Optimal allocation of testing resources for statistical simulations

NASA Astrophysics Data System (ADS)

Quintana, Carolina; Millwater, Harry R.; Singh, Gulshan; Golden, Patrick

2015-07-01

Statistical estimates from simulation involve uncertainty caused by the variability in the input random variables due to limited data. Allocating resources to obtain more experimental data of the input variables to better characterize their probability distributions can reduce the variance of statistical estimates. The methodology proposed determines the optimal number of additional experiments required to minimize the variance of the output moments given single or multiple constraints. The method uses multivariate t-distribution and Wishart distribution to generate realizations of the population mean and covariance of the input variables, respectively, given an amount of available data. This method handles independent and correlated random variables. A particle swarm method is used for the optimization. The optimal number of additional experiments per variable depends on the number and variance of the initial data, the influence of the variable in the output function and the cost of each additional experiment. The methodology is demonstrated using a fretting fatigue example.

Relevance of anisotropy and spatial variability of gas diffusivity for soil-gas transport

NASA Astrophysics Data System (ADS)

Schack-Kirchner, Helmer; Kühne, Anke; Lang, Friederike

2017-04-01

Models of soil gas transport generally do not consider neither direction dependence of gas diffusivity, nor its small-scale variability. However, in a recent study, we could provide evidence for anisotropy favouring vertical gas diffusion in natural soils. We hypothesize that gas transport models based on gas diffusion data measured with soil rings are strongly influenced by both, anisotropy and spatial variability and the use of averaged diffusivities could be misleading. To test this we used a 2-dimensional model of soil gas transport to under compacted wheel tracks to model the soil-air oxygen distribution in the soil. The model was parametrized with data obtained from soil-ring measurements with its central tendency and variability. The model includes vertical parameter variability as well as variation perpendicular to the elongated wheel track. Different parametrization types have been tested: [i)]Averaged values for wheel track and undisturbed. em [ii)]Random distribution of soil cells with normally distributed variability within the strata. em [iii)]Random distributed soil cells with uniformly distributed variability within the strata. All three types of small-scale variability has been tested for [j)] isotropic gas diffusivity and em [jj)]reduced horizontal gas diffusivity (constant factor), yielding in total six models. As expected the different parametrizations had an important influence to the aeration state under wheel tracks with the strongest oxygen depletion in case of uniformly distributed variability and anisotropy towards higher vertical diffusivity. The simple simulation approach clearly showed the relevance of anisotropy and spatial variability in case of identical central tendency measures of gas diffusivity. However, until now it did not consider spatial dependency of variability, that could even aggravate effects. To consider anisotropy and spatial variability in gas transport models we recommend a) to measure soil-gas transport parameters spatially explicit including different directions and b) to use random-field stochastic models to assess the possible effects for gas-exchange models.

On the Wigner law in dilute random matrices

NASA Astrophysics Data System (ADS)

Khorunzhy, A.; Rodgers, G. J.

1998-12-01

We consider ensembles of N × N symmetric matrices whose entries are weakly dependent random variables. We show that random dilution can change the limiting eigenvalue distribution of such matrices. We prove that under general and natural conditions the normalised eigenvalue counting function coincides with the semicircle (Wigner) distribution in the limit N → ∞. This can be explained by the observation that dilution (or more generally, random modulation) eliminates the weak dependence (or correlations) between random matrix entries. It also supports our earlier conjecture that the Wigner distribution is stable to random dilution and modulation.

Measurement variability error for estimates of volume change

Treesearch

James A. Westfall; Paul L. Patterson

2007-01-01

Using quality assurance data, measurement variability distributions were developed for attributes that affect tree volume prediction. Random deviations from the measurement variability distributions were applied to 19381 remeasured sample trees in Maine. The additional error due to measurement variation and measurement bias was estimated via a simulation study for...

Selection of Variables in Cluster Analysis: An Empirical Comparison of Eight Procedures

ERIC Educational Resources Information Center

Steinley, Douglas; Brusco, Michael J.

2008-01-01

Eight different variable selection techniques for model-based and non-model-based clustering are evaluated across a wide range of cluster structures. It is shown that several methods have difficulties when non-informative variables (i.e., random noise) are included in the model. Furthermore, the distribution of the random noise greatly impacts the…

A random effects meta-analysis model with Box-Cox transformation.

PubMed

Yamaguchi, Yusuke; Maruo, Kazushi; Partlett, Christopher; Riley, Richard D

2017-07-19

In a random effects meta-analysis model, true treatment effects for each study are routinely assumed to follow a normal distribution. However, normality is a restrictive assumption and the misspecification of the random effects distribution may result in a misleading estimate of overall mean for the treatment effect, an inappropriate quantification of heterogeneity across studies and a wrongly symmetric prediction interval. We focus on problems caused by an inappropriate normality assumption of the random effects distribution, and propose a novel random effects meta-analysis model where a Box-Cox transformation is applied to the observed treatment effect estimates. The proposed model aims to normalise an overall distribution of observed treatment effect estimates, which is sum of the within-study sampling distributions and the random effects distribution. When sampling distributions are approximately normal, non-normality in the overall distribution will be mainly due to the random effects distribution, especially when the between-study variation is large relative to the within-study variation. The Box-Cox transformation addresses this flexibly according to the observed departure from normality. We use a Bayesian approach for estimating parameters in the proposed model, and suggest summarising the meta-analysis results by an overall median, an interquartile range and a prediction interval. The model can be applied for any kind of variables once the treatment effect estimate is defined from the variable. A simulation study suggested that when the overall distribution of treatment effect estimates are skewed, the overall mean and conventional I 2 from the normal random effects model could be inappropriate summaries, and the proposed model helped reduce this issue. We illustrated the proposed model using two examples, which revealed some important differences on summary results, heterogeneity measures and prediction intervals from the normal random effects model. The random effects meta-analysis with the Box-Cox transformation may be an important tool for examining robustness of traditional meta-analysis results against skewness on the observed treatment effect estimates. Further critical evaluation of the method is needed.

Rupture Propagation for Stochastic Fault Models

NASA Astrophysics Data System (ADS)

Favreau, P.; Lavallee, D.; Archuleta, R.

2003-12-01

The inversion of strong motion data of large earhquakes give the spatial distribution of pre-stress on the ruptured faults and it can be partially reproduced by stochastic models, but a fundamental question remains: how rupture propagates, constrained by the presence of spatial heterogeneity? For this purpose we investigate how the underlying random variables, that control the pre-stress spatial variability, condition the propagation of the rupture. Two stochastic models of prestress distributions are considered, respectively based on Cauchy and Gaussian random variables. The parameters of the two stochastic models have values corresponding to the slip distribution of the 1979 Imperial Valley earthquake. We use a finite difference code to simulate the spontaneous propagation of shear rupture on a flat fault in a 3D continuum elastic body. The friction law is the slip dependent friction law. The simulations show that the propagation of the rupture front is more complex, incoherent or snake-like for a prestress distribution based on Cauchy random variables. This may be related to the presence of a higher number of asperities in this case. These simulations suggest that directivity is stronger in the Cauchy scenario, compared to the smoother rupture of the Gauss scenario.

Copula Models for Sociology: Measures of Dependence and Probabilities for Joint Distributions

ERIC Educational Resources Information Center

Vuolo, Mike

2017-01-01

Often in sociology, researchers are confronted with nonnormal variables whose joint distribution they wish to explore. Yet, assumptions of common measures of dependence can fail or estimating such dependence is computationally intensive. This article presents the copula method for modeling the joint distribution of two random variables, including…

Smooth conditional distribution function and quantiles under random censorship.

PubMed

Leconte, Eve; Poiraud-Casanova, Sandrine; Thomas-Agnan, Christine

2002-09-01

We consider a nonparametric random design regression model in which the response variable is possibly right censored. The aim of this paper is to estimate the conditional distribution function and the conditional alpha-quantile of the response variable. We restrict attention to the case where the response variable as well as the explanatory variable are unidimensional and continuous. We propose and discuss two classes of estimators which are smooth with respect to the response variable as well as to the covariate. Some simulations demonstrate that the new methods have better mean square error performances than the generalized Kaplan-Meier estimator introduced by Beran (1981) and considered in the literature by Dabrowska (1989, 1992) and Gonzalez-Manteiga and Cadarso-Suarez (1994).

Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part I: Fundamentals

NASA Astrophysics Data System (ADS)

Yan, Wang-Ji; Ren, Wei-Xin

2016-12-01

Recent advances in signal processing and structural dynamics have spurred the adoption of transmissibility functions in academia and industry alike. Due to the inherent randomness of measurement and variability of environmental conditions, uncertainty impacts its applications. This study is focused on statistical inference for raw scalar transmissibility functions modeled as complex ratio random variables. The goal is achieved through companion papers. This paper (Part I) is dedicated to dealing with a formal mathematical proof. New theorems on multivariate circularly-symmetric complex normal ratio distribution are proved on the basis of principle of probabilistic transformation of continuous random vectors. The closed-form distributional formulas for multivariate ratios of correlated circularly-symmetric complex normal random variables are analytically derived. Afterwards, several properties are deduced as corollaries and lemmas to the new theorems. Monte Carlo simulation (MCS) is utilized to verify the accuracy of some representative cases. This work lays the mathematical groundwork to find probabilistic models for raw scalar transmissibility functions, which are to be expounded in detail in Part II of this study.

Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

NASA Astrophysics Data System (ADS)

Pato, Mauricio P.; Oshanin, Gleb

2013-03-01

We study the probability distribution function P(β)n(w) of the Schmidt-like random variable w = x21/(∑j = 1nx2j/n), where xj, (j = 1, 2, …, n), are unordered eigenvalues of a given n × n β-Gaussian random matrix, β being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual (randomly chosen) eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n → ∞ and for arbitrary β the distribution P(β)n(w) converges to the Marčenko-Pastur form, i.e. is defined as P_{n}^{( \\beta )}(w) \\sim \\sqrt{(4 - w)/w} for w ∈ [0, 4] and equals zero outside of the support, despite the fact that formally w is defined on the interval [0, n]. Furthermore, for Gaussian unitary ensembles (β = 2) we present exact explicit expressions for P(β = 2)n(w) which are valid for arbitrary n and analyse their behaviour.

SETI and SEH (Statistical Equation for Habitables)

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2011-01-01

The statistics of habitable planets may be based on a set of ten (and possibly more) astrobiological requirements first pointed out by Stephen H. Dole in his book "Habitable planets for man" (1964). In this paper, we first provide the statistical generalization of the original and by now too simplistic Dole equation. In other words, a product of ten positive numbers is now turned into the product of ten positive random variables. This we call the SEH, an acronym standing for "Statistical Equation for Habitables". The mathematical structure of the SEH is then derived. The proof 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. In conclusion, we show that The new random variable NHab, yielding the number of habitables (i.e. habitable planets) in the Galaxy, follows the lognormal distribution. By construction, the mean value of this lognormal distribution is the total number of habitable planets as given by the statistical Dole equation. But now we also derive the standard deviation, the mode, the median and all the moments of this new lognormal NHab random variable. The ten (or more) astrobiological factors are now positive random variables. The probability distribution of each random variable may be arbitrary. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our SEH by allowing an arbitrary probability distribution for each factor. This is both astrobiologically realistic and useful for any further investigations. An application of our SEH then follows. The (average) distancebetween any two nearby habitable planets in the Galaxy may be shown to be inversely proportional to the cubic root of NHab. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density function, apparently previously unknown and dubbed "Maccone distribution" by Paul Davies in 2008. Data Enrichment Principle. It should be noticed that ANY positive number of random variables in the SEH is compatible with the CLT. So, our generalization allows for many more factors to be added in the future as long as more refined scientific knowledge about each factor will be known to the scientists. This capability to make room for more future factors in the SEH we call the "Data Enrichment Principle", and we regard it as the key to more profound future results in the fields of Astrobiology and SETI. A practical example is then given of how our SEH works numerically. We work out in detail the case where each of the ten random variables is uniformly distributed around its own mean value as given by Dole back in 1964 and has an assumed standard deviation of 10%. The conclusion is that the average number of habitable planets in the Galaxy should be around 100 million±200 million, and the average distance in between any couple of nearby habitable planets should be about 88 light years±40 light years. Finally, we match our SEH results against the results of the Statistical Drake Equation that we introduced in our 2008 IAC presentation. As expected, the number of currently communicating ET civilizations in the Galaxy turns out to be much smaller than the number of habitable planets (about 10,000 against 100 million, i.e. one ET civilization out of 10,000 habitable planets). And the average distance between any two nearby habitable planets turns out to be much smaller than the average distance between any two neighboring ET civilizations: 88 light years vs. 2000 light years, respectively. This means an ET average distance about 20 times higher than the average distance between any couple of adjacent habitable planets.

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings.

PubMed

Tang, Yang; Gao, Huijun; Zou, Wei; Kurths, Jürgen

2013-02-01

In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes.

PubMed

Hougaard, P; Lee, M L; Whitmore, G A

1997-12-01

Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.

A Unifying Probability Example.

ERIC Educational Resources Information Center

Maruszewski, Richard F., Jr.

2002-01-01

Presents an example from probability and statistics that ties together several topics including the mean and variance of a discrete random variable, the binomial distribution and its particular mean and variance, the sum of independent random variables, the mean and variance of the sum, and the central limit theorem. Uses Excel to illustrate these…

A Random Variable Transformation Process.

ERIC Educational Resources Information Center

Scheuermann, Larry

1989-01-01

Provides a short BASIC program, RANVAR, which generates random variates for various theoretical probability distributions. The seven variates include: uniform, exponential, normal, binomial, Poisson, Pascal, and triangular. (MVL)

Evaluation of Kurtosis into the product of two normally distributed variables

NASA Astrophysics Data System (ADS)

Oliveira, Amílcar; Oliveira, Teresa; Seijas-Macías, Antonio

2016-06-01

Kurtosis (κ) is any measure of the "peakedness" of a distribution of a real-valued random variable. We study the evolution of the Kurtosis for the product of two normally distributed variables. Product of two normal variables is a very common problem for some areas of study, like, physics, economics, psychology, … Normal variables have a constant value for kurtosis (κ = 3), independently of the value of the two parameters: mean and variance. In fact, the excess kurtosis is defined as κ- 3 and the Normal Distribution Kurtosis is zero. The product of two normally distributed variables is a function of the parameters of the two variables and the correlation between then, and the range for kurtosis is in [0, 6] for independent variables and in [0, 12] when correlation between then is allowed.

Sums and Products of Jointly Distributed Random Variables: A Simplified Approach

ERIC Educational Resources Information Center

Stein, Sheldon H.

2005-01-01

Three basic theorems concerning expected values and variances of sums and products of random variables play an important role in mathematical statistics and its applications in education, business, the social sciences, and the natural sciences. A solid understanding of these theorems requires that students be familiar with the proofs of these…

An instrumental variable random-coefficients model for binary outcomes

PubMed Central

Chesher, Andrew; Rosen, Adam M

2014-01-01

In this paper, we study a random-coefficients model for a binary outcome. We allow for the possibility that some or even all of the explanatory variables are arbitrarily correlated with the random coefficients, thus permitting endogeneity. We assume the existence of observed instrumental variables Z that are jointly independent with the random coefficients, although we place no structure on the joint determination of the endogenous variable X and instruments Z, as would be required for a control function approach. The model fits within the spectrum of generalized instrumental variable models, and we thus apply identification results from our previous studies of such models to the present context, demonstrating their use. Specifically, we characterize the identified set for the distribution of random coefficients in the binary response model with endogeneity via a collection of conditional moment inequalities, and we investigate the structure of these sets by way of numerical illustration. PMID:25798048

Multivariate stochastic simulation with subjective multivariate normal distributions

Treesearch

P. J. Ince; J. Buongiorno

1991-01-01

In many applications of Monte Carlo simulation in forestry or forest products, it may be known that some variables are correlated. However, for simplicity, in most simulations it has been assumed that random variables are independently distributed. This report describes an alternative Monte Carlo simulation technique for subjectively assesed multivariate normal...

Optimal partitioning of random programs across two processors

NASA Technical Reports Server (NTRS)

Nicol, D. M.

1986-01-01

The optimal partitioning of random distributed programs is discussed. It is concluded that the optimal partitioning of a homogeneous random program over a homogeneous distributed system either assigns all modules to a single processor, or distributes the modules as evenly as possible among all processors. The analysis rests heavily on the approximation which equates the expected maximum of a set of independent random variables with the set's maximum expectation. The results are strengthened by providing an approximation-free proof of this result for two processors under general conditions on the module execution time distribution. It is also shown that use of this approximation causes two of the previous central results to be false.

Anderson localization for radial tree-like random quantum graphs

NASA Astrophysics Data System (ADS)

Hislop, Peter D.; Post, Olaf

We prove that certain random models associated with radial, tree-like, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model (RLM) and the random Kirchhoff model (RKM). In the RLM, the lengths of each generation of edges form a family of independent, identically distributed random variables (iid). For the RKM, the iid random variables are associated with each generation of vertices and moderate the current flow through the vertex. We consider extensions to various families of decorated graphs and prove stability of localization with respect to decoration. In particular, we prove Anderson localization for the random necklace model.

Designing management strategies for carbon dioxide storage and utilization under uncertainty using inexact modelling

NASA Astrophysics Data System (ADS)

Wang, Yu; Fan, Jie; Xu, Ye; Sun, Wei; Chen, Dong

2017-06-01

Effective application of carbon capture, utilization and storage (CCUS) systems could help to alleviate the influence of climate change by reducing carbon dioxide (CO2) emissions. The research objective of this study is to develop an equilibrium chance-constrained programming model with bi-random variables (ECCP model) for supporting the CCUS management system under random circumstances. The major advantage of the ECCP model is that it tackles random variables as bi-random variables with a normal distribution, where the mean values follow a normal distribution. This could avoid irrational assumptions and oversimplifications in the process of parameter design and enrich the theory of stochastic optimization. The ECCP model is solved by an equilibrium change-constrained programming algorithm, which provides convenience for decision makers to rank the solution set using the natural order of real numbers. The ECCP model is applied to a CCUS management problem, and the solutions could be useful in helping managers to design and generate rational CO2-allocation patterns under complexities and uncertainties.

The Newcomb-Benford law in its relation to some common distributions.

PubMed

Formann, Anton K

2010-05-07

An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors.

Algebraic Functions of H-Functions with Specific Dependency Structure.

DTIC Science & Technology

1984-05-01

a study of its characteristic function. Such analysis is reproduced in books by Springer (17), Anderson (23), Feller (34,35), Mood and Graybill (52...following linearity property for expectations of jointly distributed random variables is derived. r 1 Theorem 1.1: If X and Y are real random variables...appear in American Journal of Mathematical and Management Science. 13. Mathai, A.M., and R.K. Saxena, "On linear combinations of stochastic variables

The study of combining Latin Hypercube Sampling method and LU decomposition method (LULHS method) for constructing spatial random field

NASA Astrophysics Data System (ADS)

WANG, P. T.

2015-12-01

Groundwater modeling requires to assign hydrogeological properties to every numerical grid. Due to the lack of detailed information and the inherent spatial heterogeneity, geological properties can be treated as random variables. Hydrogeological property is assumed to be a multivariate distribution with spatial correlations. By sampling random numbers from a given statistical distribution and assigning a value to each grid, a random field for modeling can be completed. Therefore, statistics sampling plays an important role in the efficiency of modeling procedure. Latin Hypercube Sampling (LHS) is a stratified random sampling procedure that provides an efficient way to sample variables from their multivariate distributions. This study combines the the stratified random procedure from LHS and the simulation by using LU decomposition to form LULHS. Both conditional and unconditional simulations of LULHS were develpoed. The simulation efficiency and spatial correlation of LULHS are compared to the other three different simulation methods. The results show that for the conditional simulation and unconditional simulation, LULHS method is more efficient in terms of computational effort. Less realizations are required to achieve the required statistical accuracy and spatial correlation.

Comonotonic bounds on the survival probabilities in the Lee-Carter model for mortality projection

NASA Astrophysics Data System (ADS)

Denuit, Michel; Dhaene, Jan

2007-06-01

In the Lee-Carter framework, future survival probabilities are random variables with an intricate distribution function. In large homogeneous portfolios of life annuities, value-at-risk or conditional tail expectation of the total yearly payout of the company are approximately equal to the corresponding quantities involving random survival probabilities. This paper aims to derive some bounds in the increasing convex (or stop-loss) sense on these random survival probabilities. These bounds are obtained with the help of comonotonic upper and lower bounds on sums of correlated random variables.

Bayesian statistics and Monte Carlo methods

NASA Astrophysics Data System (ADS)

Koch, K. R.

2018-03-01

The Bayesian approach allows an intuitive way to derive the methods of statistics. Probability is defined as a measure of the plausibility of statements or propositions. Three rules are sufficient to obtain the laws of probability. If the statements refer to the numerical values of variables, the so-called random variables, univariate and multivariate distributions follow. They lead to the point estimation by which unknown quantities, i.e. unknown parameters, are computed from measurements. The unknown parameters are random variables, they are fixed quantities in traditional statistics which is not founded on Bayes' theorem. Bayesian statistics therefore recommends itself for Monte Carlo methods, which generate random variates from given distributions. Monte Carlo methods, of course, can also be applied in traditional statistics. The unknown parameters, are introduced as functions of the measurements, and the Monte Carlo methods give the covariance matrix and the expectation of these functions. A confidence region is derived where the unknown parameters are situated with a given probability. Following a method of traditional statistics, hypotheses are tested by determining whether a value for an unknown parameter lies inside or outside the confidence region. The error propagation of a random vector by the Monte Carlo methods is presented as an application. If the random vector results from a nonlinearly transformed vector, its covariance matrix and its expectation follow from the Monte Carlo estimate. This saves a considerable amount of derivatives to be computed, and errors of the linearization are avoided. The Monte Carlo method is therefore efficient. If the functions of the measurements are given by a sum of two or more random vectors with different multivariate distributions, the resulting distribution is generally not known. TheMonte Carlo methods are then needed to obtain the covariance matrix and the expectation of the sum.

Simulation of the Effects of Random Measurement Errors

ERIC Educational Resources Information Center

Kinsella, I. A.; Hannaidh, P. B. O.

1978-01-01

Describes a simulation method for measurement of errors that requires calculators and tables of random digits. Each student simulates the random behaviour of the component variables in the function and by combining the results of all students, the outline of the sampling distribution of the function can be obtained. (GA)

Compiling probabilistic, bio-inspired circuits on a field programmable analog array

PubMed Central

Marr, Bo; Hasler, Jennifer

2014-01-01

A field programmable analog array (FPAA) is presented as an energy and computational efficiency engine: a mixed mode processor for which functions can be compiled at significantly less energy costs using probabilistic computing circuits. More specifically, it will be shown that the core computation of any dynamical system can be computed on the FPAA at significantly less energy per operation than a digital implementation. A stochastic system that is dynamically controllable via voltage controlled amplifier and comparator thresholds is implemented, which computes Bernoulli random variables. From Bernoulli variables it is shown exponentially distributed random variables, and random variables of an arbitrary distribution can be computed. The Gillespie algorithm is simulated to show the utility of this system by calculating the trajectory of a biological system computed stochastically with this probabilistic hardware where over a 127X performance improvement over current software approaches is shown. The relevance of this approach is extended to any dynamical system. The initial circuits and ideas for this work were generated at the 2008 Telluride Neuromorphic Workshop. PMID:24847199

The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells.

PubMed

Levine, M W

1991-01-01

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity.(ABSTRACT TRUNCATED AT 250 WORDS)

Quantiles for Finite Mixtures of Normal Distributions

ERIC Educational Resources Information Center

Rahman, Mezbahur; Rahman, Rumanur; Pearson, Larry M.

2006-01-01

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

Pigeons' Choices between Fixed-Interval and Random-Interval Schedules: Utility of Variability?

ERIC Educational Resources Information Center

Andrzejewski, Matthew E.; Cardinal, Claudia D.; Field, Douglas P.; Flannery, Barbara A.; Johnson, Michael; Bailey, Kathleen; Hineline, Philip N.

2005-01-01

Pigeons' choosing between fixed-interval and random-interval schedules of reinforcement was investigated in three experiments using a discrete-trial procedure. In all three experiments, the random-interval schedule was generated by sampling a probability distribution at an interval (and in multiples of the interval) equal to that of the…

Transcription, intercellular variability and correlated random walk.

PubMed

Müller, Johannes; Kuttler, Christina; Hense, Burkhard A; Zeiser, Stefan; Liebscher, Volkmar

2008-11-01

We develop a simple model for the random distribution of a gene product. It is assumed that the only source of variance is due to switching transcription on and off by a random process. Under the condition that the transition rates between on and off are constant we find that the amount of mRNA follows a scaled Beta distribution. Additionally, a simple positive feedback loop is considered. The simplicity of the model allows for an explicit solution also in this setting. These findings in turn allow, e.g., for easy parameter scans. We find that bistable behavior translates into bimodal distributions. These theoretical findings are in line with experimental results.

Reward and uncertainty in exploration programs

NASA Technical Reports Server (NTRS)

Kaufman, G. M.; Bradley, P. G.

1971-01-01

A set of variables which are crucial to the economic outcome of petroleum exploration are discussed. These are treated as random variables; the values they assume indicate the number of successes that occur in a drilling program and determine, for a particular discovery, the unit production cost and net economic return if that reservoir is developed. In specifying the joint probability law for those variables, extreme and probably unrealistic assumptions are made. In particular, the different random variables are assumed to be independently distributed. Using postulated probability functions and specified parameters, values are generated for selected random variables, such as reservoir size. From this set of values the economic magnitudes of interest, net return and unit production cost are computed. This constitutes a single trial, and the procedure is repeated many times. The resulting histograms approximate the probability density functions of the variables which describe the economic outcomes of an exploratory drilling program.

A single-loop optimization method for reliability analysis with second order uncertainty

NASA Astrophysics Data System (ADS)

Xie, Shaojun; Pan, Baisong; Du, Xiaoping

2015-08-01

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush-Kuhn-Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.

Survival curve estimation with dependent left truncated data using Cox's model.

PubMed

Mackenzie, Todd

2012-10-19

The Kaplan-Meier and closely related Lynden-Bell estimators are used to provide nonparametric estimation of the distribution of a left-truncated random variable. These estimators assume that the left-truncation variable is independent of the time-to-event. This paper proposes a semiparametric method for estimating the marginal distribution of the time-to-event that does not require independence. It models the conditional distribution of the time-to-event given the truncation variable using Cox's model for left truncated data, and uses inverse probability weighting. We report the results of simulations and illustrate the method using a survival study.

Do bioclimate variables improve performance of climate envelope models?

USGS Publications Warehouse

Watling, James I.; Romañach, Stephanie S.; Bucklin, David N.; Speroterra, Carolina; Brandt, Laura A.; Pearlstine, Leonard G.; Mazzotti, Frank J.

2012-01-01

Climate envelope models are widely used to forecast potential effects of climate change on species distributions. A key issue in climate envelope modeling is the selection of predictor variables that most directly influence species. To determine whether model performance and spatial predictions were related to the selection of predictor variables, we compared models using bioclimate variables with models constructed from monthly climate data for twelve terrestrial vertebrate species in the southeastern USA using two different algorithms (random forests or generalized linear models), and two model selection techniques (using uncorrelated predictors or a subset of user-defined biologically relevant predictor variables). There were no differences in performance between models created with bioclimate or monthly variables, but one metric of model performance was significantly greater using the random forest algorithm compared with generalized linear models. Spatial predictions between maps using bioclimate and monthly variables were very consistent using the random forest algorithm with uncorrelated predictors, whereas we observed greater variability in predictions using generalized linear models.

Random dopant fluctuations and statistical variability in n-channel junctionless FETs

NASA Astrophysics Data System (ADS)

Akhavan, N. D.; Umana-Membreno, G. A.; Gu, R.; Antoszewski, J.; Faraone, L.

2018-01-01

The influence of random dopant fluctuations on the statistical variability of the electrical characteristics of n-channel silicon junctionless nanowire transistor (JNT) has been studied using three dimensional quantum simulations based on the non-equilibrium Green’s function (NEGF) formalism. Average randomly distributed body doping densities of 2 × 1019, 6 × 1019 and 1 × 1020 cm-3 have been considered employing an atomistic model for JNTs with gate lengths of 5, 10 and 15 nm. We demonstrate that by properly adjusting the doping density in the JNT, a near ideal statistical variability and electrical performance can be achieved, which can pave the way for the continuation of scaling in silicon CMOS technology.

A Geostatistical Scaling Approach for the Generation of Non Gaussian Random Variables and Increments

NASA Astrophysics Data System (ADS)

Guadagnini, Alberto; Neuman, Shlomo P.; Riva, Monica; Panzeri, Marco

2016-04-01

We address manifestations of non-Gaussian statistical scaling displayed by many variables, Y, and their (spatial or temporal) increments. Evidence of such behavior includes symmetry of increment distributions at all separation distances (or lags) with sharp peaks and heavy tails which tend to decay asymptotically as lag increases. Variables reported to exhibit such distributions include quantities of direct relevance to hydrogeological sciences, e.g. porosity, log permeability, electrical resistivity, soil and sediment texture, sediment transport rate, rainfall, measured and simulated turbulent fluid velocity, and other. No model known to us captures all of the documented statistical scaling behaviors in a unique and consistent manner. We recently proposed a generalized sub-Gaussian model (GSG) which reconciles within a unique theoretical framework the probability distributions of a target variable and its increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. In this context, we demonstrated the feasibility of estimating all key parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random field, and explore them on one- and two-dimensional synthetic test cases.

Stochastical analysis of surfactant-enhanced remediation of denser-than-water nonaqueous phase liquid (DNAPL)-contaminated soils.

PubMed

Zhang, Renduo; Wood, A Lynn; Enfield, Carl G; Jeong, Seung-Woo

2003-01-01

Stochastical analysis was performed to assess the effect of soil spatial variability and heterogeneity on the recovery of denser-than-water nonaqueous phase liquids (DNAPL) during the process of surfactant-enhanced remediation. UTCHEM, a three-dimensional, multicomponent, multiphase, compositional model, was used to simulate water flow and chemical transport processes in heterogeneous soils. Soil spatial variability and heterogeneity were accounted for by considering the soil permeability as a spatial random variable and a geostatistical method was used to generate random distributions of the permeability. The randomly generated permeability fields were incorporated into UTCHEM to simulate DNAPL transport in heterogeneous media and stochastical analysis was conducted based on the simulated results. From the analysis, an exponential relationship between average DNAPL recovery and soil heterogeneity (defined as the standard deviation of log of permeability) was established with a coefficient of determination (r2) of 0.991, which indicated that DNAPL recovery decreased exponentially with increasing soil heterogeneity. Temporal and spatial distributions of relative saturations in the water phase, DNAPL, and microemulsion in heterogeneous soils were compared with those in homogeneous soils and related to soil heterogeneity. Cleanup time and uncertainty to determine DNAPL distributions in heterogeneous soils were also quantified. The study would provide useful information to design strategies for the characterization and remediation of nonaqueous phase liquid-contaminated soils with spatial variability and heterogeneity.

Visualizing Time-Varying Distribution Data in EOS Application

NASA Technical Reports Server (NTRS)

Shen, Han-Wei

2004-01-01

In this research, we have developed several novel visualization methods for spatial probability density function data. Our focus has been on 2D spatial datasets, where each pixel is a random variable, and has multiple samples which are the results of experiments on that random variable. We developed novel clustering algorithms as a means to reduce the information contained in these datasets; and investigated different ways of interpreting and clustering the data.

Correlated Sources in Distributed Networks--Data Transmission, Common Information Characterization and Inferencing

ERIC Educational Resources Information Center

Liu, Wei

2011-01-01

Correlation is often present among observations in a distributed system. This thesis deals with various design issues when correlated data are observed at distributed terminals, including: communicating correlated sources over interference channels, characterizing the common information among dependent random variables, and testing the presence of…

The beta distribution: A statistical model for world cloud cover

NASA Technical Reports Server (NTRS)

Falls, L. W.

1973-01-01

Much work has been performed in developing empirical global cloud cover models. This investigation was made to determine an underlying theoretical statistical distribution to represent worldwide cloud cover. The beta distribution with probability density function is given to represent the variability of this random variable. It is shown that the beta distribution possesses the versatile statistical characteristics necessary to assume the wide variety of shapes exhibited by cloud cover. A total of 160 representative empirical cloud cover distributions were investigated and the conclusion was reached that this study provides sufficient statical evidence to accept the beta probability distribution as the underlying model for world cloud cover.

Qualitatively Assessing Randomness in SVD Results

NASA Astrophysics Data System (ADS)

Lamb, K. W.; Miller, W. P.; Kalra, A.; Anderson, S.; Rodriguez, A.

2012-12-01

Singular Value Decomposition (SVD) is a powerful tool for identifying regions of significant co-variability between two spatially distributed datasets. SVD has been widely used in atmospheric research to define relationships between sea surface temperatures, geopotential height, wind, precipitation and streamflow data for myriad regions across the globe. A typical application for SVD is to identify leading climate drivers (as observed in the wind or pressure data) for a particular hydrologic response variable such as precipitation, streamflow, or soil moisture. One can also investigate the lagged relationship between a climate variable and the hydrologic response variable using SVD. When performing these studies it is important to limit the spatial bounds of the climate variable to reduce the chance of random co-variance relationships being identified. On the other hand, a climate region that is too small may ignore climate signals which have more than a statistical relationship to a hydrologic response variable. The proposed research seeks to identify a qualitative method of identifying random co-variability relationships between two data sets. The research identifies the heterogeneous correlation maps from several past results and compares these results with correlation maps produced using purely random and quasi-random climate data. The comparison identifies a methodology to determine if a particular region on a correlation map may be explained by a physical mechanism or is simply statistical chance.

Single-photon continuous-variable quantum key distribution based on the energy-time uncertainty relation.

PubMed

Qi, Bing

2006-09-15

We propose a new quantum key distribution protocol in which information is encoded on continuous variables of a single photon. In this protocol, Alice randomly encodes her information on either the central frequency of a narrowband single-photon pulse or the time delay of a broadband single-photon pulse, while Bob randomly chooses to do either frequency measurement or time measurement. The security of this protocol rests on the energy-time uncertainty relation, which prevents Eve from simultaneously determining both frequency and time information with arbitrarily high resolution. Since no interferometer is employed in this scheme, it is more robust against various channel noises, such as polarization and phase fluctuations.

Joint probabilities and quantum cognition

NASA Astrophysics Data System (ADS)

de Barros, J. Acacio

2012-12-01

In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.

Effect of randomness in logistic maps

NASA Astrophysics Data System (ADS)

Khaleque, Abdul; Sen, Parongama

2015-01-01

We study a random logistic map xt+1 = atxt[1 - xt] where at are bounded (q1 ≤ at ≤ q2), random variables independently drawn from a distribution. xt does not show any regular behavior in time. We find that xt shows fully ergodic behavior when the maximum allowed value of at is 4. However , averaged over different realizations reaches a fixed point. For 1 ≤ at ≤ 4, the system shows nonchaotic behavior and the Lyapunov exponent is strongly dependent on the asymmetry of the distribution from which at is drawn. Chaotic behavior is seen to occur beyond a threshold value of q1(q2) when q2(q1) is varied. The most striking result is that the random map is chaotic even when q2 is less than the threshold value 3.5699⋯ at which chaos occurs in the nonrandom map. We also employ a different method in which a different set of random variables are used for the evolution of two initially identical x values, here the chaotic regime exists for all q1 ≠ q2 values.

Does the central limit theorem always apply to phase noise? Some implications for radar problems

NASA Astrophysics Data System (ADS)

Gray, John E.; Addison, Stephen R.

2017-05-01

The phase noise problem or Rayleigh problem occurs in all aspects of radar. It is an effect that a radar engineer or physicist always has to take into account as part of a design or in attempt to characterize the physics of a problem such as reverberation. Normally, the mathematical difficulties of phase noise characterization are avoided by assuming the phase noise probability distribution function (PDF) is uniformly distributed, and the Central Limit Theorem (CLT) is invoked to argue that the superposition of relatively few random components obey the CLT and hence the superposition can be treated as a normal distribution. By formalizing the characterization of phase noise (see Gray and Alouani) for an individual random variable, the summation of identically distributed random variables is the product of multiple characteristic functions (CF). The product of the CFs for phase noise has a CF that can be analyzed to understand the limitations CLT when applied to phase noise. We mirror Kolmogorov's original proof as discussed in Papoulis to show the CLT can break down for receivers that gather limited amounts of data as well as the circumstances under which it can fail for certain phase noise distributions. We then discuss the consequences of this for matched filter design as well the implications for some physics problems.

Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory

NASA Astrophysics Data System (ADS)

Alvarez, Diego A.; Uribe, Felipe; Hurtado, Jorge E.

2018-02-01

Random set theory is a general framework which comprises uncertainty in the form of probability boxes, possibility distributions, cumulative distribution functions, Dempster-Shafer structures or intervals; in addition, the dependence between the input variables can be expressed using copulas. In this paper, the lower and upper bounds on the probability of failure are calculated by means of random set theory. In order to accelerate the calculation, a well-known and efficient probability-based reliability method known as subset simulation is employed. This method is especially useful for finding small failure probabilities in both low- and high-dimensional spaces, disjoint failure domains and nonlinear limit state functions. The proposed methodology represents a drastic reduction of the computational labor implied by plain Monte Carlo simulation for problems defined with a mixture of representations for the input variables, while delivering similar results. Numerical examples illustrate the efficiency of the proposed approach.

Multivariate non-normally distributed random variables in climate research - introduction to the copula approach

NASA Astrophysics Data System (ADS)

Schölzel, C.; Friederichs, P.

2008-10-01

Probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts which is due to a possible nonlinear dependence between the random variables. One approach to this problem is the use of copulas, which have become popular over recent years, especially in fields like econometrics, finance, risk management, or insurance. Since this newly emerging field includes various practices, a controversial discussion, and vast field of literature, it is difficult to get an overview. The aim of this paper is therefore to provide an brief overview of copulas for application in meteorology and climate research. We examine the advantages and disadvantages compared to alternative approaches like e.g. mixture models, summarize the current problem of goodness-of-fit (GOF) tests for copulas, and discuss the connection with multivariate extremes. An application to station data shows the simplicity and the capabilities as well as the limitations of this approach. Observations of daily precipitation and temperature are fitted to a bivariate model and demonstrate, that copulas are valuable complement to the commonly used methods.

Scaling exponents for ordered maxima

DOE PAGES

Ben-Naim, E.; Krapivsky, P. L.; Lemons, N. W.

2015-12-22

We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running maxima of m independent sequences and investigate the probability S N that the maxima are perfectly ordered, that is, the running maximum of the first sequence is always larger than that of the second sequence, which is always larger than the running maximum of the third sequence, and so on. The probability S N is universal: it does not depend on themore » distribution from which the random variables are drawn. For two sequences, S N~N –1/2, and in general, the decay is algebraic, S N~N –σm, for large N. We analytically obtain the exponent σ 3≅1.302931 as root of a transcendental equation. Moreover, the exponents σ m grow with m, and we show that σ m~m for large m.« less

Two Universality Properties Associated with the Monkey Model of Zipf's Law

NASA Astrophysics Data System (ADS)

Perline, Richard; Perline, Ron

2016-03-01

The distribution of word probabilities in the monkey model of Zipf's law is associated with two universality properties: (1) the power law exponent converges strongly to $-1$ as the alphabet size increases and the letter probabilities are specified as the spacings from a random division of the unit interval for any distribution with a bounded density function on $[0,1]$; and (2), on a logarithmic scale the version of the model with a finite word length cutoff and unequal letter probabilities is approximately normally distributed in the part of the distribution away from the tails. The first property is proved using a remarkably general limit theorem for the logarithm of sample spacings from Shao and Hahn, and the second property follows from Anscombe's central limit theorem for a random number of i.i.d. random variables. The finite word length model leads to a hybrid Zipf-lognormal mixture distribution closely related to work in other areas.

[The reentrant binomial model of nuclear anomalies growth in rhabdomyosarcoma RA-23 cell populations under increasing doze of rare ionizing radiation].

PubMed

Alekseeva, N P; Alekseev, A O; Vakhtin, Iu B; Kravtsov, V Iu; Kuzovatov, S N; Skorikova, T I

2008-01-01

Distributions of nuclear morphology anomalies in transplantable rabdomiosarcoma RA-23 cell populations were investigated under effect of ionizing radiation from 0 to 45 Gy. Internuclear bridges, nuclear protrusions and dumbbell-shaped nuclei were accepted for morphological anomalies. Empirical distributions of the number of anomalies per 100 nuclei were used. The adequate model of reentrant binomial distribution has been found. The sum of binomial random variables with binomial number of summands has such distribution. Averages of these random variables were named, accordingly, internal and external average reentrant components. Their maximum likelihood estimations were received. Statistical properties of these estimations were investigated by means of statistical modeling. It has been received that at equally significant correlation between the radiation dose and the average of nuclear anomalies in cell populations after two-three cellular cycles from the moment of irradiation in vivo the irradiation doze significantly correlates with internal average reentrant component, and in remote descendants of cell transplants irradiated in vitro - with external one.

Random walk in nonhomogeneous environments: A possible approach to human and animal mobility

NASA Astrophysics Data System (ADS)

Srokowski, Tomasz

2017-03-01

The random walk process in a nonhomogeneous medium, characterized by a Lévy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is affected by the variable width and the variance may be finite; then all kinds of the anomalous diffusion are predicted. In the former case, only the time characteristics are sensitive to the variable width. The corresponding Langevin equation with different interpretations of the multiplicative noise is discussed. The dependence of the distribution width on position after jump is interpreted in terms of cognitive abilities and related to such problems as migration in a human population and foraging habits of animals.

Reliability of stiffened structural panels: Two examples

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson; Davis, D. Dale, Jr.; Maring, Lise D.; Krishnamurthy, Thiagaraja; Elishakoff, Isaac

1992-01-01

The reliability of two graphite-epoxy stiffened panels that contain uncertainties is examined. For one panel, the effect of an overall bow-type initial imperfection is studied. The size of the bow is assumed to be a random variable. The failure mode is buckling. The benefits of quality control are explored by using truncated distributions. For the other panel, the effect of uncertainties in a strain-based failure criterion is studied. The allowable strains are assumed to be random variables. A geometrically nonlinear analysis is used to calculate a detailed strain distribution near an elliptical access hole in a wing panel that was tested to failure. Calculated strains are used to predict failure. Results are compared with the experimental failure load of the panel.

Random trinomial tree models and vanilla options

NASA Astrophysics Data System (ADS)

Ganikhodjaev, Nasir; Bayram, Kamola

2013-09-01

In this paper we introduce and study random trinomial model. The usual trinomial model is prescribed by triple of numbers (u, d, m). We call the triple (u, d, m) an environment of the trinomial model. A triple (Un, Dn, Mn), where {Un}, {Dn} and {Mn} are the sequences of independent, identically distributed random variables with 0 < Dn < 1 < Un and Mn = 1 for all n, is called a random environment and trinomial tree model with random environment is called random trinomial model. The random trinomial model is considered to produce more accurate results than the random binomial model or usual trinomial model.

On the Use of the Beta Distribution in Probabilistic Resource Assessments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olea, Ricardo A., E-mail: olea@usgs.gov

2011-12-15

The triangular distribution is a popular choice when it comes to modeling bounded continuous random variables. Its wide acceptance derives mostly from its simple analytic properties and the ease with which modelers can specify its three parameters through the extremes and the mode. On the negative side, hardly any real process follows a triangular distribution, which from the outset puts at a disadvantage any model employing triangular distributions. At a time when numerical techniques such as the Monte Carlo method are displacing analytic approaches in stochastic resource assessments, easy specification remains the most attractive characteristic of the triangular distribution. Themore » beta distribution is another continuous distribution defined within a finite interval offering wider flexibility in style of variation, thus allowing consideration of models in which the random variables closely follow the observed or expected styles of variation. Despite its more complex definition, generation of values following a beta distribution is as straightforward as generating values following a triangular distribution, leaving the selection of parameters as the main impediment to practically considering beta distributions. This contribution intends to promote the acceptance of the beta distribution by explaining its properties and offering several suggestions to facilitate the specification of its two shape parameters. In general, given the same distributional parameters, use of the beta distributions in stochastic modeling may yield significantly different results, yet better estimates, than the triangular distribution.« less

Probabilistic evaluation of fuselage-type composite structures

NASA Technical Reports Server (NTRS)

Shiao, Michael C.; Chamis, Christos C.

1992-01-01

A methodology is developed to computationally simulate the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, natural frequencies, displacements, stress/strain etc., which are the consequences of the random variation (scatter) of the primitive (independent random) variables in the constituent, ply, laminate and structural levels. This methodology is implemented in the IPACS (Integrated Probabilistic Assessment of Composite Structures) computer code. A fuselage-type composite structure is analyzed to demonstrate the code's capability. The probability distribution functions of the buckling loads, natural frequency, displacement, strain and stress are computed. The sensitivity of each primitive (independent random) variable to a given structural response is also identified from the analyses.

Characterizing ISI and sub-threshold membrane potential distributions: Ensemble of IF neurons with random squared-noise intensity.

PubMed

Kumar, Sanjeev; Karmeshu

2018-04-01

A theoretical investigation is presented that characterizes the emerging sub-threshold membrane potential and inter-spike interval (ISI) distributions of an ensemble of IF neurons that group together and fire together. The squared-noise intensity σ 2 of the ensemble of neurons is treated as a random variable to account for the electrophysiological variations across population of nearly identical neurons. Employing superstatistical framework, both ISI distribution and sub-threshold membrane potential distribution of neuronal ensemble are obtained in terms of generalized K-distribution. The resulting distributions exhibit asymptotic behavior akin to stretched exponential family. Extensive simulations of the underlying SDE with random σ 2 are carried out. The results are found to be in excellent agreement with the analytical results. The analysis has been extended to cover the case corresponding to independent random fluctuations in drift in addition to random squared-noise intensity. The novelty of the proposed analytical investigation for the ensemble of IF neurons is that it yields closed form expressions of probability distributions in terms of generalized K-distribution. Based on a record of spiking activity of thousands of neurons, the findings of the proposed model are validated. The squared-noise intensity σ 2 of identified neurons from the data is found to follow gamma distribution. The proposed generalized K-distribution is found to be in excellent agreement with that of empirically obtained ISI distribution of neuronal ensemble. Copyright © 2018 Elsevier B.V. All rights reserved.

Scaling the Poisson Distribution

ERIC Educational Resources Information Center

Farnsworth, David L.

2014-01-01

We derive the additive property of Poisson random variables directly from the probability mass function. An important application of the additive property to quality testing of computer chips is presented.

Scenario generation for stochastic optimization problems via the sparse grid method

DOE PAGES

Chen, Michael; Mehrotra, Sanjay; Papp, David

2015-04-19

We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid methodmore » can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.« less

System Lifetimes, The Memoryless Property, Euler's Constant, and Pi

ERIC Educational Resources Information Center

Agarwal, Anurag; Marengo, James E.; Romero, Likin Simon

2013-01-01

A "k"-out-of-"n" system functions as long as at least "k" of its "n" components remain operational. Assuming that component failure times are independent and identically distributed exponential random variables, we find the distribution of system failure time. After some examples, we find the limiting…

Is the Non-Dipole Magnetic Field Random?

NASA Technical Reports Server (NTRS)

Walker, Andrew D.; Backus, George E.

1996-01-01

Statistical modelling of the Earth's magnetic field B has a long history. In particular, the spherical harmonic coefficients of scalar fields derived from B can be treated as Gaussian random variables. In this paper, we give examples of highly organized fields whose spherical harmonic coefficients pass tests for independent Gaussian random variables. The fact that coefficients at some depth may be usefully summarized as independent samples from a normal distribution need not imply that there really is some physical, random process at that depth. In fact, the field can be extremely structured and still be regarded for some purposes as random. In this paper, we examined the radial magnetic field B(sub r) produced by the core, but the results apply to any scalar field on the core-mantle boundary (CMB) which determines B outside the CMB.

Simulation of Crack Propagation in Engine Rotating Components under Variable Amplitude Loading

NASA Technical Reports Server (NTRS)

Bonacuse, P. J.; Ghosn, L. J.; Telesman, J.; Calomino, A. M.; Kantzos, P.

1998-01-01

The crack propagation life of tested specimens has been repeatedly shown to strongly depend on the loading history. Overloads and extended stress holds at temperature can either retard or accelerate the crack growth rate. Therefore, to accurately predict the crack propagation life of an actual component, it is essential to approximate the true loading history. In military rotorcraft engine applications, the loading profile (stress amplitudes, temperature, and number of excursions) can vary significantly depending on the type of mission flown. To accurately assess the durability of a fleet of engines, the crack propagation life distribution of a specific component should account for the variability in the missions performed (proportion of missions flown and sequence). In this report, analytical and experimental studies are described that calibrate/validate the crack propagation prediction capability ]or a disk alloy under variable amplitude loading. A crack closure based model was adopted to analytically predict the load interaction effects. Furthermore, a methodology has been developed to realistically simulate the actual mission mix loading on a fleet of engines over their lifetime. A sequence of missions is randomly selected and the number of repeats of each mission in the sequence is determined assuming a Poisson distributed random variable with a given mean occurrence rate. Multiple realizations of random mission histories are generated in this manner and are used to produce stress, temperature, and time points for fracture mechanics calculations. The result is a cumulative distribution of crack propagation lives for a given, life limiting, component location. This information can be used to determine a safe retirement life or inspection interval for the given location.

Planetarium instructional efficacy: A research synthesis

NASA Astrophysics Data System (ADS)

Brazell, Bruce D.

The purpose of the current study was to explore the instructional effectiveness of the planetarium in astronomy education using meta-analysis. A review of the literature revealed 46 studies related to planetarium efficacy. However, only 19 of the studies satisfied selection criteria for inclusion in the meta-analysis. Selected studies were then subjected to coding procedures, which extracted information such as subject characteristics, experimental design, and outcome measures. From these data, 24 effect sizes were calculated in the area of student achievement and five effect sizes were determined in the area of student attitudes using reported statistical information. Mean effect sizes were calculated for both the achievement and the attitude distributions. Additionally, each effect size distribution was subjected to homogeneity analysis. The attitude distribution was found to be homogeneous with a mean effect size of -0.09, which was not significant, p = .2535. The achievement distribution was found to be heterogeneous with a statistically significant mean effect size of +0.28, p < .05. Since the achievement distribution was heterogeneous, the analog to the ANOVA procedure was employed to explore variability in this distribution in terms of the coded variables. The analog to the ANOVA procedure revealed that the variability introduced by the coded variables did not fully explain the variability in the achievement distribution beyond subject-level sampling error under a fixed effects model. Therefore, a random effects model analysis was performed which resulted in a mean effect size of +0.18, which was not significant, p = .2363. However, a large random effect variance component was determined indicating that the differences between studies were systematic and yet to be revealed. The findings of this meta-analysis showed that the planetarium has been an effective instructional tool in astronomy education in terms of student achievement. However, the meta-analysis revealed that the planetarium has not been a very effective tool for improving student attitudes towards astronomy.

General Exact Solution to the Problem of the Probability Density for Sums of Random Variables

NASA Astrophysics Data System (ADS)

Tribelsky, Michael I.

2002-07-01

The exact explicit expression for the probability density pN(x) for a sum of N random, arbitrary correlated summands is obtained. The expression is valid for any number N and any distribution of the random summands. Most attention is paid to application of the developed approach to the case of independent and identically distributed summands. The obtained results reproduce all known exact solutions valid for the, so called, stable distributions of the summands. It is also shown that if the distribution is not stable, the profile of pN(x) may be divided into three parts, namely a core (small x), a tail (large x), and a crossover from the core to the tail (moderate x). The quantitative description of all three parts as well as that for the entire profile is obtained. A number of particular examples are considered in detail.

General exact solution to the problem of the probability density for sums of random variables.

PubMed

Tribelsky, Michael I

2002-08-12

The exact explicit expression for the probability density p(N)(x) for a sum of N random, arbitrary correlated summands is obtained. The expression is valid for any number N and any distribution of the random summands. Most attention is paid to application of the developed approach to the case of independent and identically distributed summands. The obtained results reproduce all known exact solutions valid for the, so called, stable distributions of the summands. It is also shown that if the distribution is not stable, the profile of p(N)(x) may be divided into three parts, namely a core (small x), a tail (large x), and a crossover from the core to the tail (moderate x). The quantitative description of all three parts as well as that for the entire profile is obtained. A number of particular examples are considered in detail.

A probabilistic fatigue analysis of multiple site damage

NASA Technical Reports Server (NTRS)

Rohrbaugh, S. M.; Ruff, D.; Hillberry, B. M.; Mccabe, G.; Grandt, A. F., Jr.

1994-01-01

The variability in initial crack size and fatigue crack growth is incorporated in a probabilistic model that is used to predict the fatigue lives for unstiffened aluminum alloy panels containing multiple site damage (MSD). The uncertainty of the damage in the MSD panel is represented by a distribution of fatigue crack lengths that are analytically derived from equivalent initial flaw sizes. The variability in fatigue crack growth rate is characterized by stochastic descriptions of crack growth parameters for a modified Paris crack growth law. A Monte-Carlo simulation explicitly describes the MSD panel by randomly selecting values from the stochastic variables and then grows the MSD cracks with a deterministic fatigue model until the panel fails. Different simulations investigate the influences of the fatigue variability on the distributions of remaining fatigue lives. Six cases that consider fixed and variable conditions of initial crack size and fatigue crack growth rate are examined. The crack size distribution exhibited a dominant effect on the remaining fatigue life distribution, and the variable crack growth rate exhibited a lesser effect on the distribution. In addition, the probabilistic model predicted that only a small percentage of the life remains after a lead crack develops in the MSD panel.

CDC6600 subroutine for normal random variables. [RVNORM (RMU, SIG)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amos, D.E.

1977-04-01

A value y for a uniform variable on (0,1) is generated and a table of 96-percent points for the (0,1) normal distribution is interpolated for a value of the normal variable x(0,1) on 0.02 less than or equal to y less than or equal to 0.98. For the tails, the inverse normal is computed by a rational Chebyshev approximation in an appropriate variable. Then X = x sigma + ..mu.. gives the X(..mu..,sigma) variable.

Sound Effects for Children's Comprehension of Variably-Paced Television Programs.

ERIC Educational Resources Information Center

Calvert, Sandra L.; Scott, M. Catherine

In this study, children's selective attention to, and comprehension of, variably-paced television programs were examined as a function of sound effects. Sixty-four children, equally distributed by sex and by preschool and fourth grades, were randomly assigned to one of four treatment conditions which crossed two levels of sound effects (presence…

Random variability explains apparent global clustering of large earthquakes

USGS Publications Warehouse

Michael, A.J.

2011-01-01

The occurrence of 5 Mw ≥ 8.5 earthquakes since 2004 has created a debate over whether or not we are in a global cluster of large earthquakes, temporarily raising risks above long-term levels. I use three classes of statistical tests to determine if the record of M ≥ 7 earthquakes since 1900 can reject a null hypothesis of independent random events with a constant rate plus localized aftershock sequences. The data cannot reject this null hypothesis. Thus, the temporal distribution of large global earthquakes is well-described by a random process, plus localized aftershocks, and apparent clustering is due to random variability. Therefore the risk of future events has not increased, except within ongoing aftershock sequences, and should be estimated from the longest possible record of events.

A Dynamic Bayesian Network Model for the Production and Inventory Control

NASA Astrophysics Data System (ADS)

Shin, Ji-Sun; Takazaki, Noriyuki; Lee, Tae-Hong; Kim, Jin-Il; Lee, Hee-Hyol

In general, the production quantities and delivered goods are changed randomly and then the total stock is also changed randomly. This paper deals with the production and inventory control using the Dynamic Bayesian Network. Bayesian Network is a probabilistic model which represents the qualitative dependence between two or more random variables by the graph structure, and indicates the quantitative relations between individual variables by the conditional probability. The probabilistic distribution of the total stock is calculated through the propagation of the probability on the network. Moreover, an adjusting rule of the production quantities to maintain the probability of a lower limit and a ceiling of the total stock to certain values is shown.

On the Use of the Beta Distribution in Probabilistic Resource Assessments

USGS Publications Warehouse

Olea, R.A.

2011-01-01

The triangular distribution is a popular choice when it comes to modeling bounded continuous random variables. Its wide acceptance derives mostly from its simple analytic properties and the ease with which modelers can specify its three parameters through the extremes and the mode. On the negative side, hardly any real process follows a triangular distribution, which from the outset puts at a disadvantage any model employing triangular distributions. At a time when numerical techniques such as the Monte Carlo method are displacing analytic approaches in stochastic resource assessments, easy specification remains the most attractive characteristic of the triangular distribution. The beta distribution is another continuous distribution defined within a finite interval offering wider flexibility in style of variation, thus allowing consideration of models in which the random variables closely follow the observed or expected styles of variation. Despite its more complex definition, generation of values following a beta distribution is as straightforward as generating values following a triangular distribution, leaving the selection of parameters as the main impediment to practically considering beta distributions. This contribution intends to promote the acceptance of the beta distribution by explaining its properties and offering several suggestions to facilitate the specification of its two shape parameters. In general, given the same distributional parameters, use of the beta distributions in stochastic modeling may yield significantly different results, yet better estimates, than the triangular distribution. ?? 2011 International Association for Mathematical Geology (outside the USA).

Logistic quantile regression provides improved estimates for bounded avian counts: A case study of California Spotted Owl fledgling production

USGS Publications Warehouse

Cade, Brian S.; Noon, Barry R.; Scherer, Rick D.; Keane, John J.

2017-01-01

Counts of avian fledglings, nestlings, or clutch size that are bounded below by zero and above by some small integer form a discrete random variable distribution that is not approximated well by conventional parametric count distributions such as the Poisson or negative binomial. We developed a logistic quantile regression model to provide estimates of the empirical conditional distribution of a bounded discrete random variable. The logistic quantile regression model requires that counts are randomly jittered to a continuous random variable, logit transformed to bound them between specified lower and upper values, then estimated in conventional linear quantile regression, repeating the 3 steps and averaging estimates. Back-transformation to the original discrete scale relies on the fact that quantiles are equivariant to monotonic transformations. We demonstrate this statistical procedure by modeling 20 years of California Spotted Owl fledgling production (0−3 per territory) on the Lassen National Forest, California, USA, as related to climate, demographic, and landscape habitat characteristics at territories. Spotted Owl fledgling counts increased nonlinearly with decreasing precipitation in the early nesting period, in the winter prior to nesting, and in the prior growing season; with increasing minimum temperatures in the early nesting period; with adult compared to subadult parents; when there was no fledgling production in the prior year; and when percentage of the landscape surrounding nesting sites (202 ha) with trees ≥25 m height increased. Changes in production were primarily driven by changes in the proportion of territories with 2 or 3 fledglings. Average variances of the discrete cumulative distributions of the estimated fledgling counts indicated that temporal changes in climate and parent age class explained 18% of the annual variance in owl fledgling production, which was 34% of the total variance. Prior fledgling production explained as much of the variance in the fledgling counts as climate, parent age class, and landscape habitat predictors. Our logistic quantile regression model can be used for any discrete response variables with fixed upper and lower bounds.

Evaluation of a Class of Simple and Effective Uncertainty Methods for Sparse Samples of Random Variables and Functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romero, Vicente; Bonney, Matthew; Schroeder, Benjamin

When very few samples of a random quantity are available from a source distribution of unknown shape, it is usually not possible to accurately infer the exact distribution from which the data samples come. Under-estimation of important quantities such as response variance and failure probabilities can result. For many engineering purposes, including design and risk analysis, we attempt to avoid under-estimation with a strategy to conservatively estimate (bound) these types of quantities -- without being overly conservative -- when only a few samples of a random quantity are available from model predictions or replicate experiments. This report examines a classmore » of related sparse-data uncertainty representation and inference approaches that are relatively simple, inexpensive, and effective. Tradeoffs between the methods' conservatism, reliability, and risk versus number of data samples (cost) are quantified with multi-attribute metrics use d to assess method performance for conservative estimation of two representative quantities: central 95% of response; and 10 -4 probability of exceeding a response threshold in a tail of the distribution. Each method's performance is characterized with 10,000 random trials on a large number of diverse and challenging distributions. The best method and number of samples to use in a given circumstance depends on the uncertainty quantity to be estimated, the PDF character, and the desired reliability of bounding the true value. On the basis of this large data base and study, a strategy is proposed for selecting the method and number of samples for attaining reasonable credibility levels in bounding these types of quantities when sparse samples of random variables or functions are available from experiments or simulations.« less

On the null distribution of Bayes factors in linear regression

USDA-ARS?s Scientific Manuscript database

We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...

Multiplicative processes in visual cognition

NASA Astrophysics Data System (ADS)

Credidio, H. F.; Teixeira, E. N.; Reis, S. D. S.; Moreira, A. A.; Andrade, J. S.

2014-03-01

The Central Limit Theorem (CLT) is certainly one of the most important results in the field of statistics. The simple fact that the addition of many random variables can generate the same probability curve, elucidated the underlying process for a broad spectrum of natural systems, ranging from the statistical distribution of human heights to the distribution of measurement errors, to mention a few. An extension of the CLT can be applied to multiplicative processes, where a given measure is the result of the product of many random variables. The statistical signature of these processes is rather ubiquitous, appearing in a diverse range of natural phenomena, including the distributions of incomes, body weights, rainfall, and fragment sizes in a rock crushing process. Here we corroborate results from previous studies which indicate the presence of multiplicative processes in a particular type of visual cognition task, namely, the visual search for hidden objects. Precisely, our results from eye-tracking experiments show that the distribution of fixation times during visual search obeys a log-normal pattern, while the fixational radii of gyration follow a power-law behavior.

Mathematical and physical meaning of the Bell inequalities

NASA Astrophysics Data System (ADS)

Santos, Emilio

2016-09-01

It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values \\{0,1\\}. A hidden variables model may be defined as a mapping between a set of quantum projection operators and a set of random variables. The model is noncontextual if there is a joint probability distribution. The Bell inequalities are necessary conditions for its existence. The inequalities are most relevant when measurements are performed at space-like separation, thus showing a conflict between quantum mechanics and local realism (Bell's theorem). The relations of the Bell inequalities with contextuality, the Kochen-Specker theorem, and quantum entanglement are briefly discussed.

A unified approach for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties

NASA Astrophysics Data System (ADS)

Lü, Hui; Shangguan, Wen-Bin; Yu, Dejie

2017-09-01

Automotive brake systems are always subjected to various types of uncertainties and two types of random-fuzzy uncertainties may exist in the brakes. In this paper, a unified approach is proposed for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties. In the proposed approach, two uncertainty analysis models with mixed variables are introduced to model the random-fuzzy uncertainties. The first one is the random and fuzzy model, in which random variables and fuzzy variables exist simultaneously and independently. The second one is the fuzzy random model, in which uncertain parameters are all treated as random variables while their distribution parameters are expressed as fuzzy numbers. Firstly, the fuzziness is discretized by using α-cut technique and the two uncertainty analysis models are simplified into random-interval models. Afterwards, by temporarily neglecting interval uncertainties, the random-interval models are degraded into random models, in which the expectations, variances, reliability indexes and reliability probabilities of system stability functions are calculated. And then, by reconsidering the interval uncertainties, the bounds of the expectations, variances, reliability indexes and reliability probabilities are computed based on Taylor series expansion. Finally, by recomposing the analysis results at each α-cut level, the fuzzy reliability indexes and probabilities can be obtained, by which the brake squeal instability can be evaluated. The proposed approach gives a general framework to deal with both types of random-fuzzy uncertainties that may exist in the brakes and its effectiveness is demonstrated by numerical examples. It will be a valuable supplement to the systematic study of brake squeal considering uncertainty.

Polynomial chaos representation of databases on manifolds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soize, C., E-mail: christian.soize@univ-paris-est.fr; Ghanem, R., E-mail: ghanem@usc.edu

2017-04-15

Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. Themore » method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.« less

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Englander, Arnold C.

2014-01-01

Trajectory optimization methods using monotonic basin hopping (MBH) have become well developed during the past decade [1, 2, 3, 4, 5, 6]. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing random variable (RV)s from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by J. Englander [3, 6]) significantly improves monotonic basin hopping (MBH) performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness. Efficiency is finding better solutions in less time. Robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive random walks (RWs) originally developed in the field of statistical physics.

Computational procedure of optimal inventory model involving controllable backorder rate and variable lead time with defective units

NASA Astrophysics Data System (ADS)

Lee, Wen-Chuan; Wu, Jong-Wuu; Tsou, Hsin-Hui; Lei, Chia-Ling

2012-10-01

This article considers that the number of defective units in an arrival order is a binominal random variable. We derive a modified mixture inventory model with backorders and lost sales, in which the order quantity and lead time are decision variables. In our studies, we also assume that the backorder rate is dependent on the length of lead time through the amount of shortages and let the backorder rate be a control variable. In addition, we assume that the lead time demand follows a mixture of normal distributions, and then relax the assumption about the form of the mixture of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. Furthermore, we develop an algorithm procedure to obtain the optimal ordering strategy for each case. Finally, three numerical examples are also given to illustrate the results.

Benford's law and continuous dependent random variables

NASA Astrophysics Data System (ADS)

Becker, Thealexa; Burt, David; Corcoran, Taylor C.; Greaves-Tunnell, Alec; Iafrate, Joseph R.; Jing, Joy; Miller, Steven J.; Porfilio, Jaclyn D.; Ronan, Ryan; Samranvedhya, Jirapat; Strauch, Frederick W.; Talbut, Blaine

2018-01-01

Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11% of the time, as one would expect if all digits were equally likely, but rather 30%. This phenomenon is known as Benford's Law. Analyzing which datasets adhere to Benford's Law and how quickly Benford behavior sets in are the two most important problems in the field. Most previous work studied systems of independent random variables, and relied on the independence in their analyses. Inspired by natural processes such as particle decay, we study the dependent random variables that emerge from models of decomposition of conserved quantities. We prove that in many instances the distribution of lengths of the resulting pieces converges to Benford behavior as the number of divisions grow, and give several conjectures for other fragmentation processes. The main difficulty is that the resulting random variables are dependent. We handle this by using tools from Fourier analysis and irrationality exponents to obtain quantified convergence rates as well as introducing and developing techniques to measure and control the dependencies. The construction of these tools is one of the major motivations of this work, as our approach can be applied to many other dependent systems. As an example, we show that the n ! entries in the determinant expansions of n × n matrices with entries independently drawn from nice random variables converges to Benford's Law.

Making statistical inferences about software reliability

NASA Technical Reports Server (NTRS)

Miller, Douglas R.

1988-01-01

Failure times of software undergoing random debugging can be modelled as order statistics of independent but nonidentically distributed exponential random variables. Using this model inferences can be made about current reliability and, if debugging continues, future reliability. This model also shows the difficulty inherent in statistical verification of very highly reliable software such as that used by digital avionics in commercial aircraft.

Robust portfolio selection based on asymmetric measures of variability of stock returns

NASA Astrophysics Data System (ADS)

Chen, Wei; Tan, Shaohua

2009-10-01

This paper addresses a new uncertainty set--interval random uncertainty set for robust optimization. The form of interval random uncertainty set makes it suitable for capturing the downside and upside deviations of real-world data. These deviation measures capture distributional asymmetry and lead to better optimization results. We also apply our interval random chance-constrained programming to robust mean-variance portfolio selection under interval random uncertainty sets in the elements of mean vector and covariance matrix. Numerical experiments with real market data indicate that our approach results in better portfolio performance.

Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model

NASA Astrophysics Data System (ADS)

Margarint, Vlad

2018-06-01

We consider Hermitian random band matrices H in d ≥slant 1 dimensions. The matrix elements H_{xy}, indexed by x, y \\in Λ \\subset Z^d, are independent, uniformly distributed random variable if |x-y| is less than the band width W, and zero otherwise. We update the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The result is uniformly in the size |Λ| of the matrix.

A Permutation-Randomization Approach to Test the Spatial Distribution of Plant Diseases.

PubMed

Lione, G; Gonthier, P

2016-01-01

The analysis of the spatial distribution of plant diseases requires the availability of trustworthy geostatistical methods. The mean distance tests (MDT) are here proposed as a series of permutation and randomization tests to assess the spatial distribution of plant diseases when the variable of phytopathological interest is categorical. A user-friendly software to perform the tests is provided. Estimates of power and type I error, obtained with Monte Carlo simulations, showed the reliability of the MDT (power > 0.80; type I error < 0.05). A biological validation on the spatial distribution of spores of two fungal pathogens causing root rot on conifers was successfully performed by verifying the consistency between the MDT responses and previously published data. An application of the MDT was carried out to analyze the relation between the plantation density and the distribution of the infection of Gnomoniopsis castanea, an emerging fungal pathogen causing nut rot on sweet chestnut. Trees carrying nuts infected by the pathogen were randomly distributed in areas with different plantation densities, suggesting that the distribution of G. castanea was not related to the plantation density. The MDT could be used to analyze the spatial distribution of plant diseases both in agricultural and natural ecosystems.

SU-F-BRD-09: A Random Walk Model Algorithm for Proton Dose Calculation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yao, W; Farr, J

2015-06-15

Purpose: To develop a random walk model algorithm for calculating proton dose with balanced computation burden and accuracy. Methods: Random walk (RW) model is sometimes referred to as a density Monte Carlo (MC) simulation. In MC proton dose calculation, the use of Gaussian angular distribution of protons due to multiple Coulomb scatter (MCS) is convenient, but in RW the use of Gaussian angular distribution requires an extremely large computation and memory. Thus, our RW model adopts spatial distribution from the angular one to accelerate the computation and to decrease the memory usage. From the physics and comparison with the MCmore » simulations, we have determined and analytically expressed those critical variables affecting the dose accuracy in our RW model. Results: Besides those variables such as MCS, stopping power, energy spectrum after energy absorption etc., which have been extensively discussed in literature, the following variables were found to be critical in our RW model: (1) inverse squared law that can significantly reduce the computation burden and memory, (2) non-Gaussian spatial distribution after MCS, and (3) the mean direction of scatters at each voxel. In comparison to MC results, taken as reference, for a water phantom irradiated by mono-energetic proton beams from 75 MeV to 221.28 MeV, the gamma test pass rate was 100% for the 2%/2mm/10% criterion. For a highly heterogeneous phantom consisting of water embedded by a 10 cm cortical bone and a 10 cm lung in the Bragg peak region of the proton beam, the gamma test pass rate was greater than 98% for the 3%/3mm/10% criterion. Conclusion: We have determined key variables in our RW model for proton dose calculation. Compared with commercial pencil beam algorithms, our RW model much improves the dose accuracy in heterogeneous regions, and is about 10 times faster than MC simulations.« less

Probabilistic SSME blades structural response under random pulse loading

NASA Technical Reports Server (NTRS)

Shiao, Michael; Rubinstein, Robert; Nagpal, Vinod K.

1987-01-01

The purpose is to develop models of random impacts on a Space Shuttle Main Engine (SSME) turbopump blade and to predict the probabilistic structural response of the blade to these impacts. The random loading is caused by the impact of debris. The probabilistic structural response is characterized by distribution functions for stress and displacements as functions of the loading parameters which determine the random pulse model. These parameters include pulse arrival, amplitude, and location. The analysis can be extended to predict level crossing rates. This requires knowledge of the joint distribution of the response and its derivative. The model of random impacts chosen allows the pulse arrivals, pulse amplitudes, and pulse locations to be random. Specifically, the pulse arrivals are assumed to be governed by a Poisson process, which is characterized by a mean arrival rate. The pulse intensity is modelled as a normally distributed random variable with a zero mean chosen independently at each arrival. The standard deviation of the distribution is a measure of pulse intensity. Several different models were used for the pulse locations. For example, three points near the blade tip were chosen at which pulses were allowed to arrive with equal probability. Again, the locations were chosen independently at each arrival. The structural response was analyzed both by direct Monte Carlo simulation and by a semi-analytical method.

Reliability-Based Design Optimization of a Composite Airframe Component

NASA Technical Reports Server (NTRS)

Pai, Shantaram S.; Coroneos, Rula; Patnaik, Surya N.

2011-01-01

A stochastic optimization methodology (SDO) has been developed to design airframe structural components made of metallic and composite materials. The design method accommodates uncertainties in load, strength, and material properties that are defined by distribution functions with mean values and standard deviations. A response parameter, like a failure mode, has become a function of reliability. The primitive variables like thermomechanical loads, material properties, and failure theories, as well as variables like depth of beam or thickness of a membrane, are considered random parameters with specified distribution functions defined by mean values and standard deviations.

A Dasymetric-Based Monte Carlo Simulation Approach to the Probabilistic Analysis of Spatial Variables

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morton, April M; Piburn, Jesse O; McManamay, Ryan A

2017-01-01

Monte Carlo simulation is a popular numerical experimentation technique used in a range of scientific fields to obtain the statistics of unknown random output variables. Despite its widespread applicability, it can be difficult to infer required input probability distributions when they are related to population counts unknown at desired spatial resolutions. To overcome this challenge, we propose a framework that uses a dasymetric model to infer the probability distributions needed for a specific class of Monte Carlo simulations which depend on population counts.

On Probability Domains IV

NASA Astrophysics Data System (ADS)

Frič, Roman; Papčo, Martin

2017-12-01

Stressing a categorical approach, we continue our study of fuzzified domains of probability, in which classical random events are replaced by measurable fuzzy random events. In operational probability theory (S. Bugajski) classical random variables are replaced by statistical maps (generalized distribution maps induced by random variables) and in fuzzy probability theory (S. Gudder) the central role is played by observables (maps between probability domains). We show that to each of the two generalized probability theories there corresponds a suitable category and the two resulting categories are dually equivalent. Statistical maps and observables become morphisms. A statistical map can send a degenerated (pure) state to a non-degenerated one —a quantum phenomenon and, dually, an observable can map a crisp random event to a genuine fuzzy random event —a fuzzy phenomenon. The dual equivalence means that the operational probability theory and the fuzzy probability theory coincide and the resulting generalized probability theory has two dual aspects: quantum and fuzzy. We close with some notes on products and coproducts in the dual categories.

Resampling and Distribution of the Product Methods for Testing Indirect Effects in Complex Models

ERIC Educational Resources Information Center

Williams, Jason; MacKinnon, David P.

2008-01-01

Recent advances in testing mediation have found that certain resampling methods and tests based on the mathematical distribution of 2 normal random variables substantially outperform the traditional "z" test. However, these studies have primarily focused only on models with a single mediator and 2 component paths. To address this limitation, a…

Controls on the spatial variability of key soil properties: comparing field data with a mechanistic soilscape evolution model

NASA Astrophysics Data System (ADS)

Vanwalleghem, T.; Román, A.; Giraldez, J. V.

2016-12-01

There is a need for better understanding the processes influencing soil formation and the resulting distribution of soil properties. Soil properties can exhibit strong spatial variation, even at the small catchment scale. Especially soil carbon pools in semi-arid, mountainous areas are highly uncertain because bulk density and stoniness are very heterogeneous and rarely measured explicitly. In this study, we explore the spatial variability in key soil properties (soil carbon stocks, stoniness, bulk density and soil depth) as a function of processes shaping the critical zone (weathering, erosion, soil water fluxes and vegetation patterns). We also compare the potential of a geostatistical versus a mechanistic soil formation model (MILESD) for predicting these key soil properties. Soil core samples were collected from 67 locations at 6 depths. Total soil organic carbon stocks were 4.38 kg m-2. Solar radiation proved to be the key variable controlling soil carbon distribution. Stone content was mostly controlled by slope, indicating the importance of erosion. Spatial distribution of bulk density was found to be highly random. Finally, total carbon stocks were predicted using a random forest model whose main covariates were solar radiation and NDVI. The model predicts carbon stocks that are double as high on north versus south-facing slopes. However, validation showed that these covariates only explained 25% of the variation in the dataset. Apparently, present-day landscape and vegetation properties are not sufficient to fully explain variability in the soil carbon stocks in this complex terrain under natural vegetation. This is attributed to a high spatial variability in bulk density and stoniness, key variables controlling carbon stocks. Similar results were obtained with the mechanistic soil formation model MILESD, suggesting that more complex models might be needed to further explore this high spatial variability.

Quantum probabilistic logic programming

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan

2015-05-01

We describe a quantum mechanics based logic programming language that supports Horn clauses, random variables, and covariance matrices to express and solve problems in probabilistic logic. The Horn clauses of the language wrap random variables, including infinite valued, to express probability distributions and statistical correlations, a powerful feature to capture relationship between distributions that are not independent. The expressive power of the language is based on a mechanism to implement statistical ensembles and to solve the underlying SAT instances using quantum mechanical machinery. We exploit the fact that classical random variables have quantum decompositions to build the Horn clauses. We establish the semantics of the language in a rigorous fashion by considering an existing probabilistic logic language called PRISM with classical probability measures defined on the Herbrand base and extending it to the quantum context. In the classical case H-interpretations form the sample space and probability measures defined on them lead to consistent definition of probabilities for well formed formulae. In the quantum counterpart, we define probability amplitudes on Hinterpretations facilitating the model generations and verifications via quantum mechanical superpositions and entanglements. We cast the well formed formulae of the language as quantum mechanical observables thus providing an elegant interpretation for their probabilities. We discuss several examples to combine statistical ensembles and predicates of first order logic to reason with situations involving uncertainty.

A Probabilistic Design Method Applied to Smart Composite Structures

NASA Technical Reports Server (NTRS)

Shiao, Michael C.; Chamis, Christos C.

1995-01-01

A probabilistic design method is described and demonstrated using a smart composite wing. Probabilistic structural design incorporates naturally occurring uncertainties including those in constituent (fiber/matrix) material properties, fabrication variables, structure geometry and control-related parameters. Probabilistic sensitivity factors are computed to identify those parameters that have a great influence on a specific structural reliability. Two performance criteria are used to demonstrate this design methodology. The first criterion requires that the actuated angle at the wing tip be bounded by upper and lower limits at a specified reliability. The second criterion requires that the probability of ply damage due to random impact load be smaller than an assigned value. When the relationship between reliability improvement and the sensitivity factors is assessed, the results show that a reduction in the scatter of the random variable with the largest sensitivity factor (absolute value) provides the lowest failure probability. An increase in the mean of the random variable with a negative sensitivity factor will reduce the failure probability. Therefore, the design can be improved by controlling or selecting distribution parameters associated with random variables. This can be implemented during the manufacturing process to obtain maximum benefit with minimum alterations.

Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape

PubMed Central

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for ‘difficult’ variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we assess a range of candidate distributions, including the Sichel, Delaporte, Box-Cox Green and Cole, and Box-Cox t distributions. We find that the Box-Cox t distribution, with appropriate modeling of its parameters, best fits the conditional distribution of phonemic inventory size. We finally discuss the specificities of phoneme counts, weak effects, and how GAMLSS should be considered for other linguistic variables. PMID:29713298

Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape.

PubMed

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for 'difficult' variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we assess a range of candidate distributions, including the Sichel, Delaporte, Box-Cox Green and Cole, and Box-Cox t distributions. We find that the Box-Cox t distribution, with appropriate modeling of its parameters, best fits the conditional distribution of phonemic inventory size. We finally discuss the specificities of phoneme counts, weak effects, and how GAMLSS should be considered for other linguistic variables.

Ecological impacts and management strategies for western larch in the face of climate-change

Treesearch

Gerald E. Rehfeldt; Barry C. Jaquish

2010-01-01

Approximately 185,000 forest inventory and ecological plots from both USA and Canada were used to predict the contemporary distribution of western larch (Larix occidentalis Nutt.) from climate variables. The random forests algorithm, using an 8-variable model, produced an overall error rate of about 2.9 %, nearly all of which consisted of predicting presence at...

Methods for Combining Payload Parameter Variations with Input Environment

NASA Technical Reports Server (NTRS)

Merchant, D. H.; Straayer, J. W.

1975-01-01

Methods are presented for calculating design limit loads compatible with probabilistic structural design criteria. The approach is based on the concept that the desired limit load, defined as the largest load occuring in a mission, is a random variable having a specific probability distribution which may be determined from extreme-value theory. The design limit load, defined as a particular value of this random limit load, is the value conventionally used in structural design. Methods are presented for determining the limit load probability distributions from both time-domain and frequency-domain dynamic load simulations. Numerical demonstrations of the methods are also presented.

Probability Distribution Estimated From the Minimum, Maximum, and Most Likely Values: Applied to Turbine Inlet Temperature Uncertainty

NASA Technical Reports Server (NTRS)

Holland, Frederic A., Jr.

2004-01-01

Modern engineering design practices are tending more toward the treatment of design parameters as random variables as opposed to fixed, or deterministic, values. The probabilistic design approach attempts to account for the uncertainty in design parameters by representing them as a distribution of values rather than as a single value. The motivations for this effort include preventing excessive overdesign as well as assessing and assuring reliability, both of which are important for aerospace applications. However, the determination of the probability distribution is a fundamental problem in reliability analysis. A random variable is often defined by the parameters of the theoretical distribution function that gives the best fit to experimental data. In many cases the distribution must be assumed from very limited information or data. Often the types of information that are available or reasonably estimated are the minimum, maximum, and most likely values of the design parameter. For these situations the beta distribution model is very convenient because the parameters that define the distribution can be easily determined from these three pieces of information. Widely used in the field of operations research, the beta model is very flexible and is also useful for estimating the mean and standard deviation of a random variable given only the aforementioned three values. However, an assumption is required to determine the four parameters of the beta distribution from only these three pieces of information (some of the more common distributions, like the normal, lognormal, gamma, and Weibull distributions, have two or three parameters). The conventional method assumes that the standard deviation is a certain fraction of the range. The beta parameters are then determined by solving a set of equations simultaneously. A new method developed in-house at the NASA Glenn Research Center assumes a value for one of the beta shape parameters based on an analogy with the normal distribution (ref.1). This new approach allows for a very simple and direct algebraic solution without restricting the standard deviation. The beta parameters obtained by the new method are comparable to the conventional method (and identical when the distribution is symmetrical). However, the proposed method generally produces a less peaked distribution with a slightly larger standard deviation (up to 7 percent) than the conventional method in cases where the distribution is asymmetric or skewed. The beta distribution model has now been implemented into the Fast Probability Integration (FPI) module used in the NESSUS computer code for probabilistic analyses of structures (ref. 2).

A Random Forest Approach to Predict the Spatial Distribution ...

EPA Pesticide Factsheets

Modeling the magnitude and distribution of sediment-bound pollutants in estuaries is often limited by incomplete knowledge of the site and inadequate sample density. To address these modeling limitations, a decision-support tool framework was conceived that predicts sediment contamination from the sub-estuary to broader estuary extent. For this study, a Random Forest (RF) model was implemented to predict the distribution of a model contaminant, triclosan (5-chloro-2-(2,4-dichlorophenoxy)phenol) (TCS), in Narragansett Bay, Rhode Island, USA. TCS is an unregulated contaminant used in many personal care products. The RF explanatory variables were associated with TCS transport and fate (proxies) and direct and indirect environmental entry. The continuous RF TCS concentration predictions were discretized into three levels of contamination (low, medium, and high) for three different quantile thresholds. The RF model explained 63% of the variance with a minimum number of variables. Total organic carbon (TOC) (transport and fate proxy) was a strong predictor of TCS contamination causing a mean squared error increase of 59% when compared to permutations of randomized values of TOC. Additionally, combined sewer overflow discharge (environmental entry) and sand (transport and fate proxy) were strong predictors. The discretization models identified a TCS area of greatest concern in the northern reach of Narragansett Bay (Providence River sub-estuary), which was validated wi

Optimal approximations for risk measures of sums of lognormals based on conditional expectations

NASA Astrophysics Data System (ADS)

Vanduffel, S.; Chen, X.; Dhaene, J.; Goovaerts, M.; Henrard, L.; Kaas, R.

2008-11-01

In this paper we investigate the approximations for the distribution function of a sum S of lognormal random variables. These approximations are obtained by considering the conditional expectation E[S|[Lambda

THE DISTRIBUTION OF ROUNDS FIRED IN STOCHASTIC DUELS

DTIC Science & Technology

This paper continues the development of the theory of Stochastic Duels to include the distribution of the number of rounds fired. Most generally...the duel between two contestants who fire at each other with constant kill probabilities per round is considered. The time between rounds fired may be...at the beginning of the duel may be limited and is a discrete random variable. Besides the distribution of rounds fired, its first two moments and

Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes

NASA Astrophysics Data System (ADS)

Orsingher, Enzo; Polito, Federico

2012-08-01

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N α ( t), N β ( t), t>0, we have that N_{α}(N_{β}(t)) stackrel{d}{=} sum_{j=1}^{N_{β}(t)} Xj, where the X j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form N_{α}(tauk^{ν}), ν∈(0,1], where tauk^{ν} is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ( N( t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.

Circular distributions based on nonnegative trigonometric sums.

PubMed

Fernández-Durán, J J

2004-06-01

A new family of distributions for circular random variables is proposed. It is based on nonnegative trigonometric sums and can be used to model data sets which present skewness and/or multimodality. In this family of distributions, the trigonometric moments are easily expressed in terms of the parameters of the distribution. The proposed family is applied to two data sets, one related with the directions taken by ants and the other with the directions taken by turtles, to compare their goodness of fit versus common distributions used in the literature.

Testing homogeneity in Weibull-regression models.

PubMed

Bolfarine, Heleno; Valença, Dione M

2005-10-01

In survival studies with families or geographical units it may be of interest testing whether such groups are homogeneous for given explanatory variables. In this paper we consider score type tests for group homogeneity based on a mixing model in which the group effect is modelled as a random variable. As opposed to hazard-based frailty models, this model presents survival times that conditioned on the random effect, has an accelerated failure time representation. The test statistics requires only estimation of the conventional regression model without the random effect and does not require specifying the distribution of the random effect. The tests are derived for a Weibull regression model and in the uncensored situation, a closed form is obtained for the test statistic. A simulation study is used for comparing the power of the tests. The proposed tests are applied to real data sets with censored data.

Incorporating abundance information and guiding variable selection for climate-based ensemble forecasting of species' distributional shifts.

PubMed

Tanner, Evan P; Papeş, Monica; Elmore, R Dwayne; Fuhlendorf, Samuel D; Davis, Craig A

2017-01-01

Ecological niche models (ENMs) have increasingly been used to estimate the potential effects of climate change on species' distributions worldwide. Recently, predictions of species abundance have also been obtained with such models, though knowledge about the climatic variables affecting species abundance is often lacking. To address this, we used a well-studied guild (temperate North American quail) and the Maxent modeling algorithm to compare model performance of three variable selection approaches: correlation/variable contribution (CVC), biological (i.e., variables known to affect species abundance), and random. We then applied the best approach to forecast potential distributions, under future climatic conditions, and analyze future potential distributions in light of available abundance data and presence-only occurrence data. To estimate species' distributional shifts we generated ensemble forecasts using four global circulation models, four representative concentration pathways, and two time periods (2050 and 2070). Furthermore, we present distributional shifts where 75%, 90%, and 100% of our ensemble models agreed. The CVC variable selection approach outperformed our biological approach for four of the six species. Model projections indicated species-specific effects of climate change on future distributions of temperate North American quail. The Gambel's quail (Callipepla gambelii) was the only species predicted to gain area in climatic suitability across all three scenarios of ensemble model agreement. Conversely, the scaled quail (Callipepla squamata) was the only species predicted to lose area in climatic suitability across all three scenarios of ensemble model agreement. Our models projected future loss of areas for the northern bobwhite (Colinus virginianus) and scaled quail in portions of their distributions which are currently areas of high abundance. Climatic variables that influence local abundance may not always scale up to influence species' distributions. Special attention should be given to selecting variables for ENMs, and tests of model performance should be used to validate the choice of variables.

Phenomenological picture of fluctuations in branching random walks

NASA Astrophysics Data System (ADS)

Mueller, A. H.; Munier, S.

2014-10-01

We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the 1 /√{t } correction to the average position of the rightmost particle of a branching random walk for large times t ≫1 , computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of a branching random walk.

A stochastic Markov chain model to describe lung cancer growth and metastasis.

PubMed

Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila A; Nieva, Jorge; Kuhn, Peter

2012-01-01

A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.

Random parameter models for accident prediction on two-lane undivided highways in India.

PubMed

Dinu, R R; Veeraragavan, A

2011-02-01

Generalized linear modeling (GLM), with the assumption of Poisson or negative binomial error structure, has been widely employed in road accident modeling. A number of explanatory variables related to traffic, road geometry, and environment that contribute to accident occurrence have been identified and accident prediction models have been proposed. The accident prediction models reported in literature largely employ the fixed parameter modeling approach, where the magnitude of influence of an explanatory variable is considered to be fixed for any observation in the population. Similar models have been proposed for Indian highways too, which include additional variables representing traffic composition. The mixed traffic on Indian highways comes with a lot of variability within, ranging from difference in vehicle types to variability in driver behavior. This could result in variability in the effect of explanatory variables on accidents across locations. Random parameter models, which can capture some of such variability, are expected to be more appropriate for the Indian situation. The present study is an attempt to employ random parameter modeling for accident prediction on two-lane undivided rural highways in India. Three years of accident history, from nearly 200 km of highway segments, is used to calibrate and validate the models. The results of the analysis suggest that the model coefficients for traffic volume, proportion of cars, motorized two-wheelers and trucks in traffic, and driveway density and horizontal and vertical curvatures are randomly distributed across locations. The paper is concluded with a discussion on modeling results and the limitations of the present study. Copyright © 2010 Elsevier Ltd. All rights reserved.

A probabilistic model of a porous heat exchanger

NASA Technical Reports Server (NTRS)

Agrawal, O. P.; Lin, X. A.

1995-01-01

This paper presents a probabilistic one-dimensional finite element model for heat transfer processes in porous heat exchangers. The Galerkin approach is used to develop the finite element matrices. Some of the submatrices are asymmetric due to the presence of the flow term. The Neumann expansion is used to write the temperature distribution as a series of random variables, and the expectation operator is applied to obtain the mean and deviation statistics. To demonstrate the feasibility of the formulation, a one-dimensional model of heat transfer phenomenon in superfluid flow through a porous media is considered. Results of this formulation agree well with the Monte-Carlo simulations and the analytical solutions. Although the numerical experiments are confined to parametric random variables, a formulation is presented to account for the random spatial variations.

Robustness-Based Design Optimization Under Data Uncertainty

NASA Technical Reports Server (NTRS)

Zaman, Kais; McDonald, Mark; Mahadevan, Sankaran; Green, Lawrence

2010-01-01

This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-to-orbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables.

Rates of profit as correlated sums of random variables

NASA Astrophysics Data System (ADS)

Greenblatt, R. E.

2013-10-01

Profit realization is the dominant feature of market-based economic systems, determining their dynamics to a large extent. Rather than attaining an equilibrium, profit rates vary widely across firms, and the variation persists over time. Differing definitions of profit result in differing empirical distributions. To study the statistical properties of profit rates, I used data from a publicly available database for the US Economy for 2009-2010 (Risk Management Association). For each of three profit rate measures, the sample space consists of 771 points. Each point represents aggregate data from a small number of US manufacturing firms of similar size and type (NAICS code of principal product). When comparing the empirical distributions of profit rates, significant ‘heavy tails’ were observed, corresponding principally to a number of firms with larger profit rates than would be expected from simple models. An apparently novel correlated sum of random variables statistical model was used to model the data. In the case of operating and net profit rates, a number of firms show negative profits (losses), ruling out simple gamma or lognormal distributions as complete models for these data.

Performance analysis of MIMO wireless optical communication system with Q-ary PPM over correlated log-normal fading channel

NASA Astrophysics Data System (ADS)

Wang, Huiqin; Wang, Xue; Lynette, Kibe; Cao, Minghua

2018-06-01

The performance of multiple-input multiple-output wireless optical communication systems that adopt Q-ary pulse position modulation over spatial correlated log-normal fading channel is analyzed in terms of its un-coded bit error rate and ergodic channel capacity. The analysis is based on the Wilkinson's method which approximates the distribution of a sum of correlated log-normal random variables to a log-normal random variable. The analytical and simulation results corroborate the increment of correlation coefficients among sub-channels lead to system performance degradation. Moreover, the receiver diversity has better performance in resistance of spatial correlation caused channel fading.

Finite-sample corrected generalized estimating equation of population average treatment effects in stepped wedge cluster randomized trials.

PubMed

Scott, JoAnna M; deCamp, Allan; Juraska, Michal; Fay, Michael P; Gilbert, Peter B

2017-04-01

Stepped wedge designs are increasingly commonplace and advantageous for cluster randomized trials when it is both unethical to assign placebo, and it is logistically difficult to allocate an intervention simultaneously to many clusters. We study marginal mean models fit with generalized estimating equations for assessing treatment effectiveness in stepped wedge cluster randomized trials. This approach has advantages over the more commonly used mixed models that (1) the population-average parameters have an important interpretation for public health applications and (2) they avoid untestable assumptions on latent variable distributions and avoid parametric assumptions about error distributions, therefore, providing more robust evidence on treatment effects. However, cluster randomized trials typically have a small number of clusters, rendering the standard generalized estimating equation sandwich variance estimator biased and highly variable and hence yielding incorrect inferences. We study the usual asymptotic generalized estimating equation inferences (i.e., using sandwich variance estimators and asymptotic normality) and four small-sample corrections to generalized estimating equation for stepped wedge cluster randomized trials and for parallel cluster randomized trials as a comparison. We show by simulation that the small-sample corrections provide improvement, with one correction appearing to provide at least nominal coverage even with only 10 clusters per group. These results demonstrate the viability of the marginal mean approach for both stepped wedge and parallel cluster randomized trials. We also study the comparative performance of the corrected methods for stepped wedge and parallel designs, and describe how the methods can accommodate interval censoring of individual failure times and incorporate semiparametric efficient estimators.

Inference for the Bivariate and Multivariate Hidden Truncated Pareto(type II) and Pareto(type IV) Distribution and Some Measures of Divergence Related to Incompatibility of Probability Distribution

ERIC Educational Resources Information Center

Ghosh, Indranil

2011-01-01

Consider a discrete bivariate random variable (X, Y) with possible values x[subscript 1], x[subscript 2],..., x[subscript I] for X and y[subscript 1], y[subscript 2],..., y[subscript J] for Y. Further suppose that the corresponding families of conditional distributions, for X given values of Y and of Y for given values of X are available. We…

Derivation of a Multiparameter Gamma Model for Analyzing the Residence-Time Distribution Function for Nonideal Flow Systems as an Alternative to the Advection-Dispersion Equation

DOE PAGES

Embry, Irucka; Roland, Victor; Agbaje, Oluropo; ...

2013-01-01

A new residence-time distribution (RTD) function has been developed and applied to quantitative dye studies as an alternative to the traditional advection-dispersion equation (AdDE). The new method is based on a jointly combined four-parameter gamma probability density function (PDF). The gamma residence-time distribution (RTD) function and its first and second moments are derived from the individual two-parameter gamma distributions of randomly distributed variables, tracer travel distance, and linear velocity, which are based on their relationship with time. The gamma RTD function was used on a steady-state, nonideal system modeled as a plug-flow reactor (PFR) in the laboratory to validate themore » effectiveness of the model. The normalized forms of the gamma RTD and the advection-dispersion equation RTD were compared with the normalized tracer RTD. The normalized gamma RTD had a lower mean-absolute deviation (MAD) (0.16) than the normalized form of the advection-dispersion equation (0.26) when compared to the normalized tracer RTD. The gamma RTD function is tied back to the actual physical site due to its randomly distributed variables. The results validate using the gamma RTD as a suitable alternative to the advection-dispersion equation for quantitative tracer studies of non-ideal flow systems.« less

Using the Quantile Mapping to improve a weather generator

NASA Astrophysics Data System (ADS)

Chen, Y.; Themessl, M.; Gobiet, A.

2012-04-01

We developed a weather generator (WG) by using statistical and stochastic methods, among them are quantile mapping (QM), Monte-Carlo, auto-regression, empirical orthogonal function (EOF). One of the important steps in the WG is using QM, through which all the variables, no matter what distribution they originally are, are transformed into normal distributed variables. Therefore, the WG can work on normally distributed variables, which greatly facilitates the treatment of random numbers in the WG. Monte-Carlo and auto-regression are used to generate the realization; EOFs are employed for preserving spatial relationships and the relationships between different meteorological variables. We have established a complete model named WGQM (weather generator and quantile mapping), which can be applied flexibly to generate daily or hourly time series. For example, with 30-year daily (hourly) data and 100-year monthly (daily) data as input, the 100-year daily (hourly) data would be relatively reasonably produced. Some evaluation experiments with WGQM have been carried out in the area of Austria and the evaluation results will be presented.

Epidemics in networks: a master equation approach

NASA Astrophysics Data System (ADS)

Cotacallapa, M.; Hase, M. O.

2016-02-01

A problem closely related to epidemiology, where a subgraph of ‘infected’ links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link is able to propagate a disease/information. The relaxation timescale of this random variable is examined in both annealed and quenched limits, and the effectiveness of propagation of disease/information is analyzed. The dynamics of the model is governed by a master equation and two types of underlying network are considered: one is scale-free and the other has exponential degree distribution. We have shown that the relaxation timescale of the contagion variable has a major influence on the topology of the subgraph of infected links, which determines the efficiency of spreading of disease/information over the network.

FAST TRACK COMMUNICATION: Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.; Bouchaud, Jean-Philippe

2008-09-01

We investigate some implications of the freezing scenario proposed by Carpentier and Le Doussal (CLD) for a random energy model (REM) with logarithmically correlated random potential. We introduce a particular (circular) variant of the model, and show that the integer moments of the partition function in the high-temperature phase are given by the well-known Dyson Coulomb gas integrals. The CLD freezing scenario allows one to use those moments for extracting the distribution of the free energy in both high- and low-temperature phases. In particular, it yields the full distribution of the minimal value in the potential sequence. This provides an explicit new class of extreme-value statistics for strongly correlated variables, manifestly different from the standard Gumbel class.

Moderation analysis with missing data in the predictors.

PubMed

Zhang, Qian; Wang, Lijuan

2017-12-01

The most widely used statistical model for conducting moderation analysis is the moderated multiple regression (MMR) model. In MMR modeling, missing data could pose a challenge, mainly because the interaction term is a product of two or more variables and thus is a nonlinear function of the involved variables. In this study, we consider a simple MMR model, where the effect of the focal predictor X on the outcome Y is moderated by a moderator U. The primary interest is to find ways of estimating and testing the moderation effect with the existence of missing data in X. We mainly focus on cases when X is missing completely at random (MCAR) and missing at random (MAR). Three methods are compared: (a) Normal-distribution-based maximum likelihood estimation (NML); (b) Normal-distribution-based multiple imputation (NMI); and (c) Bayesian estimation (BE). Via simulations, we found that NML and NMI could lead to biased estimates of moderation effects under MAR missingness mechanism. The BE method outperformed NMI and NML for MMR modeling with missing data in the focal predictor, missingness depending on the moderator and/or auxiliary variables, and correctly specified distributions for the focal predictor. In addition, more robust BE methods are needed in terms of the distribution mis-specification problem of the focal predictor. An empirical example was used to illustrate the applications of the methods with a simple sensitivity analysis. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

A Simple Game to Derive Lognormal Distribution

ERIC Educational Resources Information Center

Omey, E.; Van Gulck, S.

2007-01-01

In the paper we present a simple game that students can play in the classroom. The game can be used to show that random variables can behave in an unexpected way: the expected mean can tend to zero or to infinity; the variance can tend to zero or to infinity. The game can also be used to introduce the lognormal distribution. (Contains 1 table and…

Stimulant Treatment Reduces Lapses in Attention among Children with ADHD: The Effects of Methylphenidate on Intra-Individual Response Time Distributions

ERIC Educational Resources Information Center

Spencer, Sarah V.; Hawk, Larry W., Jr.; Richards, Jerry B.; Shiels, Keri; Pelham, William E., Jr.; Waxmonsky, James G.

2009-01-01

Recent research has suggested that intra-individual variability in reaction time (RT) distributions of children with ADHD is characterized by a particularly large rightward skew that may reflect lapses in attention. The purpose of the study was to provide the first randomized, placebo-controlled test of the effects of the stimulant methylphenidate…

Spatial vs. individual variability with inheritance in a stochastic Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Dobramysl, Ulrich; Tauber, Uwe C.

2012-02-01

We investigate a stochastic spatial Lotka-Volterra predator-prey model with randomized interaction rates that are either affixed to the lattice sites and quenched, and / or specific to individuals in either population. In the latter situation, we include rate inheritance with mutations from the particles' progenitors. Thus we arrive at a simple model for competitive evolution with environmental variability and selection pressure. We employ Monte Carlo simulations in zero and two dimensions to study the time evolution of both species' densities and their interaction rate distributions. The predator and prey concentrations in the ensuing steady states depend crucially on the environmental variability, whereas the temporal evolution of the individualized rate distributions leads to largely neutral optimization. Contrary to, e.g., linear gene expression models, this system does not experience fixation at extreme values. An approximate description of the resulting data is achieved by means of an effective master equation approach for the interaction rate distribution.

Analysis on flood generation processes by means of a continuous simulation model

NASA Astrophysics Data System (ADS)

Fiorentino, M.; Gioia, A.; Iacobellis, V.; Manfreda, S.

2006-03-01

In the present research, we exploited a continuous hydrological simulation to investigate on key variables responsible of flood peak formation. With this purpose, a distributed hydrological model (DREAM) is used in cascade with a rainfall generator (IRP-Iterated Random Pulse) to simulate a large number of extreme events providing insight into the main controls of flood generation mechanisms. Investigated variables are those used in theoretically derived probability distribution of floods based on the concept of partial contributing area (e.g. Iacobellis and Fiorentino, 2000). The continuous simulation model is used to investigate on the hydrological losses occurring during extreme events, the variability of the source area contributing to the flood peak and its lag-time. Results suggest interesting simplification for the theoretical probability distribution of floods according to the different climatic and geomorfologic environments. The study is applied to two basins located in Southern Italy with different climatic characteristics.

Magneto-transport properties of a random distribution of few-layer graphene patches

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iacovella, Fabrice; Mitioglu, Anatolie; Pierre, Mathieu

In this study, we address the electronic properties of conducting films constituted of an array of randomly distributed few layer graphene patches and investigate on their most salient galvanometric features in the moderate and extreme disordered limit. We demonstrate that, in annealed devices, the ambipolar behaviour and the onset of Landau level quantization in high magnetic field constitute robust hallmarks of few-layer graphene films. In the strong disorder limit, however, the magneto-transport properties are best described by a variable-range hopping behaviour. A large negative magneto-conductance is observed at the charge neutrality point, in consistency with localized transport regime.

Modeling Stochastic Variability in the Numbers of Surviving Salmonella enterica, Enterohemorrhagic Escherichia coli, and Listeria monocytogenes Cells at the Single-Cell Level in a Desiccated Environment

PubMed Central

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso

2016-01-01

ABSTRACT Despite effective inactivation procedures, small numbers of bacterial cells may still remain in food samples. The risk that bacteria will survive these procedures has not been estimated precisely because deterministic models cannot be used to describe the uncertain behavior of bacterial populations. We used the Poisson distribution as a representative probability distribution to estimate the variability in bacterial numbers during the inactivation process. Strains of four serotypes of Salmonella enterica, three serotypes of enterohemorrhagic Escherichia coli, and one serotype of Listeria monocytogenes were evaluated for survival. We prepared bacterial cell numbers following a Poisson distribution (indicated by the parameter λ, which was equal to 2) and plated the cells in 96-well microplates, which were stored in a desiccated environment at 10% to 20% relative humidity and at 5, 15, and 25°C. The survival or death of the bacterial cells in each well was confirmed by adding tryptic soy broth as an enrichment culture. Changes in the Poisson distribution parameter during the inactivation process, which represent the variability in the numbers of surviving bacteria, were described by nonlinear regression with an exponential function based on a Weibull distribution. We also examined random changes in the number of surviving bacteria using a random number generator and computer simulations to determine whether the number of surviving bacteria followed a Poisson distribution during the bacterial death process by use of the Poisson process. For small initial cell numbers, more than 80% of the simulated distributions (λ = 2 or 10) followed a Poisson distribution. The results demonstrate that variability in the number of surviving bacteria can be described as a Poisson distribution by use of the model developed by use of the Poisson process. IMPORTANCE We developed a model to enable the quantitative assessment of bacterial survivors of inactivation procedures because the presence of even one bacterium can cause foodborne disease. The results demonstrate that the variability in the numbers of surviving bacteria was described as a Poisson distribution by use of the model developed by use of the Poisson process. Description of the number of surviving bacteria as a probability distribution rather than as the point estimates used in a deterministic approach can provide a more realistic estimation of risk. The probability model should be useful for estimating the quantitative risk of bacterial survival during inactivation. PMID:27940547

Modeling Stochastic Variability in the Numbers of Surviving Salmonella enterica, Enterohemorrhagic Escherichia coli, and Listeria monocytogenes Cells at the Single-Cell Level in a Desiccated Environment.

PubMed

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu

2017-02-15

Despite effective inactivation procedures, small numbers of bacterial cells may still remain in food samples. The risk that bacteria will survive these procedures has not been estimated precisely because deterministic models cannot be used to describe the uncertain behavior of bacterial populations. We used the Poisson distribution as a representative probability distribution to estimate the variability in bacterial numbers during the inactivation process. Strains of four serotypes of Salmonella enterica, three serotypes of enterohemorrhagic Escherichia coli, and one serotype of Listeria monocytogenes were evaluated for survival. We prepared bacterial cell numbers following a Poisson distribution (indicated by the parameter λ, which was equal to 2) and plated the cells in 96-well microplates, which were stored in a desiccated environment at 10% to 20% relative humidity and at 5, 15, and 25°C. The survival or death of the bacterial cells in each well was confirmed by adding tryptic soy broth as an enrichment culture. Changes in the Poisson distribution parameter during the inactivation process, which represent the variability in the numbers of surviving bacteria, were described by nonlinear regression with an exponential function based on a Weibull distribution. We also examined random changes in the number of surviving bacteria using a random number generator and computer simulations to determine whether the number of surviving bacteria followed a Poisson distribution during the bacterial death process by use of the Poisson process. For small initial cell numbers, more than 80% of the simulated distributions (λ = 2 or 10) followed a Poisson distribution. The results demonstrate that variability in the number of surviving bacteria can be described as a Poisson distribution by use of the model developed by use of the Poisson process. We developed a model to enable the quantitative assessment of bacterial survivors of inactivation procedures because the presence of even one bacterium can cause foodborne disease. The results demonstrate that the variability in the numbers of surviving bacteria was described as a Poisson distribution by use of the model developed by use of the Poisson process. Description of the number of surviving bacteria as a probability distribution rather than as the point estimates used in a deterministic approach can provide a more realistic estimation of risk. The probability model should be useful for estimating the quantitative risk of bacterial survival during inactivation. Copyright © 2017 Koyama et al.

Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach

NASA Astrophysics Data System (ADS)

Comolli, Alessandro; Dentz, Marco

2017-09-01

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in heterogeneous natural and engineered porous materials. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

A New Approach to Extreme Value Estimation Applicable to a Wide Variety of Random Variables

NASA Technical Reports Server (NTRS)

Holland, Frederic A., Jr.

1997-01-01

Designing reliable structures requires an estimate of the maximum and minimum values (i.e., strength and load) that may be encountered in service. Yet designs based on very extreme values (to insure safety) can result in extra material usage and hence, uneconomic systems. In aerospace applications, severe over-design cannot be tolerated making it almost mandatory to design closer to the assumed limits of the design random variables. The issue then is predicting extreme values that are practical, i.e. neither too conservative or non-conservative. Obtaining design values by employing safety factors is well known to often result in overly conservative designs and. Safety factor values have historically been selected rather arbitrarily, often lacking a sound rational basis. To answer the question of how safe a design needs to be has lead design theorists to probabilistic and statistical methods. The so-called three-sigma approach is one such method and has been described as the first step in utilizing information about the data dispersion. However, this method is based on the assumption that the random variable is dispersed symmetrically about the mean and is essentially limited to normally distributed random variables. Use of this method can therefore result in unsafe or overly conservative design allowables if the common assumption of normality is incorrect.

A Fast Numerical Method for Max-Convolution and the Application to Efficient Max-Product Inference in Bayesian Networks.

PubMed

Serang, Oliver

2015-08-01

Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in log-transformed form and denoted as "infimal convolution," "min-convolution," or "convolution on the tropical semiring"), for which no O(k log(k)) method is currently known. Presented here is an O(k log(k)) numerical method for estimating the max-convolution of two nonnegative vectors (e.g., two probability mass functions), where k is the length of the larger vector. This numerical max-convolution method is then demonstrated by performing fast max-product inference on a convolution tree, a data structure for performing fast inference given information on the sum of n discrete random variables in O(nk log(nk)log(n)) steps (where each random variable has an arbitrary prior distribution on k contiguous possible states). The numerical max-convolution method can be applied to specialized classes of hidden Markov models to reduce the runtime of computing the Viterbi path from nk(2) to nk log(k), and has potential application to the all-pairs shortest paths problem.

Statistical analysis of multivariate atmospheric variables. [cloud cover

NASA Technical Reports Server (NTRS)

Tubbs, J. D.

1979-01-01

Topics covered include: (1) estimation in discrete multivariate distributions; (2) a procedure to predict cloud cover frequencies in the bivariate case; (3) a program to compute conditional bivariate normal parameters; (4) the transformation of nonnormal multivariate to near-normal; (5) test of fit for the extreme value distribution based upon the generalized minimum chi-square; (6) test of fit for continuous distributions based upon the generalized minimum chi-square; (7) effect of correlated observations on confidence sets based upon chi-square statistics; and (8) generation of random variates from specified distributions.

The Contribution of Vegetation and Landscape Configuration for Predicting Environmental Change Impacts on Iberian Birds

PubMed Central

Triviño, Maria; Thuiller, Wilfried; Cabeza, Mar; Hickler, Thomas; Araújo, Miguel B.

2011-01-01

Although climate is known to be one of the key factors determining animal species distributions amongst others, projections of global change impacts on their distributions often rely on bioclimatic envelope models. Vegetation structure and landscape configuration are also key determinants of distributions, but they are rarely considered in such assessments. We explore the consequences of using simulated vegetation structure and composition as well as its associated landscape configuration in models projecting global change effects on Iberian bird species distributions. Both present-day and future distributions were modelled for 168 bird species using two ensemble forecasting methods: Random Forests (RF) and Boosted Regression Trees (BRT). For each species, several models were created, differing in the predictor variables used (climate, vegetation, and landscape configuration). Discrimination ability of each model in the present-day was then tested with four commonly used evaluation methods (AUC, TSS, specificity and sensitivity). The different sets of predictor variables yielded similar spatial patterns for well-modelled species, but the future projections diverged for poorly-modelled species. Models using all predictor variables were not significantly better than models fitted with climate variables alone for ca. 50% of the cases. Moreover, models fitted with climate data were always better than models fitted with landscape configuration variables, and vegetation variables were found to correlate with bird species distributions in 26–40% of the cases with BRT, and in 1–18% of the cases with RF. We conclude that improvements from including vegetation and its landscape configuration variables in comparison with climate only variables might not always be as great as expected for future projections of Iberian bird species. PMID:22216263

On generalisations of the log-Normal distribution by means of a new product definition in the Kapteyn process

NASA Astrophysics Data System (ADS)

Duarte Queirós, Sílvio M.

2012-07-01

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 q<1) or large (when q>1) 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.

Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution

NASA Astrophysics Data System (ADS)

Saputro, D. R. S.; Amalia, F.; Widyaningsih, P.; Affan, R. C.

2018-05-01

Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

Variable versus conventional lung protective mechanical ventilation during open abdominal surgery: study protocol for a randomized controlled trial.

PubMed

Spieth, Peter M; Güldner, Andreas; Uhlig, Christopher; Bluth, Thomas; Kiss, Thomas; Schultz, Marcus J; Pelosi, Paolo; Koch, Thea; Gama de Abreu, Marcelo

2014-05-02

General anesthesia usually requires mechanical ventilation, which is traditionally accomplished with constant tidal volumes in volume- or pressure-controlled modes. Experimental studies suggest that the use of variable tidal volumes (variable ventilation) recruits lung tissue, improves pulmonary function and reduces systemic inflammatory response. However, it is currently not known whether patients undergoing open abdominal surgery might benefit from intraoperative variable ventilation. The PROtective VARiable ventilation trial ('PROVAR') is a single center, randomized controlled trial enrolling 50 patients who are planning for open abdominal surgery expected to last longer than 3 hours. PROVAR compares conventional (non-variable) lung protective ventilation (CV) with variable lung protective ventilation (VV) regarding pulmonary function and inflammatory response. The primary endpoint of the study is the forced vital capacity on the first postoperative day. Secondary endpoints include further lung function tests, plasma cytokine levels, spatial distribution of ventilation assessed by means of electrical impedance tomography and postoperative pulmonary complications. We hypothesize that VV improves lung function and reduces systemic inflammatory response compared to CV in patients receiving mechanical ventilation during general anesthesia for open abdominal surgery longer than 3 hours. PROVAR is the first randomized controlled trial aiming at intra- and postoperative effects of VV on lung function. This study may help to define the role of VV during general anesthesia requiring mechanical ventilation. Clinicaltrials.gov NCT01683578 (registered on September 3 3012).

Review of probabilistic analysis of dynamic response of systems with random parameters

NASA Technical Reports Server (NTRS)

Kozin, F.; Klosner, J. M.

1989-01-01

The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.

CMOS-based Stochastically Spiking Neural Network for Optimization under Uncertainties

DTIC Science & Technology

2017-03-01

inverse tangent characteristics at varying input voltage (VIN) [Fig. 3], thereby it is suitable for Kernel function implementation. By varying bias...cost function/constraint variables are generated based on inverse transform on CDF. In Fig. 5, F-1(u) for uniformly distributed random number u [0, 1...extracts random samples of x varying with CDF of F(x). In Fig. 6, we present a successive approximation (SA) circuit to evaluate inverse

An Integrated Framework for Model-Based Distributed Diagnosis and Prognosis

DTIC Science & Technology

2012-09-01

0 : t) denotes all measurements observed up to time t. The goal of prognosis is to determine the end of (use- ful) life ( EOL ) of a system, and/or its...remaining useful life (RUL). For a given fault, f , using the fault estimate, p(xf (t),θf (t)|y(0 : t)), a probability distribution of EOL , p(EOLf (tP...is stochas- tic, EOL /RUL are random variables and we represent them by probability distributions. The acceptable behavior of the system is expressed

Scan Order in Gibbs Sampling: Models in Which it Matters and Bounds on How Much.

PubMed

He, Bryan; De Sa, Christopher; Mitliagkas, Ioannis; Ré, Christopher

2016-01-01

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance.

Scan Order in Gibbs Sampling: Models in Which it Matters and Bounds on How Much

PubMed Central

He, Bryan; De Sa, Christopher; Mitliagkas, Ioannis; Ré, Christopher

2016-01-01

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance. PMID:28344429

An analytic solution of the stochastic storage problem applicable to soil water

USGS Publications Warehouse

Milly, P.C.D.

1993-01-01

The accumulation of soil water during rainfall events and the subsequent depletion of soil water by evaporation between storms can be described, to first order, by simple accounting models. When the alternating supplies (precipitation) and demands (potential evaporation) are viewed as random variables, it follows that soil-water storage, evaporation, and runoff are also random variables. If the forcing (supply and demand) processes are stationary for a sufficiently long period of time, an asymptotic regime should eventually be reached where the probability distribution functions of storage, evaporation, and runoff are stationary and uniquely determined by the distribution functions of the forcing. Under the assumptions that the potential evaporation rate is constant, storm arrivals are Poisson-distributed, rainfall is instantaneous, and storm depth follows an exponential distribution, it is possible to derive the asymptotic distributions of storage, evaporation, and runoff analytically for a simple balance model. A particular result is that the fraction of rainfall converted to runoff is given by (1 - R−1)/(eα(1−R−1) − R−1), in which R is the ratio of mean potential evaporation to mean rainfall and a is the ratio of soil water-holding capacity to mean storm depth. The problem considered here is analogous to the well-known problem of storage in a reservoir behind a dam, for which the present work offers a new solution for reservoirs of finite capacity. A simple application of the results of this analysis suggests that random, intraseasonal fluctuations of precipitation cannot by themselves explain the observed dependence of the annual water balance on annual totals of precipitation and potential evaporation.

New distributed fusion filtering algorithm based on covariances over sensor networks with random packet dropouts

NASA Astrophysics Data System (ADS)

Caballero-Águila, R.; Hermoso-Carazo, A.; Linares-Pérez, J.

2017-07-01

This paper studies the distributed fusion estimation problem from multisensor measured outputs perturbed by correlated noises and uncertainties modelled by random parameter matrices. Each sensor transmits its outputs to a local processor over a packet-erasure channel and, consequently, random losses may occur during transmission. Different white sequences of Bernoulli variables are introduced to model the transmission losses. For the estimation, each lost output is replaced by its estimator based on the information received previously, and only the covariances of the processes involved are used, without requiring the signal evolution model. First, a recursive algorithm for the local least-squares filters is derived by using an innovation approach. Then, the cross-correlation matrices between any two local filters is obtained. Finally, the distributed fusion filter weighted by matrices is obtained from the local filters by applying the least-squares criterion. The performance of the estimators and the influence of both sensor uncertainties and transmission losses on the estimation accuracy are analysed in a numerical example.

Logistic quantile regression provides improved estimates for bounded avian counts: a case study of California Spotted Owl fledgling production

Treesearch

Brian S. Cade; Barry R. Noon; Rick D. Scherer; John J. Keane

2017-01-01

Counts of avian fledglings, nestlings, or clutch size that are bounded below by zero and above by some small integer form a discrete random variable distribution that is not approximated well by conventional parametric count distributions such as the Poisson or negative binomial. We developed a logistic quantile regression model to provide estimates of the empirical...

High performance frame synchronization for continuous variable quantum key distribution systems.

PubMed

Lin, Dakai; Huang, Peng; Huang, Duan; Wang, Chao; Peng, Jinye; Zeng, Guihua

2015-08-24

Considering a practical continuous variable quantum key distribution(CVQKD) system, synchronization is of significant importance as it is hardly possible to extract secret keys from unsynchronized strings. In this paper, we proposed a high performance frame synchronization method for CVQKD systems which is capable to operate under low signal-to-noise(SNR) ratios and is compatible with random phase shift induced by quantum channel. A practical implementation of this method with low complexity is presented and its performance is analysed. By adjusting the length of synchronization frame, this method can work well with large range of SNR values which paves the way for longer distance CVQKD.

Integration of quantum key distribution and private classical communication through continuous variable

NASA Astrophysics Data System (ADS)

Wang, Tianyi; Gong, Feng; Lu, Anjiang; Zhang, Damin; Zhang, Zhengping

2017-12-01

In this paper, we propose a scheme that integrates quantum key distribution and private classical communication via continuous variables. The integrated scheme employs both quadratures of a weak coherent state, with encrypted bits encoded on the signs and Gaussian random numbers encoded on the values of the quadratures. The integration enables quantum and classical data to share the same physical and logical channel. Simulation results based on practical system parameters demonstrate that both classical communication and quantum communication can be implemented over distance of tens of kilometers, thus providing a potential solution for simultaneous transmission of quantum communication and classical communication.

Determining the factors affecting the distribution of Muscari latifolium, an endemic plant of Turkey, and a mapping species distribution model.

PubMed

Yilmaz, Hatice; Yilmaz, Osman Yalçın; Akyüz, Yaşar Feyza

2017-02-01

Species distribution modeling was used to determine factors among the large predictor candidate data set that affect the distribution of Muscari latifolium , an endemic bulbous plant species of Turkey, to quantify the relative importance of each factor and make a potential spatial distribution map of M. latifolium . Models were built using the Boosted Regression Trees method based on 35 presence and 70 absence records obtained through field sampling in the Gönen Dam watershed area of the Kazdağı Mountains in West Anatolia. Large candidate variables of monthly and seasonal climate, fine-scale land surface, and geologic and biotic variables were simplified using a BRT simplifying procedure. Analyses performed on these resources, direct and indirect variables showed that there were 14 main factors that influence the species' distribution. Five of the 14 most important variables influencing the distribution of the species are bedrock type, Quercus cerris density, precipitation during the wettest month, Pinus nigra density, and northness. These variables account for approximately 60% of the relative importance for determining the distribution of the species. Prediction performance was assessed by 10 random subsample data sets and gave a maximum the area under a receiver operating characteristic curve (AUC) value of 0.93 and an average AUC value of 0.8. This study provides a significant contribution to the knowledge of the habitat requirements and ecological characteristics of this species. The distribution of this species is explained by a combination of biotic and abiotic factors. Hence, using biotic interaction and fine-scale land surface variables in species distribution models improved the accuracy and precision of the model. The knowledge of the relationships between distribution patterns and environmental factors and biotic interaction of M. latifolium can help develop a management and conservation strategy for this species.

Solution of the finite Milne problem in stochastic media with RVT Technique

NASA Astrophysics Data System (ADS)

Slama, Howida; El-Bedwhey, Nabila A.; El-Depsy, Alia; Selim, Mustafa M.

2017-12-01

This paper presents the solution to the Milne problem in the steady state with isotropic scattering phase function. The properties of the medium are considered as stochastic ones with Gaussian or exponential distributions and hence the problem treated as a stochastic integro-differential equation. To get an explicit form for the radiant energy density, the linear extrapolation distance, reflectivity and transmissivity in the deterministic case the problem is solved using the Pomraning-Eddington method. The obtained solution is found to be dependent on the optical space variable and thickness of the medium which are considered as random variables. The random variable transformation (RVT) technique is used to find the first probability density function (1-PDF) of the solution process. Then the stochastic linear extrapolation distance, reflectivity and transmissivity are calculated. For illustration, numerical results with conclusions are provided.

Satisfiability Test with Synchronous Simulated Annealing on the Fujitsu AP1000 Massively-Parallel Multiprocessor

NASA Technical Reports Server (NTRS)

Sohn, Andrew; Biswas, Rupak

1996-01-01

Solving the hard Satisfiability Problem is time consuming even for modest-sized problem instances. Solving the Random L-SAT Problem is especially difficult due to the ratio of clauses to variables. This report presents a parallel synchronous simulated annealing method for solving the Random L-SAT Problem on a large-scale distributed-memory multiprocessor. In particular, we use a parallel synchronous simulated annealing procedure, called Generalized Speculative Computation, which guarantees the same decision sequence as sequential simulated annealing. To demonstrate the performance of the parallel method, we have selected problem instances varying in size from 100-variables/425-clauses to 5000-variables/21,250-clauses. Experimental results on the AP1000 multiprocessor indicate that our approach can satisfy 99.9 percent of the clauses while giving almost a 70-fold speedup on 500 processors.

Population pharmacokinetics of valnemulin in swine.

PubMed

Zhao, D H; Zhang, Z; Zhang, C Y; Liu, Z C; Deng, H; Yu, J J; Guo, J P; Liu, Y H

2014-02-01

This study was carried out in 121 pigs to develop a population pharmacokinetic (PPK) model by oral (p.o.) administration of valnemulin at a single dose of 10 mg/kg. Serum biochemistry parameters of each pig were determined prior to drug administration. Three to five blood samples were collected at random time points, but uniformly distributed in the absorption, distribution, and elimination phases of drug disposition. Plasma concentrations of valnemulin were determined by high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS). The concentration-time data were fitted to PPK models using nonlinear mixed effect modeling (NONMEM) with G77 FORTRAN compiler. NONMEM runs were executed using Wings for NONMEM. Fixed effects of weight, age, sex as well as biochemistry parameters, which may influence the PK of valnemulin, were investigated. The drug concentration-time data were adequately described by a one-compartmental model with first-order absorption. A random effect model of valnemulin revealed a pattern of log-normal distribution, and it satisfactorily characterized the observed interindividual variability. The distribution of random residual errors, however, suggested an additive model for the initial phase (<12 h) followed by a combined model that consists of both proportional and additive features (≥ 12 h), so that the intra-individual variability could be sufficiently characterized. Covariate analysis indicated that body weight had a conspicuous effect on valnemulin clearance (CL/F). The featured population PK values of Ka , V/F and CL/F were 0.292/h, 63.0 L and 41.3 L/h, respectively. © 2013 John Wiley & Sons Ltd.

Simulating the component counts of combinatorial structures.

PubMed

Arratia, Richard; Barbour, A D; Ewens, W J; Tavaré, Simon

2018-02-09

This article describes and compares methods for simulating the component counts of random logarithmic combinatorial structures such as permutations and mappings. We exploit the Feller coupling for simulating permutations to provide a very fast method for simulating logarithmic assemblies more generally. For logarithmic multisets and selections, this approach is replaced by an acceptance/rejection method based on a particular conditioning relationship that represents the distribution of the combinatorial structure as that of independent random variables conditioned on a weighted sum. We show how to improve its acceptance rate. We illustrate the method by estimating the probability that a random mapping has no repeated component sizes, and establish the asymptotic distribution of the difference between the number of components and the number of distinct component sizes for a very general class of logarithmic structures. Copyright © 2018. Published by Elsevier Inc.

The quotient of normal random variables and application to asset price fat tails

NASA Astrophysics Data System (ADS)

Caginalp, Carey; Caginalp, Gunduz

2018-06-01

The quotient of random variables with normal distributions is examined and proven to have power law decay, with density f(x) ≃f0x-2, with the coefficient depending on the means and variances of the numerator and denominator and their correlation. We also obtain the conditional probability densities for each of the four quadrants given by the signs of the numerator and denominator for arbitrary correlation ρ ∈ [ - 1 , 1) . For ρ = - 1 we obtain a particularly simple closed form solution for all x ∈ R. The results are applied to a basic issue in economics and finance, namely the density of relative price changes. Classical finance stipulates a normal distribution of relative price changes, though empirical studies suggest a power law at the tail end. By considering the supply and demand in a basic price change model, we prove that the relative price change has density that decays with an x-2 power law. Various parameter limits are established.

The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey's h Transformation as a Special Case

PubMed Central

Goerg, Georg M.

2015-01-01

I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert  W × F X random variable depends on a tail parameter δ ≥ 0: for δ = 0, Y ≡ X, for δ > 0 Y has heavier tails than X. For X being Gaussian it reduces to Tukey's h distribution. The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data. It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey's h pdf and cdf. Parameters can be estimated by maximum likelihood and applications to S&P 500 log-returns demonstrate the usefulness of the presented methodology. The R package LambertW implements most of the introduced methodology and is publicly available on CRAN. PMID:26380372

Probabilistic analysis of a materially nonlinear structure

NASA Technical Reports Server (NTRS)

Millwater, H. R.; Wu, Y.-T.; Fossum, A. F.

1990-01-01

A probabilistic finite element program is used to perform probabilistic analysis of a materially nonlinear structure. The program used in this study is NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), under development at Southwest Research Institute. The cumulative distribution function (CDF) of the radial stress of a thick-walled cylinder under internal pressure is computed and compared with the analytical solution. In addition, sensitivity factors showing the relative importance of the input random variables are calculated. Significant plasticity is present in this problem and has a pronounced effect on the probabilistic results. The random input variables are the material yield stress and internal pressure with Weibull and normal distributions, respectively. The results verify the ability of NESSUS to compute the CDF and sensitivity factors of a materially nonlinear structure. In addition, the ability of the Advanced Mean Value (AMV) procedure to assess the probabilistic behavior of structures which exhibit a highly nonlinear response is shown. Thus, the AMV procedure can be applied with confidence to other structures which exhibit nonlinear behavior.

Probabilistic graphs as a conceptual and computational tool in hydrology and water management

NASA Astrophysics Data System (ADS)

Schoups, Gerrit

2014-05-01

Originally developed in the fields of machine learning and artificial intelligence, probabilistic graphs constitute a general framework for modeling complex systems in the presence of uncertainty. The framework consists of three components: 1. Representation of the model as a graph (or network), with nodes depicting random variables in the model (e.g. parameters, states, etc), which are joined together by factors. Factors are local probabilistic or deterministic relations between subsets of variables, which, when multiplied together, yield the joint distribution over all variables. 2. Consistent use of probability theory for quantifying uncertainty, relying on basic rules of probability for assimilating data into the model and expressing unknown variables as a function of observations (via the posterior distribution). 3. Efficient, distributed approximation of the posterior distribution using general-purpose algorithms that exploit model structure encoded in the graph. These attributes make probabilistic graphs potentially useful as a conceptual and computational tool in hydrology and water management (and beyond). Conceptually, they can provide a common framework for existing and new probabilistic modeling approaches (e.g. by drawing inspiration from other fields of application), while computationally they can make probabilistic inference feasible in larger hydrological models. The presentation explores, via examples, some of these benefits.

Do simple screening statistical tools help to detect reporting bias?

PubMed

Pirracchio, Romain; Resche-Rigon, Matthieu; Chevret, Sylvie; Journois, Didier

2013-09-02

As a result of reporting bias, or frauds, false or misunderstood findings may represent the majority of published research claims. This article provides simple methods that might help to appraise the quality of the reporting of randomized, controlled trials (RCT). This evaluation roadmap proposed herein relies on four steps: evaluation of the distribution of the reported variables; evaluation of the distribution of the reported p values; data simulation using parametric bootstrap and explicit computation of the p values. Such an approach was illustrated using published data from a retracted RCT comparing a hydroxyethyl starch versus albumin-based priming for cardiopulmonary bypass. Despite obvious nonnormal distributions, several variables are presented as if they were normally distributed. The set of 16 p values testing for differences in baseline characteristics across randomized groups did not follow a Uniform distribution on [0,1] (p = 0.045). The p values obtained by explicit computations were different from the results reported by the authors for the two following variables: urine output at 5 hours (calculated p value < 10-6, reported p ≥ 0.05); packed red blood cells (PRBC) during surgery (calculated p value = 0.08; reported p < 0.05). Finally, parametric bootstrap found p value > 0.05 in only 5 of the 10,000 simulated datasets concerning urine output 5 hours after surgery. Concerning PRBC transfused during surgery, parametric bootstrap showed that only the corresponding p value had less than a 50% chance to be inferior to 0.05 (3,920/10,000, p value < 0.05). Such simple evaluation methods might offer some warning signals. However, it should be emphasized that such methods do not allow concluding to the presence of error or fraud but should rather be used to justify asking for an access to the raw data.

Continuous Variable Quantum Key Distribution Using Polarized Coherent States

NASA Astrophysics Data System (ADS)

Vidiella-Barranco, A.; Borelli, L. F. M.

We discuss a continuous variables method of quantum key distribution employing strongly polarized coherent states of light. The key encoding is performed using the variables known as Stokes parameters, rather than the field quadratures. Their quantum counterpart, the Stokes operators Ŝi (i=1,2,3), constitute a set of non-commuting operators, being the precision of simultaneous measurements of a pair of them limited by an uncertainty-like relation. Alice transmits a conveniently modulated two-mode coherent state, and Bob randomly measures one of the Stokes parameters of the incoming beam. After performing reconciliation and privacy amplification procedures, it is possible to distill a secret common key. We also consider a non-ideal situation, in which coherent states with thermal noise, instead of pure coherent states, are used for encoding.

A Model of the Base Civil Engineering Work Request/Work Order Processing System.

DTIC Science & Technology

1979-09-01

changes to the work order processing system. This research identifies the variables that significantly affect the accomplishment time and proposes a... order processing system and its behavior with respect to work order processing time. A conceptual model was developed to describe the work request...work order processing system as a stochastic queueing system in which the processing times and the various distributions are treated as random variables

Methods for combining payload parameter variations with input environment. [calculating design limit loads compatible with probabilistic structural design criteria

NASA Technical Reports Server (NTRS)

Merchant, D. H.

1976-01-01

Methods are presented for calculating design limit loads compatible with probabilistic structural design criteria. The approach is based on the concept that the desired limit load, defined as the largest load occurring in a mission, is a random variable having a specific probability distribution which may be determined from extreme-value theory. The design limit load, defined as a particular of this random limit load, is the value conventionally used in structural design. Methods are presented for determining the limit load probability distributions from both time-domain and frequency-domain dynamic load simulations. Numerical demonstrations of the method are also presented.

Multiple imputation in the presence of non-normal data.

PubMed

Lee, Katherine J; Carlin, John B

2017-02-20

Multiple imputation (MI) is becoming increasingly popular for handling missing data. Standard approaches for MI assume normality for continuous variables (conditionally on the other variables in the imputation model). However, it is unclear how to impute non-normally distributed continuous variables. Using simulation and a case study, we compared various transformations applied prior to imputation, including a novel non-parametric transformation, to imputation on the raw scale and using predictive mean matching (PMM) when imputing non-normal data. We generated data from a range of non-normal distributions, and set 50% to missing completely at random or missing at random. We then imputed missing values on the raw scale, following a zero-skewness log, Box-Cox or non-parametric transformation and using PMM with both type 1 and 2 matching. We compared inferences regarding the marginal mean of the incomplete variable and the association with a fully observed outcome. We also compared results from these approaches in the analysis of depression and anxiety symptoms in parents of very preterm compared with term-born infants. The results provide novel empirical evidence that the decision regarding how to impute a non-normal variable should be based on the nature of the relationship between the variables of interest. If the relationship is linear in the untransformed scale, transformation can introduce bias irrespective of the transformation used. However, if the relationship is non-linear, it may be important to transform the variable to accurately capture this relationship. A useful alternative is to impute the variable using PMM with type 1 matching. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Optimal estimation for discrete time jump processes

NASA Technical Reports Server (NTRS)

Vaca, M. V.; Tretter, S. A.

1978-01-01

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Demythologizing sex education in Oklahoma: an attitudinal study.

PubMed

Turner, N H

1983-08-01

A randomized study was conducted to determine the distribution of attitudes among Oklahomans of voting age toward sex education and to analyze the relationship of demographic, sociocultural, and attitudinal factors. The state was stratified into six regions. Forty-five percent of the sample lived in urban areas, and 55% in rural areas. Random digit dialing and random selection within households were utilized to ensure a representative sample of the population. Eighty percent of the sample was found to be favorable toward sex education in the public schools, while 20% was unfavorable. A majority of respondents in all religious groups including "fundamentalists" were favorable. Seventeen variables were found to be significant in the univariate analysis of the data; eight were not significant. In a multivariate analysis, three variables, age, Protestant denominational type and female employment, were shown to have predictive ability in determining favorability and unfavorability. Implications for building community support for sex education also are discussed.

Erlang circular model motivated by inverse stereographic projection

NASA Astrophysics Data System (ADS)

Pramesti, G.

2018-05-01

The Erlang distribution is a special case of the Gamma distribution with the shape parameter is an integer. This paper proposed a new circular model used inverse stereographic projection. The inverse stereographic projection which is a mapping that projects a random variable from a real line onto a circle can be used in circular statistics to construct a distribution on the circle from real domain. From the circular model, then can be derived the characteristics of the Erlang circular model such as the mean resultant length, mean direction, circular variance and trigonometric moments of the distribution.

Neyman Pearson detection of K-distributed random variables

NASA Astrophysics Data System (ADS)

Tucker, J. Derek; Azimi-Sadjadi, Mahmood R.

2010-04-01

In this paper a new detection method for sonar imagery is developed in K-distributed background clutter. The equation for the log-likelihood is derived and compared to the corresponding counterparts derived for the Gaussian and Rayleigh assumptions. Test results of the proposed method on a data set of synthetic underwater sonar images is also presented. This database contains images with targets of different shapes inserted into backgrounds generated using a correlated K-distributed model. Results illustrating the effectiveness of the K-distributed detector are presented in terms of probability of detection, false alarm, and correct classification rates for various bottom clutter scenarios.

A model for the flux-r.m.s. correlation in blazar variability or the minijets-in-a-jet statistical model

NASA Astrophysics Data System (ADS)

Biteau, J.; Giebels, B.

2012-12-01

Very high energy gamma-ray variability of blazar emission remains of puzzling origin. Fast flux variations down to the minute time scale, as observed with H.E.S.S. during flares of the blazar PKS 2155-304, suggests that variability originates from the jet, where Doppler boosting can be invoked to relax causal constraints on the size of the emission region. The observation of log-normality in the flux distributions should rule out additive processes, such as those resulting from uncorrelated multiple-zone emission models, and favour an origin of the variability from multiplicative processes not unlike those observed in a broad class of accreting systems. We show, using a simple kinematic model, that Doppler boosting of randomly oriented emitting regions generates flux distributions following a Pareto law, that the linear flux-r.m.s. relation found for a single zone holds for a large number of emitting regions, and that the skewed distribution of the total flux is close to a log-normal, despite arising from an additive process.

Quantification of variability and uncertainty for air toxic emission inventories with censored emission factor data.

PubMed

Frey, H Christopher; Zhao, Yuchao

2004-11-15

Probabilistic emission inventories were developed for urban air toxic emissions of benzene, formaldehyde, chromium, and arsenic for the example of Houston. Variability and uncertainty in emission factors were quantified for 71-97% of total emissions, depending upon the pollutant and data availability. Parametric distributions for interunit variability were fit using maximum likelihood estimation (MLE), and uncertainty in mean emission factors was estimated using parametric bootstrap simulation. For data sets containing one or more nondetected values, empirical bootstrap simulation was used to randomly sample detection limits for nondetected values and observations for sample values, and parametric distributions for variability were fit using MLE estimators for censored data. The goodness-of-fit for censored data was evaluated by comparison of cumulative distributions of bootstrap confidence intervals and empirical data. The emission inventory 95% uncertainty ranges are as small as -25% to +42% for chromium to as large as -75% to +224% for arsenic with correlated surrogates. Uncertainty was dominated by only a few source categories. Recommendations are made for future improvements to the analysis.

A double hit model for the distribution of time to AIDS onset

NASA Astrophysics Data System (ADS)

Chillale, Nagaraja Rao

2013-09-01

Incubation time is a key epidemiologic descriptor of an infectious disease. In the case of HIV infection this is a random variable and is probably the longest one. The probability distribution of incubation time is the major determinant of the relation between the incidences of HIV infection and its manifestation to Aids. This is also one of the key factors used for accurate estimation of AIDS incidence in a region. The present article i) briefly reviews the work done, points out uncertainties in estimation of AIDS onset time and stresses the need for its precise estimation, ii) highlights some of the modelling features of onset distribution including immune failure mechanism, and iii) proposes a 'Double Hit' model for the distribution of time to AIDS onset in the cases of (a) independent and (b) dependent time variables of the two markers and examined the applicability of a few standard probability models.

Random isotropic one-dimensional XY-model

NASA Astrophysics Data System (ADS)

Gonçalves, L. L.; Vieira, A. P.

1998-01-01

The 1D isotropic s = ½XY-model ( N sites), with random exchange interaction in a transverse random field is considered. The random variables satisfy bimodal quenched distributions. The solution is obtained by using the Jordan-Wigner fermionization and a canonical transformation, reducing the problem to diagonalizing an N × N matrix, corresponding to a system of N noninteracting fermions. The calculations are performed numerically for N = 1000, and the field-induced magnetization at T = 0 is obtained by averaging the results for the different samples. For the dilute case, in the uniform field limit, the magnetization exhibits various discontinuities, which are the consequence of the existence of disconnected finite clusters distributed along the chain. Also in this limit, for finite exchange constants J A and J B, as the probability of J A varies from one to zero, the saturation field is seen to vary from Γ A to Γ B, where Γ A(Γ B) is the value of the saturation field for the pure case with exchange constant equal to J A(J B) .

Comment on Pisarenko et al., "Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory"

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2016-02-01

In this short note, I comment on the research of Pisarenko et al. (Pure Appl. Geophys 171:1599-1624, 2014) regarding the extreme value theory and statistics in the case of earthquake magnitudes. The link between the generalized extreme value distribution (GEVD) as an asymptotic model for the block maxima of a random variable and the generalized Pareto distribution (GPD) as a model for the peaks over threshold (POT) of the same random variable is presented more clearly. Inappropriately, Pisarenko et al. (Pure Appl. Geophys 171:1599-1624, 2014) have neglected to note that the approximations by GEVD and GPD work only asymptotically in most cases. This is particularly the case with truncated exponential distribution (TED), a popular distribution model for earthquake magnitudes. I explain why the classical models and methods of the extreme value theory and statistics do not work well for truncated exponential distributions. Consequently, these classical methods should be used for the estimation of the upper bound magnitude and corresponding parameters. Furthermore, I comment on various issues of statistical inference in Pisarenko et al. and propose alternatives. I argue why GPD and GEVD would work for various types of stochastic earthquake processes in time, and not only for the homogeneous (stationary) Poisson process as assumed by Pisarenko et al. (Pure Appl. Geophys 171:1599-1624, 2014). The crucial point of earthquake magnitudes is the poor convergence of their tail distribution to the GPD, and not the earthquake process over time.

δ-exceedance records and random adaptive walks

NASA Astrophysics Data System (ADS)

Park, Su-Chan; Krug, Joachim

2016-08-01

We study a modified record process where the kth record in a series of independent and identically distributed random variables is defined recursively through the condition {Y}k\\gt {Y}k-1-{δ }k-1 with a deterministic sequence {δ }k\\gt 0 called the handicap. For constant {δ }k\\equiv δ and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of δ between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records (Park et al 2015 Phys. Rev. E 91 042707). Here we explore the behavior for general probability distributions and decreasing and increasing sequences {δ }k, focusing in particular on the case when {δ }k matches the typical spacing between subsequent records in the underlying simple record process without handicap. We find that a continuous phase transition occurs only in the exponential case, but a novel kind of first order transition emerges when {δ }k is increasing. The problem is partly motivated by the dynamics of evolutionary adaptation in biological fitness landscapes, where {δ }k corresponds to the change of the deterministic fitness component after k mutational steps. The results for the record process are used to compute the mean number of steps that a population performs in such a landscape before being trapped at a local fitness maximum.

Degradation modeling of mid-power white-light LEDs by using Wiener process.

PubMed

Huang, Jianlin; Golubović, Dušan S; Koh, Sau; Yang, Daoguo; Li, Xiupeng; Fan, Xuejun; Zhang, G Q

2015-07-27

The IES standard TM-21-11 provides a guideline for lifetime prediction of LED devices. As it uses average normalized lumen maintenance data and performs non-linear regression for lifetime modeling, it cannot capture dynamic and random variation of the degradation process of LED devices. In addition, this method cannot capture the failure distribution, although it is much more relevant in reliability analysis. Furthermore, the TM-21-11 only considers lumen maintenance for lifetime prediction. Color shift, as another important performance characteristic of LED devices, may also render significant degradation during service life, even though the lumen maintenance has not reached the critical threshold. In this study, a modified Wiener process has been employed for the modeling of the degradation of LED devices. By using this method, dynamic and random variations, as well as the non-linear degradation behavior of LED devices, can be easily accounted for. With a mild assumption, the parameter estimation accuracy has been improved by including more information into the likelihood function while neglecting the dependency between the random variables. As a consequence, the mean time to failure (MTTF) has been obtained and shows comparable result with IES TM-21-11 predictions, indicating the feasibility of the proposed method. Finally, the cumulative failure distribution was presented corresponding to different combinations of lumen maintenance and color shift. The results demonstrate that a joint failure distribution of LED devices could be modeled by simply considering their lumen maintenance and color shift as two independent variables.

Super Generalized Central Limit Theorem —Limit Distributions for Sums of Non-identical Random Variables with Power Laws—

NASA Astrophysics Data System (ADS)

Shintani, Masaru; Umeno, Ken

2018-04-01

The power law is present ubiquitously in nature and in our societies. Therefore, it is important to investigate the characteristics of power laws in the current era of big data. In this paper we prove that the superposition of non-identical stochastic processes with power laws converges in density to a unique stable distribution. This property can be used to explain the universality of stable laws that the sums of the logarithmic returns of non-identical stock price fluctuations follow stable distributions.

Sampling in health geography: reconciling geographical objectives and probabilistic methods. An example of a health survey in Vientiane (Lao PDR)

PubMed Central

Vallée, Julie; Souris, Marc; Fournet, Florence; Bochaton, Audrey; Mobillion, Virginie; Peyronnie, Karine; Salem, Gérard

2007-01-01

Background Geographical objectives and probabilistic methods are difficult to reconcile in a unique health survey. Probabilistic methods focus on individuals to provide estimates of a variable's prevalence with a certain precision, while geographical approaches emphasise the selection of specific areas to study interactions between spatial characteristics and health outcomes. A sample selected from a small number of specific areas creates statistical challenges: the observations are not independent at the local level, and this results in poor statistical validity at the global level. Therefore, it is difficult to construct a sample that is appropriate for both geographical and probability methods. Methods We used a two-stage selection procedure with a first non-random stage of selection of clusters. Instead of randomly selecting clusters, we deliberately chose a group of clusters, which as a whole would contain all the variation in health measures in the population. As there was no health information available before the survey, we selected a priori determinants that can influence the spatial homogeneity of the health characteristics. This method yields a distribution of variables in the sample that closely resembles that in the overall population, something that cannot be guaranteed with randomly-selected clusters, especially if the number of selected clusters is small. In this way, we were able to survey specific areas while minimising design effects and maximising statistical precision. Application We applied this strategy in a health survey carried out in Vientiane, Lao People's Democratic Republic. We selected well-known health determinants with unequal spatial distribution within the city: nationality and literacy. We deliberately selected a combination of clusters whose distribution of nationality and literacy is similar to the distribution in the general population. Conclusion This paper describes the conceptual reasoning behind the construction of the survey sample and shows that it can be advantageous to choose clusters using reasoned hypotheses, based on both probability and geographical approaches, in contrast to a conventional, random cluster selection strategy. PMID:17543100

Sampling in health geography: reconciling geographical objectives and probabilistic methods. An example of a health survey in Vientiane (Lao PDR).

PubMed

Vallée, Julie; Souris, Marc; Fournet, Florence; Bochaton, Audrey; Mobillion, Virginie; Peyronnie, Karine; Salem, Gérard

2007-06-01

Geographical objectives and probabilistic methods are difficult to reconcile in a unique health survey. Probabilistic methods focus on individuals to provide estimates of a variable's prevalence with a certain precision, while geographical approaches emphasise the selection of specific areas to study interactions between spatial characteristics and health outcomes. A sample selected from a small number of specific areas creates statistical challenges: the observations are not independent at the local level, and this results in poor statistical validity at the global level. Therefore, it is difficult to construct a sample that is appropriate for both geographical and probability methods. We used a two-stage selection procedure with a first non-random stage of selection of clusters. Instead of randomly selecting clusters, we deliberately chose a group of clusters, which as a whole would contain all the variation in health measures in the population. As there was no health information available before the survey, we selected a priori determinants that can influence the spatial homogeneity of the health characteristics. This method yields a distribution of variables in the sample that closely resembles that in the overall population, something that cannot be guaranteed with randomly-selected clusters, especially if the number of selected clusters is small. In this way, we were able to survey specific areas while minimising design effects and maximising statistical precision. We applied this strategy in a health survey carried out in Vientiane, Lao People's Democratic Republic. We selected well-known health determinants with unequal spatial distribution within the city: nationality and literacy. We deliberately selected a combination of clusters whose distribution of nationality and literacy is similar to the distribution in the general population. This paper describes the conceptual reasoning behind the construction of the survey sample and shows that it can be advantageous to choose clusters using reasoned hypotheses, based on both probability and geographical approaches, in contrast to a conventional, random cluster selection strategy.

Can Process Understanding Help Elucidate The Structure Of The Critical Zone? Comparing Process-Based Soil Formation Models With Digital Soil Mapping.

NASA Astrophysics Data System (ADS)

Vanwalleghem, T.; Román, A.; Peña, A.; Laguna, A.; Giráldez, J. V.

2017-12-01

There is a need for better understanding the processes influencing soil formation and the resulting distribution of soil properties in the critical zone. Soil properties can exhibit strong spatial variation, even at the small catchment scale. Especially soil carbon pools in semi-arid, mountainous areas are highly uncertain because bulk density and stoniness are very heterogeneous and rarely measured explicitly. In this study, we explore the spatial variability in key soil properties (soil carbon stocks, stoniness, bulk density and soil depth) as a function of processes shaping the critical zone (weathering, erosion, soil water fluxes and vegetation patterns). We also compare the potential of traditional digital soil mapping versus a mechanistic soil formation model (MILESD) for predicting these key soil properties. Soil core samples were collected from 67 locations at 6 depths. Total soil organic carbon stocks were 4.38 kg m-2. Solar radiation proved to be the key variable controlling soil carbon distribution. Stone content was mostly controlled by slope, indicating the importance of erosion. Spatial distribution of bulk density was found to be highly random. Finally, total carbon stocks were predicted using a random forest model whose main covariates were solar radiation and NDVI. The model predicts carbon stocks that are double as high on north versus south-facing slopes. However, validation showed that these covariates only explained 25% of the variation in the dataset. Apparently, present-day landscape and vegetation properties are not sufficient to fully explain variability in the soil carbon stocks in this complex terrain under natural vegetation. This is attributed to a high spatial variability in bulk density and stoniness, key variables controlling carbon stocks. Similar results were obtained with the mechanistic soil formation model MILESD, suggesting that more complex models might be needed to further explore this high spatial variability.

Probabilistic simulation of multi-scale composite behavior

NASA Technical Reports Server (NTRS)

Liaw, D. G.; Shiao, M. C.; Singhal, S. N.; Chamis, Christos C.

1993-01-01

A methodology is developed to computationally assess the probabilistic composite material properties at all composite scale levels due to the uncertainties in the constituent (fiber and matrix) properties and in the fabrication process variables. The methodology is computationally efficient for simulating the probability distributions of material properties. The sensitivity of the probabilistic composite material property to each random variable is determined. This information can be used to reduce undesirable uncertainties in material properties at the macro scale of the composite by reducing the uncertainties in the most influential random variables at the micro scale. This methodology was implemented into the computer code PICAN (Probabilistic Integrated Composite ANalyzer). The accuracy and efficiency of this methodology are demonstrated by simulating the uncertainties in the material properties of a typical laminate and comparing the results with the Monte Carlo simulation method. The experimental data of composite material properties at all scales fall within the scatters predicted by PICAN.

Multivariate normal maximum likelihood with both ordinal and continuous variables, and data missing at random.

PubMed

Pritikin, Joshua N; Brick, Timothy R; Neale, Michael C

2018-04-01

A novel method for the maximum likelihood estimation of structural equation models (SEM) with both ordinal and continuous indicators is introduced using a flexible multivariate probit model for the ordinal indicators. A full information approach ensures unbiased estimates for data missing at random. Exceeding the capability of prior methods, up to 13 ordinal variables can be included before integration time increases beyond 1 s per row. The method relies on the axiom of conditional probability to split apart the distribution of continuous and ordinal variables. Due to the symmetry of the axiom, two similar methods are available. A simulation study provides evidence that the two similar approaches offer equal accuracy. A further simulation is used to develop a heuristic to automatically select the most computationally efficient approach. Joint ordinal continuous SEM is implemented in OpenMx, free and open-source software.

Some limit theorems for ratios of order statistics from uniform random variables.

PubMed

Xu, Shou-Fang; Miao, Yu

2017-01-01

In this paper, we study the ratios of order statistics based on samples drawn from uniform distribution and establish some limit properties such as the almost sure central limit theorem, the large deviation principle, the Marcinkiewicz-Zygmund law of large numbers and complete convergence.

Probability Distributions of Minkowski Distances between Discrete Random Variables.

ERIC Educational Resources Information Center

Schroger, Erich; And Others

1993-01-01

Minkowski distances are used to indicate similarity of two vectors in an N-dimensional space. How to compute the probability function, the expectation, and the variance for Minkowski distances and the special cases City-block distance and Euclidean distance. Critical values for tests of significance are presented in tables. (SLD)

Large Deviations: Advanced Probability for Undergrads

ERIC Educational Resources Information Center

Rolls, David A.

2007-01-01

In the branch of probability called "large deviations," rates of convergence (e.g. of the sample mean) are considered. The theory makes use of the moment generating function. So, particularly for sums of independent and identically distributed random variables, the theory can be made accessible to senior undergraduates after a first course in…

MANCOVA for one way classification with homogeneity of regression coefficient vectors

NASA Astrophysics Data System (ADS)

Mokesh Rayalu, G.; Ravisankar, J.; Mythili, G. Y.

2017-11-01

The MANOVA and MANCOVA are the extensions of the univariate ANOVA and ANCOVA techniques to multidimensional or vector valued observations. The assumption of a Gaussian distribution has been replaced with the Multivariate Gaussian distribution for the vectors data and residual term variables in the statistical models of these techniques. The objective of MANCOVA is to determine if there are statistically reliable mean differences that can be demonstrated between groups later modifying the newly created variable. When randomization assignment of samples or subjects to groups is not possible, multivariate analysis of covariance (MANCOVA) provides statistical matching of groups by adjusting dependent variables as if all subjects scored the same on the covariates. In this research article, an extension has been made to the MANCOVA technique with more number of covariates and homogeneity of regression coefficient vectors is also tested.

Local-scale spatio-temporal distribution of questing Ixodes ricinus L. (Acari: Ixodidae)-A case study from a riparian urban forest in Wrocław, SW Poland.

PubMed

Kiewra, Dorota; Stefańska-Krzaczek, Ewa; Szymanowski, Mariusz; Szczepańska, Anna

2017-03-01

This paper presents the distribution of questing Ixodes ricinus ticks in suburban forest intensively visited by people. The local-scale observations conducted during a 4-year study at 99 plots (of 100m 2 each) located throughout the entire area of a riparian urban forest, showed a high variation in the density of ticks from year to year. Although I. ricinus is generally permanent in the study area, spatial distribution of sample plots harbouring I. ricinus is variable, i.e. mainly random for adults and larvae, and random or clustered for nymphs. Among the most common plant species in the herb layer, there were not any species which had a statistically significant and constant impact on the occurrence of any of the development stages of I. ricinus. Also relations between the density of tick development stages and vegetation variables, including cover of the herb layer, total species number, species number of the herb layer, and percentage coverage of particular species, as well as ecological indices for light, soil moisture, reaction, and nutrients, did not show any constant and predictable pattern in subsequent years of the study. Only tree and shrub layers were found as variables positively affecting the density of ticks. Although small, suburban forests can be considered as tick-borne risk areas, it is impossible to determine in details areas of tick-borne risk. Copyright © 2017 Elsevier GmbH. All rights reserved.

A Comprehensive Comparison of Multiparty Secure Additions with Differential Privacy

PubMed Central

Goryczka, Slawomir; Xiong, Li

2016-01-01

This paper considers the problem of secure data aggregation (mainly summation) in a distributed setting, while ensuring differential privacy of the result. We study secure multiparty addition protocols using well known security schemes: Shamir’s secret sharing, perturbation-based, and various encryptions. We supplement our study with our new enhanced encryption scheme EFT, which is efficient and fault tolerant. Differential privacy of the final result is achieved by either distributed Laplace or Geometric mechanism (respectively DLPA or DGPA), while approximated differential privacy is achieved by diluted mechanisms. Distributed random noise is generated collectively by all participants, which draw random variables from one of several distributions: Gamma, Gauss, Geometric, or their diluted versions. We introduce a new distributed privacy mechanism with noise drawn from the Laplace distribution, which achieves smaller redundant noise with efficiency. We compare complexity and security characteristics of the protocols with different differential privacy mechanisms and security schemes. More importantly, we implemented all protocols and present an experimental comparison on their performance and scalability in a real distributed environment. Based on the evaluations, we identify our security scheme and Laplace DLPA as the most efficient for secure distributed data aggregation with privacy. PMID:28919841

A Comprehensive Comparison of Multiparty Secure Additions with Differential Privacy.

PubMed

Goryczka, Slawomir; Xiong, Li

2017-01-01

This paper considers the problem of secure data aggregation (mainly summation) in a distributed setting, while ensuring differential privacy of the result. We study secure multiparty addition protocols using well known security schemes: Shamir's secret sharing, perturbation-based, and various encryptions. We supplement our study with our new enhanced encryption scheme EFT, which is efficient and fault tolerant. Differential privacy of the final result is achieved by either distributed Laplace or Geometric mechanism (respectively DLPA or DGPA), while approximated differential privacy is achieved by diluted mechanisms. Distributed random noise is generated collectively by all participants, which draw random variables from one of several distributions: Gamma, Gauss, Geometric, or their diluted versions. We introduce a new distributed privacy mechanism with noise drawn from the Laplace distribution, which achieves smaller redundant noise with efficiency. We compare complexity and security characteristics of the protocols with different differential privacy mechanisms and security schemes. More importantly, we implemented all protocols and present an experimental comparison on their performance and scalability in a real distributed environment. Based on the evaluations, we identify our security scheme and Laplace DLPA as the most efficient for secure distributed data aggregation with privacy.

Multivariate Analysis and Its Applications

DTIC Science & Technology

1989-02-14

defined in situations where measurements are taken on natural clusters of individuals like brothers in a family. A number of problems arise in the study of...intraclass correlations. How do we estimate it when observations are available on clusters of different sizes? How do we test the hypothesis that the...the random variable y(X) = #I X + G2X 2 + ... + GmX m , follows an exponential distribution with mean unity. Such a class of life distributions, has a

Robust Bayesian clustering.

PubMed

Archambeau, Cédric; Verleysen, Michel

2007-01-01

A new variational Bayesian learning algorithm for Student-t mixture models is introduced. This algorithm leads to (i) robust density estimation, (ii) robust clustering and (iii) robust automatic model selection. Gaussian mixture models are learning machines which are based on a divide-and-conquer approach. They are commonly used for density estimation and clustering tasks, but are sensitive to outliers. The Student-t distribution has heavier tails than the Gaussian distribution and is therefore less sensitive to any departure of the empirical distribution from Gaussianity. As a consequence, the Student-t distribution is suitable for constructing robust mixture models. In this work, we formalize the Bayesian Student-t mixture model as a latent variable model in a different way from Svensén and Bishop [Svensén, M., & Bishop, C. M. (2005). Robust Bayesian mixture modelling. Neurocomputing, 64, 235-252]. The main difference resides in the fact that it is not necessary to assume a factorized approximation of the posterior distribution on the latent indicator variables and the latent scale variables in order to obtain a tractable solution. Not neglecting the correlations between these unobserved random variables leads to a Bayesian model having an increased robustness. Furthermore, it is expected that the lower bound on the log-evidence is tighter. Based on this bound, the model complexity, i.e. the number of components in the mixture, can be inferred with a higher confidence.

Stochastic analysis of uncertain thermal parameters for random thermal regime of frozen soil around a single freezing pipe

NASA Astrophysics Data System (ADS)

Wang, Tao; Zhou, Guoqing; Wang, Jianzhou; Zhou, Lei

2018-03-01

The artificial ground freezing method (AGF) is widely used in civil and mining engineering, and the thermal regime of frozen soil around the freezing pipe affects the safety of design and construction. The thermal parameters can be truly random due to heterogeneity of the soil properties, which lead to the randomness of thermal regime of frozen soil around the freezing pipe. The purpose of this paper is to study the one-dimensional (1D) random thermal regime problem on the basis of a stochastic analysis model and the Monte Carlo (MC) method. Considering the uncertain thermal parameters of frozen soil as random variables, stochastic processes and random fields, the corresponding stochastic thermal regime of frozen soil around a single freezing pipe are obtained and analyzed. Taking the variability of each stochastic parameter into account individually, the influences of each stochastic thermal parameter on stochastic thermal regime are investigated. The results show that the mean temperatures of frozen soil around the single freezing pipe with three analogy method are the same while the standard deviations are different. The distributions of standard deviation have a great difference at different radial coordinate location and the larger standard deviations are mainly at the phase change area. The computed data with random variable method and stochastic process method have a great difference from the measured data while the computed data with random field method well agree with the measured data. Each uncertain thermal parameter has a different effect on the standard deviation of frozen soil temperature around the single freezing pipe. These results can provide a theoretical basis for the design and construction of AGF.

Predicting active-layer soil thickness using topographic variables at a small watershed scale

PubMed Central

Li, Aidi; Tan, Xing; Wu, Wei; Liu, Hongbin; Zhu, Jie

2017-01-01

Knowledge about the spatial distribution of active-layer (AL) soil thickness is indispensable for ecological modeling, precision agriculture, and land resource management. However, it is difficult to obtain the details on AL soil thickness by using conventional soil survey method. In this research, the objective is to investigate the possibility and accuracy of mapping the spatial distribution of AL soil thickness through random forest (RF) model by using terrain variables at a small watershed scale. A total of 1113 soil samples collected from the slope fields were randomly divided into calibration (770 soil samples) and validation (343 soil samples) sets. Seven terrain variables including elevation, aspect, relative slope position, valley depth, flow path length, slope height, and topographic wetness index were derived from a digital elevation map (30 m). The RF model was compared with multiple linear regression (MLR), geographically weighted regression (GWR) and support vector machines (SVM) approaches based on the validation set. Model performance was evaluated by precision criteria of mean error (ME), mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R2). Comparative results showed that RF outperformed MLR, GWR and SVM models. The RF gave better values of ME (0.39 cm), MAE (7.09 cm), and RMSE (10.85 cm) and higher R2 (62%). The sensitivity analysis demonstrated that the DEM had less uncertainty than the AL soil thickness. The outcome of the RF model indicated that elevation, flow path length and valley depth were the most important factors affecting the AL soil thickness variability across the watershed. These results demonstrated the RF model is a promising method for predicting spatial distribution of AL soil thickness using terrain parameters. PMID:28877196

Optimizing placements of ground-based snow sensors for areal snow cover estimation using a machine-learning algorithm and melt-season snow-LiDAR data

NASA Astrophysics Data System (ADS)

Oroza, C.; Zheng, Z.; Glaser, S. D.; Bales, R. C.; Conklin, M. H.

2016-12-01

We present a structured, analytical approach to optimize ground-sensor placements based on time-series remotely sensed (LiDAR) data and machine-learning algorithms. We focused on catchments within the Merced and Tuolumne river basins, covered by the JPL Airborne Snow Observatory LiDAR program. First, we used a Gaussian mixture model to identify representative sensor locations in the space of independent variables for each catchment. Multiple independent variables that govern the distribution of snow depth were used, including elevation, slope, and aspect. Second, we used a Gaussian process to estimate the areal distribution of snow depth from the initial set of measurements. This is a covariance-based model that also estimates the areal distribution of model uncertainty based on the independent variable weights and autocorrelation. The uncertainty raster was used to strategically add sensors to minimize model uncertainty. We assessed the temporal accuracy of the method using LiDAR-derived snow-depth rasters collected in water-year 2014. In each area, optimal sensor placements were determined using the first available snow raster for the year. The accuracy in the remaining LiDAR surveys was compared to 100 configurations of sensors selected at random. We found the accuracy of the model from the proposed placements to be higher and more consistent in each remaining survey than the average random configuration. We found that a relatively small number of sensors can be used to accurately reproduce the spatial patterns of snow depth across the basins, when placed using spatial snow data. Our approach also simplifies sensor placement. At present, field surveys are required to identify representative locations for such networks, a process that is labor intensive and provides limited guarantees on the networks' representation of catchment independent variables.

Minimization for conditional simulation: Relationship to optimal transport

NASA Astrophysics Data System (ADS)

Oliver, Dean S.

2014-05-01

In this paper, we consider the problem of generating independent samples from a conditional distribution when independent samples from the prior distribution are available. Although there are exact methods for sampling from the posterior (e.g. Markov chain Monte Carlo or acceptance/rejection), these methods tend to be computationally demanding when evaluation of the likelihood function is expensive, as it is for most geoscience applications. As an alternative, in this paper we discuss deterministic mappings of variables distributed according to the prior to variables distributed according to the posterior. Although any deterministic mappings might be equally useful, we will focus our discussion on a class of algorithms that obtain implicit mappings by minimization of a cost function that includes measures of data mismatch and model variable mismatch. Algorithms of this type include quasi-linear estimation, randomized maximum likelihood, perturbed observation ensemble Kalman filter, and ensemble of perturbed analyses (4D-Var). When the prior pdf is Gaussian and the observation operators are linear, we show that these minimization-based simulation methods solve an optimal transport problem with a nonstandard cost function. When the observation operators are nonlinear, however, the mapping of variables from the prior to the posterior obtained from those methods is only approximate. Errors arise from neglect of the Jacobian determinant of the transformation and from the possibility of discontinuous mappings.

A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing

NASA Astrophysics Data System (ADS)

Zhou, Yuan; Rangarajan, Anand; Gader, Paul D.

2018-05-01

Hyperspectral unmixing while considering endmember variability is usually performed by the normal compositional model (NCM), where the endmembers for each pixel are assumed to be sampled from unimodal Gaussian distributions. However, in real applications, the distribution of a material is often not Gaussian. In this paper, we use Gaussian mixture models (GMM) to represent the endmember variability. We show, given the GMM starting premise, that the distribution of the mixed pixel (under the linear mixing model) is also a GMM (and this is shown from two perspectives). The first perspective originates from the random variable transformation and gives a conditional density function of the pixels given the abundances and GMM parameters. With proper smoothness and sparsity prior constraints on the abundances, the conditional density function leads to a standard maximum a posteriori (MAP) problem which can be solved using generalized expectation maximization. The second perspective originates from marginalizing over the endmembers in the GMM, which provides us with a foundation to solve for the endmembers at each pixel. Hence, our model can not only estimate the abundances and distribution parameters, but also the distinct endmember set for each pixel. We tested the proposed GMM on several synthetic and real datasets, and showed its potential by comparing it to current popular methods.

Derivation of an eigenvalue probability density function relating to the Poincaré disk

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Krishnapur, Manjunath

2009-09-01

A result of Zyczkowski and Sommers (2000 J. Phys. A: Math. Gen. 33 2045-57) gives the eigenvalue probability density function for the top N × N sub-block of a Haar distributed matrix from U(N + n). In the case n >= N, we rederive this result, starting from knowledge of the distribution of the sub-blocks, introducing the Schur decomposition and integrating over all variables except the eigenvalues. The integration is done by identifying a recursive structure which reduces the dimension. This approach is inspired by an analogous approach which has been recently applied to determine the eigenvalue probability density function for random matrices A-1B, where A and B are random matrices with entries standard complex normals. We relate the eigenvalue distribution of the sub-blocks to a many-body quantum state, and to the one-component plasma, on the pseudosphere.

Using an Informative Missing Data Model to Predict the Ability to Assess Recovery of Balance Control after Spaceflight

NASA Technical Reports Server (NTRS)

Feiveson, Alan H.; Wood, Scott J.; Jain, Varsha

2008-01-01

Astronauts show degraded balance control immediately after spaceflight. To assess this change, astronauts' ability to maintain a fixed stance under several challenging stimuli on a movable platform is quantified by "equilibrium" scores (EQs) on a scale of 0 to 100, where 100 represents perfect control (sway angle of 0) and 0 represents data loss where no sway angle is observed because the subject has to be restrained from falling. By comparing post- to pre-flight EQs for actual astronauts vs. controls, we built a classifier for deciding when an astronaut has recovered. Future diagnostic performance depends both on the sampling distribution of the classifier as well as the distribution of its input data. Taking this into consideration, we constructed a predictive ROC by simulation after modeling P(EQ = 0) in terms of a latent EQ-like beta-distributed random variable with random effects.

Improved Results for Route Planning in Stochastic Transportation Networks

NASA Technical Reports Server (NTRS)

Boyan, Justin; Mitzenmacher, Michael

2000-01-01

In the bus network problem, the goal is to generate a plan for getting from point X to point Y within a city using buses in the smallest expected time. Because bus arrival times are not determined by a fixed schedule but instead may be random. the problem requires more than standard shortest path techniques. In recent work, Datar and Ranade provide algorithms in the case where bus arrivals are assumed to be independent and exponentially distributed. We offer solutions to two important generalizations of the problem, answering open questions posed by Datar and Ranade. First, we provide a polynomial time algorithm for a much wider class of arrival distributions, namely those with increasing failure rate. This class includes not only exponential distributions but also uniform, normal, and gamma distributions. Second, in the case where bus arrival times are independent and geometric discrete random variable,. we provide an algorithm for transportation networks of buses and trains, where trains run according to a fixed schedule.

Stochastic Seismic Response of an Algiers Site with Random Depth to Bedrock

NASA Astrophysics Data System (ADS)

Badaoui, M.; Berrah, M. K.; Mébarki, A.

2010-05-01

Among the important effects of the Boumerdes earthquake (Algeria, May 21st 2003) was that, within the same zone, the destructions in certain parts were more important than in others. This phenomenon is due to site effects which alter the characteristics of seismic motions and cause concentration of damage during earthquakes. Local site effects such as thickness and mechanical properties of soil layers have important effects on the surface ground motions. This paper deals with the effect of the randomness aspect of the depth to bedrock (soil layers heights) which is assumed to be a random variable with lognormal distribution. This distribution is suitable for strictly non-negative random variables with large values of the coefficient of variation. In this case, Monte Carlo simulations are combined with the stiffness matrix method, used herein as a deterministic method, for evaluating the effect of the depth to bedrock uncertainty on the seismic response of a multilayered soil. This study considers a P and SV wave propagation pattern using input accelerations collected at Keddara station, located at 20 km from the epicenter, as it is located directly on the bedrock. A parametric study is conducted do derive the stochastic behavior of the peak ground acceleration and its response spectrum, the transfer function and the amplification factors. It is found that the soil height heterogeneity causes a widening of the frequency content and an increase in the fundamental frequency of the soil profile, indicating that the resonance phenomenon concerns a larger number of structures.

Time-dependent breakdown of fiber networks: Uncertainty of lifetime

NASA Astrophysics Data System (ADS)

Mattsson, Amanda; Uesaka, Tetsu

2017-05-01

Materials often fail when subjected to stresses over a prolonged period. The time to failure, also called the lifetime, is known to exhibit large variability of many materials, particularly brittle and quasibrittle materials. For example, a coefficient of variation reaches 100% or even more. Its distribution shape is highly skewed toward zero lifetime, implying a large number of premature failures. This behavior contrasts with that of normal strength, which shows a variation of only 4%-10% and a nearly bell-shaped distribution. The fundamental cause of this large and unique variability of lifetime is not well understood because of the complex interplay between stochastic processes taking place on the molecular level and the hierarchical and disordered structure of the material. We have constructed fiber network models, both regular and random, as a paradigm for general material structures. With such networks, we have performed Monte Carlo simulations of creep failure to establish explicit relationships among fiber characteristics, network structures, system size, and lifetime distribution. We found that fiber characteristics have large, sometimes dominating, influences on the lifetime variability of a network. Among the factors investigated, geometrical disorders of the network were found to be essential to explain the large variability and highly skewed shape of the lifetime distribution. With increasing network size, the distribution asymptotically approaches a double-exponential form. The implication of this result is that, so-called "infant mortality," which is often predicted by the Weibull approximation of the lifetime distribution, may not exist for a large system.

The use of the multi-cumulant tensor analysis for the algorithmic optimisation of investment portfolios

NASA Astrophysics Data System (ADS)

Domino, Krzysztof

2017-02-01

The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd- 6'th cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent. Remark that the algorithm is based on cumulant tensors up to the 6'th order calculated for a multidimensional random variable, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.

Continuous-variable phase estimation with unitary and random linear disturbance

NASA Astrophysics Data System (ADS)

Delgado de Souza, Douglas; Genoni, Marco G.; Kim, M. S.

2014-10-01

We address the problem of continuous-variable quantum phase estimation in the presence of linear disturbance at the Hamiltonian level by means of Gaussian probe states. In particular we discuss both unitary and random disturbance by considering the parameter which characterizes the unwanted linear term present in the Hamiltonian as fixed (unitary disturbance) or random with a given probability distribution (random disturbance). We derive the optimal input Gaussian states at fixed energy, maximizing the quantum Fisher information over the squeezing angle and the squeezing energy fraction, and we discuss the scaling of the quantum Fisher information in terms of the output number of photons, nout. We observe that, in the case of unitary disturbance, the optimal state is a squeezed vacuum state and the quadratic scaling is conserved. As regards the random disturbance, we observe that the optimal squeezing fraction may not be equal to one and, for any nonzero value of the noise parameter, the quantum Fisher information scales linearly with the average number of photons. Finally, we discuss the performance of homodyne measurement by comparing the achievable precision with the ultimate limit imposed by the quantum Cramér-Rao bound.

Lindley frailty model for a class of compound Poisson processes

NASA Astrophysics Data System (ADS)

Kadilar, Gamze Özel; Ata, Nihal

2013-10-01

The Lindley distribution gain importance in survival analysis for the similarity of exponential distribution and allowance for the different shapes of hazard function. Frailty models provide an alternative to proportional hazards model where misspecified or omitted covariates are described by an unobservable random variable. Despite of the distribution of the frailty is generally assumed to be continuous, it is appropriate to consider discrete frailty distributions In some circumstances. In this paper, frailty models with discrete compound Poisson process for the Lindley distributed failure time are introduced. Survival functions are derived and maximum likelihood estimation procedures for the parameters are studied. Then, the fit of the models to the earthquake data set of Turkey are examined.

Multilevel covariance regression with correlated random effects in the mean and variance structure.

PubMed

Quintero, Adrian; Lesaffre, Emmanuel

2017-09-01

Multivariate regression methods generally assume a constant covariance matrix for the observations. In case a heteroscedastic model is needed, the parametric and nonparametric covariance regression approaches can be restrictive in the literature. We propose a multilevel regression model for the mean and covariance structure, including random intercepts in both components and allowing for correlation between them. The implied conditional covariance function can be different across clusters as a result of the random effect in the variance structure. In addition, allowing for correlation between the random intercepts in the mean and covariance makes the model convenient for skewedly distributed responses. Furthermore, it permits us to analyse directly the relation between the mean response level and the variability in each cluster. Parameter estimation is carried out via Gibbs sampling. We compare the performance of our model to other covariance modelling approaches in a simulation study. Finally, the proposed model is applied to the RN4CAST dataset to identify the variables that impact burnout of nurses in Belgium. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Empirical Histograms in Item Response Theory with Ordinal Data

ERIC Educational Resources Information Center

Woods, Carol M.

2007-01-01

The purpose of this research is to describe, test, and illustrate a new implementation of the empirical histogram (EH) method for ordinal items. The EH method involves the estimation of item response model parameters simultaneously with the approximation of the distribution of the random latent variable (theta) as a histogram. Software for the EH…

Accounting for range uncertainties in the optimization of intensity modulated proton therapy.

PubMed

Unkelbach, Jan; Chan, Timothy C Y; Bortfeld, Thomas

2007-05-21

Treatment plans optimized for intensity modulated proton therapy (IMPT) may be sensitive to range variations. The dose distribution may deteriorate substantially when the actual range of a pencil beam does not match the assumed range. We present two treatment planning concepts for IMPT which incorporate range uncertainties into the optimization. The first method is a probabilistic approach. The range of a pencil beam is assumed to be a random variable, which makes the delivered dose and the value of the objective function a random variable too. We then propose to optimize the expectation value of the objective function. The second approach is a robust formulation that applies methods developed in the field of robust linear programming. This approach optimizes the worst case dose distribution that may occur, assuming that the ranges of the pencil beams may vary within some interval. Both methods yield treatment plans that are considerably less sensitive to range variations compared to conventional treatment plans optimized without accounting for range uncertainties. In addition, both approaches--although conceptually different--yield very similar results on a qualitative level.

Meaner king uses biased bases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reimpell, Michael; Werner, Reinhard F.

2007-06-15

The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement made in one of several different orthonormal bases. Alice is allowed to prepare the state of the system and to do a final measurement, possibly including an entangled copy. However, Alice gains knowledge about which basis was measured only after she no longer has access to the quantum system or its copy. We give a necessary and sufficient condition on the bases, for Alice to have a strategy to solve this problem, without assuming that the bases aremore » mutually unbiased. The condition requires the existence of an overall joint probability distribution for random variables, whose marginal pair distributions are fixed as the transition probability matrices of the given bases. In particular, in the qubit case the problem is decided by Bell's original three variable inequality. In the standard setting of mutually unbiased bases, when they do exist, Alice can always succeed. However, for randomly chosen bases her success probability rapidly goes to zero with increasing dimension.« less

Continuous operation of four-state continuous-variable quantum key distribution system

NASA Astrophysics Data System (ADS)

Matsubara, Takuto; Ono, Motoharu; Oguri, Yusuke; Ichikawa, Tsubasa; Hirano, Takuya; Kasai, Kenta; Matsumoto, Ryutaroh; Tsurumaru, Toyohiro

2016-10-01

We report on the development of continuous-variable quantum key distribution (CV-QKD) system that are based on discrete quadrature amplitude modulation (QAM) and homodyne detection of coherent states of light. We use a pulsed light source whose wavelength is 1550 nm and repetition rate is 10 MHz. The CV-QKD system can continuously generate secret key which is secure against entangling cloner attack. Key generation rate is 50 kbps when the quantum channel is a 10 km optical fiber. The CV-QKD system we have developed utilizes the four-state and post-selection protocol [T. Hirano, et al., Phys. Rev. A 68, 042331 (2003).]; Alice randomly sends one of four states {|+/-α⟩,|+/-𝑖α⟩}, and Bob randomly performs x- or p- measurement by homodyne detection. A commercially available balanced receiver is used to realize shot-noise-limited pulsed homodyne detection. GPU cards are used to accelerate the software-based post-processing. We use a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification.

Meaner king uses biased bases

NASA Astrophysics Data System (ADS)

Reimpell, Michael; Werner, Reinhard F.

2007-06-01

The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement made in one of several different orthonormal bases. Alice is allowed to prepare the state of the system and to do a final measurement, possibly including an entangled copy. However, Alice gains knowledge about which basis was measured only after she no longer has access to the quantum system or its copy. We give a necessary and sufficient condition on the bases, for Alice to have a strategy to solve this problem, without assuming that the bases are mutually unbiased. The condition requires the existence of an overall joint probability distribution for random variables, whose marginal pair distributions are fixed as the transition probability matrices of the given bases. In particular, in the qubit case the problem is decided by Bell’s original three variable inequality. In the standard setting of mutually unbiased bases, when they do exist, Alice can always succeed. However, for randomly chosen bases her success probability rapidly goes to zero with increasing dimension.

Stochastic transfer of polarized radiation in finite cloudy atmospheric media with reflective boundaries

NASA Astrophysics Data System (ADS)

Sallah, M.

2014-03-01

The problem of monoenergetic radiative transfer in a finite planar stochastic atmospheric medium with polarized (vector) Rayleigh scattering is proposed. The solution is presented for an arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function is also used to average the solution in order to exclude the probable negative values of the optical variable. Pomraning-Eddington approximation is used, at first, to obtain the deterministic analytical solution for both the total intensity and the difference function used to describe the polarized radiation. The problem is treated with specular reflecting boundaries and angular-dependent externally incident flux upon the medium from one side and with no flux from the other side. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the average reflectivity and average transmissivity are obtained for both Gaussian and modified Gaussian probability density functions at the different degrees of polarization.

Bayesian Hierarchical Random Intercept Model Based on Three Parameter Gamma Distribution

NASA Astrophysics Data System (ADS)

Wirawati, Ika; Iriawan, Nur; Irhamah

2017-06-01

Hierarchical data structures are common throughout many areas of research. Beforehand, the existence of this type of data was less noticed in the analysis. The appropriate statistical analysis to handle this type of data is the hierarchical linear model (HLM). This article will focus only on random intercept model (RIM), as a subclass of HLM. This model assumes that the intercept of models in the lowest level are varied among those models, and their slopes are fixed. The differences of intercepts were suspected affected by some variables in the upper level. These intercepts, therefore, are regressed against those upper level variables as predictors. The purpose of this paper would demonstrate a proven work of the proposed two level RIM of the modeling on per capita household expenditure in Maluku Utara, which has five characteristics in the first level and three characteristics of districts/cities in the second level. The per capita household expenditure data in the first level were captured by the three parameters Gamma distribution. The model, therefore, would be more complex due to interaction of many parameters for representing the hierarchical structure and distribution pattern of the data. To simplify the estimation processes of parameters, the computational Bayesian method couple with Markov Chain Monte Carlo (MCMC) algorithm and its Gibbs Sampling are employed.

Effect of Fault Parameter Uncertainties on PSHA explored by Monte Carlo Simulations: A case study for southern Apennines, Italy

NASA Astrophysics Data System (ADS)

Akinci, A.; Pace, B.

2017-12-01

In this study, we discuss the seismic hazard variability of peak ground acceleration (PGA) at 475 years return period in the Southern Apennines of Italy. The uncertainty and parametric sensitivity are presented to quantify the impact of the several fault parameters on ground motion predictions for 10% exceedance in 50-year hazard. A time-independent PSHA model is constructed based on the long-term recurrence behavior of seismogenic faults adopting the characteristic earthquake model for those sources capable of rupturing the entire fault segment with a single maximum magnitude. The fault-based source model uses the dimensions and slip rates of mapped fault to develop magnitude-frequency estimates for characteristic earthquakes. Variability of the selected fault parameter is given with a truncated normal random variable distribution presented by standard deviation about a mean value. A Monte Carlo approach, based on the random balanced sampling by logic tree, is used in order to capture the uncertainty in seismic hazard calculations. For generating both uncertainty and sensitivity maps, we perform 200 simulations for each of the fault parameters. The results are synthesized both in frequency-magnitude distribution of modeled faults as well as the different maps: the overall uncertainty maps provide a confidence interval for the PGA values and the parameter uncertainty maps determine the sensitivity of hazard assessment to variability of every logic tree branch. These branches of logic tree, analyzed through the Monte Carlo approach, are maximum magnitudes, fault length, fault width, fault dip and slip rates. The overall variability of these parameters is determined by varying them simultaneously in the hazard calculations while the sensitivity of each parameter to overall variability is determined varying each of the fault parameters while fixing others. However, in this study we do not investigate the sensitivity of mean hazard results to the consideration of different GMPEs. Distribution of possible seismic hazard results is illustrated by 95% confidence factor map, which indicates the dispersion about mean value, and coefficient of variation map, which shows percent variability. The results of our study clearly illustrate the influence of active fault parameters to probabilistic seismic hazard maps.

Variable step random walks, self-similar distributions, and pricing of options (Invited Paper)

NASA Astrophysics Data System (ADS)

Gunaratne, Gemunu H.; McCauley, Joseph L.

2005-05-01

A new theory for pricing of options is presented. It is based on the assumption that successive movements depend on the value of the return. The solution to the Fokker-Planck equation is shown to be an asymmetric exponential distribution, similar to those observed in intra-day currency markets. The "volatility smile", used by traders to correct the Black-Scholes pricing is shown to be a heuristic mechanism to implement options pricing formulae derived from our theory.

Effect of signal jitter on the spectrum of rotor impulsive noise

NASA Technical Reports Server (NTRS)

Brooks, Thomas F.

1987-01-01

The effect of randomness or jitter of the acoustic waveform on the spectrum of rotor impulsive noise is studied because of its importance for data interpretation. An acoustic waveform train is modelled representing rotor impulsive noise. The amplitude, shape, and period between occurrences of individual pulses are allowed to be randomized assuming normal probability distributions. Results, in terms of the standard deviations of the variable quantities, are given for the autospectrum as well as special processed spectra designed to separate harmonic and broadband rotor noise components. Consideration is given to the effect of accuracy in triggering or keying to a rotor one per revolution signal. An example is given showing the resultant spectral smearing at the high frequencies due to the pulse signal period variability.

Effect of signal jitter on the spectrum of rotor impulsive noise

NASA Technical Reports Server (NTRS)

Brooks, Thomas F.

1988-01-01

The effect of randomness or jitter of the acoustic waveform on the spectrum of rotor impulsive noise is studied because of its importance for data interpretation. An acoustic waveform train is modeled representing rotor impulsive noise. The amplitude, shape, and period between occurrences of individual pulses are allowed to be randomized assuming normal probability distributions. Results, in terms of the standard deviations of the variable quantities, are given for the autospectrum as well as special processed spectra designed to separate harmonic and broadband rotor noise components. Consideration is given to the effect of accuracy in triggering or keying to a rotor one per revolution signal. An example is given showing the resultant spectral smearing at the high frequencies due to the pulse signal period variability.

A computer model of molecular arrangement in a n-paraffinic liquid

NASA Astrophysics Data System (ADS)

Vacatello, Michele; Avitabile, Gustavo; Corradini, Paolo; Tuzi, Angela

1980-07-01

A computer model of a bulk liquid polymer was built to investigate the problem of local order. The model is made of C30 n-alkane molecules; it is not a lattice model, but it allows for a continuous variability of torsion angles and interchain distances, subject to realistic intra- and intermolecular potentials. Experimental x-ray scattering curves and radial distribution functions are well reproduced. Calculated properties like end-to-end distances, distribution of torsion angles, radial distribution functions, and chain direction correlation parameters, all indicate a random coil conformation and no tendency to form bundles of parallel chains.

Maximum likelihood estimation for life distributions with competing failure modes

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1979-01-01

Systems which are placed on test at time zero, function for a period and die at some random time were studied. Failure may be due to one of several causes or modes. The parameters of the life distribution may depend upon the levels of various stress variables the item is subject to. Maximum likelihood estimation methods are discussed. Specific methods are reported for the smallest extreme-value distributions of life. Monte-Carlo results indicate the methods to be promising. Under appropriate conditions, the location parameters are nearly unbiased, the scale parameter is slight biased, and the asymptotic covariances are rapidly approached.

Two-Part and Related Regression Models for Longitudinal Data

PubMed Central

Farewell, V.T.; Long, D.L.; Tom, B.D.M.; Yiu, S.; Su, L.

2017-01-01

Statistical models that involve a two-part mixture distribution are applicable in a variety of situations. Frequently, the two parts are a model for the binary response variable and a model for the outcome variable that is conditioned on the binary response. Two common examples are zero-inflated or hurdle models for count data and two-part models for semicontinuous data. Recently, there has been particular interest in the use of these models for the analysis of repeated measures of an outcome variable over time. The aim of this review is to consider motivations for the use of such models in this context and to highlight the central issues that arise with their use. We examine two-part models for semicontinuous and zero-heavy count data, and we also consider models for count data with a two-part random effects distribution. PMID:28890906

Testing Pairwise Association between Spatially Autocorrelated Variables: A New Approach Using Surrogate Lattice Data

PubMed Central

Deblauwe, Vincent; Kennel, Pol; Couteron, Pierre

2012-01-01

Background Independence between observations is a standard prerequisite of traditional statistical tests of association. This condition is, however, violated when autocorrelation is present within the data. In the case of variables that are regularly sampled in space (i.e. lattice data or images), such as those provided by remote-sensing or geographical databases, this problem is particularly acute. Because analytic derivation of the null probability distribution of the test statistic (e.g. Pearson's r) is not always possible when autocorrelation is present, we propose instead the use of a Monte Carlo simulation with surrogate data. Methodology/Principal Findings The null hypothesis that two observed mapped variables are the result of independent pattern generating processes is tested here by generating sets of random image data while preserving the autocorrelation function of the original images. Surrogates are generated by matching the dual-tree complex wavelet spectra (and hence the autocorrelation functions) of white noise images with the spectra of the original images. The generated images can then be used to build the probability distribution function of any statistic of association under the null hypothesis. We demonstrate the validity of a statistical test of association based on these surrogates with both actual and synthetic data and compare it with a corrected parametric test and three existing methods that generate surrogates (randomization, random rotations and shifts, and iterative amplitude adjusted Fourier transform). Type I error control was excellent, even with strong and long-range autocorrelation, which is not the case for alternative methods. Conclusions/Significance The wavelet-based surrogates are particularly appropriate in cases where autocorrelation appears at all scales or is direction-dependent (anisotropy). We explore the potential of the method for association tests involving a lattice of binary data and discuss its potential for validation of species distribution models. An implementation of the method in Java for the generation of wavelet-based surrogates is available online as supporting material. PMID:23144961

Azimuthal Dependence of the Ground Motion Variability from Scenario Modeling of the 2014 Mw6.0 South Napa, California, Earthquake Using an Advanced Kinematic Source Model

NASA Astrophysics Data System (ADS)

Gallovič, F.

2017-09-01

Strong ground motion simulations require physically plausible earthquake source model. Here, I present the application of such a kinematic model introduced originally by Ruiz et al. (Geophys J Int 186:226-244, 2011). The model is constructed to inherently provide synthetics with the desired omega-squared spectral decay in the full frequency range. The source is composed of randomly distributed overlapping subsources with fractal number-size distribution. The position of the subsources can be constrained by prior knowledge of major asperities (stemming, e.g., from slip inversions), or can be completely random. From earthquake physics point of view, the model includes positive correlation between slip and rise time as found in dynamic source simulations. Rupture velocity and rise time follows local S-wave velocity profile, so that the rupture slows down and rise times increase close to the surface, avoiding unrealistically strong ground motions. Rupture velocity can also have random variations, which result in irregular rupture front while satisfying the causality principle. This advanced kinematic broadband source model is freely available and can be easily incorporated into any numerical wave propagation code, as the source is described by spatially distributed slip rate functions, not requiring any stochastic Green's functions. The source model has been previously validated against the observed data due to the very shallow unilateral 2014 Mw6 South Napa, California, earthquake; the model reproduces well the observed data including the near-fault directivity (Seism Res Lett 87:2-14, 2016). The performance of the source model is shown here on the scenario simulations for the same event. In particular, synthetics are compared with existing ground motion prediction equations (GMPEs), emphasizing the azimuthal dependence of the between-event ground motion variability. I propose a simple model reproducing the azimuthal variations of the between-event ground motion variability, providing an insight into possible refinement of GMPEs' functional forms.

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

A random forest approach for predicting the presence of Echinococcus multilocularis intermediate host Ochotona spp. presence in relation to landscape characteristics in western China

PubMed Central

Marston, Christopher G.; Danson, F. Mark; Armitage, Richard P.; Giraudoux, Patrick; Pleydell, David R.J.; Wang, Qian; Qui, Jiamin; Craig, Philip S.

2014-01-01

Understanding distribution patterns of hosts implicated in the transmission of zoonotic disease remains a key goal of parasitology. Here, random forests are employed to model spatial patterns of the presence of the plateau pika (Ochotona spp.) small mammal intermediate host for the parasitic tapeworm Echinococcus multilocularis which is responsible for a significant burden of human zoonoses in western China. Landsat ETM+ satellite imagery and digital elevation model data were utilized to generate quantified measures of environmental characteristics across a study area in Sichuan Province, China. Land cover maps were generated identifying the distribution of specific land cover types, with landscape metrics employed to describe the spatial organisation of land cover patches. Random forests were used to model spatial patterns of Ochotona spp. presence, enabling the relative importance of the environmental characteristics in relation to Ochotona spp. presence to be ranked. An index of habitat aggregation was identified as the most important variable in influencing Ochotona spp. presence, with area of degraded grassland the most important land cover class variable. 71% of the variance in Ochotona spp. presence was explained, with a 90.98% accuracy rate as determined by ‘out-of-bag’ error assessment. Identification of the environmental characteristics influencing Ochotona spp. presence enables us to better understand distribution patterns of hosts implicated in the transmission of Em. The predictive mapping of this Em host enables the identification of human populations at increased risk of infection, enabling preventative strategies to be adopted. PMID:25386042

A Random Forest approach to predict the spatial distribution of sediment pollution in an estuarine system

PubMed Central

Kreakie, Betty J.; Cantwell, Mark G.; Nacci, Diane

2017-01-01

Modeling the magnitude and distribution of sediment-bound pollutants in estuaries is often limited by incomplete knowledge of the site and inadequate sample density. To address these modeling limitations, a decision-support tool framework was conceived that predicts sediment contamination from the sub-estuary to broader estuary extent. For this study, a Random Forest (RF) model was implemented to predict the distribution of a model contaminant, triclosan (5-chloro-2-(2,4-dichlorophenoxy)phenol) (TCS), in Narragansett Bay, Rhode Island, USA. TCS is an unregulated contaminant used in many personal care products. The RF explanatory variables were associated with TCS transport and fate (proxies) and direct and indirect environmental entry. The continuous RF TCS concentration predictions were discretized into three levels of contamination (low, medium, and high) for three different quantile thresholds. The RF model explained 63% of the variance with a minimum number of variables. Total organic carbon (TOC) (transport and fate proxy) was a strong predictor of TCS contamination causing a mean squared error increase of 59% when compared to permutations of randomized values of TOC. Additionally, combined sewer overflow discharge (environmental entry) and sand (transport and fate proxy) were strong predictors. The discretization models identified a TCS area of greatest concern in the northern reach of Narragansett Bay (Providence River sub-estuary), which was validated with independent test samples. This decision-support tool performed well at the sub-estuary extent and provided the means to identify areas of concern and prioritize bay-wide sampling. PMID:28738089

Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

NASA Astrophysics Data System (ADS)

Feres, Renato; Ng, Jasmine; Zhang, Hong-Kun

2013-10-01

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P h , depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that ( P h - I)/ h converges for small h to a second order elliptic differential operator on compactly supported functions and that the Markov chain process associated to P h converges to a diffusion with infinitesimal generator . Both P h and are self-adjoint (densely) defined on the space of square-integrable functions over the (lower) half-space in , where η is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.

The Central Limit Theorem for Supercritical Oriented Percolation in Two Dimensions

NASA Astrophysics Data System (ADS)

Tzioufas, Achillefs

2018-04-01

We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the standard normal law. This resolves a longstanding open problem pointed out to in several instances in the literature. The result applies also to the continuous-time analog of the process, viz. the basic one-dimensional contact process. We also derive general random-indices central limit theorems for associated random variables as byproducts of our proof.

The Central Limit Theorem for Supercritical Oriented Percolation in Two Dimensions

NASA Astrophysics Data System (ADS)

Tzioufas, Achillefs

2018-06-01

We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the standard normal law. This resolves a longstanding open problem pointed out to in several instances in the literature. The result applies also to the continuous-time analog of the process, viz. the basic one-dimensional contact process. We also derive general random-indices central limit theorems for associated random variables as byproducts of our proof.

Nematode distributions as spatial null models for macroinvertebrate species richness across environmental gradients: A case from mountain lakes.

PubMed

de Mendoza, Guillermo; Traunspurger, Walter; Palomo, Alejandro; Catalan, Jordi

2017-05-01

Nematode species are widely tolerant of environmental conditions and disperse passively. Therefore, the species richness distribution in this group might largely depend on the topological distribution of the habitats and main aerial and aquatic dispersal pathways connecting them. If so, the nematode species richness distributions may serve as null models for evaluating that of other groups more affected by environmental gradients. We investigated this hypothesis in lakes across an altitudinal gradient in the Pyrenees. We compared the altitudinal distribution, environmental tolerance, and species richness, of nematodes with that of three other invertebrate groups collected during the same sampling: oligochaetes, chironomids, and nonchironomid insects. We tested the altitudinal bias in distributions with t -tests and the significance of narrow-ranging altitudinal distributions with randomizations. We compared results between groups with Fisher's exact tests. We then explored the influence of environmental factors on species assemblages in all groups with redundancy analysis (RDA), using 28 environmental variables. And, finally, we analyzed species richness patterns across altitude with simple linear and quadratic regressions. Nematode species were rarely biased from random distributions (5% of species) in contrast with other groups (35%, 47%, and 50%, respectively). The altitudinal bias most often shifted toward low altitudes (85% of biased species). Nematodes showed a lower portion of narrow-ranging species than any other group, and differed significantly from nonchironomid insects (10% and 43%, respectively). Environmental variables barely explained nematode assemblages (RDA adjusted R 2  = 0.02), in contrast with other groups (0.13, 0.19 and 0.24). Despite these substantial differences in the response to environmental factors, species richness across altitude was unimodal, peaking at mid elevations, in all groups. This similarity indicates that the spatial distribution of lakes across altitude is a primary driver of invertebrate richness. Provided that nematodes are ubiquitous, their distribution offers potential null models to investigate species richness across environmental gradients in other ecosystem types and biogeographic regions.

Resource Utilization and Environmental and Spatio-Temporal Overlap of a Hilltopping Lycaenid Butterfly Community in the Colombian Andes

PubMed Central

Prieto, Carlos; Dahners, Hans W.

2009-01-01

Coexistence by a great number of species could reflect niche segregation at several resource axes. Differences in the use of a hilltop as mating site for a Eumaeini (Lycaenidae) community were measured to test whether niche segregation exists within this group. Specimens were collected throughout 21 samplings between July-October of 2004 and July-October of 2005. Two environmental variables and three temporal-spacial variables were analyzed utilizing null models with three randomization algorithms. Significant differences were found among the species with respect to utilization of vertical space, horizontal space, temporary distribution and environmental temperature. The species did not show significant differences with respect to light intensity. For all samplings, the niche overlap observed in the two environmental variables were higher or significantly higher than expected by chance, suggesting that niche segregation does not exist due to competition within these variables. Similar results were observed for temporal distribution. Some evidence of niche segregation was found in vertical space and horizontal space variables where some samples presented lower overlap than expected by chance. The results pointed out that community's assemblage could be mainly shaped in two ways. The first is that species with determined habitat requirements fit into unoccupied niche spaces. The second is by niche segregation in the vertical space distribution variable. PMID:19613456

A systematic examination of a random sampling strategy for source apportionment calculations.

PubMed

Andersson, August

2011-12-15

Estimating the relative contributions from multiple potential sources of a specific component in a mixed environmental matrix is a general challenge in diverse fields such as atmospheric, environmental and earth sciences. Perhaps the most common strategy for tackling such problems is by setting up a system of linear equations for the fractional influence of different sources. Even though an algebraic solution of this approach is possible for the common situation with N+1 sources and N source markers, such methodology introduces a bias, since it is implicitly assumed that the calculated fractions and the corresponding uncertainties are independent of the variability of the source distributions. Here, a random sampling (RS) strategy for accounting for such statistical bias is examined by investigating rationally designed synthetic data sets. This random sampling methodology is found to be robust and accurate with respect to reproducibility and predictability. This method is also compared to a numerical integration solution for a two-source situation where source variability also is included. A general observation from this examination is that the variability of the source profiles not only affects the calculated precision but also the mean/median source contributions. Copyright © 2011 Elsevier B.V. All rights reserved.

Quantum key distribution using basis encoding of Gaussian-modulated coherent states

NASA Astrophysics Data System (ADS)

Huang, Peng; Huang, Jingzheng; Zhang, Zheshen; Zeng, Guihua

2018-04-01

The continuous-variable quantum key distribution (CVQKD) has been demonstrated to be available in practical secure quantum cryptography. However, its performance is restricted strongly by the channel excess noise and the reconciliation efficiency. In this paper, we present a quantum key distribution (QKD) protocol by encoding the secret keys on the random choices of two measurement bases: the conjugate quadratures X and P . The employed encoding method can dramatically weaken the effects of channel excess noise and reconciliation efficiency on the performance of the QKD protocol. Subsequently, the proposed scheme exhibits the capability to tolerate much higher excess noise and enables us to reach a much longer secure transmission distance even at lower reconciliation efficiency. The proposal can work alternatively to strengthen significantly the performance of the known Gaussian-modulated CVQKD protocol and serve as a multiplier for practical secure quantum cryptography with continuous variables.

Exact extreme-value statistics at mixed-order transitions.

PubMed

Bar, Amir; Majumdar, Satya N; Schehr, Grégory; Mukamel, David

2016-05-01

We study extreme-value statistics for spatially extended models exhibiting mixed-order phase transitions (MOT). These are phase transitions that exhibit features common to both first-order (discontinuity of the order parameter) and second-order (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising model, which is a prototypical model exhibiting MOT, and study analytically the extreme-value statistics of the domain lengths The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size L. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length l_{max} converges, in the large L limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of l_{max} are governed by novel distributions, which we compute exactly. Our main analytical results are verified by numerical simulations.

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

Error Distribution Evaluation of the Third Vanishing Point Based on Random Statistical Simulation

NASA Astrophysics Data System (ADS)

Li, C.

2012-07-01

POS, integrated by GPS / INS (Inertial Navigation Systems), has allowed rapid and accurate determination of position and attitude of remote sensing equipment for MMS (Mobile Mapping Systems). However, not only does INS have system error, but also it is very expensive. Therefore, in this paper error distributions of vanishing points are studied and tested in order to substitute INS for MMS in some special land-based scene, such as ground façade where usually only two vanishing points can be detected. Thus, the traditional calibration approach based on three orthogonal vanishing points is being challenged. In this article, firstly, the line clusters, which parallel to each others in object space and correspond to the vanishing points, are detected based on RANSAC (Random Sample Consensus) and parallelism geometric constraint. Secondly, condition adjustment with parameters is utilized to estimate nonlinear error equations of two vanishing points (VX, VY). How to set initial weights for the adjustment solution of single image vanishing points is presented. Solving vanishing points and estimating their error distributions base on iteration method with variable weights, co-factor matrix and error ellipse theory. Thirdly, under the condition of known error ellipses of two vanishing points (VX, VY) and on the basis of the triangle geometric relationship of three vanishing points, the error distribution of the third vanishing point (VZ) is calculated and evaluated by random statistical simulation with ignoring camera distortion. Moreover, Monte Carlo methods utilized for random statistical estimation are presented. Finally, experimental results of vanishing points coordinate and their error distributions are shown and analyzed.

Study on probability distribution of prices in electricity market: A case study of zhejiang province, china

NASA Astrophysics Data System (ADS)

Zhou, H.; Chen, B.; Han, Z. X.; Zhang, F. Q.

2009-05-01

The study on probability density function and distribution function of electricity prices contributes to the power suppliers and purchasers to estimate their own management accurately, and helps the regulator monitor the periods deviating from normal distribution. Based on the assumption of normal distribution load and non-linear characteristic of the aggregate supply curve, this paper has derived the distribution of electricity prices as the function of random variable of load. The conclusion has been validated with the electricity price data of Zhejiang market. The results show that electricity prices obey normal distribution approximately only when supply-demand relationship is loose, whereas the prices deviate from normal distribution and present strong right-skewness characteristic. Finally, the real electricity markets also display the narrow-peak characteristic when undersupply occurs.

Multivariate hydrological frequency analysis for extreme events using Archimedean copula. Case study: Lower Tunjuelo River basin (Colombia)

NASA Astrophysics Data System (ADS)

Gómez, Wilmar

2017-04-01

By analyzing the spatial and temporal variability of extreme precipitation events we can prevent or reduce the threat and risk. Many water resources projects require joint probability distributions of random variables such as precipitation intensity and duration, which can not be independent with each other. The problem of defining a probability model for observations of several dependent variables is greatly simplified by the joint distribution in terms of their marginal by taking copulas. This document presents a general framework set frequency analysis bivariate and multivariate using Archimedean copulas for extreme events of hydroclimatological nature such as severe storms. This analysis was conducted in the lower Tunjuelo River basin in Colombia for precipitation events. The results obtained show that for a joint study of the intensity-duration-frequency, IDF curves can be obtained through copulas and thus establish more accurate and reliable information from design storms and associated risks. It shows how the use of copulas greatly simplifies the study of multivariate distributions that introduce the concept of joint return period used to represent the needs of hydrological designs properly in frequency analysis.

The effect of signal variability on the histograms of anthropomorphic channel outputs: factors resulting in non-normally distributed data

NASA Astrophysics Data System (ADS)

Elshahaby, Fatma E. A.; Ghaly, Michael; Jha, Abhinav K.; Frey, Eric C.

2015-03-01

Model Observers are widely used in medical imaging for the optimization and evaluation of instrumentation, acquisition parameters and image reconstruction and processing methods. The channelized Hotelling observer (CHO) is a commonly used model observer in nuclear medicine and has seen increasing use in other modalities. An anthropmorphic CHO consists of a set of channels that model some aspects of the human visual system and the Hotelling Observer, which is the optimal linear discriminant. The optimality of the CHO is based on the assumption that the channel outputs for data with and without the signal present have a multivariate normal distribution with equal class covariance matrices. The channel outputs result from the dot product of channel templates with input images and are thus the sum of a large number of random variables. The central limit theorem is thus often used to justify the assumption that the channel outputs are normally distributed. In this work, we aim to examine this assumption for realistically simulated nuclear medicine images when various types of signal variability are present.

A general theoretical framework for interpreting patient-reported outcomes estimated from ordinally scaled item responses.

PubMed

Massof, Robert W

2014-10-01

A simple theoretical framework explains patient responses to items in rating scale questionnaires. Fixed latent variables position each patient and each item on the same linear scale. Item responses are governed by a set of fixed category thresholds, one for each ordinal response category. A patient's item responses are magnitude estimates of the difference between the patient variable and the patient's estimate of the item variable, relative to his/her personally defined response category thresholds. Differences between patients in their personal estimates of the item variable and in their personal choices of category thresholds are represented by random variables added to the corresponding fixed variables. Effects of intervention correspond to changes in the patient variable, the patient's response bias, and/or latent item variables for a subset of items. Intervention effects on patients' item responses were simulated by assuming the random variables are normally distributed with a constant scalar covariance matrix. Rasch analysis was used to estimate latent variables from the simulated responses. The simulations demonstrate that changes in the patient variable and changes in response bias produce indistinguishable effects on item responses and manifest as changes only in the estimated patient variable. Changes in a subset of item variables manifest as intervention-specific differential item functioning and as changes in the estimated person variable that equals the average of changes in the item variables. Simulations demonstrate that intervention-specific differential item functioning produces inefficiencies and inaccuracies in computer adaptive testing. © The Author(s) 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

Aggregate and Individual Replication Probability within an Explicit Model of the Research Process

ERIC Educational Resources Information Center

Miller, Jeff; Schwarz, Wolf

2011-01-01

We study a model of the research process in which the true effect size, the replication jitter due to changes in experimental procedure, and the statistical error of effect size measurement are all normally distributed random variables. Within this model, we analyze the probability of successfully replicating an initial experimental result by…

Pedagogical Simulation of Sampling Distributions and the Central Limit Theorem

ERIC Educational Resources Information Center

Hagtvedt, Reidar; Jones, Gregory Todd; Jones, Kari

2007-01-01

Students often find the fact that a sample statistic is a random variable very hard to grasp. Even more mysterious is why a sample mean should become ever more Normal as the sample size increases. This simulation tool is meant to illustrate the process, thereby giving students some intuitive grasp of the relationship between a parent population…

Exact Markov chains versus diffusion theory for haploid random mating.

PubMed

Tyvand, Peder A; Thorvaldsen, Steinar

2010-05-01

Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck. 2010 Elsevier Inc. All rights reserved.

Evaluation of Gas Phase Dispersion in Flotation under Predetermined Hydrodynamic Conditions

NASA Astrophysics Data System (ADS)

Młynarczykowska, Anna; Oleksik, Konrad; Tupek-Murowany, Klaudia

2018-03-01

Results of various investigations shows the relationship between the flotation parameters and gas distribution in a flotation cell. The size of gas bubbles is a random variable with a specific distribution. The analysis of this distribution is useful to make mathematical description of the flotation process. The flotation process depends on many variable factors. These are mainly occurrences like collision of single particle with gas bubble, adhesion of particle to the surface of bubble and detachment process. These factors are characterized by randomness. Because of that it is only possible to talk about the probability of occurence of one of these events which directly affects the speed of the process, thus a constant speed of flotation process. Probability of the bubble-particle collision in the flotation chamber with mechanical pulp agitation depends on the surface tension of the solution, air consumption, degree of pul aeration, energy dissipation and average feed particle size. Appropriate identification and description of the parameters of the dispersion of gas bubbles helps to complete the analysis of the flotation process in a specific physicochemical conditions and hydrodynamic for any raw material. The article presents the results of measurements and analysis of the gas phase dispersion by the size distribution of air bubbles in a flotation chamber under fixed hydrodynamic conditions. The tests were carried out in the Laboratory of Instrumental Methods in Department of Environmental Engineering and Mineral Processing, Faculty of Mining and Geoengineerin, AGH Univeristy of Science and Technology in Krakow.

Meta-analysis of prediction model performance across multiple studies: Which scale helps ensure between-study normality for the C-statistic and calibration measures?

PubMed

Snell, Kym Ie; Ensor, Joie; Debray, Thomas Pa; Moons, Karel Gm; Riley, Richard D

2017-01-01

If individual participant data are available from multiple studies or clusters, then a prediction model can be externally validated multiple times. This allows the model's discrimination and calibration performance to be examined across different settings. Random-effects meta-analysis can then be used to quantify overall (average) performance and heterogeneity in performance. This typically assumes a normal distribution of 'true' performance across studies. We conducted a simulation study to examine this normality assumption for various performance measures relating to a logistic regression prediction model. We simulated data across multiple studies with varying degrees of variability in baseline risk or predictor effects and then evaluated the shape of the between-study distribution in the C-statistic, calibration slope, calibration-in-the-large, and E/O statistic, and possible transformations thereof. We found that a normal between-study distribution was usually reasonable for the calibration slope and calibration-in-the-large; however, the distributions of the C-statistic and E/O were often skewed across studies, particularly in settings with large variability in the predictor effects. Normality was vastly improved when using the logit transformation for the C-statistic and the log transformation for E/O, and therefore we recommend these scales to be used for meta-analysis. An illustrated example is given using a random-effects meta-analysis of the performance of QRISK2 across 25 general practices.

Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms With Directed Gossip Communication

NASA Astrophysics Data System (ADS)

Jakovetic, Dusan; Xavier, João; Moura, José M. F.

2011-08-01

We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.

Testing statistical self-similarity in the topology of river networks

USGS Publications Warehouse

Troutman, Brent M.; Mantilla, Ricardo; Gupta, Vijay K.

2010-01-01

Recent work has demonstrated that the topological properties of real river networks deviate significantly from predictions of Shreve's random model. At the same time the property of mean self-similarity postulated by Tokunaga's model is well supported by data. Recently, a new class of network model called random self-similar networks (RSN) that combines self-similarity and randomness has been introduced to replicate important topological features observed in real river networks. We investigate if the hypothesis of statistical self-similarity in the RSN model is supported by data on a set of 30 basins located across the continental United States that encompass a wide range of hydroclimatic variability. We demonstrate that the generators of the RSN model obey a geometric distribution, and self-similarity holds in a statistical sense in 26 of these 30 basins. The parameters describing the distribution of interior and exterior generators are tested to be statistically different and the difference is shown to produce the well-known Hack's law. The inter-basin variability of RSN parameters is found to be statistically significant. We also test generator dependence on two climatic indices, mean annual precipitation and radiative index of dryness. Some indication of climatic influence on the generators is detected, but this influence is not statistically significant with the sample size available. Finally, two key applications of the RSN model to hydrology and geomorphology are briefly discussed.

Enhancing Multimedia Imbalanced Concept Detection Using VIMP in Random Forests.

PubMed

Sadiq, Saad; Yan, Yilin; Shyu, Mei-Ling; Chen, Shu-Ching; Ishwaran, Hemant

2016-07-01

Recent developments in social media and cloud storage lead to an exponential growth in the amount of multimedia data, which increases the complexity of managing, storing, indexing, and retrieving information from such big data. Many current content-based concept detection approaches lag from successfully bridging the semantic gap. To solve this problem, a multi-stage random forest framework is proposed to generate predictor variables based on multivariate regressions using variable importance (VIMP). By fine tuning the forests and significantly reducing the predictor variables, the concept detection scores are evaluated when the concept of interest is rare and imbalanced, i.e., having little collaboration with other high level concepts. Using classical multivariate statistics, estimating the value of one coordinate using other coordinates standardizes the covariates and it depends upon the variance of the correlations instead of the mean. Thus, conditional dependence on the data being normally distributed is eliminated. Experimental results demonstrate that the proposed framework outperforms those approaches in the comparison in terms of the Mean Average Precision (MAP) values.

Statistical analysis of the 70 meter antenna surface distortions

NASA Technical Reports Server (NTRS)

Kiedron, K.; Chian, C. T.; Chuang, K. L.

1987-01-01

Statistical analysis of surface distortions of the 70 meter NASA/JPL antenna, located at Goldstone, was performed. The purpose of this analysis is to verify whether deviations due to gravity loading can be treated as quasi-random variables with normal distribution. Histograms of the RF pathlength error distribution for several antenna elevation positions were generated. The results indicate that the deviations from the ideal antenna surface are not normally distributed. The observed density distribution for all antenna elevation angles is taller and narrower than the normal density, which results in large positive values of kurtosis and a significant amount of skewness. The skewness of the distribution changes from positive to negative as the antenna elevation changes from zenith to horizon.

Computing approximate random Delta v magnitude probability densities. [for spacecraft trajectory correction

NASA Technical Reports Server (NTRS)

Chadwick, C.

1984-01-01

This paper describes the development and use of an algorithm to compute approximate statistics of the magnitude of a single random trajectory correction maneuver (TCM) Delta v vector. The TCM Delta v vector is modeled as a three component Cartesian vector each of whose components is a random variable having a normal (Gaussian) distribution with zero mean and possibly unequal standard deviations. The algorithm uses these standard deviations as input to produce approximations to (1) the mean and standard deviation of the magnitude of Delta v, (2) points of the probability density function of the magnitude of Delta v, and (3) points of the cumulative and inverse cumulative distribution functions of Delta v. The approximates are based on Monte Carlo techniques developed in a previous paper by the author and extended here. The algorithm described is expected to be useful in both pre-flight planning and in-flight analysis of maneuver propellant requirements for space missions.

Data Applicability of Heritage and New Hardware For Launch Vehicle Reliability Models

NASA Technical Reports Server (NTRS)

Al Hassan, Mohammad; Novack, Steven

2015-01-01

Bayesian reliability requires the development of a prior distribution to represent degree of belief about the value of a parameter (such as a component's failure rate) before system specific data become available from testing or operations. Generic failure data are often provided in reliability databases as point estimates (mean or median). A component's failure rate is considered a random variable where all possible values are represented by a probability distribution. The applicability of the generic data source is a significant source of uncertainty that affects the spread of the distribution. This presentation discusses heuristic guidelines for quantifying uncertainty due to generic data applicability when developing prior distributions mainly from reliability predictions.

Uncertainty in Random Forests: What does it mean in a spatial context?

NASA Astrophysics Data System (ADS)

Klump, Jens; Fouedjio, Francky

2017-04-01

Geochemical surveys are an important part of exploration for mineral resources and in environmental studies. The samples and chemical analyses are often laborious and difficult to obtain and therefore come at a high cost. As a consequence, these surveys are characterised by datasets with large numbers of variables but relatively few data points when compared to conventional big data problems. With more remote sensing platforms and sensor networks being deployed, large volumes of auxiliary data of the surveyed areas are becoming available. The use of these auxiliary data has the potential to improve the prediction of chemical element concentrations over the whole study area. Kriging is a well established geostatistical method for the prediction of spatial data but requires significant pre-processing and makes some basic assumptions about the underlying distribution of the data. Some machine learning algorithms, on the other hand, may require less data pre-processing and are non-parametric. In this study we used a dataset provided by Kirkwood et al. [1] to explore the potential use of Random Forest in geochemical mapping. We chose Random Forest because it is a well understood machine learning method and has the advantage that it provides us with a measure of uncertainty. By comparing Random Forest to Kriging we found that both methods produced comparable maps of estimated values for our variables of interest. Kriging outperformed Random Forest for variables of interest with relatively strong spatial correlation. The measure of uncertainty provided by Random Forest seems to be quite different to the measure of uncertainty provided by Kriging. In particular, the lack of spatial context can give misleading results in areas without ground truth data. In conclusion, our preliminary results show that the model driven approach in geostatistics gives us more reliable estimates for our target variables than Random Forest for variables with relatively strong spatial correlation. However, in cases of weak spatial correlation Random Forest, as a nonparametric method, may give the better results once we have a better understanding of the meaning of its uncertainty measures in a spatial context. References [1] Kirkwood, C., M. Cave, D. Beamish, S. Grebby, and A. Ferreira (2016), A machine learning approach to geochemical mapping, Journal of Geochemical Exploration, 163, 28-40, doi:10.1016/j.gexplo.2016.05.003.

Performance of Distributed CFAR Processors in Pearson Distributed Clutter

NASA Astrophysics Data System (ADS)

Messali, Zoubeida; Soltani, Faouzi

2006-12-01

This paper deals with the distributed constant false alarm rate (CFAR) radar detection of targets embedded in heavy-tailed Pearson distributed clutter. In particular, we extend the results obtained for the cell averaging (CA), order statistics (OS), and censored mean level CMLD CFAR processors operating in positive alpha-stable (P&S) random variables to more general situations, specifically to the presence of interfering targets and distributed CFAR detectors. The receiver operating characteristics of the greatest of (GO) and the smallest of (SO) CFAR processors are also determined. The performance characteristics of distributed systems are presented and compared in both homogeneous and in presence of interfering targets. We demonstrate, via simulation results, that the distributed systems when the clutter is modelled as positive alpha-stable distribution offer robustness properties against multiple target situations especially when using the "OR" fusion rule.

Generating variable and random schedules of reinforcement using Microsoft Excel macros.

PubMed

Bancroft, Stacie L; Bourret, Jason C

2008-01-01

Variable reinforcement schedules are used to arrange the availability of reinforcement following varying response ratios or intervals of time. Random reinforcement schedules are subtypes of variable reinforcement schedules that can be used to arrange the availability of reinforcement at a constant probability across number of responses or time. Generating schedule values for variable and random reinforcement schedules can be difficult. The present article describes the steps necessary to write macros in Microsoft Excel that will generate variable-ratio, variable-interval, variable-time, random-ratio, random-interval, and random-time reinforcement schedule values.

Stochastic Seismic Response of an Algiers Site with Random Depth to Bedrock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Badaoui, M.; Mebarki, A.; Berrah, M. K.

2010-05-21

Among the important effects of the Boumerdes earthquake (Algeria, May 21{sup st} 2003) was that, within the same zone, the destructions in certain parts were more important than in others. This phenomenon is due to site effects which alter the characteristics of seismic motions and cause concentration of damage during earthquakes. Local site effects such as thickness and mechanical properties of soil layers have important effects on the surface ground motions.This paper deals with the effect of the randomness aspect of the depth to bedrock (soil layers heights) which is assumed to be a random variable with lognormal distribution. Thismore » distribution is suitable for strictly non-negative random variables with large values of the coefficient of variation. In this case, Monte Carlo simulations are combined with the stiffness matrix method, used herein as a deterministic method, for evaluating the effect of the depth to bedrock uncertainty on the seismic response of a multilayered soil. This study considers a P and SV wave propagation pattern using input accelerations collected at Keddara station, located at 20 km from the epicenter, as it is located directly on the bedrock.A parametric study is conducted do derive the stochastic behavior of the peak ground acceleration and its response spectrum, the transfer function and the amplification factors. It is found that the soil height heterogeneity causes a widening of the frequency content and an increase in the fundamental frequency of the soil profile, indicating that the resonance phenomenon concerns a larger number of structures.« less

Design and implementation of a dental caries prevention trial in remote Canadian Aboriginal communities.

PubMed

Harrison, Rosamund; Veronneau, Jacques; Leroux, Brian

2010-05-13

The goal of this cluster randomized trial is to test the effectiveness of a counseling approach, Motivational Interviewing, to control dental caries in young Aboriginal children. Motivational Interviewing, a client-centred, directive counseling style, has not yet been evaluated as an approach for promotion of behaviour change in indigenous communities in remote settings. Aboriginal women were hired from the 9 communities to recruit expectant and new mothers to the trial, administer questionnaires and deliver the counseling to mothers in the test communities. The goal is for mothers to receive the intervention during pregnancy and at their child's immunization visits. Data on children's dental health status and family dental health practices will be collected when children are 30-months of age. The communities were randomly allocated to test or control group by a random "draw" over community radio. Sample size and power were determined based on an anticipated 20% reduction in caries prevalence. Randomization checks were conducted between groups. In the 5 test and 4 control communities, 272 of the original target sample size of 309 mothers have been recruited over a two-and-a-half year period. A power calculation using the actual attained sample size showed power to be 79% to detect a treatment effect. If an attrition fraction of 4% per year is maintained, power will remain at 80%. Power will still be > 90% to detect a 25% reduction in caries prevalence. The distribution of most baseline variables was similar for the two randomized groups of mothers. However, despite the random assignment of communities to treatment conditions, group differences exist for stage of pregnancy and prior tooth extractions in the family. Because of the group imbalances on certain variables, control of baseline variables will be done in the analyses of treatment effects. This paper explains the challenges of conducting randomized trials in remote settings, the importance of thorough community collaboration, and also illustrates the likelihood that some baseline variables that may be clinically important will be unevenly split in group-randomized trials when the number of groups is small. This trial is registered as ISRCTN41467632.

Design and implementation of a dental caries prevention trial in remote Canadian Aboriginal communities

PubMed Central

2010-01-01

Background The goal of this cluster randomized trial is to test the effectiveness of a counseling approach, Motivational Interviewing, to control dental caries in young Aboriginal children. Motivational Interviewing, a client-centred, directive counseling style, has not yet been evaluated as an approach for promotion of behaviour change in indigenous communities in remote settings. Methods/design Aboriginal women were hired from the 9 communities to recruit expectant and new mothers to the trial, administer questionnaires and deliver the counseling to mothers in the test communities. The goal is for mothers to receive the intervention during pregnancy and at their child's immunization visits. Data on children's dental health status and family dental health practices will be collected when children are 30-months of age. The communities were randomly allocated to test or control group by a random "draw" over community radio. Sample size and power were determined based on an anticipated 20% reduction in caries prevalence. Randomization checks were conducted between groups. Discussion In the 5 test and 4 control communities, 272 of the original target sample size of 309 mothers have been recruited over a two-and-a-half year period. A power calculation using the actual attained sample size showed power to be 79% to detect a treatment effect. If an attrition fraction of 4% per year is maintained, power will remain at 80%. Power will still be > 90% to detect a 25% reduction in caries prevalence. The distribution of most baseline variables was similar for the two randomized groups of mothers. However, despite the random assignment of communities to treatment conditions, group differences exist for stage of pregnancy and prior tooth extractions in the family. Because of the group imbalances on certain variables, control of baseline variables will be done in the analyses of treatment effects. This paper explains the challenges of conducting randomized trials in remote settings, the importance of thorough community collaboration, and also illustrates the likelihood that some baseline variables that may be clinically important will be unevenly split in group-randomized trials when the number of groups is small. Trial registration This trial is registered as ISRCTN41467632. PMID:20465831

[Gene method for inconsistent hydrological frequency calculation. I: Inheritance, variability and evolution principles of hydrological genes].

PubMed

Xie, Ping; Wu, Zi Yi; Zhao, Jiang Yan; Sang, Yan Fang; Chen, Jie

2018-04-01

A stochastic hydrological process is influenced by both stochastic and deterministic factors. A hydrological time series contains not only pure random components reflecting its inheri-tance characteristics, but also deterministic components reflecting variability characteristics, such as jump, trend, period, and stochastic dependence. As a result, the stochastic hydrological process presents complicated evolution phenomena and rules. To better understand these complicated phenomena and rules, this study described the inheritance and variability characteristics of an inconsistent hydrological series from two aspects: stochastic process simulation and time series analysis. In addition, several frequency analysis approaches for inconsistent time series were compared to reveal the main problems in inconsistency study. Then, we proposed a new concept of hydrological genes origined from biological genes to describe the inconsistent hydrolocal processes. The hydrologi-cal genes were constructed using moments methods, such as general moments, weight function moments, probability weight moments and L-moments. Meanwhile, the five components, including jump, trend, periodic, dependence and pure random components, of a stochastic hydrological process were defined as five hydrological bases. With this method, the inheritance and variability of inconsistent hydrological time series were synthetically considered and the inheritance, variability and evolution principles were fully described. Our study would contribute to reveal the inheritance, variability and evolution principles in probability distribution of hydrological elements.

Country, Cover or Protection: What Shapes the Distribution of Red Deer and Roe Deer in the Bohemian Forest Ecosystem?

PubMed Central

Heurich, Marco; Brand, Tom T. G.; Kaandorp, Manon Y.; Šustr, Pavel; Müller, Jörg; Reineking, Björn

2015-01-01

The Bohemian Forest Ecosystem encompasses various wildlife management systems. Two large, contiguous national parks (one in Germany and one in the Czech Republic) form the centre of the area, are surrounded by private hunting grounds, and hunting regulations in each country differ. Here we aimed at unravelling the influence of management-related and environmental factors on the distribution of red deer (Cervus elaphus) and roe deer (Capreolus capreolus) in this ecosystem. We used the standing crop method based on counts of pellet groups, with point counts every 100 m along 218 randomly distributed transects. Our analysis, which accounted for overdispersion as well as zero inflation and spatial autocorrelation, corroborated the view that both human management and the physical and biological environment drive ungulate distribution in mountainous areas in Central Europe. In contrast to our expectations, protection by national parks was the least important variable for red deer and the third important out of four variables for roe deer; protection negatively influenced roe deer distribution in both parks and positively influenced red deer distribution in Germany. Country was the most influential variable for both red and roe deer, with higher counts of pellet groups in the Czech Republic than in Germany. Elevation, which indicates increasing environmental harshness, was the second most important variable for both species. Forest cover was the least important variable for roe deer and the third important variable for red deer; the relationship for roe deer was positive and linear, and optimal forest cover for red deer was about 70% within a 500 m radius. Our results have direct implications for the future conservation management of deer in protected areas in Central Europe and show in particular that large non-intervention zones may not cause agglomerations of deer that could lead to conflicts along the border of protected, mountainous areas. PMID:25781942

Country, cover or protection: what shapes the distribution of red deer and roe deer in the Bohemian Forest Ecosystem?

PubMed

Heurich, Marco; Brand, Tom T G; Kaandorp, Manon Y; Šustr, Pavel; Müller, Jörg; Reineking, Björn

2015-01-01

The Bohemian Forest Ecosystem encompasses various wildlife management systems. Two large, contiguous national parks (one in Germany and one in the Czech Republic) form the centre of the area, are surrounded by private hunting grounds, and hunting regulations in each country differ. Here we aimed at unravelling the influence of management-related and environmental factors on the distribution of red deer (Cervus elaphus) and roe deer (Capreolus capreolus) in this ecosystem. We used the standing crop method based on counts of pellet groups, with point counts every 100 m along 218 randomly distributed transects. Our analysis, which accounted for overdispersion as well as zero inflation and spatial autocorrelation, corroborated the view that both human management and the physical and biological environment drive ungulate distribution in mountainous areas in Central Europe. In contrast to our expectations, protection by national parks was the least important variable for red deer and the third important out of four variables for roe deer; protection negatively influenced roe deer distribution in both parks and positively influenced red deer distribution in Germany. Country was the most influential variable for both red and roe deer, with higher counts of pellet groups in the Czech Republic than in Germany. Elevation, which indicates increasing environmental harshness, was the second most important variable for both species. Forest cover was the least important variable for roe deer and the third important variable for red deer; the relationship for roe deer was positive and linear, and optimal forest cover for red deer was about 70% within a 500 m radius. Our results have direct implications for the future conservation management of deer in protected areas in Central Europe and show in particular that large non-intervention zones may not cause agglomerations of deer that could lead to conflicts along the border of protected, mountainous areas.

[Random Variable Read Me File

NASA Technical Reports Server (NTRS)

Teubert, Christopher; Sankararaman, Shankar; Cullo, Aiden

2017-01-01

Readme for the Random Variable Toolbox usable manner. is a Web-based Git version control repository hosting service. It is mostly used for computer code. It offers all of the distributed version control and source code management (SCM) functionality of Git as well as adding its own features. It provides access control and several collaboration features such as bug tracking, feature requests, task management, and wikis for every project.[3] GitHub offers both plans for private and free repositories on the same account[4] which are commonly used to host open-source software projects.[5] As of April 2017, GitHub reports having almost 20 million users and 57 million repositories,[6] making it the largest host of source code in the world.[7] GitHub has a mascot called Octocat, a cat with five tentacles and a human-like face

Missing Data and Multiple Imputation: An Unbiased Approach

NASA Technical Reports Server (NTRS)

Foy, M.; VanBaalen, M.; Wear, M.; Mendez, C.; Mason, S.; Meyers, V.; Alexander, D.; Law, J.

2014-01-01

The default method of dealing with missing data in statistical analyses is to only use the complete observations (complete case analysis), which can lead to unexpected bias when data do not meet the assumption of missing completely at random (MCAR). For the assumption of MCAR to be met, missingness cannot be related to either the observed or unobserved variables. A less stringent assumption, missing at random (MAR), requires that missingness not be associated with the value of the missing variable itself, but can be associated with the other observed variables. When data are truly MAR as opposed to MCAR, the default complete case analysis method can lead to biased results. There are statistical options available to adjust for data that are MAR, including multiple imputation (MI) which is consistent and efficient at estimating effects. Multiple imputation uses informing variables to determine statistical distributions for each piece of missing data. Then multiple datasets are created by randomly drawing on the distributions for each piece of missing data. Since MI is efficient, only a limited number, usually less than 20, of imputed datasets are required to get stable estimates. Each imputed dataset is analyzed using standard statistical techniques, and then results are combined to get overall estimates of effect. A simulation study will be demonstrated to show the results of using the default complete case analysis, and MI in a linear regression of MCAR and MAR simulated data. Further, MI was successfully applied to the association study of CO2 levels and headaches when initial analysis showed there may be an underlying association between missing CO2 levels and reported headaches. Through MI, we were able to show that there is a strong association between average CO2 levels and the risk of headaches. Each unit increase in CO2 (mmHg) resulted in a doubling in the odds of reported headaches.

Impact of Health Research Systems on Under-5 Mortality Rate: A Trend Analysis.

PubMed

Yazdizadeh, Bahareh; Parsaeian, Mahboubeh; Majdzadeh, Reza; Nikooee, Sima

2016-11-26

Between 1990 and 2015, under-5 mortality rate (U5MR) declined by 53%, from an estimated rate of 91 deaths per 1000 live births to 43, globally. The aim of this study was to determine the share of health research systems in this decrease alongside other influential factors. We used random effect regression models including the 'random intercept' and 'random intercept and random slope' models to analyze the panel data from 1990 to 2010. We selected the countries with U5MRs falling between the first and third quartiles in 1990. We used both the total articles (TA) and the number of child-specific articles (CSA) as a proxy of the health research system. In order to account for the impact of other factors, measles vaccination coverage (MVC) (as a proxy of health system performance), gross domestic product (GDP), human development index (HDI), and corruption perception index (CPI) (as proxies of development), were embedded in the model. Among all the models, 'the random intercept and random slope models' had lower residuals. The same variables of CSA, HDI, and time were significant and the coefficient of CSA was estimated at -0.17; meaning, with the addition of every 100 CSA, the rate of U5MR decreased by 17 per 1000 live births. Although the number of CSA has contributed to the reduction of U5MR, the amount of its contribution is negligible compared to the countries' development. We recommend entering different types of researches into the model separately in future research and including the variable of 'exchange between knowledge generator and user.' © 2017 The Author(s); Published by Kerman University of Medical Sciences. This is an open-access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Distribution functions of probabilistic automata

NASA Technical Reports Server (NTRS)

Vatan, F.

2001-01-01

Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.

Reducing seed dependent variability of non-uniformly sampled multidimensional NMR data

NASA Astrophysics Data System (ADS)

Mobli, Mehdi

2015-07-01

The application of NMR spectroscopy to study the structure, dynamics and function of macromolecules requires the acquisition of several multidimensional spectra. The one-dimensional NMR time-response from the spectrometer is extended to additional dimensions by introducing incremented delays in the experiment that cause oscillation of the signal along "indirect" dimensions. For a given dimension the delay is incremented at twice the rate of the maximum frequency (Nyquist rate). To achieve high-resolution requires acquisition of long data records sampled at the Nyquist rate. This is typically a prohibitive step due to time constraints, resulting in sub-optimal data records to the detriment of subsequent analyses. The multidimensional NMR spectrum itself is typically sparse, and it has been shown that in such cases it is possible to use non-Fourier methods to reconstruct a high-resolution multidimensional spectrum from a random subset of non-uniformly sampled (NUS) data. For a given acquisition time, NUS has the potential to improve the sensitivity and resolution of a multidimensional spectrum, compared to traditional uniform sampling. The improvements in sensitivity and/or resolution achieved by NUS are heavily dependent on the distribution of points in the random subset acquired. Typically, random points are selected from a probability density function (PDF) weighted according to the NMR signal envelope. In extreme cases as little as 1% of the data is subsampled. The heavy under-sampling can result in poor reproducibility, i.e. when two experiments are carried out where the same number of random samples is selected from the same PDF but using different random seeds. Here, a jittered sampling approach is introduced that is shown to improve random seed dependent reproducibility of multidimensional spectra generated from NUS data, compared to commonly applied NUS methods. It is shown that this is achieved due to the low variability of the inherent sensitivity of the random subset chosen from a given PDF. Finally, it is demonstrated that metrics used to find optimal NUS distributions are heavily dependent on the inherent sensitivity of the random subset, and such optimisation is therefore less critical when using the proposed sampling scheme.

Generating Variable and Random Schedules of Reinforcement Using Microsoft Excel Macros

PubMed Central

Bancroft, Stacie L; Bourret, Jason C

2008-01-01

Variable reinforcement schedules are used to arrange the availability of reinforcement following varying response ratios or intervals of time. Random reinforcement schedules are subtypes of variable reinforcement schedules that can be used to arrange the availability of reinforcement at a constant probability across number of responses or time. Generating schedule values for variable and random reinforcement schedules can be difficult. The present article describes the steps necessary to write macros in Microsoft Excel that will generate variable-ratio, variable-interval, variable-time, random-ratio, random-interval, and random-time reinforcement schedule values. PMID:18595286

Combining Probability Distributions of Wind Waves and Sea Level Variations to Assess Return Periods of Coastal Floods

NASA Astrophysics Data System (ADS)

Leijala, U.; Bjorkqvist, J. V.; Pellikka, H.; Johansson, M. M.; Kahma, K. K.

2017-12-01

Predicting the behaviour of the joint effect of sea level and wind waves is of great significance due to the major impact of flooding events in densely populated coastal regions. As mean sea level rises, the effect of sea level variations accompanied by the waves will be even more harmful in the future. The main challenge when evaluating the effect of waves and sea level variations is that long time series of both variables rarely exist. Wave statistics are also highly location-dependent, thus requiring wave buoy measurements and/or high-resolution wave modelling. As an initial approximation of the joint effect, the variables may be treated as independent random variables, to achieve the probability distribution of their sum. We present results of a case study based on three probability distributions: 1) wave run-up constructed from individual wave buoy measurements, 2) short-term sea level variability based on tide gauge data, and 3) mean sea level projections based on up-to-date regional scenarios. The wave measurements were conducted during 2012-2014 on the coast of city of Helsinki located in the Gulf of Finland in the Baltic Sea. The short-term sea level distribution contains the last 30 years (1986-2015) of hourly data from Helsinki tide gauge, and the mean sea level projections are scenarios adjusted for the Gulf of Finland. Additionally, we present a sensitivity test based on six different theoretical wave height distributions representing different wave behaviour in relation to sea level variations. As these wave distributions are merged with one common sea level distribution, we can study how the different shapes of the wave height distribution affect the distribution of the sum, and which one of the components is dominating under different wave conditions. As an outcome of the method, we obtain a probability distribution of the maximum elevation of the continuous water mass, which enables a flexible tool for evaluating different risk levels in the current and future climate.

Calculating radiotherapy margins based on Bayesian modelling of patient specific random errors

NASA Astrophysics Data System (ADS)

Herschtal, A.; te Marvelde, L.; Mengersen, K.; Hosseinifard, Z.; Foroudi, F.; Devereux, T.; Pham, D.; Ball, D.; Greer, P. B.; Pichler, P.; Eade, T.; Kneebone, A.; Bell, L.; Caine, H.; Hindson, B.; Kron, T.

2015-02-01

Collected real-life clinical target volume (CTV) displacement data show that some patients undergoing external beam radiotherapy (EBRT) demonstrate significantly more fraction-to-fraction variability in their displacement (‘random error’) than others. This contrasts with the common assumption made by historical recipes for margin estimation for EBRT, that the random error is constant across patients. In this work we present statistical models of CTV displacements in which random errors are characterised by an inverse gamma (IG) distribution in order to assess the impact of random error variability on CTV-to-PTV margin widths, for eight real world patient cohorts from four institutions, and for different sites of malignancy. We considered a variety of clinical treatment requirements and penumbral widths. The eight cohorts consisted of a total of 874 patients and 27 391 treatment sessions. Compared to a traditional margin recipe that assumes constant random errors across patients, for a typical 4 mm penumbral width, the IG based margin model mandates that in order to satisfy the common clinical requirement that 90% of patients receive at least 95% of prescribed RT dose to the entire CTV, margins be increased by a median of 10% (range over the eight cohorts -19% to +35%). This substantially reduces the proportion of patients for whom margins are too small to satisfy clinical requirements.

Alternate methods for FAAT S-curve generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaufman, A.M.

The FAAT (Foreign Asset Assessment Team) assessment methodology attempts to derive a probability of effect as a function of incident field strength. The probability of effect is the likelihood that the stress put on a system exceeds its strength. In the FAAT methodology, both the stress and strength are random variables whose statistical properties are estimated by experts. Each random variable has two components of uncertainty: systematic and random. The systematic uncertainty drives the confidence bounds in the FAAT assessment. Its variance can be reduced by improved information. The variance of the random uncertainty is not reducible. The FAAT methodologymore » uses an assessment code called ARES to generate probability of effect curves (S-curves) at various confidence levels. ARES assumes log normal distributions for all random variables. The S-curves themselves are log normal cumulants associated with the random portion of the uncertainty. The placement of the S-curves depends on confidence bounds. The systematic uncertainty in both stress and strength is usually described by a mode and an upper and lower variance. Such a description is not consistent with the log normal assumption of ARES and an unsatisfactory work around solution is used to obtain the required placement of the S-curves at each confidence level. We have looked into this situation and have found that significant errors are introduced by this work around. These errors are at least several dB-W/cm{sup 2} at all confidence levels, but they are especially bad in the estimate of the median. In this paper, we suggest two alternate solutions for the placement of S-curves. To compare these calculational methods, we have tabulated the common combinations of upper and lower variances and generated the relevant S-curves offsets from the mode difference of stress and strength.« less

Mendelian Randomization.

PubMed

Grover, Sandeep; Del Greco M, Fabiola; Stein, Catherine M; Ziegler, Andreas

2017-01-01

Confounding and reverse causality have prevented us from drawing meaningful clinical interpretation even in well-powered observational studies. Confounding may be attributed to our inability to randomize the exposure variable in observational studies. Mendelian randomization (MR) is one approach to overcome confounding. It utilizes one or more genetic polymorphisms as a proxy for the exposure variable of interest. Polymorphisms are randomly distributed in a population, they are static throughout an individual's lifetime, and may thus help in inferring directionality in exposure-outcome associations. Genome-wide association studies (GWAS) or meta-analyses of GWAS are characterized by large sample sizes and the availability of many single nucleotide polymorphisms (SNPs), making GWAS-based MR an attractive approach. GWAS-based MR comes with specific challenges, including multiple causality. Despite shortcomings, it still remains one of the most powerful techniques for inferring causality.With MR still an evolving concept with complex statistical challenges, the literature is relatively scarce in terms of providing working examples incorporating real datasets. In this chapter, we provide a step-by-step guide for causal inference based on the principles of MR with a real dataset using both individual and summary data from unrelated individuals. We suggest best possible practices and give recommendations based on the current literature.

Learning Probabilities From Random Observables in High Dimensions: The Maximum Entropy Distribution and Others

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Cocco, Simona; Monasson, Rémi

2015-11-01

We consider the problem of learning a target probability distribution over a set of N binary variables from the knowledge of the expectation values (with this target distribution) of M observables, drawn uniformly at random. The space of all probability distributions compatible with these M expectation values within some fixed accuracy, called version space, is studied. We introduce a biased measure over the version space, which gives a boost increasing exponentially with the entropy of the distributions and with an arbitrary inverse `temperature' Γ . The choice of Γ allows us to interpolate smoothly between the unbiased measure over all distributions in the version space (Γ =0) and the pointwise measure concentrated at the maximum entropy distribution (Γ → ∞ ). Using the replica method we compute the volume of the version space and other quantities of interest, such as the distance R between the target distribution and the center-of-mass distribution over the version space, as functions of α =(log M)/N and Γ for large N. Phase transitions at critical values of α are found, corresponding to qualitative improvements in the learning of the target distribution and to the decrease of the distance R. However, for fixed α the distance R does not vary with Γ which means that the maximum entropy distribution is not closer to the target distribution than any other distribution compatible with the observable values. Our results are confirmed by Monte Carlo sampling of the version space for small system sizes (N≤ 10).

The JCMT Transient Survey: Stochastic and Secular Variability of Protostars and Disks In the Submillimeter Region Observed over 18 Months

NASA Astrophysics Data System (ADS)

Johnstone, Doug; Herczeg, Gregory J.; Mairs, Steve; Hatchell, Jennifer; Bower, Geoffrey C.; Kirk, Helen; Lane, James; Bell, Graham S.; Graves, Sarah; Aikawa, Yuri; Chen, Huei-Ru Vivien; Chen, Wen-Ping; Kang, Miju; Kang, Sung-Ju; Lee, Jeong-Eun; Morata, Oscar; Pon, Andy; Scicluna, Peter; Scholz, Aleks; Takahashi, Satoko; Yoo, Hyunju; The JCMT Transient Team

2018-02-01

We analyze results from the first 18 months of monthly submillimeter monitoring of eight star-forming regions in the JCMT Transient Survey. In our search for stochastic variability in 1643 bright peaks, only the previously identified source, EC 53, shows behavior well above the expected measurement uncertainty. Another four sources—two disks and two protostars—show moderately enhanced standard deviations in brightness, as expected for stochastic variables. For the two protostars, this apparent variability is the result of single epochs that are much brighter than the mean. In our search for secular brightness variations that are linear in time, we measure the fractional brightness change per year for 150 bright peaks, 50 of which are protostellar. The ensemble distribution of slopes is well fit by a normal distribution with σ ∼ 0.023. Most sources are not rapidly brightening or fading at submillimeter wavelengths. Comparison against time-randomized realizations shows that the width of the distribution is dominated by the uncertainty in the individual brightness measurements of the sources. A toy model for secular variability reveals that an underlying Gaussian distribution of linear fractional brightness change σ = 0.005 would be unobservable in the present sample, whereas an underlying distribution with σ = 0.02 is ruled out. Five protostellar sources, 10% of the protostellar sample, are found to have robust secular measures deviating from a constant flux. The sensitivity to secular brightness variations will improve significantly with a sample over a longer time duration, with an improvement by factor of two expected by the conclusion of our 36 month survey.

Estimation of the Ratio of Scale Parameters in the Two Sample Problem with Arbitrary Right Censorship.

DTIC Science & Technology

1980-06-01

70. AWST RC 7 Coeittu an rewwase ati of nee*aa.ean mimDdentify by black n,.mboJ T two-sample version of the Cram~ r -von Mines statistic for right...estimator for exponential distributions. KEY WORDS: Cram~ r -von Mtses distance; Kaplan-Meier estimators; Right censorship; Scale parameter; lodgea and...suppose that two positive random variables ’i 2 S0 and ’ r differ in distribution only by their scale parameters. That is, there exists a positive

Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

NASA Astrophysics Data System (ADS)

César Mansur Filho, Júlio; Dickman, Ronald

2011-05-01

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32 000 sites. The resulting estimates for critical exponents β, \\beta /\

Random bursts determine dynamics of active filaments.

PubMed

Weber, Christoph A; Suzuki, Ryo; Schaller, Volker; Aranson, Igor S; Bausch, Andreas R; Frey, Erwin

2015-08-25

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system's dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model.

Random bursts determine dynamics of active filaments

PubMed Central

Weber, Christoph A.; Suzuki, Ryo; Schaller, Volker; Aranson, Igor S.; Bausch, Andreas R.; Frey, Erwin

2015-01-01

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system’s dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model. PMID:26261319

Exponential order statistic models of software reliability growth

NASA Technical Reports Server (NTRS)

Miller, D. R.

1985-01-01

Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

Redshift data and statistical inference

NASA Technical Reports Server (NTRS)

Newman, William I.; Haynes, Martha P.; Terzian, Yervant

1994-01-01

Frequency histograms and the 'power spectrum analysis' (PSA) method, the latter developed by Yu & Peebles (1969), have been widely employed as techniques for establishing the existence of periodicities. We provide a formal analysis of these two classes of methods, including controlled numerical experiments, to better understand their proper use and application. In particular, we note that typical published applications of frequency histograms commonly employ far greater numbers of class intervals or bins than is advisable by statistical theory sometimes giving rise to the appearance of spurious patterns. The PSA method generates a sequence of random numbers from observational data which, it is claimed, is exponentially distributed with unit mean and variance, essentially independent of the distribution of the original data. We show that the derived random processes is nonstationary and produces a small but systematic bias in the usual estimate of the mean and variance. Although the derived variable may be reasonably described by an exponential distribution, the tail of the distribution is far removed from that of an exponential, thereby rendering statistical inference and confidence testing based on the tail of the distribution completely unreliable. Finally, we examine a number of astronomical examples wherein these methods have been used giving rise to widespread acceptance of statistically unconfirmed conclusions.

Ensembles of Spiking Neurons with Noise Support Optimal Probabilistic Inference in a Dynamically Changing Environment

PubMed Central

Legenstein, Robert; Maass, Wolfgang

2014-01-01

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information. PMID:25340749

A study of optimal abstract jamming strategies vs. noncoherent MFSK

NASA Technical Reports Server (NTRS)

Mceliece, R. J.; Rodemich, E. R.

1983-01-01

The present investigation is concerned with the performance of uncoded MFSK modulation in the presence of arbitrary additive jamming, taking into account the objective to devise robust antijamming strategies. An abstract model is considered, giving attention to the signal strength as a nonnegative real number X, the employment of X as a random variable, its distribution function G(x), the transmitter's strategy G, the jamming noise as an M-dimensional random vector Z, and the error probability. A summary of previous work on the considered problem is provided, and the results of the current study are presented.

Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime

NASA Astrophysics Data System (ADS)

Braides, Andrea; Causin, Andrea; Piatnitski, Andrey; Solci, Margherita

2018-06-01

We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability 1-p and p, respectively, according to an i.i.d. random variable. We study minimizers of the corresponding nearest-neighbour spin energy on large domains in Z^2. We prove that there exists p_0 such that for p≤ p_0 such minimizers are characterized by a majority phase; i.e., they take identically the value 1 or - 1 except for small disconnected sets. A deterministic analogue is also proved.

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

NASA Astrophysics Data System (ADS)

Benaych-Georges, Florent; Guionnet, Alice; Male, Camille

2014-07-01

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.

Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime

NASA Astrophysics Data System (ADS)

Braides, Andrea; Causin, Andrea; Piatnitski, Andrey; Solci, Margherita

2018-04-01

We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability 1-p and p, respectively, according to an i.i.d. random variable. We study minimizers of the corresponding nearest-neighbour spin energy on large domains in Z^2 . We prove that there exists p_0 such that for p≤p_0 such minimizers are characterized by a majority phase; i.e., they take identically the value 1 or - 1 except for small disconnected sets. A deterministic analogue is also proved.

An analysis of random projection for changeable and privacy-preserving biometric verification.

PubMed

Wang, Yongjin; Plataniotis, Konstantinos N

2010-10-01

Changeability and privacy protection are important factors for widespread deployment of biometrics-based verification systems. This paper presents a systematic analysis of a random-projection (RP)-based method for addressing these problems. The employed method transforms biometric data using a random matrix with each entry an independent and identically distributed Gaussian random variable. The similarity- and privacy-preserving properties, as well as the changeability of the biometric information in the transformed domain, are analyzed in detail. Specifically, RP on both high-dimensional image vectors and dimensionality-reduced feature vectors is discussed and compared. A vector translation method is proposed to improve the changeability of the generated templates. The feasibility of the introduced solution is well supported by detailed theoretical analyses. Extensive experimentation on a face-based biometric verification problem shows the effectiveness of the proposed method.

Accretion rates of protoplanets 2: Gaussian distribution of planestesimal velocities

NASA Technical Reports Server (NTRS)

Greenzweig, Yuval; Lissauer, Jack J.

1991-01-01

The growth rate of a protoplanet embedded in a uniform surface density disk of planetesimals having a triaxial Gaussian velocity distribution was calculated. The longitudes of the aspses and nodes of the planetesimals are uniformly distributed, and the protoplanet is on a circular orbit. The accretion rate in the two body approximation is enhanced by a factor of approximately 3, compared to the case where all planetesimals have eccentricity and inclination equal to the root mean square (RMS) values of those variables in the Gaussian distribution disk. Numerical three body integrations show comparable enhancements, except when the RMS initial planetesimal eccentricities are extremely small. This enhancement in accretion rate should be incorporated by all models, analytical or numerical, which assume a single random velocity for all planetesimals, in lieu of a Gaussian distribution.

Quasar microlensing models with constraints on the Quasar light curves

NASA Astrophysics Data System (ADS)

Tie, S. S.; Kochanek, C. S.

2018-01-01

Quasar microlensing analyses implicitly generate a model of the variability of the source quasar. The implied source variability may be unrealistic yet its likelihood is generally not evaluated. We used the damped random walk (DRW) model for quasar variability to evaluate the likelihood of the source variability and applied the revized algorithm to a microlensing analysis of the lensed quasar RX J1131-1231. We compared estimates of the size of the quasar disc and the average stellar mass of the lens galaxy with and without applying the DRW likelihoods for the source variability model and found no significant effect on the estimated physical parameters. The most likely explanation is that unreliastic source light-curve models are generally associated with poor microlensing fits that already make a negligible contribution to the probability distributions of the derived parameters.

Population density approach for discrete mRNA distributions in generalized switching models for stochastic gene expression.

PubMed

Stinchcombe, Adam R; Peskin, Charles S; Tranchina, Daniel

2012-06-01

We present a generalization of a population density approach for modeling and analysis of stochastic gene expression. In the model, the gene of interest fluctuates stochastically between an inactive state, in which transcription cannot occur, and an active state, in which discrete transcription events occur; and the individual mRNA molecules are degraded stochastically in an independent manner. This sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mRNA copy number. In our generalization, the random dwell times in the inactive and active states, T_{0} and T_{1}, respectively, are independent random variables drawn from any specified distributions. Consequently, the probability per unit time of switching out of a state depends on the time since entering that state. Our method exploits a connection between the fully discrete random process and a related continuous process. We present numerical methods for computing steady-state mRNA distributions and an analytical derivation of the mRNA autocovariance function. We find that empirical estimates of the steady-state mRNA probability mass function from Monte Carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes. However, in these parameter regimes and where the autocovariance function has negative lobes, the autocovariance function disambiguates the two types of models. Our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching.

Alpine bird distributions along elevation gradients: the consistency of climate and habitat effects across geographic regions.

PubMed

Chamberlain, Dan; Brambilla, Mattia; Caprio, Enrico; Pedrini, Paolo; Rolando, Antonio

2016-08-01

Many species have shown recent shifts in their distributions in response to climate change. Patterns in species occurrence or abundance along altitudinal gradients often serve as the basis for detecting such changes and assessing future sensitivity. Quantifying the distribution of species along altitudinal gradients acts as a fundamental basis for future studies on environmental change impacts, but in order for models of altitudinal distribution to have wide applicability, it is necessary to know the extent to which altitudinal trends in occurrence are consistent across geographically separated areas. This was assessed by fitting models of bird species occurrence across altitudinal gradients in relation to habitat and climate variables in two geographically separated alpine regions, Piedmont and Trentino. The ten species studied showed non-random altitudinal distributions which in most cases were consistent across regions in terms of pattern. Trends in relation to altitude and differences between regions could be explained mostly by habitat or a combination of habitat and climate variables. Variation partitioning showed that most variation explained by the models was attributable to habitat, or habitat and climate together, rather than climate alone or geographic region. The shape and position of the altitudinal distribution curve is important as it can be related to vulnerability where the available space is limited, i.e. where mountains are not of sufficient altitude for expansion. This study therefore suggests that incorporating habitat and climate variables should be sufficient to construct models with high transferability for many alpine species.

Probability techniques for reliability analysis of composite materials

NASA Technical Reports Server (NTRS)

Wetherhold, Robert C.; Ucci, Anthony M.

1994-01-01

Traditional design approaches for composite materials have employed deterministic criteria for failure analysis. New approaches are required to predict the reliability of composite structures since strengths and stresses may be random variables. This report will examine and compare methods used to evaluate the reliability of composite laminae. The two types of methods that will be evaluated are fast probability integration (FPI) methods and Monte Carlo methods. In these methods, reliability is formulated as the probability that an explicit function of random variables is less than a given constant. Using failure criteria developed for composite materials, a function of design variables can be generated which defines a 'failure surface' in probability space. A number of methods are available to evaluate the integration over the probability space bounded by this surface; this integration delivers the required reliability. The methods which will be evaluated are: the first order, second moment FPI methods; second order, second moment FPI methods; the simple Monte Carlo; and an advanced Monte Carlo technique which utilizes importance sampling. The methods are compared for accuracy, efficiency, and for the conservativism of the reliability estimation. The methodology involved in determining the sensitivity of the reliability estimate to the design variables (strength distributions) and importance factors is also presented.

Sharp Boundary Inversion of 2D Magnetotelluric Data using Bayesian Method.

NASA Astrophysics Data System (ADS)

Zhou, S.; Huang, Q.

2017-12-01

Normally magnetotelluric(MT) inversion method cannot show the distribution of underground resistivity with clear boundary, even if there are obviously different blocks. Aiming to solve this problem, we develop a Bayesian structure to inverse 2D MT sharp boundary data, using boundary location and inside resistivity as the random variables. Firstly, we use other MT inversion results, like ModEM, to analyze the resistivity distribution roughly. Then, we select the suitable random variables and change its data format to traditional staggered grid parameters, which can be used to do finite difference forward part. Finally, we can shape the posterior probability density(PPD), which contains all the prior information and model-data correlation, by Markov Chain Monte Carlo(MCMC) sampling from prior distribution. The depth, resistivity and their uncertainty can be valued. It also works for sensibility estimation. We applied the method to a synthetic case, which composes two large abnormal blocks in a trivial background. We consider the boundary smooth and the near true model weight constrains that mimic joint inversion or constrained inversion, then we find that the model results a more precise and focused depth distribution. And we also test the inversion without constrains and find that the boundary could also be figured, though not as well. Both inversions have a good valuation of resistivity. The constrained result has a lower root mean square than ModEM inversion result. The data sensibility obtained via PPD shows that the resistivity is the most sensible, center depth comes second and both sides are the worst.

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta‐analysis and group level studies

PubMed Central

Bakbergenuly, Ilyas; Morgenthaler, Stephan

2016-01-01

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group‐level studies or in meta‐analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log‐odds and arcsine transformations of the estimated probability p^, both for single‐group studies and in combining results from several groups or studies in meta‐analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta‐analysis and result in abysmal coverage of the combined effect for large K. We also propose bias‐correction for the arcsine transformation. Our simulations demonstrate that this bias‐correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta‐analyses of prevalence. PMID:27192062

Extending existing structural identifiability analysis methods to mixed-effects models.

PubMed

Janzén, David L I; Jirstrand, Mats; Chappell, Michael J; Evans, Neil D

2018-01-01

The concept of structural identifiability for state-space models is expanded to cover mixed-effects state-space models. Two methods applicable for the analytical study of the structural identifiability of mixed-effects models are presented. The two methods are based on previously established techniques for non-mixed-effects models; namely the Taylor series expansion and the input-output form approach. By generating an exhaustive summary, and by assuming an infinite number of subjects, functions of random variables can be derived which in turn determine the distribution of the system's observation function(s). By considering the uniqueness of the analytical statistical moments of the derived functions of the random variables, the structural identifiability of the corresponding mixed-effects model can be determined. The two methods are applied to a set of examples of mixed-effects models to illustrate how they work in practice. Copyright © 2017 Elsevier Inc. All rights reserved.

Random Distribution Pattern and Non-adaptivity of Genome Size in a Highly Variable Population of Festuca pallens

PubMed Central

Šmarda, Petr; Bureš, Petr; Horová, Lucie

2007-01-01

Background and Aims The spatial and statistical distribution of genome sizes and the adaptivity of genome size to some types of habitat, vegetation or microclimatic conditions were investigated in a tetraploid population of Festuca pallens. The population was previously documented to vary highly in genome size and is assumed as a model for the study of the initial stages of genome size differentiation. Methods Using DAPI flow cytometry, samples were measured repeatedly with diploid Festuca pallens as the internal standard. Altogether 172 plants from 57 plots (2·25 m2), distributed in contrasting habitats over the whole locality in South Moravia, Czech Republic, were sampled. The differences in DNA content were confirmed by the double peaks of simultaneously measured samples. Key Results At maximum, a 1·115-fold difference in genome size was observed. The statistical distribution of genome sizes was found to be continuous and best fits the extreme (Gumbel) distribution with rare occurrences of extremely large genomes (positive-skewed), as it is similar for the log-normal distribution of the whole Angiosperms. Even plants from the same plot frequently varied considerably in genome size and the spatial distribution of genome sizes was generally random and unautocorrelated (P > 0·05). The observed spatial pattern and the overall lack of correlations of genome size with recognized vegetation types or microclimatic conditions indicate the absence of ecological adaptivity of genome size in the studied population. Conclusions These experimental data on intraspecific genome size variability in Festuca pallens argue for the absence of natural selection and the selective non-significance of genome size in the initial stages of genome size differentiation, and corroborate the current hypothetical model of genome size evolution in Angiosperms (Bennetzen et al., 2005, Annals of Botany 95: 127–132). PMID:17565968

Evaluation of Scat Deposition Transects versus Radio Telemetry for Developing a Species Distribution Model for a Rare Desert Carnivore, the Kit Fox.

PubMed

Dempsey, Steven J; Gese, Eric M; Kluever, Bryan M; Lonsinger, Robert C; Waits, Lisette P

2015-01-01

Development and evaluation of noninvasive methods for monitoring species distribution and abundance is a growing area of ecological research. While noninvasive methods have the advantage of reduced risk of negative factors associated with capture, comparisons to methods using more traditional invasive sampling is lacking. Historically kit foxes (Vulpes macrotis) occupied the desert and semi-arid regions of southwestern North America. Once the most abundant carnivore in the Great Basin Desert of Utah, the species is now considered rare. In recent decades, attempts have been made to model the environmental variables influencing kit fox distribution. Using noninvasive scat deposition surveys for determination of kit fox presence, we modeled resource selection functions to predict kit fox distribution using three popular techniques (Maxent, fixed-effects, and mixed-effects generalized linear models) and compared these with similar models developed from invasive sampling (telemetry locations from radio-collared foxes). Resource selection functions were developed using a combination of landscape variables including elevation, slope, aspect, vegetation height, and soil type. All models were tested against subsequent scat collections as a method of model validation. We demonstrate the importance of comparing multiple model types for development of resource selection functions used to predict a species distribution, and evaluating the importance of environmental variables on species distribution. All models we examined showed a large effect of elevation on kit fox presence, followed by slope and vegetation height. However, the invasive sampling method (i.e., radio-telemetry) appeared to be better at determining resource selection, and therefore may be more robust in predicting kit fox distribution. In contrast, the distribution maps created from the noninvasive sampling (i.e., scat transects) were significantly different than the invasive method, thus scat transects may be appropriate when used in an occupancy framework to predict species distribution. We concluded that while scat deposition transects may be useful for monitoring kit fox abundance and possibly occupancy, they do not appear to be appropriate for determining resource selection. On our study area, scat transects were biased to roadways, while data collected using radio-telemetry was dictated by movements of the kit foxes themselves. We recommend that future studies applying noninvasive scat sampling should consider a more robust random sampling design across the landscape (e.g., random transects or more complete road coverage) that would then provide a more accurate and unbiased depiction of resource selection useful to predict kit fox distribution.

The comparison of landslide ratio-based and general logistic regression landslide susceptibility models in the Chishan watershed after 2009 Typhoon Morakot

NASA Astrophysics Data System (ADS)

WU, Chunhung

2015-04-01

The research built the original logistic regression landslide susceptibility model (abbreviated as or-LRLSM) and landslide ratio-based ogistic regression landslide susceptibility model (abbreviated as lr-LRLSM), compared the performance and explained the error source of two models. The research assumes that the performance of the logistic regression model can be better if the distribution of landslide ratio and weighted value of each variable is similar. Landslide ratio is the ratio of landslide area to total area in the specific area and an useful index to evaluate the seriousness of landslide disaster in Taiwan. The research adopted the landside inventory induced by 2009 Typhoon Morakot in the Chishan watershed, which was the most serious disaster event in the last decade, in Taiwan. The research adopted the 20 m grid as the basic unit in building the LRLSM, and six variables, including elevation, slope, aspect, geological formation, accumulated rainfall, and bank erosion, were included in the two models. The six variables were divided as continuous variables, including elevation, slope, and accumulated rainfall, and categorical variables, including aspect, geological formation and bank erosion in building the or-LRLSM, while all variables, which were classified based on landslide ratio, were categorical variables in building the lr-LRLSM. Because the count of whole basic unit in the Chishan watershed was too much to calculate by using commercial software, the research took random sampling instead of the whole basic units. The research adopted equal proportions of landslide unit and not landslide unit in logistic regression analysis. The research took 10 times random sampling and selected the group with the best Cox & Snell R2 value and Nagelkerker R2 value as the database for the following analysis. Based on the best result from 10 random sampling groups, the or-LRLSM (lr-LRLSM) is significant at the 1% level with Cox & Snell R2 = 0.190 (0.196) and Nagelkerke R2 = 0.253 (0.260). The unit with the landslide susceptibility value > 0.5 (≦ 0.5) will be classified as a predicted landslide unit (not landslide unit). The AUC, i.e. the area under the relative operating characteristic curve, of or-LRLSM in the Chishan watershed is 0.72, while that of lr-LRLSM is 0.77. Furthermore, the average correct ratio of lr-LRLSM (73.3%) is better than that of or-LRLSM (68.3%). The research analyzed in detail the error sources from the two models. In continuous variables, using the landslide ratio-based classification in building the lr-LRLSM can let the distribution of weighted value more similar to distribution of landslide ratio in the range of continuous variable than that in building the or-LRLSM. In categorical variables, the meaning of using the landslide ratio-based classification in building the lr-LRLSM is to gather the parameters with approximate landslide ratio together. The mean correct ratio in continuous variables (categorical variables) by using the lr-LRLSM is better than that in or-LRLSM by 0.6 ~ 2.6% (1.7% ~ 6.0%). Building the landslide susceptibility model by using landslide ratio-based classification is practical and of better performance than that by using the original logistic regression.

Interpretation of sucrose gradient sedimentation pattern of deoxyribonucleic acid fragments resulting from random breaks.

PubMed

Litwin, S; Shahn, E; Kozinski, A W

1969-07-01

Mass distribution in a sucrose gradient of deoxyribonucleic acid (DNA) fragments arising as a result of random breaks is predicted by analytical means from which computer evaluations are plotted. The analytical results are compared with the results of verifying experiments: (i) a Monte Carlo computer experiment in which simulated molecules of DNA were individuals of unit length subjected to random "breaks" applied by a random number generator, and (ii) an in vitro experiment in which molecules of T4 DNA, highly labeled with (32)P, were stored in liquid nitrogen for variable periods of time during which a precisely known number of (32)P atoms decayed, causing single-stranded breaks. The distribution of sizes of the resulting fragments was measured in an alkaline sucrose gradient. The profiles obtained in this fashion were compared with the mathematical predictions. Both experiments agree with the analytical approach and thus permit the use of the graphs obtained from the latter as a means of determining the average number of random breaks in DNA from distributions obtained experimentally in a sucrose gradient. An example of the application of this procedure to a previously unresolved problem is provided in the case of DNA from ultraviolet-irradiated phage which undergoes a dose-dependent intracellular breakdown. The relationship between the number of lethal hits and the number of single-stranded breaks was not previously established. A comparison of the calculated number of nicks per strand of DNA with the known dose in phage-lethal hits reveals a relationship closely approximating one lethal hit to one single-stranded break.

Practical security analysis of continuous-variable quantum key distribution with jitter in clock synchronization

NASA Astrophysics Data System (ADS)

Xie, Cailang; Guo, Ying; Liao, Qin; Zhao, Wei; Huang, Duan; Zhang, Ling; Zeng, Guihua

2018-03-01

How to narrow the gap of security between theory and practice has been a notoriously urgent problem in quantum cryptography. Here, we analyze and provide experimental evidence of the clock jitter effect on the practical continuous-variable quantum key distribution (CV-QKD) system. The clock jitter is a random noise which exists permanently in the clock synchronization in the practical CV-QKD system, it may compromise the system security because of its impact on data sampling and parameters estimation. In particular, the practical security of CV-QKD with different clock jitter against collective attack is analyzed theoretically based on different repetition frequencies, the numerical simulations indicate that the clock jitter has more impact on a high-speed scenario. Furthermore, a simplified experiment is designed to investigate the influence of the clock jitter.

Improving Search Algorithms by Using Intelligent Coordinates

NASA Technical Reports Server (NTRS)

Wolpert, David H.; Tumer, Kagan; Bandari, Esfandiar

2004-01-01

We consider algorithms that maximize a global function G in a distributed manner, using a different adaptive computational agent to set each variable of the underlying space. Each agent eta is self-interested; it sets its variable to maximize its own function g (sub eta). Three factors govern such a distributed algorithm's performance, related to exploration/exploitation, game theory, and machine learning. We demonstrate how to exploit alI three factors by modifying a search algorithm's exploration stage: rather than random exploration, each coordinate of the search space is now controlled by a separate machine-learning-based player engaged in a noncooperative game. Experiments demonstrate that this modification improves simulated annealing (SA) by up to an order of magnitude for bin packing and for a model of an economic process run over an underlying network. These experiments also reveal interesting small-world phenomena.

Improving search algorithms by using intelligent coordinates

NASA Astrophysics Data System (ADS)

Wolpert, David; Tumer, Kagan; Bandari, Esfandiar

2004-01-01

We consider algorithms that maximize a global function G in a distributed manner, using a different adaptive computational agent to set each variable of the underlying space. Each agent η is self-interested; it sets its variable to maximize its own function gη. Three factors govern such a distributed algorithm’s performance, related to exploration/exploitation, game theory, and machine learning. We demonstrate how to exploit all three factors by modifying a search algorithm’s exploration stage: rather than random exploration, each coordinate of the search space is now controlled by a separate machine-learning-based “player” engaged in a noncooperative game. Experiments demonstrate that this modification improves simulated annealing (SA) by up to an order of magnitude for bin packing and for a model of an economic process run over an underlying network. These experiments also reveal interesting small-world phenomena.

Regression-assisted deconvolution.

PubMed

McIntyre, Julie; Stefanski, Leonard A

2011-06-30

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean-variance function regression model, where regression errors are normally distributed and independent of the measurement errors. Simulations suggest that the estimator achieves a much lower integrated squared error than the observed-data kernel density estimator when models are correctly specified and the assumption of normal regression errors is met. We illustrate the method using anthropometric measurements of newborns to estimate the density function of newborn length. Copyright © 2011 John Wiley & Sons, Ltd.

Supervised Detection of Anomalous Light Curves in Massive Astronomical Catalogs

NASA Astrophysics Data System (ADS)

Nun, Isadora; Pichara, Karim; Protopapas, Pavlos; Kim, Dae-Won

2014-09-01

The development of synoptic sky surveys has led to a massive amount of data for which resources needed for analysis are beyond human capabilities. In order to process this information and to extract all possible knowledge, machine learning techniques become necessary. Here we present a new methodology to automatically discover unknown variable objects in large astronomical catalogs. With the aim of taking full advantage of all information we have about known objects, our method is based on a supervised algorithm. In particular, we train a random forest classifier using known variability classes of objects and obtain votes for each of the objects in the training set. We then model this voting distribution with a Bayesian network and obtain the joint voting distribution among the training objects. Consequently, an unknown object is considered as an outlier insofar it has a low joint probability. By leaving out one of the classes on the training set, we perform a validity test and show that when the random forest classifier attempts to classify unknown light curves (the class left out), it votes with an unusual distribution among the classes. This rare voting is detected by the Bayesian network and expressed as a low joint probability. Our method is suitable for exploring massive data sets given that the training process is performed offline. We tested our algorithm on 20 million light curves from the MACHO catalog and generated a list of anomalous candidates. After analysis, we divided the candidates into two main classes of outliers: artifacts and intrinsic outliers. Artifacts were principally due to air mass variation, seasonal variation, bad calibration, or instrumental errors and were consequently removed from our outlier list and added to the training set. After retraining, we selected about 4000 objects, which we passed to a post-analysis stage by performing a cross-match with all publicly available catalogs. Within these candidates we identified certain known but rare objects such as eclipsing Cepheids, blue variables, cataclysmic variables, and X-ray sources. For some outliers there was no additional information. Among them we identified three unknown variability types and a few individual outliers that will be followed up in order to perform a deeper analysis.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nun, Isadora; Pichara, Karim; Protopapas, Pavlos

The development of synoptic sky surveys has led to a massive amount of data for which resources needed for analysis are beyond human capabilities. In order to process this information and to extract all possible knowledge, machine learning techniques become necessary. Here we present a new methodology to automatically discover unknown variable objects in large astronomical catalogs. With the aim of taking full advantage of all information we have about known objects, our method is based on a supervised algorithm. In particular, we train a random forest classifier using known variability classes of objects and obtain votes for each ofmore » the objects in the training set. We then model this voting distribution with a Bayesian network and obtain the joint voting distribution among the training objects. Consequently, an unknown object is considered as an outlier insofar it has a low joint probability. By leaving out one of the classes on the training set, we perform a validity test and show that when the random forest classifier attempts to classify unknown light curves (the class left out), it votes with an unusual distribution among the classes. This rare voting is detected by the Bayesian network and expressed as a low joint probability. Our method is suitable for exploring massive data sets given that the training process is performed offline. We tested our algorithm on 20 million light curves from the MACHO catalog and generated a list of anomalous candidates. After analysis, we divided the candidates into two main classes of outliers: artifacts and intrinsic outliers. Artifacts were principally due to air mass variation, seasonal variation, bad calibration, or instrumental errors and were consequently removed from our outlier list and added to the training set. After retraining, we selected about 4000 objects, which we passed to a post-analysis stage by performing a cross-match with all publicly available catalogs. Within these candidates we identified certain known but rare objects such as eclipsing Cepheids, blue variables, cataclysmic variables, and X-ray sources. For some outliers there was no additional information. Among them we identified three unknown variability types and a few individual outliers that will be followed up in order to perform a deeper analysis.« less

Fast Algorithms for Estimating Mixture Parameters

DTIC Science & Technology

1989-08-30

The investigation is a two year project with the first year sponsored by the Army Research Office and the second year by the National Science Foundation (Grant... Science Foundation during the coming year. Keywords: Fast algorithms; Algorithms Mixture Distribution Random Variables. (KR)...numerical testing of the accelerated fixed-point method was completed. The work on relaxation methods will be done under the sponsorship of the National

Modeling contemporary climate profiles of whitebark pine (Pinus albicaulis) and predicting responses to global warming

Treesearch

Marcus V. Warwell; Gerald E. Rehfeldt; Nicholas L. Crookston

2006-01-01

The Random Forests multiple regression tree was used to develop an empirically-based bioclimate model for the distribution of Pinus albicaulis (whitebark pine) in western North America, latitudes 31° to 51° N and longitudes 102° to 125° W. Independent variables included 35 simple expressions of temperature and precipitation and their interactions....

North American vegetation model for land-use planning in a changing climate: A solution to large classification problems

Treesearch

Gerald E. Rehfeldt; Nicholas L. Crookston; Cuauhtemoc Saenz-Romero; Elizabeth M. Campbell

2012-01-01

Data points intensively sampling 46 North American biomes were used to predict the geographic distribution of biomes from climate variables using the Random Forests classification tree. Techniques were incorporated to accommodate a large number of classes and to predict the future occurrence of climates beyond the contemporary climatic range of the biomes. Errors of...

[Randomised study of the relationship between the use of CPRmeter® device and the quality of chest compressions in a simulated cardiopulmonary resuscitation].

PubMed

Calvo-Buey, J A; Calvo-Marcos, D; Marcos-Camina, R M

2016-01-01

To determine whether the use of CPRmeter(®) during the resuscitation manoeuvres, is related to a higher quality of external cardiac massage, as recommended by the International Liaison Committee on Resuscitation (ILCOR). To compare the quality obtained without the use or this, and whether there are differences related to anthropometric, demographic, professional and/or occupational factors. Experimental, open trial performed with life support simulators in a stratified random sample of 88 health workers randomly distributed between groups A (without indications of the device) and B (with them). The homogeneity of their confounding variables was compared, as well as the compressions depth and compressions rate, the proportion of completed release, and distribution of the quality massage variable (according to criteria ILCOR) between the groups. The qualitative variables were analysed with the chi-square test, and quantitative variables with the Student t-test or Mann-Whitney U-test and the association between the variable quality massage variable, and use of the device with the odds ratio. Group A: mean depth 42.1mm (standard deviation 10.1), mean rate 121.3/min (21.6), percentage of complete release 71.2% (36.9). Group B: 51.2mm (5.9) 111.9/min (6.4), 92.9% (10.1) respectively. Odds ratio for quality massage regarding the use of the device was 5.170 (95% CI; 2.060-12.977). The use of CPRmeter(®) device in simulated resuscitations is related to a higher quality of cardiac massage, improving the approach to the ILCOR recommendations, regardless of the characteristics of the participants. They were 83.8% more likely to achieve a quality massage using the device than without it. Copyright © 2015 Elsevier España, S.L.U. y SEEIUC. All rights reserved.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.

PubMed

Shalymov, Dmitry S; Fradkov, Alexander L

2016-01-01

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle

PubMed Central

2016-01-01

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined. PMID:26997886

Multivariate generalized hidden Markov regression models with random covariates: Physical exercise in an elderly population.

PubMed

Punzo, Antonio; Ingrassia, Salvatore; Maruotti, Antonello

2018-04-22

A time-varying latent variable model is proposed to jointly analyze multivariate mixed-support longitudinal data. The proposal can be viewed as an extension of hidden Markov regression models with fixed covariates (HMRMFCs), which is the state of the art for modelling longitudinal data, with a special focus on the underlying clustering structure. HMRMFCs are inadequate for applications in which a clustering structure can be identified in the distribution of the covariates, as the clustering is independent from the covariates distribution. Here, hidden Markov regression models with random covariates are introduced by explicitly specifying state-specific distributions for the covariates, with the aim of improving the recovering of the clusters in the data with respect to a fixed covariates paradigm. The hidden Markov regression models with random covariates class is defined focusing on the exponential family, in a generalized linear model framework. Model identifiability conditions are sketched, an expectation-maximization algorithm is outlined for parameter estimation, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients, as well as of the hidden path parameters, are evaluated through simulation experiments and compared with those of HMRMFCs. The method is applied to physical activity data. Copyright © 2018 John Wiley & Sons, Ltd.

Assessing the significance of global and local correlations under spatial autocorrelation: a nonparametric approach.

PubMed

Viladomat, Júlia; Mazumder, Rahul; McInturff, Alex; McCauley, Douglas J; Hastie, Trevor

2014-06-01

We propose a method to test the correlation of two random fields when they are both spatially autocorrelated. In this scenario, the assumption of independence for the pair of observations in the standard test does not hold, and as a result we reject in many cases where there is no effect (the precision of the null distribution is overestimated). Our method recovers the null distribution taking into account the autocorrelation. It uses Monte-Carlo methods, and focuses on permuting, and then smoothing and scaling one of the variables to destroy the correlation with the other, while maintaining at the same time the initial autocorrelation. With this simulation model, any test based on the independence of two (or more) random fields can be constructed. This research was motivated by a project in biodiversity and conservation in the Biology Department at Stanford University. © 2014, The International Biometric Society.

Achieving flexible low-scattering metasurface based on randomly distribution of meta-elements.

PubMed

Zhao, Junming; Sima, Boyu; Jia, Nan; Wang, Cheng; Zhu, Bo; Jiang, Tian; Feng, Yijun

2016-11-28

In the paper, a flexible low-scattering metasurface is proposed and realized. The layout is composed of similar "#" shaped elements with variable sizes which are randomly distributed along the surface. The various dimensions of the meta-elements lead to different reflection phases for the meta-elements with respect to the incident plane wave, resulting a diffuse reflection surface and exhibiting a broadband backward low-scattering property. In consideration of the flexibility, metasurfaces composed of printed metallic element films attaching with flexible substrate are designed, fabricated and measured in microwave domain. The measurement results show that 10dB radar cross section (RCS) reduction is obtained across the X-band by coating them to either metallic plates or metallic cylinders with only 1/8 working wavelength thickness. We think that the proposed flexible metasurface is applicable to other frequency bands and can be applied in EM stealth technology.

Stochastic transport in the presence of spatial disorder: Fluctuation-induced corrections to homogenization

NASA Astrophysics Data System (ADS)

Russell, Matthew J.; Jensen, Oliver E.; Galla, Tobias

2016-10-01

Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent random variables. We assume particles are removed from the system via first-order kinetics. We analyze the system using a hierarchy of approaches when the sinks are sparsely distributed, including a stochastic homogenization approximation that yields explicit predictions for the extrinsic disorder in the stationary state due to sink strength fluctuations. The extrinsic noise induces long-range spatial correlations in the particle concentration, unlike fluctuations due to the intrinsic noise alone. Additionally, the mean concentration profile, averaged over both intrinsic and extrinsic noise, is elevated compared with the corresponding profile from a uniform sink distribution, showing that the classical homogenization approximation can be a biased estimator of the true mean.

Singular Behavior of the Leading Lyapunov Exponent of a Product of Random {2 × 2} Matrices

NASA Astrophysics Data System (ADS)

Genovese, Giuseppe; Giacomin, Giambattista; Greenblatt, Rafael Leon

2017-05-01

We consider a certain infinite product of random {2 × 2} matrices appearing in the solution of some 1 and 1 + 1 dimensional disordered models in statistical mechanics, which depends on a parameter ɛ > 0 and on a real random variable with distribution {μ}. For a large class of {μ}, we prove the prediction by Derrida and Hilhorst (J Phys A 16:2641, 1983) that the Lyapunov exponent behaves like {C ɛ^{2 α}} in the limit {ɛ \\searrow 0}, where {α \\in (0,1)} and {C > 0} are determined by {μ}. Derrida and Hilhorst performed a two-scale analysis of the integral equation for the invariant distribution of the Markov chain associated to the matrix product and obtained a probability measure that is expected to be close to the invariant one for small {ɛ}. We introduce suitable norms and exploit contractivity properties to show that such a probability measure is indeed close to the invariant one in a sense that implies a suitable control of the Lyapunov exponent.

Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

DOE PAGES

Smallwood, David O.

1997-01-01

The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general casemore » of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.« less

Large-scale variation in subsurface stream biofilms: a cross-regional comparison of metabolic function and community similarity.

PubMed

Findlay, S; Sinsabaugh, R L

2006-10-01

We examined bacterial metabolic activity and community similarity in shallow subsurface stream sediments distributed across three regions of the eastern United States to assess whether there were parallel changes in functional and structural attributes at this large scale. Bacterial growth, oxygen consumption, and a suite of extracellular enzyme activities were assayed to describe functional variability. Community similarity was assessed using randomly amplified polymorphic DNA (RAPD) patterns. There were significant differences in streamwater chemistry, metabolic activity, and bacterial growth among regions with, for instance, twofold higher bacterial production in streams near Baltimore, MD, compared to Hubbard Brook, NH. Five of eight extracellular enzymes showed significant differences among regions. Cluster analyses of individual streams by metabolic variables showed clear groups with significant differences in representation of sites from different regions among groups. Clustering of sites based on randomly amplified polymorphic DNA banding resulted in groups with generally less internal similarity although there were still differences in distribution of regional sites. There was a marginally significant (p = 0.09) association between patterns based on functional and structural variables. There were statistically significant but weak (r2 approximately 30%) associations between landcover and measures of both structure and function. These patterns imply a large-scale organization of biofilm communities and this structure may be imposed by factor(s) such as landcover and covariates such as nutrient concentrations, which are known to also cause differences in macrobiota of stream ecosystems.

Modeling of Bacillus spores: Inactivation and Outgrowth

DTIC Science & Technology

2011-03-01

there has to be a suitable amount of repair enzymes viable to accomplish this. 34 Let ( )r eE t be the enzyme concentration for the spore population...was drawn from a Gaussian fitness distribution with mean, 0E and variance, 0 2 E , 2 0 0 2 0 0 0 0 ( 0 0 ) 2 ( , 1 ) , , 2 0. E E E E E E f e EE ...time progresses, the evolution of the distribution of ( )r eE t will approach the kill threshold. Since 0E is a random variable, ( )r eE t is also a

Probabilistic analysis of bladed turbine disks and the effect of mistuning

NASA Technical Reports Server (NTRS)

Shah, A. R.; Nagpal, V. K.; Chamis, Christos C.

1990-01-01

Probabilistic assessment of the maximum blade response on a mistuned rotor disk is performed using the computer code NESSUS. The uncertainties in natural frequency, excitation frequency, amplitude of excitation and damping are included to obtain the cumulative distribution function (CDF) of blade responses. Advanced mean value first order analysis is used to compute CDF. The sensitivities of different random variables are identified. Effect of the number of blades on a rotor on mistuning is evaluated. It is shown that the uncertainties associated with the forcing function parameters have significant effect on the response distribution of the bladed rotor.

Probabilistic analysis of bladed turbine disks and the effect of mistuning

NASA Technical Reports Server (NTRS)

Shah, Ashwin; Nagpal, V. K.; Chamis, C. C.

1990-01-01

Probabilistic assessment of the maximum blade response on a mistuned rotor disk is performed using the computer code NESSUS. The uncertainties in natural frequency, excitation frequency, amplitude of excitation and damping have been included to obtain the cumulative distribution function (CDF) of blade responses. Advanced mean value first order analysis is used to compute CDF. The sensitivities of different random variables are identified. Effect of the number of blades on a rotor on mistuning is evaluated. It is shown that the uncertainties associated with the forcing function parameters have significant effect on the response distribution of the bladed rotor.

Exact PDF equations and closure approximations for advective-reactive transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

NASA Astrophysics Data System (ADS)

Kang, Peter K.; Dentz, Marco; Le Borgne, Tanguy; Lee, Seunghak; Juanes, Ruben

2017-08-01

We investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that-even if the Eulerian fluid velocity is steady-the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes.

Monte Carlo calibration of avalanches described as Coulomb fluid flows.

PubMed

Ancey, Christophe

2005-07-15

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Since the bulk friction coefficient cannot be measured directly in the field, the friction coefficient must be calibrated by adjusting the model outputs to closely match the recorded data. Field data are readily available but are of poor quality and accuracy. We used Bayesian inference techniques to specify the model uncertainty relative to data uncertainty and to robustly and efficiently solve the inverse problem. A sample of 173 events taken from seven paths in the French Alps was used. The first analysis showed that the friction coefficient behaved as a random variable with a smooth and bell-shaped empirical distribution function. Evidence was provided that the friction coefficient varied with the avalanche volume, but any attempt to adjust a one-to-one relationship relating friction to volume produced residual errors that could be as large as three times the maximum uncertainty of field data. A tentative universal friction law is proposed: the friction coefficient is a random variable, the distribution of which can be approximated by a normal distribution with a volume-dependent mean.

Are all data created equal?--Exploring some boundary conditions for a lazy intuitive statistician.

PubMed

Lindskog, Marcus; Winman, Anders

2014-01-01

The study investigated potential effects of the presentation order of numeric information on retrospective subjective judgments of descriptive statistics of this information. The studies were theoretically motivated by the assumption in the naïve sampling model of independence between temporal encoding order of data in long-term memory and retrieval probability (i.e. as implied by a "random sampling" from memory metaphor). In Experiment 1, participants experienced Arabic numbers that varied in distribution shape/variability between the first and the second half of the information sequence. Results showed no effects of order on judgments of mean, variability or distribution shape. To strengthen the interpretation of these results, Experiment 2 used a repeated judgment procedure, with an initial judgment occurring prior to the change in distribution shape of the information half-way through data presentation. The results of Experiment 2 were in line with those from Experiment 1, and in addition showed that the act of making explicit judgments did not impair accuracy of later judgments, as would be suggested by an anchoring and insufficient adjustment strategy. Overall, the results indicated that participants were very responsive to the properties of the data while at the same time being more or less immune to order effects. The results were interpreted as being in line with the naïve sampling models in which values are stored as exemplars and sampled randomly from long-term memory.

Distribution of runup heights of the December 26, 2004 tsunami in the Indian Ocean

NASA Astrophysics Data System (ADS)

Choi, Byung Ho; Hong, Sung Jin; Pelinovsky, Efim

2006-07-01

A massive earthquake with magnitude 9.3 occurred on December 26, 2004 off the northern Sumatra generated huge tsunami waves affected many coastal countries in the Indian Ocean. A number of field surveys have been performed after this tsunami event; in particular, several surveys in the south/east coast of India, Andaman and Nicobar Islands, Sri Lanka, Sumatra, Malaysia, and Thailand have been organized by the Korean Society of Coastal and Ocean Engineers from January to August 2005. Spatial distribution of the tsunami runup is used to analyze the distribution function of the wave heights on different coasts. Theoretical interpretation of this distribution is associated with random coastal bathymetry and coastline led to the log-normal functions. Observed data also are in a very good agreement with log-normal distribution confirming the important role of the variable ocean bathymetry in the formation of the irregular wave height distribution along the coasts.

The modelling of carbon-based supercapacitors: Distributions of time constants and Pascal Equivalent Circuits

NASA Astrophysics Data System (ADS)

Fletcher, Stephen; Kirkpatrick, Iain; Dring, Roderick; Puttock, Robert; Thring, Rob; Howroyd, Simon

2017-03-01

Supercapacitors are an emerging technology with applications in pulse power, motive power, and energy storage. However, their carbon electrodes show a variety of non-ideal behaviours that have so far eluded explanation. These include Voltage Decay after charging, Voltage Rebound after discharging, and Dispersed Kinetics at long times. In the present work, we establish that a vertical ladder network of RC components can reproduce all these puzzling phenomena. Both software and hardware realizations of the network are described. In general, porous carbon electrodes contain random distributions of resistance R and capacitance C, with a wider spread of log R values than log C values. To understand what this implies, a simplified model is developed in which log R is treated as a Gaussian random variable while log C is treated as a constant. From this model, a new family of equivalent circuits is developed in which the continuous distribution of log R values is replaced by a discrete set of log R values drawn from a geometric series. We call these Pascal Equivalent Circuits. Their behaviour is shown to resemble closely that of real supercapacitors. The results confirm that distributions of RC time constants dominate the behaviour of real supercapacitors.

Incorporating imperfect detection into joint models of communites: A response to Warton et al.

USGS Publications Warehouse

Beissinger, Steven R.; Iknayan, Kelly J.; Guillera-Arroita, Gurutzeta; Zipkin, Elise; Dorazio, Robert; Royle, Andy; Kery, Marc

2016-01-01

Warton et al. [1] advance community ecology by describing a statistical framework that can jointly model abundances (or distributions) across many taxa to quantify how community properties respond to environmental variables. This framework specifies the effects of both measured and unmeasured (latent) variables on the abundance (or occurrence) of each species. Latent variables are random effects that capture the effects of both missing environmental predictors and correlations in parameter values among different species. As presented in Warton et al., however, the joint modeling framework fails to account for the common problem of detection or measurement errors that always accompany field sampling of abundance or occupancy, and are well known to obscure species- and community-level inferences.

Mapping SOC (Soil Organic Carbon) using LiDAR-derived vegetation indices in a random forest regression model

NASA Astrophysics Data System (ADS)

Will, R. M.; Glenn, N. F.; Benner, S. G.; Pierce, J. L.; Spaete, L.; Li, A.

2015-12-01

Quantifying SOC (Soil Organic Carbon) storage in complex terrain is challenging due to high spatial variability. Generally, the challenge is met by transforming point data to the entire landscape using surrogate, spatially-distributed, variables like elevation or precipitation. In many ecosystems, remotely sensed information on above-ground vegetation (e.g. NDVI) is a good predictor of below-ground carbon stocks. In this project, we are attempting to improve this predictive method by incorporating LiDAR-derived vegetation indices. LiDAR provides a mechanism for improved characterization of aboveground vegetation by providing structural parameters such as vegetation height and biomass. In this study, a random forest model is used to predict SOC using a suite of LiDAR-derived vegetation indices as predictor variables. The Reynolds Creek Experimental Watershed (RCEW) is an ideal location for a study of this type since it encompasses a strong elevation/precipitation gradient that supports lower biomass sagebrush ecosystems at low elevations and forests with more biomass at higher elevations. Sagebrush ecosystems composed of Wyoming, Low and Mountain Sagebrush have SOC values ranging from .4 to 1% (top 30 cm), while higher biomass ecosystems composed of aspen, juniper and fir have SOC values approaching 4% (top 30 cm). Large differences in SOC have been observed between canopy and interspace locations and high resolution vegetation information is likely to explain plot scale variability in SOC. Mapping of the SOC reservoir will help identify underlying controls on SOC distribution and provide insight into which processes are most important in determining SOC in semi-arid mountainous regions. In addition, airborne LiDAR has the potential to characterize vegetation communities at a high resolution and could be a tool for improving estimates of SOC at larger scales.

Low within- and between-day variability in exposure to new insulin glargine 300 U/ml.

PubMed

Becker, R H A; Nowotny, I; Teichert, L; Bergmann, K; Kapitza, C

2015-03-01

To characterize the variability in exposure and metabolic effect of insulin glargine 300 U/ml (Gla-300) at steady state in people with type 1 diabetes (T1DM). A total of 50 participants with T1DM underwent two 24-h euglycaemic clamps in steady-state conditions after six once-daily administrations of 0.4 U/kg Gla-300 in a double-blind, randomized, two-treatment, two-period, crossover clamp study. Participants were randomized to receive Gla-300 as a standard cartridge formulation in the first treatment period, and as a formulation with enhanced stability through polysorbate-20 addition in the second treatment period, or vice versa. This design allowed the assessment of bioequivalence between formulations and, subsequently, within- and between-day variability. The cumulative exposure and effect of Gla-300 developed linearly over 24 h, and were evenly distributed across 6- and 12-h intervals. Diurnal fluctuation in exposure (within-day variability) was low; the peak-to-trough ratio of insulin concentration profiles was <2, and both the swing and peak-to-trough fluctuation were <1. Day-to-day reproducibility of exposure was high: the between-day within-subject coefficients of variation for total systemic exposure (area under the serum insulin glargine concentration time curve from time 0 to 24 h after dosing) and maximum insulin concentration were 17.4% [95% confidence interval (CI) 15-21] and 33.4% (95% CI 28-41), respectively. Reproducibility of the metabolic effect was lower than that of exposure. Gla-300 provides predictable, evenly distributed 24-h coverage as a result of low fluctuation and high reproducibility in insulin exposure, and appears suitable for effective basal insulin use. © 2014 The Authors. Diabetes, Obesity and Metabolism published by John Wiley & Sons Ltd.

Sampling design for spatially distributed hydrogeologic and environmental processes

USGS Publications Warehouse

Christakos, G.; Olea, R.A.

1992-01-01

A methodology for the design of sampling networks over space is proposed. The methodology is based on spatial random field representations of nonhomogeneous natural processes, and on optimal spatial estimation techniques. One of the most important results of random field theory for physical sciences is its rationalization of correlations in spatial variability of natural processes. This correlation is extremely important both for interpreting spatially distributed observations and for predictive performance. The extent of site sampling and the types of data to be collected will depend on the relationship of subsurface variability to predictive uncertainty. While hypothesis formulation and initial identification of spatial variability characteristics are based on scientific understanding (such as knowledge of the physics of the underlying phenomena, geological interpretations, intuition and experience), the support offered by field data is statistically modelled. This model is not limited by the geometric nature of sampling and covers a wide range in subsurface uncertainties. A factorization scheme of the sampling error variance is derived, which possesses certain atttactive properties allowing significant savings in computations. By means of this scheme, a practical sampling design procedure providing suitable indices of the sampling error variance is established. These indices can be used by way of multiobjective decision criteria to obtain the best sampling strategy. Neither the actual implementation of the in-situ sampling nor the solution of the large spatial estimation systems of equations are necessary. The required values of the accuracy parameters involved in the network design are derived using reference charts (readily available for various combinations of data configurations and spatial variability parameters) and certain simple yet accurate analytical formulas. Insight is gained by applying the proposed sampling procedure to realistic examples related to sampling problems in two dimensions. ?? 1992.

Comparison modeling for alpine vegetation distribution in an arid area.

PubMed

Zhou, Jihua; Lai, Liming; Guan, Tianyu; Cai, Wetao; Gao, Nannan; Zhang, Xiaolong; Yang, Dawen; Cong, Zhentao; Zheng, Yuanrun

2016-07-01

Mapping and modeling vegetation distribution are fundamental topics in vegetation ecology. With the rise of powerful new statistical techniques and GIS tools, the development of predictive vegetation distribution models has increased rapidly. However, modeling alpine vegetation with high accuracy in arid areas is still a challenge because of the complexity and heterogeneity of the environment. Here, we used a set of 70 variables from ASTER GDEM, WorldClim, and Landsat-8 OLI (land surface albedo and spectral vegetation indices) data with decision tree (DT), maximum likelihood classification (MLC), and random forest (RF) models to discriminate the eight vegetation groups and 19 vegetation formations in the upper reaches of the Heihe River Basin in the Qilian Mountains, northwest China. The combination of variables clearly discriminated vegetation groups but failed to discriminate vegetation formations. Different variable combinations performed differently in each type of model, but the most consistently important parameter in alpine vegetation modeling was elevation. The best RF model was more accurate for vegetation modeling compared with the DT and MLC models for this alpine region, with an overall accuracy of 75 % and a kappa coefficient of 0.64 verified against field point data and an overall accuracy of 65 % and a kappa of 0.52 verified against vegetation map data. The accuracy of regional vegetation modeling differed depending on the variable combinations and models, resulting in different classifications for specific vegetation groups.

Modeling pattern in collections of parameters

USGS Publications Warehouse

Link, W.A.

1999-01-01

Wildlife management is increasingly guided by analyses of large and complex datasets. The description of such datasets often requires a large number of parameters, among which certain patterns might be discernible. For example, one may consider a long-term study producing estimates of annual survival rates; of interest is the question whether these rates have declined through time. Several statistical methods exist for examining pattern in collections of parameters. Here, I argue for the superiority of 'random effects models' in which parameters are regarded as random variables, with distributions governed by 'hyperparameters' describing the patterns of interest. Unfortunately, implementation of random effects models is sometimes difficult. Ultrastructural models, in which the postulated pattern is built into the parameter structure of the original data analysis, are approximations to random effects models. However, this approximation is not completely satisfactory: failure to account for natural variation among parameters can lead to overstatement of the evidence for pattern among parameters. I describe quasi-likelihood methods that can be used to improve the approximation of random effects models by ultrastructural models.

Record statistics of a strongly correlated time series: random walks and Lévy flights

NASA Astrophysics Data System (ADS)

Godrèche, Claude; Majumdar, Satya N.; Schehr, Grégory

2017-08-01

We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few years, it was indeed realized that random walks are a very useful ‘laboratory’ to test the effects of correlations on the record statistics. We start with the simple one-dimensional random walk with symmetric jumps (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time between two successive record breaking events. Then we review the results that were obtained for a wide variety of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of multiple independent random walkers. Finally, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.

Integrating multiple distribution models to guide conservation efforts of an endangered toad

USGS Publications Warehouse

Treglia, Michael L.; Fisher, Robert N.; Fitzgerald, Lee A.

2015-01-01

Species distribution models are used for numerous purposes such as predicting changes in species’ ranges and identifying biodiversity hotspots. Although implications of distribution models for conservation are often implicit, few studies use these tools explicitly to inform conservation efforts. Herein, we illustrate how multiple distribution models developed using distinct sets of environmental variables can be integrated to aid in identification sites for use in conservation. We focus on the endangered arroyo toad (Anaxyrus californicus), which relies on open, sandy streams and surrounding floodplains in southern California, USA, and northern Baja California, Mexico. Declines of the species are largely attributed to habitat degradation associated with vegetation encroachment, invasive predators, and altered hydrologic regimes. We had three main goals: 1) develop a model of potential habitat for arroyo toads, based on long-term environmental variables and all available locality data; 2) develop a model of the species’ current habitat by incorporating recent remotely-sensed variables and only using recent locality data; and 3) integrate results of both models to identify sites that may be employed in conservation efforts. We used a machine learning technique, Random Forests, to develop the models, focused on riparian zones in southern California. We identified 14.37% and 10.50% of our study area as potential and current habitat for the arroyo toad, respectively. Generally, inclusion of remotely-sensed variables reduced modeled suitability of sites, thus many areas modeled as potential habitat were not modeled as current habitat. We propose such sites could be made suitable for arroyo toads through active management, increasing current habitat by up to 67.02%. Our general approach can be employed to guide conservation efforts of virtually any species with sufficient data necessary to develop appropriate distribution models.

Low Probability of Intercept Waveforms via Intersymbol Dither Performance Under Multiple Conditions

DTIC Science & Technology

2009-03-01

United States Air Force, Department of Defense, or the United States Government . AFIT/GE/ENG/09-23 Low Probability of Intercept Waveforms via...21 D random variable governing the distribution of dither values 21 p (ct) D (t) probability density function of the...potential performance loss of a non-cooperative receiver compared to a cooperative receiver designed to account for ISI and multipath. 1.3 Thesis

Low Probability of Intercept Waveforms via Intersymbol Dither Performance Under Multipath Conditions

DTIC Science & Technology

2009-03-01

United States Air Force, Department of Defense, or the United States Government . AFIT/GE/ENG/09-23 Low Probability of Intercept Waveforms via...21 D random variable governing the distribution of dither values 21 p (ct) D (t) probability density function of the...potential performance loss of a non-cooperative receiver compared to a cooperative receiver designed to account for ISI and multipath. 1.3 Thesis

Network Design for Reliability and Resilience to Attack

DTIC Science & Technology

2014-03-01

attacker can destroy n arcs in the network SPNI Shortest-Path Network-Interdiction problem TSP Traveling Salesman Problem UB upper bound UKR Ukraine...elimination from the traveling salesman problem (TSP). Literature calls a walk that does not contain a cycle a path [19]. The objective function in...arc lengths as random variables with known probability distributions. The m-median problem seeks to design a network with minimum average travel cost

Factors influencing the at-sea distribution of Cassin's Auklets (Ptychoramphus aleuticus) that breed in the Channel Islands, California

USGS Publications Warehouse

Adams, Josh; Takekawa, John Y.; Carter, Harry R.; Yee, Julie L.

2010-01-01

We used radiotelemetry to evaluate at-sea habitat use by Cassin's Auklets (Ptychoramphus aleuticus) that bred at Prince Island, off southern California, from 1999 through 2001. We used logistic regression to compare paired radiotelemetry (presence) with random (pseudo-absence) location-associated habitat variables derived from (1) satellite remote-sensing of sea surface temperature and chlorophyll-a concentration and (2) bathymetry. Compared with random locations within their foraging area and after controlling for distance to colony, odds ratios indicated that Cassin's Auklets with dependent young occurred in relatively shallower, warmer, and chlorophyll-rich water associated with chlorophyll fronts near the insular shelf break. These oceanographic features characterize habitats that support key euphausiid prey (e.g., Thysanoessa spinifera) and also other krill predators. Radiotelemetry combined with satellite remote-sensing of the ocean provides an alternative to vessel-based surveys for evaluating seabird foraging habitats. In the absence of information on the actual distribution, abundance, and, hence, availability of Zooplankton prey for seabirds, environmental factors can serve as proxies to help elucidate distributional patterns of seabirds at sea.

Coverage dependent molecular assembly of anthraquinone on Au(111)

NASA Astrophysics Data System (ADS)

DeLoach, Andrew S.; Conrad, Brad R.; Einstein, T. L.; Dougherty, Daniel B.

2017-11-01

A scanning tunneling microscopy study of anthraquinone (AQ) on the Au(111) surface shows that the molecules self-assemble into several structures depending on the local surface coverage. At high coverages, a close-packed saturated monolayer is observed, while at low coverages, mobile surface molecules coexist with stable chiral hexamer clusters. At intermediate coverages, a disordered 2D porous network interlinking close-packed islands is observed in contrast to the giant honeycomb networks observed for the same molecule on Cu(111). This difference verifies the predicted extreme sensitivity [J. Wyrick et al., Nano Lett. 11, 2944 (2011)] of the pore network to small changes in the surface electronic structure. Quantitative analysis of the 2D pore network reveals that the areas of the vacancy islands are distributed log-normally. Log-normal distributions are typically associated with the product of random variables (multiplicative noise), and we propose that the distribution of pore sizes for AQ on Au(111) originates from random linear rate constants for molecules to either desorb from the surface or detach from the region of a nucleated pore.

Coverage dependent molecular assembly of anthraquinone on Au(111).

PubMed

DeLoach, Andrew S; Conrad, Brad R; Einstein, T L; Dougherty, Daniel B

2017-11-14

A scanning tunneling microscopy study of anthraquinone (AQ) on the Au(111) surface shows that the molecules self-assemble into several structures depending on the local surface coverage. At high coverages, a close-packed saturated monolayer is observed, while at low coverages, mobile surface molecules coexist with stable chiral hexamer clusters. At intermediate coverages, a disordered 2D porous network interlinking close-packed islands is observed in contrast to the giant honeycomb networks observed for the same molecule on Cu(111). This difference verifies the predicted extreme sensitivity [J. Wyrick et al., Nano Lett. 11, 2944 (2011)] of the pore network to small changes in the surface electronic structure. Quantitative analysis of the 2D pore network reveals that the areas of the vacancy islands are distributed log-normally. Log-normal distributions are typically associated with the product of random variables (multiplicative noise), and we propose that the distribution of pore sizes for AQ on Au(111) originates from random linear rate constants for molecules to either desorb from the surface or detach from the region of a nucleated pore.

On predicting receptivity to surface roughness in a compressible infinite swept wing boundary layer

NASA Astrophysics Data System (ADS)

Thomas, Christian; Mughal, Shahid; Ashworth, Richard

2017-03-01

The receptivity of crossflow disturbances on an infinite swept wing is investigated using solutions of the adjoint linearised Navier-Stokes equations. The adjoint based method for predicting the magnitude of stationary disturbances generated by randomly distributed surface roughness is described, with the analysis extended to include both surface curvature and compressible flow effects. Receptivity is predicted for a broad spectrum of spanwise wavenumbers, variable freestream Reynolds numbers, and subsonic Mach numbers. Curvature is found to play a significant role in the receptivity calculations, while compressible flow effects are only found to marginally affect the initial size of the crossflow instability. A Monte Carlo type analysis is undertaken to establish the mean amplitude and variance of crossflow disturbances generated by the randomly distributed surface roughness. Mean amplitudes are determined for a range of flow parameters that are maximised for roughness distributions containing a broad spectrum of roughness wavelengths, including those that are most effective in generating stationary crossflow disturbances. A control mechanism is then developed where the short scale roughness wavelengths are damped, leading to significant reductions in the receptivity amplitude.

Ranking of patient and surgeons' perspectives for endpoints in randomized controlled trials--lessons learned from the POVATI trial [ISRCTN 60734227].

PubMed

Fischer, Lars; Deckert, Andreas; Diener, Markus K; Zimmermann, Johannes B; Büchler, Markus W; Seiler, Christoph M

2011-10-01

Surgical trials focus mainly on mortality and morbidity rates, which may be not the most important endpoints from the patient's perspective. Evaluation of expectations and needs of patients enrolled in clinical trials can be analyzed using a procedure called ranking. Within the Postsurgical Pain Outcome of Vertical and Transverse Abdominal Incision randomized trial (POVATI), the perspectives of participating patients and surgeons were assessed as well as the influence of the surgical intervention on patients' needs. All included patients of the POVATI trial were asked preoperatively and postoperatively to rank predetermined outcome variables concerning the upcoming surgical procedure (e.g., pain, complication, cosmetic result) hierarchically according to their importance. Preoperatively, the surgeons were asked to do the same. One hundred eighty two out of 200 randomized patients (71 females, 111 males; mean age 59 years) returned the ranking questionnaire preoperatively and 152 patients (67 females, 85 males; mean age 60 years) on the day of discharge. There were no differences between the two groups with respect to the distribution of ranking variables (p > 0.05). Thirty-five surgeons (7 residents, 6 fellows, and 22 consultants) completed the same ranking questionnaire. The order of the four most important ranking variables for both patients and surgeons were death, avoiding of postoperative complications, avoiding of intraoperative complications, and pain. Surgeons ranked the variable "cosmetic result" significantly as more important compared to patients (p = 0.034, Fisher's exact test). Patients and surgeons did not differ in ranking predetermined outcomes in the POVATI trial. Only the variable "cosmetic result" is significantly more important from the surgeon's than from the patient's perspective. Ranking of outcomes might be a beneficial tool and can be a proper addition to RCTs.

Ising Critical Behavior of Inhomogeneous Curie-Weiss Models and Annealed Random Graphs

NASA Astrophysics Data System (ADS)

Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa

2016-11-01

We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant {J_{ij}(β)} for the edge {ij} on the complete graph is given by {J_{ij}(β)=β w_iw_j/( {sum_{kin[N]}w_k})}. We call the product form of these couplings the rank-1 inhomogeneous Curie-Weiss model. This model also arises [with inverse temperature {β} replaced by {sinh(β)} ] from the annealed Ising model on the generalized random graph. We assume that the vertex weights {(w_i)_{iin[N]}} are regular, in the sense that their empirical distribution converges and the second moment converges as well. We identify the critical temperatures and exponents for these models, as well as a non-classical limit theorem for the total spin at the critical point. These depend sensitively on the number of finite moments of the weight distribution. When the fourth moment of the weight distribution converges, then the critical behavior is the same as on the (homogeneous) Curie-Weiss model, so that the inhomogeneity is weak. When the fourth moment of the weights converges to infinity, and the weights satisfy an asymptotic power law with exponent {τ} with {τin(3,5)}, then the critical exponents depend sensitively on {τ}. In addition, at criticality, the total spin {S_N} satisfies that {S_N/N^{(τ-2)/(τ-1)}} converges in law to some limiting random variable whose distribution we explicitly characterize.

Integrated Logistics Support Analysis of the International Space Station Alpha, Background and Summary of Mathematical Modeling and Failure Density Distributions Pertaining to Maintenance Time Dependent Parameters

NASA Technical Reports Server (NTRS)

Sepehry-Fard, F.; Coulthard, Maurice H.

1995-01-01

The process of predicting the values of maintenance time dependent variable parameters such as mean time between failures (MTBF) over time must be one that will not in turn introduce uncontrolled deviation in the results of the ILS analysis such as life cycle costs, spares calculation, etc. A minor deviation in the values of the maintenance time dependent variable parameters such as MTBF over time will have a significant impact on the logistics resources demands, International Space Station availability and maintenance support costs. There are two types of parameters in the logistics and maintenance world: a. Fixed; b. Variable Fixed parameters, such as cost per man hour, are relatively easy to predict and forecast. These parameters normally follow a linear path and they do not change randomly. However, the variable parameters subject to the study in this report such as MTBF do not follow a linear path and they normally fall within the distribution curves which are discussed in this publication. The very challenging task then becomes the utilization of statistical techniques to accurately forecast the future non-linear time dependent variable arisings and events with a high confidence level. This, in turn, shall translate in tremendous cost savings and improved availability all around.

An Entropy-Based Measure of Dependence between Two Groups of Random Variables. Research Report. ETS RR-07-20

ERIC Educational Resources Information Center

Kong, Nan

2007-01-01

In multivariate statistics, the linear relationship among random variables has been fully explored in the past. This paper looks into the dependence of one group of random variables on another group of random variables using (conditional) entropy. A new measure, called the K-dependence coefficient or dependence coefficient, is defined using…

Stress and reliability analyses of multilayered composite cylinder under thermal and mechanical loads

NASA Astrophysics Data System (ADS)

Wang, Xiaohua

The coupling resulting from the mutual influence of material thermal and mechanical parameters is examined in the thermal stress analysis of a multilayered isotropic composite cylinder subjected to sudden axisymmetric external and internal temperature. The method of complex frequency response functions together with the Fourier transform technique is utilized. Because the coupling parameters for some composite materials, such as carbon-carbon, are very small, the effect of coupling is neglected in the orthotropic thermal stress analysis. The stress distributions in multilayered orthotropic cylinders subjected to sudden axisymmetric temperature loading combined with dynamic pressure as well as asymmetric temperature loading are also obtained. The method of Fourier series together with the Laplace transform is utilized in solving the heat conduction equation and thermal stress analysis. For brittle materials, like carbon-carbon composites, the strength variability is represented by two or three parameter Weibull distributions. The 'weakest link' principle which takes into account both the carbon-carbon composite cylinders. The complex frequency response analysis is performed on a multilayered orthotropic cylinder under asymmetrical thermal load. Both deterministic and random thermal stress and reliability analyses can be based on the results of this frequency response analysis. The stress and displacement distributions and reliability of rocket motors under static or dynamic line loads are analyzed by an elasticity approach. Rocket motors are modeled as long hollow multilayered cylinders with an air core, a thick isotropic propellant inner layer and a thin orthotropic kevlar-epoxy case. The case is treated as a single orthotropic layer or a ten layered orthotropic structure. Five material properties and the load are treated as random variable with normal distributions when the reliability of the rocket motor is analyzed by the first-order, second-moment method (FOSM).

Safety assessment of a shallow foundation using the random finite element method

NASA Astrophysics Data System (ADS)

Zaskórski, Łukasz; Puła, Wojciech

2015-04-01

A complex structure of soil and its random character are reasons why soil modeling is a cumbersome task. Heterogeneity of soil has to be considered even within a homogenous layer of soil. Therefore an estimation of shear strength parameters of soil for the purposes of a geotechnical analysis causes many problems. In applicable standards (Eurocode 7) there is not presented any explicit method of an evaluation of characteristic values of soil parameters. Only general guidelines can be found how these values should be estimated. Hence many approaches of an assessment of characteristic values of soil parameters are presented in literature and can be applied in practice. In this paper, the reliability assessment of a shallow strip footing was conducted using a reliability index β. Therefore some approaches of an estimation of characteristic values of soil properties were compared by evaluating values of reliability index β which can be achieved by applying each of them. Method of Orr and Breysse, Duncan's method, Schneider's method, Schneider's method concerning influence of fluctuation scales and method included in Eurocode 7 were examined. Design values of the bearing capacity based on these approaches were referred to the stochastic bearing capacity estimated by the random finite element method (RFEM). Design values of the bearing capacity were conducted for various widths and depths of a foundation in conjunction with design approaches DA defined in Eurocode. RFEM was presented by Griffiths and Fenton (1993). It combines deterministic finite element method, random field theory and Monte Carlo simulations. Random field theory allows to consider a random character of soil parameters within a homogenous layer of soil. For this purpose a soil property is considered as a separate random variable in every element of a mesh in the finite element method with proper correlation structure between points of given area. RFEM was applied to estimate which theoretical probability distribution fits the empirical probability distribution of bearing capacity basing on 3000 realizations. Assessed probability distribution was applied to compute design values of the bearing capacity and related reliability indices β. Conducted analysis were carried out for a cohesion soil. Hence a friction angle and a cohesion were defined as a random parameters and characterized by two dimensional random fields. A friction angle was described by a bounded distribution as it differs within limited range. While a lognormal distribution was applied in case of a cohesion. Other properties - Young's modulus, Poisson's ratio and unit weight were assumed as deterministic values because they have negligible influence on the stochastic bearing capacity. Griffiths D. V., & Fenton G. A. (1993). Seepage beneath water retaining structures founded on spatially random soil. Géotechnique, 43(6), 577-587.

Non-equilibrium Green's functions study of discrete dopants variability on an ultra-scaled FinFET

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valin, R., E-mail: r.valinferreiro@swansea.ac.uk; Martinez, A., E-mail: a.e.Martinez@swansea.ac.uk; Barker, J. R., E-mail: john.barker@glasgow.ac.uk

In this paper, we study the effect of random discrete dopants on the performance of a 6.6 nm channel length silicon FinFET. The discrete dopants have been distributed randomly in the source/drain region of the device. Due to the small dimensions of the FinFET, a quantum transport formalism based on the non-equilibrium Green's functions has been deployed. The transfer characteristics for several devices that differ in location and number of dopants have been calculated. Our results demonstrate that discrete dopants modify the effective channel length and the height of the source/drain barrier, consequently changing the channel control of the charge. Thismore » effect becomes more significant at high drain bias. As a consequence, there is a strong effect on the variability of the on-current, off-current, sub-threshold slope, and threshold voltage. Finally, we have also calculated the mean and standard deviation of these parameters to quantify their variability. The obtained results show that the variability at high drain bias is 1.75 larger than at low drain bias. However, the variability of the on-current, off-current, and sub-threshold slope remains independent of the drain bias. In addition, we have found that a large source to drain current by tunnelling current occurs at low gate bias.« less

Penetration and Growth Rates of Mobile Phones in Developing Countries: An Analytical Classification

PubMed Central

2010-01-01

This brief paper uses a simple arithmetic framework to classify and explain the performance of developing countries in closing the absolute digital divide. Four categories are created on the basis of two variables, namely, the penetration and rate of growth of mobile phones. The paper answers questions such as: Which countries do well and badly on both variables? Are the countries in these categories drawn from specific regions or similar income levels or is the distribution more random? How can similar countries from the same region appear in two diametrically opposite categories? What does this imply for policy? PMID:20835391

Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing

NASA Astrophysics Data System (ADS)

Zhang, Fode; Shi, Yimin; Wang, Ruibing

2017-02-01

In the information geometry suggested by Amari (1985) and Amari et al. (1987), a parametric statistical model can be regarded as a differentiable manifold with the parameter space as a coordinate system. Note that the q-exponential distribution plays an important role in Tsallis statistics (see Tsallis, 2009), this paper investigates the geometry of the q-exponential distribution with dependent competing risks and accelerated life testing (ALT). A copula function based on the q-exponential function, which can be considered as the generalized Gumbel copula, is discussed to illustrate the structure of the dependent random variable. Employing two iterative algorithms, simulation results are given to compare the performance of estimations and levels of association under different hybrid progressively censoring schemes (HPCSs).

Universal statistics of selected values

NASA Astrophysics Data System (ADS)

Smerlak, Matteo; Youssef, Ahmed

2017-03-01

Selection, the tendency of some traits to become more frequent than others under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social phenomena. Yet a general theory of selection, analogous to the Fisher-Tippett-Gnedenko theory of extreme events, is lacking. Here we introduce a probabilistic definition of selection and show that selected values are attracted to a universal family of limiting distributions which generalize the log-normal distribution. The universality classes and scaling exponents are determined by the tail thickness of the random variable under selection. Our results provide a possible explanation for skewed distributions observed in diverse contexts where selection plays a key role, from molecular biology to agriculture and sport.

Randomized central limit theorems: A unified theory.

PubMed

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

Randomized central limit theorems: A unified theory

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

Informed herbivore movement and interplant communication determine the effects of induced resistance in an individual-based model.

PubMed

Rubin, Ilan N; Ellner, Stephen P; Kessler, André; Morrell, Kimberly A

2015-09-01

1. Plant induced resistance to herbivory affects the spatial distribution of herbivores, as well as their performance. In recent years, theories regarding the benefit to plants of induced resistance have shifted from ideas of optimal resource allocation towards a more eclectic set of theories that consider spatial and temporal plant variability and the spatial distribution of herbivores among plants. However, consensus is lacking on whether induced resistance causes increased herbivore aggregation or increased evenness, as both trends have been experimentally documented. 2. We created a spatial individual-based model that can describe many plant-herbivore systems with induced resistance, in order to analyse how different aspects of induced resistance might affect herbivore distribution, and the total damage to a plant population, during a growing season. 3. We analyse the specific effects on herbivore aggregation of informed herbivore movement (preferential movement to less-damaged plants) and of information transfer between plants about herbivore attacks, in order to identify mechanisms driving both aggregation and evenness. We also investigate how the resulting herbivore distributions affect the total damage to plants and aggregation of damage. 4. Even, random and aggregated herbivore distributions can all occur in our model with induced resistance. Highest levels of aggregation occurred in the models with informed herbivore movement, and the most even distributions occurred when the average number of herbivores per plant was low. With constitutive resistance, only random distributions occur. Damage to plants was spatially correlated, unless plants recover very quickly from damage; herbivore spatial autocorrelation was always weak. 5. Our model and results provide a simple explanation for the apparent conflict between experimental results, indicating that both increased aggregation and increased evenness of herbivores can result from induced resistance. We demonstrate that information transfer from plants to herbivores, and from plants to neighbouring plants, can both be major factors in determining non-random herbivore distributions. © 2015 The Authors. Journal of Animal Ecology © 2015 British Ecological Society.

Multi-hazard Assessment and Scenario Toolbox (MhAST): A Framework for Analyzing Compounding Effects of Multiple Hazards

NASA Astrophysics Data System (ADS)

Sadegh, M.; Moftakhari, H.; AghaKouchak, A.

2017-12-01

Many natural hazards are driven by multiple forcing variables, and concurrence/consecutive extreme events significantly increases risk of infrastructure/system failure. It is a common practice to use univariate analysis based upon a perceived ruling driver to estimate design quantiles and/or return periods of extreme events. A multivariate analysis, however, permits modeling simultaneous occurrence of multiple forcing variables. In this presentation, we introduce the Multi-hazard Assessment and Scenario Toolbox (MhAST) that comprehensively analyzes marginal and joint probability distributions of natural hazards. MhAST also offers a wide range of scenarios of return period and design levels and their likelihoods. Contribution of this study is four-fold: 1. comprehensive analysis of marginal and joint probability of multiple drivers through 17 continuous distributions and 26 copulas, 2. multiple scenario analysis of concurrent extremes based upon the most likely joint occurrence, one ruling variable, and weighted random sampling of joint occurrences with similar exceedance probabilities, 3. weighted average scenario analysis based on a expected event, and 4. uncertainty analysis of the most likely joint occurrence scenario using a Bayesian framework.

Multivariate η-μ fading distribution with arbitrary correlation model

NASA Astrophysics Data System (ADS)

Ghareeb, Ibrahim; Atiani, Amani

2018-03-01

An extensive analysis for the multivariate ? distribution with arbitrary correlation is presented, where novel analytical expressions for the multivariate probability density function, cumulative distribution function and moment generating function (MGF) of arbitrarily correlated and not necessarily identically distributed ? power random variables are derived. Also, this paper provides exact-form expression for the MGF of the instantaneous signal-to-noise ratio at the combiner output in a diversity reception system with maximal-ratio combining and post-detection equal-gain combining operating in slow frequency nonselective arbitrarily correlated not necessarily identically distributed ?-fading channels. The average bit error probability of differentially detected quadrature phase shift keying signals with post-detection diversity reception system over arbitrarily correlated and not necessarily identical fading parameters ?-fading channels is determined by using the MGF-based approach. The effect of fading correlation between diversity branches, fading severity parameters and diversity level is studied.

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta-analysis and group level studies.

PubMed

Bakbergenuly, Ilyas; Kulinskaya, Elena; Morgenthaler, Stephan

2016-07-01

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log-odds and arcsine transformations of the estimated probability p̂, both for single-group studies and in combining results from several groups or studies in meta-analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta-analysis and result in abysmal coverage of the combined effect for large K. We also propose bias-correction for the arcsine transformation. Our simulations demonstrate that this bias-correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta-analyses of prevalence. © 2016 The Authors. Biometrical Journal Published by Wiley-VCH Verlag GmbH & Co. KGaA.

The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms.

PubMed

Biehler, J; Wall, W A

2018-02-01

If computational models are ever to be used in high-stakes decision making in clinical practice, the use of personalized models and predictive simulation techniques is a must. This entails rigorous quantification of uncertainties as well as harnessing available patient-specific data to the greatest extent possible. Although researchers are beginning to realize that taking uncertainty in model input parameters into account is a necessity, the predominantly used probabilistic description for these uncertain parameters is based on elementary random variable models. In this work, we set out for a comparison of different probabilistic models for uncertain input parameters using the example of an uncertain wall thickness in finite element models of abdominal aortic aneurysms. We provide the first comparison between a random variable and a random field model for the aortic wall and investigate the impact on the probability distribution of the computed peak wall stress. Moreover, we show that the uncertainty about the prevailing peak wall stress can be reduced if noninvasively available, patient-specific data are harnessed for the construction of the probabilistic wall thickness model. Copyright © 2017 John Wiley & Sons, Ltd.

The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs

NASA Astrophysics Data System (ADS)

Serinaldi, Francesco; Kilsby, Chris G.

2013-06-01

The information contained in hyetographs and hydrographs is often synthesized by using key properties such as the peak or maximum value Xp, volume V, duration D, and average intensity I. These variables play a fundamental role in hydrologic engineering as they are used, for instance, to define design hyetographs and hydrographs as well as to model and simulate the rainfall and streamflow processes. Given their inherent variability and the empirical evidence of the presence of a significant degree of association, such quantities have been studied as correlated random variables suitable to be modeled by multivariate joint distribution functions. The advent of copulas in geosciences simplified the inference procedures allowing for splitting the analysis of the marginal distributions and the study of the so-called dependence structure or copula. However, the attention paid to the modeling task has overlooked a more thorough study of the true nature and origin of the relationships that link Xp,V,D, and I. In this study, we apply a set of ad hoc bootstrap algorithms to investigate these aspects by analyzing the hyetographs and hydrographs extracted from 282 daily rainfall series from central eastern Europe, three 5 min rainfall series from central Italy, 80 daily streamflow series from the continental United States, and two sets of 200 simulated universal multifractal time series. Our results show that all the pairwise dependence structures between Xp,V,D, and I exhibit some key properties that can be reproduced by simple bootstrap algorithms that rely on a standard univariate resampling without resort to multivariate techniques. Therefore, the strong similarities between the observed dependence structures and the agreement between the observed and bootstrap samples suggest the existence of a numerical generating mechanism based on the superposition of the effects of sampling data at finite time steps and the process of summing realizations of independent random variables over random durations. We also show that the pairwise dependence structures are weakly dependent on the internal patterns of the hyetographs and hydrographs, meaning that the temporal evolution of the rainfall and runoff events marginally influences the mutual relationships of Xp,V,D, and I. Finally, our findings point out that subtle and often overlooked deterministic relationships between the properties of the event hyetographs and hydrographs exist. Confusing these relationships with genuine stochastic relationships can lead to an incorrect application of multivariate distributions and copulas and to misleading results.

Minimal Distance to Approximating Noncontextual System as a Measure of Contextuality

NASA Astrophysics Data System (ADS)

Kujala, Janne V.

2017-07-01

Let random vectors Rc={Rpc:p\\in Pc} represent joint measurements of certain subsets Pc\\subset P of properties p\\in P in different contexts c\\in C. Such a system is traditionally called noncontextual if there exists a jointly distributed set {Qp:p\\in P} of random variables such that Rc has the same distribution as {Qp:p\\in Pc} for all c\\in C. A trivial necessary condition for noncontextuality and a precondition for many measures of contextuality is that the system is consistently connected, i.e., all Rpc,Rp^{c^' }},\\dots measuring the same property p\\in P have the same distribution. The contextuality-by-default (CbD) approach allows defining more general measures of contextuality that apply to inconsistently connected systems as well, but at the price of a higher computational cost. In this paper we propose a novel measure of contextuality that shares the generality of the CbD approach and the computational benefits of the previously proposed negative probability (NP) approach. The present approach differs from CbD in that instead of considering all possible joints of the double-indexed random variables Rpc, it considers all possible approximating single-indexed systems {Qp:p\\in P}. The degree of contextuality is defined based on the minimum possible probabilistic distance of the actual measurements Rc from {Qp:p\\in Pc}. We show that this measure, called the optimal approximation (OA) measure, agrees with a certain measure of contextuality of the CbD approach for all systems where each property enters in exactly two contexts. The OA measure can be calculated far more efficiently than the CbD measure and even more efficiently than the NP measure for sufficiently large systems. We also define a variant, the OA-NP measure of contextuality that agrees with the NP measure for consistently connected (non-signaling) systems while extending it to inconsistently connected systems.

Bayesian LASSO, scale space and decision making in association genetics.

PubMed

Pasanen, Leena; Holmström, Lasse; Sillanpää, Mikko J

2015-01-01

LASSO is a penalized regression method that facilitates model fitting in situations where there are as many, or even more explanatory variables than observations, and only a few variables are relevant in explaining the data. We focus on the Bayesian version of LASSO and consider four problems that need special attention: (i) controlling false positives, (ii) multiple comparisons, (iii) collinearity among explanatory variables, and (iv) the choice of the tuning parameter that controls the amount of shrinkage and the sparsity of the estimates. The particular application considered is association genetics, where LASSO regression can be used to find links between chromosome locations and phenotypic traits in a biological organism. However, the proposed techniques are relevant also in other contexts where LASSO is used for variable selection. We separate the true associations from false positives using the posterior distribution of the effects (regression coefficients) provided by Bayesian LASSO. We propose to solve the multiple comparisons problem by using simultaneous inference based on the joint posterior distribution of the effects. Bayesian LASSO also tends to distribute an effect among collinear variables, making detection of an association difficult. We propose to solve this problem by considering not only individual effects but also their functionals (i.e. sums and differences). Finally, whereas in Bayesian LASSO the tuning parameter is often regarded as a random variable, we adopt a scale space view and consider a whole range of fixed tuning parameters, instead. The effect estimates and the associated inference are considered for all tuning parameters in the selected range and the results are visualized with color maps that provide useful insights into data and the association problem considered. The methods are illustrated using two sets of artificial data and one real data set, all representing typical settings in association genetics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Antonysamy, A.A., E-mail: alphons.antonysamy@GKNAerospace.com; Meyer, J., E-mail: jonathan.meyer@eads.com; Prangnell, P.B., E-mail: philip.prangnell@manchester.ac.uk

With titanium alloys, the solidification conditions in Additive Manufacturing (AM) frequently lead to coarse columnar β-grain structures. The effect of geometry on the variability in the grain structure and texture, seen in Ti-6Al-4V alloy components produced by Selective Electron Beam Melting (SEBM), has been investigated. Reconstruction of the primary β-phase, from α-phase EBSD data, has confirmed that in bulk sections where in-fill “hatching” is employed growth selection favours columnar grains aligned with an <001> {sub β} direction normal to the deposited powder layers; this results in a coarse β-grain structure with a strong < 001 > {sub β} fibre texturemore » (up 8 x random) that can oscillate between a near random distribution around the fibre axis and cube reinforcement with build height. It is proposed that this behaviour is related to the highly elongated melt pool and the raster directions alternating between two orthogonal directions every layer, which on average favours grains with cube alignment. In contrast, the outline, or “contour”, pass produces a distinctly different grain structure and texture resulting in a skin layer on wall surfaces, where nucleation occurs off the surrounding powder and growth follows the curved surface of the melt pool. This structure becomes increasingly important in thin sections. Local heterogeneities have also been found within different section transitions, resulting from the growth of skin grain structures into thicker sections. Texture simulations have shown that the far weaker α-texture (∼ 3 x random), seen in the final product, arises from transformation on cooling occurring with a near random distribution of α-plates across the 12 variants possible from the Burgers relationship. - Highlights: • Distinctly different skin and bulk structures are produced by the contour and hatching passes. • Bulk sections contain coarse β-grains with a < 001 > fibre texture in the build direction. • This oscillates between a random distribution around the axis and cube reinforcement. • In the skin layer nucleation occurs off the surrounding powder bed and growth occurs inwards. • Simulations show that a weak α-texture results from a random distribution across habit variants.« less

A Data-Driven Framework for Rapid Modeling of Wireless Communication Channels

DTIC Science & Technology

2013-12-01

Committee Chair Mathias Kolsch Joel Young Associate Professor of Computer Science Assistant Professor of Computer Science Timothy Chung John J . Leonard...74 xiii Figure 7.8 RSS measurements (relative to S2 buoy) partitioned into 4 groupings anno - tated by the red, green blue and magenta...distribution of this random variable. Suppose it was possible to take additional measurements at other locations (x j | x j 6= xi). In order to do

Blind Deconvolution Method of Image Deblurring Using Convergence of Variance

DTIC Science & Technology

2011-03-24

random variable x is [9] fX (x) = 1√ 2πσ e−(x−m) 2/2σ2 −∞ < x <∞, σ > 0 (6) where m is the mean and σ is the variance. 7 Figure 1: Gaussian distribution...of the MAP Estimation algorithm when N was set to 50. The APEX method is not without its own difficulties when dealing with astro - nomical data

Novel composites for wing and fuselage applications

NASA Technical Reports Server (NTRS)

Sobel, L. H.; Buttitta, C.; Suarez, J. A.

1995-01-01

Probabilistic predictions based on the IPACS code are presented for the material and structural response of unnotched and notched, IM6/3501-6 Gr/Ep laminates. Comparisons of predicted and measured modulus and strength distributions are given for unnotched unidirectional, cross-ply and quasi-isotropic laminates. The predicted modulus distributions were found to correlate well with the test results for all three unnotched laminates. Correlations of strength distributions for the unnotched laminates are judged good for the unidirectional laminate and fair for the cross-ply laminate, whereas the strength correlation for the quasi-isotropic laminate is judged poor because IPACS did not have a progressive failure capability at the time this work was performed. The report also presents probabilistic and structural reliability analysis predictions for the strain concentration factor (SCF) for an open-hole, quasi-isotropic laminate subjected to longitudinal tension. A special procedure was developed to adapt IPACS for the structural reliability analysis. The reliability results show the importance of identifying the most significant random variables upon which the SCF depends, and of having accurate scatter values for these variables.

Probabilistic and structural reliability analysis of laminated composite structures based on the IPACS code

NASA Technical Reports Server (NTRS)

Sobel, Larry; Buttitta, Claudio; Suarez, James

1993-01-01

Probabilistic predictions based on the Integrated Probabilistic Assessment of Composite Structures (IPACS) code are presented for the material and structural response of unnotched and notched, 1M6/3501-6 Gr/Ep laminates. Comparisons of predicted and measured modulus and strength distributions are given for unnotched unidirectional, cross-ply, and quasi-isotropic laminates. The predicted modulus distributions were found to correlate well with the test results for all three unnotched laminates. Correlations of strength distributions for the unnotched laminates are judged good for the unidirectional laminate and fair for the cross-ply laminate, whereas the strength correlation for the quasi-isotropic laminate is deficient because IPACS did not yet have a progressive failure capability. The paper also presents probabilistic and structural reliability analysis predictions for the strain concentration factor (SCF) for an open-hole, quasi-isotropic laminate subjected to longitudinal tension. A special procedure was developed to adapt IPACS for the structural reliability analysis. The reliability results show the importance of identifying the most significant random variables upon which the SCF depends, and of having accurate scatter values for these variables.

Statistical self-similarity of width function maxima with implications to floods

USGS Publications Warehouse

Veitzer, S.A.; Gupta, V.K.

2001-01-01

Recently a new theory of random self-similar river networks, called the RSN model, was introduced to explain empirical observations regarding the scaling properties of distributions of various topologic and geometric variables in natural basins. The RSN model predicts that such variables exhibit statistical simple scaling, when indexed by Horton-Strahler order. The average side tributary structure of RSN networks also exhibits Tokunaga-type self-similarity which is widely observed in nature. We examine the scaling structure of distributions of the maximum of the width function for RSNs for nested, complete Strahler basins by performing ensemble simulations. The maximum of the width function exhibits distributional simple scaling, when indexed by Horton-Strahler order, for both RSNs and natural river networks extracted from digital elevation models (DEMs). We also test a powerlaw relationship between Horton ratios for the maximum of the width function and drainage areas. These results represent first steps in formulating a comprehensive physical statistical theory of floods at multiple space-time scales for RSNs as discrete hierarchical branching structures. ?? 2001 Published by Elsevier Science Ltd.

ADAPTIVE MATCHING IN RANDOMIZED TRIALS AND OBSERVATIONAL STUDIES

PubMed Central

van der Laan, Mark J.; Balzer, Laura B.; Petersen, Maya L.

2014-01-01

SUMMARY In many randomized and observational studies the allocation of treatment among a sample of n independent and identically distributed units is a function of the covariates of all sampled units. As a result, the treatment labels among the units are possibly dependent, complicating estimation and posing challenges for statistical inference. For example, cluster randomized trials frequently sample communities from some target population, construct matched pairs of communities from those included in the sample based on some metric of similarity in baseline community characteristics, and then randomly allocate a treatment and a control intervention within each matched pair. In this case, the observed data can neither be represented as the realization of n independent random variables, nor, contrary to current practice, as the realization of n/2 independent random variables (treating the matched pair as the independent sampling unit). In this paper we study estimation of the average causal effect of a treatment under experimental designs in which treatment allocation potentially depends on the pre-intervention covariates of all units included in the sample. We define efficient targeted minimum loss based estimators for this general design, present a theorem that establishes the desired asymptotic normality of these estimators and allows for asymptotically valid statistical inference, and discuss implementation of these estimators. We further investigate the relative asymptotic efficiency of this design compared with a design in which unit-specific treatment assignment depends only on the units’ covariates. Our findings have practical implications for the optimal design and analysis of pair matched cluster randomized trials, as well as for observational studies in which treatment decisions may depend on characteristics of the entire sample. PMID:25097298

A modified hybrid uncertain analysis method for dynamic response field of the LSOAAC with random and interval parameters

NASA Astrophysics Data System (ADS)

Zi, Bin; Zhou, Bin

2016-07-01

For the prediction of dynamic response field of the luffing system of an automobile crane (LSOAAC) with random and interval parameters, a hybrid uncertain model is introduced. In the hybrid uncertain model, the parameters with certain probability distribution are modeled as random variables, whereas, the parameters with lower and upper bounds are modeled as interval variables instead of given precise values. Based on the hybrid uncertain model, the hybrid uncertain dynamic response equilibrium equation, in which different random and interval parameters are simultaneously included in input and output terms, is constructed. Then a modified hybrid uncertain analysis method (MHUAM) is proposed. In the MHUAM, based on random interval perturbation method, the first-order Taylor series expansion and the first-order Neumann series, the dynamic response expression of the LSOAAC is developed. Moreover, the mathematical characteristics of extrema of bounds of dynamic response are determined by random interval moment method and monotonic analysis technique. Compared with the hybrid Monte Carlo method (HMCM) and interval perturbation method (IPM), numerical results show the feasibility and efficiency of the MHUAM for solving the hybrid LSOAAC problems. The effects of different uncertain models and parameters on the LSOAAC response field are also investigated deeply, and numerical results indicate that the impact made by the randomness in the thrust of the luffing cylinder F is larger than that made by the gravity of the weight in suspension Q . In addition, the impact made by the uncertainty in the displacement between the lower end of the lifting arm and the luffing cylinder a is larger than that made by the length of the lifting arm L .

Two stochastic models useful in petroleum exploration

NASA Technical Reports Server (NTRS)

Kaufman, G. M.; Bradley, P. G.

1972-01-01

A model of the petroleum exploration process that tests empirically the hypothesis that at an early stage in the exploration of a basin, the process behaves like sampling without replacement is proposed along with a model of the spatial distribution of petroleum reserviors that conforms to observed facts. In developing the model of discovery, the following topics are discussed: probabilitistic proportionality, likelihood function, and maximum likelihood estimation. In addition, the spatial model is described, which is defined as a stochastic process generating values of a sequence or random variables in a way that simulates the frequency distribution of areal extent, the geographic location, and shape of oil deposits

Continuous variable quantum cryptography using coherent states.

PubMed

Grosshans, Frédéric; Grangier, Philippe

2002-02-04

We propose several methods for quantum key distribution (QKD) based on the generation and transmission of random distributions of coherent or squeezed states, and we show that they are secure against individual eavesdropping attacks. These protocols require that the transmission of the optical line between Alice and Bob is larger than 50%, but they do not rely on "sub-shot-noise" features such as squeezing. Their security is a direct consequence of the no-cloning theorem, which limits the signal-to-noise ratio of possible quantum measurements on the transmission line. Our approach can also be used for evaluating various QKD protocols using light with Gaussian statistics.

Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities

NASA Technical Reports Server (NTRS)

Greenzweig, Yuval; Lissauer, Jack J.

1992-01-01

In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.

Effect of source tampering in the security of quantum cryptography

NASA Astrophysics Data System (ADS)

Sun, Shi-Hai; Xu, Feihu; Jiang, Mu-Sheng; Ma, Xiang-Chun; Lo, Hoi-Kwong; Liang, Lin-Mei

2015-08-01

The security of source has become an increasingly important issue in quantum cryptography. Based on the framework of measurement-device-independent quantum key distribution (MDI-QKD), the source becomes the only region exploitable by a potential eavesdropper (Eve). Phase randomization is a cornerstone assumption in most discrete-variable (DV) quantum communication protocols (e.g., QKD, quantum coin tossing, weak-coherent-state blind quantum computing, and so on), and the violation of such an assumption is thus fatal to the security of those protocols. In this paper, we show a simple quantum hacking strategy, with commercial and homemade pulsed lasers, by Eve that allows her to actively tamper with the source and violate such an assumption, without leaving a trace afterwards. Furthermore, our attack may also be valid for continuous-variable (CV) QKD, which is another main class of QKD protocol, since, excepting the phase random assumption, other parameters (e.g., intensity) could also be changed, which directly determine the security of CV-QKD.

Effects of Spatial Variability of Soil Properties on the Triggering of Rainfall-Induced Shallow Landslides

NASA Astrophysics Data System (ADS)

Fan, Linfeng; Lehmann, Peter; Or, Dani

2015-04-01

Naturally-occurring spatial variations in soil properties (e.g., soil depth, moisture, and texture) affect key hydrological processes and potentially the mechanical response of soil to hydromechanical loading (relative to the commonly-assumed uniform soil mantle). We quantified the effects of soil spatial variability on the triggering of rainfall-induced shallow landslides at the hillslope- and catchment-scales, using a physically-based landslide triggering model that considers interacting soil columns with mechanical strength thresholds (represented by the Fiber Bundle Model). The spatial variations in soil properties are represented as Gaussian random distributions and the level of variation is characterized by the coefficient of variation and correlation lengths of soil properties (i.e., soil depth, soil texture and initial water content in this study). The impacts of these spatial variations on landslide triggering characteristics were measured by comparing the times to triggering and landslide volumes for heterogeneous soil properties and homogeneous cases. Results at hillslope scale indicate that for spatial variations of an individual property (without cross correlation), the increasing of coefficient of variation introduces weak spots where mechanical damage is accelerated and leads to earlier onset of landslide triggering and smaller volumes. Increasing spatial correlation length of soil texture and initial water content also induces early landslide triggering and small released volumes due to the transition of failure mode from brittle to ductile failure. In contrast, increasing spatial correlation length of soil depth "reduces" local steepness and postpones landslide triggering. Cross-correlated soil properties generally promote landslide initiation, but depending on the internal structure of spatial distribution of each soil property, landslide triggering may be reduced. The effects of cross-correlation between initial water content and soil texture were investigated in detail at the catchment scale by incorporating correlations of both variables with topography. Results indicate that the internal structure of the spatial distribution of each soil property together with their interplays determine the overall performance of the coupled spatial variability. This study emphasizes the importance of both the randomness and spatial structure of soil properties on landslide triggering and characteristics.

Community change in the variable resource habitat of the abyssal northeast Pacific.

PubMed

Ruhl, Henry A

2008-04-01

Research capable of differentiating resource-related community-level change from random ecological drift in natural systems has been limited. Evidence for nonrandom, resource-driven change is presented here for an epibenthic megafauna community in the abyssal northeast Pacific Ocean from 1989 to 2004. The sinking particulate organic carbon food supply is linked not only to species-specific abundances, but also to species composition and equitability. Shifts in rank abundance distributions (RADs) and evenness, from more to less equitable, correlated to increased food supply during La Niña phases of the El Niño Southern Oscillation. The results suggest that each taxon exhibited a differential response to a sufficiently low dimension resource, which led to changes in community composition and equitability. Thus the shifts were not likely due to random ecological drift. Although the community can undergo population-level variations of one or more orders of magnitude, and the shape of the RADs was variable, the organization retained a significant consistency, providing evidence of limits for such changes. The growing evidence for limited resource-driven changes in RADs and evenness further emphasizes the potential importance of temporally variable disequilibria in understanding why communities have certain basic attributes.

Modeling the spatial distribution of Chagas disease vectors using environmental variables and people´s knowledge.

PubMed

Hernández, Jaime; Núñez, Ignacia; Bacigalupo, Antonella; Cattan, Pedro E

2013-05-31

Chagas disease is caused by the protozoan Trypanosoma cruzi, which is transmitted to mammal hosts by triatomine insect vectors. The goal of this study was to model the spatial distribution of triatomine species in an endemic area. Vector's locations were obtained with a rural householders' survey. This information was combined with environmental data obtained from remote sensors, land use maps and topographic SRTM data, using the machine learning algorithm Random Forests to model species distribution. We analysed the combination of variables on three scales: 10 km, 5 km and 2.5 km cell size grids. The best estimation, explaining 46.2% of the triatomines spatial distribution, was obtained for 5 km of spatial resolution. Presence probability distribution increases from central Chile towards the north, tending to cover the central-coastal region and avoiding areas of the Andes range. The methodology presented here was useful to model the distribution of triatomines in an endemic area; it is best explained using 5 km of spatial resolution, and their presence increases in the northern part of the study area. This study's methodology can be replicated in other countries with Chagas disease or other vectorial transmitted diseases, and be used to locate high risk areas and to optimize resource allocation, for prevention and control of vectorial diseases.

Modeling the spatial distribution of Chagas disease vectors using environmental variables and people´s knowledge

PubMed Central

2013-01-01

Background Chagas disease is caused by the protozoan Trypanosoma cruzi, which is transmitted to mammal hosts by triatomine insect vectors. The goal of this study was to model the spatial distribution of triatomine species in an endemic area. Methods Vector’s locations were obtained with a rural householders’ survey. This information was combined with environmental data obtained from remote sensors, land use maps and topographic SRTM data, using the machine learning algorithm Random Forests to model species distribution. We analysed the combination of variables on three scales: 10 km, 5 km and 2.5 km cell size grids. Results The best estimation, explaining 46.2% of the triatomines spatial distribution, was obtained for 5 km of spatial resolution. Presence probability distribution increases from central Chile towards the north, tending to cover the central-coastal region and avoiding areas of the Andes range. Conclusions The methodology presented here was useful to model the distribution of triatomines in an endemic area; it is best explained using 5 km of spatial resolution, and their presence increases in the northern part of the study area. This study’s methodology can be replicated in other countries with Chagas disease or other vectorial transmitted diseases, and be used to locate high risk areas and to optimize resource allocation, for prevention and control of vectorial diseases. PMID:23724993

Bayesian statistical inference enhances the interpretation of contemporary randomized controlled trials.

PubMed

Wijeysundera, Duminda N; Austin, Peter C; Hux, Janet E; Beattie, W Scott; Laupacis, Andreas

2009-01-01

Randomized trials generally use "frequentist" statistics based on P-values and 95% confidence intervals. Frequentist methods have limitations that might be overcome, in part, by Bayesian inference. To illustrate these advantages, we re-analyzed randomized trials published in four general medical journals during 2004. We used Medline to identify randomized superiority trials with two parallel arms, individual-level randomization and dichotomous or time-to-event primary outcomes. Studies with P<0.05 in favor of the intervention were deemed "positive"; otherwise, they were "negative." We used several prior distributions and exact conjugate analyses to calculate Bayesian posterior probabilities for clinically relevant effects. Of 88 included studies, 39 were positive using a frequentist analysis. Although the Bayesian posterior probabilities of any benefit (relative risk or hazard ratio<1) were high in positive studies, these probabilities were lower and variable for larger benefits. The positive studies had only moderate probabilities for exceeding the effects that were assumed for calculating the sample size. By comparison, there were moderate probabilities of any benefit in negative studies. Bayesian and frequentist analyses complement each other when interpreting the results of randomized trials. Future reports of randomized trials should include both.

Single-phase and two-phase flow properties of mesaverde tight sandstone formation; random-network modeling approach

NASA Astrophysics Data System (ADS)

Bashtani, Farzad; Maini, Brij; Kantzas, Apostolos

2016-08-01

3D random networks are constructed in order to represent the tight Mesaverde formation which is located in north Wyoming, USA. The porous-space is represented by pore bodies of different shapes and sizes which are connected to each other by pore throats of varying length and diameter. Pore bodies are randomly distributed in space and their connectivity varies based on the connectivity number distribution which is used in order to generate the network. Network representations are then validated using publicly available mercury porosimetry experiments. The network modeling software solves the fundamental equations of two-phase immiscible flow incorporating wettability and contact angle variability. Quasi-static displacement is assumed. Single phase macroscopic properties (porosity, permeability) are calculated and whenever possible are compared to experimental data. Using this information drainage and imbibition capillary pressure, and relative permeability curves are predicted and (whenever possible) compared to experimental data. The calculated information is grouped and compared to available literature information on typical behavior of tight formations. Capillary pressure curve for primary drainage process is predicted and compared to experimental mercury porosimetry in order to validate the virtual porous media by history matching. Relative permeability curves are also calculated and presented.

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

NASA Astrophysics Data System (ADS)

Sposini, Vittoria; Chechkin, Aleksei V.; Seno, Flavio; Pagnini, Gianni; Metzler, Ralf

2018-04-01

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.

Echinoid associations with coral habitats differ with taxon in the deep sea and the influence of other echinoids, depth, and fishing history on their distribution

NASA Astrophysics Data System (ADS)

Stevenson, Angela; Davies, Jaime S.; Williams, Alan; Althaus, Franziska; Rowden, Ashley A.; Bowden, David A.; Clark, Malcolm R.; Mitchell, Fraser J. G.

2018-03-01

Patterns of habitat use by animals and knowledge of the environmental factors affecting these spatial patterns are important for understanding the structure and dynamics of ecological communities. Both aspects are poorly known for deep-sea habitats. The present study investigates echinoid distributions within cold water coral (CWC) habitats on continental margins off France, Australia, and New Zealand. It further examines the influence of habitat-related variables that might help explain the observed distribution of echinoid taxa. Six echinoid taxa were examined from video and photographic transects to reveal taxon-specific distribution patterns and habitat-related influences. The Echinoidea were found in all habitats studied, but tended to aggregate in architecturally complex habitats associated with living cold-water corals. However, a taxon-specific investigation found that such associations were largely an artefact of the dominant taxa observed in a specific region. Despite the food and shelter resources offered to echinoids by matrix-forming coral habitats, not all taxa were associated with these habitats, and some had a random association with the habitats examined, while others displayed non-random associations. Echinoid distribution was correlated with several variables; the presence of other echinoids, depth, and fishing history were the most influential factors. This study indicates that image data can be a useful tool to detect trends in echinoid habitat associations. It also suggests that refinement of the methods, in particular with studies conducted at a more precise taxon and habitat scale, would facilitate better quantitative analyses of habitat associations and paint a more realistic picture of a population's ecology. Most deep-sea ecological studies to date have been conducted at a relatively coarse taxonomic and habitat resolution, and lack sufficient resolution to provide useful information for the conservation of vulnerable deep-sea habitats.

Theory and generation of conditional, scalable sub-Gaussian random fields

NASA Astrophysics Data System (ADS)

Panzeri, M.; Riva, M.; Guadagnini, A.; Neuman, S. P.

2016-03-01

Many earth and environmental (as well as a host of other) variables, Y, and their spatial (or temporal) increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture key aspects of such non-Gaussian scaling by treating Y and/or ΔY as sub-Gaussian random fields (or processes). This however left unaddressed the empirical finding that whereas sample frequency distributions of Y tend to display relatively mild non-Gaussian peaks and tails, those of ΔY often reveal peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we proposed a generalized sub-Gaussian model (GSG) which resolves this apparent inconsistency between the statistical scaling behaviors of observed variables and their increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. Most importantly, we demonstrated the feasibility of estimating all parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments, ΔY. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random fields, introduce two approximate versions of this algorithm to reduce CPU time, and explore them on one and two-dimensional synthetic test cases.

Hoeffding Type Inequalities and their Applications in Statistics and Operations Research

NASA Astrophysics Data System (ADS)

Daras, Tryfon

2007-09-01

Large Deviation theory is the branch of Probability theory that deals with rare events. Sometimes, these events can be described by the sum of random variables that deviates from its mean more than a "normal" amount. A precise calculation of the probabilities of such events turns out to be crucial in a variety of different contents (e.g. in Probability Theory, Statistics, Operations Research, Statistical Physics, Financial Mathematics e.t.c.). Recent applications of the theory deal with random walks in random environments, interacting diffusions, heat conduction, polymer chains [1]. In this paper we prove an inequality of exponential type, namely theorem 2.1, which gives a large deviation upper bound for a specific sequence of r.v.s. Inequalities of this type have many applications in Combinatorics [2]. The inequality generalizes already proven results of this type, in the case of symmetric probability measures. We get as consequences to the inequality: (a) large deviations upper bounds for exchangeable Bernoulli sequences of random variables, generalizing results proven for independent and identically distributed Bernoulli sequences of r.v.s. and (b) a general form of Bernstein's inequality. We compare the inequality with large deviation results already proven by the author and try to see its advantages. Finally, using the inequality, we solve one of the basic problems of Operations Research (bin packing problem) in the case of exchangeable r.v.s.

Adaptive random walks on the class of Web graphs

NASA Astrophysics Data System (ADS)

Tadić, B.

2001-09-01

We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [B. Tadić, Physica A 293, 273 (2001)], and are characterized by a pair of power-law distributions of out- and in-degree for each value of the parameter β, which measures the degree of rewiring in the graph. The walker adapts its move strategy according to locally available information both on out-degree of the visited node and in-degree of target node. A standard random walk, on the other hand, uses the out-degree only. We compute the distribution of connected subgraphs visited by an ensemble of walkers, the average access time and survival probability of the walks. We discuss these properties of the walk dynamics relative to the changes in the global graph structure when the control parameter β is varied. For β≥ 3, corresponding to the world-wide Web, the access time of the walk to a given level of hierarchy on the graph is much shorter compared to the standard random walk on the same graph. By reducing the amount of rewiring towards rigidity limit β↦βc≲ 0.1, corresponding to the range of naturally occurring biochemical networks, the survival probability of adaptive and standard random walk become increasingly similar. The adaptive random walk can be used as an efficient message-passing algorithm on this class of graphs for large degree of rewiring.

A Variance Distribution Model of Surface EMG Signals Based on Inverse Gamma Distribution.

PubMed

Hayashi, Hideaki; Furui, Akira; Kurita, Yuichi; Tsuji, Toshio

2017-11-01

Objective: This paper describes the formulation of a surface electromyogram (EMG) model capable of representing the variance distribution of EMG signals. Methods: In the model, EMG signals are handled based on a Gaussian white noise process with a mean of zero for each variance value. EMG signal variance is taken as a random variable that follows inverse gamma distribution, allowing the representation of noise superimposed onto this variance. Variance distribution estimation based on marginal likelihood maximization is also outlined in this paper. The procedure can be approximated using rectified and smoothed EMG signals, thereby allowing the determination of distribution parameters in real time at low computational cost. Results: A simulation experiment was performed to evaluate the accuracy of distribution estimation using artificially generated EMG signals, with results demonstrating that the proposed model's accuracy is higher than that of maximum-likelihood-based estimation. Analysis of variance distribution using real EMG data also suggested a relationship between variance distribution and signal-dependent noise. Conclusion: The study reported here was conducted to examine the performance of a proposed surface EMG model capable of representing variance distribution and a related distribution parameter estimation method. Experiments using artificial and real EMG data demonstrated the validity of the model. Significance: Variance distribution estimated using the proposed model exhibits potential in the estimation of muscle force. Objective: This paper describes the formulation of a surface electromyogram (EMG) model capable of representing the variance distribution of EMG signals. Methods: In the model, EMG signals are handled based on a Gaussian white noise process with a mean of zero for each variance value. EMG signal variance is taken as a random variable that follows inverse gamma distribution, allowing the representation of noise superimposed onto this variance. Variance distribution estimation based on marginal likelihood maximization is also outlined in this paper. The procedure can be approximated using rectified and smoothed EMG signals, thereby allowing the determination of distribution parameters in real time at low computational cost. Results: A simulation experiment was performed to evaluate the accuracy of distribution estimation using artificially generated EMG signals, with results demonstrating that the proposed model's accuracy is higher than that of maximum-likelihood-based estimation. Analysis of variance distribution using real EMG data also suggested a relationship between variance distribution and signal-dependent noise. Conclusion: The study reported here was conducted to examine the performance of a proposed surface EMG model capable of representing variance distribution and a related distribution parameter estimation method. Experiments using artificial and real EMG data demonstrated the validity of the model. Significance: Variance distribution estimated using the proposed model exhibits potential in the estimation of muscle force.

Climate envelope predictions indicate an enlarged suitable wintering distribution for Great Bustards (Otis tarda dybowskii) in China for the 21st century

PubMed Central

Mi, Chunrong; Falk, Huettmann

2016-01-01

The rapidly changing climate makes humans realize that there is a critical need to incorporate climate change adaptation into conservation planning. Whether the wintering habitats of Great Bustards (Otis tarda dybowskii), a globally endangered migratory subspecies whose population is approximately 1,500–2,200 individuals in China, would be still suitable in a changing climate environment, and where this could be found, is an important protection issue. In this study, we selected the most suitable species distribution model for bustards using climate envelopes from four machine learning models, combining two modelling approaches (TreeNet and Random Forest) with two sets of variables (correlated variables removed or not). We used common evaluation methods area under the receiver operating characteristic curves (AUC) and the True Skill Statistic (TSS) as well as independent test data to identify the most suitable model. As often found elsewhere, we found Random Forest with all environmental variables outperformed in all assessment methods. When we projected the best model to the latest IPCC-CMIP5 climate scenarios (Representative Concentration Pathways (RCPs) 2.6, 4.5 and 8.5 in three Global Circulation Models (GCMs)), and averaged the project results of the three models, we found that suitable wintering habitats in the current bustard distribution would increase during the 21st century. The Northeast Plain and the south of North China were projected to become two major wintering areas for bustards. However, the models suggest that some currently suitable habitats will experience a reduction, such as Dongting Lake and Poyang Lake in the Middle and Lower Yangtze River Basin. Although our results suggested that suitable habitats in China would widen with climate change, greater efforts should be undertaken to assess and mitigate unstudied human disturbance, such as pollution, hunting, agricultural development, infrastructure construction, habitat fragmentation, and oil and mine exploitation. All of these are negatively and intensely linked with global change. PMID:26855870

A probabilistic approach for shallow rainfall-triggered landslide modeling at basin scale. A case study in the Luquillo Forest, Puerto Rico

NASA Astrophysics Data System (ADS)

Dialynas, Y. G.; Arnone, E.; Noto, L. V.; Bras, R. L.

2013-12-01

Slope stability depends on geotechnical and hydrological factors that exhibit wide natural spatial variability, yet sufficient measurements of the related parameters are rarely available over entire study areas. The uncertainty associated with the inability to fully characterize hydrologic behavior has an impact on any attempt to model landslide hazards. This work suggests a way to systematically account for this uncertainty in coupled distributed hydrological-stability models for shallow landslide hazard assessment. A probabilistic approach for the prediction of rainfall-triggered landslide occurrence at basin scale was implemented in an existing distributed eco-hydrological and landslide model, tRIBS-VEGGIE -landslide (Triangulated Irregular Network (TIN)-based Real-time Integrated Basin Simulator - VEGetation Generator for Interactive Evolution). More precisely, we upgraded tRIBS-VEGGIE- landslide to assess the likelihood of shallow landslides by accounting for uncertainty related to geotechnical and hydrological factors that directly affect slope stability. Natural variability of geotechnical soil characteristics was considered by randomizing soil cohesion and friction angle. Hydrological uncertainty related to the estimation of matric suction was taken into account by considering soil retention parameters as correlated random variables. The probability of failure is estimated through an assumed theoretical Factor of Safety (FS) distribution, conditioned on soil moisture content. At each cell, the temporally variant FS statistics are approximated by the First Order Second Moment (FOSM) method, as a function of parameters statistical properties. The model was applied on the Rio Mameyes Basin, located in the Luquillo Experimental Forest in Puerto Rico, where previous landslide analyses have been carried out. At each time step, model outputs include the probability of landslide occurrence across the basin, and the most probable depth of failure at each soil column. The use of the proposed probabilistic approach for shallow landslide prediction is able to reveal and quantify landslide risk at slopes assessed as stable by simpler deterministic methods.

Climate envelope predictions indicate an enlarged suitable wintering distribution for Great Bustards (Otis tarda dybowskii) in China for the 21st century.

PubMed

Mi, Chunrong; Falk, Huettmann; Guo, Yumin

2016-01-01

The rapidly changing climate makes humans realize that there is a critical need to incorporate climate change adaptation into conservation planning. Whether the wintering habitats of Great Bustards (Otis tarda dybowskii), a globally endangered migratory subspecies whose population is approximately 1,500-2,200 individuals in China, would be still suitable in a changing climate environment, and where this could be found, is an important protection issue. In this study, we selected the most suitable species distribution model for bustards using climate envelopes from four machine learning models, combining two modelling approaches (TreeNet and Random Forest) with two sets of variables (correlated variables removed or not). We used common evaluation methods area under the receiver operating characteristic curves (AUC) and the True Skill Statistic (TSS) as well as independent test data to identify the most suitable model. As often found elsewhere, we found Random Forest with all environmental variables outperformed in all assessment methods. When we projected the best model to the latest IPCC-CMIP5 climate scenarios (Representative Concentration Pathways (RCPs) 2.6, 4.5 and 8.5 in three Global Circulation Models (GCMs)), and averaged the project results of the three models, we found that suitable wintering habitats in the current bustard distribution would increase during the 21st century. The Northeast Plain and the south of North China were projected to become two major wintering areas for bustards. However, the models suggest that some currently suitable habitats will experience a reduction, such as Dongting Lake and Poyang Lake in the Middle and Lower Yangtze River Basin. Although our results suggested that suitable habitats in China would widen with climate change, greater efforts should be undertaken to assess and mitigate unstudied human disturbance, such as pollution, hunting, agricultural development, infrastructure construction, habitat fragmentation, and oil and mine exploitation. All of these are negatively and intensely linked with global change.

Accounting for stimulus-specific variation in precision reveals a discrete capacity limit in visual working memory

PubMed Central

Pratte, Michael S.; Park, Young Eun; Rademaker, Rosanne L.; Tong, Frank

2016-01-01

If we view a visual scene that contains many objects, then momentarily close our eyes, some details persist while others seem to fade. Discrete models of visual working memory (VWM) assume that only a few items can be actively maintained in memory, beyond which pure guessing will emerge. Alternatively, continuous resource models assume that all items in a visual scene can be stored with some precision. Distinguishing between these competing models is challenging, however, as resource models that allow for stochastically variable precision (across items and trials) can produce error distributions that resemble random guessing behavior. Here, we evaluated the hypothesis that a major source of variability in VWM performance arises from systematic variation in precision across the stimuli themselves; such stimulus-specific variability can be incorporated into both discrete-capacity and variable-precision resource models. Participants viewed multiple oriented gratings, and then reported the orientation of a cued grating from memory. When modeling the overall distribution of VWM errors, we found that the variable-precision resource model outperformed the discrete model. However, VWM errors revealed a pronounced “oblique effect”, with larger errors for oblique than cardinal orientations. After this source of variability was incorporated into both models, we found that the discrete model provided a better account of VWM errors. Our results demonstrate that variable precision across the stimulus space can lead to an unwarranted advantage for resource models that assume stochastically variable precision. When these deterministic sources are adequately modeled, human working memory performance reveals evidence of a discrete capacity limit. PMID:28004957

Accounting for stimulus-specific variation in precision reveals a discrete capacity limit in visual working memory.

PubMed

Pratte, Michael S; Park, Young Eun; Rademaker, Rosanne L; Tong, Frank

2017-01-01

If we view a visual scene that contains many objects, then momentarily close our eyes, some details persist while others seem to fade. Discrete models of visual working memory (VWM) assume that only a few items can be actively maintained in memory, beyond which pure guessing will emerge. Alternatively, continuous resource models assume that all items in a visual scene can be stored with some precision. Distinguishing between these competing models is challenging, however, as resource models that allow for stochastically variable precision (across items and trials) can produce error distributions that resemble random guessing behavior. Here, we evaluated the hypothesis that a major source of variability in VWM performance arises from systematic variation in precision across the stimuli themselves; such stimulus-specific variability can be incorporated into both discrete-capacity and variable-precision resource models. Participants viewed multiple oriented gratings, and then reported the orientation of a cued grating from memory. When modeling the overall distribution of VWM errors, we found that the variable-precision resource model outperformed the discrete model. However, VWM errors revealed a pronounced "oblique effect," with larger errors for oblique than cardinal orientations. After this source of variability was incorporated into both models, we found that the discrete model provided a better account of VWM errors. Our results demonstrate that variable precision across the stimulus space can lead to an unwarranted advantage for resource models that assume stochastically variable precision. When these deterministic sources are adequately modeled, human working memory performance reveals evidence of a discrete capacity limit. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Optimizing Constrained Single Period Problem under Random Fuzzy Demand

NASA Astrophysics Data System (ADS)

Taleizadeh, Ata Allah; Shavandi, Hassan; Riazi, Afshin

2008-09-01

In this paper, we consider the multi-product multi-constraint newsboy problem with random fuzzy demands and total discount. The demand of the products is often stochastic in the real word but the estimation of the parameters of distribution function may be done by fuzzy manner. So an appropriate option to modeling the demand of products is using the random fuzzy variable. The objective function of proposed model is to maximize the expected profit of newsboy. We consider the constraints such as warehouse space and restriction on quantity order for products, and restriction on budget. We also consider the batch size for products order. Finally we introduce a random fuzzy multi-product multi-constraint newsboy problem (RFM-PM-CNP) and it is changed to a multi-objective mixed integer nonlinear programming model. Furthermore, a hybrid intelligent algorithm based on genetic algorithm, Pareto and TOPSIS is presented for the developed model. Finally an illustrative example is presented to show the performance of the developed model and algorithm.

Security of BB84 with weak randomness and imperfect qubit encoding

NASA Astrophysics Data System (ADS)

Zhao, Liang-Yuan; Yin, Zhen-Qiang; Li, Hong-Wei; Chen, Wei; Fang, Xi; Han, Zheng-Fu; Huang, Wei

2018-03-01

The main threats for the well-known Bennett-Brassard 1984 (BB84) practical quantum key distribution (QKD) systems are that its encoding is inaccurate and measurement device may be vulnerable to particular attacks. Thus, a general physical model or security proof to tackle these loopholes simultaneously and quantitatively is highly desired. Here we give a framework on the security of BB84 when imperfect qubit encoding and vulnerability of measurement device are both considered. In our analysis, the potential attacks to measurement device are generalized by the recently proposed weak randomness model which assumes the input random numbers are partially biased depending on a hidden variable planted by an eavesdropper. And the inevitable encoding inaccuracy is also introduced here. From a fundamental view, our work reveals the potential information leakage due to encoding inaccuracy and weak randomness input. For applications, our result can be viewed as a useful tool to quantitatively evaluate the security of a practical QKD system.

Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes

PubMed Central

Soltani, Mohammad; Vargas-Garcia, Cesar A.; Antunes, Duarte; Singh, Abhyudai

2016-01-01

Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between two daughter cells are significant. We derive analytical formulas for the total noise in protein levels when the cell-cycle duration follows a general class of probability distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise, but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes, noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where transcription rate is increased at a random point in the cell cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome-duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from synchronized and asynchronized single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells. PMID:27536771

Do bacterial cell numbers follow a theoretical Poisson distribution? Comparison of experimentally obtained numbers of single cells with random number generation via computer simulation.

PubMed

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu

2016-12-01

We investigated a bacterial sample preparation procedure for single-cell studies. In the present study, we examined whether single bacterial cells obtained via 10-fold dilution followed a theoretical Poisson distribution. Four serotypes of Salmonella enterica, three serotypes of enterohaemorrhagic Escherichia coli and one serotype of Listeria monocytogenes were used as sample bacteria. An inoculum of each serotype was prepared via a 10-fold dilution series to obtain bacterial cell counts with mean values of one or two. To determine whether the experimentally obtained bacterial cell counts follow a theoretical Poisson distribution, a likelihood ratio test between the experimentally obtained cell counts and Poisson distribution which parameter estimated by maximum likelihood estimation (MLE) was conducted. The bacterial cell counts of each serotype sufficiently followed a Poisson distribution. Furthermore, to examine the validity of the parameters of Poisson distribution from experimentally obtained bacterial cell counts, we compared these with the parameters of a Poisson distribution that were estimated using random number generation via computer simulation. The Poisson distribution parameters experimentally obtained from bacterial cell counts were within the range of the parameters estimated using a computer simulation. These results demonstrate that the bacterial cell counts of each serotype obtained via 10-fold dilution followed a Poisson distribution. The fact that the frequency of bacterial cell counts follows a Poisson distribution at low number would be applied to some single-cell studies with a few bacterial cells. In particular, the procedure presented in this study enables us to develop an inactivation model at the single-cell level that can estimate the variability of survival bacterial numbers during the bacterial death process. Copyright © 2016 Elsevier Ltd. All rights reserved.

Regression Discontinuity for Causal Effect Estimation in Epidemiology.

PubMed

Oldenburg, Catherine E; Moscoe, Ellen; Bärnighausen, Till

Regression discontinuity analyses can generate estimates of the causal effects of an exposure when a continuously measured variable is used to assign the exposure to individuals based on a threshold rule. Individuals just above the threshold are expected to be similar in their distribution of measured and unmeasured baseline covariates to individuals just below the threshold, resulting in exchangeability. At the threshold exchangeability is guaranteed if there is random variation in the continuous assignment variable, e.g., due to random measurement error. Under exchangeability, causal effects can be identified at the threshold. The regression discontinuity intention-to-treat (RD-ITT) effect on an outcome can be estimated as the difference in the outcome between individuals just above (or below) versus just below (or above) the threshold. This effect is analogous to the ITT effect in a randomized controlled trial. Instrumental variable methods can be used to estimate the effect of exposure itself utilizing the threshold as the instrument. We review the recent epidemiologic literature reporting regression discontinuity studies and find that while regression discontinuity designs are beginning to be utilized in a variety of applications in epidemiology, they are still relatively rare, and analytic and reporting practices vary. Regression discontinuity has the potential to greatly contribute to the evidence base in epidemiology, in particular on the real-life and long-term effects and side-effects of medical treatments that are provided based on threshold rules - such as treatments for low birth weight, hypertension or diabetes.

The effects of demand uncertainty on strategic gaming in the merit-order electricity pool market

NASA Astrophysics Data System (ADS)

Frem, Bassam

In a merit-order electricity pool market, generating companies (Gencos) game with their offered incremental cost to meet the electricity demand and earn bigger market shares and higher profits. However when the demand is treated as a random variable instead of as a known constant, these Genco gaming strategies become more complex. After a brief introduction of electricity markets and gaming, the effects of demand uncertainty on strategic gaming are studied in two parts: (1) Demand modelled as a discrete random variable (2) Demand modelled as a continuous random variable. In the first part, we proposed an algorithm, the discrete stochastic strategy (DSS) algorithm that generates a strategic set of offers from the perspective of the Gencos' profits. The DSS offers were tested and compared to the deterministic Nash equilibrium (NE) offers based on the predicted demand. This comparison, based on the expected Genco profits, showed the DSS to be a better strategy in a probabilistic sense than the deterministic NE. In the second part, we presented three gaming strategies: (1) Deterministic NE (2) No-Risk (3) Risk-Taking. The strategies were then tested and their profit performances were compared using two assessment tools: (a) Expected value and standard deviation (b) Inverse cumulative distribution. We concluded that despite yielding higher profit performance under the right conjectures, Risk-Taking strategies are very sensitive to incorrect conjectures on the competitors' gaming decisions. As such, despite its lower profit performance, the No-Risk strategy was deemed preferable.

Probabilistic structural analysis methods and applications

NASA Technical Reports Server (NTRS)

Cruse, T. A.; Wu, Y.-T.; Dias, B.; Rajagopal, K. R.

1988-01-01

An advanced algorithm for simulating the probabilistic distribution of structural responses due to statistical uncertainties in loads, geometry, material properties, and boundary conditions is reported. The method effectively combines an advanced algorithm for calculating probability levels for multivariate problems (fast probability integration) together with a general-purpose finite-element code for stress, vibration, and buckling analysis. Application is made to a space propulsion system turbine blade for which the geometry and material properties are treated as random variables.

Generation of Some First-Order Autoregressive Markovian Sequences of Positive Random Variables with Given Marginal Distributions,

DTIC Science & Technology

1981-03-01

Again E( XnX 1 Xn) Xn + (l-aB)/X PlXn-1 + (l-Pl)/x 2.11) and X0 E0 gives a stationary sequence. Thus the correla- tions and regressions are the...sequence, although the sample paths will tend to have runs-up. A similar analysis given in Lawrance and Lewis [5] shows that 1 1 + i a + au (3.7) E( XnX

Optimal hash arrangement of tentacles in jellyfish

NASA Astrophysics Data System (ADS)

Okabe, Takuya; Yoshimura, Jin

2016-06-01

At first glance, the trailing tentacles of a jellyfish appear to be randomly arranged. However, close examination of medusae has revealed that the arrangement and developmental order of the tentacles obey a mathematical rule. Here, we show that medusa jellyfish adopt the best strategy to achieve the most uniform distribution of a variable number of tentacles. The observed order of tentacles is a real-world example of an optimal hashing algorithm known as Fibonacci hashing in computer science.

Students' Misconceptions about Random Variables

ERIC Educational Resources Information Center

Kachapova, Farida; Kachapov, Ilias

2012-01-01

This article describes some misconceptions about random variables and related counter-examples, and makes suggestions about teaching initial topics on random variables in general form instead of doing it separately for discrete and continuous cases. The focus is on post-calculus probability courses. (Contains 2 figures.)

Probabilistic Analysis of Solid Oxide Fuel Cell Based Hybrid Gas Turbine System

NASA Technical Reports Server (NTRS)

Gorla, Rama S. R.; Pai, Shantaram S.; Rusick, Jeffrey J.

2003-01-01

The emergence of fuel cell systems and hybrid fuel cell systems requires the evolution of analysis strategies for evaluating thermodynamic performance. A gas turbine thermodynamic cycle integrated with a fuel cell was computationally simulated and probabilistically evaluated in view of the several uncertainties in the thermodynamic performance parameters. Cumulative distribution functions and sensitivity factors were computed for the overall thermal efficiency and net specific power output due to the uncertainties in the thermodynamic random variables. These results can be used to quickly identify the most critical design variables in order to optimize the design and make it cost effective. The analysis leads to the selection of criteria for gas turbine performance.

SAMPLING OSCILLOSCOPE

DOEpatents

Sugarman, R.M.

1960-08-30

An oscilloscope is designed for displaying transient signal waveforms having random time and amplitude distributions. The oscilloscopc is a sampling device that selects for display a portion of only those waveforms having a particular range of amplitudes. For this purpose a pulse-height analyzer is provided to screen the pulses. A variable voltage-level shifter and a time-scale rampvoltage generator take the pulse height relative to the start of the waveform. The variable voltage shifter produces a voltage level raised one step for each sequential signal waveform to be sampled and this results in an unsmeared record of input signal waveforms. Appropriate delay devices permit each sample waveform to pass its peak amplitude before the circuit selects it for display.

Equivalence of binormal likelihood-ratio and bi-chi-squared ROC curve models

PubMed Central

Hillis, Stephen L.

2015-01-01

A basic assumption for a meaningful diagnostic decision variable is that there is a monotone relationship between it and its likelihood ratio. This relationship, however, generally does not hold for a decision variable that results in a binormal ROC curve. As a result, receiver operating characteristic (ROC) curve estimation based on the assumption of a binormal ROC-curve model produces improper ROC curves that have “hooks,” are not concave over the entire domain, and cross the chance line. Although in practice this “improperness” is usually not noticeable, sometimes it is evident and problematic. To avoid this problem, Metz and Pan proposed basing ROC-curve estimation on the assumption of a binormal likelihood-ratio (binormal-LR) model, which states that the decision variable is an increasing transformation of the likelihood-ratio function of a random variable having normal conditional diseased and nondiseased distributions. However, their development is not easy to follow. I show that the binormal-LR model is equivalent to a bi-chi-squared model in the sense that the families of corresponding ROC curves are the same. The bi-chi-squared formulation provides an easier-to-follow development of the binormal-LR ROC curve and its properties in terms of well-known distributions. PMID:26608405

Evaluating thermoregulation in reptiles: an appropriate null model.

PubMed

Christian, Keith A; Tracy, Christopher R; Tracy, C Richard

2006-09-01

Established indexes of thermoregulation in ectotherms compare body temperatures of real animals with a null distribution of operative temperatures from a physical or mathematical model with the same size, shape, and color as the actual animal but without mass. These indexes, however, do not account for thermal inertia or the effects of inertia when animals move through thermally heterogeneous environments. Some recent models have incorporated body mass, to account for thermal inertia and the physiological control of warming and cooling rates seen in most reptiles, and other models have incorporated movement through the environment, but none includes all pertinent variables explaining body temperature. We present a new technique for calculating the distribution of body temperatures available to ectotherms that have thermal inertia, random movements, and different rates of warming and cooling. The approach uses a biophysical model of heat exchange in ectotherms and a model of random interaction with thermal environments over the course of a day to create a null distribution of body temperatures that can be used with conventional thermoregulation indexes. This new technique provides an unbiased method for evaluating thermoregulation in large ectotherms that store heat while moving through complex environments, but it can also generate null models for ectotherms of all sizes.

Geographic Information Systems to Assess External Validity in Randomized Trials.

PubMed

Savoca, Margaret R; Ludwig, David A; Jones, Stedman T; Jason Clodfelter, K; Sloop, Joseph B; Bollhalter, Linda Y; Bertoni, Alain G

2017-08-01

To support claims that RCTs can reduce health disparities (i.e., are translational), it is imperative that methodologies exist to evaluate the tenability of external validity in RCTs when probabilistic sampling of participants is not employed. Typically, attempts at establishing post hoc external validity are limited to a few comparisons across convenience variables, which must be available in both sample and population. A Type 2 diabetes RCT was used as an example of a method that uses a geographic information system to assess external validity in the absence of a priori probabilistic community-wide diabetes risk sampling strategy. A geographic information system, 2009-2013 county death certificate records, and 2013-2014 electronic medical records were used to identify community-wide diabetes prevalence. Color-coded diabetes density maps provided visual representation of these densities. Chi-square goodness of fit statistic/analysis tested the degree to which distribution of RCT participants varied across density classes compared to what would be expected, given simple random sampling of the county population. Analyses were conducted in 2016. Diabetes prevalence areas as represented by death certificate and electronic medical records were distributed similarly. The simple random sample model was not a good fit for death certificate record (chi-square, 17.63; p=0.0001) and electronic medical record data (chi-square, 28.92; p<0.0001). Generally, RCT participants were oversampled in high-diabetes density areas. Location is a highly reliable "principal variable" associated with health disparities. It serves as a directly measurable proxy for high-risk underserved communities, thus offering an effective and practical approach for examining external validity of RCTs. Copyright © 2017 American Journal of Preventive Medicine. Published by Elsevier Inc. All rights reserved.

Design of Probabilistic Random Forests with Applications to Anticancer Drug Sensitivity Prediction

PubMed Central

Rahman, Raziur; Haider, Saad; Ghosh, Souparno; Pal, Ranadip

2015-01-01

Random forests consisting of an ensemble of regression trees with equal weights are frequently used for design of predictive models. In this article, we consider an extension of the methodology by representing the regression trees in the form of probabilistic trees and analyzing the nature of heteroscedasticity. The probabilistic tree representation allows for analytical computation of confidence intervals (CIs), and the tree weight optimization is expected to provide stricter CIs with comparable performance in mean error. We approached the ensemble of probabilistic trees’ prediction from the perspectives of a mixture distribution and as a weighted sum of correlated random variables. We applied our methodology to the drug sensitivity prediction problem on synthetic and cancer cell line encyclopedia dataset and illustrated that tree weights can be selected to reduce the average length of the CI without increase in mean error. PMID:27081304

Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

PubMed

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering

NASA Technical Reports Server (NTRS)

Deepak, A.; Fluellen, A.

1978-01-01

An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.

Simultaneous classical communication and quantum key distribution using continuous variables*

NASA Astrophysics Data System (ADS)

Qi, Bing

2016-10-01

Presently, classical optical communication systems employing strong laser pulses and quantum key distribution (QKD) systems working at single-photon levels are very different communication modalities. Dedicated devices are commonly required to implement QKD. In this paper, we propose a scheme which allows classical communication and QKD to be implemented simultaneously using the same communication infrastructure. More specially, we propose a coherent communication scheme where both the bits for classical communication and the Gaussian distributed random numbers for QKD are encoded on the same weak coherent pulse and decoded by the same coherent receiver. Simulation results based on practical system parameters show that both deterministic classical communication with a bit error rate of 10-9 and secure key distribution could be achieved over tens of kilometers of single-mode fibers. It is conceivable that in the future coherent optical communication network, QKD will be operated in the background of classical communication at a minimal cost.

Derivation of Hunt equation for suspension distribution using Shannon entropy theory

NASA Astrophysics Data System (ADS)

Kundu, Snehasis

2017-12-01

In this study, the Hunt equation for computing suspension concentration in sediment-laden flows is derived using Shannon entropy theory. Considering the inverse of the void ratio as a random variable and using principle of maximum entropy, probability density function and cumulative distribution function of suspension concentration is derived. A new and more general cumulative distribution function for the flow domain is proposed which includes several specific other models of CDF reported in literature. This general form of cumulative distribution function also helps to derive the Rouse equation. The entropy based approach helps to estimate model parameters using suspension data of sediment concentration which shows the advantage of using entropy theory. Finally model parameters in the entropy based model are also expressed as functions of the Rouse number to establish a link between the parameters of the deterministic and probabilistic approaches.

Multinomial mixture model with heterogeneous classification probabilities

USGS Publications Warehouse

Holland, M.D.; Gray, B.R.

2011-01-01

Royle and Link (Ecology 86(9):2505-2512, 2005) proposed an analytical method that allowed estimation of multinomial distribution parameters and classification probabilities from categorical data measured with error. While useful, we demonstrate algebraically and by simulations that this method yields biased multinomial parameter estimates when the probabilities of correct category classifications vary among sampling units. We address this shortcoming by treating these probabilities as logit-normal random variables within a Bayesian framework. We use Markov chain Monte Carlo to compute Bayes estimates from a simulated sample from the posterior distribution. Based on simulations, this elaborated Royle-Link model yields nearly unbiased estimates of multinomial and correct classification probability estimates when classification probabilities are allowed to vary according to the normal distribution on the logit scale or according to the Beta distribution. The method is illustrated using categorical submersed aquatic vegetation data. ?? 2010 Springer Science+Business Media, LLC.

On the probabilistic structure of water age

NASA Astrophysics Data System (ADS)

Porporato, Amilcare; Calabrese, Salvatore

2015-05-01

The age distribution of water in hydrologic systems has received renewed interest recently, especially in relation to watershed response to rainfall inputs. The purpose of this contribution is first to draw attention to existing theories of age distributions in population dynamics, fluid mechanics and stochastic groundwater, and in particular to the McKendrick-von Foerster equation and its generalizations and solutions. A second and more important goal is to clarify that, when hydrologic fluxes are modeled by means of time-varying stochastic processes, the age distributions must themselves be treated as random functions. Once their probabilistic structure is obtained, it can be used to characterize the variability of age distributions in real systems and thus help quantify the inherent uncertainty in the field determination of water age. We illustrate these concepts with reference to a stochastic storage model, which has been used as a minimalist model of soil moisture and streamflow dynamics.

Inverting Monotonic Nonlinearities by Entropy Maximization

PubMed Central

López-de-Ipiña Pena, Karmele; Caiafa, Cesar F.

2016-01-01

This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results. PMID:27780261

Inverting Monotonic Nonlinearities by Entropy Maximization.

PubMed

Solé-Casals, Jordi; López-de-Ipiña Pena, Karmele; Caiafa, Cesar F

2016-01-01

This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results.

Entropy of spatial network ensembles

NASA Astrophysics Data System (ADS)

Coon, Justin P.; Dettmann, Carl P.; Georgiou, Orestis

2018-04-01

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly in space and links formed independently between pairs of nodes with probability given by a specified function (the "pair connection function") of their mutual distance. We consider the general case where randomness arises in node positions as well as pairwise connections (i.e., for a given pair distance, the corresponding edge state is a random variable). Classical random geometric graph and exponential graph models can be recovered in certain limits. We derive a simple bound for the entropy of a spatial network ensemble and calculate the conditional entropy of an ensemble given the node location distribution for hard and soft (probabilistic) pair connection functions. Under this formalism, we derive the connection function that yields maximum entropy under general constraints. Finally, we apply our analytical framework to study two practical examples: ad hoc wireless networks and the US flight network. Through the study of these examples, we illustrate that both exhibit properties that are indicative of nearly maximally entropic ensembles.

Modeling intersubject variability of bronchial doses for inhaled radon progeny.

PubMed

Hofmann, Werner; Winkler-Heil, Renate; Hussain, Majid

2010-10-01

The main sources of intersubject variations considered in the present study were: (1) size and structure of nasal and oral passages, affecting extrathoracic deposition and, in further consequence, the fraction of the inhaled activity reaching the bronchial region; (2) size and asymmetric branching of the human bronchial airway system, leading to variations of diameters, lengths, branching angles, etc.; (3) respiratory parameters, such as tidal volume, and breathing frequency; (4) mucociliary clearance rates; and (5) thickness of the bronchial epithelium and depth of target cells, related to airway diameters. For the calculation of deposition fractions, retained surface activities, and bronchial doses, parameter values were randomly selected from their corresponding probability density functions, derived from experimental data, by applying Monte Carlo methods. Bronchial doses, expressed in mGy WLM-1, were computed for specific mining conditions, i.e., for defined size distributions, unattached fractions, and physical activities. Resulting bronchial dose distributions could be approximated by lognormal distributions. Geometric standard deviations illustrating intersubject variations ranged from about 2 in the trachea to about 7 in peripheral bronchiolar airways. The major sources of the intersubject variability of bronchial doses for inhaled radon progeny are the asymmetry and variability of the linear airway dimensions, the filtering efficiency of the nasal passages, and the thickness of the bronchial epithelium, while fluctuations of the respiratory parameters and mucociliary clearance rates seem to compensate each other.

Surrogacy Assessment Using Principal Stratification and a Gaussian Copula Model

PubMed Central

Taylor, J.M.G.; Elliott, M.R.

2014-01-01

In clinical trials, a surrogate outcome (S) can be measured before the outcome of interest (T) and may provide early information regarding the treatment (Z) effect on T. Many methods of surrogacy validation rely on models for the conditional distribution of T given Z and S. However, S is a post-randomization variable, and unobserved, simultaneous predictors of S and T may exist, resulting in a non-causal interpretation. Frangakis and Rubin1 developed the concept of principal surrogacy, stratifying on the joint distribution of the surrogate marker under treatment and control to assess the association between the causal effects of treatment on the marker and the causal effects of treatment on the clinical outcome. Working within the principal surrogacy framework, we address the scenario of an ordinal categorical variable as a surrogate for a censored failure time true endpoint. A Gaussian copula model is used to model the joint distribution of the potential outcomes of T, given the potential outcomes of S. Because the proposed model cannot be fully identified from the data, we use a Bayesian estimation approach with prior distributions consistent with reasonable assumptions in the surrogacy assessment setting. The method is applied to data from a colorectal cancer clinical trial, previously analyzed by Burzykowski et al..2 PMID:24947559

Determining on-fault earthquake magnitude distributions from integer programming

NASA Astrophysics Data System (ADS)

Geist, Eric L.; Parsons, Tom

2018-02-01

Earthquake magnitude distributions among faults within a fault system are determined from regional seismicity and fault slip rates using binary integer programming. A synthetic earthquake catalog (i.e., list of randomly sampled magnitudes) that spans millennia is first formed, assuming that regional seismicity follows a Gutenberg-Richter relation. Each earthquake in the synthetic catalog can occur on any fault and at any location. The objective is to minimize misfits in the target slip rate for each fault, where slip for each earthquake is scaled from its magnitude. The decision vector consists of binary variables indicating which locations are optimal among all possibilities. Uncertainty estimates in fault slip rates provide explicit upper and lower bounding constraints to the problem. An implicit constraint is that an earthquake can only be located on a fault if it is long enough to contain that earthquake. A general mixed-integer programming solver, consisting of a number of different algorithms, is used to determine the optimal decision vector. A case study is presented for the State of California, where a 4 kyr synthetic earthquake catalog is created and faults with slip ≥3 mm/yr are considered, resulting in >106 variables. The optimal magnitude distributions for each of the faults in the system span a rich diversity of shapes, ranging from characteristic to power-law distributions.

Surrogacy assessment using principal stratification and a Gaussian copula model.

PubMed

Conlon, Asc; Taylor, Jmg; Elliott, M R

2017-02-01

In clinical trials, a surrogate outcome ( S) can be measured before the outcome of interest ( T) and may provide early information regarding the treatment ( Z) effect on T. Many methods of surrogacy validation rely on models for the conditional distribution of T given Z and S. However, S is a post-randomization variable, and unobserved, simultaneous predictors of S and T may exist, resulting in a non-causal interpretation. Frangakis and Rubin developed the concept of principal surrogacy, stratifying on the joint distribution of the surrogate marker under treatment and control to assess the association between the causal effects of treatment on the marker and the causal effects of treatment on the clinical outcome. Working within the principal surrogacy framework, we address the scenario of an ordinal categorical variable as a surrogate for a censored failure time true endpoint. A Gaussian copula model is used to model the joint distribution of the potential outcomes of T, given the potential outcomes of S. Because the proposed model cannot be fully identified from the data, we use a Bayesian estimation approach with prior distributions consistent with reasonable assumptions in the surrogacy assessment setting. The method is applied to data from a colorectal cancer clinical trial, previously analyzed by Burzykowski et al.

On the degree distribution of horizontal visibility graphs associated with Markov processes and dynamical systems: diagrammatic and variational approaches

NASA Astrophysics Data System (ADS)

Lacasa, Lucas

2014-09-01

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical time series analysis and signal processing and (ii) characterizing classes of dynamical systems and stochastic processes using the tools of graph theory. Recent works show that the degree distribution of these graphs encapsulates much information on the signals' variability, and therefore constitutes a fundamental feature for statistical learning purposes. However, exact solutions for the degree distributions are only known in a few cases, such as for uncorrelated random processes. Here we analytically explore these distributions in a list of situations. We present a diagrammatic formalism which computes for all degrees their corresponding probability as a series expansion in a coupling constant which is the number of hidden variables. We offer a constructive solution for general Markovian stochastic processes and deterministic maps. As case tests we focus on Ornstein-Uhlenbeck processes, fully chaotic and quasiperiodic maps. Whereas only for certain degree probabilities can all diagrams be summed exactly, in the general case we show that the perturbation theory converges. In a second part, we make use of a variational technique to predict the complete degree distribution for special classes of Markovian dynamics with fast-decaying correlations. In every case we compare the theory with numerical experiments.

Multilevel discretized random field models with 'spin' correlations for the simulation of environmental spatial data

NASA Astrophysics Data System (ADS)

Žukovič, Milan; Hristopulos, Dionissios T.

2009-02-01

A current problem of practical significance is how to analyze large, spatially distributed, environmental data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show by means of numerical simulations that the spatial correlations between variables can be captured by interactions between 'spins'. The spins represent multilevel discretizations of environmental variables with respect to a number of pre-defined thresholds. The spatial dependence between the 'spins' is imposed by means of short-range interactions. We present two approaches, inspired by the Ising and Potts models, that generate conditional simulations of spatially distributed variables from samples with missing data. Currently, the sampling and simulation points are assumed to be at the nodes of a regular grid. The conditional simulations of the 'spin system' are forced to respect locally the sample values and the system statistics globally. The second constraint is enforced by minimizing a cost function representing the deviation between normalized correlation energies of the simulated and the sample distributions. In the approach based on the Nc-state Potts model, each point is assigned to one of Nc classes. The interactions involve all the points simultaneously. In the Ising model approach, a sequential simulation scheme is used: the discretization at each simulation level is binomial (i.e., ± 1). Information propagates from lower to higher levels as the simulation proceeds. We compare the two approaches in terms of their ability to reproduce the target statistics (e.g., the histogram and the variogram of the sample distribution), to predict data at unsampled locations, as well as in terms of their computational complexity. The comparison is based on a non-Gaussian data set (derived from a digital elevation model of the Walker Lake area, Nevada, USA). We discuss the impact of relevant simulation parameters, such as the domain size, the number of discretization levels, and the initial conditions.

[Spatial differentiation and impact factors of Yutian Oasis's soil surface salt based on GWR model].

PubMed

Yuan, Yu Yun; Wahap, Halik; Guan, Jing Yun; Lu, Long Hui; Zhang, Qin Qin

2016-10-01

In this paper, topsoil salinity data gathered from 24 sampling sites in the Yutian Oasis were used, nine different kinds of environmental variables closely related to soil salinity were selec-ted as influencing factors, then, the spatial distribution characteristics of topsoil salinity and spatial heterogeneity of influencing factors were analyzed by combining the spatial autocorrelation with traditional regression analysis and geographically weighted regression model. Results showed that the topsoil salinity in Yutian Oasis was not of random distribution but had strong spatial dependence, and the spatial autocorrelation index for topsoil salinity was 0.479. Groundwater salinity, groundwater depth, elevation and temperature were the main factors influencing topsoil salt accumulation in arid land oases and they were spatially heterogeneous. The nine selected environmental variables except soil pH had significant influences on topsoil salinity with spatial disparity. GWR model was superior to the OLS model on interpretation and estimation of spatial non-stationary data, also had a remarkable advantage in visualization of modeling parameters.

Practical secure quantum communications

NASA Astrophysics Data System (ADS)

Diamanti, Eleni

2015-05-01

We review recent advances in the field of quantum cryptography, focusing in particular on practical implementations of two central protocols for quantum network applications, namely key distribution and coin flipping. The former allows two parties to share secret messages with information-theoretic security, even in the presence of a malicious eavesdropper in the communication channel, which is impossible with classical resources alone. The latter enables two distrustful parties to agree on a random bit, again with information-theoretic security, and with a cheating probability lower than the one that can be reached in a classical scenario. Our implementations rely on continuous-variable technology for quantum key distribution and on a plug and play discrete-variable system for coin flipping, and necessitate a rigorous security analysis adapted to the experimental schemes and their imperfections. In both cases, we demonstrate the protocols with provable security over record long distances in optical fibers and assess the performance of our systems as well as their limitations. The reported advances offer a powerful toolbox for practical applications of secure communications within future quantum networks.

High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing.

PubMed

Qu, Zhen; Djordjevic, Ivan B

2017-04-03

A high-speed four-state continuous-variable quantum key distribution (CV-QKD) system, enabled by wavelength-division multiplexing, polarization multiplexing, and orbital angular momentum (OAM) multiplexing, is studied in the presence of atmospheric turbulence. The atmospheric turbulence channel is emulated by two spatial light modulators (SLMs) on which two randomly generated azimuthal phase patterns yielding Andrews' spectrum are recorded. The phase noise is mitigated by the phase noise cancellation (PNC) stage, and channel transmittance can be monitored directly by the D.C. level in our PNC stage. After the system calibration, a total SKR of >1.68 Gbit/s can be reached in the ideal system, featured with lossless channel and free of excess noise. In our experiment, based on commercial photodetectors, the minimum transmittances of 0.21 and 0.29 are required for OAM states of 2 (or -2) and 6 (or -6), respectively, to guarantee the secure transmission, while a total SKR of 120 Mbit/s can be obtained in case of mean transmittances.

Accounting for Heterogeneity in Relative Treatment Effects for Use in Cost-Effectiveness Models and Value-of-Information Analyses

PubMed Central

Soares, Marta O.; Palmer, Stephen; Ades, Anthony E.; Harrison, David; Shankar-Hari, Manu; Rowan, Kathy M.

2015-01-01

Cost-effectiveness analysis (CEA) models are routinely used to inform health care policy. Key model inputs include relative effectiveness of competing treatments, typically informed by meta-analysis. Heterogeneity is ubiquitous in meta-analysis, and random effects models are usually used when there is variability in effects across studies. In the absence of observed treatment effect modifiers, various summaries from the random effects distribution (random effects mean, predictive distribution, random effects distribution, or study-specific estimate [shrunken or independent of other studies]) can be used depending on the relationship between the setting for the decision (population characteristics, treatment definitions, and other contextual factors) and the included studies. If covariates have been measured that could potentially explain the heterogeneity, then these can be included in a meta-regression model. We describe how covariates can be included in a network meta-analysis model and how the output from such an analysis can be used in a CEA model. We outline a model selection procedure to help choose between competing models and stress the importance of clinical input. We illustrate the approach with a health technology assessment of intravenous immunoglobulin for the management of adult patients with severe sepsis in an intensive care setting, which exemplifies how risk of bias information can be incorporated into CEA models. We show that the results of the CEA and value-of-information analyses are sensitive to the model and highlight the importance of sensitivity analyses when conducting CEA in the presence of heterogeneity. The methods presented extend naturally to heterogeneity in other model inputs, such as baseline risk. PMID:25712447

Accounting for Heterogeneity in Relative Treatment Effects for Use in Cost-Effectiveness Models and Value-of-Information Analyses.

PubMed

Welton, Nicky J; Soares, Marta O; Palmer, Stephen; Ades, Anthony E; Harrison, David; Shankar-Hari, Manu; Rowan, Kathy M

2015-07-01

Cost-effectiveness analysis (CEA) models are routinely used to inform health care policy. Key model inputs include relative effectiveness of competing treatments, typically informed by meta-analysis. Heterogeneity is ubiquitous in meta-analysis, and random effects models are usually used when there is variability in effects across studies. In the absence of observed treatment effect modifiers, various summaries from the random effects distribution (random effects mean, predictive distribution, random effects distribution, or study-specific estimate [shrunken or independent of other studies]) can be used depending on the relationship between the setting for the decision (population characteristics, treatment definitions, and other contextual factors) and the included studies. If covariates have been measured that could potentially explain the heterogeneity, then these can be included in a meta-regression model. We describe how covariates can be included in a network meta-analysis model and how the output from such an analysis can be used in a CEA model. We outline a model selection procedure to help choose between competing models and stress the importance of clinical input. We illustrate the approach with a health technology assessment of intravenous immunoglobulin for the management of adult patients with severe sepsis in an intensive care setting, which exemplifies how risk of bias information can be incorporated into CEA models. We show that the results of the CEA and value-of-information analyses are sensitive to the model and highlight the importance of sensitivity analyses when conducting CEA in the presence of heterogeneity. The methods presented extend naturally to heterogeneity in other model inputs, such as baseline risk. © The Author(s) 2015.

Variable versus conventional lung protective mechanical ventilation during open abdominal surgery (PROVAR): a randomised controlled trial.

PubMed

Spieth, P M; Güldner, A; Uhlig, C; Bluth, T; Kiss, T; Conrad, C; Bischlager, K; Braune, A; Huhle, R; Insorsi, A; Tarantino, F; Ball, L; Schultz, M J; Abolmaali, N; Koch, T; Pelosi, P; Gama de Abreu, M

2018-03-01

Experimental studies showed that controlled variable ventilation (CVV) yielded better pulmonary function compared to non-variable ventilation (CNV) in injured lungs. We hypothesized that CVV improves intraoperative and postoperative respiratory function in patients undergoing open abdominal surgery. Fifty patients planned for open abdominal surgery lasting >3 h were randomly assigned to receive either CVV or CNV. Mean tidal volumes and PEEP were set at 8 ml kg -1 (predicted body weight) and 5 cm H 2 O, respectively. In CVV, tidal volumes varied randomly, following a normal distribution, on a breath-by-breath basis. The primary endpoint was the forced vital capacity (FVC) on postoperative Day 1. Secondary endpoints were oxygenation, non-aerated lung volume, distribution of ventilation, and pulmonary and extrapulmonary complications until postoperative Day 5. FVC did not differ significantly between CVV and CNV on postoperative Day 1, 61.5 (standard deviation 22.1) % vs 61.9 (23.6) %, respectively; mean [95% confidence interval (CI)] difference, -0.4 (-13.2-14.0), P=0.95. Intraoperatively, CVV did not result in improved respiratory function, haemodynamics, or redistribution of ventilation compared to CNV. Postoperatively, FVC, forced expiratory volume at the first second (FEV 1 ), and FEV 1 /FVC deteriorated, while atelectasis volume and plasma levels of interleukin-6 and interleukin-8 increased, but values did not differ between groups. The incidence of postoperative pulmonary and extrapulmonary complications was comparable in CVV and CNV. In patients undergoing open abdominal surgery, CVV did not improve intraoperative and postoperative respiratory function compared with CNV. NCT 01683578. Copyright © 2017 British Journal of Anaesthesia. Published by Elsevier Ltd. All rights reserved.

Postoperative pain after manual and mechanical glide path: a randomized clinical trial.

PubMed

Pasqualini, Damiano; Mollo, Livio; Scotti, Nicola; Cantatore, Giuseppe; Castellucci, Arnaldo; Migliaretti, Giuseppe; Berutti, Elio

2012-01-01

This prospective randomized clinical trial evaluated the incidence of postoperative pain after glide path performed with PathFile (PF) (Dentsply Maillefer, Ballaigues, Switzerland) versus stainless-steel K-file (KF). In 149 subjects, the mechanical glide path was performed with nickel-titanium (NiTi) rotary PF; in 146 subjects, the manual glide path was performed with stainless-steel KFs. Postoperative pain, analgesics consumption, and the number of days to complete pain resolution were evaluated in the following 7 days. An analysis of variance model for repeated measures was used to compare the variation of pain-scale values (P < .05). The Student's t test for continuous variables normally distributed, the nonparametric Mann-Whitney U test for the nonnormally distributed variables, and the chi-square test for dichotomous variables were used (P < .05). Despite homogeneous baseline conditions at diagnosis, tooth type, pain prevalence, and scores, the postoperative pain prevalence curves in PF group evidenced a more favorable trend in terms of time to pain resolution compared with the KF group (P = .004). The difference was also evident in the model adjusted for analgesics consumption in both groups (P = .012). The mean analgesics intake per subject was significantly higher in the KF group (3.7 ± 2.2) compared with the PF group (2 ± 1.7) (P < .001). Mean pain stop values were also significantly higher in the KF group (2.7) compared with the PF group (1.7) (P = .001). The glide path with NiTi Rotary PF leads to less postoperative pain and faster symptom resolution. Copyright © 2012 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Exploring the impact of forcing error characteristics on physically based snow simulations within a global sensitivity analysis framework

NASA Astrophysics Data System (ADS)

Raleigh, M. S.; Lundquist, J. D.; Clark, M. P.

2015-07-01

Physically based models provide insights into key hydrologic processes but are associated with uncertainties due to deficiencies in forcing data, model parameters, and model structure. Forcing uncertainty is enhanced in snow-affected catchments, where weather stations are scarce and prone to measurement errors, and meteorological variables exhibit high variability. Hence, there is limited understanding of how forcing error characteristics affect simulations of cold region hydrology and which error characteristics are most important. Here we employ global sensitivity analysis to explore how (1) different error types (i.e., bias, random errors), (2) different error probability distributions, and (3) different error magnitudes influence physically based simulations of four snow variables (snow water equivalent, ablation rates, snow disappearance, and sublimation). We use the Sobol' global sensitivity analysis, which is typically used for model parameters but adapted here for testing model sensitivity to coexisting errors in all forcings. We quantify the Utah Energy Balance model's sensitivity to forcing errors with 1 840 000 Monte Carlo simulations across four sites and five different scenarios. Model outputs were (1) consistently more sensitive to forcing biases than random errors, (2) generally less sensitive to forcing error distributions, and (3) critically sensitive to different forcings depending on the relative magnitude of errors. For typical error magnitudes found in areas with drifting snow, precipitation bias was the most important factor for snow water equivalent, ablation rates, and snow disappearance timing, but other forcings had a more dominant impact when precipitation uncertainty was due solely to gauge undercatch. Additionally, the relative importance of forcing errors depended on the model output of interest. Sensitivity analysis can reveal which forcing error characteristics matter most for hydrologic modeling.

Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids

PubMed Central

Ali, S. M.; Mehmood, C. A; Khan, B.; Jawad, M.; Farid, U; Jadoon, J. K.; Ali, M.; Tareen, N. K.; Usman, S.; Majid, M.; Anwar, S. M.

2016-01-01

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion. PMID:27314229

Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids.

PubMed

Ali, S M; Mehmood, C A; Khan, B; Jawad, M; Farid, U; Jadoon, J K; Ali, M; Tareen, N K; Usman, S; Majid, M; Anwar, S M

2016-01-01

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion.

Drop Spreading with Random Viscosity

NASA Astrophysics Data System (ADS)

Xu, Feng; Jensen, Oliver

2016-11-01

Airway mucus acts as a barrier to protect the lung. However as a biological material, its physical properties are known imperfectly and can be spatially heterogeneous. In this study we assess the impact of these uncertainties on the rate of spreading of a drop (representing an inhaled aerosol) over a mucus film. We model the film as Newtonian, having a viscosity that depends linearly on the concentration of a passive solute (a crude proxy for mucin proteins). Given an initial random solute (and hence viscosity) distribution, described as a Gaussian random field with a given correlation structure, we seek to quantify the uncertainties in outcomes as the drop spreads. Using lubrication theory, we describe the spreading of the drop in terms of a system of coupled nonlinear PDEs governing the evolution of film height and the vertically-averaged solute concentration. We perform Monte Carlo simulations to predict the variability in the drop centre location and width (1D) or area (2D). We show how simulation results are well described (at much lower computational cost) by a low-order model using a weak disorder expansion. Our results show for example how variability in the drop location is a non-monotonic function of the solute correlation length increases. Engineering and Physical Sciences Research Council.

Random Predictor Models for Rigorous Uncertainty Quantification: Part 2

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2015-01-01

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean, the variance, and the range of the model's parameter, thus of the output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, is bounded rigorously.

Random Predictor Models for Rigorous Uncertainty Quantification: Part 1

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2015-01-01

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean and the variance of the model's parameters, thus of the predicted output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, can be bounded tightly and rigorously.

A stochastic-geometric model of soil variation in Pleistocene patterned ground

NASA Astrophysics Data System (ADS)

Lark, Murray; Meerschman, Eef; Van Meirvenne, Marc

2013-04-01

In this paper we examine the spatial variability of soil in parent material with complex spatial structure which arises from complex non-linear geomorphic processes. We show that this variability can be better-modelled by a stochastic-geometric model than by a standard Gaussian random field. The benefits of the new model are seen in the reproduction of features of the target variable which influence processes like water movement and pollutant dispersal. Complex non-linear processes in the soil give rise to properties with non-Gaussian distributions. Even under a transformation to approximate marginal normality, such variables may have a more complex spatial structure than the Gaussian random field model of geostatistics can accommodate. In particular the extent to which extreme values of the variable are connected in spatially coherent regions may be misrepresented. As a result, for example, geostatistical simulation generally fails to reproduce the pathways for preferential flow in an environment where coarse infill of former fluvial channels or coarse alluvium of braided streams creates pathways for rapid movement of water. Multiple point geostatistics has been developed to deal with this problem. Multiple point methods proceed by sampling from a set of training images which can be assumed to reproduce the non-Gaussian behaviour of the target variable. The challenge is to identify appropriate sources of such images. In this paper we consider a mode of soil variation in which the soil varies continuously, exhibiting short-range lateral trends induced by local effects of the factors of soil formation which vary across the region of interest in an unpredictable way. The trends in soil variation are therefore only apparent locally, and the soil variation at regional scale appears random. We propose a stochastic-geometric model for this mode of soil variation called the Continuous Local Trend (CLT) model. We consider a case study of soil formed in relict patterned ground with pronounced lateral textural variations arising from the presence of infilled ice-wedges of Pleistocene origin. We show how knowledge of the pedogenetic processes in this environment, along with some simple descriptive statistics, can be used to select and fit a CLT model for the apparent electrical conductivity (ECa) of the soil. We use the model to simulate realizations of the CLT process, and compare these with realizations of a fitted Gaussian random field. We show how statistics that summarize the spatial coherence of regions with small values of ECa, which are expected to have coarse texture and so larger saturated hydraulic conductivity, are better reproduced by the CLT model than by the Gaussian random field. This suggests that the CLT model could be used to generate an unlimited supply of training images to allow multiple point geostatistical simulation or prediction of this or similar variables.

High throughput nonparametric probability density estimation.

PubMed

Farmer, Jenny; Jacobs, Donald

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.

High throughput nonparametric probability density estimation

PubMed Central

Farmer, Jenny

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference. PMID:29750803

Randomly displaced phase distribution design and its advantage in page-data recording of Fourier transform holograms.

PubMed

Emoto, Akira; Fukuda, Takashi

2013-02-20

For Fourier transform holography, an effective random phase distribution with randomly displaced phase segments is proposed for obtaining a smooth finite optical intensity distribution in the Fourier transform plane. Since unitary phase segments are randomly distributed in-plane, the blanks give various spatial frequency components to an image, and thus smooth the spectrum. Moreover, by randomly changing the phase segment size, spike generation from the unitary phase segment size in the spectrum can be reduced significantly. As a result, a smooth spectrum including sidebands can be formed at a relatively narrow extent. The proposed phase distribution sustains the primary functions of a random phase mask for holographic-data recording and reconstruction. Therefore, this distribution is expected to find applications in high-density holographic memory systems, replacing conventional random phase mask patterns.

The SIMRAND methodology: Theory and application for the simulation of research and development projects

NASA Technical Reports Server (NTRS)

Miles, R. F., Jr.

1986-01-01

A research and development (R&D) project often involves a number of decisions that must be made concerning which subset of systems or tasks are to be undertaken to achieve the goal of the R&D project. To help in this decision making, SIMRAND (SIMulation of Research ANd Development Projects) is a methodology for the selection of the optimal subset of systems or tasks to be undertaken on an R&D project. Using alternative networks, the SIMRAND methodology models the alternative subsets of systems or tasks under consideration. Each path through an alternative network represents one way of satisfying the project goals. Equations are developed that relate the system or task variables to the measure of reference. Uncertainty is incorporated by treating the variables of the equations probabilistically as random variables, with cumulative distribution functions assessed by technical experts. Analytical techniques of probability theory are used to reduce the complexity of the alternative networks. Cardinal utility functions over the measure of preference are assessed for the decision makers. A run of the SIMRAND Computer I Program combines, in a Monte Carlo simulation model, the network structure, the equations, the cumulative distribution functions, and the utility functions.

Alignment of nematic liquid crystals by inhomogeneous surfaces

NASA Astrophysics Data System (ADS)

Ong, Hiap Liew; Hurd, Alan J.; Meyer, Robert B.

1985-01-01

Variable oblique alignment of nematic liquid crystals has been achieved on microscopically inhomogeneous surfaces. The surfaces consist of small patches favoring vertical (homeotropic) alignment surrounded by a matrix favoring a planar alignment. The construction of these surfaces employs randomly distributed microscopic metal islands formed by certain metals as vapor-deposited films. Larger scale periodic patterns were made as well to verify the techniques. The results are interpreted in terms of a continuum elasticity theory and azimuthal degeneracy is also discussed.

Proceedings of the Symposium on the Interface of Computer Science and Statistics (17th) Held in Lexington, Kentucky on 17-19 March 1985.

DTIC Science & Technology

1986-03-04

satisfied, but the availability of the machinery will entice developments to appear over the next few years. TABULATION AND DISPLAY To gain access to...independent, identicallyof the optimal predictor and the mean square distributed random variables with mean 0 and difference between the optimal forecast... optimal forecast (the conditional mean of YT+, given qute approximation to a2 1 j For the% Yl ~ ~ ~ ~ ~ ~ ~ . ... ,FT) thehtm-[ ]# rn-1 Y1...;,YT) and

Stochastic Calculus and Differential Equations for Physics and Finance

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2013-02-01

1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.

Influence of material uncertainties on the RLC parameters of wound inductors modeled using the finite element method

NASA Astrophysics Data System (ADS)

Lossa, Geoffrey; Deblecker, Olivier; Grève, Zacharie De

2018-05-01

In this work, we highlight the influence of the material uncertainties (magnetic permeability, electric conductivity of a Mn-Zn ferrite core, and electric permittivity of wire insulation) on the RLC parameters of a wound inductor extracted from the finite element method. To that end, the finite element method is embedded in a Monte Carlo simulation. We show that considering mentioned different material properties as real random variables, leads to significant variations in the distributions of the RLC parameters.

Efficient Estimation of Mutual Information for Strongly Dependent Variables

DTIC Science & Technology

2015-05-11

the two possibilities: for a fixed dimension d and near- est neighbor parameter k, we find a constant ↵ k,d , such that if V̄ (i)/V (i) < ↵ k,d , then...also compare the results to several baseline estima- tors: KSG (Kraskov et al., 2004), generalized near- est neighbor graph (GNN) (Pál et al., 2010...Amaury Lendasse, and Francesco Corona. A boundary corrected expansion of the moments of near- est neighbor distributions. Random Struct. Algorithms

Continuous Decision Support

DTIC Science & Technology

2015-12-24

but the fundamental approach remains unchanged. We consider the case of a sports memorabilia shop whose owner is an avid personal collector of baseball...collector’s competition 15 days from now. Between now and then, as customers bring in antique baseball cards, he must decide which ones to purchase for his...purchased from the shop each day is a random variable that is Poisson distributed with λout = 2. • 20% of cards are 5.25 in2, 10% are 9.97 in2, and 70% are

Spatial Variability of Soil-Water Storage in the Southern Sierra Critical Zone Observatory: Measurement and Prediction

NASA Astrophysics Data System (ADS)

Oroza, C.; Bales, R. C.; Zheng, Z.; Glaser, S. D.

2017-12-01

Predicting the spatial distribution of soil moisture in mountain environments is confounded by multiple factors, including complex topography, spatial variably of soil texture, sub-surface flow paths, and snow-soil interactions. While remote-sensing tools such as passive-microwave monitoring can measure spatial variability of soil moisture, they only capture near-surface soil layers. Large-scale sensor networks are increasingly providing soil-moisture measurements at high temporal resolution across a broader range of depths than are accessible from remote sensing. It may be possible to combine these in-situ measurements with high-resolution LIDAR topography and canopy cover to estimate the spatial distribution of soil moisture at high spatial resolution at multiple depths. We study the feasibility of this approach using six years (2009-2014) of daily volumetric water content measurements at 10-, 30-, and 60-cm depths from the Southern Sierra Critical Zone Observatory. A non-parametric, multivariate regression algorithm, Random Forest, was used to predict the spatial distribution of depth-integrated soil-water storage, based on the in-situ measurements and a combination of node attributes (topographic wetness, northness, elevation, soil texture, and location with respect to canopy cover). We observe predictable patterns of predictor accuracy and independent variable ranking during the six-year study period. Predictor accuracy is highest during the snow-cover and early recession periods but declines during the dry period. Soil texture has consistently high feature importance. Other landscape attributes exhibit seasonal trends: northness peaks during the wet-up period, and elevation and topographic-wetness index peak during the recession and dry period, respectively.

Extinction in the Star Cluster SAI 113 and Galactic Structure in Carina

NASA Astrophysics Data System (ADS)

Carraro, Giovanni; Turner, David G.; Majaess, Daniel J.; Baume, Gustavo L.; Gamen, Roberto; Molina Lera, José A.

2017-04-01

Photometric CCD UB VI C photometry obtained for 4860 stars surrounding the embedded southern cluster SAI 113 (Skiff 8) is used to examine the reddening in the field and derive the distance to the cluster and nearby van Genderen 1. Spectroscopic color excesses for bright cluster stars, photometric reddenings for A3 dwarfs, and dereddening of cluster stars imply that the reddening and extinction laws match results derived for other young clusters in Carina: {E}U-B/{E}B-V≃ 0.64 and {R}V≃ 4. SAI 113 displays features that may be linked to a history of dynamical interactions among member stars: possible circumstellar reddening and rapid rotation of late B-type members, ringlike features in star density, and a compact core, with most stars distributed randomly across the field. The group van Genderen 1 resembles a stellar asterism, with potential members distributed randomly across the field. Distances of 3.90 ± 0.19 kpc and 2.49 ± 0.09 kpc are derived for SAI 113 and van Genderen 1, respectively, with variable reddenings {E}B-V ranging from 0.84 to 1.29 and 0.23 to 1.28. The SRC variables CK Car and EV Car may be outlying members of van Genderen 1, thereby of use for calibrating the period-luminosity relation for pulsating M supergiants. More importantly, the anomalous reddening and extinction evident in Carina and nearby regions of the Galactic plane in the fourth quadrant impact the mapping of spiral structure from young open clusters. The distribution of spiral arms in the fourth quadrant may be significantly different from how it is often portrayed.

Microstructure and Mechanical Property of Glutaraldehyde-Treated Porcine Pulmonary Ligament.

PubMed

Chen, Huan; Zhao, Xuefeng; Berwick, Zachary C; Krieger, Joshua F; Chambers, Sean; Kassab, Ghassan S

2016-06-01

There is a significant need for fixed biological tissues with desired structural and material constituents for tissue engineering applications. Here, we introduce the lung ligament as a fixed biological material that may have clinical utility for tissue engineering. To characterize the lung tissue for potential clinical applications, we studied glutaraldehyde-treated porcine pulmonary ligament (n = 11) with multiphoton microscopy (MPM) and conducted biaxial planar experiments to characterize the mechanical property of the tissue. The MPM imaging revealed that there are generally two families of collagen fibers distributed in two distinct layers: The first family largely aligns along the longitudinal direction with a mean angle of θ = 10.7 ± 9.3 deg, while the second one exhibits a random distribution with a mean θ = 36.6 ± 27.4. Elastin fibers appear in some intermediate sublayers with a random orientation distribution with a mean θ = 39.6 ± 23 deg. Based on the microstructural observation, a microstructure-based constitutive law was proposed to model the elastic property of the tissue. The material parameters were identified by fitting the model to the biaxial stress-strain data of specimens, and good fitting quality was achieved. The parameter e0 (which denotes the strain beyond which the collagen can withstand tension) of glutaraldehyde-treated tissues demonstrated low variability implying a relatively consistent collagen undulation in different samples, while the stiffness parameters for elastin and collagen fibers showed relatively greater variability. The fixed tissues presented a smaller e0 than that of fresh specimen, confirming that glutaraldehyde crosslinking increases the mechanical strength of collagen-based biomaterials. The present study sheds light on the biomechanics of glutaraldehyde-treated porcine pulmonary ligament that may be a candidate for tissue engineering.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simonen, F.A.; Khaleel, M.A.

This paper describes a statistical evaluation of the through-thickness copper variation for welds in reactor pressure vessels, and reviews the historical basis for the static and arrest fracture toughness (K{sub Ic} and K{sub Ia}) equations used in the VISA-II code. Copper variability in welds is due to fabrication procedures with copper contents being randomly distributed, variable from one location to another through the thickness of the vessel. The VISA-II procedure of sampling the copper content from a statistical distribution for every 6.35- to 12.7-mm (1/4- to 1/2-in.) layer through the thickness was found to be consistent with the statistical observations.more » However, the parameters of the VISA-II distribution and statistical limits required further investigation. Copper contents at few locations through the thickness were found to exceed the 0.4% upper limit of the VISA-II code. The data also suggest that the mean copper content varies systematically through the thickness. While, the assumption of normality is not clearly supported by the available data, a statistical evaluation based on all the available data results in mean and standard deviations within the VISA-II code limits.« less

Parallelization of a spatial random field characterization process using the Method of Anchored Distributions and the HTCondor high throughput computing system

NASA Astrophysics Data System (ADS)

Osorio-Murillo, C. A.; Over, M. W.; Frystacky, H.; Ames, D. P.; Rubin, Y.

2013-12-01

A new software application called MAD# has been coupled with the HTCondor high throughput computing system to aid scientists and educators with the characterization of spatial random fields and enable understanding the spatial distribution of parameters used in hydrogeologic and related modeling. MAD# is an open source desktop software application used to characterize spatial random fields using direct and indirect information through Bayesian inverse modeling technique called the Method of Anchored Distributions (MAD). MAD relates indirect information with a target spatial random field via a forward simulation model. MAD# executes inverse process running the forward model multiple times to transfer information from indirect information to the target variable. MAD# uses two parallelization profiles according to computational resources available: one computer with multiple cores and multiple computers - multiple cores through HTCondor. HTCondor is a system that manages a cluster of desktop computers for submits serial or parallel jobs using scheduling policies, resources monitoring, job queuing mechanism. This poster will show how MAD# reduces the time execution of the characterization of random fields using these two parallel approaches in different case studies. A test of the approach was conducted using 1D problem with 400 cells to characterize saturated conductivity, residual water content, and shape parameters of the Mualem-van Genuchten model in four materials via the HYDRUS model. The number of simulations evaluated in the inversion was 10 million. Using the one computer approach (eight cores) were evaluated 100,000 simulations in 12 hours (10 million - 1200 hours approximately). In the evaluation on HTCondor, 32 desktop computers (132 cores) were used, with a processing time of 60 hours non-continuous in five days. HTCondor reduced the processing time for uncertainty characterization by a factor of 20 (1200 hours reduced to 60 hours.)

Generalization of symmetric α-stable Lévy distributions for q >1

NASA Astrophysics Data System (ADS)

Umarov, Sabir; Tsallis, Constantino; Gell-Mann, Murray; Steinberg, Stanly

2010-03-01

The α-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,α)-stable distributions. These sequences are generalizations of independent and identically distributed α-stable distributions and have not been previously studied. Long-range dependent (q,α)-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 α-stable Lévy distributions. In the present paper we establish basic properties of (q,α)-stable distributions and generalize the result of Umarov et al. [Milan J. Math. 76, 307 (2008)], where the particular case α =2,qɛ[1,3) was considered, to the whole range of stability and nonextensivity parameters α ɛ(0,2] and q ɛ[1,3), respectively. We also discuss possible further extensions of the results that we obtain and formulate some conjectures.

Predicting Blood Lactate Concentration and Oxygen Uptake from sEMG Data during Fatiguing Cycling Exercise.

PubMed

Ražanskas, Petras; Verikas, Antanas; Olsson, Charlotte; Viberg, Per-Arne

2015-08-19

This article presents a study of the relationship between electromyographic (EMG) signals from vastus lateralis, rectus femoris, biceps femoris and semitendinosus muscles, collected during fatiguing cycling exercises, and other physiological measurements, such as blood lactate concentration and oxygen consumption. In contrast to the usual practice of picking one particular characteristic of the signal, e.g., the median or mean frequency, multiple variables were used to obtain a thorough characterization of EMG signals in the spectral domain. Based on these variables, linear and non-linear (random forest) models were built to predict blood lactate concentration and oxygen consumption. The results showed that mean and median frequencies are sub-optimal choices for predicting these physiological quantities in dynamic exercises, as they did not exhibit significant changes over the course of our protocol and only weakly correlated with blood lactate concentration or oxygen uptake. Instead, the root mean square of the original signal and backward difference, as well as parameters describing the tails of the EMG power distribution were the most important variables for these models. Coefficients of determination ranging from R(2) = 0:77 to R(2) = 0:98 (for blood lactate) and from R(2) = 0:81 to R(2) = 0:97 (for oxygen uptake) were obtained when using random forest regressors.

Quantifying Effects of Voids in Woven Ceramic Matrix Composites

NASA Technical Reports Server (NTRS)

Goldsmith, Marlana B.; Sankar, Bhavani V.; Haftka, Raphael T.; Goldberg, Robert K.

2013-01-01

Randomness in woven ceramic matrix composite architecture has been found to cause large variability in stiffness and strength. The inherent voids are an aspect of the architecture that may cause a significant portion of the variability. A study is undertaken to investigate the effects of many voids of random sizes and distributions. Response surface approximations were formulated based on void parameters such as area and length fractions to provide an estimate of the effective stiffness. Obtaining quantitative relationships between the properties of the voids and their effects on stiffness of ceramic matrix composites are of ultimate interest, but the exploratory study presented here starts by first modeling the effects of voids on an isotropic material. Several cases with varying void parameters were modeled which resulted in a large amount of variability of the transverse stiffness and out-of-plane shear stiffness. An investigation into a physical explanation for the stiffness degradation led to the observation that the voids need to be treated as an entity that reduces load bearing capabilities in a space larger than what the void directly occupies through a corrected length fraction or area fraction. This provides explanation as to why void volume fraction is not the only important factor to consider when computing loss of stiffness.

Fault Diagnosis Strategies for SOFC-Based Power Generation Plants

PubMed Central

Costamagna, Paola; De Giorgi, Andrea; Gotelli, Alberto; Magistri, Loredana; Moser, Gabriele; Sciaccaluga, Emanuele; Trucco, Andrea

2016-01-01

The success of distributed power generation by plants based on solid oxide fuel cells (SOFCs) is hindered by reliability problems that can be mitigated through an effective fault detection and isolation (FDI) system. However, the numerous operating conditions under which such plants can operate and the random size of the possible faults make identifying damaged plant components starting from the physical variables measured in the plant very difficult. In this context, we assess two classical FDI strategies (model-based with fault signature matrix and data-driven with statistical classification) and the combination of them. For this assessment, a quantitative model of the SOFC-based plant, which is able to simulate regular and faulty conditions, is used. Moreover, a hybrid approach based on the random forest (RF) classification method is introduced to address the discrimination of regular and faulty situations due to its practical advantages. Working with a common dataset, the FDI performances obtained using the aforementioned strategies, with different sets of monitored variables, are observed and compared. We conclude that the hybrid FDI strategy, realized by combining a model-based scheme with a statistical classifier, outperforms the other strategies. In addition, the inclusion of two physical variables that should be measured inside the SOFCs can significantly improve the FDI performance, despite the actual difficulty in performing such measurements. PMID:27556472

Geometrical effects on the electron residence time in semiconductor nano-particles.

PubMed

Koochi, Hakimeh; Ebrahimi, Fatemeh

2014-09-07

We have used random walk (RW) numerical simulations to investigate the influence of the geometry on the statistics of the electron residence time τ(r) in a trap-limited diffusion process through semiconductor nano-particles. This is an important parameter in coarse-grained modeling of charge carrier transport in nano-structured semiconductor films. The traps have been distributed randomly on the surface (r(2) model) or through the whole particle (r(3) model) with a specified density. The trap energies have been taken from an exponential distribution and the traps release time is assumed to be a stochastic variable. We have carried out (RW) simulations to study the effect of coordination number, the spatial arrangement of the neighbors and the size of nano-particles on the statistics of τ(r). It has been observed that by increasing the coordination number n, the average value of electron residence time, τ̅(r) rapidly decreases to an asymptotic value. For a fixed coordination number n, the electron's mean residence time does not depend on the neighbors' spatial arrangement. In other words, τ̅(r) is a porosity-dependence, local parameter which generally varies remarkably from site to site, unless we are dealing with highly ordered structures. We have also examined the effect of nano-particle size d on the statistical behavior of τ̅(r). Our simulations indicate that for volume distribution of traps, τ̅(r) scales as d(2). For a surface distribution of traps τ(r) increases almost linearly with d. This leads to the prediction of a linear dependence of the diffusion coefficient D on the particle size d in ordered structures or random structures above the critical concentration which is in accordance with experimental observations.

Conditional random matrix ensembles and the stability of dynamical systems

NASA Astrophysics Data System (ADS)

Kirk, Paul; Rolando, Delphine M. Y.; MacLean, Adam L.; Stumpf, Michael P. H.

2015-08-01

Random matrix theory (RMT) has found applications throughout physics and applied mathematics, in subject areas as diverse as communications networks, population dynamics, neuroscience, and models of the banking system. Many of these analyses exploit elegant analytical results, particularly the circular law and its extensions. In order to apply these results, assumptions must be made about the distribution of matrix elements. Here we demonstrate that the choice of matrix distribution is crucial. In particular, adopting an unrealistic matrix distribution for the sake of analytical tractability is liable to lead to misleading conclusions. We focus on the application of RMT to the long-standing, and at times fractious, ‘diversity-stability debate’, which is concerned with establishing whether large complex systems are likely to be stable. Early work (and subsequent elaborations) brought RMT to bear on the debate by modelling the entries of a system’s Jacobian matrix as independent and identically distributed (i.i.d.) random variables. These analyses were successful in yielding general results that were not tied to any specific system, but relied upon a restrictive i.i.d. assumption. Other studies took an opposing approach, seeking to elucidate general principles of stability through the analysis of specific systems. Here we develop a statistical framework that reconciles these two contrasting approaches. We use a range of illustrative dynamical systems examples to demonstrate that: (i) stability probability cannot be summarily deduced from any single property of the system (e.g. its diversity); and (ii) our assessment of stability depends on adequately capturing the details of the systems analysed. Failing to condition on the structure of dynamical systems will skew our analysis and can, even for very small systems, result in an unnecessarily pessimistic diagnosis of their stability.

Mapping Sub-Antarctic Cushion Plants Using Random Forests to Combine Very High Resolution Satellite Imagery and Terrain Modelling

PubMed Central

Bricher, Phillippa K.; Lucieer, Arko; Shaw, Justine; Terauds, Aleks; Bergstrom, Dana M.

2013-01-01

Monitoring changes in the distribution and density of plant species often requires accurate and high-resolution baseline maps of those species. Detecting such change at the landscape scale is often problematic, particularly in remote areas. We examine a new technique to improve accuracy and objectivity in mapping vegetation, combining species distribution modelling and satellite image classification on a remote sub-Antarctic island. In this study, we combine spectral data from very high resolution WorldView-2 satellite imagery and terrain variables from a high resolution digital elevation model to improve mapping accuracy, in both pixel- and object-based classifications. Random forest classification was used to explore the effectiveness of these approaches on mapping the distribution of the critically endangered cushion plant Azorella macquariensis Orchard (Apiaceae) on sub-Antarctic Macquarie Island. Both pixel- and object-based classifications of the distribution of Azorella achieved very high overall validation accuracies (91.6–96.3%, κ = 0.849–0.924). Both two-class and three-class classifications were able to accurately and consistently identify the areas where Azorella was absent, indicating that these maps provide a suitable baseline for monitoring expected change in the distribution of the cushion plants. Detecting such change is critical given the threats this species is currently facing under altering environmental conditions. The method presented here has applications to monitoring a range of species, particularly in remote and isolated environments. PMID:23940805

Effect of elevation on extreme precipitation of short durations: evidences of orographic signature on the parameters of Depth-Duration-Frequency curves

NASA Astrophysics Data System (ADS)

Avanzi, Francesco; De Michele, Carlo; Gabriele, Salvatore; Ghezzi, Antonio; Rosso, Renzo

2015-04-01

Here, we show how atmospheric circulation and topography rule the variability of depth-duration-frequency (DDF) curves parameters, and we discuss how this variability has physical implications on the formation of extreme precipitations at high elevations. A DDF is a curve ruling the value of the maximum annual precipitation H as a function of duration D and the level of probability F. We consider around 1500 stations over the Italian territory, with at least 20 years of data of maximum annual precipitation depth at different durations. We estimated the DDF parameters at each location by using the asymptotic distribution of extreme values, i.e. the so-called Generalized Extreme Value (GEV) distribution, and considering a statistical simple scale invariance hypothesis. Consequently, a DDF curve depends on five different parameters. A first set relates H with the duration (namely, the mean value of annual maximum precipitation depth for unit duration and the scaling exponent), while a second set links H to F (namely, a scale, position and shape parameter). The value of the shape parameter has consequences on the type of random variable (unbounded, upper or lower bounded). This extensive analysis shows that the variability of the mean value of annual maximum precipitation depth for unit duration obeys to the coupled effect of topography and modal direction of moisture flux during extreme events. Median values of this parameter decrease with elevation. We called this phenomenon "reverse orographic effect" on extreme precipitation of short durations, since it is in contrast with general knowledge about the orographic effect on mean precipitation. Moreover, the scaling exponent is mainly driven by topography alone (with increasing values of this parameter at increasing elevations). Therefore, the quantiles of H(D,F) at durations greater than unit turn to be more variable at high elevations than at low elevations. Additionally, the analysis of the variability of the shape parameter with elevation shows that extreme events at high elevations appear to be distributed according to an upper bounded probability distribution. These evidences could be a characteristic sign of the formation of extreme precipitation events at high elevations.

Comparison of five modelling techniques to predict the spatial distribution and abundance of seabirds

USGS Publications Warehouse

O'Connell, Allan F.; Gardner, Beth; Oppel, Steffen; Meirinho, Ana; Ramírez, Iván; Miller, Peter I.; Louzao, Maite

2012-01-01

Knowledge about the spatial distribution of seabirds at sea is important for conservation. During marine conservation planning, logistical constraints preclude seabird surveys covering the complete area of interest and spatial distribution of seabirds is frequently inferred from predictive statistical models. Increasingly complex models are available to relate the distribution and abundance of pelagic seabirds to environmental variables, but a comparison of their usefulness for delineating protected areas for seabirds is lacking. Here we compare the performance of five modelling techniques (generalised linear models, generalised additive models, Random Forest, boosted regression trees, and maximum entropy) to predict the distribution of Balearic Shearwaters (Puffinus mauretanicus) along the coast of the western Iberian Peninsula. We used ship transect data from 2004 to 2009 and 13 environmental variables to predict occurrence and density, and evaluated predictive performance of all models using spatially segregated test data. Predicted distribution varied among the different models, although predictive performance varied little. An ensemble prediction that combined results from all five techniques was robust and confirmed the existence of marine important bird areas for Balearic Shearwaters in Portugal and Spain. Our predictions suggested additional areas that would be of high priority for conservation and could be proposed as protected areas. Abundance data were extremely difficult to predict, and none of five modelling techniques provided a reliable prediction of spatial patterns. We advocate the use of ensemble modelling that combines the output of several methods to predict the spatial distribution of seabirds, and use these predictions to target separate surveys assessing the abundance of seabirds in areas of regular use.

Fluid Structure Interaction in a Turbine Blade

NASA Technical Reports Server (NTRS)

Gorla, Rama S. R.

2004-01-01

An unsteady, three dimensional Navier-Stokes solution in rotating frame formulation for turbomachinery applications is presented. Casting the governing equations in a rotating frame enabled the freezing of grid motion and resulted in substantial savings in computer time. The turbine blade was computationally simulated and probabilistically evaluated in view of several uncertainties in the aerodynamic, structural, material and thermal variables that govern the turbine blade. The interconnection between the computational fluid dynamics code and finite element structural analysis code was necessary to couple the thermal profiles with the structural design. The stresses and their variations were evaluated at critical points on the Turbine blade. Cumulative distribution functions and sensitivity factors were computed for stress responses due to aerodynamic, geometric, mechanical and thermal random variables.

Probabilistic Component Mode Synthesis of Nondeterministic Substructures

NASA Technical Reports Server (NTRS)

Brown, Andrew M.; Ferri, Aldo A.

1996-01-01

Standard methods of structural dynamic analysis assume that the structural characteristics are deterministic. Recognizing that these characteristics are actually statistical in nature researchers have recently developed a variety of methods that use this information to determine probabilities of a desired response characteristic, such as natural frequency, without using expensive Monte Carlo simulations. One of the problems in these methods is correctly identifying the statistical properties of primitive variables such as geometry, stiffness, and mass. We present a method where the measured dynamic properties of substructures are used instead as the random variables. The residual flexibility method of component mode synthesis is combined with the probabilistic methods to determine the cumulative distribution function of the system eigenvalues. A simple cantilever beam test problem is presented that illustrates the theory.

Jitter Reduces Response-Time Variability in ADHD: An Ex-Gaussian Analysis.

PubMed

Lee, Ryan W Y; Jacobson, Lisa A; Pritchard, Alison E; Ryan, Matthew S; Yu, Qilu; Denckla, Martha B; Mostofsky, Stewart; Mahone, E Mark

2015-09-01

"Jitter" involves randomization of intervals between stimulus events. Compared with controls, individuals with ADHD demonstrate greater intrasubject variability (ISV) performing tasks with fixed interstimulus intervals (ISIs). Because Gaussian curves mask the effect of extremely slow or fast response times (RTs), ex-Gaussian approaches have been applied to study ISV. This study applied ex-Gaussian analysis to examine the effects of jitter on RT variability in children with and without ADHD. A total of 75 children, aged 9 to 14 years (44 ADHD, 31 controls), completed a go/no-go test with two conditions: fixed ISI and jittered ISI. ADHD children showed greater variability, driven by elevations in exponential (tau), but not normal (sigma) components of the RT distribution. Jitter decreased tau in ADHD to levels not statistically different than controls, reducing lapses in performance characteristic of impaired response control. Jitter may provide a nonpharmacologic mechanism to facilitate readiness to respond and reduce lapses from sustained (controlled) performance. © 2012 SAGE Publications.

Turbulent, Extreme Multi-zone Model for Simulating Flux and Polarization Variability in Blazars

NASA Astrophysics Data System (ADS)

Marscher, Alan P.

2014-01-01

The author presents a model for variability of the flux and polarization of blazars in which turbulent plasma flowing at a relativistic speed down a jet crosses a standing conical shock. The shock compresses the plasma and accelerates electrons to energies up to γmax >~ 104 times their rest-mass energy, with the value of γmax determined by the direction of the magnetic field relative to the shock front. The turbulence is approximated in a computer code as many cells, each with a uniform magnetic field whose direction is selected randomly. The density of high-energy electrons in the plasma changes randomly with time in a manner consistent with the power spectral density of flux variations derived from observations of blazars. The variations in flux and polarization are therefore caused by continuous noise processes rather than by singular events such as explosive injection of energy at the base of the jet. Sample simulations illustrate the behavior of flux and linear polarization versus time that such a model produces. The variations in γ-ray flux generated by the code are often, but not always, correlated with those at lower frequencies, and many of the flares are sharply peaked. The mean degree of polarization of synchrotron radiation is higher and its timescale of variability shorter toward higher frequencies, while the polarization electric vector sometimes randomly executes apparent rotations. The slope of the spectral energy distribution exhibits sharper breaks than can arise solely from energy losses. All of these results correspond to properties observed in blazars.

Statistics of optimal information flow in ensembles of regulatory motifs

NASA Astrophysics Data System (ADS)

Crisanti, Andrea; De Martino, Andrea; Fiorentino, Jonathan

2018-02-01

Genetic regulatory circuits universally cope with different sources of noise that limit their ability to coordinate input and output signals. In many cases, optimal regulatory performance can be thought to correspond to configurations of variables and parameters that maximize the mutual information between inputs and outputs. Since the mid-2000s, such optima have been well characterized in several biologically relevant cases. Here we use methods of statistical field theory to calculate the statistics of the maximal mutual information (the "capacity") achievable by tuning the input variable only in an ensemble of regulatory motifs, such that a single controller regulates N targets. Assuming (i) sufficiently large N , (ii) quenched random kinetic parameters, and (iii) small noise affecting the input-output channels, we can accurately reproduce numerical simulations both for the mean capacity and for the whole distribution. Our results provide insight into the inherent variability in effectiveness occurring in regulatory systems with heterogeneous kinetic parameters.

Genome scanning for detecting adaptive genes along environmental gradients in the Japanese conifer, Cryptomeria japonica.

PubMed

Tsumura, Y; Uchiyama, K; Moriguchi, Y; Ueno, S; Ihara-Ujino, T

2012-12-01

Local adaptation is important in evolutionary processes and speciation. We used multiple tests to identify several candidate genes that may be involved in local adaptation from 1026 loci in 14 natural populations of Cryptomeria japonica, the most economically important forestry tree in Japan. We also studied the relationships between genotypes and environmental variables to obtain information on the selective pressures acting on individual populations. Outlier loci were mapped onto a linkage map, and the positions of loci associated with specific environmental variables are considered. The outlier loci were not randomly distributed on the linkage map; linkage group 11 was identified as a genomic island of divergence. Three loci in this region were also associated with environmental variables such as mean annual temperature, daily maximum temperature, maximum snow depth, and so on. Outlier loci identified with high significance levels will be essential for conservation purposes and for future work on molecular breeding.

Biologically-variable rhythmic auditory cues are superior to isochronous cues in fostering natural gait variability in Parkinson's disease.

PubMed

Dotov, D G; Bayard, S; Cochen de Cock, V; Geny, C; Driss, V; Garrigue, G; Bardy, B; Dalla Bella, S

2017-01-01

Rhythmic auditory cueing improves certain gait symptoms of Parkinson's disease (PD). Cues are typically stimuli or beats with a fixed inter-beat interval. We show that isochronous cueing has an unwanted side-effect in that it exacerbates one of the motor symptoms characteristic of advanced PD. Whereas the parameters of the stride cycle of healthy walkers and early patients possess a persistent correlation in time, or long-range correlation (LRC), isochronous cueing renders stride-to-stride variability random. Random stride cycle variability is also associated with reduced gait stability and lack of flexibility. To investigate how to prevent patients from acquiring a random stride cycle pattern, we tested rhythmic cueing which mimics the properties of variability found in healthy gait (biological variability). PD patients (n=19) and age-matched healthy participants (n=19) walked with three rhythmic cueing stimuli: isochronous, with random variability, and with biological variability (LRC). Synchronization was not instructed. The persistent correlation in gait was preserved only with stimuli with biological variability, equally for patients and controls (p's<0.05). In contrast, cueing with isochronous or randomly varying inter-stimulus/beat intervals removed the LRC in the stride cycle. Notably, the individual's tendency to synchronize steps with beats determined the amount of negative effects of isochronous and random cues (p's<0.05) but not the positive effect of biological variability. Stimulus variability and patients' propensity to synchronize play a critical role in fostering healthier gait dynamics during cueing. The beneficial effects of biological variability provide useful guidelines for improving existing cueing treatments. Copyright © 2016 Elsevier B.V. All rights reserved.

Oxygen distribution in tumors: A qualitative analysis and modeling study providing a novel Monte Carlo approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lagerlöf, Jakob H., E-mail: Jakob@radfys.gu.se; Kindblom, Jon; Bernhardt, Peter

2014-09-15

Purpose: To construct a Monte Carlo (MC)-based simulation model for analyzing the dependence of tumor oxygen distribution on different variables related to tumor vasculature [blood velocity, vessel-to-vessel proximity (vessel proximity), and inflowing oxygen partial pressure (pO{sub 2})]. Methods: A voxel-based tissue model containing parallel capillaries with square cross-sections (sides of 10 μm) was constructed. Green's function was used for diffusion calculations and Michaelis-Menten's kinetics to manage oxygen consumption. The model was tuned to approximately reproduce the oxygenational status of a renal carcinoma; the depth oxygenation curves (DOC) were fitted with an analytical expression to facilitate rapid MC simulations of tumormore » oxygen distribution. DOCs were simulated with three variables at three settings each (blood velocity, vessel proximity, and inflowing pO{sub 2}), which resulted in 27 combinations of conditions. To create a model that simulated variable oxygen distributions, the oxygen tension at a specific point was randomly sampled with trilinear interpolation in the dataset from the first simulation. Six correlations between blood velocity, vessel proximity, and inflowing pO{sub 2} were hypothesized. Variable models with correlated parameters were compared to each other and to a nonvariable, DOC-based model to evaluate the differences in simulated oxygen distributions and tumor radiosensitivities for different tumor sizes. Results: For tumors with radii ranging from 5 to 30 mm, the nonvariable DOC model tended to generate normal or log-normal oxygen distributions, with a cut-off at zero. The pO{sub 2} distributions simulated with the six-variable DOC models were quite different from the distributions generated with the nonvariable DOC model; in the former case the variable models simulated oxygen distributions that were more similar to in vivo results found in the literature. For larger tumors, the oxygen distributions became truncated in the lower end, due to anoxia, but smaller tumors showed undisturbed oxygen distributions. The six different models with correlated parameters generated three classes of oxygen distributions. The first was a hypothetical, negative covariance between vessel proximity and pO{sub 2} (VPO-C scenario); the second was a hypothetical positive covariance between vessel proximity and pO{sub 2} (VPO+C scenario); and the third was the hypothesis of no correlation between vessel proximity and pO{sub 2} (UP scenario). The VPO-C scenario produced a distinctly different oxygen distribution than the two other scenarios. The shape of the VPO-C scenario was similar to that of the nonvariable DOC model, and the larger the tumor, the greater the similarity between the two models. For all simulations, the mean oxygen tension decreased and the hypoxic fraction increased with tumor size. The absorbed dose required for definitive tumor control was highest for the VPO+C scenario, followed by the UP and VPO-C scenarios. Conclusions: A novel MC algorithm was presented which simulated oxygen distributions and radiation response for various biological parameter values. The analysis showed that the VPO-C scenario generated a clearly different oxygen distribution from the VPO+C scenario; the former exhibited a lower hypoxic fraction and higher radiosensitivity. In future studies, this modeling approach might be valuable for qualitative analyses of factors that affect oxygen distribution as well as analyses of specific experimental and clinical situations.« less

Oxygen distribution in tumors: a qualitative analysis and modeling study providing a novel Monte Carlo approach.

PubMed

Lagerlöf, Jakob H; Kindblom, Jon; Bernhardt, Peter

2014-09-01

To construct a Monte Carlo (MC)-based simulation model for analyzing the dependence of tumor oxygen distribution on different variables related to tumor vasculature [blood velocity, vessel-to-vessel proximity (vessel proximity), and inflowing oxygen partial pressure (pO2)]. A voxel-based tissue model containing parallel capillaries with square cross-sections (sides of 10 μm) was constructed. Green's function was used for diffusion calculations and Michaelis-Menten's kinetics to manage oxygen consumption. The model was tuned to approximately reproduce the oxygenational status of a renal carcinoma; the depth oxygenation curves (DOC) were fitted with an analytical expression to facilitate rapid MC simulations of tumor oxygen distribution. DOCs were simulated with three variables at three settings each (blood velocity, vessel proximity, and inflowing pO2), which resulted in 27 combinations of conditions. To create a model that simulated variable oxygen distributions, the oxygen tension at a specific point was randomly sampled with trilinear interpolation in the dataset from the first simulation. Six correlations between blood velocity, vessel proximity, and inflowing pO2 were hypothesized. Variable models with correlated parameters were compared to each other and to a nonvariable, DOC-based model to evaluate the differences in simulated oxygen distributions and tumor radiosensitivities for different tumor sizes. For tumors with radii ranging from 5 to 30 mm, the nonvariable DOC model tended to generate normal or log-normal oxygen distributions, with a cut-off at zero. The pO2 distributions simulated with the six-variable DOC models were quite different from the distributions generated with the nonvariable DOC model; in the former case the variable models simulated oxygen distributions that were more similar to in vivo results found in the literature. For larger tumors, the oxygen distributions became truncated in the lower end, due to anoxia, but smaller tumors showed undisturbed oxygen distributions. The six different models with correlated parameters generated three classes of oxygen distributions. The first was a hypothetical, negative covariance between vessel proximity and pO2 (VPO-C scenario); the second was a hypothetical positive covariance between vessel proximity and pO2 (VPO+C scenario); and the third was the hypothesis of no correlation between vessel proximity and pO2 (UP scenario). The VPO-C scenario produced a distinctly different oxygen distribution than the two other scenarios. The shape of the VPO-C scenario was similar to that of the nonvariable DOC model, and the larger the tumor, the greater the similarity between the two models. For all simulations, the mean oxygen tension decreased and the hypoxic fraction increased with tumor size. The absorbed dose required for definitive tumor control was highest for the VPO+C scenario, followed by the UP and VPO-C scenarios. A novel MC algorithm was presented which simulated oxygen distributions and radiation response for various biological parameter values. The analysis showed that the VPO-C scenario generated a clearly different oxygen distribution from the VPO+C scenario; the former exhibited a lower hypoxic fraction and higher radiosensitivity. In future studies, this modeling approach might be valuable for qualitative analyses of factors that affect oxygen distribution as well as analyses of specific experimental and clinical situations.

Probabilistic analysis of preload in the abutment screw of a dental implant complex.

PubMed

Guda, Teja; Ross, Thomas A; Lang, Lisa A; Millwater, Harry R

2008-09-01

Screw loosening is a problem for a percentage of implants. A probabilistic analysis to determine the cumulative probability distribution of the preload, the probability of obtaining an optimal preload, and the probabilistic sensitivities identifying important variables is lacking. The purpose of this study was to examine the inherent variability of material properties, surface interactions, and applied torque in an implant system to determine the probability of obtaining desired preload values and to identify the significant variables that affect the preload. Using software programs, an abutment screw was subjected to a tightening torque and the preload was determined from finite element (FE) analysis. The FE model was integrated with probabilistic analysis software. Two probabilistic analysis methods (advanced mean value and Monte Carlo sampling) were applied to determine the cumulative distribution function (CDF) of preload. The coefficient of friction, elastic moduli, Poisson's ratios, and applied torque were modeled as random variables and defined by probability distributions. Separate probability distributions were determined for the coefficient of friction in well-lubricated and dry environments. The probabilistic analyses were performed and the cumulative distribution of preload was determined for each environment. A distinct difference was seen between the preload probability distributions generated in a dry environment (normal distribution, mean (SD): 347 (61.9) N) compared to a well-lubricated environment (normal distribution, mean (SD): 616 (92.2) N). The probability of obtaining a preload value within the target range was approximately 54% for the well-lubricated environment and only 0.02% for the dry environment. The preload is predominately affected by the applied torque and coefficient of friction between the screw threads and implant bore at lower and middle values of the preload CDF, and by the applied torque and the elastic modulus of the abutment screw at high values of the preload CDF. Lubrication at the threaded surfaces between the abutment screw and implant bore affects the preload developed in the implant complex. For the well-lubricated surfaces, only approximately 50% of implants will have preload values within the generally accepted range. This probability can be improved by applying a higher torque than normally recommended or a more closely controlled torque than typically achieved. It is also suggested that materials with higher elastic moduli be used in the manufacture of the abutment screw to achieve a higher preload.

Polynomial chaos expansion with random and fuzzy variables

NASA Astrophysics Data System (ADS)

Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.

2016-06-01

A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.

Fuzzy probabilistic design of water distribution networks

NASA Astrophysics Data System (ADS)

Fu, Guangtao; Kapelan, Zoran

2011-05-01

The primary aim of this paper is to present a fuzzy probabilistic approach for optimal design and rehabilitation of water distribution systems, combining aleatoric and epistemic uncertainties in a unified framework. The randomness and imprecision in future water consumption are characterized using fuzzy random variables whose realizations are not real but fuzzy numbers, and the nodal head requirements are represented by fuzzy sets, reflecting the imprecision in customers' requirements. The optimal design problem is formulated as a two-objective optimization problem, with minimization of total design cost and maximization of system performance as objectives. The system performance is measured by the fuzzy random reliability, defined as the probability that the fuzzy head requirements are satisfied across all network nodes. The satisfactory degree is represented by necessity measure or belief measure in the sense of the Dempster-Shafer theory of evidence. An efficient algorithm is proposed, within a Monte Carlo procedure, to calculate the fuzzy random system reliability and is effectively combined with the nondominated sorting genetic algorithm II (NSGAII) to derive the Pareto optimal design solutions. The newly proposed methodology is demonstrated with two case studies: the New York tunnels network and Hanoi network. The results from both cases indicate that the new methodology can effectively accommodate and handle various aleatoric and epistemic uncertainty sources arising from the design process and can provide optimal design solutions that are not only cost-effective but also have higher reliability to cope with severe future uncertainties.

Biological community structure on patch reefs in Biscayne National Park, FL, USA

USGS Publications Warehouse

Kuffner, Ilsa B.; Grober-Dunsmore, Rikki; Brock, John C.; Hickey, T. Don

2010-01-01

Coral reef ecosystem management benefits from continual quantitative assessment of the resources being managed, plus assessment of factors that affect distribution patterns of organisms in the ecosystem. In this study, we investigate the relationships among physical, benthic, and fish variables in an effort to help explain the distribution patterns of organisms on patch reefs within Biscayne National Park, FL, USA. We visited a total of 196 randomly selected sampling stations on 12 shallow (<10 m) patch reefs and measured physical variables (e.g., substratum rugosity, substratum type) and benthic and fish community variables. We also incorporated data on substratum rugosity collected remotely via airborne laser surveying (Experimental Advanced Airborne Research Lidar—EAARL). Across all stations, only weak relationships were found between physical, benthic cover, and fish assemblage variables. Much of the variance was attributable to a “reef effect,” meaning that community structure and organism abundances were more variable at stations among reefs than within reefs. However, when the reef effect was accounted for and removed statistically, patterns were detected. Within reefs, juvenile scarids were most abundant at stations with high coverage of the fleshy macroalgae Dictyota spp., and the calcified alga Halimeda tuna was most abundant at stations with low EAARL rugosity. Explanations for the overwhelming importance of “reef” in explaining variance in our dataset could include the stochastic arrangement of organisms on patch reefs related to variable larval recruitment in space and time and/or strong historical effects due to patchy disturbances (e.g., hurricanes, fishing), as well as legacy effects of prior residents (“priority” effects).

Quantifying Uncertainties from Presence Data Sampling Methods for Species Distribution Modeling: Focused on Vegetation.

NASA Astrophysics Data System (ADS)

Sung, S.; Kim, H. G.; Lee, D. K.; Park, J. H.; Mo, Y.; Kil, S.; Park, C.

2016-12-01

The impact of climate change has been observed throughout the globe. The ecosystem experiences rapid changes such as vegetation shift, species extinction. In these context, Species Distribution Model (SDM) is one of the popular method to project impact of climate change on the ecosystem. SDM basically based on the niche of certain species with means to run SDM present point data is essential to find biological niche of species. To run SDM for plants, there are certain considerations on the characteristics of vegetation. Normally, to make vegetation data in large area, remote sensing techniques are used. In other words, the exact point of presence data has high uncertainties as we select presence data set from polygons and raster dataset. Thus, sampling methods for modeling vegetation presence data should be carefully selected. In this study, we used three different sampling methods for selection of presence data of vegetation: Random sampling, Stratified sampling and Site index based sampling. We used one of the R package BIOMOD2 to access uncertainty from modeling. At the same time, we included BioCLIM variables and other environmental variables as input data. As a result of this study, despite of differences among the 10 SDMs, the sampling methods showed differences in ROC values, random sampling methods showed the lowest ROC value while site index based sampling methods showed the highest ROC value. As a result of this study the uncertainties from presence data sampling methods and SDM can be quantified.

Bayesian inference for multivariate meta-analysis Box-Cox transformation models for individual patient data with applications to evaluation of cholesterol lowering drugs

PubMed Central

Kim, Sungduk; Chen, Ming-Hui; Ibrahim, Joseph G.; Shah, Arvind K.; Lin, Jianxin

2013-01-01

In this paper, we propose a class of Box-Cox transformation regression models with multidimensional random effects for analyzing multivariate responses for individual patient data (IPD) in meta-analysis. Our modeling formulation uses a multivariate normal response meta-analysis model with multivariate random effects, in which each response is allowed to have its own Box-Cox transformation. Prior distributions are specified for the Box-Cox transformation parameters as well as the regression coefficients in this complex model, and the Deviance Information Criterion (DIC) is used to select the best transformation model. Since the model is quite complex, a novel Monte Carlo Markov chain (MCMC) sampling scheme is developed to sample from the joint posterior of the parameters. This model is motivated by a very rich dataset comprising 26 clinical trials involving cholesterol lowering drugs where the goal is to jointly model the three dimensional response consisting of Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Triglycerides (TG) (LDL-C, HDL-C, TG). Since the joint distribution of (LDL-C, HDL-C, TG) is not multivariate normal and in fact quite skewed, a Box-Cox transformation is needed to achieve normality. In the clinical literature, these three variables are usually analyzed univariately: however, a multivariate approach would be more appropriate since these variables are correlated with each other. A detailed analysis of these data is carried out using the proposed methodology. PMID:23580436

Bayesian inference for multivariate meta-analysis Box-Cox transformation models for individual patient data with applications to evaluation of cholesterol-lowering drugs.

PubMed

Kim, Sungduk; Chen, Ming-Hui; Ibrahim, Joseph G; Shah, Arvind K; Lin, Jianxin

2013-10-15

In this paper, we propose a class of Box-Cox transformation regression models with multidimensional random effects for analyzing multivariate responses for individual patient data in meta-analysis. Our modeling formulation uses a multivariate normal response meta-analysis model with multivariate random effects, in which each response is allowed to have its own Box-Cox transformation. Prior distributions are specified for the Box-Cox transformation parameters as well as the regression coefficients in this complex model, and the deviance information criterion is used to select the best transformation model. Because the model is quite complex, we develop a novel Monte Carlo Markov chain sampling scheme to sample from the joint posterior of the parameters. This model is motivated by a very rich dataset comprising 26 clinical trials involving cholesterol-lowering drugs where the goal is to jointly model the three-dimensional response consisting of low density lipoprotein cholesterol (LDL-C), high density lipoprotein cholesterol (HDL-C), and triglycerides (TG) (LDL-C, HDL-C, TG). Because the joint distribution of (LDL-C, HDL-C, TG) is not multivariate normal and in fact quite skewed, a Box-Cox transformation is needed to achieve normality. In the clinical literature, these three variables are usually analyzed univariately; however, a multivariate approach would be more appropriate because these variables are correlated with each other. We carry out a detailed analysis of these data by using the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.

Residential surface soil guidance values applied worldwide to the original 2001 Stockholm Convention POP pesticides.

PubMed

Jennings, Aaron A; Li, Zijian

2015-09-01

Surface soil contamination is a worldwide problem. Many regulatory jurisdictions attempt to control human exposures with regulatory guidance values (RGVs) that specify a soil's maximum allowable concentration. Pesticides are important soil contaminants because of their intentional toxicity and widespread surface soil application. Worldwide, at least 174 regulatory jurisdictions from 54 United Nations member states have published more than 19,400 pesticide RGVs for at least 739 chemically unique pesticides. This manuscript examines the variability of the guidance values that are applied worldwide to the original 2001 Stockholm Convention persistent organic pollutants (POP) pesticides (Aldrin, Chlordane, DDT, Dieldrin, Endrin, Heptachlor, Mirex, and Toxaphene) for which at least 1667 RGVs have been promulgated. Results indicate that the spans of the RGVs applied to each of these pesticides vary from 6.1 orders of magnitude for Toxaphene to 10.0 orders of magnitude for Mirex. The distribution of values across these value spans resembles the distribution of lognormal random variables, but also contain non-random value clusters. Approximately 40% of all the POP RGVs fall within uncertainty bounds computed from the U.S. Environmental Protection Agency (USEPA) RGV cancer risk model. Another 22% of the values fall within uncertainty bounds computed from the USEPA's non-cancer risk model, but the cancer risk calculations yield the binding (lowest) value for all POP pesticides except Endrin. The results presented emphasize the continued need to rationalize the RGVs applied worldwide to important soil contaminants. Copyright © 2015 Elsevier Ltd. All rights reserved.

Measures of Residual Risk with Connections to Regression, Risk Tracking, Surrogate Models, and Ambiguity

DTIC Science & Technology

2015-01-07

vector that helps to manage , predict, and mitigate the risk in the original variable. Residual risk can be exemplified as a quantification of the improved... the random variable of interest is viewed in concert with a related random vector that helps to manage , predict, and mitigate the risk in the original...measures of risk. They view a random variable of interest in concert with an auxiliary random vector that helps to manage , predict and mitigate the risk

Raw and Central Moments of Binomial Random Variables via Stirling Numbers

ERIC Educational Resources Information Center

Griffiths, Martin

2013-01-01

We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this…

A hybrid CS-SA intelligent approach to solve uncertain dynamic facility layout problems considering dependency of demands

NASA Astrophysics Data System (ADS)

Moslemipour, Ghorbanali

2018-07-01

This paper aims at proposing a quadratic assignment-based mathematical model to deal with the stochastic dynamic facility layout problem. In this problem, product demands are assumed to be dependent normally distributed random variables with known probability density function and covariance that change from period to period at random. To solve the proposed model, a novel hybrid intelligent algorithm is proposed by combining the simulated annealing and clonal selection algorithms. The proposed model and the hybrid algorithm are verified and validated using design of experiment and benchmark methods. The results show that the hybrid algorithm has an outstanding performance from both solution quality and computational time points of view. Besides, the proposed model can be used in both of the stochastic and deterministic situations.

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

NASA Astrophysics Data System (ADS)

Frahm, Klaus M.; Shepelyansky, Dima L.

2014-04-01

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.

Analysis of speckle and material properties in laider tracer

NASA Astrophysics Data System (ADS)

Ross, Jacob W.; Rigling, Brian D.; Watson, Edward A.

2017-04-01

The SAL simulation tool Laider Tracer models speckle: the random variation in intensity of an incident light beam across a rough surface. Within Laider Tracer, the speckle field is modeled as a 2-D array of jointly Gaussian random variables projected via ray tracing onto the scene of interest. Originally, all materials in Laider Tracer were treated as ideal diffuse scatterers, for which the far-field return computed uses the Lambertian Bidirectional Reflectance Distribution Function (BRDF). As presented here, we implement material properties into Laider Tracer via the Non-conventional Exploitation Factors Data System: a database of properties for thousands of different materials sampled at various wavelengths and incident angles. We verify the intensity behavior as a function of incident angle after material properties are added to the simulation.

Probabilistic inference in discrete spaces can be implemented into networks of LIF neurons.

PubMed

Probst, Dimitri; Petrovici, Mihai A; Bytschok, Ilja; Bill, Johannes; Pecevski, Dejan; Schemmel, Johannes; Meier, Karlheinz

2015-01-01

The means by which cortical neural networks are able to efficiently solve inference problems remains an open question in computational neuroscience. Recently, abstract models of Bayesian computation in neural circuits have been proposed, but they lack a mechanistic interpretation at the single-cell level. In this article, we describe a complete theoretical framework for building networks of leaky integrate-and-fire neurons that can sample from arbitrary probability distributions over binary random variables. We test our framework for a model inference task based on a psychophysical phenomenon (the Knill-Kersten optical illusion) and further assess its performance when applied to randomly generated distributions. As the local computations performed by the network strongly depend on the interaction between neurons, we compare several types of couplings mediated by either single synapses or interneuron chains. Due to its robustness to substrate imperfections such as parameter noise and background noise correlations, our model is particularly interesting for implementation on novel, neuro-inspired computing architectures, which can thereby serve as a fast, low-power substrate for solving real-world inference problems.

Meta-analysis of diagnostic test data: a bivariate Bayesian modeling approach.

PubMed

Verde, Pablo E

2010-12-30

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. Copyright © 2010 John Wiley & Sons, Ltd.

Probabilistic inference in discrete spaces can be implemented into networks of LIF neurons

PubMed Central

Probst, Dimitri; Petrovici, Mihai A.; Bytschok, Ilja; Bill, Johannes; Pecevski, Dejan; Schemmel, Johannes; Meier, Karlheinz

2015-01-01

The means by which cortical neural networks are able to efficiently solve inference problems remains an open question in computational neuroscience. Recently, abstract models of Bayesian computation in neural circuits have been proposed, but they lack a mechanistic interpretation at the single-cell level. In this article, we describe a complete theoretical framework for building networks of leaky integrate-and-fire neurons that can sample from arbitrary probability distributions over binary random variables. We test our framework for a model inference task based on a psychophysical phenomenon (the Knill-Kersten optical illusion) and further assess its performance when applied to randomly generated distributions. As the local computations performed by the network strongly depend on the interaction between neurons, we compare several types of couplings mediated by either single synapses or interneuron chains. Due to its robustness to substrate imperfections such as parameter noise and background noise correlations, our model is particularly interesting for implementation on novel, neuro-inspired computing architectures, which can thereby serve as a fast, low-power substrate for solving real-world inference problems. PMID:25729361

Bayesian spatio-temporal discard model in a demersal trawl fishery

NASA Astrophysics Data System (ADS)

Grazia Pennino, M.; Muñoz, Facundo; Conesa, David; López-Quílez, Antonio; Bellido, José M.

2014-07-01

Spatial management of discards has recently been proposed as a useful tool for the protection of juveniles, by reducing discard rates and can be used as a buffer against management errors and recruitment failure. In this study Bayesian hierarchical spatial models have been used to analyze about 440 trawl fishing operations of two different metiers, sampled between 2009 and 2012, in order to improve our understanding of factors that influence the quantity of discards and to identify their spatio-temporal distribution in the study area. Our analysis showed that the relative importance of each variable was different for each metier, with a few similarities. In particular, the random vessel effect and seasonal variability were identified as main driving variables for both metiers. Predictive maps of the abundance of discards and maps of the posterior mean of the spatial component show several hot spots with high discard concentration for each metier. We argue how the seasonal/spatial effects, and the knowledge about the factors influential to discarding, could potentially be exploited as potential mitigation measures for future fisheries management strategies. However, misidentification of hotspots and uncertain predictions can culminate in inappropriate mitigation practices which can sometimes be irreversible. The proposed Bayesian spatial method overcomes these issues, since it offers a unified approach which allows the incorporation of spatial random-effect terms, spatial correlation of the variables and the uncertainty of the parameters in the modeling process, resulting in a better quantification of the uncertainty and accurate predictions.

Event-Based Variance-Constrained ${\\mathcal {H}}_{\\infty }$ Filtering for Stochastic Parameter Systems Over Sensor Networks With Successive Missing Measurements.

PubMed

Wang, Licheng; Wang, Zidong; Han, Qing-Long; Wei, Guoliang

2018-03-01

This paper is concerned with the distributed filtering problem for a class of discrete time-varying stochastic parameter systems with error variance constraints over a sensor network where the sensor outputs are subject to successive missing measurements. The phenomenon of the successive missing measurements for each sensor is modeled via a sequence of mutually independent random variables obeying the Bernoulli binary distribution law. To reduce the frequency of unnecessary data transmission and alleviate the communication burden, an event-triggered mechanism is introduced for the sensor node such that only some vitally important data is transmitted to its neighboring sensors when specific events occur. The objective of the problem addressed is to design a time-varying filter such that both the requirements and the variance constraints are guaranteed over a given finite-horizon against the random parameter matrices, successive missing measurements, and stochastic noises. By recurring to stochastic analysis techniques, sufficient conditions are established to ensure the existence of the time-varying filters whose gain matrices are then explicitly characterized in term of the solutions to a series of recursive matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of the developed event-triggered distributed filter design strategy.

Epidemiological characteristics of cases of death from tuberculosis and vulnerable territories1

PubMed Central

Yamamura, Mellina; Santos-Neto, Marcelino; dos Santos, Rebeca Augusto Neman; Garcia, Maria Concebida da Cunha; Nogueira, Jordana de Almeida; Arcêncio, Ricardo Alexandre

2015-01-01

Objective: to characterize the differences in the clinical and epidemiological profile of cases of death that had tuberculosis as an immediate or associated cause, and to analyze the spatial distribution of the cases of death from tuberculosis within the territories of Ribeirão Preto, Brazil. Method: an ecological study, in which the population consisted of 114 cases of death from tuberculosis. Bivariate analysis was carried out, as well as point density analysis, defined with the Kernel estimate. Results: of the cases of death from tuberculosis, 50 were the immediate cause and 64 an associated cause. Age (p=.008) and sector responsible for the death certificate (p=.003) were the variables that presented statistically significant associations with the cause of death. The spatial distribution, in both events, did not occur randomly, forming clusters in areas of the municipality. Conclusion: the difference in the profiles of the cases of death from tuberculosis, as a basic cause and as an associated cause, was governed by the age and the sector responsible for the completion of the death certificate. The non-randomness of the spatial distribution of the cases suggests areas that are vulnerable to these events. Knowing these areas can contribute to the choice of disease control strategies. PMID:26487142