Let {X ni , i???1, n???1} be an array of rowwise negatively orthant dependent random variables. Some sufficient conditions for complete convergence for arrays of rowwise negatively orthant dependent random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz?Zygmund type strong law of large numbers for weighted sums of negatively orthant dependent random variables is obtained.

Influence diagrams were originally conceived as a way of visually representing dependencies among random variables. It was recognized that they provide an effective means of communicating probabilistic information in complex, uncertain situations. They we...

We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of non-normal stable laws.

failure domains are optimally enlarged to enable global improvements in ... primary tool for assessing and pursuing acceptable levels of robustness in the control solution. .... a random variable and a random process dependent on p through the plant model. For the ...... the diagram have a bigger impact on the RMS value.

We present a new and simple approach to deviation inequalities for non-product measures, i.e., for dependent random variables. Our method is based on coupling. We illustrate our abstract results with chains with complete connections and Gibbsian random fields, both at high and low temperature.

We investigate Gaussian warped five-dimensional thick braneworlds. Identification of the graviton's wave function in the extra-dimension with a probability distribution function leads to a straightforward probabilistic interpretation of braneworlds. The extra-coordinate $y$ is regarded as a Gaussian-distributed random variable. Hence, all of the field variables and operators which depend on $y$ are, also, randomly distributed. Four-dimensional measurable (macroscopic) quantities are identified with the corresponding averaged values over the Gaussian distribution.

Statistical dependence among random hydraulic variables generally stems from a common meteorological cause. Usually, this dependence increases the probability of occurrence of floods. Therefore, in many (potential) applications in flood risk analysis there is a need for techniques that properly describe the statistical dependence among random variables. This study makes an inventory of existing bivariate correlation models as available from international literature and/or 'Dutch practice' in the design and testing of flood defence structures. Differences in correlation structures are described and quantified. Subsequently, their practical applicability is tested in two case studies.

The Yule-Simpson paradox notes that an association between random variables can be reversed when averaged over a background variable. Cox and Wermuth (2003) introduced the concept of distribution dependence between two random variables X and Y , and developed two dependence conditions, each of which guarantees that reversal cannot occur. Ma, Xie and Geng (2006) studied the collapsibility of distribution dependence over a background variable W, under a rather strong homogeneity condition. Collapsibility ensures the association remains the same for conditional and marginal models, so that Yule-Simpson reversal cannot occur. In this paper, we investigate a more general condition for avoiding e?ect reversal: A-collapsibility. The conditions of Cox and Wermuth imply A-collapsibility, without assuming homogeneity. In fact, we show that, when W is a binary variable, collapsibility is equivalent to A-collapsibility plus homogeneity, and A-collapsibility is equivalent to the conditions of Cox and Wermuth. Recently, Co...

Quantifying cooperation among random variables in predicting a single target random variable is an important problem in many biological systems with 10s to 1000s of co-dependent variables. We review the prior literature of information theoretical measures of synergy and introduce a novel synergy measure, entitled *synergistic mutual information* and compare it against the three existing measures of cooperation. We apply all four measures against a suite of binary circuits to demonstrate our measure alone quantifies the intuitive concept of synergy across all examples.

We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This lemma provides an alternative tool to Hoeffding-Azuma inequality to bound concentration of martingale values. Our second approach is based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis. We also introduce a way to apply PAC-Bayesian analysis in situation of limited feedback. We combine the new tools to derive PAC-Bayesian generalization and regret bounds for the multiarmed bandit problem. Although our regret bound is not yet as tight as state-of-the-art regret bounds based on other well-established techniques, our results significantly expand the range of potential applications of PAC-Bayesian analysis and introduce a new analysis tool to reinforcement learning and many ...

We investigate the relative information content of six measures of dependence between two random variables $X$ and $Y$ for large or extreme events for several models of interest for financial time series. The six measures of dependence are respectively the linear correlation $\\rho^+_v$ and Spearman's rho $\\rho_s(v)$ conditioned on signed exceedance of one variable above the threshold $v$, or on both variables ($\\rho_u$), the linear correlation $\\rho^s_v$ conditioned on absolute value exceedance (or large volatility) of one variable, the so-called asymptotic tail-dependence $\\lambda$ and a probability-weighted tail dependence coefficient ${\\bar \\lambda}$. The models are the bivariate Gaussian distribution, the bivariate Student's distribution, and the factor model for various distributions of the factor. We offer explicit analytical formulas as well as numerical estimations for these six measures of dependence in the limit where $v$ and $u$ go to infinity. This provides a quantitative proof that conditioning o...

In this paper we derive explicit expressions for the probability of ruin in a renewal risk model with dependence described-by/incorporated-in the real-valued random variable Zk = ?c?k + Xk , namely the loss between the (k ? 1)–th and the k–th claim. Here c represents the constant premium rate, ?k th...

We prove general exponential moment inequalities for averages of [0,1]-valued iid random variables and use them to tighten the PAC Bayesian Theorem. The logarithmic dependence on the sample count in the enumerator of the PAC Bayesian bound is halved.

This report discusses the following topics: Acoustical nondestructive evaluation of heterogeneous materials in the multiple scattering regime. Classical and quantum superdiffusion in a time-dependent random potential. Negative Magnetoresistance in Variable Range Hopping Conduction. Reproducible Conductance Fluctuations in Macroscopic Anderson Insulators. Feasibility of far-infared lasers using multiple semiconductor quantum wells.

We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion.

The ?-stable distributions introduced by Lévy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life sciences, and economics. In the present paper we study sequences of long-range dependent random variables whose distributions h...

The stochastic collocation method has recently received much attention for solving partial differential equations posed with uncertainty, i.e., where coefficients in the differential operator, boundary terms or right-hand sides are random fields. Recent work has led to the formulation of an adaptive collocation method that is capable of accurately approximating functions with discontinuities and steep gradients. These methods, however, usually depend on an assumption that the random variables involved in expressing the uncertainty are independent with marginal probability distributions that are known explicitly. In this work we combine the adaptive collocation technique with kernel density estimation to approximate the statistics of the solution when the joint distribution of the random va...

We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this “the Statistical Drake Equation”. The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. ...

The Harris-Luck criterion judges the relevance of (potentially) spatially correlated, quenched disorder induced by, e.g., random bonds, randomly diluted sites or a quasi-periodicity of the lattice, for altering the critical behavior of a coupled matter system. We investigate the applicability of this type of criterion to the case of spin variables coupled to random lattices. Their aptitude to alter critical behavior depends on the degree of spatial correlations present, which is quantified by a wandering exponent. We consider the cases of Poissonian random graphs resulting from the Voronoi-Delaunay construction and of planar, ``fat'' $\\phi^3$ Feynman diagrams and precisely determine their wandering exponents. The resulting predictions are compared to various exact and numerical results for the Potts model coupled to these quenched ensembles of random graphs.

This paper introduces a Duration Hidden Markov Model to model bull and bear market regime switches in the stock market; the duration of each state of the Markov Chain is a random variable that depends on a set of exogenous variables. The model not only allows the endogenous determination of the different regimes and but also estimates the effect of the explanatory variables on the regimes' durations. The model is estimated here on NYSE returns using the short-term interest rate and the interest rate spread as exogenous variables. The bull market regime is assigned to the identified state with the higher mean and lower variance; bull market duration is found to be negatively dependent on short-term interest rates and positively on the interest rate spread, while bear market duration depends positively the short-term interest rate and negatively on the interest rate spread.

The spatial variability of the polarization dynamics in thin film ferroelectric capacitors was probed by recognition analysis of spatially resolved spectroscopic data. Switching spectroscopy piezoresponse force microscopy (SSPFM) was used to measure local hysteresis loops and map them on a two dimensional (2D) random-bond, random-field Ising model. A neural-network based recognition approach was utilized to analyze the hysteresis loops and their spatial variability. Strong variability is observed in the polarization dynamics around macroscopic cracks because of the modified local-elastic and electric-boundary conditions, with the most pronounced effect on the length scale of ˜100 nm away from the crack. The recognition approach developed here is universal and can potentially be applied for arbitrary macroscopic and spatially resolved data, including temperature- and field-dependent hysteresis, I-V curve mapping, electron microscopy electron energy loss spectroscopy (EELS) imaging, and many others.

Abstract We study depth properties of a general class of random recursive trees where each node i attaches to the random node \\documentclass{article} \\usepackage{mathrsfs, amsmath, amssymb}\\pagestyle{empty} \\begin{document} \\begin{align*}\\left\\lfloor iX_i\\right\\rfloor\\end{align*} \\end{document}and X0,-,Xn is a sequence of i.i.d. random variables taking values in [0,1). We call such trees scaled attachment random recursive trees (sarrt). We prove that the typical depth Dn, the maximum depth (or height) Hn and the minimum depth Mn of a sarrt are asymptotically given by Dn --1 log n, Hn - max log n and Mn - min log n where ,max and min are constants depending only on the distribution of X0 whenever X0 has a density. In particular, this gives a new elementary proof for the height of uniform ra...

Summary In a recent paper, Gaugler and Akritas (unpublished manuscript) considered testing for no main effect in a two-factor mixed effects design when the traditional assumptions do not hold. Here we extend the nonparametric modeling to the random effects design and consider the problem of testing for no interaction effect. The new models for these designs allow for dependence among the random effects, heteroscedasticity in the error and interaction terms, and do not require normality. At a more systemic level, these models differ from the classical ones in that they do not consider the random interaction term as an additional, extraneous source of variability. The proposed test procedure applies to settings where the random factor in the case of the mixed model or at least one of the ran...

This paper is concerned with the reliable inference of optimal tree-approximations to the dependency structure of an unknown distribution generating data. The traditional approach to the problem measures the dependency strength between random variables by the index called mutual information. In this paper reliability is achieved by Walley's imprecise Dirichlet model, which generalizes Bayesian learning with Dirichlet priors. Adopting the imprecise Dirichlet model results in posterior interval expectation for mutual information, and in a set of plausible trees consistent with the data. Reliable inference about the actual tree is achieved by focusing on the substructure common to all the plausible trees. We develop an exact algorithm that infers the substructure in time O(m^4), m being the number of random variables. The new algorithm is applied to a set of data sampled from a known distribution. The method is shown to reliably infer edges of the actual tree even when the data are very scarce, unlike the tradit...

Let X/sub 1/,..., X/sub n/ be independent random variables with distributions depending on a possibly multidimensional theta. Let Y be an unobserved continuously distributed random variable whose distribution depends on theta. A tolerance interval for Y is desired, satisfying P(Yepsilon I(X/sub 1/,...,X/sub n/)) = ..beta... A naive interval would estimate theta from the X's, and construct the interval assuming that the estimate is exactly correct. This paper assumes standard regularity conditions, and uses Taylor approximations to construct correction terms of order l/n. The resulting interval is longer than the naive interval, because it takes into account the uncertainty in the estimate of theta. Two examples, one simple and one complex, illustrate the method.

In this paper, we investigate the precise large deviations for sums of independent identically distributed random variables with heavy-tailed distributions. We prove asymptotic relations for non-random sums and for random sums of random variables with long-tailed distributions. We apply the results on two useful counting processes, namely, renewal and compound-renewal processes.

For N=1,2,..., let S_N be a simple random sample of size n=n_N from a population A_N of size N, where 0= 0, the high order correlations Corr(k) = E (\\prod_{A \\in H} (1_A-f_N)) depend only on k, and if the sampling fraction f_N -> f as N -> infinity, then N^{k/2}Corr(k) -> [f(f-1)]^{k/2}EZ^k, k even and N^{(k+1)/2}Corr(k) -> [f(f-1)]^{(k-1)/2}(2f-1)(1/3)(k-1)EZ^{k+1}, k odd where Z is a standard normal random variable. This proves a conjecture given in [2].

Markov Random Field (MRF) models are powerful tools for contextual modeling. However, little is known about how the spatial dependence between its elements is encoded in terms of statistical information, more precisely, information-theoretic measures. In this paper, we enlight the connection between Fisher information, Shannon entropy and spatial properties of the random field in the case of Gaussian variables (a Gaussian Markov random field), by defining analytical expressions to compute the local and global versions of these measures using Besag's pseudo-likelihood function (conditional independence assumption). Besides, we use the derived expressions to define an exact expression for the asymptotic variance of the maximum pseudo-likelihood estimator of the spatial dependence parameter, showing that it does not reach the Cramer-R\\'ao lower bound, since information equality fails. The obtained results provide a rich framework for extraction of relevant statistical information in a variety of MRF applications...

We study the heat equation with a random potential term. The potential is a one-sided stable noise, with positive jumps, which does not depend on time. To avoid singularities, we define the equation in terms of a construction similar to the Skorokhod integral or Wick product. We give a criterion for existence based on the dimension of the space variable, and the parameter p of the stable noise. Our arguments are different for p1.

The paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model. The model considers time-dependent latent variables and item-specific random effects to be accountable for the interdependencies of the multivariate ordinal items. Time-dependent latent variables are linked with an autoregressive model. Simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood. Model selection criteria developed for composite likelihood estimation are used in the applications. Furthermore, lower-order residuals are used as measures-of-fit for the selected models.

Vehicle routing is an important combinatorial optimization problem. In real transport networks,the travel speed and travel time of roads have large time-variability and randomness. The study of vehicle routing problem in time-dependent network has even more practical value than static network VRP problem. This paper combines the features of time-dependent networks and gives the mathematical models of the time-dependent vehicle routing problem. On this basis, the traditional ant colony optimization algorithm is improved. A new path transfer strategy of ants and new dynamic pheromone update strategy applicable to time-dependent network are proposed. Based on these strategies, the improved ant colony algorithm is given for solving the vehicle routing problem in time-dependent networks. The simulation results show that the algorithm can effectively solve the vehicle routing problem in time-dependent network and has better computational efficiency and convergence speed.   

ABSTRACT: BACKGROUND: In addition to selection, the process of evolution is accompanied by stochastic effects, such as changing environmental conditions, genetic drift and mutations. Commonly it is believed that without genetic drift, advantageous mutations quickly fixate in a halpoid population due to strong selection and lead to a continuous increase of the average fitness. This conclusion is based on the assumption of constant fitness. However, for frequency dependent fitness, where the fitness of an individual depends on the interactions with other individuals in the population, this does not hold. RESULTS: We propose a mathematical model that allows to understand the consequences of random frequency dependent mutations on the dynamics of an infinite large population. The frequencies of different types change according to the replicator equations and the fitness of a mutant is random and frequency dependent. To capture the interactions of different types, we employ a payoff matrix of variable size and thus are able to accommodate an arbitrary number of mutations. We assume that at most one mutant type arises at a time. The payoff entries to describe the mutant type are random variables obeying a probability distribution which is related to the fitness of the parent type. CONCLUSIONS: We show that a random mutant can decrease the average fitness under frequency dependent selection, based on analytical results for two types, and on simulations for n types. Interestingly, in the case of at most two types the probabilities to increase or decrease the average fitness are independent of the concrete probability density function. Instead, they only depend on the probability that the payoff entries of the mutant are larger than the payoff entries of the parent type. PMID:22935138

A discrete-time Markov process can be compactly modeled as a dynamic Bayesian network (DBN)--a graphical model with nodes representing random variables and directed edges indicating causality between variables. Each node has a probability distribution, conditional on the variables represented by the parent nodes. A DBN's graphical structure encodes fixed conditional dependencies between variables. But in real-world systems, conditional dependencies between variables may be unknown a priori or may vary over time. Model errors can result if the DBN fails to capture all possible interactions between variables. Thus, we explore the representational framework of adaptive DBNs, whose structure and parameters can change from one time step to the next: a distribution's parameters and its set of conditional variables are dynamic. This work builds on recent work in nonparametric Bayesian modeling, such as hierarchical Dirichlet processes, infinite-state hidden Markov networks and structured priors for Bayes net learning. In this paper, we will explain the motivation for our interest in adaptive DBNs, show how popular nonparametric methods are combined to formulate the foundations for adaptive DBNs, and present preliminary results.

This paper proposes a novel statistical approach to intelligent document retrieval. It seeks to offer a more structured and extensible mathematical approach to the term generalization done in the popular Latent Semantic Analysis (LSA) approach to document indexing. A Markov Random Field (MRF) is presented that captures relationships between terms and documents as probabilistic dependence assumptions between random variables. From there, it uses the MRF-Gibbs equivalence to derive joint probabilities as well as local probabilities for document variables. A parameter learning method is proposed that utilizes rank reduction with singular value decomposition in a matter similar to LSA to reduce dimensionality of document-term relationships to that of a latent topic space. Experimental results confirm the ability of this approach to effectively and efficiently retrieve documents from substantial data sets.

where $D(P_{S_n}\\|{Po}(\\lambda))$ is the relative entropy between the distribution of $S_n$ and the Poisson($\\lambda$) distribution. The first term in this bound measures the individual smallness of the $X_i$ and the second term measures their dependence. This result can be thought of as a ``maximum entropy'' statement: Under suitable conditions, the distribution of $S_n$ converges to the distribution which has maximal entropy among all those that can be obtained as sums of independent binary random variables with fixed mean $\\lambda$. We outline a general method for obtaining corresponding bounds when approximating the distribution of a sum of general discrete random variables by an infinitely divisible distribution. Second, in the particular case when the $X_i$ are independent, we obtain a sharper bound in total variation,

This paper presents an evaluation of seismic capacity of a group of vertical U-tube type heat exchangers (HXs) with support frames to contribute to refinement of seismic capacity data for seismic Probabilistic Safety Assessment (PSA) in Japan. According to usual practice of seismic PSAs, capacity of component is represented as a log-normally distributed random variable defined by a median and logarithmic standard deviations (LSDs), which represent inherent randomness about the median, {beta} {sub r}, and uncertainty in the median due to lack of knowledge, {beta} {sub u}. Using design specifications of four HXs for residual heat removal systems of 1100 MWe BWRs, the authors evaluated a generic capacity of HXs with a LSD for uncertainty due to lack of knowledge to take into account design variability. The median capacity was evaluated by the use of a time history response analysis with a detailed model for a selected representative HX, which was extended from a model used in seismic design. The LSD for uncertainty due to lack of knowledge was evaluated with consideration of the variabilities in three influential design parameters, i.e., diameter of anchor bolt, weight of HX and position of center of gravity of HX with the detailed model and a simplified static model. The LSD for uncertainty due to randomness was determined from the variability in material property. The dominant failure mode of HXs was identified as the failure of anchor bolts of lugs mainly due to shearing stress. The capacity expressed in terms of zero period acceleration on the foundation of HX was evaluated to be 4180 Gal (4.3 g) for median, LSD for uncertainty due to randomness was 0.11 and LSD due to lack of knowledge was 0.21-0.53 depending on combination of the variabilities in design parameters to be considered.

Under the current regulatory guidelines for banks and insurance companies, the quantification of diversification benefits due to risk aggregation plays a prominent role. In this paper we establish second-order approximation of risk concentration associated with a random vector X:=(X1,X2,...,Xd) in terms of Value at Risk (VaR) within the methodological framework of second-order regular variation and the theory of Archimedean copula. Moreover, we find that the rate of convergence of the first-order approximation of risk concentration depends on the the interplay between the tail behavior of the marginal loss random variables and their dependence structure. Specifically, we find that the rate of convergence is determined by either the second-order parameter (1) of Archimedean copula generator...

The present dissertation is concerned with phenomena in the field of Random Walk in Random Environment (RWRE) and Branching Random Walks in Random Environment (BRWRE). RWRE models the movement of a particle, the randomness of which depends on the transition probabilities given at its present posit...

In diploid populations the genetic variability is largely encoded in the single nucleotide polymorphisms (SNPs).As genes are integrated in biological networks and pathways, also polymorphic loci affecting expression or function of genes do not act independently but are rather linked in a functional or epistatic network. Genome wide association studies already reveal several examples of functionally associated SNPs, indicated by significant linkage disequilibrium. Therefore, in this paper we develop a multi-locus evolutionary theory of sexually reproducing diploid populations driven by a fitness function defined on the epistatic network of genetic loci. In particular we study the genetic variability as the trade-off between random recombination, which tends to increase variability in the population, and selection that tends to reduce it. We are able to show that, since the fitness landscape is rugged, the stationary states of the population are multiple and depend on the initial conditions of the evolutionary ...

We compute the joint probability density function (jpdf) P N ( M, ? M ) of the maximum M and its position ? M for N non-intersecting Brownian excursions, on the unit time interval, in the large N limit. For N??, this jpdf is peaked around M = ?{2N} and ? M =1/2, while the typical fluctuations behave for large N like M - ?{2N} ? s N^{-1/6} and ? M -1/2? wN -1/3 where s and w are correlated random variables. One obtains an explicit expression of the limiting jpdf P( s, w) in terms of the Tracy-Widom distribution for the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory and a psi-function for the Hastings-McLeod solution to the Painlevé II equation. Our result yields, up to a rescaling of the random variables s and w, an expression for the jpdf of the maximum and its position for the Airy2 process minus a parabola. This latter describes the fluctuations in many different physical systems belonging to the Kardar-Parisi-Zhang (KPZ) universality class in 1+1 dimensions. In particular, the marginal probability density function (pdf) P( w) yields, up to a model dependent length scale, the distribution of the endpoint of the directed polymer in a random medium with one free end, at zero temperature. In the large w limit one shows the asymptotic behavior log P( w)˜- w 3/12.

Effects of applied stresses and electrochemical potential on random variables of time to initiation t{sub i}, time to crack propagation t{sub c} and time to fracture t{sub f} of zircaloy-2 in 1N-HCl solution have been analyzed by Weibull distribution method based on a stochastic process theory. The Weibull distribution of the random variables was measured during constant load stress corrosion cracking (SCC). The constant load SCC process is analyzed by assuming a probabilistic state transition model. The random variables of t{sub i}, t{sub c} and t{sub f} of zircaloy-2 alloy are found to be obey the single Weibull distribution with location parameters, and the constant load SCC phenomena can be analyzed as a function of the applied stress and electrochemical potential dependencies of Weibull's parameters. The constant load SCC is found to obey the model of probabilistic state transition. The constant load SCC process which obeys the model of probabilistic state transition, is found to be effective for estimation of accelerated SCC condition. (author).

Suppose that one can observe bivariate random variables (L,X) only when L X holds. Such data are called left-truncated data and found in many fields, such as experimental education and epidemiology. Recently, a method of fitting a parametric model on (L,X) has been considered, which can easily incorporate the dependent structure between the two variables. A primary concern for the parametric analysis is the goodness-of-fit for the imposed parametric forms. Due to the complexity of dependent truncation models, the traditional goodness-of-fit procedures, such as Kolmogorov-Smirnov type tests based on the Bootstrap approximation to null distribution, may not be computationally feasible. In this paper, we develop a computationally attractive and reliable algorithm for the goodness-of-fit test ...

The probability Psuccess(alpha, N) that stochastic greedy algorithms successfully solve the random SATisfiability problem is studied as a function of the ratio alpha of constraints per variable and the number N of variables. These algorithms assign variables according to the unit-propagation (UP) rule in presence of constraints involving a unique variable (1-clauses), to some heuristic (H) prescription otherwise. In the infinite N limit, Psuccess vanishes at some critical ratio alpha\\_H which depends on the heuristic H. We show that the critical behaviour is determined by the UP rule only. In the case where only constraints with 2 and 3 variables are present, we give the phase diagram and identify two universality classes: the power law class, where Psuccess[alpha\\_H (1+epsilon N^{-1/3}), N] ~ A(epsilon)/N^gamma; the stretched exponential class, where Psuccess[alpha\\_H (1+epsilon N^{-1/3}), N] ~ exp[-N^{1/6} Phi(epsilon)]. Which class is selected depends on the characteristic parameters of input data. The cri...

An experimental study has been performed in order to evaluate the relative contribution of several relevant parameters on the cyclic variability in spark ignition engines. The cyclic variability has been examined via five major different pressure-related identifier, i.e. P{sub max}, {theta}{sub Pmax}, IMEP, (dp/d{theta}){sub max} and {theta}(dp/d{theta}){sub max}. Due to their high sensitivity to small fluctuation in the operating conditions, the two latter were found to be problematic in the characterization of the cyclic variability. The identifier (dp/d{theta}) max was found to be highly correlated to P{sub max}. MBT ignition resulted in minimal cyclic variability. Variations in the ignition timing were found, however, to be less important under early ignition condition than under retarded ignition condition. The standard deviation of the spark jitter was found to be around 1.7 degrees and therefore cannot be ignored. Noticeable cyclic variations were observed also under motoring conditions which indicated that the role of the valves and rings leakage cannot be neglected. The spark energy and spark duration were found to be less important than suggested in the literature. On the contrary, the spark plug kind and its orientation were found to be very significant in determining the cyclic variability. This supports the idea that random fluctuations in the flow field due to the turbulence of the flow in the cylinder are important. These spatial fluctuations, that are also time-dependent, contribute to the imperfect mixing of the cylinder content, partial stratification, random convection of the spark kernel away from the electrodes, random heat transfer from the burning kernel to the spark electrodes, etc.

Acupuncture has been shown to exhibit distinct effects on the autonomic nervous system. We tested whether the autonomic and psychological response to acupuncture depends on the stimulation dose and the personality of the treated subjects. 52 healthy subjects were randomized to receive either low dose (one needle at point Hegu bilaterally) or high dose (additional 4 needles at non-acupoints bilaterally) acupuncture stimulation after stratification according to their personality to ''reduce'' or ''augment'' incoming stimuli. Outcomes were changes of electrodermal activity (EDA), high frequency component of heart rate variability, heart rate, mean arterial blood pressure, respiration rate and subjective parameters for psychological well being and perceived intensity of needling. Electrodermal...

Wadis are arid region drainage basins, mostly in the Quaternary depositions of different facies and grain size distributions depending on the paleogeologic environmental processes. Random and heterogeneous setup of the subsurface geological layer composition gives rather independent, haphazard and different aquifer numerical properties even along short distances. The aquifer storativity and transmissivity estimations from a set of wells provide spatial variability feature that can be captured by probability and statistical methodologies leading to risk assessment. Three methodologies are employed for the uncertainty assessments in this paper. The heterogeneity can be treated either through deterministic formulations by a set of assumptions or by statistical and probabilistic approaches giv...

Propagation of monochromatic electromagnetic waves in free space results in a widening of the spectral line. On the contrary, propagation preserves monochromaticity in the case of acoustic waves. In this case, the propagation can be modelled by a linear invariant filter leading to attenuations and phases changes. Due to the Beer-Lambert law, the associated transfer function is an exponential of power functions with frequency-dependent parameters. In recent papers, we have proved that the acoustic propagation time can be modelled as a random variable following a stable probability distribution. In this paper, we show that the same model can be applied to the propagation in coaxial cables.

The central limit theorem (CLT) for degenerate U-statistics with a variable symmetric kernel function has been studied under dependence by many authors, since it has many important applications in nonparametric estimation and testing problems [see, e.g. Takahata, H., and Yoshihara, K. (1987), 'Central Limit Theorems for Integrated Square Error of Nonparametric Density Estimators Based on a Absolutely Regular Random Sequences', Yokohama Mathematical Journal, 35, 95-111; Yoshihara, K. (1989), 'Limiting Behavior of Generalized Quadratic Forms Generated by Absolutely Regular Sequences II', Yokohama Mathematical Journal, 37, 109-123. Yoshihara, K. (1992), 'Limiting Behavior of Generalized Quadratic Forms Generated by Absolutely Regular Sequences III', Yokohama Mathematical Journal, 40, 1-9; Fan...

Whether self-reported lifetime civilian and war-related potential traumatic events are associated with widespread pain (WP) and if so, whether the association is attributable to posttraumatic stress disorder (PTSD) and depression has not been studied in a representative sample of the general population. In a randomly selected sample of the German general population, persons aged 60-85years answered validated self-rating instruments: Regional Pain Scale, trauma list of the Composite International Diagnostic Interview, Posttraumatic Diagnostic Scale, and Patient Health Questionnaire 2. Participants with WP were compared with participants with no or local or regional pain (controls). Stepwise hierarchical logistic regression analyses were performed with WP as the dependent variable and demogr...

The waveform morphology of intracranial pressure (ICP) pulses holds essential information about intracranial and cerebrovascular pathophysiologies. Automatic analysis of the ICP waveforms may help to predict abnormal increase of ICP and thus prevent severe complications in patients treated for traumatic brain injuries (TBIs). This article describes a probabilistic framework to track the ICP waveform morphology in real time. The model represents the correlation between different ICP morphological metrics extracted within a single pulse as well as the temporal dependence of metrics extracted between successive pulses. Morphological tracking is solved using Bayesian inference in a dynamic graphical model that associates a random variable to each morphological metric. PMID:22481746

In this article, the prediction problem of categorical spatial data, that is, the estimation of class occurrence probability for (target) locations with unknown class labels given observed class labels at sample (source) locations, is analyzed in the framework of generalized linear mixed models, where intermediate, latent (unobservable) spatially correlated Gaussian variables (random effects) are assumed for the observable non-Gaussian responses to account for spatial dependence information. Within such a framework, a spatial multinomial logistic mixed model is proposed specifically to model categorical spatial data. Analogous to the dual form of kriging family, the proposed model is represented as a multinomial logistic function of spatial covariances between target and source locations. ...

Fluorescent dichroic fibers randomly incorporated within a media provide an improved method for authentication and counterfeiting protection. The dichroism is provided by an alignment of fluorescent molecules along the length of the fibers. The fluorescent fibers provide an authentication mechanism of varying levels of capability. The authentication signature depends on four parameters; the x,y position, the dichroism and the local environment. The availability of so many non-deterministic variables makes production of counterfeit articles (e.g., currency, credit cards, etc.) essentially impossible. Counterfeit-resistant articles, an apparatus for authenticating articles, and a process for forming counterfeit-resistant media are also provided.

Let X be a continuous random variable. We study the characteristic function and moments of the integer-valued random variable obtained by rounding X+a to the nearest smallest integer, where a is a constant. The results can be regarded as exact versions of Sheppard's correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variable. This leads to oscillatory terms in asymptotics for these variables, something that often has been observed, for example in the analysis of several algorithms. We give some examples, including applications to tries, digital search trees and Patricia tries.

In this paper, an inventory policy for an item is presented with inflation and selling price dependent demand under deterministic and random planning horizons allowing and not allowing shortages. In addition, there is a provision for (i) an immediate part payment (variable) to the wholesaler, (ii) borrowing some money from money lending source for the immediate part payment, (iii) earning a discount on purchasing price and relaxation on credit period from the wholesaler against the advance payment and (iv) delay in payment for the rest allowed by wholesaler. The payment to the source is made at the end of the business period with some interest charged. Against the above conjectures, inventory models under the finite (crisp) and random planning horizons have been formulated with respect to ...

The `shock in jet' model for cm-waveband blazar variability is revisited, allowing for arbitrary shock orientation with respect to the jet flow direction, and both random and ordered magnetic field. It is shown that oblique shocks can explain events with swings in polarization position angle much less than the 90 deg. associated with transverse structures, while retaining the general characteristics of outbursts, including spectral behavior and level of peak percentage polarization. Models dominated by a force-free, minimum energy magnetic field configuration (essentially helical) display a shallow rise in percentage polarization and frequency dependent swing in polarization position angle not in agreement with the results of single-dish monitoring observations, implying that the field is predominantly random in the quiescent state. Outbursts well-explained by the `shock in jet' model are present during gamma-ray flaring in several sources, supporting the idea that shock events are responsible for activity fr...

In recent years there has been a surge of interest in the statistics of record-breaking events in stochastic processes. Along with that, many new and interesting applications of the theory of records were discovered and explored. The record statistics of uncorrelated random variables sampled from time-dependent distributions was studied extensively. The findings were applied in various areas to model and explain record-breaking events in observational data. Particularly interesting and fruitful was the study of record-breaking temperatures and their connection with global warming, but also records in sports, biology and some areas in physics were considered in the last years. Similarly, researchers have recently started to understand the record statistics of correlated processes such as random walks, which can be helpful to model record events in financial time series. This review is an attempt to summarize and evaluate the progress that was made in the field of record statistics throughout the last years.

Previous studies on heart rate variability (HRV) using chaos theory, fractal scaling analysis, and many other methods, while fruitful in many aspects, have produced much confusion in the literature. Especially the issue of whether normal HRV is chaotic or stochastic remains highly controversial. Here, we employ a new multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE), to characterize HRV. SDLE has been shown to readily characterize major models of complex time series including deterministic chaos, noisy chaos, stochastic oscillations, random 1/f processes, random Levy processes, and complex time series with multiple scaling behaviors. Here we use SDLE to characterize the relative importance of nonlinear, chaotic, and stochastic dynamics in HRV of healthy, congestive heart failure, and atrial fibrillation subjects. We show that while HRV data of all these three types are mostly stochastic, the stochasticity is different among the three groups.

An extension to two space dimensions of the gradient random walk algorithm for reaction-diffusion equations is presented. This family of algorithms is related closely to the random vortex method of computational fluid dynamics. Although the computational cost is high, the method has the desirable features of being grid free and of automatically adapting to the solution by concentrating elements where the gradient is large. In addition, the method can be extended easily to more than two space dimensions. A key feature of the method is discretization in terms of the dependent, rather than independent, variable, giving it features in common with Lagrangian particle methods. The method is derived here and its application to some simple reaction-diffusion wave propagation problems is illustrated.

A two-group randomized multivariate analysis of covariance (MANCOVA) was used to investigate the effects of cognitive-behavioral hypnosis in reducing test anxiety and improving academic performance in comparison to a Hawthorne control group. Subjects were enrolled in a rigorous introductory psychology course which covered an entire text in one quarter. In addition to randomization, two covariates were used as a statistical control for the selection threat to internal validity. The subjects were measured on two covariates and two dependent variables. The covariates were a midterm course grade for introductory psychology and a pretest on the Test Anxiety Inventory. There were a decrease in test anxiety and improvements in achievement for the hypnosis group. The treatment gains were maintained at a 6-week follow-up. The study suggests that cognitive-behavioral hypnosis is effective in reducing test anxiety and in improving academic performance. Contains 15 references. (Author/GLR)

A random hopping on a fractal network with dimension slightly above one, $d = 1 + \\epsilon$, is considered as a model of transport for conducting polymers with nonmetallic conductivity. Within the real space renormalization group method of Migdal and Kadanoff, the critical behavior near the percolation threshold is studied. In contrast to a conventional regular expansion in ^{-1}+O(e^{-1/\\epsilon })$, and of conductivity, $t\\simeq \\epsilon^{-2} exp (-1-1/\\epsilon )$, are found to be nonanalytic functions of $\\epsilon$ as obtained to be gaussian with the relative width $\\sim \\exp (-1/\\epsilon )$. In case of variable range hopping an ``1-d Mott's law'' $exp [ -( T_t/T)^{1/2}]$ dependence was found for the DC conductivity. It is shown, that the same type of strong temperature dependence is valid for the dielectric constant and the frequency-dependent conductivity, in agreement with experimental data for poorly conducting polymers.

Markov Random Fields (MRF's) have been extensively applied in Statistical Mechanics as well as in Bayesian Image Analysis. MRF's are a special class of dependent random variables located at the vertices of a graph whose joint distribution includes a parameter called the temperature. When the number of vertices of the graph tends to infinity, the normalized distribution of statistics based on these random variables converge in distribution. It can happen that for certain values of the temperature, that the rate of growth of these normalizing constants change drastically. This feature is generally used to explain the phenomenon of phase transition as understood by physicist. In this dissertation the author will show that this drastic change in normalizing constants occurs even in the relatively smooth case when all the random variables are Gaussian. Hence any image analytic MRF ought to be checked for such discontinuous behavior before any analysis is performed. Mixed limit theorems in Bayesian Image Analysis seek to replace intensive simulations of MRF's with limit theorems that approximate the distribution of the MRF's as the number of sites increases. The problem of deriving mixed limit theorems for MRF's on a one dimensional lattice graph with an acceptor function that has a second moment has been studied by Chow. A mixed limit theorem for the integer lattice graph is derived when the acceptor function does not have a second moment as for instance when the acceptor function is a symmetric stable density of index 0 < {alpha} < 2.

Modeling of random cyclic strain-life (CSL) relations of engineering material should be a basis of strain-based fatigue reliability analysis. A statistical model for the relations of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal under temperature of 240 deg. C, is presented. In the model, a verified distribution, i.e. lognormal distribution, is used as an appropriate assumed distribution of the material fatigue life data. Based on the Coffin-Manson law, the relations are modeled by mean value- and standard deviation-cyclic curves of the logarithm of fatigue life. Then, fatigue analysis at an arbitrarily given probability can be made conveniently according to the normal distribution function. An approach for estimating the curves and their confidence bounds is developed by a linear regression technique. Different from the existent reliability analysis methods that considered the material constants in the law as independently random variables, present work treats them as dependently random variables from the fit of test data. Availability of the model has been indicated by an analysis of the material test data.

A study developed a multiple regression prediction equation for each of six selected achievement variables in a popular standardized test of achievement. Subjects, 42 fourth-grade pupils randomly selected across several classes in a large elementary school in a north Florida city, were administered several standardized tests to determine predictor variables of vocabulary, general information (prior learning), arithmetic, word recognition, and listening skills. The dependent variables (reading vocabulary, reading comprehension, language total, math total, science, and social studies) were measured using subtests or combinations of subtests of the California Achievement Test, Form E. Data were processed by computer programs and yielded mean scores, a correlation matrix, multiple correlations, and regression prediction formulas for each dependent variable. The multiple correlations obtained ranged from a low of .77 for reading vocabulary to a high of .87 for mathematics total. Each regression equation also had its own constant. Suggestions are offered for improving students' word recognition skills, listening skills, and the quantity and quality of their stores of vocabulary and general information. (Three tables of data are included; 23 references are attached.) (RS)

System effects are often found in structural timber systems, e.g. due to transverse load distribution between different structural members. System effects are also related to the variation of strength and stiffness within and between members. Most studies found in the literature have been based on linear-elastic theory and the variability has been considered between timber members, but the variability within members has been neglected mainly because of lack of data. In this paper, Monte Carlo simulations of a W-truss are performed using a model describing the variability of strength and stiffness parameters between and within timber members for Norway spruce, Picea Abies. The timber members are connected by punched metal plate fasteners (nail plates). The variations in the properties of these joints have been estimated from experiments. The FE calculations are performed by TrussLab - a toolbox for MATLAB developed at Aalborg University. TrussLab considers contact between timber members and non-linear behaviour of the joints. The timber members are given linear properties. The system effect is estimated through a comparison of the simulations with a deterministic calculation of the roof truss using characteristic values as input to the model. The system effect is also determined on the basis of reliability analyses. The found system effect depends on the coefficient of variation, the distribution of the random load variable and the reliability level. Depending on the assumptions, the system effect was found to be in the interval 8% to 25%.

In the paper, we present some Baum?Katz type results for Formula Not Shown -mixing random variables with different distributions. Partial results generalize the corresponding one of Shao (Acta Math Sin 31(6):736?747, 1988). In addition, the Marcinkiewicz strong law of large numbers for Formula Not Shown -mixing random variables with different distributions is obtained.

Fix ?>0, denote by G(v/2) a Gamma random variable with parameter v/2, and let n?2 be a fixed even integer. Consider a sequence (F_k) of square integrable random variables, belonging to the nth Wiener chaos of a given Gaussian process and with variance converging to 2v. As k goes to infinity, we prov...

We obtain a new probabilistic representation for the solution of the heat equation in terms of a product for smooth random variables which is introduced and studied in this paper. This multiplication, expressed in terms of the Hida-Malliavin derivatives of the random variables involved, exhibits many useful properties which are to some extents opposite to some peculiar features of the Wick product.

Consider an $n \\times n$ non-Hermitian random matrix $M_n$ whose entries are independent real random variables. Under suitable conditions on the entries, we study the fluctuations of the diagonal elements of the matrix $f(M_n)$ where $f$ is analytic on an appropriate domain. This extends the results for symmetric random matrices to the non-Hermitian case.

In financial markets, not only prices and returns can be considered as random variables, but also the waiting time between two transactions varies randomly. In the following, we analyse the statistical properties of General Electric stock prices, traded at NYSE, in October 1999. These properties are critically revised in the framework of theoretical predictions based on a continuous-time random walk model.

We study the influence of fluctuations in molecular shape on the stability of the biaxial nematic phase by generalizing the mean field model of Mulder and Ruijgrok [Physica A {\\bf 113}, 145 (1982)]. We limit ourselves to the case when the molecular shape anisotropy, represented by the alignment tensor, is a random variable of an annealed type. A prototype of such behavior can be found in lyotropic systems - a mixture of potassium laurate, 1-decanol, and $D_2O$, where distribution of the micellar shape adjusts to actual equilibrium conditions. Further examples of materials with the biaxial nematic phase, where molecular shape is subject to fluctuations, are thermotropic materials composed of flexible trimeric- or tetrapod-like molecular units. Our calculations show that the Gaussian equilibrium distribution of the variables describing molecular shape (dispersion force) anisotropy gives rise to new classes of the phase diagrams, absent in the original model. Depending on properties of the shape fluctuations, th...

PurposeTo analyse predictors of clinical outcome in fungal keratitis.MethodsData was collected during a prospective, randomized, controlled, double-masked clinical trial of treatment for fungal keratitis. Clinical features at presentation and demographics were collected at the enrolment visit for all patients. Pre-specified clinical outcomes included 3-month visual acuity and infiltrate/scar size, time to re-epithelialization, and corneal perforation. A separate multivariable model with each outcome as the dependent variable included all predictor variables.ResultsPredictors for worse 3-month visual acuity include older age (P=0.024), worse presentation visual acuity (P<0.001), larger infiltrate size at presentation (P<0.001), and pigmented ulcer (P=0.030). Larger infiltrate size at presen...

Objective To determine availability of and test whether on-site mental health providers (MHP) is associated with greater odds of reported mental health consultation and referral among primary care pediatricians. Methods Pediatricians were identified from the American Medical Associations 2004 physician directory and stratified by region. Six hundred were randomly selected to receive a mail survey. The main independent variable was on-site MHP. The dependent variable was reported frequency (4-point rating) of mental health consultation and referral. Estimates were weighted to account for survey design and nonresponse. Results Overall response rate was 51%. The majority of respondents were male (56%), age ?46 years old (59%), white (68%), and practicing in suburban locations (52%). Approx...

In the existing methods used to forecast bucket-wheel excavator output the variability of the geological and mining conditions is estimated by means of different coefficients. Output is a function of the interaction between three real systems, ie, machine condition, the rock mass and labour management and is a random variable. Regression analysis was applied to the short-term forecast of the bucket-wheel excavator output at the Troyanovo-Sever Mine (Bulgaria). The analytical dependence describing the output is represented by a Chebyshev polynomial. This approximation is convenient because the polynomial coefficients are not interdependent. When it is necessary to raise the polynomial degree, the initially determined coefficients are preserved and the new ones calculated and added. The calculations of the forecast bucket-wheel excavator output performed using this method yield results of high accuracy. 1 ref., 1 tab.

This paper discusses the accuracy performance of training, validation and prediction of monthly water quality parameters utilizing Adaptive Neuro-Fuzzy Inference System (ANFIS). This model was used to analyse the historical data that were generated through continuous monitoring stations of water quality parameters (i.e. the dependent variable) of Johor River in order to imitate their secondary attribute (i.e. the independent variable). Nevertheless, the data arising from the monitoring stations and experiment might be polluted by noise signals owing to systematic and random errors. This noisy data often made the predicted task relatively difficult. Thus, in order to compensate for this augmented noise, the primary objective of this study was to develop a technique that could enhance the ac...

We discuss the modification of the Kapteyn multiplicative process using the q-product of Borges [E.P. Borges, A possible deformed algebra and calculus inspired in nonextensive thermostatistics, Physica A 340 (2004) 95]. Depending on the value of the index q a generalisation of the log-Normal distribution is yielded. Namely, the distribution increases the tail for small (when q1) values of the variable upon analysis. The usual log-Normal distribution is retrieved when q=1, which corresponds to the traditional Kapteyn multiplicative process. The main statistical features of this distribution as well as related random number generators and tables of quantiles of the Kolmogorov-Smirnov distance are presented. Finally, we illustrate the validity of this scenario by describing a set of variables of biological and financial origin.

Intra-individual variability over a short period of time may contain important information about how individuals differ from each other. In this article we begin by discussing diverse indicators for quantifying intra-individual variability and indicate their advantages and disadvantages. Then we propose an alternative method that models inter-individual differences in intra-individual variability by separately considering both the amplitude of fluctuations and temporal dependency in the data. In the proposed model, temporal dependency and amplitude of fluctuations are both included as random effects. Parameter estimation is done with a multiple-step approach using maximum likelihood, or with a recommended 1-step approach using a Bayesian method. The similarities and differences between the proposed method and some existing methods are discussed and investigated using diary study data from older adults. The results from empirical data analysis revealed that temporal dependency and amplitude of fluctuations have different predictability of health outcomes and thus should be modeled and considered separately. (PsycINFO Database Record (c) 2012 APA, all rights reserved). PMID:22924600

Created by Kyle Siegrist of the University of Alabama-Huntsville, this is an online, interactive lesson on probability spaces. The resource provides examples, exercises, and applets that cover conditional probability, independence, and several modes of convergence that are appropriate for random variables. This section also covers probability space, the paradigm of a random experiment and its mathematical model as well as sample spaces, events, random variables, and probability measures. This is the second of seventeen different statistics lessons provided by Siegrist.

In this paper we study the impact of the introduction of edge weights on the typical distances in a random graph and, in particular, on its diameter. Our main result consists of a precise asymptotic expression for the maximal weight of the shortest weight path between a random vertex and all others (the flooding time), as well as the (weighted) diameter of sparse random graphs, when the edge weights are i.i.d. exponential random variables.

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes. For these restricted parameters, the magnetization switches through random nucleation of a single droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency a...

Recently, a conductive coordination compound [Cu(TANC)](F)0.5 with new radical frameworks was synthesized, where TANC stands for 5,6,11,12-tetraazanaphacene. We have measured the electrical resistivity of [Cu(TANC)](F)0.5 under high pressures up to 8.0 GPa. At ambient pressure, the temperature dependence of the resistivity shows semiconducting behavior described by a variable range hopping conduction, ?(T)?exp(T0?T)?. The value of T0 increases with increasing pressure up to 6.5 GPa, beyond which it decreases abruptly. The pressure dependence of T0 is discussed in terms of the increase of the pureness of one-dimensionality and the strength of the random potential due to disordered F? ions.   

Abstract in spanish La preferencia de organismos por ciertos recursos es frecuentemente evaluada mediante pruebas de elección múltiple, sin tener en cuenta en los análisis la dependencia entre las observaciones. Este trabajo presenta distintos modelos estadísticos que permiten contemplar la falta de independencia de los datos y compara la ´performance´ de cada uno de ellos empleando datos reales no simulados. Se utilizaron cuatro tipos de modelos: Análisis de Devianza (Modelo Lineal G (more) eneralizado Mixto), Análisis de la Varianza a un factor, ANOVA a un factor con bloque al azar (ambos Modelos Lineales Generales Mixtos), y ANOVA no paramétrico con bloques (Test de Friedman). También se utilizaron una covariable y una variable compensadora (´offset´). Los resultados obtenidos sugieren que para la variable de tipo conteo (con distribución Poisson), el Modelo Lineal Generalizado Mixto fue el más potente, mientras que si se considera la medida relativizada (conteos/superficie), la mayor potencia la obtuvo el MLG con una variable compensadora. Abstract in english The preference of organisms for resources is usually evaluated through multiple-choice tests, without accounting the lack of independence present in the data. This study presents several statistical models which explicitly consider such dependence structure comparing their performance by using real non-simulated data. Four types of models were used: Analysis of Deviance (Generalized Mixed Linear Model), Analysis of Variance with a factor, One-way ANOVA with random block e (more) ffect (both General Mixed Linear Models) and Non-Parametric ANOVA with block effect (Friedman Test). A covariable and an offset variable were also added to the Mixed GLM model. Results suggest that the most powerful model for the counting-type variable (with Poisson distribution), is the Mixed GLM; whereas for the relativized variable (count/surface), is the Mixed GLM with an offset variable.

Abstract in spanish Se revisan los métodos de series temporales en los estudios epidemiológicos sobre contaminación atmosférica, ilustrándolo mediante una regresión de Poisson autoregresiva, la cual ha sido utilizada en los proyectos APHEA y EMECAM. Se relacionan las variaciones en el número diario de muertos mayores de 70 años (todas las causas, CIE-9:001-799) en Barcelona, 1991-1995, con las variaciones en los niveles diarios promedio de contaminación por humos negros. Se utiliza (more) una regresión de Poisson por cuanto la variable aleatoria dependiente sigue presumiblemente tal distribución de probabilidad. Como confusores se consideran variables meteorológicas (promedios diarios de temperatura y de humedad), comportamientos tendenciales, estacionales y efectos de calendario presentes en la mortalidad (todos ellos aproximados de forma determinista) así como cualquier otra variable que tenga un comportamiento que pueda relacionarse con la variable dependiente (ocurrencia de epidemias de gripe por ejemplo). La relación entre la mortalidad y las variables confusoras se modeliza de forma no lineal y se tienen en cuenta además los previsibles periodos de latencia (utilizando retardos de variables explicativa por ejemplo). Sin embargo, y debido a que el control no es perfecto, se opta por estimar un modelo de Poisson autoregresivo (introduciendo como variables explicativas diversos retardos de la mortalidad) corrigiendo la autocorrelación residual. La principal ventaja del método de análisis descrito es la de permitir un control de variables confusoras desde un punto determinista, con un software al alcance de todos los grupos que participan en el proyecto. Además, permite que el método se pueda aplicar de una formar protocolizada y estandarizada que facilite la comparación de resultados y permita la realización de un meta-análisis. Abstract in english The time series methods in the epidemiological studies on air pollution are reviewed, illustrated by means of an autoregressive Poisson regression which was employed in the APHEA and EMECAM Projects. A listing is provided of the variations in the daily number of deaths of people over age 70 (all causes, CIE-9:001-799) in Barcelona, 1991-1995, with the average variations in the daily smog pollution levels. A Poisson regression is used insofar as the dependent random variab (more) le presumably follows such a probability distribution. As variables possibly leading to confusion, the impact of weather variables (daily temperature and relative humidity averages), seasonal, tendency-related behaviors and day of the year on the death rate are taken into account (all estimated on a determinist basis), in addition to any other variable which behaves in a way that it can be related to the dependent variable (i.e. flu epidemics). The relationship between the death rate and the confusing-causing variables is modeled on a non-linear basis, and the foreseeable lag times are also taken into account (i.e. by using explicative variable time lags). However, due to control not being perfect, it has been decided to opt for estimating an autoregressive Poisson model (adding in some different explicative variables time giving rise to a lag in the death rate) offsetting the residual autocorrelation. The main advantage of the method of analysis described above is that of making it possible to control confusing variables from a determinist standpoint with a software to which all of the groups taking part in this Project had access. This also affords the possibility of using this method in a set, standardized manner, facilitating the comparison of results and making an objective point analysis possible.

From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for the cumulative distribution function of the sample variance of i.i.d. random variables with a gamma density, supplementing former formulas of the author. Furthermore, from the above Laplace transform Fourier series are obtained for the density and the distribution function of the sample variance of i.i.d. random variables with a uniform distribution. This distribution can be applied e.g. to a statistical test for a scale parameter.

In this paper we determine the distributional behavior of sums of free (in the sense of Voiculescu) identically distributed, infinitesimal random variables. The theory is shown to parallel the classical theory of independent random variables, though the limit laws are usually quite different. Our work subsumes all previously known instances of weak convergence of sums of free, identically distributed random variables. In particular, we determine the domains of attraction of stable distributions in the free theory. These freely stable distributions are studied in detail in the appendix, where their unimodality and duality properties are demonstrated.

In cluster randomized trials (CRTs), clusters of individuals are randomized rather than the individuals themselves. For such trials, power depends in part on the degree of similarity among responses within a cluster, which is quantified by the intaclass correlation coefficient (ICC). Thus, for a fixed sample size, power decreases with increasing ICC. In reliability studies with two observers, dichotomizing a continuous outcome variable has been shown to reduce the ICC. We checked (by a simulation study) that this property still applies to CRTs, in which cluster sizes are variable and usually greater than in reliability studies and observations (within clusters) are exchangeable. Then, in a CRT, dichotomizing a continuous outcome actually induces two antagonistic effects: decreased power because of loss of information and increased power induced by attenuation of the ICC. Therefore, we aimed to assess the impact of dichotomizing a continuous outcome on power in a CRT. We derived an analytical formula for power based on a generalized estimating equation approach after dichotomizing a continuous outcome. This theoretical result was obtained by considering equal cluster sizes, and we then assessed its accuracy (by a simulation study) in the more realistic situation of varying cluster sizes. We showed that dichotomization is associated with decreased power: attenuation of the ICC does not compensate for the loss of power induced by loss of information. Loss of power is reduced with increased initial continuous-outcome ICC and/or prevalence of success for the dichotomized outcome approaching 50%. Copyright © 2012 John Wiley & Sons, Ltd. PMID:22733454

Reliability based techniques has been an area of active research in structural design during the last decade, and different methods have been developed. The same has occurred with stochastic programming, which is a framework for modeling optimization problems involving uncertainty. The discipline of stochastic programming has grown and broadened to cover a wide range of applications, such as agriculture, capacity planning, energy, finance, fisheries management, production control, scheduling, transportation, water management, etc., and because of this, techniques for solving stochastic programming models are of great interest for the scientific community. This paper presents a new approach for solving a certain type of stochastic programming problems presenting the following characteristics: (i) the joint probability distributions of random variables are given, (ii) these do not depend on the decisions made, and (iii) random variables only affect the objective function. The method is based on mathematical programming decomposition procedures and first-order reliability methods, and constitutes an efficient method for optimizing quantiles in high-dimensional settings. The solution provided by the method allows us to make informed decisions accounting for uncertainty.

In this study, we develop a Markov Chain Monte Carlo method (MCMC) to estimate the hydraulic conductivity field conditioned on the direct measurements of hydraulic conductivity and indirect measurements of dependent variables such as hydraulic head for saturated flow in randomly heterogeneous porous media. The log hydraulic conductivity field is represented (parameterized) by the combination of some basis kernels centered at fixed spatial locations. The prior distribution for the vector of coefficients {theta} are taken from a posterior distribution {pi}({theta}/d) that is proportional to the product of the likelihood function of measurements d given parameter vector {theta} and the prior distribution of {theta}. Starting from any initial setting, a partial realization of a Markov chain is generated by updating only one component of {theta} at a time according to Metropolis rules. This ensures that output from this chain has {pi}({theta}/d) as its stationary distribution. The posterior mean of the parameter {theta} (and thus the mean log hydraulic conductivity conditional to measurements on hydraulic conductivity, and hydraulic head) can be estimated from the Markov chain realizations (ignoring some early realizations). The uncertainty associated with the mean filed can also be assessed from these realizations. In addition, the MCMC approach provides an alternative for estimating conditional predictions of hydraulic head and concentration and their associated uncertainties. Numerical examples for flow in a hypothetic random porous medium show that estimated log hydraulic conductivity field from the MCMC approach is closer to the original hypothetical random field than those obtained using kriging or cokriging methods.

The relationship between prior antidepressant treatment and prefrontal brain functional response to subsequent treatment with antidepressant medication or placebo is unknown. Eighty-nine adults with Major Depressive Disorder (MDD), characterized as antidepressant-experienced or antidepressant-naive, received one week of single-blind placebo treatment prior to eight weeks of randomized treatment with medication (fluoxetine or venlafaxine; n=47) or placebo (n=42) in one of three similar placebo-controlled trials. Brain function was assessed at baseline, end of placebo lead-in, and during randomized treatment using quantitative electroencephalography (qEEG). The authors assessed change in prefrontal theta-band cordance (PFC) in antidepressant-experienced vs. antidepressant-naive subjects. Treatment history groups differed significantly on PFC change during the placebo lead-in even when controlling for clinical and demographic variables (F(1,62)=4.27, p=.04). As assessed in linear mixed models that examined treatment history (antidepressant-experienced or antidepressant-naive), treatment assignment (medication or placebo), and their interaction as predictors, treatment history also predicted PFC change during the randomized phase of treatment even when controlling for pretreatment clinical and demographic and symptom improvement during treatment (F(1,5o)=5.20, p=.03). The interaction was not significant. Post hoc analyses showed that antidepressant-experienced subjects treated with placebo showed PFC changes that did not differ from PFC changes seen in the medication group. Results suggest that prefrontal brain functional changes during treatment for MDD may differ depending upon prior treatment with antidepressant medication. PMID:22445212

Let $X$ be a discrete random variable with support $S$ and $f : S \\to S^\\prime$ be a bijection. Then it is well-known that the entropy of $X$ is the same as the entropy of $f(X)$. This entropy preservation property has been well-utilized to establish non-trivial properties of discrete stochastic processes, e.g. queuing process \\cite{prg03}. Entropy as well as entropy preservation is well-defined only in the context of purely discrete or continuous random variables. However for a mixture of discrete and continuous random variables, which arise in many interesting situations, the notions of entropy and entropy preservation have not been well understood. In this paper, we extend the notion of entropy in a natural manner for a mixed-pair random variable, a pair of random variables with one discrete and the other continuous. Our extensions are consistent with the existing definitions of entropy in the sense that there exist natural injections from discrete or continuous random variables into mixed-pair random vari...

We consider the dynamics of a simple one dimensional model and we discuss the phenomenon of aging (i.e., the strong dependence of the dynamical correlation functions over the waiting time). Our model is the so-called random random walk, the toy model of a directed polymer evolving in a random medium.

The partly random fractal sums of pulses (PFSP) are a family of random functions that depend on a kernel function K and at least two positive parameters C and delta. Given K, the construction of F(t;C,delta) consists in adding N affine versions of a pulse as follows. The pulse height Lambda and its width W are random variables related by w/?^delta = a constant. The width is distributed according to the Poisson measure Cw-1dwdt in the "address plane" of coordinates w and t. For finite C, the increments of F(t;C,delta) fail to be strongly mixing therefore they exhibit global dependence. Indeed some PFSP resemble the icon of global dependence, which is fractional Brownian motion (FBM) with Hne1/2. When the presence of strong mixing must be tested empirically, many tests rely on the comparison of two exponents of diffusion: that of a r.f. X(t) and of a "shuffled" r.f. ˜ X(t) whose increments for ? t = 1 (say) are independent and follow the same distribution as X(t). In FBM, the diffusion exponent is H for the process itself and 1/2 for its shuffled variant. Therefore, Hne1/2 is a token of global dependence. For the Lévy stable motion (LSM) to the contrary, the diffusion exponent is the same as for the independent process with the same marginal distribution. The PFSP are not so clear-cut. The dependence is always global. But consider those tests of globality versus locality that, like R/S testing, are founded on the exponent of diffusion. Those tests will classify the dependence in many PFSP as local. Therefore, the PFSP are challenging borderline cases, while the conceptual fact is important, more important is the concrete fact that their rich properties and the absence of arbitrary grids make them excellent candidates for modeling phenomena that combine global dependence with long distribution tails. Furthermore, related structures that are discussed elsewhere, namely, the multifractal measures obtained as products of pulses, are grid-free and provide a great improvement over the now-classical multifractal measures generated by multiplicative cascades in a grid.

as random variables from a parametric distribution, By observing the .... the PAC [ Valiant84]framework– “probably”“approximately”“correct”maps onto ... We adopt a parametric statistical approach to the hypothesis evaluation problem.

This paper concerns developing methods for approximating a chance-constrained set when any information concerning the random variables must be derived from actual samples. Such a situation has not been presented in the literature. When existing chance-con...

Meteoroid zenity angle at impact, radians, random variable. ..... angle). Because of the conservation of angular momentum , the cross product of the ...... proportional to mu2vc for the experiments performed by Partridge at the University ...

We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.

studies. This article also shows the dramatic effect that different handling and testing ... Thus, the purpose of the present study was to compare ...... regimes are indi- ..... random fiber lots. [2] This is further evi- dence that variability in composite ...

maximum when displayed as a function of sampling rate, and the location of this maximum ..... Wiener has shown that power spectral density is a mean- .... In fact, a random variable which is constrained to a finite interval has maximum entropy ...

Freezing rain impingement on power network equipment can cause considerable damage in cold climate regions. The aim of this paper was to develop a means of estimating icing intensity over a wide range of conditions as well as to predict the formation of extreme ice loads. A 3-D model of ice accretion on a non-rotating cylinder simulating real-life flexibility constraints was proposed. The morphogenetic model was based on random walk modelling, with variable convective heat flux, impingement angle, and angle of inclination of the cylinder. Morphogenetic models add stochastic variability to ice accretion shapes, in order to more fully represent experimental observations. With this method, a different sequence of numbers is used in each simulation, while external conditions remain identical. Water film flowing along the ice or conductor surface was divided into fluid elements assumed to follow a random path. Three parameters were associated with the random walk model. These included the probability of freezing and the motion parameter which are both dependent on atmospheric conditions, and the shedding parameter, which is constant. The influences of the convective heat flux, impingement angle, and inclination angle of the cylinder were discussed. The morphogenetic model was in good agreement with observations in terms of its simulation of ice accretion due to freezing rain on a cylinder. The shape and mass of the ice accretion was predicted while changing the droplet impingement angle and the convective heat flux and the inclination angle of the cylinder. It was concluded that the model will provide even more realistic predictions when the impact of the wind on the heat transfer at the cylinder surface is considered. 8 refs., 7 figs.

We investigate random, discrete Schr\\"odiner operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature $\\beta$. They belong to the class of "critical" random Schr\\"odiner operators with random potentials which diminish as $|x|^{-{1/2}}$. We show that as a function of $\\beta$ their eigenstates undergo a transition from extended ($\\beta \\ge 1 $) to power-law localized ($0 < \\beta < 1$).

Using 2-loop renormalisation group calculations, we study a system of N two-dimensional Potts models with random bonds coupled together by their local energy density. This model can be seen as a generalization of the random Ashkin-Teller model. We found that, depending on the sign of the coupling term, the universality class of the system in the presence of randomness is different. Under particular consideration, this model presents an example of a first order phase transition rounded by randomness.

A random variable ..gamma.. is said to have the Laplace distribution or the double exponential distribution whenever its probability density function is given by lambda exp(-lambda absolute value (y)), where -infinity < y < infinity and lambda > 0. The random variable X = exp(..gamma..) is said to have the log-Laplace distribution. With the problem of extrapolation to low doses in dose response curves as a motivation, an axiomatic characterization of the log-Laplace distribution is obtained. 1 figure.

Abstract in portuguese Experimentos de solo realizados no campo necessitam de estudos que verifiquem a variabilidade espacial do solo. O objetivo deste trabalho foi estudar a variabilidade espacial de propriedades físico-hídricas do solo em uma parcela experimental, usando métodos geoestatísticos. O experimento foi realizado em 1982 no Centro Experimental do Instituto Agronômico em Campinas (SP), em um Latossolo Vermelho sob preparo convencional, numa parcela de 30 x 30 m, com grade de pon (more) tos a cada 5 m. As propriedades analisadas foram: teor de água do solo, porosidade, densidade do solo, resistência à penetração e retenção de água. Para analisar a variabilidade espacial, utilizou-se a geoestatística, por meio da análise de semivariogramas, interpolação dos dados por krigagem e construção de mapas de isolinhas. A dependência espacial ocorreu principalmente nas variáveis obtidas na camada superficial do solo (0-25 cm), apresentando dependência espacial moderada e forte. Houve correlação positiva significativa entre retenção de água e densidade do solo. A dependência espacial encontrada e a semelhança de comportamento entre as variáveis permitiram inferir que amostragem ao acaso seria falha, pois esconderia a variabilidade encontrada, interferindo nas respostas dos tratamentos, caso fosse instalado um experimento que exigisse independência entre amostras. Abstract in english Field experiments involving soils require previous verification of the soil spatial variability. The objective of this research was to study the spatial variability of soil physical properties of an experimental plot using geostatistics. The experiment was conducted in 1982 at the Experimental Center of the Instituto Agronômico in Campinas, state of São Paulo, Brazil, on a Red Latosol (Rhodic Ustox) under conventional tillage in a 30 x 30 m area, with sampling points ar (more) ranged in a 5 m square grid. The analyzed properties were water content, porosity, bulk density, penetration resistance, and water retention. The spatial variability was evaluated by geostatistical analysis of semivariograms and kriging interpolation of the data for the construction of maps. Spatial dependence occurred mainly for the variables from the upper soil layer (0-25 cm), showing moderate and strong spatial dependence. A significant positive correlation was found between water retention and bulk density. The observed spatial dependence and similar behavior of the variables allowed the inference that random sampling would not be enough to characterize a field, as it would fail to show the variability. In cases where an experiment requires independent samples, the response to the treatments would be affected.

A classroom/laboratory exercise has been used to introduce college students to factorial research designs, differentiate between interpretations for experimental and quasi-experimental variables, and exemplify application of laboratory research methods to test practical questions (advertising claims). The exercise involves having randomly divided groups smell either a commercial cologne/perfume or the same product to which musk oil has been added, and then rating the sample on both attracting-repelling and masculine-feminine dimensions. The exercise is presently used in a laboratory section of a beginning course in psychological research methods, but could be adapted to a classroom. Hypotheses generated by students concern the possible pheromone-like qualities of musk oil, based both on known qualities of musk and on advertising claims. Discussion of possible results with students provides an opportunity for: (1) contrasting independent and quasi-independent variables, (2) introducing the concept of interactions and the way they may qualify or nullify main effects, and (3) suggesting the usefulness of multiple dependent variables. After the discussion, students write individual experimental reports of the research. (Author/SW)

A reliability-based optimization methodology has been developed to design the raked wing tip of the Boeing 767-400 extended range airliner made of composite and metallic materials. Design is formulated for an accepted level of risk or reliability. The design variables, weight and the constraints became functions of reliability. Uncertainties in the load, strength and the material properties, as well as the design variables, were modeled as random parameters with specified distributions, like normal, Weibull or Gumbel functions. The objective function and constraint, or a failure mode, became derived functions of the risk-level. Solution to the problem produced the optimum design with weight, variables and constraints as a function of the risk-level. Optimum weight versus reliability traced out an inverted-S shaped graph. The center of the graph corresponded to a 50 percent probability of success, or one failure in two samples. Under some assumptions, this design would be quite close to the deterministic optimum solution. The weight increased when reliability exceeded 50 percent, and decreased when the reliability was compromised. A design could be selected depending on the level of risk acceptable to a situation. The optimization process achieved up to a 20-percent reduction in weight over traditional design.

Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider sample-to-population inferential approaches. This paper deals with the posterior distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean, and analytical approximations for the variance, skewness and kurtosis are derived. These approximations have a guaranteed accuracy level of the order O(1/n^3), where n is the sample size. Leading order approximations for the mean and the variance are derived in the case of incomplete samples. The derived analytical expressions allow the distribution of mutual information to be approximated reliably and quickly. In fact, the derived expressions can be computed with the same order of complexity needed for descriptive mutual information. This makes ...

The effect of vibration on the solid-to-liquid-like transition of a dense granular assembly under planar shear is studied numerically using soft particle molecular dynamics simulations in two dimensions. We focus on small systems in a thin planar Couette cell, examining the bistable region while increasing shear, with varying amounts of vertical vibration, and determine statistics of the shear required for fluidization. In the absence of vibration, the threshold value of the shear stress depends on the preparation of the system and has a broad distribution. However, adding periodic vibration both lowers the mean fluidization threshold value of the shear stress and decreased its variability. A previous study performed similar simulations using random noise; the results from these two studie...

The purpose of this study was to develop and pilot a theory-based, computer-tailored feedback system for healthy behaviors for college students at a large, public university, aiming to enhance student wellness. A total of 1300 college students were contacted. Sixty-two students completed the eight week intervention. The participants were randomly assigned into two groups and received the survey three times, consistently receiving normative or personalized feedback. The participating sample was generally healthy and mainly comprised of freshman, Caucasian, and normal weight individuals. Repeated-measure ANOVAs were run and small significant interactions were found between the type of feedback received and some of the dependent variables. This study showed potential benefits of this intervention which can help institutions in supplying preventive services as a part of the transition to university life. Suggestions are provided for delivering preventative health services related to unhealthy diet, drinking habits, or inactive lifestyle. (Contains 2 tables and 1 figure.)

In this article, we propose several quantization based stratified sampling methods to reduce the variance of a Monte-Carlo simulation. Theoretical aspects of stratification lead to a strong link between the problem of optimal $L^2$-quantization of a random variable and the variance reduction that can be achieved. We first emphasize on the consistency of quantization for designing strata in stratified sampling methods in both finite dimensional and infinite dimensional frameworks. We show that this strata design has a uniform efficiency among the class of Lipschitz continuous functionals. Then a stratified sampling algorithm based on product functional quantization is proposed for path-dependent functionals of multi-factor diffusions. The method is also available for other Gaussian processes as the Brownian bridge or an Ornstein-Uhlenbeck process. We derive in detail the quantization of the Ornstein-Uhlenbeck process. The balance between the algorithmic complexity of the simulation and the variance reduction f...

In this work, technical solutions for two remarkable environmental problems are undertaken: waste tyres (WT) valorisation by producing steam activated carbons (AC), and gas-phase polycyclic aromatic hydrocarbons (PAH) abatement, by adsorption on those solids. Firstly, the AC production process in a fixed bed reactor was modelled. For this purpose, the random pore model (RPM) was successfully applied, to model the solid evolution throughout the steam activation of WT. The model showed the capability of predicting with a high degree of accuracy both the conversion and the solid properties evolution, depending on the operational variables (i.e. temperature, steam concentration and time). The experimental results obtained in a lab-scale activation system allowed the model validation. Afterward...

We consider a study which monitors the occurrences of a recurrent event for n subjects or units. Recurrent event data have many features which are worth looking into in the estimation process. In this manuscript, we consider the problem of estimating the distribution function of the inter-event times by taking into account two of these features: correlation among the inter-event times and the dependence and informative aspect of the right-censoring random variables. The parametric approach to the problem has been dealt with in Zamba and Adekpedjou (2011) [25]. The semiparametric approach is considered in this article. We derive a Kaplan-Meier type estimator of the distribution function under the gamma frailty model and an informative monitoring model for recurrent events by extending an ap...

This review describes 40 years of experience gained at Risø The radioluminescence (RL) signal from fiber coupled Al2O3:C can be used for real-time in vivo dosimetry during radiotherapy. RL generally provides measurements with a reproducibility of 2% (one standard deviation). However, we have observed a non-random variability of the RL signal which means that the memory of the system is not fully reset by the optically stimulated luminescence (OSL) readout. Here we report an example of how this memory affects the RL signal. Measurements were performed in the range of 0–4 Gy using four Al2O3:C crystals, in cycles of irradiation and subsequent readout. We found the memory to be persistent, influencing several successive RL measurements. The induced systematic error was found to be crystal dependent, but proportional to the measurement-to-measurement dose variation (approximately 1.4% per Gy).

The relative abundances are treated as a consequence of processes in cosmic ray transport occurring during passage of the radiation through interstellar material at high velocity. Some of the subjects mentioned are nuclear fragmentation and the production of secondary nuclei, nuclear reactions, energy loss and nuclear decay, ionization, the range-energy relation and propagation variables, capture and loss of electrons, the propagation of nuclei, the transport equation, equilibrium solutions, energy-dependent path length distribution, exponential path length distributions, discrete spectra, sources, supernovae, and the origin of the abundances. The connection between the space-time features of the sources, the material traversed, and the effects of magnetic fields is established by describing the particle-field interaction as a diffusive or random-walk process.

One of the most important challenges in the integration of renewable energy sources into the power grid lies in their `intermittent' nature. The power output of sources like wind and solar varies with time and location due to factors that cannot be controlled by the provider. Two strategies have been proposed to hedge against this variability: 1) use energy storage systems to effectively average the produced power over time; 2) exploit distributed generation to effectively average production over location. We introduce a network model to study the optimal use of storage and transmission resources in the presence of random energy sources. We propose a Linear-Quadratic based methodology to design control strategies, and we show that these strategies are asymptotically optimal for some simple network topologies. For these topologies, the dependence of optimal performance on storage and transmission capacity is explicitly quantified.

When two or more univariate population means are compared, the proportion of variation in the dependent variable accounted for by population group membership is eta-squared. This effect size can be generalized by using multivariate measures of association, based on the multivariate analysis of variance (MANOVA) statistics, to establish whether population mean vectors are practically significant different. In the case of random samples from populations, approximate and asymptotically unbiased estimators of these effect sizes as well as confidence intervals are suggested under the assumptions of equal covariance matrices and normality. Statistical properties of these estimators are studied by Monte Carlo simulations. The accuracy and spread of the proposed effect sizes are also compared with those of other multivariate measures of association in Monte Carlo simulations. The proposed effect sizes are also illustrated by applying them in an empirical example using college admission test data obtained from StatSoft (2007). (Contains 5 tables and 4 figures.)

A stratified randomized sample of 525 middle age (35â??64 years old) men was used to study the relationships between self-reported level of church attendance (CA), self-reported religious faith (SRRF), religious well-being (RWB), existential well-being (EWB), self-actualization (SA), health, lifestyle, and participation in physical activity (PA). Religious measures (RWB, CA, and SRRF) were found to be dependent on psychosocial variables in terms of their relationships with PA, lifestyle, and health. On the other hand, psychosocial resourcefulness (SA, EWB, social support, and stress management) showed independent relationships with lifestyle, PA, and health. These findings indicate that the positive associations of psychological and sociological constructs with health are not related to o...

Background & Aims Hepatocellular carcinoma (HCC) prognosis strongly depends upon nuclear grade and the presence of microscopic vascular invasion (MVI). The aim of this study was to develop an artificial neural network (ANN) that is able to predict tumour grade and MVI on the basis of non-invasive variables. Methods Clinical, radiological, and histological data from 250 cirrhotic patients resected (n=200) or transplanted (n=50) for HCC were analyzed. ANN and logistic regression models were built on a training group of 175 randomly chosen patients and tested on the remaining testing group of 75. Receiver operating characteristics curve (ROC) and k-statistics were used to analyze model accuracy in the prediction of the final histological assessment of tumour grade (G1-G2 vs. G3-G4) and MVI (a...

Abstract Adherence to antiretroviral therapy (ART) has markedly improved HIV disease management, and significantly reduced HIV/AIDS-associated morbidity and mortality. Although recent studies suggest a relationship between smoking and suboptimal adherence to ART, a more in-depth understanding of this relationship is needed. We conducted a secondary analysis using data from a randomized controlled smoking cessation trial to investigate the association of nonadherence to ART with potential demographic, psychosocial (perceived stress and depression), and substance use (nicotine dependence, illicit drug use, and alcohol use) variables among persons living with HIV/AIDS (PLWHA) who smoke. The mean (standard deviation [SD]) age of participants (n=326) was 45.9 years old (SD=7.6). Additionally, t...

This work provides a comprehensive uncertainty technique to evaluate uncertainty, resulting in a more realistic evaluation of PI, thereby requiring fewer resources to address scenarios and allowing resources to be used across more scenarios. For a given set of dversary resources, two types of uncertainty are associated with PI for a scenario: (1) aleatory (random) uncertainty for detection probabilities and time delays and (2) epistemic (state of knowledge) uncertainty for the adversary resources applied during an attack. Adversary esources consist of attributes (such as equipment and training) and knowledge about the security system; to date, most evaluations have assumed an adversary with very high resources, adding to the conservatism in the evaluation of PI. The aleatory uncertainty in PI is ddressed by assigning probability distributions to detection probabilities and time delays. A numerical sampling technique is used to evaluate PI, addressing the repeated variable dependence in the equation for PI.

This paper develops a fault-tolerant variable sampling control (VSC) scheme for a class of nonlinear networked control systems (NCSs) with time-varying state and random network delays. An uncertain continuous Takagi-Sugeno (T-S) fuzzy system with both state and input varying delays, in the presence of possible actuator faults, is obtained equivalently on the basis of the input delay methodology. A tighter bounding lemma is proposed so as to gain less conservative closed-loop stability criteria. Delay-dependent conditions in terms of linear matrix inequalities are derived for the mode-independent fault-tolerant stabilizing controller of the resulting Markovian network-based system by employing a novel stochastic Lyapunov-Krasovskii (L-K) functional. An illustrative example is simulated to s...

This paper uses the block-structured state-dependent event (BSDE) approach to generalize the scalar version of the single server retrial queue with finite population. The simple scalar version only involves exponential random variables, which make the underlying Markov chain tractable. However, this is a drawback in applications where the exponentiality is not a realistic assumption and the flows are correlated. The BSDE approach provides a versatile tool to deal with a non-exponential model with correlated flows, but keeping tractable the dimensionality of the block-structured Markov chain. We focus on the investigation of the limiting distribution of the system state and the waiting time. The theory is illustrated by numerical experiments, which demonstrate that the proposed BSDE approac...

We present a methodology that combines numerical simulations of groundwater flow and advective transport in heterogeneous porous media with analytical retention models for computing the infection risk probability from pathogens in aquifers. The methodology is based on the analytical results presented in [1,2] for utilising the colloid filtration theory in a time-domain random walk framework. It is shown that in uniform flow, the results from the numerical simulations of advection yield comparable results as the analytical TDRW model for generating advection segments. It is shown that spatial variability of the attachment rate may be significant, however, it appears to affect risk in a different manner depending on if the flow is uniform or radially converging. In spite of the fact that numerous issues remain open regarding pathogen transport in aquifers on the field scale, the methodology presented here may be useful for screening purposes, and may also serve as a basis for future studies that would include greater complexity.

Performing a mass balance of radium isotopes is a commonly employed method for quantifying the flux of groundwater into the sea. However, the spatial variability of ^2^2^4Ra can compromise the results of mass balances in environmental studies. We address this uncertainty by optimizing the distribution of Ra samples within a surface survey of ^2^2^4Ra activity in the Lesina Lagoon, Italy. After checking for spatial dependence, location-allocation modeling (LAM) was utilized to determine optimal distribution of samples for thinning the sampling design. Trend surface analysis (TSA) was employed to interpolate the Ra activity throughout the lagoon. No significant change was found when using all 41 samples or only 25 randomly distributed samples. Results from the TSA showed a linear trend and b...

Fruit and vegetable consumption represents a nutritional goal to prevent obesity and chronic illness. To change dietary behaviors, people must be motivated to do so, and they must translate their motivation into actual behavior. The present experiment aims at the psychological mechanisms that support such changes, with a particular focus on dietary self-efficacy and planning skills. A randomized controlled trial compared a theory-based psychological intervention with a health education session in 114 participants. Dependent variables were fruit and vegetable consumption, intention to consume more fruit and vegetables, planning to consume more, and dietary self-efficacy, assessed before the intervention, 1 week afterwards, and at 6-week follow up. Significant group by time interactions for...

The objective of this research was to determine the effects of wellness programs on quality of life and utilization in an academic family medicine practice in two small controlled studies. One offered stress management and problem solving; the second offered a broader wellness intervention. Outcome measures consisted of scores on the Beck Anxiety Inventory, Hamilton Depression Inventory, CES-D (depression), Health Related Quality of Life, SF-12, and the number of office visits in 6?months. Subjects were randomly assigned to intervention or control groups. Statistical analysis compared pre-test and post-test values of the dependent variables between groups. In study one, where the focus was on relaxation, significant differences between groups were observed in anxiety at post-test (p?p?p?

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relations for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady-state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions.

Onboard decision support systems (DSS) are used to increase the operational safety of ships. Ideally, DSS can estimate future ship responses within a time scale of the order of 1–3 h taking into account speed and course changes, assuming stationary sea states. In principle, the calculations depend on a large amount of operational and environmental parameters, which will be known only in the statistical sense. The present paper suggests a procedure to incorporate random variables and associated uncertainties in the calculations of the outcrossing rates that are the basis for riskbased DSS. The procedure is based on parallel system analysis, and the paper derives and describes the main ideas. The concept is illustrated by an example, where the limit state of a non-linear ship response is considered. The results from the parallel system analysis are in agreement with corresponding Monte Carlo simulations. However, the computational speed of the parallel system analysis proved slower than expected.

We present a dynamic and quantitative model of a fiscal solvency crisis in a monetary union. Diverse fiscal policies, which are subject to fiscal limits and stochastic shocks, can threaten a monetary union. The fiscal limits arise due to distortionary taxation and political will. Stochastic shocks are random and could push a fiscally sound policy towards its limit. In equilibrium agents refuse to lend along a path which violates the fiscal limits, creating a fiscal solvency crisis. The dynamics leading to the crisis depend on the policy response to restore lending. We focus on two responses, default and policy switching. We simulate our model to quantify the probability of a fiscal solvency crisis in the European Monetary Union with fiscal variables at end of 2009 values. Our model predict...

Abstract This paper tries to extend the range of techniques for testing the hypothesis of -complete spatiotemporal randomness- in the case of a general type variable with a regional or spatial breakdown. The tests that we can find nowadays in the literature are not well-suited to, for the most part of, series of interest. We have generalized the use of three popular tests of spatial dependence (namely, Moran's I, the spatial BDS and the BP tests) to which we add a Lagrange multiplier test. Furthermore, with a Monte Carlo simulation, we show the finite sample behaviour of the four tests for linear and non-linear processes. The paper finishes with an empirical application to the annual growth rates of employment in European regions. Resumen Este artculo intenta ampliar el rango de tcnicas pa...

In this paper we derive closed-form expressions for the single-user adaptive capacity of generalized selection combining (GSC) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying spatially independent flat Rayleigh fading channel. The complex channel estimate and the actual channel are modelled as jointly Gaussian random variables with a correlation that depends on the estimation quality. Three adaptive transmission schemes are analyzed: (1) optimal power and rate adaptation; and (2) constant power with optimal rate adaptation, and (3) channel inversion with fixed rate. In addition to deriving an exact expression for the capacity of the aforementioned adaptive schemes, we analyze the impact of channel estimation...

We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A central limit theorem (CLT) is valid only if the dynamical system under consideration is sufficiently mixing. For the fully developed logistic map and a cubic map we analytically calculate the leading-order corrections to the CLT if only a finite number of iterates is added and rescaled, and find excellent agreement with numerical experiments. At the critical point of period doubling accumulation, a CLT is not valid anymore due to strong temporal correlations between the iterates. Nevertheless, we provide numerical evidence that in this case the probability density converges to a q -Gaussian, thus leading to a power-law generalization of the CLT. The above behavior is universal and independent of the order of the maximum of the map considered, i.e., relevant for large classes of critical dynamical systems. PMID:17500848

The construction of probabilistic models in computational mechanics requires the effective construction of probability distributions of random variables in high dimension. This paper deals with the effective construction of the probability distribution in high dimension of a vector-valued random var...

Consider a $N\\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $$ Y_{ij}^{n}=\\frac{\\sigma_{ij}(n)}{\\sqrt{n}} X_{ij}^{n}\\ , $$ the $X_{ij}^{n}$ being centered, independent and identically distributed random variables with unit variance and $(\\sigma_{ij}(n); 1\\le i\\le N, 1\\le j...

Let a n , n ? 1 be a sequence of independent standard normal random variables. Consider the random trigonometric polynomial T n (?) = ? j=1 n a j cos(j?), 0 ? ? ? 2? and let N n be the number of real roots of T n (?) in (0, 2?). In this paper it is proved that Formula Not Shown where 0 c 0 < ?.

We consider some random band matrices with band-width $N^\\mu$ whose entries are independent random variables with distribution tail in $x^{-\\alpha}$. We consider the largest eigenvalues and the associated eigenvectors and prove the following phase transition. On the one hand, when $\\alpha<2(1+\\mu^{-...

Let {S_n, n=0,1,2,...} be a random walk generated by a sequence of i.i.d. random variables X_1, X_2,... and let tau be the first descending ladder epoch. Assuming that the distribution of X_1 belongs to the domain of attraction of an alpha-stable law, we study the asymptotic behavior of P(tau=n).

Point scatterers are placed on the real line such that the distances between scatterers are independent identically distributed random variables (stationary renewal process). For a fixed configuration of scatterers a particle performs the following random walk: The particle starts at the pointx with...

Inspired by the theory of financial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in $\\R^d$ is lifted to the space $L^0(\\R^d)$ of $d$-dimensional random variables. In contrast to the classical definition, we define the essentia...

These are notes from a three-lecture mini-course on free probability given at MSRI in the Fall of 2010 and repeated a year later at Harvard. The lectures were aimed at mathematicians and mathematical physicists working in combinatorics, probability, and random matrix theory. The first lecture was a staged rediscovery of free independence from first principles, the second dealt with the additive calculus of free random variables, and the third focused on random matrix models.

Deterministic and random fractals, within the framework of Iterated Function Systems, have been used to model and study a wide range of phenomena across many areas of science and technology. However, for many applications deterministic fractals are locally too similar near distinct points while standard random fractals have too little local correlation. Random fractals are also slow and difficult to compute. These two major problems restricting further applications are solved here by the introduction of V-variable fractals and superfractals.

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well known. We consider both methods in a unified way, and discuss their relation with exhaustive generation methods. We analyse several random variables associated with the algorithms and find their grand probability generating functions, which gives easy access to moments and limit laws.

In 1986 Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well known. We consider both methods in a unified way, and discuss their relation with exhaustive generation methods. We analyse several random variables associated with the algorithms and find their grand probability generating functions, which gives easy access to moments and limit laws.

The design or optimization of engineering systems is generally based on several assumptions related to the loading conditions, physical or mechanical properties, environmental effects, initial or boundary conditions etc. The effect of those assumptions to the optimum design or the design finally adopted is generally unknown particularly in large, complex systems. A rational recourse would be to cast the problem in a probabilistic framework which accounts for the various uncertainties but also allows to quantify their effect in the response/behavior/performance of the system. In such a framework the performance function(s) of interest are also random and optimization of the system with respect to the design variables has to be reformulated with respect to statistical properties of these objectives functions (e.g. probability of exceeding certain thresholds). Analysis tools are usually restricted to elaborate legacy codes which have been developed over a long period of time and are generally well-tested (e.g. Finite Elements). These do not however include any stochastic components and their alteration is impossible or ill-advised. Furthermore as the number of uncertainties and design variables grows, the problem quickly becomes computationally intractable. The present paper advocates the use of statistical learning in order to perform these tasks for any system of arbitrary complexity as long as a deterministic solver is available. The proposed computational framework consists of two components. Firstly advanced sampling techniques are employed in order to efficiently explore the dependence of the performance with respect to the uncertain and design variables. The proposed algorithm is directly parallelizable and attempts to maximize the amount of information extracted with the least possible number of calls to the deterministic solver. The output of this process is utilized by statistical classification procedures in order to derive the dependence of the performance statistics with respect to the design variables. For that purpose we explore parametric and non-parametric (kernel) probit regression schemes and propose an a priori boosting scheme that can improve the accuracy of the estimators. In all cases a Bayesian framework is adopted that produces robust estimates and can also be utilized to obtain confidence intervals. For that purpose the present paper advocates a framework that allows for calculating the values of response statistics with respect to design variables (the latter are deterministic variables) and provide global information about the sensitivity of those statistics to the design variables of interest.

Functional limit theorem for continuous-time random walks (CTRW) are found in general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional dynamics. Probabilistic interpretation of generalized fractional evolution is given in terms of the random time change (subordination) by means of hitting times processes.

This paper proposes two alternative methods of random projections and compares their performance for robust and efficient spam detection when trained using a small number of examples. Robustness refers to learning and adaptation leading to a high level of performance despite data variability, while efficiency is concerned with (i) the complexity of the detection method employed; and (ii) the amount of training resources used for training and retraining. The first method, Random Project, employs a random projection matrix to produce linear combinations of input features, while the second method, Random Boost, employs random feature selection to enhance the performance of the Logit Boost algorithm. Random Boost is, in fact, a combination of Logit Boost and Random Forest. Experimental results...

Background The objective of this study was to analyze systematically the randomized, controlled trials that compared single-incision laparoscopic cholecystectomy (SILC) and conventional laparoscopic cholecystectomy (CLC). Methods The meta-analysis was conducted according to the Quality of Reporting of Meta-analysis (QUORUM) standards. The included studies were analyzed systematically using the statistical software package RevMan. The summated outcomes were expressed as the risk ratios (RR) for dichotomous variables and standardized mean differences (SMD) for continuous variables. Results Eleven randomized trials encompassing 858 patients were retrieved from the electronic databases. In the random effects model, postoperative pain, postoperative complications, length of hospital stay, cosme...

Let Formula Not Shown denote a set of Formula Not Shown independent identically distributed Formula Not Shown -dimensional absolutely continuous random variables. A general class of complete orderings of such random vectors is supplied by viewing them as concomitants of an auxiliary random variable. The resulting definitions of multivariate order statistics subsume and extend orderings that have been previously proposed such as norm ordering and Formula Not Shown -conditional ordering. Analogous concepts of multivariate record values and multivariate generalized order statistics are also described.

The normal phase diffusion problem in magnetic resonance imaging (MRI) is treated by means of the Langevin equation for the phase variable using only the properties of the characteristic function of Gaussian random variables. The calculation may be simply extended to anomalous diffusion using a frac...

Some major variables that largely influenced to on-road fuel economy(dependent variable) are selected by statistic method, and the optimal regression model that estimates the on-road fuel economy is established. In other to increase confidence of the resu...

Naturally sunlit, outdoor growth chambers allow plants to grow under natural light while controlling other environmental variables. Variable transmissions and reflections by chamber walls could attenuate photosynthetically active radiation (PAR) within sunlit chambers from the ambient levels depend...

Recent advances in data reduction for U-Pb geochronology have made it possible to quantitatively interrogate analytical uncertainty budgets. Although the largest sources of uncertainty vary depending on sample size, age, and other factors, uncertainties incurred in measuring the Pb isotopic composition (IC) of the sample and correcting it for mass-dependent fractionation and laboratory blank typically dominate. Systematic uncertainties, such as tracer calibration, may be reduced through better isotopic tracer and standard calibration, but reducing random uncertainties requires improved techniques to increase the resolving power of the U-Pb ID-TIMS technique. For small (Daly detector or SEM—that is capable of counting impingement of individual ions. Although these detectors are highly sensitive, only one isotope can be measured at a time. As most ion beams vary in intensity with time, calculated isotope ratios must be corrected for growth or decay between cycles of isotope measurements. Beam interpolation algorithms included in commercial mass spectrometer software have shortcomings, including unaccounted auto-correlation (e.g. Ludwig, 2010) and problematic covariance estimation. A non-parametric statistical approach avoids these pitfalls while maximizing the use of data and minimizing assumptions about the often-irregular changes in intensity with time. Implementation of a new algorithm should produce more accurate isotope ratio estimates and better quantify their uncertainty. For samples with small ratios of radiogenic to laboratory blank Pb, such as for most < 10 Ma zircons, the largest source of uncertainty in a U-Pb date is the Pb isotopic composition of the laboratory blank. It is difficult to precisely measure small blanks (less than ~0.5 pg) without the addition of a tracer with an enriched artificial isotope (e.g. 205Pb), which has the benefit of allowing the mass of the Pb blank to be determined. However, the IC of the tracer is difficult to separate from the blank IC. This circular effort can be circumvented with a novel algorithm that determines a best-fit mixing line between the laboratory blank and the tracer. Although the tracer IC cannot be located uniquely without more information, the lab blank IC can be determined independently, and its variability is a function of the scatter about the best-fit line. For larger samples with higher ratios of radiogenic Pb to laboratory blank and a single-isotope Pb tracer, the largest source of uncertainty is often variability in mass-dependent isotopic fractionation. Linear fractionation factors are typically calculated between each of the four naturally occurring Pb isotopes for repeated measurements of an isotopic standard, such as NBS 981 or 982, but assessing linearity and determining the average and variability of isotopic fractionation requires consideration of their correlated systematic and random uncertainties. A multivariate minimization algorithm is the best approach to determine an internally consistent fractionation factor. Because isotopic fractionation is the primary source of random variation in these precise U-Pb dates, correct quantification of its magnitude and variability is necessary to interpret the variability of measured datasets.

In quantifying the central tendency of the distribution of a random fuzzy number (or fuzzy random variable in Puri and Ralescu's sense), the most usual measure is the Aumann-type mean, which extends the mean of a real-valued random variable and preserves its main properties and behavior. Although such a behavior has very valuable and convenient implications, `extreme' values or changes of data entail too much influence on the Aumann-type mean of a random fuzzy number. This strong influence motivates the search for a more robust central tendency measure. In this respect, this paper aims to explore the extension of the median to random fuzzy numbers. This extension is based on the 1-norm distance and its adequacy will be shown by analyzing its properties and comparing its robustness ...

A computational framework has been developed for simulations of the behavior of solids and structures made of stochastic elastic-plastic materials. Uncertain elastic-plastic material properties are modeled as random fields, which appear as the coefficient term in the governing partial differential equation of mechanics. A spectral stochastic elastic-plastic finite element method with Fokker-Planck-Kolmogorov equation based probabilistic constitutive integrator is proposed for solution of this non-linear (elastic-plastic) partial differential equation with stochastic coefficient. To this end, the random field material properties are discretized, in both spatial and stochastic dimension, into finite numbers of independent basic random variables, using Karhunen-Loeve expansion. Those random v...

Weighted histograms in Monte-Carlo simulations are often used for the estimation of probability density functions. They are obtained as a result of random experiment with random events that have weights. In this paper the bin contents of a weighted histogram are considered as a sum of random variables with a random number of terms. Generalizations of the classical chi-square test for comparing weighted histograms are proposed. Numerical examples illustrate an application of the tests for the histograms with different statistics of events and different weighted functions. Proposed tests can be used for the comparison of experimental data histograms against simulated data histograms and for two simulated data histograms.

Chip performance and yield are increasingly limited by systematic and random variations introduced during wafer processing. Systematic variations are layout-dependent and can be broadly classified as optical or non-optical in nature. Optical effects have their origin in the lithography process including mask, RET, and resist. Non-optical effects are layout-dependent systematic variations which originate from processes other than lithography. Some examples of nonoptical effects are stress variations, well-proximity effect, spacer thickness variations and rapid thermal anneal (RTA) variations. Semiconductor scaling has led to an increase in the complexity and impact of such effects on circuit parameters. A novel technique for dataprep called electrically-driven optical proximity correction (ED-OPC) has been previously proposed which replaces the conventional OPC objective of minimization of edge placement error (EPE) with an electrical error related cost function. The introduction of electrical objectives into the OPC flow opens up the possibility of compensating for electrical variations which do not necessarily originate from the lithographic process. In this paper, we propose to utilize ED-OPC to compensate for optical as well as non-optical effects in order to mitigate circuit-limited variability and yield. We describe the impact of non-optical effects on circuit parameters such as threshold voltage and mobility. Given accurate models to predict variability of circuit parameters, we show how EDOPC can be leveraged to compensate circuit performance for matching designer intent. Compared to existing compensation techniques such as gate length biasing and metal fills, the primary advantage of using ED-OPC is that the process of fragmentation in OPC allows greater flexibility in tuning transistor properties. The benefits of using ED-OPC to compensate for non-optical effects can be observed in reduced guard-banding, leading to less conservative designs. In addition, results show a 4% average reduction in spread in timing in compensating for intra-die threshold voltage variability, which potentially translates to mitigation of circuit-limited yield.

In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level, it suffices to continue sampling until the sample sum is no less than a certain bound and then take the average of samples as an estimate for the mean of the bounded random variable. We have developed an explicit formula and a bisection search method for the determination of such bound of sample sum, without any knowledge of the bounded variable. Moreover, we have derived bounds for the distribution of sample size. In the special case of Bernoulli random variables, we have established analytical and numerical methods to further reduce the bound of sample sum and thus improve the efficiency of sampling.

A statistical theory of growth curve analysis, which makes use of smoothing splines is formulated and coded for applications. We have tested our codes extensively using computer generated data superposed with random noise of various intensities, by simultaneously fitting all data with two independent variables. We are presently evaluating various experimental data in the MFE database by making use of our codes. Our preliminary results indicate that TFTR ohmic temperature profile shape depends almost exclusively on the edge plasma safety factor, q{sub a}, as was previously shown to be true for ASDEX plasma profiles. The main advantage of the utilization of a simultaneous fitting of all (appropriately normalized) profiles as a function of more than one plasma parameter, is to improve significantly the signal to noise ratio. We also determine the amount of smoothing to be applied during the curve fitting process. An optimally selected smoothing helps to reduce the random noise, but yet allows the predictions to stay close to the data. In addition, the use of a multi-dimensional parameter field provides us with a uniformly valid representation. The curve fitting technique we employ uses a piecewise polynomial spline representation. However, we have eliminated the usually adopted method of setting a simple knot at every data point, for the reason that the experimentally obtained data is usually confined to the values of the plasma parameters bunched together in small intervals which are widely separated. Presently, we are using equally spaced knots.

In the last decades, the amount of published results on clinical diagnostic tests has expanded very rapidly. The counterpart to this development has been the formal evaluation and synthesis of diagnostic results. However, published results present substantial heterogeneity and they can be regarded as so far removed from the classical domain of meta-analysis, that they can provide a rather severe test of classical statistical methods. Recently, bivariate random effects meta-analytic methods, which model the pairs of sensitivities and specificities, have been presented from the classical point of view. In this work a bivariate Bayesian modeling approach is presented. This approach substantially extends the scope of classical bivariate methods by allowing the structural distribution of the random effects to depend on multiple sources of variability. Meta-analysis is summarized by the predictive posterior distributions for sensitivity and specificity. This new approach allows, also, to perform substantial model checking, model diagnostic and model selection. Statistical computations are implemented in the public domain statistical software (WinBUGS and R) and illustrated with real data examples. PMID:21170904

This paper deals with the nonparametric estimation in heteroscedastic regression $ Y_i=f(X_i)+\\xi_i, \\: i=1,...,n $, with incomplete information, i.e. each real random variable $ \\xi_i $ has a density $ g_{i} $ which is unknown to the statistician. The aim is to estimate the regression function $ f $ at a given point. Using a local polynomial fitting from M-estimator denoted $ \\hat f^h $ and applying Lepski's procedure for the bandwidth selection, we construct an estimator $ \\hat f^{\\hat h} $ which is adaptive over the collection of isotropic H\\"{o}lder classes. In particular, we establish new exponential inequalities to control deviations of local M-estimators allowing to construct the minimax estimator. The advantage of this estimator is that it does not depend on densities of random errors and we only assume that the probability density functions are symmetric and monotonically on $ \\bR_+ $. It is important to mention that our estimator is robust compared to extreme values of the noise.

The two-user discrete memoryless state-dependent multiple-access channel (MAC) models a scenario in which two encoders transmit independent messages to a single receiver via a MAC whose channel law is governed by the pair of encoders' inputs and by an i.i.d. state random variable. In the cooperative state-dependent MAC model it is further assumed that Message 1 is shared by both encoders whereas Message 2 is known only to Encoder 2 - the cognitive transmitter. The capacity of the cooperative state-dependent MAC where the realization of the state sequence is known non-causally to the cognitive encoder has been derived by Somekh-Baruch et. al. In this work we dispense of the assumption that Message 1 is shared a-priori by both encoders. Instead, we study the case in which Encoder 2 cribs causally from Encoder 1. We determine the capacity region for both, the case where Encoder 2 cribs strictly causal and the case where Encoder 2 cribs causally from Encoder 1.

The ?-stable distributions introduced by Lévy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life sciences, and economics. In the present paper we study sequences of long-range dependent random variables whose distributions have asymptotic power-law decay, and which are called (q,?)-stable distributions. These sequences are generalizations of independent and identically distributed ?-stable distributions and have not been previously studied. Long-range dependent (q,?)-stable distributions might arise in the description of anomalous processes in nonextensive statistical mechanics, cell biology, finance. The parameter q controls dependence. If q=1 then they are classical independent and identically distributed with ?-stable Lévy distributions. In the present paper we establish basic properties of (q,?)-stable distributions and generalize the result of Umarov et al. [Milan J. Math. 76, 307 (2008)], where the particular case ?=2,q?[1,3) was considered, to the whole range of stability and nonextensivity parameters ??(0,2] and q?[1,3), respectively. We also discuss possible further extensions of the results that we obtain and formulate some conjectures.

Accurate and reliable stream-flow predictions are an important input to water resources planning and management processes, which heavily depend upon the availability of water (e.g. river basin planning, optimal reservoir operation, irrigation system management). Hydrological processes are extremely complex, combining high non-linearity and spatial-temporal variability. The prediction of hydrological variables is therefore a challenging task, very often complicated by lack of data and/or the presence of outliers. Usually, data-driven modelling provides a good balance between model accuracy and complexity, which are ultimately critical to the adoption of optimization-based approaches. While neural networks have been widely used in hydrological modelling (e.g. Govindaraju and Rao, 2000), tree-based model is a relatively unexplored methodology (Solomatine and Dual, 2003; Solomatine and Xue, 2004; Iorgulescu and Beven, 2004; Stravs and Brilly, 2007). In this paper a new data-driven modelling approach based on Ensembles of Extremely Randomized Trees (ETs; Geurts et al., 2006) is proposed for stream-flow prediction using different hydro-meteorological predictors. By randomizing the tree construction process and merging a forest of diversified trees to predict the output, ETs alleviate the well-known poor generalization property of traditional standalone decision tress (e.g. CART), thus avoid over fitting the training data. Input to the model are selected using a tree-based feature ranking algorithm, which ranks the candidate predictors (e.g. precipitation and evaporation at different stations, linear combinations thereof) according to their contribution in explaining the variance of an underlying ETs-based model of the stream-flow process. The approach is applied in the Red river basin (Vietnam), a sub-tropical catchment characterized by extremely variable weather conditions, where strong precipitations significantly contribute to the high flow. Results shown that combining ETs and ranking techniques provides good performance, compared to other data-driven methods (e.g. neural networks or ARX models). References Geurts, P., Ernst, D., Wehenkel, L., 2006. Extremely randomized trees. Machine Learning 63 (1), 3-42. Govindaraju, R. S. , Rao, A. R., 2000. Artificial Neural Network in Hydrology. Kluwer, Dordrecht, The Netherlands. Iorgulescu, I., Beven, K., 2004. Nonparametric direct mapping of rainfall-runoff relationships: An alternative approach to data analysis and modeling?. Water Resources Research 40 (8), W08403. Solomatine, D., Dulal, K., 2003. Model trees as an alternative to neural networks in rainfall-runoff modelling. Hydrological Sciences 48 (3), 399-411. Solomatine, D., Xue, Y., 2004. M5 model trees compared to neural networks: application to flood forecasting in the upper reach of the huai river in china. ASCE Journal of Hydrologic Engineering 9 (6), 491-501. Stravs, L., Brilly, M., 2007. Development of a low-flow forecasting model using the m5 machine learning method. Hydrological Sciences 52 (3), 466-477.

A vibration isolation system with variable damping and stiffness control is practical and has good performances. However, conventional devices of variable stiffness are usually complicated. A magnetorheological (MR) fluid damper only needs a small electric current to provide the magnetic field. It is easy to achieve variable damping with an MR damper in vibration systems. In this paper, two MR fluid dampers in series were used to achieve the variable damping and stiffness for the system. The passive, variable damping, variable stiffness, and variable damping and stiffness systems were investigated in experiment and theoretical calculation. The time and frequency responses to sinusoidal, sweep and random inputs showed that the system with a variable damping and stiffness had better properties.   

Understanding changes in the solar flux over geologic timescales is essential to studies of planetary atmospheres and how planets evolve in general. To this end, we have developed quantitative estimates of the wavelength-dependent solar flux over time. Using multi-wavelength data from the Sun and solar analogs we present a parametrization of the solar flux which is nominally valid from 2-20000 nm, and from 0.02 through 7.1 Gyr. The parameterization is subject to large uncertainties inherent in primary measurement error, the unknown ages of the solar proxies, and the intrinsic variability of the solar analogs. This poster details our procedures in quantifying the effect of these uncertainties on our estimates of the evolving solar flux. From the X-ray to the near UV, we derived thousands of different power law fits to the observational data via a Monte Carlo simulation. During each iteration of the simulation, an age for each solar analog was selected randomly from age ranges found in the literature. These ages are fit against the observational data, which are themselves randomized by their measurement errors and assumed intrinsic variability. This produces multiple power laws fits for flux versus time in various wavelength regimes and strong lines, which we compare against fits assuming exact ages and flux values. We find the integrated mean error (standard deviation / mean) of our Monte Carlo simulations to never be in excess of 100%, with significant decreases in error at older stellar ages. The mean absolute error on any flux value from any wavelength is never above 50%. We therefore submit our model of the solar flux as viable for planetary atmosphere studies which are concerned with the first order evolution of the Sun in time.

Abstract in english Static lung volume (LV) measurements have a number of clinical and research applications; however, no previous studies have provided reference values for such tests using a healthy sample of the adult Brazilian population. With this as our main purpose, we prospectively evaluated 100 non-smoking subjects (50 males and 50 females), 20 to 80 years old, randomly selected from more than 8,000 individuals. Gender-specific linear prediction equations were developed by multiple (more) regression analysis with total lung capacity (TLC), functional residual capacity (FRC), residual volume (RV), RV/TLC ratio and inspiratory capacity (IC) as dependent variables, and with age, height, weight, lean body mass and indexes of physical fitness as independent ones. Simpler demographic and anthropometric variables were as useful as more complex measurements in predicting LV values, independent of gender and age (R2 values ranging from 0.49 to 0.78, P<0.001). Interestingly, prediction equations from North American and European studies overestimated the LV at low volumes and underestimated them at high volumes (P<0.05). Our results, therefore, provide a more appropriate frame of reference to evaluate the normalcy of static lung volume values in Brazilian males and females aged 20 to 80 years.

To date, opipramol has not been examined within the context of evening premedication in anaesthesiology. A suitable drug for such an application should induce anxiolytic and sleep-favouring effects. Due to its pharmacological properties, one would expect opipramol to lead to these effects. In order to test this possibility, 72 female patients were randomly assigned to 50 mg opipramol, 100 mg opipramol, or placebo (n = 24 patients per group) in the evening prior to surgery in a double-blind trial. Effects were recorded in the morning prior to the operation by means of self-rating questionnaires, regarding the patients' current subjective state and their judgement of the quality of sleep during the night before. The self-rating was done by the Multidimensional Mood Inventory BSKE (EWL), by use of the Multidimensional Somatic Symptom List (MSKL), and by use of the Würzburg Sleep Questionnaire. Further dependent variables were heart rate and blood pressure. Opipramol significantly improved sleep quality. Especially the frequency of awakening at night was reduced. These effects could be observed predominantly after 100 mg opipramol. At this dosage, inner excitement was reduced as well. The autonomic variables remained uninfluenced. There were no adverse events and no hints for interactions with anaesthesiology. PMID:12422064

Incorporating results from a previously developed finite element model, an uncertainty and parameter sensitivity analysis was conducted using preliminary site-specific data from Horonobe, Japan (data available from five boreholes as of 2003). Latin Hypercube Sampling was used to draw random parameter values from the site-specific measured, or approximated, physicochemical uncertainty distributions. Using pathlengths and groundwater velocities extracted from the three-dimensional, finite element flow and particle tracking model, breakthrough curves for multiple realizations were calculated with the semi-analytical, one-dimensional, multirate transport code, STAMMT-L. A stepwise linear regression analysis using the 5, 50, and 95% breakthrough times as the dependent variables and LHS sampled site physicochemical parameters as the independent variables was used to perform a sensitivity analysis. Results indicate that the distribution coefficients and hydraulic conductivities are the parameters responsible for most of the variation among simulated breakthrough times. This suggests that researchers and data collectors at the Horonobe site should focus on accurately assessing these parameters and quantifying their uncertainty. Because the Horonobe Underground Research Laboratory is in an early phase of its development, this work should be considered as a first step toward an integration of uncertainty and sensitivity analyses with decision analysis.

The sampling of municipal wastes for description is an important step before processing, recycling and use as fuel. In the French approach, a procedure was described in the circular of February 22, 1973, which uses a statistical method with the tenor as the random variable. However this variable looses its physical character and the heterogeneity, which is at the origin of the results dispersion, is only characterized by the experimental determination of the variance. This approach is difficult to apply because each material has its own heterogeneity (its own variance), and the variance depends on the size of the samples. Therefore numerous applications are required to describe some municipal wastes with a satisfactory precision. Thus, the sampling technique has been simplified using Gy`s sampling theory developed for ores sampling and extrapolated to municipal wastes. This theory binds the mass of the sample with its waste composition, the size of the constituents, their tenor and the relative preciseness expected for the tenors. This paper gives a comparative evaluation of both methods efficiency. (J.S.). 2 refs., 4 tabs.

Background: Stellate ganglion block (SGB) is performed for the diagnosis and treatment of sympathetic dependent pain in the head, neck and upper limbs. However, the effects of bilateral SGB on cardiovascular and autonomic regulation remain unknown. The aim of this study was to assess the effects of bilateral SGB on cardiovascular and autonomic function by measuring heart rate variability (HRV), systolic blood pressure variability (SBPV) and spontaneous baroreflex sensitivity (SBRS). Methods and Results: Twenty healthy volunteers were randomly allocated to receive right or left SGB with 8 ml 1% lidocaine solution; after 20 min, the contralateral side SGB was performed. Changes in the RR interval (RRI), systolic blood pressure (SBP), HRV, SBPV and SBRS were assessed before and after bilateral SGB. The low-frequency (LF, 0.04-0.15 Hz) and high-frequency (HF, 0.15-0.4 Hz) components of HRV and SBRS decreased significantly; however, no significant changes were found in RRI, SBP and the LF and HF components of SBPV after bilateral SGB. In subjects with symptoms of vagal blockade, HRV, SBP and SBRS were significantly affected by bilateral SGB. Conclusions: Bilateral SGB should be performed cautiously because it can reduce cardiac vagal modulation and BRS, especially for those with symptoms of vagal blockade after bilateral SGB.   

ABSTRACT: BACKGROUND: The classic determination of burnout is by means of the dimensions exhaustion, cynicism and inefficacy. A new definition of the syndrome is based on clinical subtypes, consisting of "frenetic" (involved, ambitious, overloaded), "underchallenged" (indifferent, bored, with lack of personal development) and "worn-out" (neglectful, unacknowledged, with little control). The dimensions of overload, lack of development and neglect form a shortened version of this perspective. The aims of this study were to estimate and to compare the explanatory power of both typological models, short and long, with the standard measurement. METHODS: This was a cross-sectional survey with a randomly sample of university employees (n=409). Multivariate linear regression models were constructed between the "Maslach Burnout Inventory General Survey" (MBI-GS) dimensions, as dependent variables, and the "Burnout Clinical Subtype Questionnaire" (BCSQ-36 and BCSQ-12) dimensions, as independent variables. RESULTS: The BCSQ-36 subscales together explained 53% of 'exhaustion' (pexhaustion' (pexhaustion' (p<0.001), and for 'cynicism' (p<0.001) and 'efficacy (p<0.001). CONCLUSIONS: Both BCSQ-36 and BCSQ-12 demonstrate great explanatory power over the standard MBI-GS, while offering a useful characterization of the syndrome for the evaluation and design of interventions tailored to the characteristics of each individual. The BCSQ-36 may be very useful in mental health services, given that it provides a good deal of information, while the BCSQ-12 could be used as a screening measure in primary care consultations owing to its simplicity and functional nature. PMID:23110723

Abstract in english The strength of the respiratory muscles can be evaluated from static measurements (maximal inspiratory and expiratory pressures, MIP and MEP) or inferred from dynamic maneuvers (maximal voluntary ventilation, MVV). Although these data could be suitable for a number of clinical and research applications, no previous studies have provided reference values for such tests using a healthy, randomly selected sample of the adult Brazilian population. With this main purpose, we p (more) rospectively evaluated 100 non-smoking subjects (50 males and 50 females), 20 to 80 years old, selected from more than 8,000 individuals. Gender-specific linear prediction equations for MIP, MEP and MVV were developed by multiple regression analysis: age and, secondarily, anthropometric measurements explained up to 56% of the variability of the dependent variables. The most cited previous studies using either Caucasian or non-Caucasian samples systematically underestimated the observed values of MIP (P<0.05). Interestingly, the self-reported level of regular physical activity and maximum aerobic power correlates strongly with both respiratory and peripheral muscular strength (knee extensor peak torque) (P<0.01). Our results, therefore, provide a new frame of reference to evaluate the normalcy of some useful indexes of respiratory muscle strength in Brazilian males and females aged 20 to 80.