. Surface modification of the silica, with a variety of organic moieties, facilitates the utilization of silica in conjunction with organic systems. The resulting organic/inorganic hybrid materials have significant potential applications. This work reports the synthesis and characterization of modified silica, and poly(methyl acrylate) attached to the modified silica. An observation of the thermal behavior of poly(methyl acrylate) chains covalently attached to the silica-surface is reported

Glass Transition Behavior of Poly(Methyl Acrylate) End-Grafted by ATRP to Amorphous Silica

Ultra-thin polymer films attached to solid substrates (supported films) have attracted significant interest in recent years. Supported films are used in the design of advanced materials like photoresists, lubricants and other electronic devices. Glass transition temperatures (Tgs) of supported polymer films have also been of significant interest. The Tg has been shown to depend on the thickness of the polymer film on the surface and the inherent nature of the surface. The effect of end-grafting of a polymer chain to a surface, on the Tg of the polymer has been studied previously.1 Reports on the study of glass transition behaviors of different types of supported polymer films on substrates of a varying nature exist. These studies include investigations of the dependence of Tg on various parameters like film thickness, nature of the substrate, molecular architecture, stereochemistry of the polymer and interfacial interaction effects.10-15 in this preprint, we report the study of the Tg behavior of poly(methyl acrylate) (PMA) chains covalently bonded to silica using a silane coupling agent. Several PMA-silica composite samples with different relative amounts (low, medium and high) of PMA attached to the silica were synthesized and the Tg of the attached PMA in each composite was determined using modulated differential scanning calorimetry (MDSC). The attached PMA, in the composite samples, exhibited interesting glass-transition behavior

Dynamics of Polyacrylates in Concentrated Chloroform Solutions

The dynamics of polymers in polymer solutions have not been probed in great enough detail to provide a coherent picture of the behavior of these polymers, especially in more concentrated solutions. To help understand this behavior further, we have prepared a series of backbone-labeled polymers including poly(n-butyl acrylate)-d1 (PNBA). These provide a basis for comparison of the behavior among a group of related polymers. The dynamics have been probed by using deuterium relaxation times. Since the relaxation times are relatively fast and the quadrupolar relaxation mechanism is well understood, data from this technique provide a convenient means for comparison of dynamics for different acylates. We have chosen to use the relaxation times T1 and T2 as the basis set because they probe the spectral densities of the polymers at rather different frequencies (vide infra). We have previously reported the dynamics of poly(iso-propyl acrylate) (PIPA) in chloroform solution. At that time we found that the relaxation times measured could not be adequately evaluated by the motional models tested at that time. Our original results showed that the models yielded results which were not physically realistic and resulted in, for example, correlation times getting slower with increasing temperatures. This problem has now been solved for the logχ2 model by the proper normalization of the mean, and other models for polymer segmental motion