Ising pyrochlore magnets: Low-temperature properties, "ice rules," and beyond

Pyrochlore magnets are candidates for what Harris et al. [Phys. Rev. Lett. 79, 2554 (1997)] call "spin-ice" behavior. We present theoretical simulations of relevance for the pyrochlore family R2Ti2O7 (R = rare earth) supported by magnetothermal measurements on selected systems. Ey considering long-ranged dipole-dipole as well as short-ranged superexchange interactions, we get three distinct behaviors: (i) an ordered doubly degenerate state, (ii) a highly disordered state with a broad transition to paramagnetism, and (iii) a partially ordered state with a sharp transition to paramagnetism. Closely corresponding behavior is seen in the real compounds.

Survival of the fittest and zero sum games

Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The. dynamics of this selection is studied using a simple linear model. It has similarities to features of quantum computation, in particular conservation laws leading to destructive interference. Compared to an altruistic scenario, competition introduces instability and eliminates the weaker species in a finite time.

Reducing convergence times of self-propelled swarms via modified nearest neighbor rules

Vicsek et al. proposed a biologically inspired model of self-propelled particles, which is now commonly referred to as the Vicsek model. Recently, attention has been directed at modifying the Vicsek model so as to improve convergence properties. In this paper, we propose two modification of the Vicsek model which leads to significant improvements in convergence times. The modifications involve an additional term in the heading update rule which depends only on the current or the past states of the particle's neighbors. The variation in convergence properties as the parameters of these modified versions are changed are closely investigated. It is found that in both cases, there exists an optimal value of the parameter which reduces convergence times significantly and the system undergoes a phase transition as the value of the parameter is increased beyond this optimal value. (C) 2012 Elsevier B.V. All rights reserved.

Zero-Sum Risk-Sensitive Stochastic Differential Games

We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton-Jacobi-Isaacs equations. Finally, we show that the value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups.

General-sum stochastic games: Verifiability conditions for Nash equilibria

Unlike zero-sum stochastic games, a difficult problem in general-sum stochastic games is to obtain verifiable conditions for Nash equilibria. We show in this paper that by splitting an associated non-linear optimization problem into several sub-problems, characterization of Nash equilibria in a general-sum discounted stochastic games is possible. Using the aforementioned sub-problems, we in fact derive a set of necessary and sufficient verifiable conditions (termed KKT-SP conditions) for a strategy-pair to result in Nash equilibrium. Also, we show that any algorithm which tracks the zero of the gradient of the Lagrangian of every sub-problem provides a Nash strategy-pair. (c) 2012 Elsevier Ltd. All rights reserved.

Bounds on the sum-rate capacity of the Gaussian MIMO X channel

We consider the MIMO X channel (XC), a system consisting of two transmit-receive pairs, where each transmitter communicates with both the receivers. Both the transmitters and receivers are equipped with multiple antennas. First, we derive an upper bound on the sum-rate capacity of the MIMO XC under individual power constraint at each transmitter. The sum-rate capacity of the two-user multiple access channel (MAC) that results when receiver cooperation is assumed forms an upper bound on the sum-rate capacity of the MIMO XC. We tighten this bound by considering noise correlation between the receivers and deriving the worst noise covariance matrix. It is shown that the worst noise covariance matrix is a saddle-point of a zero-sum, two-player convex-concave game, which is solved through a primal-dual interior point method that solves the maximization and the minimization parts of the problem simultaneously. Next, we propose an achievable scheme which employs dirty paper coding at the transmitters and successive decoding at the receivers. We show that the derived upper bound is close to the achievable region of the proposed scheme at low to medium SNRs.

Achievable secrecy sum-rate in a fading MAC-WT with power control and without CSI of eavesdropper

We consider a two user fading Multiple Access Channel with a wire-tapper (MAC-WT) where the transmitter has the channel state information (CSI) to the intended receiver but not to the eavesdropper (eve). We provide an achievable secrecy sum-rate with optimal power control. We next provide a secrecy sum-rate with optimal power control and cooperative jamming (CJ). We then study an achievable secrecy sum rate by employing an ON/OFF power control scheme which is more easily computable. We also employ CJ over this power control scheme. Results show that CJ boosts the secrecy sum-rate significantly even if we do not know the CSI of the eve's channel. At high SNR, the secrecy sum-rate (with CJ) without CSI of the eve exceeds the secrecy sum-rate (without CJ) with full CSI of the eve.

A scaled unscented transformation based directed Gaussian sum filter for nonlinear dynamic system identification

Impoverishment of particles, i.e. the discretely simulated sample paths of the process dynamics, poses a major obstacle in employing the particle filters for large dimensional nonlinear system identification. A known route of alleviating this impoverishment, i.e. of using an exponentially increasing ensemble size vis-a-vis the system dimension, remains computationally infeasible in most cases of practical importance. In this work, we explore the possibility of unscented transformation on Gaussian random variables, as incorporated within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional structural system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of structural dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. (C) 2013 Elsevier Ltd. All rights reserved.

Zero-sum risk-sensitive stochastic games on a countable state space

Infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled Markov chains with countably many states are analyzed. Upper and lower values for these games are established. The existence of value and saddle-point equilibria in the class of Markov strategies is proved for the discounted-cost game. The existence of value and saddle-point equilibria in the class of stationary strategies is proved under the uniform ergodicity condition for the ergodic-cost game. The value of the ergodic-cost game happens to be the product of the inverse of the risk-sensitivity factor and the logarithm of the common Perron-Frobenius eigenvalue of the associated controlled nonlinear kernels. (C) 2013 Elsevier B.V. All rights reserved.

Zero-Sum Stochastic Games with Partial Information and Average Payoff

We consider a discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we present a pair of optimal strategies for both the players.

Improving tangential resolution with a modified delay-and-sum reconstruction algorithm in photoacoustic and thermoacoustic tomography

Spatial resolution in photoacoustic and thermoacoustic tomography is ultrasound transducer (detector) bandwidth limited. For a circular scanning geometry the axial (radial) resolution is not affected by the detector aperture, but the tangential (lateral) resolution is highly dependent on the aperture size, and it is also spatially varying (depending on the location relative to the scanning center). Several approaches have been reported to counter this problem by physically attaching a negative acoustic lens in front of the nonfocused transducer or by using virtual point detectors. Here, we have implemented a modified delay-and-sum reconstruction method, which takes into account the large aperture of the detector, leading to more than fivefold improvement in the tangential resolution in photoacoustic (and thermoacoustic) tomography. Three different types of numerical phantoms were used to validate our reconstruction method. It is also shown that we were able to preserve the shape of the reconstructed objects with the modified algorithm. (C) 2014 Optical Society of America

A Modified Sum-Product Algorithm over Graphs with Isolated Short Cycles

We investigate into the limitations of the sum-product algorithm in the probability domain over graphs with isolated short cycles. By considering the statistical dependency of messages passed in a cycle of length 4, we modify the update equations for the beliefs at the variable and check nodes. We highlight an approximate log domain algebra for the modified variable node update to ensure numerical stability. At higher signal-to-noise ratios (SNR), the performance of decoding over graphs with isolated short cycles using the modified algorithm is improved compared to the original message passing algorithm (MPA).

Outer Bounds on the Sum Rate of the K-User MIMO Gaussian Interference Channel

This paper derives outer bounds on the sum rate of the K-user MIMO Gaussian interference channel (GIC). Three outer bounds are derived, under different assumptions of cooperation and providing side information to receivers. The novelty in the derivation lies in the careful selection of side information, which results in the cancellation of the negative differential entropy terms containing signal components, leading to a tractable outer bound. The overall outer bound is obtained by taking the minimum of the three outer bounds. The derived bounds are simplified for the MIMO Gaussian symmetric IC to obtain outer bounds on the generalized degrees of freedom (GDOF). The relative performance of the bounds yields insight into the performance limits of multiuser MIMO GICs and the relative merits of different schemes for interference management. These insights are confirmed by establishing the optimality of the bounds in specific cases using an inner bound on the GDOF derived by the authors in a previous work. It is also shown that many of the existing results on the GDOF of the GIC can be obtained as special cases of the bounds, e. g., by setting K = 2 or the number of antennas at each user to 1.

Novel Relay Selection Rules for Average Interference-Constrained Cognitive AF Relay Networks

Cooperative relaying combined with selection exploits spatial diversity to significantly improve the performance of interference-constrained secondary users in an underlay cognitive radio (CR) network. However, unlike conventional relaying, the state of the links between the relay and the primary receiver affects the choice of the relay. Further, while the optimal amplify-and-forward (AF) relay selection rule for underlay CR is well understood for the peak interference-constraint, this is not so for the less conservative average interference constraint. For the latter, we present three novel AF relay selection (RS) rules, namely, symbol error probability (SEP)-optimal, inverse-of-affine (IOA), and linear rules. We analyze the SEPs of the IOA and linear rules and also develop a novel, accurate approximation technique for analyzing the performance of AF relays. Extensive numerical results show that all the three rules outperform several RS rules proposed in the literature and generalize the conventional AF RS rule.

Necessary and sufficient conditions for optimality in constrained general sum stochastic games

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium. (C) 2015 Elsevier B.V. All rights reserved.