A Parallel Algorithm for Dilated Contour Extraction from Bilevel Images

We describe a simple, but efficient algorithm for the generation of dilated contours from bilevel images. The initial part of the contour extraction is explained to be a good candidate for parallel computer code generation. The remainder of the algorithm is of linear nature.Comment: 5 pages, including 3 figures. For additional detail check http://www.nis.lanl.gov/~bschlei/labvis/index.htm

Gravitational Waves from the rr-mode instability of neutron stars: effect of magnetic field

Studies have shown that emission of gravitational wave drives an instability in the $r$-modes of young rapidly rotating neutron stars carrying away most of the angular momentum through gravitational wave emission in the first year or so after their formation. Magnetic field plays a crucial role in the evolution of these $r$-modes and hence the evolution of the neutron star itself. An attempt is made here to investigate the role of magnetic field in the evolution of $r$-mode instability and detectibility of gravitational waves emitted by a newly born, hot and rapidly and differentially rotating neutron star. It is found that magnetic field tend to suppress the $r$-mode amplitude. The {\it signal-to-noise ratio} analysis shows that gravitational waves emitted from the $r$-mode instability from neutron stars with magnetic fields upto the order of $10^{14}$ gauss may be detectable by the Advanced LIGO at 20 Mpc.Comment: 16 pages, 27 figure

Actor-Critic Algorithms for Learning Nash Equilibria in N-player General-Sum Games

We consider the problem of finding stationary Nash equilibria (NE) in a finite discounted general-sum stochastic game. We first generalize a non-linear optimization problem from Filar and Vrieze [2004] to a $N$-player setting and break down this problem into simpler sub-problems that ensure there is no Bellman error for a given state and an agent. We then provide a characterization of solution points of these sub-problems that correspond to Nash equilibria of the underlying game and for this purpose, we derive a set of necessary and sufficient SG-SP (Stochastic Game - Sub-Problem) conditions. Using these conditions, we develop two actor-critic algorithms: OFF-SGSP (model-based) and ON-SGSP (model-free). Both algorithms use a critic that estimates the value function for a fixed policy and an actor that performs descent in the policy space using a descent direction that avoids local minima. We establish that both algorithms converge, in self-play, to the equilibria of a certain ordinary differential equation (ODE), whose stable limit points coincide with stationary NE of the underlying general-sum stochastic game. On a single state non-generic game (see Hart and Mas-Colell [2005]) as well as on a synthetic two-player game setup with $810,000$ states, we establish that ON-SGSP consistently outperforms NashQ ([Hu and Wellman, 2003] and FFQ [Littman, 2001] algorithms

A constrained optimization perspective on actor critic algorithms and application to network routing

We propose a novel actor-critic algorithm with guaranteed convergence to an optimal policy for a discounted reward Markov decision process. The actor incorporates a descent direction that is motivated by the solution of a certain non-linear optimization problem. We also discuss an extension to incorporate function approximation and demonstrate the practicality of our algorithms on a network routing application

Complexity Analysis in Bouncing Ball Dynamical System

Evolutionary motions in a bouncing ball system consisting of a ball having a free fall in the Earth's gravitational field have been studied systematically. Because of nonlinear form of the equations of motion, evolutions show chaos for certain set of parameters for certain initial conditions. Bifurcation diagram has been drawn to study regular and chaotic behavior. Numerical calculations have been performed to calculate Lyapunov exponents, topological entropies and correlation dimension as measures of complexity. Numerical results are shown through interesting graphicsComment: 7 papes, 7 figure

A Study of Gradient Descent Schemes for General-Sum Stochastic Games

Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for general-sum stochastic games by Filar and Vrieze [2004]. However, the optimization problem there has a non-linear objective and non-linear constraints with special structure. Since gradients of both the objective as well as constraints of this optimization problem are well defined, gradient based schemes seem to be a natural choice. We discuss a gradient scheme tuned for two-player stochastic games. We show in simulations that this scheme indeed converges to a Nash equilibrium, for a simple terrain exploration problem modelled as a general-sum stochastic game. However, it turns out that only global minima of the optimization problem correspond to Nash equilibria of the underlying general-sum stochastic game, while gradient schemes only guarantee convergence to local minima. We then provide important necessary conditions for gradient schemes to converge to Nash equilibria in general-sum stochastic games

Ag-Au alloys BCS-like Superconductors?

Prompted by the recent report on the evidence for superconductivity at ambient temperature and pressure in nanostructures of silver particles embedded into a gold matrix [arXiv:1807.08572], we have exploited first principles materials discovery approaches to predict superconductivity in the 3D bulk crystals and 2D slabs of Ag-Au binary alloys at 1 atm pressure within the phonon-mediated BCS-like pairing mechanism. In calculations, it turns out that, the estimated superconducting transition temperatures of the ensued stable and metastable Ag-Au alloys resulted in Tc as low as one mK. Whereas similar calculations for the known superconducting intermetallic compounds consisting of gold, Laves Au2Bi and A15 Nb3Au predict Tc =3.6 K and 10.1 K, respectively, corroborate with experiments. And, the hitherto unknown silver analogues, Ag2Bi and Nb3Ag are also found to be superconducting at 6.1 K and 10.8 K, respectively. Furthermore, we show that, elemental Au in its metastable 9R, and hcp phases superconduct at Tc =1 mK; but not Ag, in these hexagonal lattices.Comment: 11,

Monitoring Software Reliability using Statistical Process Control An Ordered Statistics Approach

The nature and complexity of software have changed significantly in the last few decades. With the easy availability of computing power, deeper and broader applications are made. It has been extremely necessary to produce good quality software with high precession of reliability right in the first place. Olden day's software errors and bugs were fixed at a later stage in the software development. Today to produce high quality reliable software and to keep a specific time schedule is a big challenge. To cope up the challenge many concepts, methodology and practices of software engineering have been evolved for developing reliable software. Better methods of controlling the process of software production are underway. One of such methods to assess the software reliability is using control charts. In this paper we proposed an NHPP based control mechanism by using order statistics with cumulative quantity between observations of failure data using mean value function of exponential distribution.Comment: International Journal of Computer Applications; Published by Foundation of Computer Scienc

Algorithms For Stochastic Games And Service Systems

This thesis is organized into two parts, one for my main area of research in the field of stochastic games, and the other for my contributions in the area of service systems. We first provide an abstract for my work in stochastic games. The field of stochastic games has been actively pursued over the last seven decades because of several of its important applications in oligopolistic economics. In the past, zero-sum stochastic games have been modelled and solved for Nash equilibria using the standard techniques of Markov decision processes. General-sum stochastic games on the contrary have posed difficulty as they cannot be reduced to Markov decision processes. Over the past few decades the quest for algorithms to compute Nash equilibria in general-sum stochastic games has intensified and several important algorithms such as stochastic tracing procedure [Herings and Peeters, 2004], NashQ [Hu and Wellman, 2003], FFQ [Littman, 2001], etc., and their generalised representations such as the optimization problem formulations for various reward structures [Filar and Vrieze, 1997] have been proposed. However, they suffer from either lack of generality or are intractable for even medium sized problems or both. In our venture towards algorithms for stochastic games, we start with a non-linear optimization problem and then design a simple gradient descent procedure for the same. Though this procedure gives the Nash equilibrium for a sample problem of terrain exploration, we observe that, in general, it need not be true. We characterize the necessary conditions and define KKT-N point. KKT-N points are those Karush-Kuhn-Tucker (KKT) points which corresponding to Nash equilibria. Thus, for a simple gradient based algorithm to guarantee convergence to Nash equilibrium, all KKT points of the optimization problem need to be KKT-N points, which restricts the applicability of such algorithms. We then take a step back and start looking at better characterization of those points of the optimization problem which correspond to Nash equilibria of the underlying game. As a result of this exploration, we derive two sets of necessary and sufficient conditions. The first set, KKT-SP conditions, is inspired from KKT conditions itself and is obtained by breaking down the main optimization problem into several sub-problems and then applying KKT conditions to each one of those sub-problems. The second set, SG-SP conditions, is a simplified set of conditions which characterize those Nash points more compactly. Using both KKT-SP and SG-SP conditions, we propose three algorithms, OFF-SGSP, ON-SGSP and DON-SGSP, respectively, which we show provide Nash equilibrium strategies for general-sum discounted stochastic games. Here OFF-SGSP is an off-line algorithm while ONSGSP and DON-SGSP are on-line algorithms. In particular, we believe that DON-SGSP is the first decentralized on-line algorithm for general-sum discounted stochastic games. We show that both our on-line algorithms are computationally efficient. In fact, we show that DON-SGSP is not only applicable for multi-agent scenarios but is also directly applicable for the single-agent case, i.e., MDPs (Markov Decision Processes). The second part of the thesis focuses on formulating and solving the problem of minimizing the labour-cost in service systems. We define the setting of service systems and then model the labour-cost problem as a constrained discrete parameter Markov-cost process. This Markov process is parametrized by the number of workers in various shifts and with various skill levels. With the number of workers as optimization variables, we provide a detailed formulation of a constrained optimization problem where the objective is the expected long-run averages of the single-stage labour-costs, and the main set of constraints are the expected long-run average of aggregate SLAs (Service Level Agreements). For this constrained optimization problem, we provide two stochastic optimization algorithms, SASOC-SF-N and SASOC-SF-C, which use smoothed functional approaches to estimate gradient and perform gradient descent in the aforementioned constrained optimization problem. SASOC-SF-N uses Gaussian distribution for smoothing while SASOC-SF-C uses Cauchy distribution for the same. SASOC-SF-C is the first Cauchy based smoothing algorithm which requires a fixed number (two) of simulations independent of the number of optimization variables. We show that these algorithms provide an order of magnitude better performance than existing industrial standard tool, OptQuest. We also show that SASOC-SF-C gives overall better performance

Einstein energy-momentum complex for a phantom black hole metric

In this paper we calculate the energy distribution E(r) associated with a static spherically symmetric non-singular phantom black hole metric in Einstein's prescription in general relativity. As required for Einstein energy-momentum complex, we perform calculations in quasi-Cartesian coordinates. We also calculate momentum components and get zero values as expected from the geometry of the metric.Comment: 5 pages, 2 figure