Design and performance analysis of a signal detector based on suprathreshold stochastic resonance

This paper presents the design and performance analysis of a detector based on suprathreshold stochastic resonance (SSR) for the detection of deterministic signals in heavy-tailed non-Gaussian noise. The detector consists of a matched filter preceded by an SSR system which acts as a preprocessor. The SSR system is composed of an array of 2-level quantizers with independent and identically distributed (i.i.d) noise added to the input of each quantizer. The standard deviation sigma of quantizer noise is chosen to maximize the detection probability for a given false alarm probability. In the case of a weak signal, the optimum sigma also minimizes the mean-square difference between the output of the quantizer array and the output of the nonlinear transformation of the locally optimum detector. The optimum sigma depends only on the probability density functions (pdfs) of input noise and quantizer noise for weak signals, and also on the signal amplitude and the false alarm probability for non-weak signals. Improvement in detector performance stems primarily from quantization and to a lesser extent from the optimization of quantizer noise. For most input noise pdfs, the performance of the SSR detector is very close to that of the optimum detector. (C) 2012 Elsevier B.V. All rights reserved.

Stabilization of stochastic approximation by step size adaptation

A scheme for stabilizing stochastic approximation iterates by adaptively scaling the step sizes is proposed and analyzed. This scheme leads to the same limiting differential equation as the original scheme and therefore has the same limiting behavior, while avoiding the difficulties associated with projection schemes. The proof technique requires only that the limiting o.d.e. descend a certain Lyapunov function outside an arbitrarily large bounded set. (C) 2012 Elsevier B.V. All rights reserved.

Synchronization of globally coupled two-state stochastic oscillators with a state-dependent refractory period

We present a model of identical coupled two-state stochastic units, each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition.

SPLIT-STEP FORWARD MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Ito form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order gamma = 1 in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.

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.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

Stochastic Simulations Suggest that HIV-1 Survives Close to Its Error Threshold

The use of mutagenic drugs to drive HIV-1 past its error threshold presents a novel intervention strategy, as suggested by the quasispecies theory, that may be less susceptible to failure via viral mutation-induced emergence of drug resistance than current strategies. The error threshold of HIV-1, mu(c), however, is not known. Application of the quasispecies theory to determine mu(c) poses significant challenges: Whereas the quasispecies theory considers the asexual reproduction of an infinitely large population of haploid individuals, HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We performed population genetics-based stochastic simulations of the within-host evolution of HIV-1 and estimated the structure of the HIV-1 quasispecies and mu(c). We found that with small mutation rates, the quasispecies was dominated by genomes with few mutations. Upon increasing the mutation rate, a sharp error catastrophe occurred where the quasispecies became delocalized in sequence space. Using parameter values that quantitatively captured data of viral diversification in HIV-1 patients, we estimated mu(c) to be 7 x 10(-5) -1 x 10(-4) substitutions/site/replication, similar to 2-6 fold higher than the natural mutation rate of HIV-1, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs. The latter estimate was weakly dependent on the within-host effective population size of HIV-1. With large population sizes and in the absence of recombination, our simulations converged to the quasispecies theory, bridging the gap between quasispecies theory and population genetics-based approaches to describing HIV-1 evolution. Further, mu(c) increased with the recombination rate, rendering HIV-1 less susceptible to error catastrophe, thus elucidating an added benefit of recombination to HIV-1. Our estimate of mu(c) may serve as a quantitative guideline for the use of mutagenic drugs against HIV-1.

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.

q-Gaussian based Smoothed Functional Algorithms for Stochastic Optimization

The q-Gaussian distribution results from maximizing certain generalizations of Shannon entropy under some constraints. The importance of q-Gaussian distributions stems from the fact that they exhibit power-law behavior, and also generalize Gaussian distributions. In this paper, we propose a Smoothed Functional (SF) scheme for gradient estimation using q-Gaussian distribution, and also propose an algorithm for optimization based on the above scheme. Convergence results of the algorithm are presented. Performance of the proposed algorithm is shown by simulation results on a queuing model.

Stochastic optimization for adaptive labor staffing in service systems

Service systems are labor intensive. Further, the workload tends to vary greatly with time. Adapting the staffing levels to the workloads in such systems is nontrivial due to a large number of parameters and operational variations, but crucial for business objectives such as minimal labor inventory. One of the central challenges is to optimize the staffing while maintaining system steady-state and compliance to aggregate SLA constraints. We formulate this problem as a parametrized constrained Markov process and propose a novel stochastic optimization algorithm for solving it. Our algorithm is a multi-timescale stochastic approximation scheme that incorporates a SPSA based algorithm for ‘primal descent' and couples it with a ‘dual ascent' scheme for the Lagrange multipliers. We validate this optimization scheme on five real-life service systems and compare it with a state-of-the-art optimization tool-kit OptQuest. Being two orders of magnitude faster than OptQuest, our scheme is particularly suitable for adaptive labor staffing. Also, we observe that it guarantees convergence and finds better solutions than OptQuest in many cases.

Implication of a Higgs boson at 125 GeV within the stochastic superspace framework

We revisit the issue of considering stochasticity of Grassmannian coordinates in N = 1 superspace, which was analyzed previously by Kobakhidze et al. In this stochastic supersymmetry (SUSY) framework, the soft SUSY breaking terms of the minimal supersymmetric Standard Model (MSSM) such as the bilinear Higgs mixing, trilinear coupling, as well as the gaugino mass parameters are all proportional to a single mass parameter xi, a measure of supersymmetry breaking arising out of stochasticity. While a nonvanishing trilinear coupling at the high scale is a natural outcome of the framework, a favorable signature for obtaining the lighter Higgs boson mass m(h) at 125 GeV, the model produces tachyonic sleptons or staus turning to be too light. The previous analyses took Lambda, the scale at which input parameters are given, to be larger than the gauge coupling unification scale M-G in order to generate acceptable scalar masses radiatively at the electroweak scale. Still, this was inadequate for obtaining m(h) at 125 GeV. We find that Higgs at 125 GeV is highly achievable, provided we are ready to accommodate a nonvanishing scalar mass soft SUSY breaking term similar to what is done in minimal anomaly mediated SUSY breaking (AMSB) in contrast to a pure AMSB setup. Thus, the model can easily accommodate Higgs data, LHC limits of squark masses, WMAP data for dark matter relic density, flavor physics constraints, and XENON100 data. In contrast to the previous analyses, we consider Lambda = M-G, thus avoiding any ambiguities of a post-grand unified theory physics. The idea of stochastic superspace can easily be generalized to various scenarios beyond the MSSM. DOI: 10.1103/PhysRevD.87.035022

Assessing future rainfall projections using multiple GCMs and a multi-site stochastic downscaling model

Impact of global warming on daily rainfall is examined using atmospheric variables from five General Circulation Models (GCMs) and a stochastic downscaling model. Daily rainfall at eleven raingauges over Malaprabha catchment of India and National Center for Environmental Prediction (NCEP) reanalysis data at grid points over the catchment for a continuous time period 1971-2000 (current climate) are used to calibrate the downscaling model. The downscaled rainfall simulations obtained using GCM atmospheric variables corresponding to the IPCC-SRES (Intergovernmental Panel for Climate Change - Special Report on Emission Scenarios) A2 emission scenario for the same period are used to validate the results. Following this, future downscaled rainfall projections are constructed and examined for two 20 year time slices viz. 2055 (i.e. 2046-2065) and 2090 (i.e. 2081-2100). The model results show reasonable skill in simulating the rainfall over the study region for the current climate. The downscaled rainfall projections indicate no significant changes in the rainfall regime in this catchment in the future. More specifically, 2% decrease by 2055 and 5% decrease by 2090 in monsoon (HAS) rainfall compared to the current climate (1971-2000) under global warming conditions are noticed. Also, pre-monsoon (JFMAM) and post-monsoon (OND) rainfall is projected to increase respectively, by 2% in 2055 and 6% in 2090 and, 2% in 2055 and 12% in 2090, over the region. On annual basis slight decreases of 1% and 2% are noted for 2055 and 2090, respectively.

Stochastic analysis of epidemics on adaptive time varying networks

Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an ``adaptive threshold,'' i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.

Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.

Confinement induced stochastic sensing of charged coronene and perylene aggregates in alpha-hemolysin nanochannels

Biological nanopores provide optimum dimensions and an optimal environment to study early aggregation kinetics of charged polyaromatic molecules in the nano-confined regime. It is expected that probing early stages of nucleation will enable us to design a strategy for supramolecular assembly and biocrystallization processes. Specifically, we have studied translocation dynamics of coronene and perylene based salts, through the alpha-hemolysin (alpha-HL) protein nanopore. The characteristic blocking events in the time-series signal are a function of concentration and bias voltage. We argue that different blocking events arise due to different aggregation processes as captured by all atomistic molecular dynamics (MD) simulations. These confinement induced aggregations of polyaromatic chromophores during the different stages of translocation are correlated with the spatial symmetry and charge distribution of the molecules.