Dynamics of prolate spheroidal mass distributions with varying eccentricity

In this paper we calculate the potential for a prolate spheroidal distribution as in a dark matter halo with a radially varying eccentricity. This is obtained by summing up the shell-by-shell contributions of isodensity surfaces, which are taken to be concentric and with a common polar axis and with an axis ratio that varies with radius. Interestingly, the constancy of potential inside a shell is shown to be a good approximation even when the isodensity contours are dissimilar spheroids, as long as the radial variation in eccentricity is small as seen in realistic systems. We consider three cases where the isodensity contours are more prolate at large radii, or are less prolate or have a constant eccentricity. Other relevant physical quantities like the rotation velocity, the net orbital and vertical frequency due to the halo and an exponential disc of finite thickness embedded in it are obtained. We apply this to the kinematical origin of Galactic warp, and show that a prolate-shaped halo is not conducive to making long-lived warps - contrary to what has been proposed in the literature. The results for a prolate mass distribution with a variable axis ratio obtained are general, and can be applied to other astrophysical systems, such as prolate bars, for a more realistic treatment.

Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Given a metric space with a Borel probability measure, for each integer N, we obtain a probability distribution on N x N distance matrices by considering the distances between pairs of points in a sample consisting of N points chosen independently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.

Effects of initial height on the steady-state persistence probability of linear growth models

The effects of the initial height on the temporal persistence probability of steady-state height fluctuations in up-down symmetric linear models of surface growth are investigated. We study the (1 + 1)-dimensional Family model and the (1 + 1)-and (2 + 1)-dimensional larger curvature (LC) model. Both the Family and LC models have up-down symmetry, so the positive and negative persistence probabilities in the steady state, averaged over all values of the initial height h(0), are equal to each other. However, these two probabilities are not equal if one considers a fixed nonzero value of h(0). Plots of the positive persistence probability for negative initial height versus time exhibit power-law behavior if the magnitude of the initial height is larger than the interface width at saturation. By symmetry, the negative persistence probability for positive initial height also exhibits the same behavior. The persistence exponent that describes this power-law decay decreases as the magnitude of the initial height is increased. The dependence of the persistence probability on the initial height, the system size, and the discrete sampling time is found to exhibit scaling behavior.

SEP-Optimal Transmit Power Policy for Peak Power and Interference Outage Probability Constrained Underlay Cognitive Radios

In underlay cognitive radio (CR), a secondary user (SU) can transmit concurrently with a primary user (PU) provided that it does not cause excessive interference at the primary receiver (PRx). The interference constraint fundamentally changes how the SU transmits, and makes link adaptation in underlay CR systems different from that in conventional wireless systems. In this paper, we develop a novel, symbol error probability (SEP)-optimal transmit power adaptation policy for an underlay CR system that is subject to two practically motivated constraints, namely, a peak transmit power constraint and an interference outage probability constraint. For the optimal policy, we derive its SEP and a tight upper bound for MPSK and MQAM constellations when the links from the secondary transmitter (STx) to its receiver and to the PRx follow the versatile Nakagami-m fading model. We also characterize the impact of imperfectly estimating the STx-PRx link on the SEP and the interference. Extensive simulation results are presented to validate the analysis and evaluate the impact of the constraints, fading parameters, and imperfect estimates.

Bivariate frequency analysis of floods using a diffusion based kernel density estimator

Recent focus of flood frequency analysis (FFA) studies has been on development of methods to model joint distributions of variables such as peak flow, volume, and duration that characterize a flood event, as comprehensive knowledge of flood event is often necessary in hydrological applications. Diffusion process based adaptive kernel (D-kernel) is suggested in this paper for this purpose. It is data driven, flexible and unlike most kernel density estimators, always yields a bona fide probability density function. It overcomes shortcomings associated with the use of conventional kernel density estimators in FFA, such as boundary leakage problem and normal reference rule. The potential of the D-kernel is demonstrated by application to synthetic samples of various sizes drawn from known unimodal and bimodal populations, and five typical peak flow records from different parts of the world. It is shown to be effective when compared to conventional Gaussian kernel and the best of seven commonly used copulas (Gumbel-Hougaard, Frank, Clayton, Joe, Normal, Plackett, and Student's T) in estimating joint distribution of peak flow characteristics and extrapolating beyond historical maxima. Selection of optimum number of bins is found to be critical in modeling with D-kernel.

Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse 10(d) x 10(d) matrix, with d > 6. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.

Bit Error Probability Analysis of SSK in DF Relaying with Threshold-Based Best Relay Selection and Selection Combining

In this letter, we analyze the end-to-end average bit error probability (ABEP) of space shift keying (SSK) in cooperative relaying with decode-and-forward (DF) protocol, considering multiple relays with a threshold based best relay selection, and selection combining of direct and relayed paths at the destination. We derive an exact analytical expression for the end-to-end ABEP in closed-form for binary SSK, where analytical results agree with simulation results. For non-binary SSK, approximate analytical and simulation results are presented.

Generalized scaling of misorientation angle distributions at meso-scale in deformed materials

Scaling behaviour has been observed at mesoscopic level irrespective of crystal structure, type of boundary and operative micro-mechanisms like slip and twinning. The presence of scaling at the meso-scale accompanied with that at the nano-scale clearly demonstrates the intrinsic spanning for different deformation processes and a true universal nature of scaling. The origin of a 1/2 power law in deformation of crystalline materials in terms of misorientation proportional to square root of strain is attributed to importance of interfaces in deformation processes. It is proposed that materials existing in three dimensional Euclidean spaces accommodate plastic deformation by one dimensional dislocations and their interaction with two dimensional interfaces at different length scales. This gives rise to a 1/2 power law scaling in materials. This intrinsic relationship can be incorporated in crystal plasticity models that aim to span different length and time scales to predict the deformation response of crystalline materials accurately.

Smoothed Functional Algorithms for Stochastic Optimization Using q-Gaussian Distributions

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, especially when the objective is to improve the performance of a stochastic system However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in the literature, which include Gaussian, Cauchy, and uniform distributions, among others. This article studies a new class of kernels based on the q-Gaussian distribution, which has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with a projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also demonstrate their performance numerically through simulations on a queuing model.

Zero-Crossings Based Spectrum Sensing Under Noise Uncertainties

In this work, the hypothesis testing problem of spectrum sensing in a cognitive radio is formulated as a Goodness-of-fit test against the general class of noise distributions used in most communications-related applications. A simple, general, and powerful spectrum sensing technique based on the number of weighted zero-crossings in the observations is proposed. For the cases of uniform and exponential weights, an expression for computing the near-optimal detection threshold that meets a given false alarm probability constraint is obtained. The proposed detector is shown to be robust to two commonly encountered types of noise uncertainties, namely, the noise model uncertainty, where the PDF of the noise process is not completely known, and the noise parameter uncertainty, where the parameters associated with the noise PDF are either partially or completely unknown. Simulation results validate our analysis, and illustrate the performance benefits of the proposed technique relative to existing methods, especially in the low SNR regime and in the presence of noise uncertainties.

Minimum-Error-Probability CFO Estimation for Multiuser MIMO-OFDM Systems

We consider carrier frequency offset (CFO) estimation in the context of multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems over noisy frequency-selective wireless channels with both single- and multiuser scenarios. We conceived a new approach for parameter estimation by discretizing the continuous-valued CFO parameter into a discrete set of bins and then invoked detection theory, analogous to the minimum-bit-error-ratio optimization framework for detecting the finite-alphabet received signal. Using this radical approach, we propose a novel CFO estimation method and study its performance using both analytical results and Monte Carlo simulations. We obtain expressions for the variance of the CFO estimation error and the resultant BER degradation with the single- user scenario. Our simulations demonstrate that the overall BER performance of a MIMO-OFDM system using the proposed method is substantially improved for all the modulation schemes considered, albeit this is achieved at increased complexity.

Global response sensitivity analysis using probability distance measures and generalization of Sobol's analysis

The study introduces two new alternatives for global response sensitivity analysis based on the application of the L-2-norm and Hellinger's metric for measuring distance between two probabilistic models. Both the procedures are shown to be capable of treating dependent non-Gaussian random variable models for the input variables. The sensitivity indices obtained based on the L2-norm involve second order moments of the response, and, when applied for the case of independent and identically distributed sequence of input random variables, it is shown to be related to the classical Sobol's response sensitivity indices. The analysis based on Hellinger's metric addresses variability across entire range or segments of the response probability density function. The measure is shown to be conceptually a more satisfying alternative to the Kullback-Leibler divergence based analysis which has been reported in the existing literature. Other issues addressed in the study cover Monte Carlo simulation based methods for computing the sensitivity indices and sensitivity analysis with respect to grouped variables. Illustrative examples consist of studies on global sensitivity analysis of natural frequencies of a random multi-degree of freedom system, response of a nonlinear frame, and safety margin associated with a nonlinear performance function. (C) 2015 Elsevier Ltd. All rights reserved.

1D Tight-Binding Models Render Quantum First Passage Time ``Speakable''

The calculation of First Passage Time (moreover, even its probability density in time) has so far been generally viewed as an ill-posed problem in the domain of quantum mechanics. The reasons can be summarily seen in the fact that the quantum probabilities in general do not satisfy the Kolmogorov sum rule: the probabilities for entering and non-entering of Feynman paths into a given region of space-time do not in general add up to unity, much owing to the interference of alternative paths. In the present work, it is pointed out that a special case exists (within quantum framework), in which, by design, there exists one and only one available path (i.e., door-way) to mediate the (first) passage -no alternative path to interfere with. Further, it is identified that a popular family of quantum systems - namely the 1d tight binding Hamiltonian systems - falls under this special category. For these model quantum systems, the first passage time distributions are obtained analytically by suitably applying a method originally devised for classical (stochastic) mechanics (by Schroedinger in 1915). This result is interesting especially given the fact that the tight binding models are extensively used in describing everyday phenomena in condense matter physics.

Probabilistic Models for Forecasting Earthquakes in the Northeast Region of India

Northeast India and its adjoining areas are characterized by very high seismic activity. According to the Indian seismic code, the region falls under seismic zone V, which represents the highest seismic-hazard level in the country. This region has experienced a number of great earthquakes, such as the Assam (1950) and Shillong (1897) earthquakes, that caused huge devastation in the entire northeast and adjacent areas by flooding, landslides, liquefaction, and damage to roads and buildings. In this study, an attempt has been made to find the probability of occurrence of a major earthquake (M-w > 6) in this region using an updated earthquake catalog collected from different sources. Thereafter, dividing the catalog into six different seismic regions based on different tectonic features and seismogenic factors, the probability of occurrences was estimated using three models: the lognormal, Weibull, and gamma distributions. We calculated the logarithmic probability of the likelihood function (ln L) for all six regions and the entire northeast for all three stochastic models. A higher value of ln L suggests a better model, and a lower value shows a worse model. The results show different model suits for different seismic zones, but the majority follows lognormal, which is better for forecasting magnitude size. According to the results, Weibull shows the highest conditional probabilities among the three models for small as well as large elapsed time T and time intervals t, whereas the lognormal model shows the lowest and the gamma model shows intermediate probabilities. Only for elapsed time T = 0, the lognormal model shows the highest conditional probabilities among the three models at a smaller time interval (t = 3-15 yrs). The opposite result is observed at larger time intervals (t = 15-25 yrs), which show the highest probabilities for the Weibull model. However, based on this study, the IndoBurma Range and Eastern Himalaya show a high probability of occurrence in the 5 yr period 2012-2017 with >90% probability.

Bacterial growth rate and host factors as determinants of intracellular bacterial distributions in systemic Salmonella enterica infections.

Bacteria of the species Salmonella enterica cause a range of life-threatening diseases in humans and animals worldwide. The within-host quantitative, spatial, and temporal dynamics of S. enterica interactions are key to understanding how immunity acts on these infections and how bacteria evade immune surveillance. In this study, we test hypotheses generated from mathematical models of in vivo dynamics of Salmonella infections with experimental observation of bacteria at the single-cell level in infected mouse organs to improve our understanding of the dynamic interactions between host and bacterial mechanisms that determine net growth rates of S. enterica within the host. We show that both bacterial and host factors determine the numerical distributions of bacteria within host cells and thus the level of dispersiveness of the infection.