Cell-dynamical simulation of magnetic hysteresis in the two-dimensional Ising system

We present results from numerical simulations using a ‘‘cell-dynamical system’’ to obtain solutions to the time-dependent Ginzburg-Landau equation for a scalar, two-dimensional (2D), (Φ2)2 model in the presence of a sinusoidal external magnetic field. Our results confirm a recent scaling law proposed by Rao, Krishnamurthy, and Pandit [Phys. Rev. B 42, 856 (1990)], and are also in excellent agreement with recent Monte Carlo simulations of hysteretic behavior of 2D Ising spins by Lo and Pelcovits [Phys. Rev. A 42, 7471 (1990)].

Euclideanization, topological theories, higher dimensions and all that

It is shown that the euclideanized Yukawa theory, with the Dirac fermion belonging to an irreducible representation of the Lorentz group, is not bounded from below. A one parameter family of supersymmetric actions is presented which continuously interpolates between the N = 2 SSYM and the N = 2 supersymmetric topological theory. In order to obtain a theory which is bounded from below and satisfies Osterwalder-Schrader positivity, the Dirac fermion should belong to a reducible representation of the Lorentz group and the scalar fields have to be reinterpreted as the extra components of a higher dimensional vector field.

A Shapley Value-Based Approach to Discover Influential Nodes in Social Networks

Our study concerns an important current problem, that of diffusion of information in social networks. This problem has received significant attention from the Internet research community in the recent times, driven by many potential applications such as viral marketing and sales promotions. In this paper, we focus on the target set selection problem, which involves discovering a small subset of influential players in a given social network, to perform a certain task of information diffusion. The target set selection problem manifests in two forms: 1) top-k nodes problem and 2) lambda-coverage problem. In the top-k nodes problem, we are required to find a set of k key nodes that would maximize the number of nodes being influenced in the network. The lambda-coverage problem is concerned with finding a set of k key nodes having minimal size that can influence a given percentage lambda of the nodes in the entire network. We propose a new way of solving these problems using the concept of Shapley value which is a well known solution concept in cooperative game theory. Our approach leads to algorithms which we call the ShaPley value-based Influential Nodes (SPINs) algorithms for solving the top-k nodes problem and the lambda-coverage problem. We compare the performance of the proposed SPIN algorithms with well known algorithms in the literature. Through extensive experimentation on four synthetically generated random graphs and six real-world data sets (Celegans, Jazz, NIPS coauthorship data set, Netscience data set, High-Energy Physics data set, and Political Books data set), we show that the proposed SPIN approach is more powerful and computationally efficient. Note to Practitioners-In recent times, social networks have received a high level of attention due to their proven ability in improving the performance of web search, recommendations in collaborative filtering systems, spreading a technology in the market using viral marketing techniques, etc. It is well known that the interpersonal relationships (or ties or links) between individuals cause change or improvement in the social system because the decisions made by individuals are influenced heavily by the behavior of their neighbors. An interesting and key problem in social networks is to discover the most influential nodes in the social network which can influence other nodes in the social network in a strong and deep way. This problem is called the target set selection problem and has two variants: 1) the top-k nodes problem, where we are required to identify a set of k influential nodes that maximize the number of nodes being influenced in the network and 2) the lambda-coverage problem which involves finding a set of influential nodes having minimum size that can influence a given percentage lambda of the nodes in the entire network. There are many existing algorithms in the literature for solving these problems. In this paper, we propose a new algorithm which is based on a novel interpretation of information diffusion in a social network as a cooperative game. Using this analogy, we develop an algorithm based on the Shapley value of the underlying cooperative game. The proposed algorithm outperforms the existing algorithms in terms of generality or computational complexity or both. Our results are validated through extensive experimentation on both synthetically generated and real-world data sets.

Quenching across quantum critical points: Role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z(2) invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent nu being different in different sectors. Copyright (C) EPLA, 2010

Search Strategies for Multiple UAV Search and Destroy Missions

Multiple UAVs are deployed to carry out a search and destroy mission in a bounded region. The UAVs have limited sensor range and can carry limited resources which reduce with use. The UAVs perform a search task to detect targets. When a target is detected which requires different type and quantities of resources to completely destroy, then a team of UAVs called as a coalition is formed to attack the target. The coalition members have to modify their route to attack the target, in the process, the search task is affected, as search and destroy tasks are coupled. The performance of the mission is a function of the search and the task allocation strategies. Therefore, for a given task allocation strategy, we need to devise search strategies that are efficient. In this paper, we propose three different search strategies namely; random search strategy, lanes based search strategy and grid based search strategy and analyze their performance through Monte-Carlo simulations. The results show that the grid based search strategy performs the best but with high information overhead.

Popular matchings with variable item copies

We consider the problem of matching people to items, where each person ranks a subset of items in an order of preference, possibly involving ties. There are several notions of optimality about how to best match a person to an item; in particular, popularity is a natural and appealing notion of optimality. A matching M* is popular if there is no matching M such that the number of people who prefer M to M* exceeds the number who prefer M* to M. However, popular matchings do not always provide an answer to the problem of determining an optimal matching since there are simple instances that do not admit popular matchings. This motivates the following extension of the popular matchings problem: Given a graph G = (A U 3, E) where A is the set of people and 2 is the set of items, and a list < c(1),...., c(vertical bar B vertical bar)> denoting upper bounds on the number of copies of each item, does there exist < x(1),...., x(vertical bar B vertical bar)> such that for each i, having x(i) copies of the i-th item, where 1 <= xi <= c(i), enables the resulting graph to admit a popular matching? In this paper we show that the above problem is NP-hard. We show that the problem is NP-hard even when each c(i) is 1 or 2. We show a polynomial time algorithm for a variant of the above problem where the total increase in copies is bounded by an integer k. (C) 2011 Elsevier B.V. All rights reserved.

Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where, for instance, it is employed in multiparameter estimation. While a sequence of equidistant control pulses the Carr-Purcell-Meiboom-Gill (CPMG) sequence] has been ubiquitously used for decoupling, Uhrig recently proposed that a nonequidistant pulse sequence the Uhrig dynamic decoupling (UDD) sequence] may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system qubits are C-13 nuclear spins and the environment consists of a H-1 nuclear spin bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs better than any nonequidistant DD sequence in the presence of this kind of environmental noise.

A Flexible Class of Regenerating Codes for Distributed Storage

In the distributed storage setting introduced by Dimakis et al., B units of data are stored across n nodes in the network in such a way that the data can be recovered by connecting to any k nodes. Additionally one can repair a failed node by connecting to any d nodes while downloading at most beta units of data from each node. In this paper, we introduce a flexible framework in which the data can be recovered by connecting to any number of nodes as long as the total amount of data downloaded is at least B. Similarly, regeneration of a failed node is possible if the new node connects to the network using links whose individual capacity is bounded above by beta(max) and whose sum capacity equals or exceeds a predetermined parameter gamma. In this flexible setting, we obtain the cut-set lower bound on the repair bandwidth along with a constructive proof for the existence of codes meeting this bound for all values of the parameters. An explicit code construction is provided which is optimal in certain parameter regimes.

Goal Seeking for Robots in Unknown Environments

We consider the problem of goal seeking by robots in unknown environments. We present a frontier based algorithm for finding a route to a goal in a fully unknown environment, where information about the goal region (GR), the region where the goal is most likely to be located, is available. Our algorithm efficiently chooses the best candidate frontier cell, which is on the boundary between explored space and unexplored space, having the maximum ``goal seeking index'', to reach the goal in minimal number of moves. Modification of the algorithm is also proposed to further reduce the number of moves toward the goal. The algorithm has been tested extensively in simulation runs and results demonstrate that the algorithm effectively directs the robot to the goal and completes the search task in minimal number of moves in bounded as well as unbounded environments. The algorithm is shown to perform as well as a state of the art agent centered search algorithm RTAA*, in cluttered environments if exact location of the goal is known at the beginning of the mission and is shown to perform better in uncluttered environments.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Hierarchies of circuit classes that are closed under complement

We examine three hierarchies of circuit classes and show they are closed under complementation. (1) The class of languages recognized by a family of polynomial size skew circuits with width O(w), are closed under complement. (2) The class of languages recognized by family of polynomial size circuits with width O(w) and polynomial tree-size, are closed under complement. (3) The class of languages recognized by a family of polynomial size, O(log(n)) depth, bounded AND fan-in with OR fan-in f (f⩾log(n)) circuits are closed under complement. These improve upon the results of (i) Immerman (1988) and Szelepcsenyi (1988), who show that 𝒩L𝒪𝒢 is closed under complementation, and (ii) Borodin et al. (1989), who show that L𝒪𝒢𝒞ℱL is closed under complement

Enhanced charge and spin currents in the one-dimensional disordered mesoscopic Hubbard ring

We consider a one-dimensional mesoscopic Hubbard ring with and without disorder and compute charge and spin stiffness as a measure of the permanent currents. For finite disorder we identify critical disorder strength beyond which the charge currents in a system with repulsive interactions are larger than those for a free system. The spin currents in the disordered repulsive Hubbard model are enhanced only for small U, where the magnetic state of the system corresponds to a charge-density wave pinned to the impurities. For large U, the state of the system corresponds to localized isolated spins and the spin currents are found to be suppressed. For the attractive Hubbard model we find that the charge currents are always suppressed compared to the free system at all length scales.

On boundedness and parallel to center dot parallel to(p) continuity of second quantisation

in this short note, we determine precisely which operators have the property that their (full, symmetric or antisymmetric) second quantisation is an operator which is bounded or belongs to one of the various Schatten ideals; we also note that in 'the interior' of the natural domain, the second quantisation is a continuous map.

A polynomial bound on the number of light cycles in an undirected graph

Let G be an undirected graph with a positive real weight on each edge. It is shown that the number of minimum-weight cycles of G is bounded above by a polynomial in the number of edges of G. A similar bound holds if we wish to count the number of cycles with weight at most a constant multiple of the minimum weight of a cycle of G.

Coherence of the real symmetric Hardy algebra

Let D denote the open unit disk in C centered at 0. Let H-R(infinity) denote the set of all bounded and holomorphic functions defined in D that also satisfy f(z) = <(f <(z)over bar>)over bar> for all z is an element of D. It is shown that H-R(infinity) is a coherent ring.