Study of the Wealth Inequality in the Minority Game

To demonstrate the usefulness of physical approaches for the study of realistic economic systems, we investigate the inequality of players' wealth in one of the most extensively studied econophysical models, namely, the minority game (MG). We gauge the wealth inequality of players in the MG by a well-known measure in economics known as the modified Gini index. From our numerical results, we conclude that the wealth inequality in the MG is very severe near the point of maximum cooperation among players, where the diversity of the strategy space is approximately equal to the number of strategies at play. In other words, the optimal cooperation between players comes hand in hand with severe wealth inequality. We also show that our numerical results in the asymmetric phase of the MG can be reproduced semi-analytically using a replica method.Comment: 9 pages in revtex 4 style with 3 figures; minor revision with a change of title; to appear in PR

Effect of high resistive barrier on earthing system

Substation earthing provides a low impedance path and carries current into ground under normal and fault conditions without adversely affecting continuity of service. Under a fault condition, the ground voltage may rise to a level that may endanger the public outside the vicinity of the substation. In such a case a high resistive barrier can be inserted around the vicinity of the substation to reduce the surface potentials immediately beyond the barrier. In this paper the effect of barrier on the overall performance of the earthing system has been investigated experimentally and computationally based on an earthing system consisted of combined grid and rods in a water tank. The effect of the position and depth of the barrier to the resistance of the earthing system and surface potentials in and around the substation have been examined

Improved Approximation Algorithms for Stochastic Matching

In this paper we consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. We are given an undirected graph in which every edge is assigned a probability of existence and a positive profit, and each node is assigned a positive integer called timeout. We know whether an edge exists or not only after probing it. On this random graph we are executing a process, which one-by-one probes the edges and gradually constructs a matching. The process is constrained in two ways: once an edge is taken it cannot be removed from the matching, and the timeout of node $v$ upper-bounds the number of edges incident to $v$ that can be probed. The goal is to maximize the expected profit of the constructed matching. For this problem Bansal et al. (Algorithmica 2012) provided a $3$-approximation algorithm for bipartite graphs, and a $4$-approximation for general graphs. In this work we improve the approximation factors to $2.845$ and $3.709$, respectively. We also consider an online version of the bipartite case, where one side of the partition arrives node by node, and each time a node $b$ arrives we have to decide which edges incident to $b$ we want to probe, and in which order. Here we present a $4.07$-approximation, improving on the $7.92$-approximation of Bansal et al. The main technical ingredient in our result is a novel way of probing edges according to a random but non-uniform permutation. Patching this method with an algorithm that works best for large probability edges (plus some additional ideas) leads to our improved approximation factors

Sketch-based Influence Maximization and Computation: Scaling up with Guarantees

Propagation of contagion through networks is a fundamental process. It is used to model the spread of information, influence, or a viral infection. Diffusion patterns can be specified by a probabilistic model, such as Independent Cascade (IC), or captured by a set of representative traces. Basic computational problems in the study of diffusion are influence queries (determining the potency of a specified seed set of nodes) and Influence Maximization (identifying the most influential seed set of a given size). Answering each influence query involves many edge traversals, and does not scale when there are many queries on very large graphs. The gold standard for Influence Maximization is the greedy algorithm, which iteratively adds to the seed set a node maximizing the marginal gain in influence. Greedy has a guaranteed approximation ratio of at least (1-1/e) and actually produces a sequence of nodes, with each prefix having approximation guarantee with respect to the same-size optimum. Since Greedy does not scale well beyond a few million edges, for larger inputs one must currently use either heuristics or alternative algorithms designed for a pre-specified small seed set size. We develop a novel sketch-based design for influence computation. Our greedy Sketch-based Influence Maximization (SKIM) algorithm scales to graphs with billions of edges, with one to two orders of magnitude speedup over the best greedy methods. It still has a guaranteed approximation ratio, and in practice its quality nearly matches that of exact greedy. We also present influence oracles, which use linear-time preprocessing to generate a small sketch for each node, allowing the influence of any seed set to be quickly answered from the sketches of its nodes.Comment: 10 pages, 5 figures. Appeared at the 23rd Conference on Information and Knowledge Management (CIKM 2014) in Shanghai, Chin

On the preciseness of subtyping in session types

Subtyping in concurrency has been extensively studied since early 1990s as one of the most interesting issues in type theory. The correctness of subtyping relations has been usually provided as the soundness for type safety. The converse direction, the completeness, has been largely ignored in spite of its usefulness to define the greatest subtyping relation ensuring type safety. This paper formalises preciseness (i.e. both soundness and completeness) of subtyping for mobile processes and studies it for the synchronous and the asynchronous session calculi. We first prove that the well-known session subtyping, the branching-selection subtyping, is sound and complete for the synchronous calculus. Next we show that in the asynchronous calculus, this subtyping is incomplete for type-safety: that is, there exist session types T and S such that T can safely be considered as a subtype of S, but T ≤ S is not derivable by the subtyping. We then propose an asynchronous sub-typing system which is sound and complete for the asynchronous calculus. The method gives a general guidance to design rigorous channel-based subtypings respecting desired safety properties

Separability in Cohomogeneity-2 Kerr-NUT-AdS Metrics

The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important role in the construction of generalisations of the Kerr metric, and in the uncovering of hidden symmetries associated with the existence of Killing tensors. In this paper, we show that the Hamilton-Jacobi and Klein-Gordon equations are separable in Kerr-AdS backgrounds in all dimensions, if one specialises the rotation parameters so that the metrics have cohomogeneity 2. Furthermore, we show that this property of separability extends to the NUT generalisations of these cohomogeneity-2 black holes that we obtained in a recent paper. In all these cases, we also construct the associated irreducible rank-2 Killing tensor whose existence reflects the hidden symmetry that leads to the separability. We also consider some cohomogeneity-1 specialisations of the new Kerr-NUT-AdS metrics, showing how they relate to previous results in the literature.Comment: Latex, 15 pages, minor typos correcte

Singularities of the Magnon Boundstate S-Matrix

We study the conjectured exact S-matrix for the scattering of BPS magnon boundstates in the spin-chain description of planar N=4 SUSY Yang-Mills. The conjectured S-matrix exhibits both simple and double poles at complex momenta. Some of these poles lie parametrically close to the real axis in momentum space on the branch where particle energies are positive. We show that all such poles are precisely accounted for by physical processes involving one or more on-shell intermediate particles belonging to the known BPS spectrum.Comment: 32 pages, 9 figure

On arithmetic detection of grey pulses with application to Hawking radiation

Micron-sized black holes do not necessarily have a constant horizon temperature distribution. The black hole remote-sensing problem means to find out the `surface' temperature distribution of a small black hole from the spectral measurement of its (Hawking) grey pulse. This problem has been previously considered by Rosu, who used Chen's modified Moebius inverse transform. Here, we hint on a Ramanujan generalization of Chen's modified Moebius inverse transform that may be considered as a special wavelet processing of the remote-sensed grey signal coming from a black hole or any other distant grey sourceComment: 5 pages, published versio

Double-discharge copper-vapor laser

Power supply for discharge pulses consists of two capacitors that are made to discharge synchronously with adjustable time intervals. First pulse is switched with hydrogen thyratron, and second by spark gap. Lasing action peaks for appropriate combination of these two parameters