Normal mode sound propagation in an ocean with random narrow-band surface waves

Normal mode sound propagation in an isovelocity ocean with random narrow-band surface waves is considered, assuming the root-mean-square wave height to be small compared to the acoustic wavelength. Nonresonant interaction among the normal modes is studied straightforward perturbation technique. The more interesting case of resonant interaction is investigated using the method of multiple scales to obtain a pair of stochastic coupled amplitude equations which are solved using the Peano-Baker expansion technique. Equations for the spatial evolution of the first and second moments of the mode amplitudes are also derived and solved. It is shown that, irrespective of the initial conditions, the mean values of the mode amplitudes tend to zero asymptotically with increasing range, the mean-square amplitudes tend towards a state of equipartition of energy, and the total energy of the modes is conserved.

On infinitesimal σ-fields generated by random processes

It is proved that the infinitesimal look-ahead and look-back σ-fields of a random process disagree at atmost countably many time instants.

Random sequential multilayer deposition of different‐sized k mers on a one dimensional infinite substrate

Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.

Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

Dense granular flow down an inclined plane A comparison between the hard particle model and soft particle simulations

The granular flow down an inclined plane is simulated using the discrete element (DE) technique to examine the extent to which the dynamics of an unconfined dense granular flow can be well described by a hard particle model First, we examine the average coordination number for the particles in the flow down an inclined plane using the DE technique using the linear contact model with and without friction, and the Hertzian contact model with friction The simulations show that the average coordination number decreases below 1 for values of the spring stiffness corresponding to real materials, such as sand and glass, even when the angle of inclination is only 10 larger than the angle of repose Additional measures of correlations in the system, such as the fraction of particles with multibody contact, the force ratio (average ratio of the magnitudes of the largest and the second largest force on a particle), and the angle between the two largest forces on the particle, show no evidence of force chains or other correlated motions in the system An analysis of the bond-orientational order parameter indicates that the flow is in the random state, as in event-driven (ED) simulations V Kumaran, J Fluid Mech 632, 107 (2009), J Fluid Mech 632, 145 (2009)] The results of the two simulation techniques for the Bagnold coefficients (ratio of stress and square of the strain rate) and the granular temperature (mean square of the fluctuating velocity) are compared with the theory V Kumaran, J Fluid Mech 632, 107 (2009), J Fluid Mech 632, 145 (2009)] and are found to be in quantitative agreement In addition, we also conduct a comparison of the collision frequency and the distribution of the precollisional relative velocities of particles in contact The strong correlation effects exhibited by these two quantities in event-driven simulations V Kumaran, J Fluid Mech 632, 145 (2009)] are also found in the DE simulations (C) 2010 American Institute of Physics doi 10 1063/1 3504660]

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.

Computation of restoration of ligand response in the random kinetics of a prostate cancer cell signaling pathway

Mutation and/or dysfunction of signaling proteins in the mitogen activated protein kinase (MAPK) signal transduction pathway are frequently observed in various kinds of human cancer. Consistent with this fact, in the present study, we experimentally observe that the epidermal growth factor (EGF) induced activation profile of MAP kinase signaling is not straightforward dose-dependent in the PC3 prostate cancer cells. To find out what parameters and reactions in the pathway are involved in this departure from the normal dose-dependency, a model-based pathway analysis is performed. The pathway is mathematically modeled with 28 rate equations yielding those many ordinary differential equations (ODE) with kinetic rate constants that have been reported to take random values in the existing literature. This has led to us treating the ODE model of the pathways kinetics as a random differential equations (RDE) system in which the parameters are random variables. We show that our RDE model captures the uncertainty in the kinetic rate constants as seen in the behavior of the experimental data and more importantly, upon simulation, exhibits the abnormal EGF dose-dependency of the activation profile of MAP kinase signaling in PC3 prostate cancer cells. The most likely set of values of the kinetic rate constants obtained from fitting the RDE model into the experimental data is then used in a direct transcription based dynamic optimization method for computing the changes needed in these kinetic rate constant values for the restoration of the normal EGF dose response. The last computation identifies the parameters, i.e., the kinetic rate constants in the RDE model, that are the most sensitive to the change in the EGF dose response behavior in the PC3 prostate cancer cells. The reactions in which these most sensitive parameters participate emerge as candidate drug targets on the signaling pathway. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Improved mechanical properties of polymer nanocomposites incorporating graphene-like BN: Dependence on the number of BN layers

The mechanical properties of composites of polymethylmethacrylate (PMMA) with two-dimensional graphene-like boron nitride (BN) have been investigated to explore the dependence of the properties on the number of BN layers. This study demonstrates that significantly improved mechanical properties are exhibited by the composite with the fewest number of BN layers. Thus, with incorporation of three BN layers, the hardness and elastic modulus of the composite showed an increase of 125% and 130%, respectively, relative to pure PMMA. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Central Limit Theorem for truncated heavy tailed Banach valued random vectors

In this paper the question of the extent to which truncated heavy tailed random vectors, taking values in a Banach space, retain the characteristic features of heavy tailed random vectors, is answered from the point of view of the central limit theorem.

Test Application Time Minimization for RAS using Basis Optimization of Column Decoder

Random Access Scan, which addresses individual flip-flops in a design using a memory array like row and column decoder architecture, has recently attracted widespread attention, due to its potential for lower test application time, test data volume and test power dissipation when compared to traditional Serial Scan. This is because typically only a very limited number of random ``care'' bits in a test response need be modified to create the next test vector. Unlike traditional scan, most flip-flops need not be updated. Test application efficiency can be further improved by organizing the access by word instead of by bit. In this paper we present a new decoder structure that takes advantage of basis vectors and linear algebra to further significantly optimize test application in RAS by performing the write operations on multiple bits consecutively. Simulations performed on benchmark circuits show an average of 2-3 times speed up in test write time compared to conventional RAS.

Localization of light in coherently amplifying random media

We derive and analyze the statistics of reflection coefficient of light backscattered coherently from an amplifying and disordered optical medium modeled by a spatially random refractive index having a uniform imaginary part in one dimension. We find enhancement of reflected intensity owing to a synergy between wave confinement by Anderson localization and coherent amplification by the active medium. This is not the same as that due to enhanced optical path lengths expected from photon diffusion in the random active medium. Our study is relevant to the physical realizability of a mirrorless laser by photon confinement due to Anderson localization.

An Efficient Random Walk Strategy for Sampling Based Robot Motion Planners

Sampling based planners have been successful in path planning of robots with many degrees of freedom, but still remains ineffective when the configuration space has a narrow passage. We present a new technique based on a random walk strategy to generate samples in narrow regions quickly, thus improving efficiency of Probabilistic Roadmap Planners. The algorithm substantially reduces instances of collision checking and thereby decreases computational time. The method is powerful even for cases where the structure of the narrow passage is not known, thus giving significant improvement over other known methods.

Five-level inverter scheme for an open-end winding induction machine with less number of switches

Higher level of inversion is achieved with a less number of switches in the proposed scheme. The scheme proposes a five-level inverter for an open-end winding induction motor which uses only two DC-link rectifiers of voltage rating of Vdc/4, a neutral-point clamped (NPC) three-level inverter and a two-level inverter. Even though the two-level inverter is connected to the high-voltage side, it is always in square-wave operation. Since the two-level inverter is not switching in a pulse width modulated fashion and the magnitude of switching transient is only half compared to the convention three-level NPC inverter, the switching losses and electromagnetic interference is not so high. The scheme is experimentally verified on a 2.5 kW induction machine.

Convergence of Power Control in a Random Channel Environment

In this paper, we study the Foschini Miljanic algorithm, which was originally proposed in a static channel environment. We investigate the algorithm in a random channel environment, study its convergence properties and apply the Gerschgorin theorem to derive sufficient conditions for the convergence of the algorithm. We apply the Foschini and Miljanic algorithm to cellular networks and derive sufficient conditions for the convergence of the algorithm in distribution and validate the results with simulations. In cellular networks, the conditions which ensure convergence in distribution can be easily verified.