Blackwell Games

Blackwell games are infinite games of imperfect information. The two players simultaneously make their moves, and are then informed of each other's moves. Payoff is determined by a Borel measurable function $f$ on the set of possible resulting sequences of moves. A standard result in Game Theory is that finite games of this type are determined. Blackwell proved that infinite games are determined, but only for the cases where the payoff function is the indicator function of an open or $G_\delta$ set. For games of perfect information, determinacy has been proven for games of arbitrary Borel complexity. In this paper I prove the determinacy of Blackwell games over a $G_{\delta\sigma}$ set, in a manner similar to Davis' proof of determinacy of games of $G_{\delta\sigma}$ complexity of perfect information. There is also extensive literature about the consequences of assuming AD, the axiom that _all_ such games of perfect information are determined. In the final section of this paper I formulate an analogous axiom for games of imperfect information, and explore some of the consequences of this axiom

The Query-commit Problem

In the query-commit problem we are given a graph where edges have distinct probabilities of existing. It is possible to query the edges of the graph, and if the queried edge exists then its endpoints are irrevocably matched. The goal is to find a querying strategy which maximizes the expected size of the matching obtained. This stochastic matching setup is motivated by applications in kidney exchanges and online dating. In this paper we address the query-commit problem from both theoretical and experimental perspectives. First, we show that a simple class of edges can be queried without compromising the optimality of the strategy. This property is then used to obtain in polynomial time an optimal querying strategy when the input graph is sparse. Next we turn our attentions to the kidney exchange application, focusing on instances modeled over real data from existing exchange programs. We prove that, as the number of nodes grows, almost every instance admits a strategy which matches almost all nodes. This result supports the intuition that more exchanges are possible on a larger pool of patient/donors and gives theoretical justification for unifying the existing exchange programs. Finally, we evaluate experimentally different querying strategies over kidney exchange instances. We show that even very simple heuristics perform fairly well, being within 1.5% of an optimal clairvoyant strategy, that knows in advance the edges in the graph. In such a time-sensitive application, this result motivates the use of committing strategies

Bridging the ensemble Kalman and particle filter

In many applications of Monte Carlo nonlinear filtering, the propagation step is computationally expensive, and hence, the sample size is limited. With small sample sizes, the update step becomes crucial. Particle filtering suffers from the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids this, at the expense of treating non-Gaussian features of the forecast distribution incorrectly. Here we introduce a procedure which makes a continuous transition indexed by gamma in [0,1] between the ensemble and the particle filter update. We propose automatic choices of the parameter gamma such that the update stays as close as possible to the particle filter update subject to avoiding degeneracy. In various examples, we show that this procedure leads to updates which are able to handle non-Gaussian features of the prediction sample even in high-dimensional situations

Ant routing algorithm for the Lightning Network

We propose a decentralized routing algorithm that can be implemented in Bitcoin Lightning Network. All nodes in the network contribute equally to path searching. The algorithm is inspired from ant path searching algorithms.Comment: 10 pages, 1 figur

Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory

Properties of the motion of electrically charged particles in the background of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole is presented in this paper. Radial and angular motion are studied analytically for different values of the fundamental parameter. Therefore, gravitational Rutherford scattering and Keplerian orbits are analysed in detail. Finally, this paper complements previous work by Fernando for null geodesics (Phys. Rev. D 85: 024033, 2012), Olivares & Villanueva (Eur. Phys. J. C 73: 2659, 2013) and Blaga (Automat. Comp. Appl. Math. 22, 41 (2013); Serb. Astron. J. 190, 41 (2015)) for time-like geodesics.Comment: 11 pages, 12 figure

Massive neutral particles on heterotic string theory

The motion of massive particles in the background of a charged black hole in heterotic string theory, which is characterized by a parameter $\alpha$, is studied in detail in this paper. Since it is possible to write this space-time in the Einstein frame, we perform a quantitative analysis of the time-like geodesics by means of the standard Lagrange procedure. Thus, we obtain and solve a set of differential equations and then we describe the orbits in terms of the elliptic $\wp$-Weierstra{\ss} function. Also, by making an elementary derivation developed by Cornbleet (Am. J. Phys. \textbf{61} 7, (1993) 650 - 651) we obtain the correction to the angle of advance of perihelion to first order in $\alpha$, and thus, by comparing with Mercury's data we give an estimation for the value of this parameter, which yields an {\it heterotic solar charge} $Q_{\odot}\simeq 0.728\,[\textrm{Km}]= 0.493\, M_{\odot}$. Therefore, in addition to the study on null geodesics performed by Fernando (Phys. Rev. D {\bf 85}, (2012) 024033), this work completes the geodesic structure for this class of space-time.Comment: 12 pages, 8 figures. Accepted for publication on EPJ

On the global symmetries of 6D superconformal field theories

We study global symmetry groups of six-dimensional superconformal field theories (SCFTs). In the Coulomb branch we use field theoretical arguments to predict an upper bound for the global symmetry of the SCFT. We then analyze global symmetry groups of F-theory constructions of SCFTs with a one-dimensional Coulomb branch. While in the vast majority of cases, all of the global symmetries allowed by our Coulomb branch analysis can be realized in F-theory, in a handful of cases we find that F-theory models fail to realize the full symmetry of the theory on the Coulomb branch. In one particularly mysterious case, F-theory models realize several distinct maximal subgroups of the predicted group, but not the predicted group itself.Comment: 47 pages; v2: typos corrected, added the case su(6)* to the analysis of section 5 and section 6.1. v3: references added, minor changes, published versio