On the inequivalence of the CH and CHSH inequalities due to finite statistics

NASA Astrophysics Data System (ADS)

Renou, M. O.; Rosset, D.; Martin, A.; Gisin, N.

2017-06-01

Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated using a finite number of samples. Therefore the nonsignaling conditions are only approximately satisfied and the robustness of the violation depends on the chosen inequality variant. We explain that phenomenon using the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario, and propose a method to optimize the statistical robustness of a Bell inequality. In the process, we describe the finite group composed of relabeling of parties, measurement settings and outcomes, and identify correspondences between the irreducible representations of this group and properties of outcome probability distributions such as normalization, signaling or having uniform marginals.

On-Orbit Collision Hazard Analysis in Low Earth Orbit Using the Poisson Probability Distribution (Version 1.0)

DOT National Transportation Integrated Search

1992-08-26

This document provides the basic information needed to estimate a general : probability of collision in Low Earth Orbit (LEO). Although the method : described in this primer is a first order approximation, its results are : reasonable. Furthermore, t...

Probability Density Functions of Observed Rainfall in Montana

NASA Technical Reports Server (NTRS)

Larsen, Scott D.; Johnson, L. Ronald; Smith, Paul L.

1995-01-01

The question of whether a rain rate probability density function (PDF) can vary uniformly between precipitation events is examined. Image analysis on large samples of radar echoes is possible because of advances in technology. The data provided by such an analysis easily allow development of radar reflectivity factors (and by extension rain rate) distribution. Finding a PDF becomes a matter of finding a function that describes the curve approximating the resulting distributions. Ideally, one PDF would exist for all cases; or many PDF's that have the same functional form with only systematic variations in parameters (such as size or shape) exist. Satisfying either of theses cases will, validate the theoretical basis of the Area Time Integral (ATI). Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89 percent of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit. Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89% of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit.

A dynamic programming approach to estimate the capacity value of energy storage

DOE PAGES

Sioshansi, Ramteen; Madaeni, Seyed Hossein; Denholm, Paul

2013-09-17

Here, we present a method to estimate the capacity value of storage. Our method uses a dynamic program to model the effect of power system outages on the operation and state of charge of storage in subsequent periods. We combine the optimized dispatch from the dynamic program with estimated system loss of load probabilities to compute a probability distribution for the state of charge of storage in each period. This probability distribution can be used as a forced outage rate for storage in standard reliability-based capacity value estimation methods. Our proposed method has the advantage over existing approximations that itmore » explicitly captures the effect of system shortage events on the state of charge of storage in subsequent periods. We also use a numerical case study, based on five utility systems in the U.S., to demonstrate our technique and compare it to existing approximation methods.« less

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.

General formulation of long-range degree correlations in complex networks

NASA Astrophysics Data System (ADS)

Fujiki, Yuka; Takaguchi, Taro; Yakubo, Kousuke

2018-06-01

We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One joint and four conditional probability distributions are introduced to fully describe long-range degree correlations with respect to degrees k and k' of two nodes and shortest path length l between them. We present general relations among these probability distributions and clarify the relevance to nearest-neighbor degree correlations. Unlike nearest-neighbor correlations, some of these probability distributions are meaningful only in finite-size networks. Furthermore, as a baseline to determine the existence of intrinsic long-range degree correlations in a network other than inevitable correlations caused by the finite-size effect, the functional forms of these probability distributions for random networks are analytically evaluated within a mean-field approximation. The utility of our argument is demonstrated by applying it to real-world networks.

Performance of cellular frequency-hopped spread-spectrum radio networks

NASA Astrophysics Data System (ADS)

Gluck, Jeffrey W.; Geraniotis, Evaggelos

1989-10-01

Multiple access interference is characterized for cellular mobile networks, in which users are assumed to be Poisson-distributed in the plane and employ frequency-hopped spread-spectrum signaling with transmitter-oriented assignment of frequency-hopping patterns. Exact expressions for the bit error probabilities are derived for binary coherently demodulated systems without coding. Approximations for the packet error probability are derived for coherent and noncoherent systems and these approximations are applied when forward-error-control coding is employed. In all cases, the effects of varying interference power are accurately taken into account according to some propagation law. Numerical results are given in terms of bit error probability for the exact case and throughput for the approximate analyses. Comparisons are made with previously derived bounds and it is shown that these tend to be very pessimistic.

Multidimensional stochastic approximation using locally contractive functions

NASA Technical Reports Server (NTRS)

Lawton, W. M.

1975-01-01

A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.

Optimal random search for a single hidden target.

PubMed

Snider, Joseph

2011-01-01

A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the minimum number of trials. Here it will be shown that if the searcher must get very close to the target to find it, then the best search distribution is proportional to the square root of the target distribution regardless of dimension. For a Gaussian target distribution, the optimum search distribution is approximately a Gaussian with a standard deviation that varies inversely with how close the searcher must be to the target to find it. For a network where the searcher randomly samples nodes and looks for the fixed target along edges, the optimum is either to sample a node with probability proportional to the square root of the out-degree plus 1 or not to do so at all.

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.

The Moving Group Targets of the Seeds High-Contrast Imaging Survey of Exoplanets and Disks: Results and Observations from the First Three Years

NASA Technical Reports Server (NTRS)

Brandt, Timothy D.; Kuzuhara, Masayuki; McElwain, Michael W.; Schlieder, Joshua E.; Wisniewski, John P.; Turner, Edwin L.; Carson, J.; Matsuo, T.; Biller, B.; Bonnefoy, M.;

A new probability distribution model of turbulent irradiance based on Born perturbation theory

NASA Astrophysics Data System (ADS)

Wang, Hongxing; Liu, Min; Hu, Hao; Wang, Qian; Liu, Xiguo

2010-10-01

The subject of the PDF (Probability Density Function) of the irradiance fluctuations in a turbulent atmosphere is still unsettled. Theory reliably describes the behavior in the weak turbulence regime, but theoretical description in the strong and whole turbulence regimes are still controversial. Based on Born perturbation theory, the physical manifestations and correlations of three typical PDF models (Rice-Nakagami, exponential-Bessel and negative-exponential distribution) were theoretically analyzed. It is shown that these models can be derived by separately making circular-Gaussian, strong-turbulence and strong-turbulence-circular-Gaussian approximations in Born perturbation theory, which denies the viewpoint that the Rice-Nakagami model is only applicable in the extremely weak turbulence regime and provides theoretical arguments for choosing rational models in practical applications. In addition, a common shortcoming of the three models is that they are all approximations. A new model, called the Maclaurin-spread distribution, is proposed without any approximation except for assuming the correlation coefficient to be zero. So, it is considered that the new model can exactly reflect the Born perturbation theory. Simulated results prove the accuracy of this new model.

Probabilistic Reasoning for Robustness in Automated Planning

NASA Technical Reports Server (NTRS)

Schaffer, Steven; Clement, Bradley; Chien, Steve

2007-01-01

A general-purpose computer program for planning the actions of a spacecraft or other complex system has been augmented by incorporating a subprogram that reasons about uncertainties in such continuous variables as times taken to perform tasks and amounts of resources to be consumed. This subprogram computes parametric probability distributions for time and resource variables on the basis of user-supplied models of actions and resources that they consume. The current system accepts bounded Gaussian distributions over action duration and resource use. The distributions are then combined during planning to determine the net probability distribution of each resource at any time point. In addition to a full combinatoric approach, several approximations for arriving at these combined distributions are available, including maximum-likelihood and pessimistic algorithms. Each such probability distribution can then be integrated to obtain a probability that execution of the plan under consideration would violate any constraints on the resource. The key idea is to use these probabilities of conflict to score potential plans and drive a search toward planning low-risk actions. An output plan provides a balance between the user s specified averseness to risk and other measures of optimality.

Entropy Methods For Univariate Distributions in Decision Analysis

NASA Astrophysics Data System (ADS)

Abbas, Ali E.

2003-03-01

One of the most important steps in decision analysis practice is the elicitation of the decision-maker's belief about an uncertainty of interest in the form of a representative probability distribution. However, the probability elicitation process is a task that involves many cognitive and motivational biases. Alternatively, the decision-maker may provide other information about the distribution of interest, such as its moments, and the maximum entropy method can be used to obtain a full distribution subject to the given moment constraints. In practice however, decision makers cannot readily provide moments for the distribution, and are much more comfortable providing information about the fractiles of the distribution of interest or bounds on its cumulative probabilities. In this paper we present a graphical method to determine the maximum entropy distribution between upper and lower probability bounds and provide an interpretation for the shape of the maximum entropy distribution subject to fractile constraints, (FMED). We also discuss the problems with the FMED in that it is discontinuous and flat over each fractile interval. We present a heuristic approximation to a distribution if in addition to its fractiles, we also know it is continuous and work through full examples to illustrate the approach.

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.

An experimental study of the surface elevation probability distribution and statistics of wind-generated waves

NASA Technical Reports Server (NTRS)

Huang, N. E.; Long, S. R.

1980-01-01

Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.

A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems

DOE PAGES

Kouri, Drew Philip

2017-12-19

In numerous applications, scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system. This data is then used to inform decisions such as controls and designs. Consequently, it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs. Here in this work, we consider optimal control and design problems constrained by partial differential equations with uncertain inputs. We do not assume a known probabilistic model for the inputs, but rather we formulate the problem as a distributionally robustmore » optimization problem where the outer minimization problem determines the control or design, while the inner maximization problem determines the worst-case probability measure that matches desired characteristics of the data. We analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique, based on the approximation of continuous functions, to discretize the unknown probability measure. Finally, we prove consistency of our approximated min-max problem and conclude with numerical results.« less

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.

Approximating Multivariate Normal Orthant Probabilities. ONR Technical Report. [Biometric Lab Report No. 90-1.

ERIC Educational Resources Information Center

Gibbons, Robert D.; And Others

The probability integral of the multivariate normal distribution (ND) has received considerable attention since W. F. Sheppard's (1900) and K. Pearson's (1901) seminal work on the bivariate ND. This paper evaluates the formula that represents the "n x n" correlation matrix of the "chi(sub i)" and the standardized multivariate…

Time-dependent landslide probability mapping

USGS Publications Warehouse

Campbell, Russell H.; Bernknopf, Richard L.; ,

1993-01-01

Case studies where time of failure is known for rainfall-triggered debris flows can be used to estimate the parameters of a hazard model in which the probability of failure is a function of time. As an example, a time-dependent function for the conditional probability of a soil slip is estimated from independent variables representing hillside morphology, approximations of material properties, and the duration and rate of rainfall. If probabilities are calculated in a GIS (geomorphic information system ) environment, the spatial distribution of the result for any given hour can be displayed on a map. Although the probability levels in this example are uncalibrated, the method offers a potential for evaluating different physical models and different earth-science variables by comparing the map distribution of predicted probabilities with inventory maps for different areas and different storms. If linked with spatial and temporal socio-economic variables, this method could be used for short-term risk assessment.

Approximate Bayesian evaluations of measurement uncertainty

NASA Astrophysics Data System (ADS)

Possolo, Antonio; Bodnar, Olha

2018-04-01

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

Timescales of isotropic and anisotropic cluster collapse

NASA Astrophysics Data System (ADS)

Bartelmann, M.; Ehlers, J.; Schneider, P.

1993-12-01

From a simple estimate for the formation time of galaxy clusters, Richstone et al. have recently concluded that the evidence for non-virialized structures in a large fraction of observed clusters points towards a high value for the cosmological density parameter Omega0. This conclusion was based on a study of the spherical collapse of density perturbations, assumed to follow a Gaussian probability distribution. In this paper, we extend their treatment in several respects: first, we argue that the collapse does not start from a comoving motion of the perturbation, but that the continuity equation requires an initial velocity perturbation directly related to the density perturbation. This requirement modifies the initial condition for the evolution equation and has the effect that the collapse proceeds faster than in the case where the initial velocity perturbation is set to zero; the timescale is reduced by a factor of up to approximately equal 0.5. Our results thus strengthens the conclusion of Richstone et al. for a high Omega0. In addition, we study the collapse of density fluctuations in the frame of the Zel'dovich approximation, using as starting condition the analytically known probability distribution of the eigenvalues of the deformation tensor, which depends only on the (Gaussian) width of the perturbation spectrum. Finally, we consider the anisotropic collapse of density perturbations dynamically, again with initial conditions drawn from the probability distribution of the deformation tensor. We find that in both cases of anisotropic collapse, in the Zel'dovich approximation and in the dynamical calculations, the resulting distribution of collapse times agrees remarkably well with the results from spherical collapse. We discuss this agreement and conclude that it is mainly due to the properties of the probability distribution for the eigenvalues of the Zel'dovich deformation tensor. Hence, the conclusions of Richstone et al. on the value of Omega0 can be verified and strengthened, even if a more general approach to the collapse of density perturbations is employed. A simple analytic formula for the cluster redshift distribution in an Einstein-deSitter universe is derived.

Chance-Constrained AC Optimal Power Flow for Distribution Systems With Renewables

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

DallAnese, Emiliano; Baker, Kyri; Summers, Tyler

This paper focuses on distribution systems featuring renewable energy sources (RESs) and energy storage systems, and presents an AC optimal power flow (OPF) approach to optimize system-level performance objectives while coping with uncertainty in both RES generation and loads. The proposed method hinges on a chance-constrained AC OPF formulation where probabilistic constraints are utilized to enforce voltage regulation with prescribed probability. A computationally more affordable convex reformulation is developed by resorting to suitable linear approximations of the AC power-flow equations as well as convex approximations of the chance constraints. The approximate chance constraints provide conservative bounds that hold for arbitrarymore » distributions of the forecasting errors. An adaptive strategy is then obtained by embedding the proposed AC OPF task into a model predictive control framework. Finally, a distributed solver is developed to strategically distribute the solution of the optimization problems across utility and customers.« less

Quantifying travel time variability in transportation networks.

DOT National Transportation Integrated Search

2010-03-01

Nonrecurring congestion creates significant delay on freeways in urban areas, lending importance : to the study of facility reliability. In locations where traffic detectors record and archive data, : approximate probability distributions for travel ...

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.

Anomalous Diffusion Approximation of Risk Processes in Operational Risk of Non-Financial Corporations

NASA Astrophysics Data System (ADS)

Magdziarz, M.; Mista, P.; Weron, A.

2007-05-01

We introduce an approximation of the risk processes by anomalous diffusion. In the paper we consider the case, where the waiting times between successive occurrences of the claims belong to the domain of attraction of alpha -stable distribution. The relationship between the obtained approximation and the celebrated fractional diffusion equation is emphasised. We also establish upper bounds for the ruin probability in the considered model and give some numerical examples.

Confidence Intervals for True Scores Using the Skew-Normal Distribution

ERIC Educational Resources Information Center

Garcia-Perez, Miguel A.

2010-01-01

A recent comparative analysis of alternative interval estimation approaches and procedures has shown that confidence intervals (CIs) for true raw scores determined with the Score method--which uses the normal approximation to the binomial distribution--have actual coverage probabilities that are closest to their nominal level. It has also recently…

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

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

On the probability distribution of daily streamflow in the United States

USGS Publications Warehouse

Blum, Annalise G.; Archfield, Stacey A.; Vogel, Richard M.

2017-01-01

Daily streamflows are often represented by flow duration curves (FDCs), which illustrate the frequency with which flows are equaled or exceeded. FDCs have had broad applications across both operational and research hydrology for decades; however, modeling FDCs has proven elusive. Daily streamflow is a complex time series with flow values ranging over many orders of magnitude. The identification of a probability distribution that can approximate daily streamflow would improve understanding of the behavior of daily flows and the ability to estimate FDCs at ungaged river locations. Comparisons of modeled and empirical FDCs at nearly 400 unregulated, perennial streams illustrate that the four-parameter kappa distribution provides a very good representation of daily streamflow across the majority of physiographic regions in the conterminous United States (US). Further, for some regions of the US, the three-parameter generalized Pareto and lognormal distributions also provide a good approximation to FDCs. Similar results are found for the period of record FDCs, representing the long-term hydrologic regime at a site, and median annual FDCs, representing the behavior of flows in a typical year.

Probability distribution of haplotype frequencies under the two-locus Wright-Fisher model by diffusion approximation.

PubMed

Boitard, Simon; Loisel, Patrice

2007-05-01

The probability distribution of haplotype frequencies in a population, and the way it is influenced by genetical forces such as recombination, selection, random drift ...is a question of fundamental interest in population genetics. For large populations, the distribution of haplotype frequencies for two linked loci under the classical Wright-Fisher model is almost impossible to compute because of numerical reasons. However the Wright-Fisher process can in such cases be approximated by a diffusion process and the transition density can then be deduced from the Kolmogorov equations. As no exact solution has been found for these equations, we developed a numerical method based on finite differences to solve them. It applies to transient states and models including selection or mutations. We show by several tests that this method is accurate for computing the conditional joint density of haplotype frequencies given that no haplotype has been lost. We also prove that it is far less time consuming than other methods such as Monte Carlo simulations.

On the use of Bayesian Monte-Carlo in evaluation of nuclear data

NASA Astrophysics Data System (ADS)

De Saint Jean, Cyrille; Archier, Pascal; Privas, Edwin; Noguere, Gilles

2017-09-01

As model parameters, necessary ingredients of theoretical models, are not always predicted by theory, a formal mathematical framework associated to the evaluation work is needed to obtain the best set of parameters (resonance parameters, optical models, fission barrier, average width, multigroup cross sections) with Bayesian statistical inference by comparing theory to experiment. The formal rule related to this methodology is to estimate the posterior density probability function of a set of parameters by solving an equation of the following type: pdf(posterior) ˜ pdf(prior) × a likelihood function. A fitting procedure can be seen as an estimation of the posterior density probability of a set of parameters (referred as x→?) knowing a prior information on these parameters and a likelihood which gives the probability density function of observing a data set knowing x→?. To solve this problem, two major paths could be taken: add approximations and hypothesis and obtain an equation to be solved numerically (minimum of a cost function or Generalized least Square method, referred as GLS) or use Monte-Carlo sampling of all prior distributions and estimate the final posterior distribution. Monte Carlo methods are natural solution for Bayesian inference problems. They avoid approximations (existing in traditional adjustment procedure based on chi-square minimization) and propose alternative in the choice of probability density distribution for priors and likelihoods. This paper will propose the use of what we are calling Bayesian Monte Carlo (referred as BMC in the rest of the manuscript) in the whole energy range from thermal, resonance and continuum range for all nuclear reaction models at these energies. Algorithms will be presented based on Monte-Carlo sampling and Markov chain. The objectives of BMC are to propose a reference calculation for validating the GLS calculations and approximations, to test probability density distributions effects and to provide the framework of finding global minimum if several local minimums exist. Application to resolved resonance, unresolved resonance and continuum evaluation as well as multigroup cross section data assimilation will be presented.

Distribution-Agnostic Stochastic Optimal Power Flow for Distribution Grids: Preprint

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

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

2016-09-01

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

Probability distributions for multimeric systems.

PubMed

Albert, Jaroslav; Rooman, Marianne

2016-01-01

We propose a fast and accurate method of obtaining the equilibrium mono-modal joint probability distributions for multimeric systems. The method necessitates only two assumptions: the copy number of all species of molecule may be treated as continuous; and, the probability density functions (pdf) are well-approximated by multivariate skew normal distributions (MSND). Starting from the master equation, we convert the problem into a set of equations for the statistical moments which are then expressed in terms of the parameters intrinsic to the MSND. Using an optimization package on Mathematica, we minimize a Euclidian distance function comprising of a sum of the squared difference between the left and the right hand sides of these equations. Comparison of results obtained via our method with those rendered by the Gillespie algorithm demonstrates our method to be highly accurate as well as efficient.

Probability of lensing magnification by cosmologically distributed galaxies

NASA Technical Reports Server (NTRS)

Pei, Yichuan C.

1993-01-01

We present the analytical formulae for computing the magnification probability caused by cosmologically distributed galaxies. The galaxies are assumed to be singular, truncated-isothermal spheres without both evolution and clustering in redshift. We find that, for a fixed total mass, extended galaxies produce a broader shape in the magnification probability distribution and hence are less efficient as gravitational lenses than compact galaxies. The high-magnification tail caused by large galaxies is well approximated by an A exp -3 form, while the tail by small galaxies is slightly shallower. The mean magnification as a function of redshift is, however, found to be independent of the size of the lensing galaxies. In terms of the flux conservation, our formulae for the isothermal galaxy model predict a mean magnification to within a few percent with the Dyer-Roeder model of a clumpy universe.

Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model

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

Knessl, C.; Tier, C.

1999-10-01

In Part 1 the authors formulated and solved a diffusion model for two tandem queues with exponential servers and general renewal arrivals. They thus obtained the easy traffic diffusion approximation to the steady state joint queue length distribution for this network. Here they study asymptotic and numerical properties of the diffusion approximation. In particular, analytical expressions are obtained for the tail probabilities. Both the joint distribution of the two queues and the marginal distribution of the second queue are considered. They also give numerical illustrations of how this marginal is affected by changes in the arrival and service processes.

Theory of rotational transition in atom-diatom chemical reaction

NASA Astrophysics Data System (ADS)

Nakamura, Masato; Nakamura, Hiroki

1989-05-01

Rotational transition in atom-diatom chemical reaction is theoretically studied. A new approximate theory (which we call IOS-DW approximation) is proposed on the basis of the physical idea that rotational transition in reaction is induced by the following two different mechanisms: rotationally inelastic half collision in both initial and final arrangement channels, and coordinate transformation in the reaction zone. This theory gives a fairy compact expression for the state-to-state transition probability. Introducing the additional physically reasonable assumption that reaction (particle rearrangement) takes place in a spatially localized region, we have reduced this expression into a simpler analytical form which can explicitly give overall rotational state distribution in reaction. Numerical application was made to the H+H2 reaction and demonstrated its effectiveness for the simplicity. A further simplified most naive approximation, i.e., independent events approximation was also proposed and demonstrated to work well in the test calculation of H+H2. The overall rotational state distribution is expressed simply by a product sum of the transition probabilities for the three consecutive processes in reaction: inelastic transition in the initial half collision, transition due to particle rearrangement, and inelastic transition in the final half collision.

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

NASA Technical Reports Server (NTRS)

Mashiku, Alinda; Garrison, James L.; Carpenter, J. Russell

2012-01-01

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Multi-scale Characterization and Modeling of Surface Slope Probability Distribution for ~20-km Diameter Lunar Craters

NASA Astrophysics Data System (ADS)

Mahanti, P.; Robinson, M. S.; Boyd, A. K.

2013-12-01

Craters ~20-km diameter and above significantly shaped the lunar landscape. The statistical nature of the slope distribution on their walls and floors dominate the overall slope distribution statistics for the lunar surface. Slope statistics are inherently useful for characterizing the current topography of the surface, determining accurate photometric and surface scattering properties, and in defining lunar surface trafficability [1-4]. Earlier experimental studies on the statistical nature of lunar surface slopes were restricted either by resolution limits (Apollo era photogrammetric studies) or by model error considerations (photoclinometric and radar scattering studies) where the true nature of slope probability distribution was not discernible at baselines smaller than a kilometer[2,3,5]. Accordingly, historical modeling of lunar surface slopes probability distributions for applications such as in scattering theory development or rover traversability assessment is more general in nature (use of simple statistical models such as the Gaussian distribution[1,2,5,6]). With the advent of high resolution, high precision topographic models of the Moon[7,8], slopes in lunar craters can now be obtained at baselines as low as 6-meters allowing unprecedented multi-scale (multiple baselines) modeling possibilities for slope probability distributions. Topographic analysis (Lunar Reconnaissance Orbiter Camera (LROC) Narrow Angle Camera (NAC) 2-m digital elevation models (DEM)) of ~20-km diameter Copernican lunar craters revealed generally steep slopes on interior walls (30° to 36°, locally exceeding 40°) over 15-meter baselines[9]. In this work, we extend the analysis from a probability distribution modeling point-of-view with NAC DEMs to characterize the slope statistics for the floors and walls for the same ~20-km Copernican lunar craters. The difference in slope standard deviations between the Gaussian approximation and the actual distribution (2-meter sampling) was computed over multiple scales. This slope analysis showed that local slope distributions are non-Gaussian for both crater walls and floors. Over larger baselines (~100 meters), crater wall slope probability distributions do approximate Gaussian distributions better, but have long distribution tails. Crater floor probability distributions however, were always asymmetric (for the baseline scales analyzed) and less affected by baseline scale variations. Accordingly, our results suggest that use of long tailed probability distributions (like Cauchy) and a baseline-dependant multi-scale model can be more effective in describing the slope statistics for lunar topography. Refrences: [1]Moore, H.(1971), JGR,75(11) [2]Marcus, A. H.(1969),JGR,74 (22).[3]R.J. Pike (1970),U.S. Geological Survey Working Paper [4]N. C. Costes, J. E. Farmer and E. B. George (1972),NASA Technical Report TR R-401 [5]M. N. Parker and G. L. Tyler(1973), Radio Science, 8(3),177-184 [6]Alekseev, V. A.et al (1968), Soviet Astronomy, Vol. 11, p.860 [7]Burns et al. (2012) Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XXXIX-B4, 483-488.[8]Smith et al. (2010) GRL 37, L18204, DOI: 10.1029/2010GL043751. [9]Wagner R., Robinson, M., Speyerer E., Mahanti, P., LPSC 2013, #2924.

Probability Analysis of the Wave-Slamming Pressure Values of the Horizontal Deck with Elastic Support

NASA Astrophysics Data System (ADS)

Zuo, Weiguang; Liu, Ming; Fan, Tianhui; Wang, Pengtao

2018-06-01

This paper presents the probability distribution of the slamming pressure from an experimental study of regular wave slamming on an elastically supported horizontal deck. The time series of the slamming pressure during the wave impact were first obtained through statistical analyses on experimental data. The exceeding probability distribution of the maximum slamming pressure peak and distribution parameters were analyzed, and the results show that the exceeding probability distribution of the maximum slamming pressure peak accords with the three-parameter Weibull distribution. Furthermore, the range and relationships of the distribution parameters were studied. The sum of the location parameter D and the scale parameter L was approximately equal to 1.0, and the exceeding probability was more than 36.79% when the random peak was equal to the sample average during the wave impact. The variation of the distribution parameters and slamming pressure under different model conditions were comprehensively presented, and the parameter values of the Weibull distribution of wave-slamming pressure peaks were different due to different test models. The parameter values were found to decrease due to the increased stiffness of the elastic support. The damage criterion of the structure model caused by the wave impact was initially discussed, and the structure model was destroyed when the average slamming time was greater than a certain value during the duration of the wave impact. The conclusions of the experimental study were then described.

Improved first-order uncertainty method for water-quality modeling

USGS Publications Warehouse

Melching, C.S.; Anmangandla, S.

1992-01-01

Uncertainties are unavoidable in water-quality modeling and subsequent management decisions. Monte Carlo simulation and first-order uncertainty analysis (involving linearization at central values of the uncertain variables) have been frequently used to estimate probability distributions for water-quality model output due to their simplicity. Each method has its drawbacks: Monte Carlo simulation's is mainly computational time; and first-order analysis are mainly questions of accuracy and representativeness, especially for nonlinear systems and extreme conditions. An improved (advanced) first-order method is presented, where the linearization point varies to match the output level whose exceedance probability is sought. The advanced first-order method is tested on the Streeter-Phelps equation to estimate the probability distribution of critical dissolved-oxygen deficit and critical dissolved oxygen using two hypothetical examples from the literature. The advanced first-order method provides a close approximation of the exceedance probability for the Streeter-Phelps model output estimated by Monte Carlo simulation using less computer time - by two orders of magnitude - regardless of the probability distributions assumed for the uncertain model parameters.

Computing exact bundle compliance control charts via probability generating functions.

PubMed

Chen, Binchao; Matis, Timothy; Benneyan, James

2016-06-01

Compliance to evidenced-base practices, individually and in 'bundles', remains an important focus of healthcare quality improvement for many clinical conditions. The exact probability distribution of composite bundle compliance measures used to develop corresponding control charts and other statistical tests is based on a fairly large convolution whose direct calculation can be computationally prohibitive. Various series expansions and other approximation approaches have been proposed, each with computational and accuracy tradeoffs, especially in the tails. This same probability distribution also arises in other important healthcare applications, such as for risk-adjusted outcomes and bed demand prediction, with the same computational difficulties. As an alternative, we use probability generating functions to rapidly obtain exact results and illustrate the improved accuracy and detection over other methods. Numerical testing across a wide range of applications demonstrates the computational efficiency and accuracy of this approach.

Multilevel sequential Monte Carlo samplers

DOE PAGES

Beskos, Alexandros; Jasra, Ajay; Law, Kody; ...

2016-08-24

Here, we study the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with the step-size level h L. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levelsmore » $${\\infty}$$ >h 0>h 1 ...>h L. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. In conclusion, it is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context.« less

Driven fragmentation of granular gases.

PubMed

Cruz Hidalgo, Raúl; Pagonabarraga, Ignacio

2008-06-01

The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the long velocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f(c) approximately exp(-cn) , with n approximately 1.2 , regarding less the fragmentation mechanisms.

The probability of misassociation between neighboring targets

NASA Astrophysics Data System (ADS)

Areta, Javier A.; Bar-Shalom, Yaakov; Rothrock, Ronald

2008-04-01

This paper presents procedures to calculate the probability that the measurement originating from an extraneous target will be (mis)associated with a target of interest for the cases of Nearest Neighbor and Global association. It is shown that these misassociation probabilities depend, under certain assumptions, on a particular - covariance weighted - norm of the difference between the targets' predicted measurements. For the Nearest Neighbor association, the exact solution, obtained for the case of equal innovation covariances, is based on a noncentral chi-square distribution. An approximate solution is also presented for the case of unequal innovation covariances. For the Global case an approximation is presented for the case of "similar" innovation covariances. In the general case of unequal innovation covariances where this approximation fails, an exact method based on the inversion of the characteristic function is presented. The theoretical results, confirmed by Monte Carlo simulations, quantify the benefit of Global vs. Nearest Neighbor association. These results are applied to problems of single sensor as well as centralized fusion architecture multiple sensor tracking.

Coalescence computations for large samples drawn from populations of time-varying sizes

PubMed Central

Polanski, Andrzej; Szczesna, Agnieszka; Garbulowski, Mateusz; Kimmel, Marek

2017-01-01

We present new results concerning probability distributions of times in the coalescence tree and expected allele frequencies for coalescent with large sample size. The obtained results are based on computational methodologies, which involve combining coalescence time scale changes with techniques of integral transformations and using analytical formulae for infinite products. We show applications of the proposed methodologies for computing probability distributions of times in the coalescence tree and their limits, for evaluation of accuracy of approximate expressions for times in the coalescence tree and expected allele frequencies, and for analysis of large human mitochondrial DNA dataset. PMID:28170404

Velocity statistics of the Nagel-Schreckenberg model

NASA Astrophysics Data System (ADS)

Bain, Nicolas; Emig, Thorsten; Ulm, Franz-Josef; Schreckenberg, Michael

2016-02-01

The statistics of velocities in the cellular automaton model of Nagel and Schreckenberg for traffic are studied. From numerical simulations, we obtain the probability distribution function (PDF) for vehicle velocities and the velocity-velocity (vv) covariance function. We identify the probability to find a standing vehicle as a potential order parameter that signals nicely the transition between free congested flow for a sufficiently large number of velocity states. Our results for the vv covariance function resemble features of a second-order phase transition. We develop a 3-body approximation that allows us to relate the PDFs for velocities and headways. Using this relation, an approximation to the velocity PDF is obtained from the headway PDF observed in simulations. We find a remarkable agreement between this approximation and the velocity PDF obtained from simulations.

Velocity statistics of the Nagel-Schreckenberg model.

PubMed

Bain, Nicolas; Emig, Thorsten; Ulm, Franz-Josef; Schreckenberg, Michael

2016-02-01

The statistics of velocities in the cellular automaton model of Nagel and Schreckenberg for traffic are studied. From numerical simulations, we obtain the probability distribution function (PDF) for vehicle velocities and the velocity-velocity (vv) covariance function. We identify the probability to find a standing vehicle as a potential order parameter that signals nicely the transition between free congested flow for a sufficiently large number of velocity states. Our results for the vv covariance function resemble features of a second-order phase transition. We develop a 3-body approximation that allows us to relate the PDFs for velocities and headways. Using this relation, an approximation to the velocity PDF is obtained from the headway PDF observed in simulations. We find a remarkable agreement between this approximation and the velocity PDF obtained from simulations.

Optimal Power Flow for Distribution Systems under Uncertain Forecasts: Preprint

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

Dall'Anese, Emiliano; Baker, Kyri; Summers, Tyler

2016-12-01

The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative boundsmore » that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.« less

A moment-convergence method for stochastic analysis of biochemical reaction networks.

PubMed

Zhang, Jiajun; Nie, Qing; Zhou, Tianshou

2016-05-21

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.

Crater Topography on Titan: Implications for Landscape Evolution

NASA Technical Reports Server (NTRS)

Neish, Catherine D.; Kirk, R.L.; Lorenz, R. D.; Bray, V. J.; Schenk, P.; Stiles, B. W.; Turtle, E.; Mitchell, K.; Hayes, A.

2013-01-01

We present a comprehensive review of available crater topography measurements for Saturn's moon Titan. In general, the depths of Titan's craters are within the range of depths observed for similarly sized fresh craters on Ganymede, but several hundreds of meters shallower than Ganymede's average depth vs. diameter trend. Depth-to-diameter ratios are between 0.0012 +/- 0.0003 (for the largest crater studied, Menrva, D approximately 425 km) and 0.017 +/- 0.004 (for the smallest crater studied, Ksa, D approximately 39 km). When we evaluate the Anderson-Darling goodness-of-fit parameter, we find that there is less than a 10% probability that Titan's craters have a current depth distribution that is consistent with the depth distribution of fresh craters on Ganymede. There is, however, a much higher probability that the relative depths are uniformly distributed between 0 (fresh) and 1 (completely infilled). This distribution is consistent with an infilling process that is relatively constant with time, such as aeolian deposition. Assuming that Ganymede represents a close 'airless' analogue to Titan, the difference in depths represents the first quantitative measure of the amount of modification that has shaped Titan's surface, the only body in the outer Solar System with extensive surface-atmosphere exchange.

A Bayesian approach to modeling 2D gravity data using polygon states

NASA Astrophysics Data System (ADS)

Titus, W. J.; Titus, S.; Davis, J. R.

2015-12-01

We present a Bayesian Markov chain Monte Carlo (MCMC) method for the 2D gravity inversion of a localized subsurface object with constant density contrast. Our models have four parameters: the density contrast, the number of vertices in a polygonal approximation of the object, an upper bound on the ratio of the perimeter squared to the area, and the vertices of a polygon container that bounds the object. Reasonable parameter values can be estimated prior to inversion using a forward model and geologic information. In addition, we assume that the field data have a common random uncertainty that lies between two bounds but that it has no systematic uncertainty. Finally, we assume that there is no uncertainty in the spatial locations of the measurement stations. For any set of model parameters, we use MCMC methods to generate an approximate probability distribution of polygons for the object. We then compute various probability distributions for the object, including the variance between the observed and predicted fields (an important quantity in the MCMC method), the area, the center of area, and the occupancy probability (the probability that a spatial point lies within the object). In addition, we compare probabilities of different models using parallel tempering, a technique which also mitigates trapping in local optima that can occur in certain model geometries. We apply our method to several synthetic data sets generated from objects of varying shape and location. We also analyze a natural data set collected across the Rio Grande Gorge Bridge in New Mexico, where the object (i.e. the air below the bridge) is known and the canyon is approximately 2D. Although there are many ways to view results, the occupancy probability proves quite powerful. We also find that the choice of the container is important. In particular, large containers should be avoided, because the more closely a container confines the object, the better the predictions match properties of object.

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

Dall'Anese, Emiliano; Baker, Kyri; Summers, Tyler

The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative boundsmore » that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.« less

Mean-field approximations of fixation time distributions of evolutionary game dynamics on graphs

NASA Astrophysics Data System (ADS)

Ying, Li-Min; Zhou, Jie; Tang, Ming; Guan, Shu-Guang; Zou, Yong

2018-02-01

The mean fixation time is often not accurate for describing the timescales of fixation probabilities of evolutionary games taking place on complex networks. We simulate the game dynamics on top of complex network topologies and approximate the fixation time distributions using a mean-field approach. We assume that there are two absorbing states. Numerically, we show that the mean fixation time is sufficient in characterizing the evolutionary timescales when network structures are close to the well-mixing condition. In contrast, the mean fixation time shows large inaccuracies when networks become sparse. The approximation accuracy is determined by the network structure, and hence by the suitability of the mean-field approach. The numerical results show good agreement with the theoretical predictions.

Improving the chi-squared approximation for bivariate normal tolerance regions

NASA Technical Reports Server (NTRS)

Feiveson, Alan H.

1993-01-01

Let X be a two-dimensional random variable distributed according to N2(mu,Sigma) and let bar-X and S be the respective sample mean and covariance matrix calculated from N observations of X. Given a containment probability beta and a level of confidence gamma, we seek a number c, depending only on N, beta, and gamma such that the ellipsoid R = (x: (x - bar-X)'S(exp -1) (x - bar-X) less than or = c) is a tolerance region of content beta and level gamma; i.e., R has probability gamma of containing at least 100 beta percent of the distribution of X. Various approximations for c exist in the literature, but one of the simplest to compute -- a multiple of the ratio of certain chi-squared percentage points -- is badly biased for small N. For the bivariate normal case, most of the bias can be removed by simple adjustment using a factor A which depends on beta and gamma. This paper provides values of A for various beta and gamma so that the simple approximation for c can be made viable for any reasonable sample size. The methodology provides an illustrative example of how a combination of Monte-Carlo simulation and simple regression modelling can be used to improve an existing approximation.

Fundamental finite key limits for one-way information reconciliation in quantum key distribution

NASA Astrophysics Data System (ADS)

Tomamichel, Marco; Martinez-Mateo, Jesus; Pacher, Christoph; Elkouss, David

2017-11-01

The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that one-way information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during information reconciliation is not generally valid. We propose an improved approximation that takes into account finite key effects and numerically test it against codes for two probability distributions, that we call binary-binary and binary-Gaussian, that typically appear in quantum key distribution protocols.

Energy dependence of the trapping of uranium atoms by aluminum oxide surfaces

NASA Technical Reports Server (NTRS)

Librecht, K. G.

1979-01-01

The energy dependence of the trapping probability for sputtered U-235 atoms striking an oxidized aluminum collector surface at energies between 1 eV and 184 eV was measured. At the lowest energies, approximately 10% of the uranium atoms are not trapped, while above 10 eV essentially all of them stick. Trapping probabilities averaged over the sputtered energy distribution for uranium incident on gold and mica are also presented.

Technical Reports Prepared Under Contract N00014-76-C-0475.

DTIC Science & Technology

1987-05-29

264 Approximations to Densities in Geometric H. Solomon 10/27/78 Probability M.A. Stephens 3. Technical Relort No. Title Author Date 265 Sequential ...Certain Multivariate S. Iyengar 8/12/82 Normal Probabilities 323 EDF Statistics for Testing for the Gamma M.A. Stephens 8/13/82 Distribution with...20-85 Nets 360 Random Sequential Coding By Hamming Distance Yoshiaki Itoh 07-11-85 Herbert Solomon 361 Transforming Censored Samples And Testing Fit

Cellular Analysis of Boltzmann Most Probable Ideal Gas Statistics

NASA Astrophysics Data System (ADS)

Cahill, Michael E.

2018-04-01

Exact treatment of Boltzmann's Most Probable Statistics for an Ideal Gas of Identical Mass Particles having Translational Kinetic Energy gives a Distribution Law for Velocity Phase Space Cell j which relates the Particle Energy and the Particle Population according toB e(j) = A - Ψ(n(j) + 1)where A & B are the Lagrange Multipliers and Ψ is the Digamma Function defined byΨ(x + 1) = d/dx ln(x!)A useful sufficiently accurate approximation for Ψ is given byΨ(x +1) ≈ ln(e-γ + x)where γ is the Euler constant (≈.5772156649) & so the above distribution equation is approximatelyB e(j) = A - ln(e-γ + n(j))which can be inverted to solve for n(j) givingn(j) = (eB (eH - e(j)) - 1) e-γwhere B eH = A + γ& where B eH is a unitless particle energy which replaces the parameter A. The 2 approximate distribution equations imply that eH is the highest particle energy and the highest particle population isnH = (eB eH - 1) e-γwhich is due to the facts that population becomes negative if e(j) > eH and kinetic energy becomes negative if n(j) > nH.An explicit construction of Cells in Velocity Space which are equal in volume and homogeneous for almost all cells is shown to be useful in the analysis.Plots for sample distribution properties using e(j) as the independent variable are presented.

fixedTimeEvents: An R package for the distribution of distances between discrete events in fixed time

NASA Astrophysics Data System (ADS)

Liland, Kristian Hovde; Snipen, Lars

When a series of Bernoulli trials occur within a fixed time frame or limited space, it is often interesting to assess if the successful outcomes have occurred completely at random, or if they tend to group together. One example, in genetics, is detecting grouping of genes within a genome. Approximations of the distribution of successes are possible, but they become inaccurate for small sample sizes. In this article, we describe the exact distribution of time between random, non-overlapping successes in discrete time of fixed length. A complete description of the probability mass function, the cumulative distribution function, mean, variance and recurrence relation is included. We propose an associated test for the over-representation of short distances and illustrate the methodology through relevant examples. The theory is implemented in an R package including probability mass, cumulative distribution, quantile function, random number generator, simulation functions, and functions for testing.

A Gaussian measure of quantum phase noise

NASA Technical Reports Server (NTRS)

Schleich, Wolfgang P.; Dowling, Jonathan P.

1992-01-01

We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.

Spacing distribution functions for the one-dimensional point-island model with irreversible attachment

NASA Astrophysics Data System (ADS)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2011-07-01

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density pnXY(x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for pnXY(x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.

Calibration of micromechanical parameters for DEM simulations by using the particle filter

NASA Astrophysics Data System (ADS)

Cheng, Hongyang; Shuku, Takayuki; Thoeni, Klaus; Yamamoto, Haruyuki

2017-06-01

The calibration of DEM models is typically accomplished by trail and error. However, the procedure lacks of objectivity and has several uncertainties. To deal with these issues, the particle filter is employed as a novel approach to calibrate DEM models of granular soils. The posterior probability distribution of the microparameters that give numerical results in good agreement with the experimental response of a Toyoura sand specimen is approximated by independent model trajectories, referred as `particles', based on Monte Carlo sampling. The soil specimen is modeled by polydisperse packings with different numbers of spherical grains. Prepared in `stress-free' states, the packings are subjected to triaxial quasistatic loading. Given the experimental data, the posterior probability distribution is incrementally updated, until convergence is reached. The resulting `particles' with higher weights are identified as the calibration results. The evolutions of the weighted averages and posterior probability distribution of the micro-parameters are plotted to show the advantage of using a particle filter, i.e., multiple solutions are identified for each parameter with known probabilities of reproducing the experimental response.

Modeling potential distribution of Oligoryzomys longicaudatus, the Andes virus (Genus: Hantavirus) reservoir, in Argentina.

PubMed

Andreo, Verónica; Glass, Gregory; Shields, Timothy; Provensal, Cecilia; Polop, Jaime

2011-09-01

We constructed a model to predict the potential distribution of Oligoryzomys longicaudatus, the reservoir of Andes virus (Genus: Hantavirus), in Argentina. We developed an extensive database of occurrence records from published studies and our own surveys and compared two methods to model the probability of O. longicaudatus presence; logistic regression and MaxEnt algorithm. The environmental variables used were tree, grass and bare soil cover from MODIS imagery and, altitude and 19 bioclimatic variables from WorldClim database. The models performances were evaluated and compared both by threshold dependent and independent measures. The best models included tree and grass cover, mean diurnal temperature range, and precipitation of the warmest and coldest seasons. The potential distribution maps for O. longicaudatus predicted the highest occurrence probabilities along the Andes range, from 32°S and narrowing southwards. They also predicted high probabilities for the south-central area of Argentina, reaching the Atlantic coast. The Hantavirus Pulmonary Syndrome cases coincided with mean occurrence probabilities of 95 and 77% for logistic and MaxEnt models, respectively. HPS transmission zones in Argentine Patagonia matched the areas with the highest probability of presence. Therefore, colilargos presence probability may provide an approximate risk of transmission and act as an early tool to guide control and prevention plans.

Iterative updating of model error for Bayesian inversion

NASA Astrophysics Data System (ADS)

Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew

2018-02-01

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when optimization algorithms are used to find a single estimate, or to speed up Markov chain Monte Carlo (MCMC) calculations in the Bayesian framework. The use of an approximate model introduces a discrepancy, or modeling error, that may have a detrimental effect on the solution of the ill-posed inverse problem, or it may severely distort the estimate of the posterior distribution. In the Bayesian paradigm, the modeling error can be considered as a random variable, and by using an estimate of the probability distribution of the unknown, one may estimate the probability distribution of the modeling error and incorporate it into the inversion. We introduce an algorithm which iterates this idea to update the distribution of the model error, leading to a sequence of posterior distributions that are demonstrated empirically to capture the underlying truth with increasing accuracy. Since the algorithm is not based on rejections, it requires only limited full model evaluations. We show analytically that, in the linear Gaussian case, the algorithm converges geometrically fast with respect to the number of iterations when the data is finite dimensional. For more general models, we introduce particle approximations of the iteratively generated sequence of distributions; we also prove that each element of the sequence converges in the large particle limit under a simplifying assumption. We show numerically that, as in the linear case, rapid convergence occurs with respect to the number of iterations. Additionally, we show through computed examples that point estimates obtained from this iterative algorithm are superior to those obtained by neglecting the model error.

An efficient multi-objective optimization method for water quality sensor placement within water distribution systems considering contamination probability variations.

PubMed

He, Guilin; Zhang, Tuqiao; Zheng, Feifei; Zhang, Qingzhou

2018-06-20

Water quality security within water distribution systems (WDSs) has been an important issue due to their inherent vulnerability associated with contamination intrusion. This motivates intensive studies to identify optimal water quality sensor placement (WQSP) strategies, aimed to timely/effectively detect (un)intentional intrusion events. However, these available WQSP optimization methods have consistently presumed that each WDS node has an equal contamination probability. While being simple in implementation, this assumption may do not conform to the fact that the nodal contamination probability may be significantly regionally varied owing to variations in population density and user properties. Furthermore, the low computational efficiency is another important factor that has seriously hampered the practical applications of the currently available WQSP optimization approaches. To address these two issues, this paper proposes an efficient multi-objective WQSP optimization method to explicitly account for contamination probability variations. Four different contamination probability functions (CPFs) are proposed to represent the potential variations of nodal contamination probabilities within the WDS. Two real-world WDSs are used to demonstrate the utility of the proposed method. Results show that WQSP strategies can be significantly affected by the choice of the CPF. For example, when the proposed method is applied to the large case study with the CPF accounting for user properties, the event detection probabilities of the resultant solutions are approximately 65%, while these values are around 25% for the traditional approach, and such design solutions are achieved approximately 10,000 times faster than the traditional method. This paper provides an alternative method to identify optimal WQSP solutions for the WDS, and also builds knowledge regarding the impacts of different CPFs on sensor deployments. Copyright © 2018 Elsevier Ltd. All rights reserved.

Novel approximation of misalignment fading modeled by Beckmann distribution on free-space optical links.

PubMed

Boluda-Ruiz, Rubén; García-Zambrana, Antonio; Castillo-Vázquez, Carmen; Castillo-Vázquez, Beatriz

2016-10-03

A novel accurate and useful approximation of the well-known Beckmann distribution is presented here, which is used to model generalized pointing errors in the context of free-space optical (FSO) communication systems. We derive an approximate closed-form probability density function (PDF) for the composite gamma-gamma (GG) atmospheric turbulence with the pointing error model using the proposed approximation of the Beckmann distribution, which is valid for most practical terrestrial FSO links. This approximation takes into account the effect of the beam width, different jitters for the elevation and the horizontal displacement and the simultaneous effect of nonzero boresight errors for each axis at the receiver plane. Additionally, the proposed approximation allows us to delimit two different FSO scenarios. The first of them is when atmospheric turbulence is the dominant effect in relation to generalized pointing errors, and the second one when generalized pointing error is the dominant effect in relation to atmospheric turbulence. The second FSO scenario has not been studied in-depth by the research community. Moreover, the accuracy of the method is measured both visually and quantitatively using curve-fitting metrics. Simulation results are further included to confirm the analytical results.

Estimation of distribution overlap of urn models.

PubMed

Hampton, Jerrad; Lladser, Manuel E

2012-01-01

A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically, we estimate what we call the dissimilarity probability of a sample, i.e., the probability of a draw from one distribution not being observed in [Formula: see text] draws from another distribution. We show our estimator of dissimilarity to be a [Formula: see text]-statistic and a uniformly minimum variance unbiased estimator of dissimilarity over the largest appropriate range of [Formula: see text]. Furthermore, despite the non-Markovian nature of our estimator when applied sequentially over [Formula: see text], we show it converges uniformly in probability to the dissimilarity parameter, and we present criteria when it is approximately normally distributed and admits a consistent jackknife estimator of its variance. As proof of concept, we analyze V35 16S rRNA data to discern between various microbial environments. Other potential applications concern any situation where dissimilarity of two discrete distributions may be of interest. For instance, in SELEX experiments, each urn could represent a random RNA pool and each draw a possible solution to a particular binding site problem over that pool. The dissimilarity of these pools is then related to the probability of finding binding site solutions in one pool that are absent in the other.

Rapidly assessing the probability of exceptionally high natural hazard losses

NASA Astrophysics Data System (ADS)

Gollini, Isabella; Rougier, Jonathan

2014-05-01

One of the objectives in catastrophe modeling is to assess the probability distribution of losses for a specified period, such as a year. From the point of view of an insurance company, the whole of the loss distribution is interesting, and valuable in determining insurance premiums. But the shape of the righthand tail is critical, because it impinges on the solvency of the company. A simple measure of the risk of insolvency is the probability that the annual loss will exceed the company's current operating capital. Imposing an upper limit on this probability is one of the objectives of the EU Solvency II directive. If a probabilistic model is supplied for the loss process, then this tail probability can be computed, either directly, or by simulation. This can be a lengthy calculation for complex losses. Given the inevitably subjective nature of quantifying loss distributions, computational resources might be better used in a sensitivity analysis. This requires either a quick approximation to the tail probability or an upper bound on the probability, ideally a tight one. We present several different bounds, all of which can be computed nearly instantly from a very general event loss table. We provide a numerical illustration, and discuss the conditions under which the bound is tight. Although we consider the perspective of insurance and reinsurance companies, exactly the same issues concern the risk manager, who is typically very sensitive to large losses.

Uncertainty Analysis via Failure Domain Characterization: Polynomial Requirement Functions

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Munoz, Cesar A.; Narkawicz, Anthony J.; Kenny, Sean P.; Giesy, Daniel P.

2011-01-01

This paper proposes an uncertainty analysis framework based on the characterization of the uncertain parameter space. This characterization enables the identification of worst-case uncertainty combinations and the approximation of the failure and safe domains with a high level of accuracy. Because these approximations are comprised of subsets of readily computable probability, they enable the calculation of arbitrarily tight upper and lower bounds to the failure probability. A Bernstein expansion approach is used to size hyper-rectangular subsets while a sum of squares programming approach is used to size quasi-ellipsoidal subsets. These methods are applicable to requirement functions whose functional dependency on the uncertainty is a known polynomial. Some of the most prominent features of the methodology are the substantial desensitization of the calculations from the uncertainty model assumed (i.e., the probability distribution describing the uncertainty) as well as the accommodation for changes in such a model with a practically insignificant amount of computational effort.

Uncertainty Analysis via Failure Domain Characterization: Unrestricted Requirement Functions

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2011-01-01

This paper proposes an uncertainty analysis framework based on the characterization of the uncertain parameter space. This characterization enables the identification of worst-case uncertainty combinations and the approximation of the failure and safe domains with a high level of accuracy. Because these approximations are comprised of subsets of readily computable probability, they enable the calculation of arbitrarily tight upper and lower bounds to the failure probability. The methods developed herein, which are based on nonlinear constrained optimization, are applicable to requirement functions whose functional dependency on the uncertainty is arbitrary and whose explicit form may even be unknown. Some of the most prominent features of the methodology are the substantial desensitization of the calculations from the assumed uncertainty model (i.e., the probability distribution describing the uncertainty) as well as the accommodation for changes in such a model with a practically insignificant amount of computational effort.

Exact and Approximate Probabilistic Symbolic Execution

NASA Technical Reports Server (NTRS)

Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem

2014-01-01

Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.

Integrated Sensing and Processing (ISP) Phase 2: Demonstration and Evaluation for Distributed Sensor Networks and Missile Seeker Systems

DTIC Science & Technology

2007-05-29

International Conference Acoustics Speech and Signal Processing (ICASSP 2007) conference 15 − 20 April 2007 in Honolulu, Hawaii. 1. E. Near Term...from the sensor measured in feet. The detection performance of the footstep in the presence of interfering speech was characterized in previously...investigation, we developed a simple piecewise linear approximation to the probability of detection curve with no interfering speech . This approximation was

Mean Field Approach to the Giant Wormhole Problem

NASA Astrophysics Data System (ADS)

Gamba, A.; Kolokolov, I.; Martellini, M.

We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.

Use of Fermi-Dirac statistics for defects in solids

NASA Astrophysics Data System (ADS)

Johnson, R. A.

1981-12-01

The Fermi-Dirac distribution function is an approximation describing a special case of Boltzmann statistics. A general occupation probability formula is derived and a criterion given for the use of Fermi-Dirac statistics. Application to classical problems of defects in solids is discussed.

A moment-convergence method for stochastic analysis of biochemical reaction networks

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

Zhang, Jiajun; Nie, Qing; Zhou, Tianshou, E-mail: mcszhtsh@mail.sysu.edu.cn

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in termsmore » of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.« less

A Student’s t Mixture Probability Hypothesis Density Filter for Multi-Target Tracking with Outliers

PubMed Central

Liu, Zhuowei; Chen, Shuxin; Wu, Hao; He, Renke; Hao, Lin

2018-01-01

In multi-target tracking, the outliers-corrupted process and measurement noises can reduce the performance of the probability hypothesis density (PHD) filter severely. To solve the problem, this paper proposed a novel PHD filter, called Student’s t mixture PHD (STM-PHD) filter. The proposed filter models the heavy-tailed process noise and measurement noise as a Student’s t distribution as well as approximates the multi-target intensity as a mixture of Student’s t components to be propagated in time. Then, a closed PHD recursion is obtained based on Student’s t approximation. Our approach can make full use of the heavy-tailed characteristic of a Student’s t distribution to handle the situations with heavy-tailed process and the measurement noises. The simulation results verify that the proposed filter can overcome the negative effect generated by outliers and maintain a good tracking accuracy in the simultaneous presence of process and measurement outliers. PMID:29617348

Numerical Investigation of the Microscopic Heat Current Inside a Nanofluid System Based on Molecular Dynamics Simulation and Wavelet Analysis.

PubMed

Jia, Tao; Gao, Di

2018-04-03

Molecular dynamics simulation is employed to investigate the microscopic heat current inside an argon-copper nanofluid. Wavelet analysis of the microscopic heat current inside the nanofluid system is conducted. The signal of the microscopic heat current is decomposed into two parts: one is the approximation part; the other is the detail part. The approximation part is associated with the low-frequency part of the signal, and the detail part is associated with the high-frequency part of the signal. Both the probability distributions of the high-frequency and the low-frequency parts of the signals demonstrate Gaussian-like characteristics. The curves fit to data of the probability distribution of the microscopic heat current are established, and the parameters including the mean value and the standard deviation in the mathematical formulas of the curves show dramatic changes for the cases before and after adding copper nanoparticles into the argon base fluid.

Forward and inverse uncertainty quantification using multilevel Monte Carlo algorithms for an elliptic non-local equation

DOE PAGES

Jasra, Ajay; Law, Kody J. H.; Zhou, Yan

2016-01-01

Our paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are usedmore » for a priori and a posteriori estimation, respectively, of quantities of interest. Furthermore, these algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.« less

Forward and inverse uncertainty quantification using multilevel Monte Carlo algorithms for an elliptic non-local equation

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

Jasra, Ajay; Law, Kody J. H.; Zhou, Yan

Our paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are usedmore » for a priori and a posteriori estimation, respectively, of quantities of interest. Furthermore, these algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.« less

Birth/birth-death processes and their computable transition probabilities with biological applications.

PubMed

Ho, Lam Si Tung; Xu, Jason; Crawford, Forrest W; Minin, Vladimir N; Suchard, Marc A

2018-03-01

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.

Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties

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

Stoneking, M.R.; Den Hartog, D.J.

1996-06-01

The fitting of data by {chi}{sup 2}-minimization is valid only when the uncertainties in the data are normally distributed. When analyzing spectroscopic or particle counting data at very low signal level (e.g., a Thomson scattering diagnostic), the uncertainties are distributed with a Poisson distribution. The authors have developed a maximum-likelihood method for fitting data that correctly treats the Poisson statistical character of the uncertainties. This method maximizes the total probability that the observed data are drawn from the assumed fit function using the Poisson probability function to determine the probability for each data point. The algorithm also returns uncertainty estimatesmore » for the fit parameters. They compare this method with a {chi}{sup 2}-minimization routine applied to both simulated and real data. Differences in the returned fits are greater at low signal level (less than {approximately}20 counts per measurement). the maximum-likelihood method is found to be more accurate and robust, returning a narrower distribution of values for the fit parameters with fewer outliers.« less

Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species.

PubMed

Wang, Xueying; Walton, Jay R; Parshad, Rana D

2016-01-01

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a Markov jump process model for this strategy, and we verify that there is a positive probability for wild-type females going extinct within a finite time. Moreover, when sex-reversed Trojan females are introduced at a constant population size, we formulate a stochastic differential equation (SDE) model as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the extinction time of wild-type females by solving Kolmogorov equations associated with these statistics. The results indicate how the probability distribution and expectation of the extinction time are shaped by the initial conditions and the model parameters.

Ordinal probability effect measures for group comparisons in multinomial cumulative link models.

PubMed

Agresti, Alan; Kateri, Maria

2017-03-01

We consider simple ordinal model-based probability effect measures for comparing distributions of two groups, adjusted for explanatory variables. An "ordinal superiority" measure summarizes the probability that an observation from one distribution falls above an independent observation from the other distribution, adjusted for explanatory variables in a model. The measure applies directly to normal linear models and to a normal latent variable model for ordinal response variables. It equals Φ(β/2) for the corresponding ordinal model that applies a probit link function to cumulative multinomial probabilities, for standard normal cdf Φ and effect β that is the coefficient of the group indicator variable. For the more general latent variable model for ordinal responses that corresponds to a linear model with other possible error distributions and corresponding link functions for cumulative multinomial probabilities, the ordinal superiority measure equals exp(β)/[1+exp(β)] with the log-log link and equals approximately exp(β/2)/[1+exp(β/2)] with the logit link, where β is the group effect. Another ordinal superiority measure generalizes the difference of proportions from binary to ordinal responses. We also present related measures directly for ordinal models for the observed response that need not assume corresponding latent response models. We present confidence intervals for the measures and illustrate with an example. © 2016, The International Biometric Society.

Superthermal photon bunching in terms of simple probability distributions

NASA Astrophysics Data System (ADS)

Lettau, T.; Leymann, H. A. M.; Melcher, B.; Wiersig, J.

2018-05-01

We analyze the second-order photon autocorrelation function g(2 ) with respect to the photon probability distribution and discuss the generic features of a distribution that results in superthermal photon bunching [g(2 )(0 ) >2 ]. Superthermal photon bunching has been reported for a number of optical microcavity systems that exhibit processes such as superradiance or mode competition. We show that a superthermal photon number distribution cannot be constructed from the principle of maximum entropy if only the intensity and the second-order autocorrelation are given. However, for bimodal systems, an unbiased superthermal distribution can be constructed from second-order correlations and the intensities alone. Our findings suggest modeling superthermal single-mode distributions by a mixture of a thermal and a lasinglike state and thus reveal a generic mechanism in the photon probability distribution responsible for creating superthermal photon bunching. We relate our general considerations to a physical system, i.e., a (single-emitter) bimodal laser, and show that its statistics can be approximated and understood within our proposed model. Furthermore, the excellent agreement of the statistics of the bimodal laser and our model reveals that the bimodal laser is an ideal source of bunched photons, in the sense that it can generate statistics that contain no other features but the superthermal bunching.

A novel method for correcting scanline-observational bias of discontinuity orientation

PubMed Central

Huang, Lei; Tang, Huiming; Tan, Qinwen; Wang, Dingjian; Wang, Liangqing; Ez Eldin, Mutasim A. M.; Li, Changdong; Wu, Qiong

2016-01-01

Scanline observation is known to introduce an angular bias into the probability distribution of orientation in three-dimensional space. In this paper, numerical solutions expressing the functional relationship between the scanline-observational distribution (in one-dimensional space) and the inherent distribution (in three-dimensional space) are derived using probability theory and calculus under the independence hypothesis of dip direction and dip angle. Based on these solutions, a novel method for obtaining the inherent distribution (also for correcting the bias) is proposed, an approach which includes two procedures: 1) Correcting the cumulative probabilities of orientation according to the solutions, and 2) Determining the distribution of the corrected orientations using approximation methods such as the one-sample Kolmogorov-Smirnov test. The inherent distribution corrected by the proposed method can be used for discrete fracture network (DFN) modelling, which is applied to such areas as rockmass stability evaluation, rockmass permeability analysis, rockmass quality calculation and other related fields. To maximize the correction capacity of the proposed method, the observed sample size is suggested through effectiveness tests for different distribution types, dispersions and sample sizes. The performance of the proposed method and the comparison of its correction capacity with existing methods are illustrated with two case studies. PMID:26961249

Electron number probability distributions for correlated wave functions.

PubMed

Francisco, E; Martín Pendás, A; Blanco, M A

2007-03-07

Efficient formulas for computing the probability of finding exactly an integer number of electrons in an arbitrarily chosen volume are only known for single-determinant wave functions [E. Cances et al., Theor. Chem. Acc. 111, 373 (2004)]. In this article, an algebraic method is presented that extends these formulas to the case of multideterminant wave functions and any number of disjoint volumes. The derived expressions are applied to compute the probabilities within the atomic domains derived from the space partitioning based on the quantum theory of atoms in molecules. Results for a series of test molecules are presented, paying particular attention to the effects of electron correlation and of some numerical approximations on the computed probabilities.

Probability density function learning by unsupervised neurons.

PubMed

Fiori, S

2001-10-01

In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals.

A simple low-computation-intensity model for approximating the distribution function of a sum of non-identical lognormals for financial applications

NASA Astrophysics Data System (ADS)

Messica, A.

2016-10-01

The probability distribution function of a weighted sum of non-identical lognormal random variables is required in various fields of science and engineering and specifically in finance for portfolio management as well as exotic options valuation. Unfortunately, it has no known closed form and therefore has to be approximated. Most of the approximations presented to date are complex as well as complicated for implementation. This paper presents a simple, and easy to implement, approximation method via modified moments matching and a polynomial asymptotic series expansion correction for a central limit theorem of a finite sum. The method results in an intuitively-appealing and computation-efficient approximation for a finite sum of lognormals of at least ten summands and naturally improves as the number of summands increases. The accuracy of the method is tested against the results of Monte Carlo simulationsand also compared against the standard central limit theorem andthe commonly practiced Markowitz' portfolio equations.

Extended Poisson process modelling and analysis of grouped binary data.

PubMed

Faddy, Malcolm J; Smith, David M

2012-05-01

A simple extension of the Poisson process results in binomially distributed counts of events in a time interval. A further extension generalises this to probability distributions under- or over-dispersed relative to the binomial distribution. Substantial levels of under-dispersion are possible with this modelling, but only modest levels of over-dispersion - up to Poisson-like variation. Although simple analytical expressions for the moments of these probability distributions are not available, approximate expressions for the mean and variance are derived, and used to re-parameterise the models. The modelling is applied in the analysis of two published data sets, one showing under-dispersion and the other over-dispersion. More appropriate assessment of the precision of estimated parameters and reliable model checking diagnostics follow from this more general modelling of these data sets. © 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

The Approximate Bayesian Computation methods in the localization of the atmospheric contamination source

NASA Astrophysics Data System (ADS)

Kopka, P.; Wawrzynczak, A.; Borysiewicz, M.

2015-09-01

In many areas of application, a central problem is a solution to the inverse problem, especially estimation of the unknown model parameters to model the underlying dynamics of a physical system precisely. In this situation, the Bayesian inference is a powerful tool to combine observed data with prior knowledge to gain the probability distribution of searched parameters. We have applied the modern methodology named Sequential Approximate Bayesian Computation (S-ABC) to the problem of tracing the atmospheric contaminant source. The ABC is technique commonly used in the Bayesian analysis of complex models and dynamic system. Sequential methods can significantly increase the efficiency of the ABC. In the presented algorithm, the input data are the on-line arriving concentrations of released substance registered by distributed sensor network from OVER-LAND ATMOSPHERIC DISPERSION (OLAD) experiment. The algorithm output are the probability distributions of a contamination source parameters i.e. its particular location, release rate, speed and direction of the movement, start time and duration. The stochastic approach presented in this paper is completely general and can be used in other fields where the parameters of the model bet fitted to the observable data should be found.

Velocity distributions among colliding asteroids

NASA Technical Reports Server (NTRS)

Bottke, William F., Jr.; Nolan, Michael C.; Greenberg, Richard; Kolvoord, Robert A.

1994-01-01

The probability distribution for impact velocities between two given asteroids is wide, non-Gaussian, and often contains spikes according to our new method of analysis in which each possible orbital geometry for collision is weighted according to its probability. An average value would give a good representation only if the distribution were smooth and narrow. Therefore, the complete velocity distribution we obtain for various asteroid populations differs significantly from published histograms of average velocities. For all pairs among the 682 asteroids in the main-belt with D greater than 50 km, we find that our computed velocity distribution is much wider than previously computed histograms of average velocities. In this case, the most probable impact velocity is approximately 4.4 km/sec, compared with the mean impact velocity of 5.3 km/sec. For cases of a single asteroid (e.g., Gaspra or Ida) relative to an impacting population, the distribution we find yields lower velocities than previously reported by others. The width of these velocity distributions implies that mean impact velocities must be used with caution when calculating asteroid collisional lifetimes or crater-size distributions. Since the most probable impact velocities are lower than the mean, disruption events may occur less frequently than previously estimated. However, this disruption rate may be balanced somewhat by an apparent increase in the frequency of high-velocity impacts between asteroids. These results have implications for issues such as asteroidal disruption rates, the amount/type of impact ejecta available for meteoritical delivery to the Earth, and the geology and evolution of specific asteroids like Gaspra.

A Financial Market Model Incorporating Herd Behaviour.

PubMed

Wray, Christopher M; Bishop, Steven R

2016-01-01

Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents' accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents' accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option.

Impact of temporal probability in 4D dose calculation for lung tumors.

PubMed

Rouabhi, Ouided; Ma, Mingyu; Bayouth, John; Xia, Junyi

2015-11-08

The purpose of this study was to evaluate the dosimetric uncertainty in 4D dose calculation using three temporal probability distributions: uniform distribution, sinusoidal distribution, and patient-specific distribution derived from the patient respiratory trace. Temporal probability, defined as the fraction of time a patient spends in each respiratory amplitude, was evaluated in nine lung cancer patients. Four-dimensional computed tomography (4D CT), along with deformable image registration, was used to compute 4D dose incorporating the patient's respiratory motion. First, the dose of each of 10 phase CTs was computed using the same planning parameters as those used in 3D treatment planning based on the breath-hold CT. Next, deformable image registration was used to deform the dose of each phase CT to the breath-hold CT using the deformation map between the phase CT and the breath-hold CT. Finally, the 4D dose was computed by summing the deformed phase doses using their corresponding temporal probabilities. In this study, 4D dose calculated from the patient-specific temporal probability distribution was used as the ground truth. The dosimetric evaluation matrix included: 1) 3D gamma analysis, 2) mean tumor dose (MTD), 3) mean lung dose (MLD), and 4) lung V20. For seven out of nine patients, both uniform and sinusoidal temporal probability dose distributions were found to have an average gamma passing rate > 95% for both the lung and PTV regions. Compared with 4D dose calculated using the patient respiratory trace, doses using uniform and sinusoidal distribution showed a percentage difference on average of -0.1% ± 0.6% and -0.2% ± 0.4% in MTD, -0.2% ± 1.9% and -0.2% ± 1.3% in MLD, 0.09% ± 2.8% and -0.07% ± 1.8% in lung V20, -0.1% ± 2.0% and 0.08% ± 1.34% in lung V10, 0.47% ± 1.8% and 0.19% ± 1.3% in lung V5, respectively. We concluded that four-dimensional dose computed using either a uniform or sinusoidal temporal probability distribution can approximate four-dimensional dose computed using the patient-specific respiratory trace.

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

Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model.

PubMed

Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

2017-07-01

For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α<β and β>1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 < r < 1 | α̂, β̂) as a validity measure (r is a random variable that follows a gamma distribution; α̂ and β̂ are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions β̂>(22α̂)0.50 for 0.02<α̂<2 as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | α̂, β̂) >0.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 < r < 1 | α̂, β̂), the better the approximation. The results further showed that, among the total 85 models examined, 68 models were identified as valid approximate model applications, which all had a near perfect match to the corresponding exact beta-Poisson model dose-response curve. © 2016 Society for Risk Analysis.

Distribution of apparent activation energy counterparts during thermo - And thermo-oxidative degradation of Aronia melanocarpa (black chokeberry).

PubMed

Janković, Bojan; Marinović-Cincović, Milena; Janković, Marija

2017-09-01

Kinetics of degradation for Aronia melanocarpa fresh fruits in argon and air atmospheres were investigated. The investigation was based on probability distributions of apparent activation energy of counterparts (ε a ). Isoconversional analysis results indicated that the degradation process in an inert atmosphere was governed by decomposition reactions of esterified compounds. Also, based on same kinetics approach, it was assumed that in an air atmosphere, the primary compound in degradation pathways could be anthocyanins, which undergo rapid chemical reactions. A new model of reactivity demonstrated that, under inert atmospheres, expectation values for ε a occured at levels of statistical probability. These values corresponded to decomposition processes in which polyphenolic compounds might be involved. ε a values obeyed laws of binomial distribution. It was established that, for thermo-oxidative degradation, Poisson distribution represented a very successful approximation for ε a values where there was additional mechanistic complexity and the binomial distribution was no longer valid. Copyright © 2017 Elsevier Ltd. All rights reserved.

Approximate supernova remnant dynamics with cosmic ray production

NASA Technical Reports Server (NTRS)

Voelk, H. J.; Drury, L. O.; Dorfi, E. A.

1985-01-01

Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probably sources of Cosmic Rays. Recent shock acceleration models treating the Cosmic Rays (CR's) as test particles nb a prescribed Supernova Remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the Interstellar Medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation.

A strategy for improved computational efficiency of the method of anchored distributions

NASA Astrophysics Data System (ADS)

Over, Matthew William; Yang, Yarong; Chen, Xingyuan; Rubin, Yoram

2013-06-01

This paper proposes a strategy for improving the computational efficiency of model inversion using the method of anchored distributions (MAD) by "bundling" similar model parametrizations in the likelihood function. Inferring the likelihood function typically requires a large number of forward model (FM) simulations for each possible model parametrization; as a result, the process is quite expensive. To ease this prohibitive cost, we present an approximation for the likelihood function called bundling that relaxes the requirement for high quantities of FM simulations. This approximation redefines the conditional statement of the likelihood function as the probability of a set of similar model parametrizations "bundle" replicating field measurements, which we show is neither a model reduction nor a sampling approach to improving the computational efficiency of model inversion. To evaluate the effectiveness of these modifications, we compare the quality of predictions and computational cost of bundling relative to a baseline MAD inversion of 3-D flow and transport model parameters. Additionally, to aid understanding of the implementation we provide a tutorial for bundling in the form of a sample data set and script for the R statistical computing language. For our synthetic experiment, bundling achieved a 35% reduction in overall computational cost and had a limited negative impact on predicted probability distributions of the model parameters. Strategies for minimizing error in the bundling approximation, for enforcing similarity among the sets of model parametrizations, and for identifying convergence of the likelihood function are also presented.

Digital simulation of an arbitrary stationary stochastic process by spectral representation.

PubMed

Yura, Harold T; Hanson, Steen G

2011-04-01

In this paper we present a straightforward, efficient, and computationally fast method for creating a large number of discrete samples with an arbitrary given probability density function and a specified spectral content. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In contrast to previous work, where the analyses were limited to auto regressive and or iterative techniques to obtain satisfactory results, we find that a single application of the inverse transform method yields satisfactory results for a wide class of arbitrary probability distributions. Although a single application of the inverse transform technique does not conserve the power spectra exactly, it yields highly accurate numerical results for a wide range of probability distributions and target power spectra that are sufficient for system simulation purposes and can thus be regarded as an accurate engineering approximation, which can be used for wide range of practical applications. A sufficiency condition is presented regarding the range of parameter values where a single application of the inverse transform method yields satisfactory agreement between the simulated and target power spectra, and a series of examples relevant for the optics community are presented and discussed. Outside this parameter range the agreement gracefully degrades but does not distort in shape. Although we demonstrate the method here focusing on stationary random processes, we see no reason why the method could not be extended to simulate non-stationary random processes. © 2011 Optical Society of America

Theory and simulation of the time-dependent rate coefficients of diffusion-influenced reactions.

PubMed Central

Zhou, H X; Szabo, A

1996-01-01

A general formalism is developed for calculating the time-dependent rate coefficient k(t) of an irreversible diffusion-influenced reaction. This formalism allows one to treat most factors that affect k(t), including rotational Brownian motion and conformational gating of reactant molecules and orientation constraint for product formation. At long times k(t) is shown to have the asymptotic expansion k(infinity)[1 + k(infinity) (pie Dt)-1/2 /4 pie D + ...], where D is the relative translational diffusion constant. An approximate analytical method for calculating k(t) is presented. This is based on the approximation that the probability density of the reactant pair in the reactive region keeps the equilibrium distribution but with a decreasing amplitude. The rate coefficient then is determined by the Green function in the absence of chemical reaction. Within the framework of this approximation, two general relations are obtained. The first relation allows the rate coefficient for an arbitrary amplitude of the reactivity to be found if the rate coefficient for one amplitude of the reactivity is known. The second relation allows the rate coefficient in the presence of conformational gating to be found from that in the absence of conformational gating. The ratio k(t)/k(0) is shown to be the survival probability of the reactant pair at time t starting from an initial distribution that is localized in the reactive region. This relation forms the basis of the calculation of k(t) through Brownian dynamics simulations. Two simulation procedures involving the propagation of nonreactive trajectories initiated only from the reactive region are described and illustrated on a model system. Both analytical and simulation results demonstrate the accuracy of the equilibrium-distribution approximation method. PMID:8913584

A new general method for the assessment of the molecular-weight distribution of polydisperse preparations. Its application to an intestinal epithelial glycoprotein and two dextran samples, and comparison with a monodisperse glycoprotein

PubMed Central

Gibbons, Richard A.; Dixon, Stephen N.; Pocock, David H.

1973-01-01

A specimen of intestinal glycoprotein isolated from the pig and two samples of dextran, all of which are polydisperse (that is, the preparations may be regarded as consisting of a continuous distribution of molecular weights), have been examined in the ultracentrifuge under meniscus-depletion conditions at equilibrium. They are compared with each other and with a glycoprotein from Cysticercus tenuicollis cyst fluid which is almost monodisperse. The quantity c−⅓ (c=concentration) is plotted against ξ (the reduced radius); this plot is linear when the molecular-weight distribution approximates to the `most probable', i.e. when Mn:Mw:Mz: M(z+1)....... is as 1:2:3:4: etc. The use of this plot, and related procedures, to evaluate qualitatively and semi-quantitatively molecular-weight distribution functions where they can be realistically approximated to Schulz distributions is discussed. The theoretical basis is given in an Appendix. PMID:4778265

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian—MCMC method

NASA Astrophysics Data System (ADS)

Sheng, Zheng

2013-02-01

The estimation of lower atmospheric refractivity from radar sea clutter (RFC) is a complicated nonlinear optimization problem. This paper deals with the RFC problem in a Bayesian framework. It uses the unbiased Markov Chain Monte Carlo (MCMC) sampling technique, which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework. In contrast to the global optimization algorithm, the Bayesian—MCMC can obtain not only the approximate solutions, but also the probability distributions of the solutions, that is, uncertainty analyses of solutions. The Bayesian—MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar sea-clutter data. Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter. The inversion algorithm is assessed (i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data; (ii) the one-dimensional (1D) and two-dimensional (2D) posterior probability distribution of solutions.

Dynamic probability control limits for risk-adjusted Bernoulli CUSUM charts.

PubMed

Zhang, Xiang; Woodall, William H

2015-11-10

The risk-adjusted Bernoulli cumulative sum (CUSUM) chart developed by Steiner et al. (2000) is an increasingly popular tool for monitoring clinical and surgical performance. In practice, however, the use of a fixed control limit for the chart leads to a quite variable in-control average run length performance for patient populations with different risk score distributions. To overcome this problem, we determine simulation-based dynamic probability control limits (DPCLs) patient-by-patient for the risk-adjusted Bernoulli CUSUM charts. By maintaining the probability of a false alarm at a constant level conditional on no false alarm for previous observations, our risk-adjusted CUSUM charts with DPCLs have consistent in-control performance at the desired level with approximately geometrically distributed run lengths. Our simulation results demonstrate that our method does not rely on any information or assumptions about the patients' risk distributions. The use of DPCLs for risk-adjusted Bernoulli CUSUM charts allows each chart to be designed for the corresponding particular sequence of patients for a surgeon or hospital. Copyright © 2015 John Wiley & Sons, Ltd.

Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas

PubMed Central

Bedford, Tim; Daneshkhah, Alireza

2015-01-01

Many applications of risk analysis require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modeling joint uncertainties with probability distributions. This article focuses on new methodologies for copulas by developing work of Cooke, Bedford, Kurowica, and others on vines as a way of constructing higher dimensional distributions that do not suffer from some of the restrictions of alternatives such as the multivariate Gaussian copula. The article provides a fundamental approximation result, demonstrating that we can approximate any density as closely as we like using vines. It further operationalizes this result by showing how minimum information copulas can be used to provide parametric classes of copulas that have such good levels of approximation. We extend previous approaches using vines by considering nonconstant conditional dependencies, which are particularly relevant in financial risk modeling. We discuss how such models may be quantified, in terms of expert judgment or by fitting data, and illustrate the approach by modeling two financial data sets. PMID:26332240

Statistical distribution of the vacuum energy density in racetrack Kähler uplift models in string theory

NASA Astrophysics Data System (ADS)

Sumitomo, Yoske; Tye, S.-H. Henry; Wong, Sam S. C.

2013-07-01

We study a racetrack model in the presence of the leading α'-correction in flux compactification in Type IIB string theory, for the purpose of getting conceivable de-Sitter vacua in the large compactified volume approximation. Unlike the Kähler Uplift model studied previously, the α'-correction is more controllable for the meta-stable de-Sitter vacua in the racetrack case since the constraint on the compactified volume size is very much relaxed. We find that the vacuum energy density Λ for de-Sitter vacua approaches zero exponentially as the volume grows. We also analyze properties of the probability distribution of Λ in this class of models. As in other cases studied earlier, the probability distribution again peaks sharply at Λ = 0. We also study the Racetrack Kähler Uplift model in the Swiss-Cheese type model.

Wave turbulence in shallow water models.

PubMed

Clark di Leoni, P; Cobelli, P J; Mininni, P D

2014-06-01

We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 2048{2} points. In all simulations, the Froude number varies between 0.015 and 0.05, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ∼k{-2} scaling. For deeper (Boussinesq) flows, the nonlinear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, ∼k{-4/3}. In this latter case, the nonlinear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution.

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.

Proton Straggling in Thick Silicon Detectors

NASA Technical Reports Server (NTRS)

Selesnick, R. S.; Baker, D. N.; Kanekal, S. G.

2017-01-01

Straggling functions for protons in thick silicon radiation detectors are computed by Monte Carlo simulation. Mean energy loss is constrained by the silicon stopping power, providing higher straggling at low energy and probabilities for stopping within the detector volume. By matching the first four moments of simulated energy-loss distributions, straggling functions are approximated by a log-normal distribution that is accurate for Vavilov k is greater than or equal to 0:3. They are verified by comparison to experimental proton data from a charged particle telescope.

A Statistical Study of the Mass Distribution of Neutron Stars

NASA Astrophysics Data System (ADS)

Cheng, Zheng; Zhang, Cheng-Min; Zhao, Yong-Heng; Wang, De-Hua; Pan, Yuan-Yue; Lei, Ya-Juan

2014-07-01

By reviewing the methods of mass measurements of neutron stars in four different kinds of systems, i.e., the high-mass X-ray binaries (HMXBs), low-mass X-ray binaries (LMXBs), double neutron star systems (DNSs) and neutron star-white dwarf (NS-WD) binary systems, we have collected the orbital parameters of 40 systems. By using the boot-strap method and the Monte-Carlo method, we have rebuilt the likelihood probability curves of the measured masses of 46 neutron stars. The statistical analysis of the simulation results shows that the masses of neutron stars in the X-ray neutron star systems and those in the radio pulsar systems exhibit different distributions. Besides, the Bayes statistics of these four different kind systems yields the most-probable probability density distributions of these four kind systems to be (1.340 ± 0.230)M8, (1, 505 ± 0.125)M8,(1.335 ± 0.055)M8 and (1.495 ± 0.225)M8, respectively. It is noteworthy that the masses of neutron stars in the HMXB and DNS systems are smaller than those in the other two kind systems by approximately 0.16M8. This result is consistent with the theoretical model of the pulsar to be accelerated to the millisecond order of magnitude via accretion of approximately 0.2M8. If the HMXBs and LMXBs are respectively taken to be the precursors of the BNS and NS-WD systems, then the influence of the accretion effect on the masses of neutron stars in the HMXB systems should be exceedingly small. Their mass distributions should be very close to the initial one during the formation of neutron stars. As for the LMXB and NS-WD systems, they should have already under- gone the process of suffcient accretion, hence there arises rather large deviation from the initial mass distribution.

EXACT DISTRIBUTIONS OF INTRACLASS CORRELATION AND CRONBACH'S ALPHA WITH GAUSSIAN DATA AND GENERAL COVARIANCE.

PubMed

Kistner, Emily O; Muller, Keith E

2004-09-01

Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions. New exact results allow calculating the exact distribution function and other properties of intraclass correlation and Cronbach's alpha, for Gaussian data with any covariance pattern, not just compound symmetry. Probabilities are computed in terms of the distribution function of a weighted sum of independent chi-square random variables. New F approximations for the distribution functions of intraclass correlation and Cronbach's alpha are much simpler and faster to compute than the exact forms. Assuming the covariance matrix is known, the approximations typically provide sufficient accuracy, even with as few as ten observations. Either the exact or approximate distributions may be used to create confidence intervals around an estimate of reliability. Monte Carlo simulations led to a number of conclusions. Correctly assuming that the covariance matrix is compound symmetric leads to accurate confidence intervals, as was expected from previously known results. However, assuming and estimating a general covariance matrix produces somewhat optimistically narrow confidence intervals with 10 observations. Increasing sample size to 100 gives essentially unbiased coverage. Incorrectly assuming compound symmetry leads to pessimistically large confidence intervals, with pessimism increasing with sample size. In contrast, incorrectly assuming general covariance introduces only a modest optimistic bias in small samples. Hence the new methods seem preferable for creating confidence intervals, except when compound symmetry definitely holds.

Analysis of the Hessian for Inverse Scattering Problems. Part 3. Inverse Medium Scattering of Electromagnetic Waves in Three Dimensions

DTIC Science & Technology

2012-08-01

small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This in turn enables fast solution of an appropriately...implication of the compactness of the Hessian is that for small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This...probability distribution is given by the inverse of the Hessian of the negative log likelihood function. For Gaussian data noise and model error, this

Optimal and Most Exact Confidence Intervals for Person Parameters in Item Response Theory Models

ERIC Educational Resources Information Center

Doebler, Anna; Doebler, Philipp; Holling, Heinz

2013-01-01

The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter [theta] is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given…

The nature of the dense obscuring material in the nucleus of NGC 1068

NASA Technical Reports Server (NTRS)

Tacconi, L. J.; Genzel, R.; Blietz, M.; Cameron, M.; Harris, A. I.; Madden, S.

1994-01-01

High spatial and spectral resolution observations of the distribution, physical parameters, and kinematics of the molecular interstellar medium toward the nucleus of the Seyfert 2 galaxy NGC 1068 are reported. The data consist of 2.4 by 3.4 arcseconds resolution interferometry of the 88.6 GHz HCN J = 1 towards 0 line at 17 km/s spectral resolution, single dish observations of several mm/submm isotopic lines of CO and HCN, and 0.85 arcseconds imaging spectroscopy of the 2.12 micron H2 S(1) line at a velocity resolution of 110 km/s. The central few hundred parsecs of NGC 1068 contain a system of dense (N(H2) approximately 10(exp 5) cm(exp -3)), warm (T greater than or equal to 70 K) molecular cloud cores. The low density molecular envelopes have probably been stripped by the nuclear wind and radiation. The molecular gas layer is located in the plane of NGC 1068's large scale disk (inclination approximately 35 deg) and orbits in elliptical streamlines in response to the central stellar bar. The spatial distribution of the 2 micron H2 emission suggests that gas is shocked at the leading edge of the bar, probably resulting in gas influx into the central 100 pc at a rate of a few solar mass per year. In addition to large scale streaming (with a solid body rotation curve), the HCN velocity field requires the presence of random motions of order 100 km/s. We interpret these large random motions as implying the nuclear gas disk to be very thick (scale height/radius approximately 1), probably as the result of the impact of nuclear radiation and wind on orbiting molecular clouds. Geometry and column density of the molecular cloud layer between approximately 30 pc to 300 pc from the nucleus can plausibly account for the nuclear obscuration and anisotropy of the radiation field in the visible and UV.

Improved Measures of Integrated Information

PubMed Central

Tegmark, Max

2016-01-01

Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated and classified by various desirable properties. A simple taxonomy of Φ-measures is presented where they are each characterized by their choice of factorization method (5 options), choice of probability distributions to compare (3 × 4 options) and choice of measure for comparing probability distributions (7 options). When requiring the Φ-measures to satisfy a minimum of attractive properties, these hundreds of options reduce to a mere handful, some of which turn out to be identical. Useful exact and approximate formulas are derived that can be applied to real-world data from laboratory experiments without posing unreasonable computational demands. PMID:27870846

Finding Bounded Rational Equilibria. Part 1; Iterative Focusing

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2004-01-01

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights from the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

Interplanetary ions during an energetic storm particle event - The distribution function from solar wind thermal energies to 1.6 MeV

NASA Technical Reports Server (NTRS)

Gosling, J. T.; Asbridge, J. R.; Bame, S. J.; Feldman, W. C.; Zwickl, R. D.; Paschmann, G.; Sckopke, N.; Hynds, R. J.

1981-01-01

An ion velocity distribution function of the postshock phase of an energetic storm particle (ESP) event is obtained from data from the ISEE 2 and ISEE 3 experiments. The distribution function is roughly isotropic in the solar wind frame from solar wind thermal energies to 1.6 MeV. The ESP event studied (8/27/78) is superposed upon a more energetic particle event which was predominantly field-aligned and which was probably of solar origin. The observations suggest that the ESP population is accelerated directly out of the solar wind thermal population or its quiescent suprathermal tail by a stochastic process associated with shock wave disturbance. The acceleration mechanism is sufficiently efficient so that approximately 1% of the solar wind population is accelerated to suprathermal energies. These suprathermal particles have an energy density of approximately 290 eV cubic centimeters.

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.

Prediction of Mean and Design Fatigue Lives of Self Compacting Concrete Beams in Flexure

NASA Astrophysics Data System (ADS)

Goel, S.; Singh, S. P.; Singh, P.; Kaushik, S. K.

2012-02-01

In this paper, result of an investigation conducted to study the flexural fatigue characteristics of self compacting concrete (SCC) beams in flexure are presented. An experimental programme was planned in which approximately 60 SCC beam specimens of size 100 × 100 × 500 mm were tested under flexural fatigue loading. Approximately 45 static flexural tests were also conducted to facilitate fatigue testing. The flexural fatigue and static flexural strength tests were conducted on a 100 kN servo-controlled actuator. The fatigue life data thus obtained have been used to establish the probability distributions of fatigue life of SCC using two-parameter Weibull distribution. The parameters of the Weibull distribution have been obtained by different methods of analysis. Using the distribution parameters, the mean and design fatigue lives of SCC have been estimated and compared with Normally vibrated concrete (NVC), the data for which have been taken from literature. It has been observed that SCC exhibits higher mean and design fatigue lives compared to NVC.

The distribution of stars most likely to harbor intelligent life.

PubMed

Whitmire, Daniel P; Matese, John J

2009-09-01

Simple heuristic models and recent numerical simulations show that the probability of habitable planet formation increases with stellar mass. We combine those results with the distribution of main-sequence stellar masses to obtain the distribution of stars most likely to possess habitable planets as a function of stellar lifetime. We then impose the self-selection condition that intelligent observers can only find themselves around a star with a lifetime greater than the time required for that observer to have evolved, T(i). This allows us to obtain the stellar timescale number distribution for a given value of T(i). Our results show that for habitable planets with a civilization that evolved at time T(i) = 4.5 Gyr the median stellar lifetime is 13 Gyr, corresponding approximately to a stellar type of G5, with two-thirds of the stars having lifetimes between 7 and 30 Gyr, corresponding approximately to spectral types G0-K5. For other values of T(i) the median stellar lifetime changes by less than 50%.

Clustering coefficients of protein-protein interaction networks

NASA Astrophysics Data System (ADS)

Miller, Gerald A.; Shi, Yi Y.; Qian, Hong; Bomsztyk, Karol

2007-05-01

The properties of certain networks are determined by hidden variables that are not explicitly measured. The conditional probability (propagator) that a vertex with a given value of the hidden variable is connected to k other vertices determines all measurable properties. We study hidden variable models and find an averaging approximation that enables us to obtain a general analytical result for the propagator. Analytic results showing the validity of the approximation are obtained. We apply hidden variable models to protein-protein interaction networks (PINs) in which the hidden variable is the association free energy, determined by distributions that depend on biochemistry and evolution. We compute degree distributions as well as clustering coefficients of several PINs of different species; good agreement with measured data is obtained. For the human interactome two different parameter sets give the same degree distributions, but the computed clustering coefficients differ by a factor of about 2. This shows that degree distributions are not sufficient to determine the properties of PINs.

Framework for cascade size calculations on random networks

NASA Astrophysics Data System (ADS)

Burkholz, Rebekka; Schweitzer, Frank

2018-04-01

We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary degree distribution, degree-degree correlations, and, in case of threshold models, for arbitrary threshold distribution. With our approach, we shift the perspective from the known branching process approximations to the iterative update of suitable probability distributions. Such distributions are key to capture cascade dynamics that involve possibly continuous quantities and that depend on the cascade history, e.g., if load is accumulated over time. As a proof of concept, we provide two examples: (a) Constant load models that cover many of the analytically tractable casacade models, and, as a highlight, (b) a fiber bundle model that was not tractable by branching process approximations before. Our derivations cover the whole cascade dynamics, not only their steady state. This allows us to include interventions in time or further model complexity in the analysis.

Extinction time of a stochastic predator-prey model by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao

2018-03-01

The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.

Bounds on stochastic chemical kinetic systems at steady state

NASA Astrophysics Data System (ADS)

Dowdy, Garrett R.; Barton, Paul I.

2018-02-01

The method of moments has been proposed as a potential means to reduce the dimensionality of the chemical master equation (CME) appearing in stochastic chemical kinetics. However, attempts to apply the method of moments to the CME usually result in the so-called closure problem. Several authors have proposed moment closure schemes, which allow them to obtain approximations of quantities of interest, such as the mean molecular count for each species. However, these approximations have the dissatisfying feature that they come with no error bounds. This paper presents a fundamentally different approach to the closure problem in stochastic chemical kinetics. Instead of making an approximation to compute a single number for the quantity of interest, we calculate mathematically rigorous bounds on this quantity by solving semidefinite programs. These bounds provide a check on the validity of the moment closure approximations and are in some cases so tight that they effectively provide the desired quantity. In this paper, the bounded quantities of interest are the mean molecular count for each species, the variance in this count, and the probability that the count lies in an arbitrary interval. At present, we consider only steady-state probability distributions, intending to discuss the dynamic problem in a future publication.

Optimal causal inference: estimating stored information and approximating causal architecture.

PubMed

Still, Susanne; Crutchfield, James P; Ellison, Christopher J

2010-09-01

We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate-distortion theory to use causal shielding--a natural principle of learning. We study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation. Filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. We show that in the limit in which a model-complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. From this, one can estimate the amount of historical information the process stores. More generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. Abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization. For nonideal cases with finite data, we show how the correct number of the underlying causal states can be found by optimal causal estimation. A previously derived model-complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid overfitting.

A Financial Market Model Incorporating Herd Behaviour

PubMed Central

2016-01-01

Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents’ accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents’ accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option. PMID:27007236

Cluster-based control of a separating flow over a smoothly contoured ramp

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Noack, Bernd R.; Spohn, Andreas; Cattafesta, Louis N.; Morzyński, Marek

2017-12-01

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a cluster-based discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a control-dependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the open-loop actuation in a separating flow dominated by Kelvin-Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.

Architectures of Kepler Planet Systems with Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Morehead, Robert C.; Ford, Eric B.

2015-12-01

The distribution of period normalized transit duration ratios among Kepler’s multiple transiting planet systems constrains the distributions of mutual orbital inclinations and orbital eccentricities. However, degeneracies in these parameters tied to the underlying number of planets in these systems complicate their interpretation. To untangle the true architecture of planet systems, the mutual inclination, eccentricity, and underlying planet number distributions must be considered simultaneously. The complexities of target selection, transit probability, detection biases, vetting, and follow-up observations make it impractical to write an explicit likelihood function. Approximate Bayesian computation (ABC) offers an intriguing path forward. In its simplest form, ABC generates a sample of trial population parameters from a prior distribution to produce synthetic datasets via a physically-motivated forward model. Samples are then accepted or rejected based on how close they come to reproducing the actual observed dataset to some tolerance. The accepted samples form a robust and useful approximation of the true posterior distribution of the underlying population parameters. We build on the considerable progress from the field of statistics to develop sequential algorithms for performing ABC in an efficient and flexible manner. We demonstrate the utility of ABC in exoplanet populations and present new constraints on the distributions of mutual orbital inclinations, eccentricities, and the relative number of short-period planets per star. We conclude with a discussion of the implications for other planet occurrence rate calculations, such as eta-Earth.

Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels.

PubMed

Peppas, Kostas P; Lazarakis, Fotis; Alexandridis, Antonis; Dangakis, Kostas

2012-08-01

In this Letter we investigate the error performance of multiple-input multiple-output free-space optical communication systems employing intensity modulation/direct detection and operating over strong atmospheric turbulence channels. Atmospheric-induced strong turbulence fading is modeled using the negative exponential distribution. For the considered system, an approximate yet accurate analytical expression for the average bit error probability is derived and an efficient method for its numerical evaluation is proposed. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

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.

Topological supersymmetry breaking: The definition and stochastic generalization of chaos and the limit of applicability of statistics

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Schwartz, Robert N.; Wang, Kang L.

2016-03-01

The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found supersymmetric theory of stochastics (STS), all stochastic differential equations (SDEs) possess topological or de Rahm supersymmetry and stochastic chaos is the phenomenon of its spontaneous breakdown. Even though the STS is free of approximations and thus is technically solid, it is still missing a firm interpretational basis in order to be physically sound. Here, we make a few important steps toward the construction of the interpretational foundation for the STS. In particular, we discuss that one way to understand why the ground states of chaotic SDEs are conditional (not total) probability distributions, is that some of the variables have infinite memory of initial conditions and thus are not “thermalized”, i.e., cannot be described by the initial-conditions-independent probability distributions. As a result, the definitive assumption of physical statistics that the ground state is a steady-state total probability distribution is not valid for chaotic SDEs.

A multimodal detection model of dolphins to estimate abundance validated by field experiments.

PubMed

Akamatsu, Tomonari; Ura, Tamaki; Sugimatsu, Harumi; Bahl, Rajendar; Behera, Sandeep; Panda, Sudarsan; Khan, Muntaz; Kar, S K; Kar, C S; Kimura, Satoko; Sasaki-Yamamoto, Yukiko

2013-09-01

Abundance estimation of marine mammals requires matching of detection of an animal or a group of animal by two independent means. A multimodal detection model using visual and acoustic cues (surfacing and phonation) that enables abundance estimation of dolphins is proposed. The method does not require a specific time window to match the cues of both means for applying mark-recapture method. The proposed model was evaluated using data obtained in field observations of Ganges River dolphins and Irrawaddy dolphins, as examples of dispersed and condensed distributions of animals, respectively. The acoustic detection probability was approximately 80%, 20% higher than that of visual detection for both species, regardless of the distribution of the animals in present study sites. The abundance estimates of Ganges River dolphins and Irrawaddy dolphins fairly agreed with the numbers reported in previous monitoring studies. The single animal detection probability was smaller than that of larger cluster size, as predicted by the model and confirmed by field data. However, dense groups of Irrawaddy dolphins showed difference in cluster sizes observed by visual and acoustic methods. Lower detection probability of single clusters of this species seemed to be caused by the clumped distribution of this species.

Covering Numbers for Semicontinuous Functions

DTIC Science & Technology

2016-04-29

functions, epi-distance, Attouch-Wets topology, epi-convergence, epi-spline, approximation theory . Date: April 29, 2016 1 Introduction Covering numbers of...classes of functions play central roles in parts of information theory , statistics, and applications such as machine learning; see for example [26...probability theory because there the hypo-distance metrizes weak convergence of distribution functions on IRd, which obviously are usc [22]. Thus, as an

Application of Bayesian Reliability Concepts to Cruise Missile Electronic Components

DTIC Science & Technology

1989-09-01

and contrast them with the more prevalent classical inference view. 3 II. literature Review Introduction This literature review will consider current ...events on the basis of whatever evidence is currently available. Then if additional evidence is subsequently obtained, the initial probabilities are...Chay contends there is no longer any need to approximate continuous prior distributions through discretization because current computer calculations

Supervised variational model with statistical inference and its application in medical image segmentation.

PubMed

Li, Changyang; Wang, Xiuying; Eberl, Stefan; Fulham, Michael; Yin, Yong; Dagan Feng, David

2015-01-01

Automated and general medical image segmentation can be challenging because the foreground and the background may have complicated and overlapping density distributions in medical imaging. Conventional region-based level set algorithms often assume piecewise constant or piecewise smooth for segments, which are implausible for general medical image segmentation. Furthermore, low contrast and noise make identification of the boundaries between foreground and background difficult for edge-based level set algorithms. Thus, to address these problems, we suggest a supervised variational level set segmentation model to harness the statistical region energy functional with a weighted probability approximation. Our approach models the region density distributions by using the mixture-of-mixtures Gaussian model to better approximate real intensity distributions and distinguish statistical intensity differences between foreground and background. The region-based statistical model in our algorithm can intuitively provide better performance on noisy images. We constructed a weighted probability map on graphs to incorporate spatial indications from user input with a contextual constraint based on the minimization of contextual graphs energy functional. We measured the performance of our approach on ten noisy synthetic images and 58 medical datasets with heterogeneous intensities and ill-defined boundaries and compared our technique to the Chan-Vese region-based level set model, the geodesic active contour model with distance regularization, and the random walker model. Our method consistently achieved the highest Dice similarity coefficient when compared to the other methods.

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

Versino, Daniele; Bronkhorst, Curt Allan

The computational formulation of a micro-mechanical material model for the dynamic failure of ductile metals is presented in this paper. The statistical nature of porosity initiation is accounted for by introducing an arbitrary probability density function which describes the pores nucleation pressures. Each micropore within the representative volume element is modeled as a thick spherical shell made of plastically incompressible material. The treatment of porosity by a distribution of thick-walled spheres also allows for the inclusion of micro-inertia effects under conditions of shock and dynamic loading. The second order ordinary differential equation governing the microscopic porosity evolution is solved withmore » a robust implicit procedure. A new Chebyshev collocation method is employed to approximate the porosity distribution and remapping is used to optimize memory usage. The adaptive approximation of the porosity distribution leads to a reduction of computational time and memory usage of up to two orders of magnitude. Moreover, the proposed model affords consistent performance: changing the nucleation pressure probability density function and/or the applied strain rate does not reduce accuracy or computational efficiency of the material model. The numerical performance of the model and algorithms presented is tested against three problems for high density tantalum: single void, one-dimensional uniaxial strain, and two-dimensional plate impact. Here, the results using the integration and algorithmic advances suggest a significant improvement in computational efficiency and accuracy over previous treatments for dynamic loading conditions.« less

On a growth model for complex networks capable of producing power-law out-degree distributions with wide range exponents

PubMed Central

Esquivel-Gómez, J.; Arjona-Villicaña, P. D.; Stevens-Navarro, E.; Pineda-Rico, U.; Balderas-Navarro, R. E.; Acosta-Elias, J.

2015-01-01

The out-degree distribution is one of the most reported topological properties to characterize real complex networks. This property describes the probability that a node in the network has a particular number of outgoing links. It has been found that in many real complex networks the out-degree has a behavior similar to a power-law distribution, therefore some network growth models have been proposed to approximate this behavior. This paper introduces a new growth model that allows to produce out-degree distributions that decay as a power-law with an exponent in the range from 1 to ∞. PMID:25765763

Finding Bounded Rational Equilibria. Part 2; Alternative Lagrangians and Uncountable Move Spaces

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2004-01-01

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights &om the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

Pseudochemotaxis in inhomogeneous active Brownian systems

NASA Astrophysics Data System (ADS)

Vuijk, Hidde D.; Sharma, Abhinav; Mondal, Debasish; Sommer, Jens-Uwe; Merlitz, Holger

2018-04-01

We study dynamical properties of confined, self-propelled Brownian particles in an inhomogeneous activity profile. Using Brownian dynamics simulations, we calculate the probability to reach a fixed target and the mean first passage time to the target of an active particle. We show that both these quantities are strongly influenced by the inhomogeneous activity. When the activity is distributed such that high-activity zone is located between the target and the starting location, the target finding probability is increased and the passage time is decreased in comparison to a uniformly active system. Moreover, for a continuously distributed profile, the activity gradient results in a drift of active particle up the gradient bearing resemblance to chemotaxis. Integrating out the orientational degrees of freedom, we derive an approximate Fokker-Planck equation and show that the theoretical predictions are in very good agreement with the Brownian dynamics simulations.

Spacing distribution functions for 1D point island model with irreversible attachment

NASA Astrophysics Data System (ADS)

Gonzalez, Diego; Einstein, Theodore; Pimpinelli, Alberto

2011-03-01

We study the configurational structure of the point island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density p xy n (x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for p xy n (x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system. This work was supported by the NSF-MRSEC at the University of Maryland, Grant No. DMR 05-20471, with ancillary support from the Center for Nanophysics and Advanced Materials (CNAM).

A Statistical Study of Serum Cholesterol Level by Gender and Race.

PubMed

Tharu, Bhikhari Prasad; Tsokos, Chris P

2017-07-25

Cholesterol level (CL) is growing concerned as health issue in human health since it is considered one of the causes in heart diseases. A study of cholesterol level can provide insight about its nature and characteristics. A cross-sectional study. National Health and Nutrition Examination Survey (NHANS) II was conducted on a probability sample of approximately 28,000 persons in the USA and cholesterol level is obtained from laboratory results. Samples were selected so that certain population groups thought to be at high risk of malnutrition. Study included 11,864 persons for CL cases with 9,602 males and 2,262 females with races: whites, blacks, and others. Non-parametric statistical tests and goodness of fit test have been used to identify probability distributions. The study concludes that the cholesterol level exhibits significant racial and gender differences in terms of probability distributions. The study has concluded that white people are relatively higher at risk than black people to have risk line and high risk cholesterol. The study clearly indicates that black males normally have higher cholesterol. Females have lower variation in cholesterol than males. There exists gender and racial discrepancies in cholesterol which has been identified as lognormal and gamma probability distributions. White individuals seem to be at a higher risk of having high risk cholesterol level than blacks. Females tend to have higher variation in cholesterol level than males.

An approximate methods approach to probabilistic structural analysis

NASA Technical Reports Server (NTRS)

Mcclung, R. C.; Millwater, H. R.; Wu, Y.-T.; Thacker, B. H.; Burnside, O. H.

1989-01-01

A probabilistic structural analysis method (PSAM) is described which makes an approximate calculation of the structural response of a system, including the associated probabilistic distributions, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The method employs the fast probability integration (FPI) algorithm of Wu and Wirsching. Typical solution strategies are illustrated by formulations for a representative critical component chosen from the Space Shuttle Main Engine (SSME) as part of a major NASA-sponsored program on PSAM. Typical results are presented to demonstrate the role of the methodology in engineering design and analysis.

Approximate Bayesian estimation of extinction rate in the Finnish Daphnia magna metapopulation.

PubMed

Robinson, John D; Hall, David W; Wares, John P

2013-05-01

Approximate Bayesian computation (ABC) is useful for parameterizing complex models in population genetics. In this study, ABC was applied to simultaneously estimate parameter values for a model of metapopulation coalescence and test two alternatives to a strict metapopulation model in the well-studied network of Daphnia magna populations in Finland. The models shared four free parameters: the subpopulation genetic diversity (θS), the rate of gene flow among patches (4Nm), the founding population size (N0) and the metapopulation extinction rate (e) but differed in the distribution of extinction rates across habitat patches in the system. The three models had either a constant extinction rate in all populations (strict metapopulation), one population that was protected from local extinction (i.e. a persistent source), or habitat-specific extinction rates drawn from a distribution with specified mean and variance. Our model selection analysis favoured the model including a persistent source population over the two alternative models. Of the closest 750,000 data sets in Euclidean space, 78% were simulated under the persistent source model (estimated posterior probability = 0.769). This fraction increased to more than 85% when only the closest 150,000 data sets were considered (estimated posterior probability = 0.774). Approximate Bayesian computation was then used to estimate parameter values that might produce the observed set of summary statistics. Our analysis provided posterior distributions for e that included the point estimate obtained from previous data from the Finnish D. magna metapopulation. Our results support the use of ABC and population genetic data for testing the strict metapopulation model and parameterizing complex models of demography. © 2013 Blackwell Publishing Ltd.

Mutation-selection balance in mixed mating populations.

PubMed

Kelly, John K

2007-05-21

An approximation to the average number of deleterious mutations per gamete, Q, is derived from a model allowing selection on both zygotes and male gametes. Progeny are produced by either outcrossing or self-fertilization with fixed probabilities. The genetic model is a standard in evolutionary biology: mutations occur at unlinked loci, have equivalent effects, and combine multiplicatively to determine fitness. The approximation developed here treats individual mutation counts with a generalized Poisson model conditioned on the distribution of selfing histories in the population. The approximation is accurate across the range of parameter sets considered and provides both analytical insights and greatly increased computational speed. Model predictions are discussed in relation to several outstanding problems, including the estimation of the genomic deleterious mutation rates (U), the generality of "selective interference" among loci, and the consequences of gametic selection for the joint distribution of inbreeding depression and mating system across species. Finally, conflicting results from previous analytical treatments of mutation-selection balance are resolved to assumptions about the life-cycle and the initial fate of mutations.

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2005-01-01

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.

Mean, covariance, and effective dimension of stochastic distributed delay dynamics

NASA Astrophysics Data System (ADS)

René, Alexandre; Longtin, André

2017-11-01

Dynamical models are often required to incorporate both delays and noise. However, the inherently infinite-dimensional nature of delay equations makes formal solutions to stochastic delay differential equations (SDDEs) challenging. Here, we present an approach, similar in spirit to the analysis of functional differential equations, but based on finite-dimensional matrix operators. This results in a method for obtaining both transient and stationary solutions that is directly amenable to computation, and applicable to first order differential systems with either discrete or distributed delays. With fewer assumptions on the system's parameters than other current solution methods and no need to be near a bifurcation, we decompose the solution to a linear SDDE with arbitrary distributed delays into natural modes, in effect the eigenfunctions of the differential operator, and show that relatively few modes can suffice to approximate the probability density of solutions. Thus, we are led to conclude that noise makes these SDDEs effectively low dimensional, which opens the possibility of practical definitions of probability densities over their solution space.

Universality in survivor distributions: Characterizing the winners of competitive dynamics

NASA Astrophysics Data System (ADS)

Luck, J. M.; Mehta, A.

2015-11-01

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and nonsurvivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterization is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept—the dynamical fugacity. Remarkably, in the large-mass limit, the survivor probability of a node becomes independent of network geometry and assumes a simple form which depends only on its mass and degree.

Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of molecular clouds ensembles

NASA Astrophysics Data System (ADS)

Donkov, Sava; Stefanov, Ivan Z.

2018-03-01

We have set ourselves the task of obtaining the probability distribution function of the mass density of a self-gravitating isothermal compressible turbulent fluid from its physics. We have done this in the context of a new notion: the molecular clouds ensemble. We have applied a new approach that takes into account the fractal nature of the fluid. Using the medium equations, under the assumption of steady state, we show that the total energy per unit mass is an invariant with respect to the fractal scales. As a next step we obtain a non-linear integral equation for the dimensionless scale Q which is the third root of the integral of the probability distribution function. It is solved approximately up to the leading-order term in the series expansion. We obtain two solutions. They are power-law distributions with different slopes: the first one is -1.5 at low densities, corresponding to an equilibrium between all energies at a given scale, and the second one is -2 at high densities, corresponding to a free fall at small scales.

The discrete Laplace exponential family and estimation of Y-STR haplotype frequencies.

PubMed

Andersen, Mikkel Meyer; Eriksen, Poul Svante; Morling, Niels

2013-07-21

Estimating haplotype frequencies is important in e.g. forensic genetics, where the frequencies are needed to calculate the likelihood ratio for the evidential weight of a DNA profile found at a crime scene. Estimation is naturally based on a population model, motivating the investigation of the Fisher-Wright model of evolution for haploid lineage DNA markers. An exponential family (a class of probability distributions that is well understood in probability theory such that inference is easily made by using existing software) called the 'discrete Laplace distribution' is described. We illustrate how well the discrete Laplace distribution approximates a more complicated distribution that arises by investigating the well-known population genetic Fisher-Wright model of evolution by a single-step mutation process. It was shown how the discrete Laplace distribution can be used to estimate haplotype frequencies for haploid lineage DNA markers (such as Y-chromosomal short tandem repeats), which in turn can be used to assess the evidential weight of a DNA profile found at a crime scene. This was done by making inference in a mixture of multivariate, marginally independent, discrete Laplace distributions using the EM algorithm to estimate the probabilities of membership of a set of unobserved subpopulations. The discrete Laplace distribution can be used to estimate haplotype frequencies with lower prediction error than other existing estimators. Furthermore, the calculations could be performed on a normal computer. This method was implemented in the freely available open source software R that is supported on Linux, MacOS and MS Windows. Copyright © 2013 Elsevier Ltd. All rights reserved.

Statistical physics of medical diagnostics: Study of a probabilistic model.

PubMed

Mashaghi, Alireza; Ramezanpour, Abolfazl

2018-03-01

We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses compared to a strategy that is solely based on the direct implications of the initial observations. We demonstrate this by employing the mean-field approximation of statistical physics to compute the posterior disease probabilities for a given subset of observed signs (symptoms) in a probabilistic model of signs and diseases. A Monte Carlo optimization algorithm is then used to maximize an objective function of the sequence of observations, which favors the more decisive observations resulting in more polarized disease probabilities. We see how the observed signs change the nature of the macroscopic (Gibbs) states of the sign and disease probability distributions. The structure of these macroscopic states in the configuration space of the variables affects the quality of any approximate inference algorithm (so the diagnostic performance) which tries to estimate the sign-disease marginal probabilities. In particular, we find that the simulation (or extrapolation) of the diagnostic process is helpful when the disease landscape is not trivial and the system undergoes a phase transition to an ordered phase.

Statistical physics of medical diagnostics: Study of a probabilistic model

NASA Astrophysics Data System (ADS)

Mashaghi, Alireza; Ramezanpour, Abolfazl

2018-03-01

We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses compared to a strategy that is solely based on the direct implications of the initial observations. We demonstrate this by employing the mean-field approximation of statistical physics to compute the posterior disease probabilities for a given subset of observed signs (symptoms) in a probabilistic model of signs and diseases. A Monte Carlo optimization algorithm is then used to maximize an objective function of the sequence of observations, which favors the more decisive observations resulting in more polarized disease probabilities. We see how the observed signs change the nature of the macroscopic (Gibbs) states of the sign and disease probability distributions. The structure of these macroscopic states in the configuration space of the variables affects the quality of any approximate inference algorithm (so the diagnostic performance) which tries to estimate the sign-disease marginal probabilities. In particular, we find that the simulation (or extrapolation) of the diagnostic process is helpful when the disease landscape is not trivial and the system undergoes a phase transition to an ordered phase.

Spread of information and infection on finite random networks

NASA Astrophysics Data System (ADS)

Isham, Valerie; Kaczmarska, Joanna; Nekovee, Maziar

2011-04-01

The modeling of epidemic-like processes on random networks has received considerable attention in recent years. While these processes are inherently stochastic, most previous work has been focused on deterministic models that ignore important fluctuations that may persist even in the infinite network size limit. In a previous paper, for a class of epidemic and rumor processes, we derived approximate models for the full probability distribution of the final size of the epidemic, as opposed to only mean values. In this paper we examine via direct simulations the adequacy of the approximate model to describe stochastic epidemics and rumors on several random network topologies: homogeneous networks, Erdös-Rényi (ER) random graphs, Barabasi-Albert scale-free networks, and random geometric graphs. We find that the approximate model is reasonably accurate in predicting the probability of spread. However, the position of the threshold and the conditional mean of the final size for processes near the threshold are not well described by the approximate model even in the case of homogeneous networks. We attribute this failure to the presence of other structural properties beyond degree-degree correlations, and in particular clustering, which are present in any finite network but are not incorporated in the approximate model. In order to test this “hypothesis” we perform additional simulations on a set of ER random graphs where degree-degree correlations and clustering are separately and independently introduced using recently proposed algorithms from the literature. Our results show that even strong degree-degree correlations have only weak effects on the position of the threshold and the conditional mean of the final size. On the other hand, the introduction of clustering greatly affects both the position of the threshold and the conditional mean. Similar analysis for the Barabasi-Albert scale-free network confirms the significance of clustering on the dynamics of rumor spread. For this network, though, with its highly skewed degree distribution, the addition of positive correlation had a much stronger effect on the final size distribution than was found for the simple random graph.

Spatial event cluster detection using an approximate normal distribution.

PubMed

Torabi, Mahmoud; Rosychuk, Rhonda J

2008-12-12

In geographic surveillance of disease, areas with large numbers of disease cases are to be identified so that investigations of the causes of high disease rates can be pursued. Areas with high rates are called disease clusters and statistical cluster detection tests are used to identify geographic areas with higher disease rates than expected by chance alone. Typically cluster detection tests are applied to incident or prevalent cases of disease, but surveillance of disease-related events, where an individual may have multiple events, may also be of interest. Previously, a compound Poisson approach that detects clusters of events by testing individual areas that may be combined with their neighbours has been proposed. However, the relevant probabilities from the compound Poisson distribution are obtained from a recursion relation that can be cumbersome if the number of events are large or analyses by strata are performed. We propose a simpler approach that uses an approximate normal distribution. This method is very easy to implement and is applicable to situations where the population sizes are large and the population distribution by important strata may differ by area. We demonstrate the approach on pediatric self-inflicted injury presentations to emergency departments and compare the results for probabilities based on the recursion and the normal approach. We also implement a Monte Carlo simulation to study the performance of the proposed approach. In a self-inflicted injury data example, the normal approach identifies twelve out of thirteen of the same clusters as the compound Poisson approach, noting that the compound Poisson method detects twelve significant clusters in total. Through simulation studies, the normal approach well approximates the compound Poisson approach for a variety of different population sizes and case and event thresholds. A drawback of the compound Poisson approach is that the relevant probabilities must be determined through a recursion relation and such calculations can be computationally intensive if the cluster size is relatively large or if analyses are conducted with strata variables. On the other hand, the normal approach is very flexible, easily implemented, and hence, more appealing for users. Moreover, the concepts may be more easily conveyed to non-statisticians interested in understanding the methodology associated with cluster detection test results.

Seasonal Variability of Middle Latitude Ozone in the Lowermost Stratosphere Derived from Probability Distribution Functions

NASA Technical Reports Server (NTRS)

Cerniglia, M. C.; Douglass, A. R.; Rood, R. B.; Sparling, L. C.; Nielsen, J. E.

1999-01-01

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of understanding the relative contribution to the observations of air of either distinctly tropospheric or stratospheric origin. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High [low] potential vorticity at 300 hPa suggests that the tropopause is low [high], and the identification of the two groups helps to account for dynamic variability. Conditional probability distribution functions are used to define the statistics of the mix from both observations and model simulations. Two data sources are chosen. First, several years of ozonesonde observations are used to exploit the high vertical resolution. Second, observations made by the Halogen Occultation Experiment [HALOE) on the Upper Atmosphere Research Satellite [UARS] are used to understand the impact on the results of the spatial limitations of the ozonesonde network. The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause [approximately 380K]. Despite the differences in spatial and temporal sampling, the probability distribution functions are similar for the two data sources. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. By using the model, possible mechanisms for the maintenance of mix of air in the lowermost stratosphere are revealed. The relevance of the results to the assessment of the environmental impact of aircraft effluence is discussed.

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.

Aggregate and individual replication probability within an explicit model of the research process.

PubMed

Miller, Jeff; Schwarz, Wolf

2011-09-01

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 obtaining either a statistically significant result in the same direction or any effect in that direction. We analyze both the probability of successfully replicating a particular experimental effect (i.e., the individual replication probability) and the average probability of successful replication across different studies within some research context (i.e., the aggregate replication probability), and we identify the conditions under which the latter can be approximated using the formulas of Killeen (2005a, 2007). We show how both of these probabilities depend on parameters of the research context that would rarely be known in practice. In addition, we show that the statistical uncertainty associated with the size of an initial observed effect would often prevent accurate estimation of the desired individual replication probability even if these research context parameters were known exactly. We conclude that accurate estimates of replication probability are generally unattainable.

Multiple model cardinalized probability hypothesis density filter

NASA Astrophysics Data System (ADS)

Georgescu, Ramona; Willett, Peter

2011-09-01

The Probability Hypothesis Density (PHD) filter propagates the first-moment approximation to the multi-target Bayesian posterior distribution while the Cardinalized PHD (CPHD) filter propagates both the posterior likelihood of (an unlabeled) target state and the posterior probability mass function of the number of targets. Extensions of the PHD filter to the multiple model (MM) framework have been published and were implemented either with a Sequential Monte Carlo or a Gaussian Mixture approach. In this work, we introduce the multiple model version of the more elaborate CPHD filter. We present the derivation of the prediction and update steps of the MMCPHD particularized for the case of two target motion models and proceed to show that in the case of a single model, the new MMCPHD equations reduce to the original CPHD equations.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

CUMPOIS- CUMULATIVE POISSON DISTRIBUTION PROGRAM

NASA Technical Reports Server (NTRS)

Bowerman, P. N.

1994-01-01

The Cumulative Poisson distribution program, CUMPOIS, is one of two programs which make calculations involving cumulative poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), can be used independently of one another. CUMPOIS determines the approximate cumulative binomial distribution, evaluates the cumulative distribution function (cdf) for gamma distributions with integer shape parameters, and evaluates the cdf for chi-square distributions with even degrees of freedom. It can be used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. CUMPOIS calculates the probability that n or less events (ie. cumulative) will occur within any unit when the expected number of events is given as lambda. Normally, this probability is calculated by a direct summation, from i=0 to n, of terms involving the exponential function, lambda, and inverse factorials. This approach, however, eventually fails due to underflow for sufficiently large values of n. Additionally, when the exponential term is moved outside of the summation for simplification purposes, there is a risk that the terms remaining within the summation, and the summation itself, will overflow for certain values of i and lambda. CUMPOIS eliminates these possibilities by multiplying an additional exponential factor into the summation terms and the partial sum whenever overflow/underflow situations threaten. The reciprocal of this term is then multiplied into the completed sum giving the cumulative probability. The CUMPOIS program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly on most C compilers. The program format is interactive, accepting lambda and n as inputs. It has been implemented under DOS 3.2 and has a memory requirement of 26K. CUMPOIS was developed in 1988.

Adaptive hybrid simulations for multiscale stochastic reaction networks

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

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such amore » partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.« less

Adaptive hybrid simulations for multiscale stochastic reaction networks.

PubMed

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

Modeling stochastic noise in gene regulatory systems

PubMed Central

Meister, Arwen; Du, Chao; Li, Ye Henry; Wong, Wing Hung

2014-01-01

The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady-states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems. PMID:25632368

Adaptive Detector Arrays for Optical Communications Receivers

NASA Technical Reports Server (NTRS)

Vilnrotter, V.; Srinivasan, M.

2000-01-01

The structure of an optimal adaptive array receiver for ground-based optical communications is described and its performance investigated. Kolmogorov phase screen simulations are used to model the sample functions of the focal-plane signal distribution due to turbulence and to generate realistic spatial distributions of the received optical field. This novel array detector concept reduces interference from background radiation by effectively assigning higher confidence levels at each instant of time to those detector elements that contain significant signal energy and suppressing those that do not. A simpler suboptimum structure that replaces the continuous weighting function of the optimal receiver by a hard decision on the selection of the signal detector elements also is described and evaluated. Approximations and bounds to the error probability are derived and compared with the exact calculations and receiver simulation results. It is shown that, for photon-counting receivers observing Poisson-distributed signals, performance improvements of approximately 5 dB can be obtained over conventional single-detector photon-counting receivers, when operating in high background environments.

Perturbations of linear delay differential equations at the verge of instability.

PubMed

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

Probabilistic self-organizing maps for continuous data.

PubMed

Lopez-Rubio, Ezequiel

2010-10-01

The original self-organizing feature map did not define any probability distribution on the input space. However, the advantages of introducing probabilistic methodologies into self-organizing map models were soon evident. This has led to a wide range of proposals which reflect the current emergence of probabilistic approaches to computational intelligence. The underlying estimation theories behind them derive from two main lines of thought: the expectation maximization methodology and stochastic approximation methods. Here, we present a comprehensive view of the state of the art, with a unifying perspective of the involved theoretical frameworks. In particular, we examine the most commonly used continuous probability distributions, self-organization mechanisms, and learning schemes. Special emphasis is given to the connections among them and their relative advantages depending on the characteristics of the problem at hand. Furthermore, we evaluate their performance in two typical applications of self-organizing maps: classification and visualization.

Standardized likelihood ratio test for comparing several log-normal means and confidence interval for the common mean.

PubMed

Krishnamoorthy, K; Oral, Evrim

2017-12-01

Standardized likelihood ratio test (SLRT) for testing the equality of means of several log-normal distributions is proposed. The properties of the SLRT and an available modified likelihood ratio test (MLRT) and a generalized variable (GV) test are evaluated by Monte Carlo simulation and compared. Evaluation studies indicate that the SLRT is accurate even for small samples, whereas the MLRT could be quite liberal for some parameter values, and the GV test is in general conservative and less powerful than the SLRT. Furthermore, a closed-form approximate confidence interval for the common mean of several log-normal distributions is developed using the method of variance estimate recovery, and compared with the generalized confidence interval with respect to coverage probabilities and precision. Simulation studies indicate that the proposed confidence interval is accurate and better than the generalized confidence interval in terms of coverage probabilities. The methods are illustrated using two examples.

Formal properties of the probability of fixation: identities, inequalities and approximations.

PubMed

McCandlish, David M; Epstein, Charles L; Plotkin, Joshua B

2015-02-01

The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of fixation of a new mutation under the Moran process (equivalent results hold for the approximate probability of fixation under the Wright-Fisher process, after an appropriate change of variables). We show that the logarithm of the fixation probability has particularly simple behavior when the selection coefficient is measured as a difference of Malthusian fitnesses, and we exploit this simplicity to derive inequalities and approximations. We also present a comprehensive comparison of both existing and new approximations for the fixation probability, highlighting those approximations that induce a reversible Markov chain when used to describe the dynamics of evolution under weak mutation. To demonstrate the power of these results, we consider the classical problem of determining the total substitution rate across an ensemble of biallelic loci and prove that, at equilibrium, a strict majority of substitutions are due to drift rather than selection. Copyright © 2014 Elsevier Inc. All rights reserved.

Single photon counting linear mode avalanche photodiode technologies

NASA Astrophysics Data System (ADS)

Williams, George M.; Huntington, Andrew S.

2011-10-01

The false count rate of a single-photon-sensitive photoreceiver consisting of a high-gain, low-excess-noise linear-mode InGaAs avalanche photodiode (APD) and a high-bandwidth transimpedance amplifier (TIA) is fit to a statistical model. The peak height distribution of the APD's multiplied dark current is approximated by the weighted sum of McIntyre distributions, each characterizing dark current generated at a different location within the APD's junction. The peak height distribution approximated in this way is convolved with a Gaussian distribution representing the input-referred noise of the TIA to generate the statistical distribution of the uncorrelated sum. The cumulative distribution function (CDF) representing count probability as a function of detection threshold is computed, and the CDF model fit to empirical false count data. It is found that only k=0 McIntyre distributions fit the empirically measured CDF at high detection threshold, and that false count rate drops faster than photon count rate as detection threshold is raised. Once fit to empirical false count data, the model predicts the improvement of the false count rate to be expected from reductions in TIA noise and APD dark current. Improvement by at least three orders of magnitude is thought feasible with further manufacturing development and a capacitive-feedback TIA (CTIA).

Transmission characteristics of Bessel-Gaussian vortex beams propagating along both longitudinal and transverse directions in a subway tunnel

NASA Astrophysics Data System (ADS)

Wang, Xiaohui; Song, Yingxiong

2018-02-01

By exploiting the non-Kolmogorov model and Rytov approximation theory, a propagation model of Bessel-Gaussian vortex beams (BGVB) propagating in a subway tunnel is derived. Based on the propagation model, a model of orbital angular momentum (OAM) mode probability distribution is established to evaluate the propagation performance when the beam propagates along both longitudinal and transverse directions in the subway tunnel. By numerical simulations and experimental verifications, the influences of the various parameters of BGVB and turbulence on the OAM mode probability distribution are evaluated, and the results of simulations are consistent with the experimental statistics. The results verify that the middle area of turbulence is more beneficial for the vortex beam propagation than the edge; when the BGVB propagates along the longitudinal direction in the subway tunnel, the effects of turbulence on the OAM mode probability distribution can be decreased by selecting a larger anisotropy parameter, smaller coherence length, larger non-Kolmogorov power spectrum coefficient, smaller topological charge number, deeper subway tunnel, lower train speed, and longer wavelength. When the BGVB propagates along the transverse direction, the influences can be also mitigated by adopting a larger topological charge number, less non-Kolmogorov power spectrum coefficient, smaller refractive structure index, shorter wavelength, and shorter propagation distance.

Applications of the Galton Watson process to human DNA evolution and demography

NASA Astrophysics Data System (ADS)

Neves, Armando G. M.; Moreira, Carlos H. C.

2006-08-01

We show that the problem of existence of a mitochondrial Eve can be understood as an application of the Galton-Watson process and presents interesting analogies with critical phenomena in Statistical Mechanics. In the approximation of small survival probability, and assuming limited progeny, we are able to find for a genealogic tree the maximum and minimum survival probabilities over all probability distributions for the number of children per woman constrained to a given mean. As a consequence, we can relate existence of a mitochondrial Eve to quantitative demographic data of early mankind. In particular, we show that a mitochondrial Eve may exist even in an exponentially growing population, provided that the mean number of children per woman Nbar is constrained to a small range depending on the probability p that a child is a female. Assuming that the value p≈0.488 valid nowadays has remained fixed for thousands of generations, the range where a mitochondrial Eve occurs with sizeable probability is 2.0492

Confined active Brownian particles: theoretical description of propulsion-induced accumulation

NASA Astrophysics Data System (ADS)

Das, Shibananda; Gompper, Gerhard; Winkler, Roland G.

2018-01-01

The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein-Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker-Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.

Parameters affecting the resilience of scale-free networks to random failures.

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

Link, Hamilton E.; LaViolette, Randall A.; Lane, Terran

2005-09-01

It is commonly believed that scale-free networks are robust to massive numbers of random node deletions. For example, Cohen et al. in (1) study scale-free networks including some which approximate the measured degree distribution of the Internet. Their results suggest that if each node in this network failed independently with probability 0.99, most of the remaining nodes would still be connected in a giant component. In this paper, we show that a large and important subclass of scale-free networks are not robust to massive numbers of random node deletions. In particular, we study scale-free networks which have minimum node degreemore » of 1 and a power-law degree distribution beginning with nodes of degree 1 (power-law networks). We show that, in a power-law network approximating the Internet's reported distribution, when the probability of deletion of each node is 0.5 only about 25% of the surviving nodes in the network remain connected in a giant component, and the giant component does not persist beyond a critical failure rate of 0.9. The new result is partially due to improved analytical accommodation of the large number of degree-0 nodes that result after node deletions. Our results apply to power-law networks with a wide range of power-law exponents, including Internet-like networks. We give both analytical and empirical evidence that such networks are not generally robust to massive random node deletions.« less

A computationally efficient ductile damage model accounting for nucleation and micro-inertia at high triaxialities

DOE PAGES

Versino, Daniele; Bronkhorst, Curt Allan

2018-01-31

The computational formulation of a micro-mechanical material model for the dynamic failure of ductile metals is presented in this paper. The statistical nature of porosity initiation is accounted for by introducing an arbitrary probability density function which describes the pores nucleation pressures. Each micropore within the representative volume element is modeled as a thick spherical shell made of plastically incompressible material. The treatment of porosity by a distribution of thick-walled spheres also allows for the inclusion of micro-inertia effects under conditions of shock and dynamic loading. The second order ordinary differential equation governing the microscopic porosity evolution is solved withmore » a robust implicit procedure. A new Chebyshev collocation method is employed to approximate the porosity distribution and remapping is used to optimize memory usage. The adaptive approximation of the porosity distribution leads to a reduction of computational time and memory usage of up to two orders of magnitude. Moreover, the proposed model affords consistent performance: changing the nucleation pressure probability density function and/or the applied strain rate does not reduce accuracy or computational efficiency of the material model. The numerical performance of the model and algorithms presented is tested against three problems for high density tantalum: single void, one-dimensional uniaxial strain, and two-dimensional plate impact. Here, the results using the integration and algorithmic advances suggest a significant improvement in computational efficiency and accuracy over previous treatments for dynamic loading conditions.« less

Binding energies and spatial structures of small carrier complexes in monolayer transition-metal dichalcogenides via diffusion Monte Carlo

DOE PAGES

Mayers, Matthew Z.; Berkelbach, Timothy C.; Hybertsen, Mark S.; ...

2015-10-09

Ground-state diffusion Monte Carlo is used to investigate the binding energies and intercarrier radial probability distributions of excitons, trions, and biexcitons in a variety of two-dimensional transition-metal dichalcogenide materials. We compare these results to approximate variational calculations, as well as to analogous Monte Carlo calculations performed with simplified carrier interaction potentials. Our results highlight the successes and failures of approximate approaches as well as the physical features that determine the stability of small carrier complexes in monolayer transition-metal dichalcogenide materials. In conclusion, we discuss points of agreement and disagreement with recent experiments.

Seasonal Variability of Middle Latitude Ozone in the Lowermost Stratosphere Derived from Probability Distribution Functions

NASA Technical Reports Server (NTRS)

Rood, Richard B.; Douglass, Anne R.; Cerniglia, Mark C.; Sparling, Lynn C.; Nielsen, J. Eric

1999-01-01

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of characterizing the observed variability. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High (low) potential vorticity at 300 hPa indicates that the tropopause is low (high), and the identification of these two groups is made to account for the dynamic variability. Conditional probability distribution functions are used to define the statistics of the ozone distribution from both observations and a three-dimensional model simulation using winds from the Goddard Earth Observing System Data Assimilation System for transport. Ozone data sets include ozonesonde observations from northern midlatitude stations (1991-96) and midlatitude observations made by the Halogen Occultation Experiment (HALOE) on the Upper Atmosphere Research Satellite (UARS) (1994- 1998). The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause (approximately 380K). The probability distribution functions are similar for the two data sources, despite differences in horizontal and vertical resolution and spatial and temporal sampling. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. Results show that during summer, much of the observed variability is explained by the height of the tropopause. During the winter and spring, when the tropopause fluctuations are larger, less of the variability is explained by tropopause height. This suggests that more mixing occurs during these seasons. During all seasons, there is a transition zone near the tropopause that contains air characteristic of both the troposphere and the stratosphere. The relevance of the results to the assessment of the environmental impact of aircraft effluence is also discussed.

Distribution of tsunami interevent times

NASA Astrophysics Data System (ADS)

Geist, Eric L.; Parsons, Tom

2008-01-01

The distribution of tsunami interevent times is analyzed using global and site-specific (Hilo, Hawaii) tsunami catalogs. An empirical probability density distribution is determined by binning the observed interevent times during a period in which the observation rate is approximately constant. The empirical distributions for both catalogs exhibit non-Poissonian behavior in which there is an abundance of short interevent times compared to an exponential distribution. Two types of statistical distributions are used to model this clustering behavior: (1) long-term clustering described by a universal scaling law, and (2) Omori law decay of aftershocks and triggered sources. The empirical and theoretical distributions all imply an increased hazard rate after a tsunami, followed by a gradual decrease with time approaching a constant hazard rate. Examination of tsunami sources suggests that many of the short interevent times are caused by triggered earthquakes, though the triggered events are not necessarily on the same fault.

The ranking probability approach and its usage in design and analysis of large-scale studies.

PubMed

Kuo, Chia-Ling; Zaykin, Dmitri

2013-01-01

In experiments with many statistical tests there is need to balance type I and type II error rates while taking multiplicity into account. In the traditional approach, the nominal [Formula: see text]-level such as 0.05 is adjusted by the number of tests, [Formula: see text], i.e., as 0.05/[Formula: see text]. Assuming that some proportion of tests represent "true signals", that is, originate from a scenario where the null hypothesis is false, power depends on the number of true signals and the respective distribution of effect sizes. One way to define power is for it to be the probability of making at least one correct rejection at the assumed [Formula: see text]-level. We advocate an alternative way of establishing how "well-powered" a study is. In our approach, useful for studies with multiple tests, the ranking probability [Formula: see text] is controlled, defined as the probability of making at least [Formula: see text] correct rejections while rejecting hypotheses with [Formula: see text] smallest P-values. The two approaches are statistically related. Probability that the smallest P-value is a true signal (i.e., [Formula: see text]) is equal to the power at the level [Formula: see text], to an very good excellent approximation. Ranking probabilities are also related to the false discovery rate and to the Bayesian posterior probability of the null hypothesis. We study properties of our approach when the effect size distribution is replaced for convenience by a single "typical" value taken to be the mean of the underlying distribution. We conclude that its performance is often satisfactory under this simplification; however, substantial imprecision is to be expected when [Formula: see text] is very large and [Formula: see text] is small. Precision is largely restored when three values with the respective abundances are used instead of a single typical effect size value.

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

NASA Astrophysics Data System (ADS)

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

2017-11-01

In Hezaveh et al. we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational-lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data, as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single variational parameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that the application of approximate Bayesian neural networks to astrophysical modeling problems can be a fast alternative to Monte Carlo Markov Chains, allowing orders of magnitude improvement in speed.

Statistical time-dependent model for the interstellar gas

NASA Technical Reports Server (NTRS)

Gerola, H.; Kafatos, M.; Mccray, R.

1974-01-01

We present models for temperature and ionization structure of low, uniform-density (approximately 0.3 per cu cm) interstellar gas in a galactic disk which is exposed to soft X rays from supernova outbursts occurring randomly in space and time. The structure was calculated by computing the time record of temperature and ionization at a given point by Monte Carlo simulation. The calculation yields probability distribution functions for ionized fraction, temperature, and their various observable moments. These time-dependent models predict a bimodal temperature distribution of the gas that agrees with various observations. Cold regions in the low-density gas may have the appearance of clouds in 21-cm absorption. The time-dependent model, in contrast to the steady-state model, predicts large fluctuations in ionization rate and the existence of cold (approximately 30 K), ionized (ionized fraction equal to about 0.1) regions.

THE DISTRIBUTION OF COOK’S D STATISTIC

PubMed Central

Muller, Keith E.; Mok, Mario Chen

2013-01-01

Cook (1977) proposed a diagnostic to quantify the impact of deleting an observation on the estimated regression coefficients of a General Linear Univariate Model (GLUM). Simulations of models with Gaussian response and predictors demonstrate that his suggestion of comparing the diagnostic to the median of the F for overall regression captures an erratically varying proportion of the values. We describe the exact distribution of Cook’s statistic for a GLUM with Gaussian predictors and response. We also present computational forms, simple approximations, and asymptotic results. A simulation supports the accuracy of the results. The methods allow accurate evaluation of a single value or the maximum value from a regression analysis. The approximations work well for a single value, but less well for the maximum. In contrast, the cut-point suggested by Cook provides widely varying tail probabilities. As with all diagnostics, the data analyst must use scientific judgment in deciding how to treat highlighted observations. PMID:24363487

Microwave inversion of leaf area and inclination angle distributions from backscattered data

NASA Technical Reports Server (NTRS)

Lang, R. H.; Saleh, H. A.

1985-01-01

The backscattering coefficient from a slab of thin randomly oriented dielectric disks over a flat lossy ground is used to reconstruct the inclination angle and area distributions of the disks. The disks are employed to model a leafy agricultural crop, such as soybeans, in the L-band microwave region of the spectrum. The distorted Born approximation, along with a thin disk approximation, is used to obtain a relationship between the horizontal-like polarized backscattering coefficient and the joint probability density of disk inclination angle and disk radius. Assuming large skin depth reduces the relationship to a linear Fredholm integral equation of the first kind. Due to the ill-posed nature of this equation, a Phillips-Twomey regularization method with a second difference smoothing condition is used to find the inversion. Results are obtained in the presence of 1 and 10 percent noise for both leaf inclination angle and leaf radius densities.

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.

GIS-based probability assessment of natural hazards in forested landscapes of Central and South-Eastern Europe.

PubMed

Lorz, C; Fürst, C; Galic, Z; Matijasic, D; Podrazky, V; Potocic, N; Simoncic, P; Strauch, M; Vacik, H; Makeschin, F

2010-12-01

We assessed the probability of three major natural hazards--windthrow, drought, and forest fire--for Central and South-Eastern European forests which are major threats for the provision of forest goods and ecosystem services. In addition, we analyzed spatial distribution and implications for a future oriented management of forested landscapes. For estimating the probability of windthrow, we used rooting depth and average wind speed. Probabilities of drought and fire were calculated from climatic and total water balance during growing season. As an approximation to climate change scenarios, we used a simplified approach with a general increase of pET by 20%. Monitoring data from the pan-European forests crown condition program and observed burnt areas and hot spots from the European Forest Fire Information System were used to test the plausibility of probability maps. Regions with high probabilities of natural hazard are identified and management strategies to minimize probability of natural hazards are discussed. We suggest future research should focus on (i) estimating probabilities using process based models (including sensitivity analysis), (ii) defining probability in terms of economic loss, (iii) including biotic hazards, (iv) using more detailed data sets on natural hazards, forest inventories and climate change scenarios, and (v) developing a framework of adaptive risk management.

Distribution and mixing of a liquid bolus in pleural space.

PubMed

Bodega, Francesca; Tresoldi, Claudio; Porta, Cristina; Zocchi, Luciano; Agostoni, Emilio

2006-02-28

Distribution and mixing time of boluses with labeled albumin in pleural space of anesthetized, supine rabbits were determined by sampling pleural liquid at different times in various intercostal spaces (ics), and in cranial and caudal mediastinum. During sampling, lung and chest wall were kept apposed by lung inflation. This was not necessary in costo-phrenic sinus. Here, 10 min after injection, lung inflation increased concentration of labeled albumin by 50%. Lung inflation probably displaces some pleural liquid cranio-caudally, increasing labeled albumin concentration caudally to injection point (6th ics), and decreasing it cranially. Boluses of 0.1-1 ml did not preferentially reach mediastinal regions, as maintained by others. Time for an approximate mixing was approximately 1 h for 0.1 ml, and approximately 30 min for 1 ml. This relatively long mixing time does not substantially affect determination of contribution of lymphatic drainage through stomata to overall removal of labeled albumin from 0.3 ml hydrothoraces lasting 3 h [Bodega, F., Agostoni, E., 2004. Contribution of lymphatic drainage through stomata to albumin removal from pleural space. Respir. Physiol. Neurobiol. 142, 251-263].

Financial derivative pricing under probability operator via Esscher transfomation

NASA Astrophysics Data System (ADS)

Achi, Godswill U.

2014-10-01

The problem of pricing contingent claims has been extensively studied for non-Gaussian models, and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was first developed in insurance pricing9 where the original distortion function was defined in terms of the normal distribution. This approach was later studied6 where they compared the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula using the distribution. Similarly, in a financial market in which the asset price represented by a stochastic differential equation with respect to Brownian Motion, the price mechanism based on characteristic Esscher measure can generate approximate arbitrage free financial derivative prices. The price representation derived involves probability Esscher measure and Esscher Martingale measure and under a new complex valued measure φ (u) evaluated at the characteristic exponents φx(u) of Xt we recuperate the Black-Scholes formula for financial derivative prices.

Discriminative Bayesian Dictionary Learning for Classification.

PubMed

Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal

2016-12-01

We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a finite approximation of Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.

Minimum relative entropy distributions with a large mean are Gaussian

NASA Astrophysics Data System (ADS)

Smerlak, Matteo

2016-12-01

Entropy optimization principles are versatile tools with wide-ranging applications from statistical physics to engineering to ecology. Here we consider the following constrained problem: Given a prior probability distribution q , find the posterior distribution p minimizing the relative entropy (also known as the Kullback-Leibler divergence) with respect to q under the constraint that mean (p ) is fixed and large. We show that solutions to this problem are approximately Gaussian. We discuss two applications of this result. In the context of dissipative dynamics, the equilibrium distribution of a Brownian particle confined in a strong external field is independent of the shape of the confining potential. We also derive an H -type theorem for evolutionary dynamics: The entropy of the (standardized) distribution of fitness of a population evolving under natural selection is eventually increasing in time.

Structural Reliability Analysis and Optimization: Use of Approximations

NASA Technical Reports Server (NTRS)

Grandhi, Ramana V.; Wang, Liping

1999-01-01

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.

The rates and time-delay distribution of multiply imaged supernovae behind lensing clusters

NASA Astrophysics Data System (ADS)

Li, Xue; Hjorth, Jens; Richard, Johan

2012-11-01

Time delays of gravitationally lensed sources can be used to constrain the mass model of a deflector and determine cosmological parameters. We here present an analysis of the time-delay distribution of multiply imaged sources behind 17 strong lensing galaxy clusters with well-calibrated mass models. We find that for time delays less than 1000 days, at z = 3.0, their logarithmic probability distribution functions are well represented by P(log Δt) = 5.3 × 10-4Δttilde beta/M2502tilde beta, with tilde beta = 0.77, where M250 is the projected cluster mass inside 250 kpc (in 1014M⊙), and tilde beta is the power-law slope of the distribution. The resultant probability distribution function enables us to estimate the time-delay distribution in a lensing cluster of known mass. For a cluster with M250 = 2 × 1014M⊙, the fraction of time delays less than 1000 days is approximately 3%. Taking Abell 1689 as an example, its dark halo and brightest galaxies, with central velocity dispersions σ>=500kms-1, mainly produce large time delays, while galaxy-scale mass clumps are responsible for generating smaller time delays. We estimate the probability of observing multiple images of a supernova in the known images of Abell 1689. A two-component model of estimating the supernova rate is applied in this work. For a magnitude threshold of mAB = 26.5, the yearly rate of Type Ia (core-collapse) supernovae with time delays less than 1000 days is 0.004±0.002 (0.029±0.001). If the magnitude threshold is lowered to mAB ~ 27.0, the rate of core-collapse supernovae suitable for time delay observation is 0.044±0.015 per year.

Frequency-Locked Detector Threshold Setting Criteria Based on Mean-Time-To-Lose-Lock (MTLL) for GPS Receivers

PubMed Central

Zhao, Na; Qin, Honglei; Sun, Kewen; Ji, Yuanfa

2017-01-01

Frequency-locked detector (FLD) has been widely utilized in tracking loops of Global Positioning System (GPS) receivers to indicate their locking status. The relation between FLD and lock status has been seldom discussed. The traditional PLL experience is not suitable for FLL. In this paper, the threshold setting criteria for frequency-locked detector in the GPS receiver has been proposed by analyzing statistical characteristic of FLD output. The approximate probability distribution of frequency-locked detector is theoretically derived by using a statistical approach, which reveals the relationship between probabilities of frequency-locked detector and the carrier-to-noise ratio (C/N0) of the received GPS signal. The relationship among mean-time-to-lose-lock (MTLL), detection threshold and lock probability related to C/N0 can be further discovered by utilizing this probability. Therefore, a theoretical basis for threshold setting criteria in frequency locked loops for GPS receivers is provided based on mean-time-to-lose-lock analysis. PMID:29207546

Frequency-Locked Detector Threshold Setting Criteria Based on Mean-Time-To-Lose-Lock (MTLL) for GPS Receivers.

PubMed

Jin, Tian; Yuan, Heliang; Zhao, Na; Qin, Honglei; Sun, Kewen; Ji, Yuanfa

2017-12-04

Frequency-locked detector (FLD) has been widely utilized in tracking loops of Global Positioning System (GPS) receivers to indicate their locking status. The relation between FLD and lock status has been seldom discussed. The traditional PLL experience is not suitable for FLL. In this paper, the threshold setting criteria for frequency-locked detector in the GPS receiver has been proposed by analyzing statistical characteristic of FLD output. The approximate probability distribution of frequency-locked detector is theoretically derived by using a statistical approach, which reveals the relationship between probabilities of frequency-locked detector and the carrier-to-noise ratio ( C / N ₀) of the received GPS signal. The relationship among mean-time-to-lose-lock (MTLL), detection threshold and lock probability related to C / N ₀ can be further discovered by utilizing this probability. Therefore, a theoretical basis for threshold setting criteria in frequency locked loops for GPS receivers is provided based on mean-time-to-lose-lock analysis.

Alternative Derivations of the Statistical Mechanical Distribution Laws

PubMed Central

Wall, Frederick T.

1971-01-01

A new approach is presented for the derivation of statistical mechanical distribution laws. The derivations are accomplished by minimizing the Helmholtz free energy under constant temperature and volume, instead of maximizing the entropy under constant energy and volume. An alternative method involves stipulating equality of chemical potential, or equality of activity, for particles in different energy levels. This approach leads to a general statement of distribution laws applicable to all systems for which thermodynamic probabilities can be written. The methods also avoid use of the calculus of variations, Lagrangian multipliers, and Stirling's approximation for the factorial. The results are applied specifically to Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. The special significance of chemical potential and activity is discussed for microscopic systems. PMID:16578712

Alternative derivations of the statistical mechanical distribution laws.

PubMed

Wall, F T

1971-08-01

A new approach is presented for the derivation of statistical mechanical distribution laws. The derivations are accomplished by minimizing the Helmholtz free energy under constant temperature and volume, instead of maximizing the entropy under constant energy and volume. An alternative method involves stipulating equality of chemical potential, or equality of activity, for particles in different energy levels. This approach leads to a general statement of distribution laws applicable to all systems for which thermodynamic probabilities can be written. The methods also avoid use of the calculus of variations, Lagrangian multipliers, and Stirling's approximation for the factorial. The results are applied specifically to Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. The special significance of chemical potential and activity is discussed for microscopic systems.

Random local temporal structure of category fluency responses.

PubMed

Meyer, David J; Messer, Jason; Singh, Tanya; Thomas, Peter J; Woyczynski, Wojbor A; Kaye, Jeffrey; Lerner, Alan J

2012-04-01

The Category Fluency Test (CFT) provides a sensitive measurement of cognitive capabilities in humans related to retrieval from semantic memory. In particular, it is widely used to assess progress of cognitive impairment in patients with dementia. Previous research shows that, in the first approximation, the intensity of tested individuals' responses within a standard 60-s test period decays exponentially with time, with faster decay rates for more cognitively impaired patients. Such decay rate can then be viewed as a global (macro) diagnostic parameter of each test. In the present paper we focus on the statistical properties of the properly de-trended time intervals between consecutive responses (inter-call times) in the Category Fluency Test. In a sense, those properties reflect the local (micro) structure of the response generation process. We find that a good approximation for the distribution of the de-trended inter-call times is provided by the Weibull Distribution, a probability distribution that appears naturally in this context as a distribution of a minimum of independent random quantities and is the standard tool in industrial reliability theory. This insight leads us to a new interpretation of the concept of "navigating a semantic space" via patient responses.

How extreme was the October 2015 flood in the Carolinas? An assessment of flood frequency analysis and distribution tails

NASA Astrophysics Data System (ADS)

Phillips, R. C.; Samadi, S. Z.; Meadows, M. E.

2018-07-01

This paper examines the frequency, distribution tails, and peak-over-threshold (POT) of extreme floods through analysis that centers on the October 2015 flooding in North Carolina (NC) and South Carolina (SC), United States (US). The most striking features of the October 2015 flooding were a short time to peak (Tp) and a multi-hour continuous flood peak which caused intensive and widespread damages to human lives, properties, and infrastructure. The 2015 flooding was produced by a sequence of intense rainfall events which originated from category 4 hurricane Joaquin over a period of four days. Here, the probability distribution and distribution parameters (i.e., location, scale, and shape) of floods were investigated by comparing the upper part of empirical distributions of the annual maximum flood (AMF) and POT with light- to heavy- theoretical tails: Fréchet, Pareto, Gumbel, Weibull, Beta, and Exponential. Specifically, four sets of U.S. Geological Survey (USGS) gauging data from the central Carolinas with record lengths from approximately 65-125 years were used. Analysis suggests that heavier-tailed distributions are in better agreement with the POT and somewhat AMF data than more often used exponential (light) tailed probability distributions. Further, the threshold selection and record length affect the heaviness of the tail and fluctuations of the parent distributions. The shape parameter and its evolution in the period of record play a critical and poorly understood role in determining the scaling of flood response to intense rainfall.

Application of the Approximate Bayesian Computation methods in the stochastic estimation of atmospheric contamination parameters for mobile sources

NASA Astrophysics Data System (ADS)

Kopka, Piotr; Wawrzynczak, Anna; Borysiewicz, Mieczyslaw

2016-11-01

In this paper the Bayesian methodology, known as Approximate Bayesian Computation (ABC), is applied to the problem of the atmospheric contamination source identification. The algorithm input data are on-line arriving concentrations of the released substance registered by the distributed sensors network. This paper presents the Sequential ABC algorithm in detail and tests its efficiency in estimation of probabilistic distributions of atmospheric release parameters of a mobile contamination source. The developed algorithms are tested using the data from Over-Land Atmospheric Diffusion (OLAD) field tracer experiment. The paper demonstrates estimation of seven parameters characterizing the contamination source, i.e.: contamination source starting position (x,y), the direction of the motion of the source (d), its velocity (v), release rate (q), start time of release (ts) and its duration (td). The online-arriving new concentrations dynamically update the probability distributions of search parameters. The atmospheric dispersion Second-order Closure Integrated PUFF (SCIPUFF) Model is used as the forward model to predict the concentrations at the sensors locations.

cosmoabc: Likelihood-free inference for cosmology

NASA Astrophysics Data System (ADS)

Ishida, Emille E. O.; Vitenti, Sandro D. P.; Penna-Lima, Mariana; Trindade, Arlindo M.; Cisewski, Jessi; M.; de Souza, Rafael; Cameron, Ewan; Busti, Vinicius C.

2015-05-01

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogs. cosmoabc is a Python Approximate Bayesian Computation (ABC) sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code can be coupled to an external simulator to allow incorporation of arbitrary distance and prior functions. When coupled with the numcosmo library, it has been used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function.

Impact of signal scattering and parametric uncertainties on receiver operating characteristics

NASA Astrophysics Data System (ADS)

Wilson, D. Keith; Breton, Daniel J.; Hart, Carl R.; Pettit, Chris L.

2017-05-01

The receiver operating characteristic (ROC curve), which is a plot of the probability of detection as a function of the probability of false alarm, plays a key role in the classical analysis of detector performance. However, meaningful characterization of the ROC curve is challenging when practically important complications such as variations in source emissions, environmental impacts on the signal propagation, uncertainties in the sensor response, and multiple sources of interference are considered. In this paper, a relatively simple but realistic model for scattered signals is employed to explore how parametric uncertainties impact the ROC curve. In particular, we show that parametric uncertainties in the mean signal and noise power substantially raise the tails of the distributions; since receiver operation with a very low probability of false alarm and a high probability of detection is normally desired, these tails lead to severely degraded performance. Because full a priori knowledge of such parametric uncertainties is rarely available in practice, analyses must typically be based on a finite sample of environmental states, which only partially characterize the range of parameter variations. We show how this effect can lead to misleading assessments of system performance. For the cases considered, approximately 64 or more statistically independent samples of the uncertain parameters are needed to accurately predict the probabilities of detection and false alarm. A connection is also described between selection of suitable distributions for the uncertain parameters, and Bayesian adaptive methods for inferring the parameters.

Estimation from incomplete multinomial data. Ph.D. Thesis - Harvard Univ.

NASA Technical Reports Server (NTRS)

Credeur, K. R.

1978-01-01

The vector of multinomial cell probabilities was estimated from incomplete data, incomplete in that it contains partially classified observations. Each such partially classified observation was observed to fall in one of two or more selected categories but was not classified further into a single category. The data were assumed to be incomplete at random. The estimation criterion was minimization of risk for quadratic loss. The estimators were the classical maximum likelihood estimate, the Bayesian posterior mode, and the posterior mean. An approximation was developed for the posterior mean. The Dirichlet, the conjugate prior for the multinomial distribution, was assumed for the prior distribution.

Multi-level methods and approximating distribution functions

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

Wilson, D., E-mail: daniel.wilson@dtc.ox.ac.uk; Baker, R. E.

2016-07-15

Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparablemore » to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.« less

A risk-based multi-objective model for optimal placement of sensors in water distribution system

NASA Astrophysics Data System (ADS)

Naserizade, Sareh S.; Nikoo, Mohammad Reza; Montaseri, Hossein

2018-02-01

In this study, a new stochastic model based on Conditional Value at Risk (CVaR) and multi-objective optimization methods is developed for optimal placement of sensors in water distribution system (WDS). This model determines minimization of risk which is caused by simultaneous multi-point contamination injection in WDS using CVaR approach. The CVaR considers uncertainties of contamination injection in the form of probability distribution function and calculates low-probability extreme events. In this approach, extreme losses occur at tail of the losses distribution function. Four-objective optimization model based on NSGA-II algorithm is developed to minimize losses of contamination injection (through CVaR of affected population and detection time) and also minimize the two other main criteria of optimal placement of sensors including probability of undetected events and cost. Finally, to determine the best solution, Preference Ranking Organization METHod for Enrichment Evaluation (PROMETHEE), as a subgroup of Multi Criteria Decision Making (MCDM) approach, is utilized to rank the alternatives on the trade-off curve among objective functions. Also, sensitivity analysis is done to investigate the importance of each criterion on PROMETHEE results considering three relative weighting scenarios. The effectiveness of the proposed methodology is examined through applying it to Lamerd WDS in the southwestern part of Iran. The PROMETHEE suggests 6 sensors with suitable distribution that approximately cover all regions of WDS. Optimal values related to CVaR of affected population and detection time as well as probability of undetected events for the best optimal solution are equal to 17,055 persons, 31 mins and 0.045%, respectively. The obtained results of the proposed methodology in Lamerd WDS show applicability of CVaR-based multi-objective simulation-optimization model for incorporating the main uncertainties of contamination injection in order to evaluate extreme value of losses in WDS.

Fish Behavior, Presence, and Distribution in a Tidally Dynamic Region, with and without a Tidal Energy Device

NASA Astrophysics Data System (ADS)

Zydlewski, G. B.; Staines, G.; Viehman, H.; Shen, H.

2016-02-01

Fish responses, presence, and use of tidally dynamic regions are not well documented. Baseline and effect data were collected to examine responses of fish to the introduction of a tidal power device. In 2012 Ocean Renewable Power Company's TidGen® was deployed for one year and in 2014 their OCGen® was deployed for 2.5 months. We used this opportunity to determine (1) the vertical distribution of fishes before and after device deployment; (2) how fish behaved when approaching a device; and (3) the probability of fish encountering a device. From 2010 to 2013, 21 twenty-four-hour down-looking hydroacoustic surveys were performed at a project and control site. Prior to deployment (2010-2012) fish were generally distributed near the sea floor and more evenly distributed in the water column at night than during the day and there were significant differences between two of three before/after comparisons of vertical fish distributions, indicating an effect of the device. DIDSON acoustic cameras were used to document behavioral responses to a device. Most fish observed were <10 cm and moved in the same direction as the current. Approximately 50% of individuals and 67% of schools did not interact with the turbine. Less than 1% of individuals and 15% of schools showed avoidance behavior, and 35% of individuals and 14% of schools entered or exited the turbine. Turbine rotation reduced the probability of turbine entry by 35% and increased the probability of avoiding and passing by 120% and 97%, respectively. In 2014 we combined down-looking hydroacoustics with mobile transects to determine that the probability of fish being at the depth of the moving foils ( 6-9 m) ranged from 0.083 to 0.093. These data indicate how fish respond to this novel object and are important for understanding fish use of such a dynamic ecosystem.

Linear approximations of global behaviors in nonlinear systems with moderate or strong noise

NASA Astrophysics Data System (ADS)

Liang, Junhao; Din, Anwarud; Zhou, Tianshou

2018-03-01

While many physical or chemical systems can be modeled by nonlinear Langevin equations (LEs), dynamical analysis of these systems is challenging in the cases of moderate and strong noise. Here we develop a linear approximation scheme, which can transform an often intractable LE into a linear set of binomial moment equations (BMEs). This scheme provides a feasible way to capture nonlinear behaviors in the sense of probability distribution and is effective even when the noise is moderate or big. Based on BMEs, we further develop a noise reduction technique, which can effectively handle tough cases where traditional small-noise theories are inapplicable. The overall method not only provides an approximation-based paradigm to analysis of the local and global behaviors of nonlinear noisy systems but also has a wide range of applications.

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

NASA Technical Reports Server (NTRS)

Newman, Perry A.; Putko, Michele M.; Taylor, Arthur C., III

2004-01-01

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

STOCHASTIC DUELS--II

DTIC Science & Technology

of his time to fire a single round. The solution of the simple duel in the case where each protagonist’s time-to-kill is distributed as a gamma-variate...general simple duel . An expansion of the moment-generating function of the marksman’s time-to- kill in powers of his kill probability is next derived and...found to provide a good approximation to the solution of the simple duel ; various properties of the expansion are also considered. A stochastic battle

Modeling Multiple Risks: Hidden Domain of Attraction

DTIC Science & Technology

2012-01-01

improve joint tail probability approximation but the deficiency can be remedied by a more general approach which we call hidden domain of attraction ( HDA ...HRV is a special case of HDA . If the distribution of X does not have MRV but (1.2) still holds, we may retrieve the MRV setup by transforming the...potential advantage in some circumstances of the notion of HDA is that it does not require that we transform components. Performing such transformations on

A method for approximating acoustic-field-amplitude uncertainty caused by environmental uncertainties.

PubMed

James, Kevin R; Dowling, David R

2008-09-01

In underwater acoustics, the accuracy of computational field predictions is commonly limited by uncertainty in environmental parameters. An approximate technique for determining the probability density function (PDF) of computed field amplitude, A, from known environmental uncertainties is presented here. The technique can be applied to several, N, uncertain parameters simultaneously, requires N+1 field calculations, and can be used with any acoustic field model. The technique implicitly assumes independent input parameters and is based on finding the optimum spatial shift between field calculations completed at two different values of each uncertain parameter. This shift information is used to convert uncertain-environmental-parameter distributions into PDF(A). The technique's accuracy is good when the shifted fields match well. Its accuracy is evaluated in range-independent underwater sound channels via an L(1) error-norm defined between approximate and numerically converged results for PDF(A). In 50-m- and 100-m-deep sound channels with 0.5% uncertainty in depth (N=1) at frequencies between 100 and 800 Hz, and for ranges from 1 to 8 km, 95% of the approximate field-amplitude distributions generated L(1) values less than 0.52 using only two field calculations. Obtaining comparable accuracy from traditional methods requires of order 10 field calculations and up to 10(N) when N>1.

Gaussian closure technique applied to the hysteretic Bouc model with non-zero mean white noise excitation

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

Biological monitoring of environmental quality: The use of developmental instability

USGS Publications Warehouse

Freeman, D.C.; Emlen, J.M.; Graham, J.H.; Hough, R. A.; Bannon, T.A.

1994-01-01

Distributed robustness is thought to influence the buffering of random phenotypic variation through the scale-free topology of gene regulatory, metabolic, and protein-protein interaction networks. If this hypothesis is true, then the phenotypic response to the perturbation of particular nodes in such a network should be proportional to the number of links those nodes make with neighboring nodes. This suggests a probability distribution approximating an inverse power-law of random phenotypic variation. Zero phenotypic variation, however, is impossible, because random molecular and cellular processes are essential to normal development. Consequently, a more realistic distribution should have a y-intercept close to zero in the lower tail, a mode greater than zero, and a long (fat) upper tail. The double Pareto-lognormal (DPLN) distribution is an ideal candidate distribution. It consists of a mixture of a lognormal body and upper and lower power-law tails.

Beyond Zipf's Law: The Lavalette Rank Function and Its Properties.

PubMed

Fontanelli, Oscar; Miramontes, Pedro; Yang, Yaning; Cocho, Germinal; Li, Wentian

Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf's law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf's law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.

The Forecast Interpretation Tool—a Monte Carlo technique for blending climatic distributions with probabilistic forecasts

USGS Publications Warehouse

Husak, Gregory J.; Michaelsen, Joel; Kyriakidis, P.; Verdin, James P.; Funk, Chris; Galu, Gideon

2011-01-01

Probabilistic forecasts are produced from a variety of outlets to help predict rainfall, and other meteorological events, for periods of 1 month or more. Such forecasts are expressed as probabilities of a rainfall event, e.g. being in the upper, middle, or lower third of the relevant distribution of rainfall in the region. The impact of these forecasts on the expectation for the event is not always clear or easily conveyed. This article proposes a technique based on Monte Carlo simulation for adjusting existing climatologic statistical parameters to match forecast information, resulting in new parameters defining the probability of events for the forecast interval. The resulting parameters are shown to approximate the forecasts with reasonable accuracy. To show the value of the technique as an application for seasonal rainfall, it is used with consensus forecast developed for the Greater Horn of Africa for the 2009 March-April-May season. An alternative, analytical approach is also proposed, and discussed in comparison to the first simulation-based technique.

Robustness of survival estimates for radio-marked animals

USGS Publications Warehouse

Bunck, C.M.; Chen, C.-L.

1992-01-01

Telemetry techniques are often used to study the survival of birds and mammals; particularly whcn mark-recapture approaches are unsuitable. Both parametric and nonparametric methods to estimate survival have becn developed or modified from other applications. An implicit assumption in these approaches is that the probability of re-locating an animal with a functioning transmitter is one. A Monte Carlo study was conducted to determine the bias and variance of the Kaplan-Meier estimator and an estimator based also on the assumption of constant hazard and to eva!uate the performance of the two-sample tests associated with each. Modifications of each estimator which allow a re-Iocation probability of less than one are described and evaluated. Generallv the unmodified estimators were biased but had lower variance. At low sample sizes all estimators performed poorly. Under the null hypothesis, the distribution of all test statistics reasonably approximated the null distribution when survival was low but not when it was high. The power of the two-sample tests were similar.

A Bayesian approach to microwave precipitation profile retrieval

NASA Technical Reports Server (NTRS)

Evans, K. Franklin; Turk, Joseph; Wong, Takmeng; Stephens, Graeme L.

1995-01-01

A multichannel passive microwave precipitation retrieval algorithm is developed. Bayes theorem is used to combine statistical information from numerical cloud models with forward radiative transfer modeling. A multivariate lognormal prior probability distribution contains the covariance information about hydrometeor distribution that resolves the nonuniqueness inherent in the inversion process. Hydrometeor profiles are retrieved by maximizing the posterior probability density for each vector of observations. The hydrometeor profile retrieval method is tested with data from the Advanced Microwave Precipitation Radiometer (10, 19, 37, and 85 GHz) of convection over ocean and land in Florida. The CP-2 multiparameter radar data are used to verify the retrieved profiles. The results show that the method can retrieve approximate hydrometeor profiles, with larger errors over land than water. There is considerably greater accuracy in the retrieval of integrated hydrometeor contents than of profiles. Many of the retrieval errors are traced to problems with the cloud model microphysical information, and future improvements to the algorithm are suggested.

Sizing aerosolized fractal nanoparticle aggregates through Bayesian analysis of wide-angle light scattering (WALS) data

NASA Astrophysics Data System (ADS)

Huber, Franz J. T.; Will, Stefan; Daun, Kyle J.

2016-11-01

Inferring the size distribution of aerosolized fractal aggregates from the angular distribution of elastically scattered light is a mathematically ill-posed problem. This paper presents a procedure for analyzing Wide-Angle Light Scattering (WALS) data using Bayesian inference. The outcome is probability densities for the recovered size distribution and aggregate morphology parameters. This technique is applied to both synthetic data and experimental data collected on soot-laden aerosols, using a measurement equation derived from Rayleigh-Debye-Gans fractal aggregate (RDG-FA) theory. In the case of experimental data, the recovered aggregate size distribution parameters are generally consistent with TEM-derived values, but the accuracy is impaired by the well-known limited accuracy of RDG-FA theory. Finally, we show how this bias could potentially be avoided using the approximation error technique.

Application of a multipurpose unequal probability stream survey in the Mid-Atlantic Coastal Plain

USGS Publications Warehouse

Ator, S.W.; Olsen, A.R.; Pitchford, A.M.; Denver, J.M.

2003-01-01

A stratified, spatially balanced sample with unequal probability selection was used to design a multipurpose survey of headwater streams in the Mid-Atlantic Coastal Plain. Objectives for the survey include unbiased estimates of regional stream conditions, and adequate coverage of unusual but significant environmental settings to support empirical modeling of the factors affecting those conditions. The design and field application of the survey are discussed in light of these multiple objectives. A probability (random) sample of 175 first-order nontidal streams was selected for synoptic sampling of water chemistry and benthic and riparian ecology during late winter and spring 2000. Twenty-five streams were selected within each of seven hydrogeologic subregions (strata) that were delineated on the basis of physiography and surficial geology. In each subregion, unequal inclusion probabilities were used to provide an approximately even distribution of streams along a gradient of forested to developed (agricultural or urban) land in the contributing watershed. Alternate streams were also selected. Alternates were included in groups of five in each subregion when field reconnaissance demonstrated that primary streams were inaccessible or otherwise unusable. Despite the rejection and replacement of a considerable number of primary streams during reconnaissance (up to 40 percent in one subregion), the desired land use distribution was maintained within each hydrogeologic subregion without sacrificing the probabilistic design.

Maximum-entropy probability distributions under Lp-norm constraints

NASA Technical Reports Server (NTRS)

Dolinar, S.

1991-01-01

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

Blocking performance approximation in flexi-grid networks

NASA Astrophysics Data System (ADS)

Ge, Fei; Tan, Liansheng

2016-12-01

The blocking probability to the path requests is an important issue in flexible bandwidth optical communications. In this paper, we propose a blocking probability approximation method of path requests in flexi-grid networks. It models the bundled neighboring carrier allocation with a group of birth-death processes and provides a theoretical analysis to the blocking probability under variable bandwidth traffic. The numerical results show the effect of traffic parameters to the blocking probability of path requests. We use the first fit algorithm in network nodes to allocate neighboring carriers to path requests in simulations, and verify approximation results.

Estimation of rates-across-sites distributions in phylogenetic substitution models.

PubMed

Susko, Edward; Field, Chris; Blouin, Christian; Roger, Andrew J

2003-10-01

Previous work has shown that it is often essential to account for the variation in rates at different sites in phylogenetic models in order to avoid phylogenetic artifacts such as long branch attraction. In most current models, the gamma distribution is used for the rates-across-sites distributions and is implemented as an equal-probability discrete gamma. In this article, we introduce discrete distribution estimates with large numbers of equally spaced rate categories allowing us to investigate the appropriateness of the gamma model. With large numbers of rate categories, these discrete estimates are flexible enough to approximate the shape of almost any distribution. Likelihood ratio statistical tests and a nonparametric bootstrap confidence-bound estimation procedure based on the discrete estimates are presented that can be used to test the fit of a parametric family. We applied the methodology to several different protein data sets, and found that although the gamma model often provides a good parametric model for this type of data, rate estimates from an equal-probability discrete gamma model with a small number of categories will tend to underestimate the largest rates. In cases when the gamma model assumption is in doubt, rate estimates coming from the discrete rate distribution estimate with a large number of rate categories provide a robust alternative to gamma estimates. An alternative implementation of the gamma distribution is proposed that, for equal numbers of rate categories, is computationally more efficient during optimization than the standard gamma implementation and can provide more accurate estimates of site rates.

Analyzing signal attenuation in PFG anomalous diffusion via a non-Gaussian phase distribution approximation approach by fractional derivatives.

PubMed

Lin, Guoxing

2016-11-21

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in nuclear magnetic resonance and magnetic resonance imaging. However, the interpretation of PFG anomalous diffusion is complicated. Moreover, the exact signal attenuation expression including the finite gradient pulse width effect has not been obtained based on fractional derivatives for PFG anomalous diffusion. In this paper, a new method, a Mainardi-Luchko-Pagnini (MLP) phase distribution approximation, is proposed to describe PFG fractional diffusion. MLP phase distribution is a non-Gaussian phase distribution. From the fractional derivative model, both the probability density function (PDF) of a spin in real space and the PDF of the spin's accumulating phase shift in virtual phase space are MLP distributions. The MLP phase distribution leads to a Mittag-Leffler function based PFG signal attenuation, which differs significantly from the exponential attenuation for normal diffusion and from the stretched exponential attenuation for fractional diffusion based on the fractal derivative model. A complete signal attenuation expression E α (-D f b α,β * ) including the finite gradient pulse width effect was obtained and it can handle all three types of PFG fractional diffusions. The result was also extended in a straightforward way to give a signal attenuation expression of fractional diffusion in PFG intramolecular multiple quantum coherence experiments, which has an n β dependence upon the order of coherence which is different from the familiar n 2 dependence in normal diffusion. The results obtained in this study are in agreement with the results from the literature. The results in this paper provide a set of new, convenient approximation formalisms to interpret complex PFG fractional diffusion experiments.

Solving the chemical master equation using sliding windows

PubMed Central

2010-01-01

Background The chemical master equation (CME) is a system of ordinary differential equations that describes the evolution of a network of chemical reactions as a stochastic process. Its solution yields the probability density vector of the system at each point in time. Solving the CME numerically is in many cases computationally expensive or even infeasible as the number of reachable states can be very large or infinite. We introduce the sliding window method, which computes an approximate solution of the CME by performing a sequence of local analysis steps. In each step, only a manageable subset of states is considered, representing a "window" into the state space. In subsequent steps, the window follows the direction in which the probability mass moves, until the time period of interest has elapsed. We construct the window based on a deterministic approximation of the future behavior of the system by estimating upper and lower bounds on the populations of the chemical species. Results In order to show the effectiveness of our approach, we apply it to several examples previously described in the literature. The experimental results show that the proposed method speeds up the analysis considerably, compared to a global analysis, while still providing high accuracy. Conclusions The sliding window method is a novel approach to address the performance problems of numerical algorithms for the solution of the chemical master equation. The method efficiently approximates the probability distributions at the time points of interest for a variety of chemically reacting systems, including systems for which no upper bound on the population sizes of the chemical species is known a priori. PMID:20377904

Notes on SAW Tag Interrogation Techniques

NASA Technical Reports Server (NTRS)

Barton, Richard J.

2010-01-01

We consider the problem of interrogating a single SAW RFID tag with a known ID and known range in the presence of multiple interfering tags under the following assumptions: (1) The RF propagation environment is well approximated as a simple delay channel with geometric power-decay constant alpha >/= 2. (2) The interfering tag IDs are unknown but well approximated as independent, identically distributed random samples from a probability distribution of tag ID waveforms with known second-order properties, and the tag of interest is drawn independently from the same distribution. (3) The ranges of the interfering tags are unknown but well approximated as independent, identically distributed realizations of a random variable rho with a known probability distribution f(sub rho) , and the tag ranges are independent of the tag ID waveforms. In particular, we model the tag waveforms as random impulse responses from a wide-sense-stationary, uncorrelated-scattering (WSSUS) fading channel with known bandwidth and scattering function. A brief discussion of the properties of such channels and the notation used to describe them in this document is given in the Appendix. Under these assumptions, we derive the expression for the output signal-to-noise ratio (SNR) for an arbitrary combination of transmitted interrogation signal and linear receiver filter. Based on this expression, we derive the optimal interrogator configuration (i.e., transmitted signal/receiver filter combination) in the two extreme noise/interference regimes, i.e., noise-limited and interference-limited, under the additional assumption that the coherence bandwidth of the tags is much smaller than the total tag bandwidth. Finally, we evaluate the performance of both optimal interrogators over a broad range of operating scenarios using both numerical simulation based on the assumed model and Monte Carlo simulation based on a small sample of measured tag waveforms. The performance evaluation results not only provide guidelines for proper interrogator design, but also provide some insight on the validity of the assumed signal model. It should be noted that the assumption that the impulse response of the tag of interest is known precisely implies that the temperature and range of the tag are also known precisely, which is generally not the case in practice. However, analyzing interrogator performance under this simplifying assumption is much more straightforward and still provides a great deal of insight into the nature of the problem.

Exact p-values for pairwise comparison of Friedman rank sums, with application to comparing classifiers.

PubMed

Eisinga, Rob; Heskes, Tom; Pelzer, Ben; Te Grotenhuis, Manfred

2017-01-25

The Friedman rank sum test is a widely-used nonparametric method in computational biology. In addition to examining the overall null hypothesis of no significant difference among any of the rank sums, it is typically of interest to conduct pairwise comparison tests. Current approaches to such tests rely on large-sample approximations, due to the numerical complexity of computing the exact distribution. These approximate methods lead to inaccurate estimates in the tail of the distribution, which is most relevant for p-value calculation. We propose an efficient, combinatorial exact approach for calculating the probability mass distribution of the rank sum difference statistic for pairwise comparison of Friedman rank sums, and compare exact results with recommended asymptotic approximations. Whereas the chi-squared approximation performs inferiorly to exact computation overall, others, particularly the normal, perform well, except for the extreme tail. Hence exact calculation offers an improvement when small p-values occur following multiple testing correction. Exact inference also enhances the identification of significant differences whenever the observed values are close to the approximate critical value. We illustrate the proposed method in the context of biological machine learning, were Friedman rank sum difference tests are commonly used for the comparison of classifiers over multiple datasets. We provide a computationally fast method to determine the exact p-value of the absolute rank sum difference of a pair of Friedman rank sums, making asymptotic tests obsolete. Calculation of exact p-values is easy to implement in statistical software and the implementation in R is provided in one of the Additional files and is also available at http://www.ru.nl/publish/pages/726696/friedmanrsd.zip .

Time Dependence of Collision Probabilities During Satellite Conjunctions

NASA Technical Reports Server (NTRS)

Hall, Doyle T.; Hejduk, Matthew D.; Johnson, Lauren C.

2017-01-01

The NASA Conjunction Assessment Risk Analysis (CARA) team has recently implemented updated software to calculate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm can employ complex dynamical models for orbital motion, and account for the effects of non-linear trajectories as well as both position and velocity uncertainties. This “3D P (sub c)” method entails computing a 3-dimensional numerical integral for each estimated probability. Our analysis indicates that the 3D method provides several new insights over the traditional “2D P (sub c)” method, even when approximating the orbital motion using the relatively simple Keplerian two-body dynamical model. First, the formulation provides the means to estimate variations in the time derivative of the collision probability, or the probability rate, R (sub c). For close-proximity satellites, such as those orbiting in formations or clusters, R (sub c) variations can show multiple peaks that repeat or blend with one another, providing insight into the ongoing temporal distribution of risk. For single, isolated conjunctions, R (sub c) analysis provides the means to identify and bound the times of peak collision risk. Additionally, analysis of multiple actual archived conjunctions demonstrates that the commonly used “2D P (sub c)” approximation can occasionally provide inaccurate estimates. These include cases in which the 2D method yields negligibly small probabilities (e.g., P (sub c)) is greater than 10 (sup -10)), but the 3D estimates are sufficiently large to prompt increased monitoring or collision mitigation (e.g., P (sub c) is greater than or equal to 10 (sup -5)). Finally, the archive analysis indicates that a relatively efficient calculation can be used to identify which conjunctions will have negligibly small probabilities. This small-P (sub c) screening test can significantly speed the overall risk analysis computation for large numbers of conjunctions.

Black swans, power laws, and dragon-kings: Earthquakes, volcanic eruptions, landslides, wildfires, floods, and SOC models

NASA Astrophysics Data System (ADS)

Sachs, M. K.; Yoder, M. R.; Turcotte, D. L.; Rundle, J. B.; Malamud, B. D.

2012-05-01

Extreme events that change global society have been characterized as black swans. The frequency-size distributions of many natural phenomena are often well approximated by power-law (fractal) distributions. An important question is whether the probability of extreme events can be estimated by extrapolating the power-law distributions. Events that exceed these extrapolations have been characterized as dragon-kings. In this paper we consider extreme events for earthquakes, volcanic eruptions, wildfires, landslides and floods. We also consider the extreme event behavior of three models that exhibit self-organized criticality (SOC): the slider-block, forest-fire, and sand-pile models. Since extrapolations using power-laws are widely used in probabilistic hazard assessment, the occurrence of dragon-king events have important practical implications.

Intermittent particle distribution in synthetic free-surface turbulent flows.

PubMed

Ducasse, Lauris; Pumir, Alain

2008-06-01

Tracer particles on the surface of a turbulent flow have a very intermittent distribution. This preferential concentration effect is studied in a two-dimensional synthetic compressible flow, both in the inertial (self-similar) and in the dissipative (smooth) range of scales, as a function of the compressibility C . The second moment of the concentration coarse grained over a scale r , n_{r};{2} , behaves as a power law in both the inertial and the dissipative ranges of scale, with two different exponents. The shapes of the probability distribution functions of the coarse-grained density n_{r} vary as a function of scale r and of compressibility C through the combination C/r;{kappa} (kappa approximately 0.5) , corresponding to the compressibility, coarse grained over a domain of scale r , averaged over Lagrangian trajectories.

Target intersection probabilities for parallel-line and continuous-grid types of search

USGS Publications Warehouse

McCammon, R.B.

1977-01-01

The expressions for calculating the probability of intersection of hidden targets of different sizes and shapes for parallel-line and continuous-grid types of search can be formulated by vsing the concept of conditional probability. When the prior probability of the orientation of a widden target is represented by a uniform distribution, the calculated posterior probabilities are identical with the results obtained by the classic methods of probability. For hidden targets of different sizes and shapes, the following generalizations about the probability of intersection can be made: (1) to a first approximation, the probability of intersection of a hidden target is proportional to the ratio of the greatest dimension of the target (viewed in plane projection) to the minimum line spacing of the search pattern; (2) the shape of the hidden target does not greatly affect the probability of the intersection when the largest dimension of the target is small relative to the minimum spacing of the search pattern, (3) the probability of intersecting a target twice for a particular type of search can be used as a lower bound if there is an element of uncertainty of detection for a particular type of tool; (4) the geometry of the search pattern becomes more critical when the largest dimension of the target equals or exceeds the minimum spacing of the search pattern; (5) for elongate targets, the probability of intersection is greater for parallel-line search than for an equivalent continuous square-grid search when the largest dimension of the target is less than the minimum spacing of the search pattern, whereas the opposite is true when the largest dimension exceeds the minimum spacing; (6) the probability of intersection for nonorthogonal continuous-grid search patterns is not greatly different from the probability of intersection for the equivalent orthogonal continuous-grid pattern when the orientation of the target is unknown. The probability of intersection for an elliptically shaped target can be approximated by treating the ellipse as intermediate between a circle and a line. A search conducted along a continuous rectangular grid can be represented as intermediate between a search along parallel lines and along a continuous square grid. On this basis, an upper and lower bound for the probability of intersection of an elliptically shaped target for a continuous rectangular grid can be calculated. Charts have been constructed that permit the values for these probabilities to be obtained graphically. The use of conditional probability allows the explorationist greater flexibility in considering alternate search strategies for locating hidden targets. ?? 1977 Plenum Publishing Corp.

A new probabilistic seismic hazard assessment for greater Tokyo.

PubMed

Stein, Ross S; Toda, Shinji; Parsons, Tom; Grunewald, Elliot

2006-08-15

Tokyo and its outlying cities are home to one-quarter of Japan's 127 million people. Highly destructive earthquakes struck the capital in 1703, 1855 and 1923, the last of which took 105,000 lives. Fuelled by greater Tokyo's rich seismological record, but challenged by its magnificent complexity, our joint Japanese-US group carried out a new study of the capital's earthquake hazards. We used the prehistoric record of great earthquakes preserved by uplifted marine terraces and tsunami deposits (17 M approximately 8 shocks in the past 7000 years), a newly digitized dataset of historical shaking (10000 observations in the past 400 years), the dense modern seismic network (300,000 earthquakes in the past 30 years), and Japan's GeoNet array (150 GPS vectors in the past 10 years) to reinterpret the tectonic structure, identify active faults and their slip rates and estimate their earthquake frequency. We propose that a dislodged fragment of the Pacific plate is jammed between the Pacific, Philippine Sea and Eurasian plates beneath the Kanto plain on which Tokyo sits. We suggest that the Kanto fragment controls much of Tokyo's seismic behaviour for large earthquakes, including the damaging 1855 M approximately 7.3 Ansei-Edo shock. On the basis of the frequency of earthquakes beneath greater Tokyo, events with magnitude and location similar to the M approximately 7.3 Ansei-Edo event have a ca 20% likelihood in an average 30 year period. In contrast, our renewal (time-dependent) probability for the great M > or = 7.9 plate boundary shocks such as struck in 1923 and 1703 is 0.5% for the next 30 years, with a time-averaged 30 year probability of ca 10%. The resulting net likelihood for severe shaking (ca 0.9 g peak ground acceleration (PGA)) in Tokyo, Kawasaki and Yokohama for the next 30 years is ca 30%. The long historical record in Kanto also affords a rare opportunity to calculate the probability of shaking in an alternative manner exclusively from intensity observations. This approach permits robust estimates for the spatial distribution of expected shaking, even for sites with few observations. The resulting probability of severe shaking is ca 35% in Tokyo, Kawasaki and Yokohama and ca 10% in Chiba for an average 30 year period, in good agreement with our independent estimate, and thus bolstering our view that Tokyo's hazard looms large. Given 1 trillion US dollars estimates for the cost of an M approximately 7.3 shock beneath Tokyo, our probability implies a 13 billion US dollars annual probable loss.

Uncertainty Analysis Based on Sparse Grid Collocation and Quasi-Monte Carlo Sampling with Application in Groundwater Modeling

NASA Astrophysics Data System (ADS)

Zhang, G.; Lu, D.; Ye, M.; Gunzburger, M.

2011-12-01

Markov Chain Monte Carlo (MCMC) methods have been widely used in many fields of uncertainty analysis to estimate the posterior distributions of parameters and credible intervals of predictions in the Bayesian framework. However, in practice, MCMC may be computationally unaffordable due to slow convergence and the excessive number of forward model executions required, especially when the forward model is expensive to compute. Both disadvantages arise from the curse of dimensionality, i.e., the posterior distribution is usually a multivariate function of parameters. Recently, sparse grid method has been demonstrated to be an effective technique for coping with high-dimensional interpolation or integration problems. Thus, in order to accelerate the forward model and avoid the slow convergence of MCMC, we propose a new method for uncertainty analysis based on sparse grid interpolation and quasi-Monte Carlo sampling. First, we construct a polynomial approximation of the forward model in the parameter space by using the sparse grid interpolation. This approximation then defines an accurate surrogate posterior distribution that can be evaluated repeatedly at minimal computational cost. Second, instead of using MCMC, a quasi-Monte Carlo method is applied to draw samples in the parameter space. Then, the desired probability density function of each prediction is approximated by accumulating the posterior density values of all the samples according to the prediction values. Our method has the following advantages: (1) the polynomial approximation of the forward model on the sparse grid provides a very efficient evaluation of the surrogate posterior distribution; (2) the quasi-Monte Carlo method retains the same accuracy in approximating the PDF of predictions but avoids all disadvantages of MCMC. The proposed method is applied to a controlled numerical experiment of groundwater flow modeling. The results show that our method attains the same accuracy much more efficiently than traditional MCMC.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1978-01-01

This paper addresses the problem of obtaining numerically maximum-likelihood estimates of the parameters for a mixture of normal distributions. In recent literature, a certain successive-approximations procedure, based on the likelihood equations, was shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, we introduce a general iterative procedure, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. We show that, with probability 1 as the sample size grows large, this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. We also show that the step-size which yields optimal local convergence rates for large samples is determined in a sense by the 'separation' of the component normal densities and is bounded below by a number between 1 and 2.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, 2

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1976-01-01

The problem of obtaining numerically maximum likelihood estimates of the parameters for a mixture of normal distributions is addressed. In recent literature, a certain successive approximations procedure, based on the likelihood equations, is shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, a general iterative procedure is introduced, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. With probability 1 as the sample size grows large, it is shown that this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. The step-size which yields optimal local convergence rates for large samples is determined in a sense by the separation of the component normal densities and is bounded below by a number between 1 and 2.

Improved key-rate bounds for practical decoy-state quantum-key-distribution systems

NASA Astrophysics Data System (ADS)

Zhang, Zhen; Zhao, Qi; Razavi, Mohsen; Ma, Xiongfeng

2017-01-01

The decoy-state scheme is the most widely implemented quantum-key-distribution protocol in practice. In order to account for the finite-size key effects on the achievable secret key generation rate, a rigorous statistical fluctuation analysis is required. Originally, a heuristic Gaussian-approximation technique was used for this purpose, which, despite its analytical convenience, was not sufficiently rigorous. The fluctuation analysis has recently been made rigorous by using the Chernoff bound. There is a considerable gap, however, between the key-rate bounds obtained from these techniques and that obtained from the Gaussian assumption. Here we develop a tighter bound for the decoy-state method, which yields a smaller failure probability. This improvement results in a higher key rate and increases the maximum distance over which secure key exchange is possible. By optimizing the system parameters, our simulation results show that our method almost closes the gap between the two previously proposed techniques and achieves a performance similar to that of conventional Gaussian approximations.

Statistical mechanics of letters in words

PubMed Central

Stephens, Greg J.; Bialek, William

2013-01-01

We consider words as a network of interacting letters, and approximate the probability distribution of states taken on by this network. Despite the intuition that the rules of English spelling are highly combinatorial and arbitrary, we find that maximum entropy models consistent with pairwise correlations among letters provide a surprisingly good approximation to the full statistics of words, capturing ~92% of the multi-information in four-letter words and even “discovering” words that were not represented in the data. These maximum entropy models incorporate letter interactions through a set of pairwise potentials and thus define an energy landscape on the space of possible words. Guided by the large letter redundancy we seek a lower-dimensional encoding of the letter distribution and show that distinctions between local minima in the landscape account for ~68% of the four-letter entropy. We suggest that these states provide an effective vocabulary which is matched to the frequency of word use and much smaller than the full lexicon. PMID:20866490

Statistics of Sxy estimates

NASA Technical Reports Server (NTRS)

Freilich, M. H.; Pawka, S. S.

1987-01-01

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.

Statistical properties and correlation functions for drift waves

NASA Technical Reports Server (NTRS)

Horton, W.

1986-01-01

The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Development of Genuine Neural Network Prototype Chip

DTIC Science & Technology

1991-01-28

priori distribution is equivalent, and more readily visualized with a rank curve . The sonar signal data consisted of approximately 85% class Target and...15% class Clutter. For this reason, the rank curves for the class Clutter were used for device parameter analysis. R & D STATUS REPORT 1/28/91 N00014...the signal CLASSLD#. Four 10-bit class probabilities are available on the output bus (C0-C9, C16-C25, C32-C41 and C48- C57 ) at each clock cycle. A

Financial derivative pricing under probability operator via Esscher transfomation

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

Achi, Godswill U., E-mail: achigods@yahoo.com

2014-10-24

The problem of pricing contingent claims has been extensively studied for non-Gaussian models, and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was first developed in insurance pricing{sup 9} where the original distortion function was defined in terms of the normal distribution. This approach was later studied6 where they compared the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula usingmore » the distribution. Similarly, in a financial market in which the asset price represented by a stochastic differential equation with respect to Brownian Motion, the price mechanism based on characteristic Esscher measure can generate approximate arbitrage free financial derivative prices. The price representation derived involves probability Esscher measure and Esscher Martingale measure and under a new complex valued measure φ (u) evaluated at the characteristic exponents φ{sub x}(u) of X{sub t} we recuperate the Black-Scholes formula for financial derivative prices.« less

Ion componsition of zipper events

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

Kaye, S.M.; Shelley, E.G.; Sharp, R.D.

1981-05-01

A class of ion distributions has recently been identified by Fennell et al. (this issue). The distributions are composed of two components, a low-energy component with peak fluxes directed along the field line and a high-energy component with peak fluxes in the perpendicular direction. The transiton between the two components occur over a very narrow range of energies but can occur anywhere between approximately several hundred electron volts and 20 keV. Because of the appearance of this distribution on an energy versus time spectrogram, the ion events have been called zippers. The purpose of this report is to examine themore » mass composition of the zipper events. We find that the low-energy and parallel component is composed primarily of O/sup +/, with, to a lesser degree, H/sup +/ and a trace of He/sup +/. The high-energy and perpendicular component is predominantly H/sup +/, with the relative abundances of O/sup +/ and He/sup +/ down from those of the low-energy component by a factor of approx.10. These results suggest that whereas the low-energy component is probably ionospheric in origin, the source of the high-energy components is most probably the plsamasheet.« less

Total coliform and E. coli in public water systems using undisinfected ground water in the United States.

PubMed

Messner, Michael J; Berger, Philip; Javier, Julie

2017-06-01

Public water systems (PWSs) in the United States generate total coliform (TC) and Escherichia coli (EC) monitoring data, as required by the Total Coliform Rule (TCR). We analyzed data generated in 2011 by approximately 38,000 small (serving fewer than 4101 individuals) undisinfected public water systems (PWSs). We used statistical modeling to characterize a distribution of TC detection probabilities for each of nine groupings of PWSs based on system type (community, non-transient non-community, and transient non-community) and population served (less than 101, 101-1000 and 1001-4100 people). We found that among PWS types sampled in 2011, on average, undisinfected transient PWSs test positive for TC 4.3% of the time as compared with 3% for undisinfected non-transient PWSs and 2.5% for undisinfected community PWSs. Within each type of PWS, the smaller systems have higher median TC detection than the larger systems. All TC-positive samples were assayed for EC. Among TC-positive samples from small undisinfected PWSs, EC is detected in about 5% of samples, regardless of PWS type or size. We evaluated the upper tail of the TC detection probability distributions and found that significant percentages of some system types have high TC detection probabilities. For example, assuming the systems providing data are nationally-representative, then 5.0% of the ∼50,000 small undisinfected transient PWSs in the U.S. have TC detection probabilities of 20% or more. Communities with such high TC detection probabilities may have elevated risk of acute gastrointestinal (AGI) illness - perhaps as great or greater than the attributable risk to drinking water (6-22%) calculated for 14 Wisconsin community PWSs with much lower TC detection probabilities (about 2.3%, Borchardt et al., 2012). Published by Elsevier GmbH.

Typical performance of approximation algorithms for NP-hard problems

NASA Astrophysics Data System (ADS)

Takabe, Satoshi; Hukushima, Koji

2016-11-01

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linear-programming relaxation, loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using a statistical-mechanical technique, whereas the average-case analysis of the last one is conducted using the generating function method. These algorithms have a threshold in the typical performance with increasing average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases, determined by the order of the typical performance thresholds. In addition, we provide some conditions for classification of the graph ensembles and demonstrate explicitly some examples for the difference in thresholds.

Complete Numerical Solution of the Diffusion Equation of Random Genetic Drift

PubMed Central

Zhao, Lei; Yue, Xingye; Waxman, David

2013-01-01

A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size. PMID:23749318

Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model

NASA Astrophysics Data System (ADS)

Berglund, Nils; Landon, Damien

2012-08-01

We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of neuronal action potentials in parameter regimes characterized by mixed-mode oscillations. The interspike time interval is related to the random number of small-amplitude oscillations separating consecutive spikes. We prove that this number has an asymptotically geometric distribution, whose parameter is related to the principal eigenvalue of a substochastic Markov chain. We provide rigorous bounds on this eigenvalue in the small-noise regime and derive an approximation of its dependence on the system's parameters for a large range of noise intensities. This yields a precise description of the probability distribution of observed mixed-mode patterns and interspike intervals.

Probabilistic biosphere modeling for the long-term safety assessment of geological disposal facilities for radioactive waste using first- and second-order Monte Carlo simulation.

PubMed

Ciecior, Willy; Röhlig, Klaus-Jürgen; Kirchner, Gerald

2018-10-01

In the present paper, deterministic as well as first- and second-order probabilistic biosphere modeling approaches are compared. Furthermore, the sensitivity of the influence of the probability distribution function shape (empirical distribution functions and fitted lognormal probability functions) representing the aleatory uncertainty (also called variability) of a radioecological model parameter as well as the role of interacting parameters are studied. Differences in the shape of the output distributions for the biosphere dose conversion factor from first-order Monte Carlo uncertainty analysis using empirical and fitted lognormal distribution functions for input parameters suggest that a lognormal approximation is possibly not always an adequate representation of the aleatory uncertainty of a radioecological parameter. Concerning the comparison of the impact of aleatory and epistemic parameter uncertainty on the biosphere dose conversion factor, the latter here is described using uncertain moments (mean, variance) while the distribution itself represents the aleatory uncertainty of the parameter. From the results obtained, the solution space of second-order Monte Carlo simulation is much larger than that from first-order Monte Carlo simulation. Therefore, the influence of epistemic uncertainty of a radioecological parameter on the output result is much larger than that one caused by its aleatory uncertainty. Parameter interactions are only of significant influence in the upper percentiles of the distribution of results as well as only in the region of the upper percentiles of the model parameters. Copyright © 2018 Elsevier Ltd. All rights reserved.

Relaxation of ferroelectric states in 2D distributions of quantum dots: EELS simulation

NASA Astrophysics Data System (ADS)

Cortés, C. M.; Meza-Montes, L.; Moctezuma, R. E.; Carrillo, J. L.

2016-06-01

The relaxation time of collective electronic states in a 2D distribution of quantum dots is investigated theoretically by simulating EELS experiments. From the numerical calculation of the probability of energy loss of an electron beam, traveling parallel to the distribution, it is possible to estimate the damping time of ferroelectric-like states. We generate this collective response of the distribution by introducing a mean field interaction among the quantum dots, and then, the model is extended incorporating effects of long-range correlations through a Bragg-Williams approximation. The behavior of the dielectric function, the energy loss function, and the relaxation time of ferroelectric-like states is then investigated as a function of the temperature of the distribution and the damping constant of the electronic states in the single quantum dots. The robustness of the trends and tendencies of our results indicate that this scheme of analysis can guide experimentalists to develop tailored quantum dots distributions for specific applications.

An application of the Krylov-FSP-SSA method to parameter fitting with maximum likelihood

NASA Astrophysics Data System (ADS)

Dinh, Khanh N.; Sidje, Roger B.

2017-12-01

Monte Carlo methods such as the stochastic simulation algorithm (SSA) have traditionally been employed in gene regulation problems. However, there has been increasing interest to directly obtain the probability distribution of the molecules involved by solving the chemical master equation (CME). This requires addressing the curse of dimensionality that is inherent in most gene regulation problems. The finite state projection (FSP) seeks to address the challenge and there have been variants that further reduce the size of the projection or that accelerate the resulting matrix exponential. The Krylov-FSP-SSA variant has proved numerically efficient by combining, on one hand, the SSA to adaptively drive the FSP, and on the other hand, adaptive Krylov techniques to evaluate the matrix exponential. Here we apply this Krylov-FSP-SSA to a mutual inhibitory gene network synthetically engineered in Saccharomyces cerevisiae, in which bimodality arises. We show numerically that the approach can efficiently approximate the transient probability distribution, and this has important implications for parameter fitting, where the CME has to be solved for many different parameter sets. The fitting scheme amounts to an optimization problem of finding the parameter set so that the transient probability distributions fit the observations with maximum likelihood. We compare five optimization schemes for this difficult problem, thereby providing further insights into this approach of parameter estimation that is often applied to models in systems biology where there is a need to calibrate free parameters. Work supported by NSF grant DMS-1320849.

Fission fragment mass and total kinetic energy distributions of spontaneously fissioning plutonium isotopes

NASA Astrophysics Data System (ADS)

Pomorski, K.; Nerlo-Pomorska, B.; Bartel, J.; Schmitt, C.

2018-03-01

The fission-fragment mass and total kinetic energy (TKE) distributions are evaluated in a quantum mechanical framework using elongation, mass asymmetry, neck degree of freedom as the relevant collective parameters in the Fourier shape parametrization recently developed by us. The potential energy surfaces (PES) are calculated within the macroscopic-microscopic model based on the Lublin-Strasbourg Drop (LSD), the Yukawa-folded (YF) single-particle potential and a monopole pairing force. The PES are presented and analysed in detail for even-even Plutonium isotopes with A = 236-246. They reveal deep asymmetric valleys. The fission-fragment mass and TKE distributions are obtained from the ground state of a collective Hamiltonian computed within the Born-Oppenheimer approximation, in the WKB approach by introducing a neck-dependent fission probability. The calculated mass and total kinetic energy distributions are found in good agreement with the data.

Species abundance distribution and population dynamics in a two-community model of neutral ecology

NASA Astrophysics Data System (ADS)

Vallade, M.; Houchmandzadeh, B.

2006-11-01

Explicit formulas for the steady-state distribution of species in two interconnected communities of arbitrary sizes are derived in the framework of Hubbell’s neutral model of biodiversity. Migrations of seeds from both communities as well as mutations in both of them are taken into account. These results generalize those previously obtained for the “island-continent” model and they allow an analysis of the influence of the ratio of the sizes of the two communities on the dominance/diversity equilibrium. Exact expressions for species abundance distributions are deduced from a master equation for the joint probability distribution of species in the two communities. Moreover, an approximate self-consistent solution is derived. It corresponds to a generalization of previous results and it proves to be accurate over a broad range of parameters. The dynamical correlations between the abundances of a species in both communities are also discussed.

Assessing the Clinical Impact of Approximations in Analytical Dose Calculations for Proton Therapy

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

Schuemann, Jan, E-mail: jschuemann@mgh.harvard.edu; Giantsoudi, Drosoula; Grassberger, Clemens

2015-08-01

Purpose: To assess the impact of approximations in current analytical dose calculation methods (ADCs) on tumor control probability (TCP) in proton therapy. Methods: Dose distributions planned with ADC were compared with delivered dose distributions as determined by Monte Carlo simulations. A total of 50 patients were investigated in this analysis with 10 patients per site for 5 treatment sites (head and neck, lung, breast, prostate, liver). Differences were evaluated using dosimetric indices based on a dose-volume histogram analysis, a γ-index analysis, and estimations of TCP. Results: We found that ADC overestimated the target doses on average by 1% to 2%more » for all patients considered. The mean dose, D95, D50, and D02 (the dose value covering 95%, 50% and 2% of the target volume, respectively) were predicted within 5% of the delivered dose. The γ-index passing rate for target volumes was above 96% for a 3%/3 mm criterion. Differences in TCP were up to 2%, 2.5%, 6%, 6.5%, and 11% for liver and breast, prostate, head and neck, and lung patients, respectively. Differences in normal tissue complication probabilities for bladder and anterior rectum of prostate patients were less than 3%. Conclusion: Our results indicate that current dose calculation algorithms lead to underdosage of the target by as much as 5%, resulting in differences in TCP of up to 11%. To ensure full target coverage, advanced dose calculation methods like Monte Carlo simulations may be necessary in proton therapy. Monte Carlo simulations may also be required to avoid biases resulting from systematic discrepancies in calculated dose distributions for clinical trials comparing proton therapy with conventional radiation therapy.« less

Improving the efficiency of configurational-bias Monte Carlo: A density-guided method for generating bending angle trials for linear and branched molecules

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

Sepehri, Aliasghar; Loeffler, Troy D.; Chen, Bin, E-mail: binchen@lsu.edu

2014-08-21

A new method has been developed to generate bending angle trials to improve the acceptance rate and the speed of configurational-bias Monte Carlo. Whereas traditionally the trial geometries are generated from a uniform distribution, in this method we attempt to use the exact probability density function so that each geometry generated is likely to be accepted. In actual practice, due to the complexity of this probability density function, a numerical representation of this distribution function would be required. This numerical table can be generated a priori from the distribution function. This method has been tested on a united-atom model ofmore » alkanes including propane, 2-methylpropane, and 2,2-dimethylpropane, that are good representatives of both linear and branched molecules. It has been shown from these test cases that reasonable approximations can be made especially for the highly branched molecules to reduce drastically the dimensionality and correspondingly the amount of the tabulated data that is needed to be stored. Despite these approximations, the dependencies between the various geometrical variables can be still well considered, as evident from a nearly perfect acceptance rate achieved. For all cases, the bending angles were shown to be sampled correctly by this method with an acceptance rate of at least 96% for 2,2-dimethylpropane to more than 99% for propane. Since only one trial is required to be generated for each bending angle (instead of thousands of trials required by the conventional algorithm), this method can dramatically reduce the simulation time. The profiling results of our Monte Carlo simulation code show that trial generation, which used to be the most time consuming process, is no longer the time dominating component of the simulation.« less

An effective inversion algorithm for retrieving bimodal aerosol particle size distribution from spectral extinction data

NASA Astrophysics Data System (ADS)

He, Zhenzong; Qi, Hong; Yao, Yuchen; Ruan, Liming

2014-12-01

The Ant Colony Optimization algorithm based on the probability density function (PDF-ACO) is applied to estimate the bimodal aerosol particle size distribution (PSD). The direct problem is solved by the modified Anomalous Diffraction Approximation (ADA, as an approximation for optically large and soft spheres, i.e., χ⪢1 and |m-1|⪡1) and the Beer-Lambert law. First, a popular bimodal aerosol PSD and three other bimodal PSDs are retrieved in the dependent model by the multi-wavelength extinction technique. All the results reveal that the PDF-ACO algorithm can be used as an effective technique to investigate the bimodal PSD. Then, the Johnson's SB (J-SB) function and the modified beta (M-β) function are employed as the general distribution function to retrieve the bimodal PSDs under the independent model. Finally, the J-SB and M-β functions are applied to recover actual measurement aerosol PSDs over Beijing and Shanghai obtained from the aerosol robotic network (AERONET). The numerical simulation and experimental results demonstrate that these two general functions, especially the J-SB function, can be used as a versatile distribution function to retrieve the bimodal aerosol PSD when no priori information about the PSD is available.

Greenhouse-gas emission targets for limiting global warming to 2 degrees C.

PubMed

Meinshausen, Malte; Meinshausen, Nicolai; Hare, William; Raper, Sarah C B; Frieler, Katja; Knutti, Reto; Frame, David J; Allen, Myles R

2009-04-30

More than 100 countries have adopted a global warming limit of 2 degrees C or below (relative to pre-industrial levels) as a guiding principle for mitigation efforts to reduce climate change risks, impacts and damages. However, the greenhouse gas (GHG) emissions corresponding to a specified maximum warming are poorly known owing to uncertainties in the carbon cycle and the climate response. Here we provide a comprehensive probabilistic analysis aimed at quantifying GHG emission budgets for the 2000-50 period that would limit warming throughout the twenty-first century to below 2 degrees C, based on a combination of published distributions of climate system properties and observational constraints. We show that, for the chosen class of emission scenarios, both cumulative emissions up to 2050 and emission levels in 2050 are robust indicators of the probability that twenty-first century warming will not exceed 2 degrees C relative to pre-industrial temperatures. Limiting cumulative CO(2) emissions over 2000-50 to 1,000 Gt CO(2) yields a 25% probability of warming exceeding 2 degrees C-and a limit of 1,440 Gt CO(2) yields a 50% probability-given a representative estimate of the distribution of climate system properties. As known 2000-06 CO(2) emissions were approximately 234 Gt CO(2), less than half the proven economically recoverable oil, gas and coal reserves can still be emitted up to 2050 to achieve such a goal. Recent G8 Communiqués envisage halved global GHG emissions by 2050, for which we estimate a 12-45% probability of exceeding 2 degrees C-assuming 1990 as emission base year and a range of published climate sensitivity distributions. Emissions levels in 2020 are a less robust indicator, but for the scenarios considered, the probability of exceeding 2 degrees C rises to 53-87% if global GHG emissions are still more than 25% above 2000 levels in 2020.

Multivariate flood risk assessment: reinsurance perspective

NASA Astrophysics Data System (ADS)

Ghizzoni, Tatiana; Ellenrieder, Tobias

2013-04-01

For insurance and re-insurance purposes the knowledge of the spatial characteristics of fluvial flooding is fundamental. The probability of simultaneous flooding at different locations during one event and the associated severity and losses have to be estimated in order to assess premiums and for accumulation control (Probable Maximum Losses calculation). Therefore, the identification of a statistical model able to describe the multivariate joint distribution of flood events in multiple location is necessary. In this context, copulas can be viewed as alternative tools for dealing with multivariate simulations as they allow to formalize dependence structures of random vectors. An application of copula function for flood scenario generation is presented for Australia (Queensland, New South Wales and Victoria) where 100.000 possible flood scenarios covering approximately 15.000 years were simulated.

Viscoelasticity, postseismic slip, fault interactions, and the recurrence of large earthquakes

USGS Publications Warehouse

Michael, A.J.

2005-01-01

The Brownian Passage Time (BPT) model for earthquake recurrence is modified to include transient deformation due to either viscoelasticity or deep post seismic slip. Both of these processes act to increase the rate of loading on the seismogenic fault for some time after a large event. To approximate these effects, a decaying exponential term is added to the BPT model's uniform loading term. The resulting interevent time distributions remain approximately lognormal, but the balance between the level of noise (e.g., unknown fault interactions) and the coefficient of variability of the interevent time distribution changes depending on the shape of the loading function. For a given level of noise in the loading process, transient deformation has the effect of increasing the coefficient of variability of earthquake interevent times. Conversely, the level of noise needed to achieve a given level of variability is reduced when transient deformation is included. Using less noise would then increase the effect of known fault interactions modeled as stress or strain steps because they would be larger with respect to the noise. If we only seek to estimate the shape of the interevent time distribution from observed earthquake occurrences, then the use of a transient deformation model will not dramatically change the results of a probability study because a similar shaped distribution can be achieved with either uniform or transient loading functions. However, if the goal is to estimate earthquake probabilities based on our increasing understanding of the seismogenic process, including earthquake interactions, then including transient deformation is important to obtain accurate results. For example, a loading curve based on the 1906 earthquake, paleoseismic observations of prior events, and observations of recent deformation in the San Francisco Bay region produces a 40% greater variability in earthquake recurrence than a uniform loading model with the same noise level.

Rough Sets and Stomped Normal Distribution for Simultaneous Segmentation and Bias Field Correction in Brain MR Images.

PubMed

Banerjee, Abhirup; Maji, Pradipta

2015-12-01

The segmentation of brain MR images into different tissue classes is an important task for automatic image analysis technique, particularly due to the presence of intensity inhomogeneity artifact in MR images. In this regard, this paper presents a novel approach for simultaneous segmentation and bias field correction in brain MR images. It integrates judiciously the concept of rough sets and the merit of a novel probability distribution, called stomped normal (SN) distribution. The intensity distribution of a tissue class is represented by SN distribution, where each tissue class consists of a crisp lower approximation and a probabilistic boundary region. The intensity distribution of brain MR image is modeled as a mixture of finite number of SN distributions and one uniform distribution. The proposed method incorporates both the expectation-maximization and hidden Markov random field frameworks to provide an accurate and robust segmentation. The performance of the proposed approach, along with a comparison with related methods, is demonstrated on a set of synthetic and real brain MR images for different bias fields and noise levels.

Random phenotypic variation of yeast (Saccharomyces cerevisiae) single-gene knockouts fits a double pareto-lognormal distribution.

PubMed

Graham, John H; Robb, Daniel T; Poe, Amy R

2012-01-01

Distributed robustness is thought to influence the buffering of random phenotypic variation through the scale-free topology of gene regulatory, metabolic, and protein-protein interaction networks. If this hypothesis is true, then the phenotypic response to the perturbation of particular nodes in such a network should be proportional to the number of links those nodes make with neighboring nodes. This suggests a probability distribution approximating an inverse power-law of random phenotypic variation. Zero phenotypic variation, however, is impossible, because random molecular and cellular processes are essential to normal development. Consequently, a more realistic distribution should have a y-intercept close to zero in the lower tail, a mode greater than zero, and a long (fat) upper tail. The double Pareto-lognormal (DPLN) distribution is an ideal candidate distribution. It consists of a mixture of a lognormal body and upper and lower power-law tails. If our assumptions are true, the DPLN distribution should provide a better fit to random phenotypic variation in a large series of single-gene knockout lines than other skewed or symmetrical distributions. We fit a large published data set of single-gene knockout lines in Saccharomyces cerevisiae to seven different probability distributions: DPLN, right Pareto-lognormal (RPLN), left Pareto-lognormal (LPLN), normal, lognormal, exponential, and Pareto. The best model was judged by the Akaike Information Criterion (AIC). Phenotypic variation among gene knockouts in S. cerevisiae fits a double Pareto-lognormal (DPLN) distribution better than any of the alternative distributions, including the right Pareto-lognormal and lognormal distributions. A DPLN distribution is consistent with the hypothesis that developmental stability is mediated, in part, by distributed robustness, the resilience of gene regulatory, metabolic, and protein-protein interaction networks. Alternatively, multiplicative cell growth, and the mixing of lognormal distributions having different variances, may generate a DPLN distribution.

Boundary curves of individual items in the distribution of total depressive symptom scores approximate an exponential pattern in a general population.

PubMed

Tomitaka, Shinichiro; Kawasaki, Yohei; Ide, Kazuki; Akutagawa, Maiko; Yamada, Hiroshi; Furukawa, Toshiaki A; Ono, Yutaka

2016-01-01

Previously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item threshold. To verify this hypothesis, we investigated the boundary curves of the distribution of total depressive symptom scores in a general population. Data collected from 21,040 subjects who had completed the Center for Epidemiologic Studies Depression Scale (CES-D) questionnaire as part of a national Japanese survey were analyzed. The CES-D consists of 20 items (16 negative items and four positive items). The boundary curves of adjacent item scores in the distribution of total depressive symptom scores for the 16 negative items were analyzed using log-normal scales and curve fitting. The boundary curves of adjacent item scores for a given symptom approximated a common linear pattern on a log normal scale. Curve fitting showed that an exponential fit had a markedly higher coefficient of determination than either linear or quadratic fits. With negative affect items, the gap between the total score curve and boundary curve continuously increased with increasing total depressive symptom scores on a log-normal scale, whereas the boundary curves of positive affect items, which are not considered manifest variables of the latent trait, did not exhibit such increases in this gap. The results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an exponential mathematical pattern.

Boundary curves of individual items in the distribution of total depressive symptom scores approximate an exponential pattern in a general population

PubMed Central

Kawasaki, Yohei; Akutagawa, Maiko; Yamada, Hiroshi; Furukawa, Toshiaki A.; Ono, Yutaka

2016-01-01

Background Previously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item threshold. To verify this hypothesis, we investigated the boundary curves of the distribution of total depressive symptom scores in a general population. Methods Data collected from 21,040 subjects who had completed the Center for Epidemiologic Studies Depression Scale (CES-D) questionnaire as part of a national Japanese survey were analyzed. The CES-D consists of 20 items (16 negative items and four positive items). The boundary curves of adjacent item scores in the distribution of total depressive symptom scores for the 16 negative items were analyzed using log-normal scales and curve fitting. Results The boundary curves of adjacent item scores for a given symptom approximated a common linear pattern on a log normal scale. Curve fitting showed that an exponential fit had a markedly higher coefficient of determination than either linear or quadratic fits. With negative affect items, the gap between the total score curve and boundary curve continuously increased with increasing total depressive symptom scores on a log-normal scale, whereas the boundary curves of positive affect items, which are not considered manifest variables of the latent trait, did not exhibit such increases in this gap. Discussion The results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an exponential mathematical pattern. PMID:27761346

On the distribution of a product of N Gaussian random variables

NASA Astrophysics Data System (ADS)

Stojanac, Željka; Suess, Daniel; Kliesch, Martin

2017-08-01

The product of Gaussian random variables appears naturally in many applications in probability theory and statistics. It has been known that the distribution of a product of N such variables can be expressed in terms of a Meijer G-function. Here, we compute a similar representation for the corresponding cumulative distribution function (CDF) and provide a power-log series expansion of the CDF based on the theory of the more general Fox H-functions. Numerical computations show that for small values of the argument the CDF of products of Gaussians is well approximated by the lowest orders of this expansion. Analogous results are also shown for the absolute value as well as the square of such products of N Gaussian random variables. For the latter two settings, we also compute the moment generating functions in terms of Meijer G-functions.

Spatial dynamics of invasion: the geometry of introduced species.

PubMed

Korniss, Gyorgy; Caraco, Thomas

2005-03-07

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyse this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single- and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almost-deterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.

An Estimation of the Likelihood of Significant Eruptions During 2000-2009 Using Poisson Statistics on Two-Point Moving Averages of the Volcanic Time Series

NASA Technical Reports Server (NTRS)

Wilson, Robert M.

2001-01-01

Since 1750, the number of cataclysmic volcanic eruptions (volcanic explosivity index (VEI)>=4) per decade spans 2-11, with 96 percent located in the tropics and extra-tropical Northern Hemisphere. A two-point moving average of the volcanic time series has higher values since the 1860's than before, being 8.00 in the 1910's (the highest value) and 6.50 in the 1980's, the highest since the 1910's peak. Because of the usual behavior of the first difference of the two-point moving averages, one infers that its value for the 1990's will measure approximately 6.50 +/- 1, implying that approximately 7 +/- 4 cataclysmic volcanic eruptions should be expected during the present decade (2000-2009). Because cataclysmic volcanic eruptions (especially those having VEI>=5) nearly always have been associated with short-term episodes of global cooling, the occurrence of even one might confuse our ability to assess the effects of global warming. Poisson probability distributions reveal that the probability of one or more events with a VEI>=4 within the next ten years is >99 percent. It is approximately 49 percent for an event with a VEI>=5, and 18 percent for an event with a VEI>=6. Hence, the likelihood that a climatically significant volcanic eruption will occur within the next ten years appears reasonably high.

Universal patterns of inequality

NASA Astrophysics Data System (ADS)

Banerjee, Anand; Yakovenko, Victor M.

2010-07-01

Probability distributions of money, income and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the investigated variables. A non-equilibrium difference of money temperatures between different systems generates net fluxes of money and population. To describe income distribution, a stochastic process with additive and multiplicative components is introduced. The resultant distribution interpolates between exponential at the low end and power law at the high end, in agreement with the empirical data for the USA. We show that the increase in income inequality in the USA originates primarily from the increase in the income fraction going to the upper tail, which now exceeds 20% of the total income. Analyzing the data from the World Resources Institute, we find that the distribution of energy consumption per capita around the world can be approximately described by the exponential function. Comparing the data for 1990, 2000 and 2005, we discuss the effect of globalization on the inequality of energy consumption.

Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system structural components

NASA Technical Reports Server (NTRS)

Cruse, T. A.

1987-01-01

The objective is the development of several modular structural analysis packages capable of predicting the probabilistic response distribution for key structural variables such as maximum stress, natural frequencies, transient response, etc. The structural analysis packages are to include stochastic modeling of loads, material properties, geometry (tolerances), and boundary conditions. The solution is to be in terms of the cumulative probability of exceedance distribution (CDF) and confidence bounds. Two methods of probability modeling are to be included as well as three types of structural models - probabilistic finite-element method (PFEM); probabilistic approximate analysis methods (PAAM); and probabilistic boundary element methods (PBEM). The purpose in doing probabilistic structural analysis is to provide the designer with a more realistic ability to assess the importance of uncertainty in the response of a high performance structure. Probabilistic Structural Analysis Method (PSAM) tools will estimate structural safety and reliability, while providing the engineer with information on the confidence that should be given to the predicted behavior. Perhaps most critically, the PSAM results will directly provide information on the sensitivity of the design response to those variables which are seen to be uncertain.

Probabilistic Structural Analysis Methods for select space propulsion system structural components (PSAM)

NASA Technical Reports Server (NTRS)

Cruse, T. A.; Burnside, O. H.; Wu, Y.-T.; Polch, E. Z.; Dias, J. B.

1988-01-01

The objective is the development of several modular structural analysis packages capable of predicting the probabilistic response distribution for key structural variables such as maximum stress, natural frequencies, transient response, etc. The structural analysis packages are to include stochastic modeling of loads, material properties, geometry (tolerances), and boundary conditions. The solution is to be in terms of the cumulative probability of exceedance distribution (CDF) and confidence bounds. Two methods of probability modeling are to be included as well as three types of structural models - probabilistic finite-element method (PFEM); probabilistic approximate analysis methods (PAAM); and probabilistic boundary element methods (PBEM). The purpose in doing probabilistic structural analysis is to provide the designer with a more realistic ability to assess the importance of uncertainty in the response of a high performance structure. Probabilistic Structural Analysis Method (PSAM) tools will estimate structural safety and reliability, while providing the engineer with information on the confidence that should be given to the predicted behavior. Perhaps most critically, the PSAM results will directly provide information on the sensitivity of the design response to those variables which are seen to be uncertain.

A study of the application of power-spectral methods of generalized harmonic analysis to gust loads on airplanes

NASA Technical Reports Server (NTRS)

Press, Harry; Mazelsky, Bernard

1954-01-01

The applicability of some results from the theory of generalized harmonic analysis (or power-spectral analysis) to the analysis of gust loads on airplanes in continuous rough air is examined. The general relations for linear systems between power spectrums of a random input disturbance and an output response are used to relate the spectrum of airplane load in rough air to the spectrum of atmospheric gust velocity. The power spectrum of loads is shown to provide a measure of the load intensity in terms of the standard deviation (root mean square) of the load distribution for an airplane in flight through continuous rough air. For the case of a load output having a normal distribution, which appears from experimental evidence to apply to homogeneous rough air, the standard deviation is shown to describe the probability distribution of loads or the proportion of total time that the load has given values. Thus, for airplane in flight through homogeneous rough air, the probability distribution of loads may be determined from a power-spectral analysis. In order to illustrate the application of power-spectral analysis to gust-load analysis and to obtain an insight into the relations between loads and airplane gust-response characteristics, two selected series of calculations are presented. The results indicate that both methods of analysis yield results that are consistent to a first approximation.

Design and simulation of stratified probability digital receiver with application to the multipath communication

NASA Technical Reports Server (NTRS)

Deal, J. H.

1975-01-01

One approach to the problem of simplifying complex nonlinear filtering algorithms is through using stratified probability approximations where the continuous probability density functions of certain random variables are represented by discrete mass approximations. This technique is developed in this paper and used to simplify the filtering algorithms developed for the optimum receiver for signals corrupted by both additive and multiplicative noise.

Projection methods for the numerical solution of Markov chain models

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

Approximation of Failure Probability Using Conditional Sampling

NASA Technical Reports Server (NTRS)

Giesy. Daniel P.; Crespo, Luis G.; Kenney, Sean P.

2008-01-01

In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.

Fixation Probability in a Haploid-Diploid Population

PubMed Central

Bessho, Kazuhiro; Otto, Sarah P.

2017-01-01

Classical population genetic theory generally assumes either a fully haploid or fully diploid life cycle. However, many organisms exhibit more complex life cycles, with both free-living haploid and diploid stages. Here we ask what the probability of fixation is for selected alleles in organisms with haploid-diploid life cycles. We develop a genetic model that considers the population dynamics using both the Moran model and Wright–Fisher model. Applying a branching process approximation, we obtain an accurate fixation probability assuming that the population is large and the net effect of the mutation is beneficial. We also find the diffusion approximation for the fixation probability, which is accurate even in small populations and for deleterious alleles, as long as selection is weak. These fixation probabilities from branching process and diffusion approximations are similar when selection is weak for beneficial mutations that are not fully recessive. In many cases, particularly when one phase predominates, the fixation probability differs substantially for haploid-diploid organisms compared to either fully haploid or diploid species. PMID:27866168

Serial Founder Effects During Range Expansion: A Spatial Analog of Genetic Drift

PubMed Central

Slatkin, Montgomery; Excoffier, Laurent

2012-01-01

Range expansions cause a series of founder events. We show that, in a one-dimensional habitat, these founder events are the spatial analog of genetic drift in a randomly mating population. The spatial series of allele frequencies created by successive founder events is equivalent to the time series of allele frequencies in a population of effective size ke, the effective number of founders. We derive an expression for ke in a discrete-population model that allows for local population growth and migration among established populations. If there is selection, the net effect is determined approximately by the product of the selection coefficients and the number of generations between successive founding events. We use the model of a single population to compute analytically several quantities for an allele present in the source population: (i) the probability that it survives the series of colonization events, (ii) the probability that it reaches a specified threshold frequency in the last population, and (iii) the mean and variance of the frequencies in each population. We show that the analytic theory provides a good approximation to simulation results. A consequence of our approximation is that the average heterozygosity of neutral alleles decreases by a factor of 1 – 1/(2ke) in each new population. Therefore, the population genetic consequences of surfing can be predicted approximately by the effective number of founders and the effective selection coefficients, even in the presence of migration among populations. We also show that our analytic results are applicable to a model of range expansion in a continuously distributed population. PMID:22367031

Serial founder effects during range expansion: a spatial analog of genetic drift.

PubMed

Slatkin, Montgomery; Excoffier, Laurent

2012-05-01

Range expansions cause a series of founder events. We show that, in a one-dimensional habitat, these founder events are the spatial analog of genetic drift in a randomly mating population. The spatial series of allele frequencies created by successive founder events is equivalent to the time series of allele frequencies in a population of effective size ke, the effective number of founders. We derive an expression for ke in a discrete-population model that allows for local population growth and migration among established populations. If there is selection, the net effect is determined approximately by the product of the selection coefficients and the number of generations between successive founding events. We use the model of a single population to compute analytically several quantities for an allele present in the source population: (i) the probability that it survives the series of colonization events, (ii) the probability that it reaches a specified threshold frequency in the last population, and (iii) the mean and variance of the frequencies in each population. We show that the analytic theory provides a good approximation to simulation results. A consequence of our approximation is that the average heterozygosity of neutral alleles decreases by a factor of 1-1/(2ke) in each new population. Therefore, the population genetic consequences of surfing can be predicted approximately by the effective number of founders and the effective selection coefficients, even in the presence of migration among populations. We also show that our analytic results are applicable to a model of range expansion in a continuously distributed population.

Note: Precise radial distribution of charged particles in a magnetic guiding field

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

Backe, H., E-mail: backe@kph.uni-mainz.de

2015-07-15

Current high precision beta decay experiments of polarized neutrons, employing magnetic guiding fields in combination with position sensitive and energy dispersive detectors, resulted in a detailed study of the mono-energetic point spread function (PSF) for a homogeneous magnetic field. A PSF describes the radial probability distribution of mono-energetic electrons at the detector plane emitted from a point-like source. With regard to accuracy considerations, unwanted singularities occur as a function of the radial detector coordinate which have recently been investigated by subdividing the radial coordinate into small bins or employing analytical approximations. In this note, a series expansion of the PSFmore » is presented which can numerically be evaluated with arbitrary precision.« less

Rings in above-threshold ionization: A quasiclassical analysis

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

Lewenstein, M.; Kulander, K.C.; Schafer, K.J.

1995-02-01

A generalized strong-field approximation is formulated to describe atoms interacting with intense laser fields. We apply it to determine angular distributions of electrons in above-threshold ionization (ATI). The theory treats the effects of an electron rescattering from its parent ion core in a systematic perturbation series. Probability amplitudes for ionization are interpreted in terms of quasiclassical electron trajectories. We demonstrate that contributions from the direct tunneling processes in the absence of rescattering are not sufficient to describe the observed ATI spectra. We show that the high-energy portion of the spectrum, including recently discovered rings (i.e., complex features in the angularmore » distributions of outgoing electrons) are due to rescattering processes. We compare our quasiclassical results with exact numerical solutions.« less

Metocean design parameter estimation for fixed platform based on copula functions

NASA Astrophysics Data System (ADS)

Zhai, Jinjin; Yin, Qilin; Dong, Sheng

2017-08-01

Considering the dependent relationship among wave height, wind speed, and current velocity, we construct novel trivariate joint probability distributions via Archimedean copula functions. Total 30-year data of wave height, wind speed, and current velocity in the Bohai Sea are hindcast and sampled for case study. Four kinds of distributions, namely, Gumbel distribution, lognormal distribution, Weibull distribution, and Pearson Type III distribution, are candidate models for marginal distributions of wave height, wind speed, and current velocity. The Pearson Type III distribution is selected as the optimal model. Bivariate and trivariate probability distributions of these environmental conditions are established based on four bivariate and trivariate Archimedean copulas, namely, Clayton, Frank, Gumbel-Hougaard, and Ali-Mikhail-Haq copulas. These joint probability models can maximize marginal information and the dependence among the three variables. The design return values of these three variables can be obtained by three methods: univariate probability, conditional probability, and joint probability. The joint return periods of different load combinations are estimated by the proposed models. Platform responses (including base shear, overturning moment, and deck displacement) are further calculated. For the same return period, the design values of wave height, wind speed, and current velocity obtained by the conditional and joint probability models are much smaller than those by univariate probability. Considering the dependence among variables, the multivariate probability distributions provide close design parameters to actual sea state for ocean platform design.

Models of multidimensional discrete distribution of probabilities of random variables in information systems

NASA Astrophysics Data System (ADS)

Gromov, Yu Yu; Minin, Yu V.; Ivanova, O. G.; Morozova, O. N.

2018-03-01

Multidimensional discrete distributions of probabilities of independent random values were received. Their one-dimensional distribution is widely used in probability theory. Producing functions of those multidimensional distributions were also received.

A binomial stochastic kinetic approach to the Michaelis-Menten mechanism

NASA Astrophysics Data System (ADS)

Lente, Gábor

2013-05-01

This Letter presents a new method that gives an analytical approximation of the exact solution of the stochastic Michaelis-Menten mechanism without computationally demanding matrix operations. The method is based on solving the deterministic rate equations and then using the results as guiding variables of calculating probability values using binomial distributions. This principle can be generalized to a number of different kinetic schemes and is expected to be very useful in the evaluation of measurements focusing on the catalytic activity of one or a few individual enzyme molecules.

Adaptive Optics Communications Performance Analysis

NASA Technical Reports Server (NTRS)

Srinivasan, M.; Vilnrotter, V.; Troy, M.; Wilson, K.

2004-01-01

The performance improvement obtained through the use of adaptive optics for deep-space communications in the presence of atmospheric turbulence is analyzed. Using simulated focal-plane signal-intensity distributions, uncoded pulse-position modulation (PPM) bit-error probabilities are calculated assuming the use of an adaptive focal-plane detector array as well as an adaptively sized single detector. It is demonstrated that current practical adaptive optics systems can yield performance gains over an uncompensated system ranging from approximately 1 dB to 6 dB depending upon the PPM order and background radiation level.

Potential Sources of Polarized Light from a Plant Canopy

NASA Technical Reports Server (NTRS)

Vanderbilt, Vern; Daughtry, Craig; Dahlgren, Robert

2016-01-01

Field measurements have demonstrated that sunlight polarized during a first surface reflection by shiny leaves dominates the optical polarization of the light reflected by shiny-leafed plant canopies having approximately spherical leaf angle probability density functions ("Leaf Angle Distributions" - LAD). Yet for other canopies - specifically those without shiny leaves and/or spherical LADs - potential sources of optically polarized light may not always be obvious. Here we identify possible sources of polarized light within those other canopies and speculate on the ecologically important information polarization measurements of those sources might contain.

Bayesian network models for error detection in radiotherapy plans

NASA Astrophysics Data System (ADS)

Kalet, Alan M.; Gennari, John H.; Ford, Eric C.; Phillips, Mark H.

2015-04-01

The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network’s conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.

Probability-based nitrate contamination map of groundwater in Kinmen.

PubMed

Liu, Chen-Wuing; Wang, Yeuh-Bin; Jang, Cheng-Shin

2013-12-01

Groundwater supplies over 50% of drinking water in Kinmen. Approximately 16.8% of groundwater samples in Kinmen exceed the drinking water quality standard (DWQS) of NO3 (-)-N (10 mg/L). The residents drinking high nitrate-polluted groundwater pose a potential risk to health. To formulate effective water quality management plan and assure a safe drinking water in Kinmen, the detailed spatial distribution of nitrate-N in groundwater is a prerequisite. The aim of this study is to develop an efficient scheme for evaluating spatial distribution of nitrate-N in residential well water using logistic regression (LR) model. A probability-based nitrate-N contamination map in Kinmen is constructed. The LR model predicted the binary occurrence probability of groundwater nitrate-N concentrations exceeding DWQS by simple measurement variables as independent variables, including sampling season, soil type, water table depth, pH, EC, DO, and Eh. The analyzed results reveal that three statistically significant explanatory variables, soil type, pH, and EC, are selected for the forward stepwise LR analysis. The total ratio of correct classification reaches 92.7%. The highest probability of nitrate-N contamination map presents in the central zone, indicating that groundwater in the central zone should not be used for drinking purposes. Furthermore, a handy EC-pH-probability curve of nitrate-N exceeding the threshold of DWQS was developed. This curve can be used for preliminary screening of nitrate-N contamination in Kinmen groundwater. This study recommended that the local agency should implement the best management practice strategies to control nonpoint nitrogen sources and carry out a systematic monitoring of groundwater quality in residential wells of the high nitrate-N contamination zones.

Using the Reliability Theory for Assessing the Decision Confidence Probability for Comparative Life Cycle Assessments.

PubMed

Wei, Wei; Larrey-Lassalle, Pyrène; Faure, Thierry; Dumoulin, Nicolas; Roux, Philippe; Mathias, Jean-Denis

2016-03-01

Comparative decision making process is widely used to identify which option (system, product, service, etc.) has smaller environmental footprints and for providing recommendations that help stakeholders take future decisions. However, the uncertainty problem complicates the comparison and the decision making. Probability-based decision support in LCA is a way to help stakeholders in their decision-making process. It calculates the decision confidence probability which expresses the probability of a option to have a smaller environmental impact than the one of another option. Here we apply the reliability theory to approximate the decision confidence probability. We compare the traditional Monte Carlo method with a reliability method called FORM method. The Monte Carlo method needs high computational time to calculate the decision confidence probability. The FORM method enables us to approximate the decision confidence probability with fewer simulations than the Monte Carlo method by approximating the response surface. Moreover, the FORM method calculates the associated importance factors that correspond to a sensitivity analysis in relation to the probability. The importance factors allow stakeholders to determine which factors influence their decision. Our results clearly show that the reliability method provides additional useful information to stakeholders as well as it reduces the computational time.

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

DOE PAGES

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

2017-11-15

In Hezaveh et al. (2017) we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data,more » as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single hyperparameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that neural networks can be a fast alternative to Monte Carlo Markov Chains for parameter uncertainty estimation in many practical applications, allowing more than seven orders of magnitude improvement in speed.« less

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

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

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

In Hezaveh et al. (2017) we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data,more » as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single hyperparameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that neural networks can be a fast alternative to Monte Carlo Markov Chains for parameter uncertainty estimation in many practical applications, allowing more than seven orders of magnitude improvement in speed.« less

Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Incorporation of Delayed Link Failure in the Presence of Aleatory Uncertainty.

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

Helton, Jon C.; Brooks, Dusty Marie; Sallaberry, Cedric Jean-Marie.

Probability of loss of assured safety (PLOAS) is modeled for weak link (WL)/strong link (SL) systems in which one or more WLs or SLs could potentially degrade into a precursor condition to link failure that will be followed by an actual failure after some amount of elapsed time. The following topics are considered: (i) Definition of precursor occurrence time cumulative distribution functions (CDFs) for individual WLs and SLs, (ii) Formal representation of PLOAS with constant delay times, (iii) Approximation and illustration of PLOAS with constant delay times, (iv) Formal representation of PLOAS with aleatory uncertainty in delay times, (v) Approximationmore » and illustration of PLOAS with aleatory uncertainty in delay times, (vi) Formal representation of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, (vii) Approximation and illustration of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, and (viii) Procedures for the verification of PLOAS calculations for the three indicated definitions of delayed link failure.« less

The orientation distribution of tunneling-related quantities

NASA Astrophysics Data System (ADS)

Seif, W. M.; Refaie, A. I.; Botros, M. M.

2018-03-01

In the nuclear tunneling processes involving deformed nuclei, most of the tunneling-related quantities depend on the relative orientations of the participating nuclei. In the presence of different multipole deformations, we study the variation of a few relevant quantities for the α-decay and the sub-barrier fusion processes, in an orientation degree of freedom. The knocking frequency and the penetration probability are evaluated within the Wentzel-Kramers-Brillouin approximation. The interaction potential is calculated with Skyrme-type nucleon-nucleon interaction. We found that the width of the potential pocket, the Coulomb barrier radius, the penetration probability, the α-decay width, and the fusion cross-section follow consistently the orientation-angle variation of the radius of the deformed nucleus. The orientation distribution patterns of the pocket width, the barrier radius, the logarithms of the penetrability, the decay width, and the fusion cross-section are found to be highly analogous to pattern of the deformed-nucleus radius. The curve patterns of the orientation angle distributions of the internal pocket depth, the Coulomb barrier height and width, as well as the knocking frequency simulate inversely the variation of the deformed nucleus radius. The predicted orientation behaviors will be of a special interest in predicting the optimum orientations for the tunneling processes.

Direct test of the Gaussian auxiliary field ansatz in nonconserved order parameter phase ordering dynamics

NASA Astrophysics Data System (ADS)

Yeung, Chuck

2018-06-01

The assumption that the local order parameter is related to an underlying spatially smooth auxiliary field, u (r ⃗,t ) , is a common feature in theoretical approaches to non-conserved order parameter phase separation dynamics. In particular, the ansatz that u (r ⃗,t ) is a Gaussian random field leads to predictions for the decay of the autocorrelation function which are consistent with observations, but distinct from predictions using alternative theoretical approaches. In this paper, the auxiliary field is obtained directly from simulations of the time-dependent Ginzburg-Landau equation in two and three dimensions. The results show that u (r ⃗,t ) is equivalent to the distance to the nearest interface. In two dimensions, the probability distribution, P (u ) , is well approximated as Gaussian except for small values of u /L (t ) , where L (t ) is the characteristic length-scale of the patterns. The behavior of P (u ) in three dimensions is more complicated; the non-Gaussian region for small u /L (t ) is much larger than that in two dimensions but the tails of P (u ) begin to approach a Gaussian form at intermediate times. However, at later times, the tails of the probability distribution appear to decay faster than a Gaussian distribution.

Comparison of three methods for wind turbine capacity factor estimation.

PubMed

Ditkovich, Y; Kuperman, A

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first "quasiexact" approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second "analytic" approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third "approximate" approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation.

A general moment expansion method for stochastic kinetic models

NASA Astrophysics Data System (ADS)

Ale, Angelique; Kirk, Paul; Stumpf, Michael P. H.

2013-05-01

Moment approximation methods are gaining increasing attention for their use in the approximation of the stochastic kinetics of chemical reaction systems. In this paper we derive a general moment expansion method for any type of propensities and which allows expansion up to any number of moments. For some chemical reaction systems, more than two moments are necessary to describe the dynamic properties of the system, which the linear noise approximation is unable to provide. Moreover, also for systems for which the mean does not have a strong dependence on higher order moments, moment approximation methods give information about higher order moments of the underlying probability distribution. We demonstrate the method using a dimerisation reaction, Michaelis-Menten kinetics and a model of an oscillating p53 system. We show that for the dimerisation reaction and Michaelis-Menten enzyme kinetics system higher order moments have limited influence on the estimation of the mean, while for the p53 system, the solution for the mean can require several moments to converge to the average obtained from many stochastic simulations. We also find that agreement between lower order moments does not guarantee that higher moments will agree. Compared to stochastic simulations, our approach is numerically highly efficient at capturing the behaviour of stochastic systems in terms of the average and higher moments, and we provide expressions for the computational cost for different system sizes and orders of approximation. We show how the moment expansion method can be employed to efficiently quantify parameter sensitivity. Finally we investigate the effects of using too few moments on parameter estimation, and provide guidance on how to estimate if the distribution can be accurately approximated using only a few moments.

Global Distribution of Density Irregularities in the Equatorial Ionosphere

NASA Technical Reports Server (NTRS)

Kil, Hyosub; Heelis, R. A.

1998-01-01

We analyzed measurements of ion number density made by the retarding potential analyzer aboard the Atmosphere Explorer-E (AE-E) satellite, which was in an approximately circular orbit at an altitude near 300 km in 1977 and later at an altitude near 400 km. Large-scale (greater than 60 km) density measurements in the high-altitude regions show large depletions of bubble-like structures which are confined to narrow local time longitude, and magnetic latitude ranges, while those in the low-altitude regions show relatively small depletions which are broadly distributed,in space. For this reason we considered the altitude regions below 300 km and above 350 km and investigated the global distribution of irregularities using the rms deviation delta N/N over a path length of 18 km as an indicator of overall irregularity intensity. Seasonal variations of irregularity occurrence probability are significant in the Pacific regions, while the occurrence probability is always high in die Atlantic-African regions and is always low in die Indian regions. We find that the high occurrence probability in the Pacific regions is associated with isolated bubble structures, while that near 0 deg longitude is produced by large depictions with bubble structures which are superimposed on a large-scale wave-like background. Considerations of longitude variations due to seeding mechanisms and due to F region winds and drifts are necessary to adequately explain the observations at low and high altitudes. Seeding effects are most obvious near 0 deg longitude, while the most easily observed effect of the F region is the suppression of irregularity growth by interhemispheric neutral winds.

Stochastic dynamics and logistic population growth

NASA Astrophysics Data System (ADS)

Méndez, Vicenç; Assaf, Michael; Campos, Daniel; Horsthemke, Werner

2015-06-01

The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources, respectively. We investigate analytically and numerically the simplest possible microscopic scenarios that give rise to the logistic equation in the deterministic mean-field limit. We provide a definition of the two parameters of the Verhulst equation in terms of microscopic parameters. In addition, we derive the conditions for extinction or persistence of the population by employing either the momentum-space spectral theory or the real-space Wentzel-Kramers-Brillouin approximation to determine the probability distribution function and the mean time to extinction of the population. Our analytical results agree well with numerical simulations.

Limitations of shallow nets approximation.

PubMed

Lin, Shao-Bo

2017-10-01

In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

Conservative Analytical Collision Probabilities for Orbital Formation Flying

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Conservative Analytical Collision Probability for Design of Orbital Formations

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Statistical tests for whether a given set of independent, identically distributed draws comes from a specified probability density.

PubMed

Tygert, Mark

2010-09-21

We discuss several tests for determining whether a given set of independent and identically distributed (i.i.d.) draws does not come from a specified probability density function. The most commonly used are Kolmogorov-Smirnov tests, particularly Kuiper's variant, which focus on discrepancies between the cumulative distribution function for the specified probability density and the empirical cumulative distribution function for the given set of i.i.d. draws. Unfortunately, variations in the probability density function often get smoothed over in the cumulative distribution function, making it difficult to detect discrepancies in regions where the probability density is small in comparison with its values in surrounding regions. We discuss tests without this deficiency, complementing the classical methods. The tests of the present paper are based on the plain fact that it is unlikely to draw a random number whose probability is small, provided that the draw is taken from the same distribution used in calculating the probability (thus, if we draw a random number whose probability is small, then we can be confident that we did not draw the number from the same distribution used in calculating the probability).

Dealing with non-unique and non-monotonic response in particle sizing instruments

NASA Astrophysics Data System (ADS)

Rosenberg, Phil

2017-04-01

A number of instruments used as de-facto standards for measuring particle size distributions are actually incapable of uniquely determining the size of an individual particle. This is due to non-unique or non-monotonic response functions. Optical particle counters have non monotonic response due to oscillations in the Mie response curves, especially for large aerosol and small cloud droplets. Scanning mobility particle sizers respond identically to two particles where the ratio of particle size to particle charge is approximately the same. Images of two differently sized cloud or precipitation particles taken by an optical array probe can have similar dimensions or shadowed area depending upon where they are in the imaging plane. A number of methods exist to deal with these issues, including assuming that positive and negative errors cancel, smoothing response curves, integrating regions in measurement space before conversion to size space and matrix inversion. Matrix inversion (also called kernel inversion) has the advantage that it determines the size distribution which best matches the observations, given specific information about the instrument (a matrix which specifies the probability that a particle of a given size will be measured in a given instrument size bin). In this way it maximises use of the information in the measurements. However this technique can be confused by poor counting statistics which can cause erroneous results and negative concentrations. Also an effective method for propagating uncertainties is yet to be published or routinely implemented. Her we present a new alternative which overcomes these issues. We use Bayesian methods to determine the probability that a given size distribution is correct given a set of instrument data and then we use Markov Chain Monte Carlo methods to sample this many dimensional probability distribution function to determine the expectation and (co)variances - hence providing a best guess and an uncertainty for the size distribution which includes contributions from the non-unique response curve, counting statistics and can propagate calibration uncertainties.

Time difference of arrival estimation of microseismic signals based on alpha-stable distribution

NASA Astrophysics Data System (ADS)

Jia, Rui-Sheng; Gong, Yue; Peng, Yan-Jun; Sun, Hong-Mei; Zhang, Xing-Li; Lu, Xin-Ming

2018-05-01

Microseismic signals are generally considered to follow the Gauss distribution. A comparison of the dynamic characteristics of sample variance and the symmetry of microseismic signals with the signals which follow α-stable distribution reveals that the microseismic signals have obvious pulse characteristics and that the probability density curve of the microseismic signal is approximately symmetric. Thus, the hypothesis that microseismic signals follow the symmetric α-stable distribution is proposed. On the premise of this hypothesis, the characteristic exponent α of the microseismic signals is obtained by utilizing the fractional low-order statistics, and then a new method of time difference of arrival (TDOA) estimation of microseismic signals based on fractional low-order covariance (FLOC) is proposed. Upon applying this method to the TDOA estimation of Ricker wavelet simulation signals and real microseismic signals, experimental results show that the FLOC method, which is based on the assumption of the symmetric α-stable distribution, leads to enhanced spatial resolution of the TDOA estimation relative to the generalized cross correlation (GCC) method, which is based on the assumption of the Gaussian distribution.

Electrostatic field and charge distribution in small charged dielectric droplets

NASA Astrophysics Data System (ADS)

Storozhev, V. B.

2004-08-01

The charge distribution in small dielectric droplets is calculated on the basis of continuum medium approximation. There are considered charged liquid spherical droplets of methanol in the range of nanometer sizes. The problem is solved by the following way. We find the free energy of some ion in dielectric droplet, which is a function of distribution of other ions in the droplet. The probability of location of the ion in some element of volume in the droplet is a function of its free energy in this element of volume. The same approach can be applied to other ions in the droplet. The obtained charge distribution differs considerably from the surface distribution. The curve of the charge distribution in the droplet as a function of radius has maximum near the surface. Relative concentration of charges in the vicinity of the center of the droplet does not equal to zero, and it is the higher, the less is the total charge of the droplet. According to the estimates the model is applicable if the droplet radius is larger than 10 nm.

On the proportional abundance of species: Integrating population genetics and community ecology.

PubMed

Marquet, Pablo A; Espinoza, Guillermo; Abades, Sebastian R; Ganz, Angela; Rebolledo, Rolando

2017-12-01

The frequency of genes in interconnected populations and of species in interconnected communities are affected by similar processes, such as birth, death and immigration. The equilibrium distribution of gene frequencies in structured populations is known since the 1930s, under Wright's metapopulation model known as the island model. The equivalent distribution for the species frequency (i.e. the species proportional abundance distribution (SPAD)), at the metacommunity level, however, is unknown. In this contribution, we develop a stochastic model to analytically account for this distribution (SPAD). We show that the same as for genes SPAD follows a beta distribution, which provides a good description of empirical data and applies across a continuum of scales. This stochastic model, based upon a diffusion approximation, provides an alternative to neutral models for the species abundance distribution (SAD), which focus on number of individuals instead of proportions, and demonstrate that the relative frequency of genes in local populations and of species within communities follow the same probability law. We hope our contribution will help stimulate the mathematical and conceptual integration of theories in genetics and ecology.

Publication Bias in Meta-Analysis: Confidence Intervals for Rosenthal's Fail-Safe Number.

PubMed

Fragkos, Konstantinos C; Tsagris, Michail; Frangos, Christos C

2014-01-01

The purpose of the present paper is to assess the efficacy of confidence intervals for Rosenthal's fail-safe number. Although Rosenthal's estimator is highly used by researchers, its statistical properties are largely unexplored. First of all, we developed statistical theory which allowed us to produce confidence intervals for Rosenthal's fail-safe number. This was produced by discerning whether the number of studies analysed in a meta-analysis is fixed or random. Each case produces different variance estimators. For a given number of studies and a given distribution, we provided five variance estimators. Confidence intervals are examined with a normal approximation and a nonparametric bootstrap. The accuracy of the different confidence interval estimates was then tested by methods of simulation under different distributional assumptions. The half normal distribution variance estimator has the best probability coverage. Finally, we provide a table of lower confidence intervals for Rosenthal's estimator.

Publication Bias in Meta-Analysis: Confidence Intervals for Rosenthal's Fail-Safe Number

PubMed Central

Fragkos, Konstantinos C.; Tsagris, Michail; Frangos, Christos C.

2014-01-01

The purpose of the present paper is to assess the efficacy of confidence intervals for Rosenthal's fail-safe number. Although Rosenthal's estimator is highly used by researchers, its statistical properties are largely unexplored. First of all, we developed statistical theory which allowed us to produce confidence intervals for Rosenthal's fail-safe number. This was produced by discerning whether the number of studies analysed in a meta-analysis is fixed or random. Each case produces different variance estimators. For a given number of studies and a given distribution, we provided five variance estimators. Confidence intervals are examined with a normal approximation and a nonparametric bootstrap. The accuracy of the different confidence interval estimates was then tested by methods of simulation under different distributional assumptions. The half normal distribution variance estimator has the best probability coverage. Finally, we provide a table of lower confidence intervals for Rosenthal's estimator. PMID:27437470

Software reliability: Additional investigations into modeling with replicated experiments

NASA Technical Reports Server (NTRS)

Nagel, P. M.; Schotz, F. M.; Skirvan, J. A.

1984-01-01

The effects of programmer experience level, different program usage distributions, and programming languages are explored. All these factors affect performance, and some tentative relational hypotheses are presented. An analytic framework for replicated and non-replicated (traditional) software experiments is presented. A method of obtaining an upper bound on the error rate of the next error is proposed. The method was validated empirically by comparing forecasts with actual data. In all 14 cases the bound exceeded the observed parameter, albeit somewhat conservatively. Two other forecasting methods are proposed and compared to observed results. Although demonstrated relative to this framework that stages are neither independent nor exponentially distributed, empirical estimates show that the exponential assumption is nearly valid for all but the extreme tails of the distribution. Except for the dependence in the stage probabilities, Cox's model approximates to a degree what is being observed.

Remembrance of inferences past: Amortization in human hypothesis generation.

PubMed

Dasgupta, Ishita; Schulz, Eric; Goodman, Noah D; Gershman, Samuel J

2018-05-21

Bayesian models of cognition assume that people compute probability distributions over hypotheses. However, the required computations are frequently intractable or prohibitively expensive. Since people often encounter many closely related distributions, selective reuse of computations (amortized inference) is a computationally efficient use of the brain's limited resources. We present three experiments that provide evidence for amortization in human probabilistic reasoning. When sequentially answering two related queries about natural scenes, participants' responses to the second query systematically depend on the structure of the first query. This influence is sensitive to the content of the queries, only appearing when the queries are related. Using a cognitive load manipulation, we find evidence that people amortize summary statistics of previous inferences, rather than storing the entire distribution. These findings support the view that the brain trades off accuracy and computational cost, to make efficient use of its limited cognitive resources to approximate probabilistic inference. Copyright © 2018 Elsevier B.V. All rights reserved.

Spatial distribution on high-order-harmonic generation of an H2+ molecule in intense laser fields

NASA Astrophysics Data System (ADS)

Zhang, Jun; Ge, Xin-Lei; Wang, Tian; Xu, Tong-Tong; Guo, Jing; Liu, Xue-Shen

2015-07-01

High-order-harmonic generation (HHG) for the H2 + molecule in a 3-fs, 800-nm few-cycle Gaussian laser pulse combined with a static field is investigated by solving the one-dimensional electronic and one-dimensional nuclear time-dependent Schrödinger equation within the non-Born-Oppenheimer approximation. The spatial distribution in HHG is demonstrated and the results present the recombination process of the electron with the two nuclei, respectively. The spatial distribution of the HHG spectra shows that there is little possibility of the recombination of the electron with the nuclei around the origin z =0 a.u. and equilibrium internuclear positions z =±1.3 a.u. This characteristic is irrelevant to laser parameters and is only attributed to the molecular structure. Furthermore, we investigate the time-dependent electron-nuclear wave packet and ionization probability to further explain the underlying physical mechanism.

The EM Method in a Probabilistic Wavelet-Based MRI Denoising

PubMed Central

2015-01-01

Human body heat emission and others external causes can interfere in magnetic resonance image acquisition and produce noise. In this kind of images, the noise, when no signal is present, is Rayleigh distributed and its wavelet coefficients can be approximately modeled by a Gaussian distribution. Noiseless magnetic resonance images can be modeled by a Laplacian distribution in the wavelet domain. This paper proposes a new magnetic resonance image denoising method to solve this fact. This method performs shrinkage of wavelet coefficients based on the conditioned probability of being noise or detail. The parameters involved in this filtering approach are calculated by means of the expectation maximization (EM) method, which avoids the need to use an estimator of noise variance. The efficiency of the proposed filter is studied and compared with other important filtering techniques, such as Nowak's, Donoho-Johnstone's, Awate-Whitaker's, and nonlocal means filters, in different 2D and 3D images. PMID:26089959

The EM Method in a Probabilistic Wavelet-Based MRI Denoising.

PubMed

Martin-Fernandez, Marcos; Villullas, Sergio

2015-01-01

Human body heat emission and others external causes can interfere in magnetic resonance image acquisition and produce noise. In this kind of images, the noise, when no signal is present, is Rayleigh distributed and its wavelet coefficients can be approximately modeled by a Gaussian distribution. Noiseless magnetic resonance images can be modeled by a Laplacian distribution in the wavelet domain. This paper proposes a new magnetic resonance image denoising method to solve this fact. This method performs shrinkage of wavelet coefficients based on the conditioned probability of being noise or detail. The parameters involved in this filtering approach are calculated by means of the expectation maximization (EM) method, which avoids the need to use an estimator of noise variance. The efficiency of the proposed filter is studied and compared with other important filtering techniques, such as Nowak's, Donoho-Johnstone's, Awate-Whitaker's, and nonlocal means filters, in different 2D and 3D images.

Probabilistic assessment of sea level during the last interglacial stage.

PubMed

Kopp, Robert E; Simons, Frederik J; Mitrovica, Jerry X; Maloof, Adam C; Oppenheimer, Michael

2009-12-17

With polar temperatures approximately 3-5 degrees C warmer than today, the last interglacial stage (approximately 125 kyr ago) serves as a partial analogue for 1-2 degrees C global warming scenarios. Geological records from several sites indicate that local sea levels during the last interglacial were higher than today, but because local sea levels differ from global sea level, accurately reconstructing past global sea level requires an integrated analysis of globally distributed data sets. Here we present an extensive compilation of local sea level indicators and a statistical approach for estimating global sea level, local sea levels, ice sheet volumes and their associated uncertainties. We find a 95% probability that global sea level peaked at least 6.6 m higher than today during the last interglacial; it is likely (67% probability) to have exceeded 8.0 m but is unlikely (33% probability) to have exceeded 9.4 m. When global sea level was close to its current level (>or=-10 m), the millennial average rate of global sea level rise is very likely to have exceeded 5.6 m kyr(-1) but is unlikely to have exceeded 9.2 m kyr(-1). Our analysis extends previous last interglacial sea level studies by integrating literature observations within a probabilistic framework that accounts for the physics of sea level change. The results highlight the long-term vulnerability of ice sheets to even relatively low levels of sustained global warming.

The probability of lava inundation at the proposed and existing Kulani prison sites

USGS Publications Warehouse

Kauahikaua, J.P.; Trusdell, F.A.; Heliker, C.C.

1998-01-01

The State of Hawai`i has proposed building a 2,300-bed medium-security prison about 10 km downslope from the existing Kulani medium-security correctional facility. The proposed and existing facilities lie on the northeast rift zone of Mauna Loa, which last erupted in 1984 in this same general area. We use the best available geologic mapping and dating with GIS software to estimate the average recurrence interval between lava flows that inundate these sites. Three different methods are used to adjust the number of flows exposed at the surface for those flows that are buried to allow a better representation of the recurrence interval. Probabilities are then computed, based on these recurrence intervals, assuming that the data match a Poisson distribution. The probability of lava inundation for the existing prison site is estimated to be 11- 12% in the next 50 years. The probability of lava inundation for the proposed sites B and C are 2- 3% and 1-2%, respectively, in the same period. The probabilities are based on estimated recurrence intervals for lava flows, which are approximately proportional to the area considered. The probability of having to evacuate the prison is certainly higher than the probability of lava entering the site. Maximum warning times between eruption and lava inundation of a site are estimated to be 24 hours for the existing prison site and 72 hours for proposed sites B and C. Evacuation plans should take these times into consideration.

Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

NASA Astrophysics Data System (ADS)

Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

2010-03-01

We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

Fixation Probability in a Haploid-Diploid Population.

PubMed

Bessho, Kazuhiro; Otto, Sarah P

2017-01-01

Classical population genetic theory generally assumes either a fully haploid or fully diploid life cycle. However, many organisms exhibit more complex life cycles, with both free-living haploid and diploid stages. Here we ask what the probability of fixation is for selected alleles in organisms with haploid-diploid life cycles. We develop a genetic model that considers the population dynamics using both the Moran model and Wright-Fisher model. Applying a branching process approximation, we obtain an accurate fixation probability assuming that the population is large and the net effect of the mutation is beneficial. We also find the diffusion approximation for the fixation probability, which is accurate even in small populations and for deleterious alleles, as long as selection is weak. These fixation probabilities from branching process and diffusion approximations are similar when selection is weak for beneficial mutations that are not fully recessive. In many cases, particularly when one phase predominates, the fixation probability differs substantially for haploid-diploid organisms compared to either fully haploid or diploid species. Copyright © 2017 by the Genetics Society of America.

Remote sensing of mesospheric electric fields using MF radars

NASA Astrophysics Data System (ADS)

Meek, C. E.; Manson, A. H.; Martynenko, S. I.; Rozumenko, V. T.; Tyrnov, O. F.

2004-07-01

Large mesospheric electric fields can play an essential role in middle atmospheric electrodynamics (see, e.g., Goldberg, R. A., Middle Atmospheric Electrodynamics during MAP, Adv. Space Res. 10 (10) (1990) 209). The V/m electric fields of atmospheric origin can be the possible cause of large variations in the electron collision frequency at mesospheric altitudes, and this provides a unique opportunity to take measurements of electric fields in the lower ionosphere by using remote sensing instruments employing radiowave techniques. A technique has been proposed for making estimates of large mesospheric electric field intensities on the lower edge of the ionosphere by using MF radar data and the inherent effective electron collision frequency. To do this, data collected in Canada and Ukraine were utilized. The developed technique permits the changes in mesospheric electric field intensities to be derived from MF radar data in real time. The statistical analysis of data consistent with large mesospheric electric field intensities in the 60-67km region resulted in the following inferences. There are at least two mechanisms for the generation of large mesospheric electric fields in the mesosphere. The most likely mechanism, with a probability of 60-70%, is the summation of random fields from a large number of elementary small-scale mesospheric generators, which results in a one-parameter Rayleigh distribution of the total large mesospheric electric field intensity E with a mean value of approximately 0.7-0.9V/m in the 60-67km altitude region, or in the corresponding one-parameter exponential distribution of the intensity squared E2 of large mesospheric electric fields. The second mechanism of unknown nature, with 5-15% probability, gives rise to the sporadic appearance of large mesospheric electric field intensities E>2.5V/m with a mean of 4V/m. Statistically significant seasonal differences in the averaged large mesospheric electric field parameters have not been revealed. The probability of the absence of local large mesospheric electric fields amounts to approximately 25% for Ukraine and approximately 30% for Canada. A comparison of the Ukrainian and Canadian data indicates the possible existence of a latitudinal dependence in mean large mesospheric electric field features. Hence, the large electric fields are an additional source of electron heating that must be taken into account in studying a disturbed lower ionosphere and radio wave propagation within it.

The energetic ion signature of an O-type neutral line in the geomagnetic tail

NASA Technical Reports Server (NTRS)

Martin, R. F., Jr.; Johnson, D. F.; Speiser, T. W.

1991-01-01

An energetic ion signature is presented which has the potential for remote sensing of an O-type neutral line embedded in a current sheet. A source plasma with a tailward flowing Kappa distribution yields a strongly non-Kappa distribution after interacting with the neutral line: sharp jumps, or ridges, occur in the velocity space distribution function f(nu-perpendicular, nu-parallel) associated with both increases and decreases in f. The jumps occur when orbits are reversed in the x-direction: a reversal causing initially earthward particles (low probability in the source distribution) to be observed results in a decrease in f, while a reversal causing initially tailward particles to be observed produces an increase in f. The reversals, and hence the jumps, occur at approximately constant values of perpendicular velocity in both the positive nu parallel and negative nu parallel half planes. The results were obtained using single particle simulations in a fixed magnetic field model.

Tree attenuation at 20 GHz: Foliage effects

NASA Technical Reports Server (NTRS)

Vogel, Wolfhard J.; Goldhirsh, Julius

1993-01-01

Static tree attenuation measurements at 20 GHz (K-Band) on a 30 deg slant path through a mature Pecan tree with and without leaves showed median fades exceeding approximately 23 dB and 7 dB, respectively. The corresponding 1% probability fades were 43 dB and 25 dB. Previous 1.6 GHz (L-Band) measurements for the bare tree case showed fades larger than those at K-Band by 3.4 dB for the median and smaller by approximately 7 dB at the 1% probability. While the presence of foliage had only a small effect on fading at L-Band (approximately 1 dB additional for the median to 1% probability range), the attenuation increase was significant at K-Band, where it increased by about 17 dB over the same probability range.

Tree attenuation at 20 GHz: Foliage effects

NASA Astrophysics Data System (ADS)

Vogel, Wolfhard J.; Goldhirsh, Julius

1993-08-01

Static tree attenuation measurements at 20 GHz (K-Band) on a 30 deg slant path through a mature Pecan tree with and without leaves showed median fades exceeding approximately 23 dB and 7 dB, respectively. The corresponding 1% probability fades were 43 dB and 25 dB. Previous 1.6 GHz (L-Band) measurements for the bare tree case showed fades larger than those at K-Band by 3.4 dB for the median and smaller by approximately 7 dB at the 1% probability. While the presence of foliage had only a small effect on fading at L-Band (approximately 1 dB additional for the median to 1% probability range), the attenuation increase was significant at K-Band, where it increased by about 17 dB over the same probability range.

Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances

NASA Astrophysics Data System (ADS)

Ma, Wenchao; Ma, Zhihao; Wang, Hengyan; Chen, Zhihua; Liu, Ying; Kong, Fei; Li, Zhaokai; Peng, Xinhua; Shi, Mingjun; Shi, Fazhan; Fei, Shao-Ming; Du, Jiangfeng

2016-04-01

Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously.

Optimal decision making on the basis of evidence represented in spike trains.

PubMed

Zhang, Jiaxiang; Bogacz, Rafal

2010-05-01

Experimental data indicate that perceptual decision making involves integration of sensory evidence in certain cortical areas. Theoretical studies have proposed that the computation in neural decision circuits approximates statistically optimal decision procedures (e.g., sequential probability ratio test) that maximize the reward rate in sequential choice tasks. However, these previous studies assumed that the sensory evidence was represented by continuous values from gaussian distributions with the same variance across alternatives. In this article, we make a more realistic assumption that sensory evidence is represented in spike trains described by the Poisson processes, which naturally satisfy the mean-variance relationship observed in sensory neurons. We show that for such a representation, the neural circuits involving cortical integrators and basal ganglia can approximate the optimal decision procedures for two and multiple alternative choice tasks.

Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances.

PubMed

Ma, Wenchao; Ma, Zhihao; Wang, Hengyan; Chen, Zhihua; Liu, Ying; Kong, Fei; Li, Zhaokai; Peng, Xinhua; Shi, Mingjun; Shi, Fazhan; Fei, Shao-Ming; Du, Jiangfeng

2016-04-22

Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously.

Investigation of Dielectric Breakdown Characteristics for Double-break Vacuum Interrupter and Dielectric Breakdown Probability Distribution in Vacuum Interrupter

NASA Astrophysics Data System (ADS)

Shioiri, Tetsu; Asari, Naoki; Sato, Junichi; Sasage, Kosuke; Yokokura, Kunio; Homma, Mitsutaka; Suzuki, Katsumi

To investigate the reliability of equipment of vacuum insulation, a study was carried out to clarify breakdown probability distributions in vacuum gap. Further, a double-break vacuum circuit breaker was investigated for breakdown probability distribution. The test results show that the breakdown probability distribution of the vacuum gap can be represented by a Weibull distribution using a location parameter, which shows the voltage that permits a zero breakdown probability. The location parameter obtained from Weibull plot depends on electrode area. The shape parameter obtained from Weibull plot of vacuum gap was 10∼14, and is constant irrespective non-uniform field factor. The breakdown probability distribution after no-load switching can be represented by Weibull distribution using a location parameter. The shape parameter after no-load switching was 6∼8.5, and is constant, irrespective of gap length. This indicates that the scatter of breakdown voltage was increased by no-load switching. If the vacuum circuit breaker uses a double break, breakdown probability at low voltage becomes lower than single-break probability. Although potential distribution is a concern in the double-break vacuum cuicuit breaker, its insulation reliability is better than that of the single-break vacuum interrupter even if the bias of the vacuum interrupter's sharing voltage is taken into account.

Fishnet statistics for probabilistic strength and scaling of nacreous imbricated lamellar materials

NASA Astrophysics Data System (ADS)

Luo, Wen; Bažant, Zdeněk P.

2017-12-01

Similar to nacre (or brick masonry), imbricated (or staggered) lamellar structures are widely found in nature and man-made materials, and are of interest for biomimetics. They can achieve high defect insensitivity and fracture toughness, as demonstrated in previous studies. But the probability distribution with a realistic far-left tail is apparently unknown. Here, strictly for statistical purposes, the microstructure of nacre is approximated by a diagonally pulled fishnet with quasibrittle links representing the shear bonds between parallel lamellae (or platelets). The probability distribution of fishnet strength is calculated as a sum of a rapidly convergent series of the failure probabilities after the rupture of one, two, three, etc., links. Each of them represents a combination of joint probabilities and of additive probabilities of disjoint events, modified near the zone of failed links by the stress redistributions caused by previously failed links. Based on previous nano- and multi-scale studies at Northwestern, the strength distribution of each link, characterizing the interlamellar shear bond, is assumed to be a Gauss-Weibull graft, but with a deeper Weibull tail than in Type 1 failure of non-imbricated quasibrittle materials. The autocorrelation length is considered equal to the link length. The size of the zone of failed links at maximum load increases with the coefficient of variation (CoV) of link strength, and also with fishnet size. With an increasing width-to-length aspect ratio, a rectangular fishnet gradually transits from the weakest-link chain to the fiber bundle, as the limit cases. The fishnet strength at failure probability 10-6 grows with the width-to-length ratio. For a square fishnet boundary, the strength at 10-6 failure probability is about 11% higher, while at fixed load the failure probability is about 25-times higher than it is for the non-imbricated case. This is a major safety advantage of the fishnet architecture over particulate or fiber reinforced materials. There is also a strong size effect, partly similar to that of Type 1 while the curves of log-strength versus log-size for different sizes could cross each other. The predicted behavior is verified by about a million Monte Carlo simulations for each of many fishnet geometries, sizes and CoVs of link strength. In addition to the weakest-link or fiber bundle, the fishnet becomes the third analytically tractable statistical model of structural strength, and has the former two as limit cases.

Advanced reliability methods for structural evaluation

NASA Technical Reports Server (NTRS)

Wirsching, P. H.; Wu, Y.-T.

1985-01-01

Fast probability integration (FPI) methods, which can yield approximate solutions to such general structural reliability problems as the computation of the probabilities of complicated functions of random variables, are known to require one-tenth the computer time of Monte Carlo methods for a probability level of 0.001; lower probabilities yield even more dramatic differences. A strategy is presented in which a computer routine is run k times with selected perturbed values of the variables to obtain k solutions for a response variable Y. An approximating polynomial is fit to the k 'data' sets, and FPI methods are employed for this explicit form.

The effect of maternal healthcare on the probability of child survival in Azerbaijan.

PubMed

Habibov, Nazim; Fan, Lida

2014-01-01

This study assesses the effects of maternal healthcare on child survival by using nonrandomized data from a cross-sectional survey in Azerbaijan. Using 2SLS and simultaneous equation bivariate probit models, we estimate the effects of delivering in healthcare facility on probability of child survival taking into account self-selection into the treatment. For women who delivered at healthcare facilities, the probability of child survival increases by approximately 18%. Furthermore, if every woman had the opportunity to deliver in healthcare facility, then the probability of child survival in Azerbaijan as a whole would have increased by approximately 16%.

Using a Betabinomial distribution to estimate the prevalence of adherence to physical activity guidelines among children and youth.

PubMed

Garriguet, Didier

2016-04-01

Estimates of the prevalence of adherence to physical activity guidelines in the population are generally the result of averaging individual probability of adherence based on the number of days people meet the guidelines and the number of days they are assessed. Given this number of active and inactive days (days assessed minus days active), the conditional probability of meeting the guidelines that has been used in the past is a Beta (1 + active days, 1 + inactive days) distribution assuming the probability p of a day being active is bounded by 0 and 1 and averages 50%. A change in the assumption about the distribution of p is required to better match the discrete nature of the data and to better assess the probability of adherence when the percentage of active days in the population differs from 50%. Using accelerometry data from the Canadian Health Measures Survey, the probability of adherence to physical activity guidelines is estimated using a conditional probability given the number of active and inactive days distributed as a Betabinomial(n, a + active days , β + inactive days) assuming that p is randomly distributed as Beta(a, β) where the parameters a and β are estimated by maximum likelihood. The resulting Betabinomial distribution is discrete. For children aged 6 or older, the probability of meeting physical activity guidelines 7 out of 7 days is similar to published estimates. For pre-schoolers, the Betabinomial distribution yields higher estimates of adherence to the guidelines than the Beta distribution, in line with the probability of being active on any given day. In estimating the probability of adherence to physical activity guidelines, the Betabinomial distribution has several advantages over the previously used Beta distribution. It is a discrete distribution and maximizes the richness of accelerometer data.

Statistical Hypothesis Testing in Intraspecific Phylogeography: NCPA versus ABC

PubMed Central

Templeton, Alan R.

2009-01-01

Nested clade phylogeographic analysis (NCPA) and approximate Bayesian computation (ABC) have been used to test phylogeographic hypotheses. Multilocus NCPA tests null hypotheses, whereas ABC discriminates among a finite set of alternatives. The interpretive criteria of NCPA are explicit and allow complex models to be built from simple components. The interpretive criteria of ABC are ad hoc and require the specification of a complete phylogeographic model. The conclusions from ABC are often influenced by implicit assumptions arising from the many parameters needed to specify a complex model. These complex models confound many assumptions so that biological interpretations are difficult. Sampling error is accounted for in NCPA, but ABC ignores important sources of sampling error that creates pseudo-statistical power. NCPA generates the full sampling distribution of its statistics, but ABC only yields local probabilities, which in turn make it impossible to distinguish between a good fitting model, a non-informative model, and an over-determined model. Both NCPA and ABC use approximations, but convergences of the approximations used in NCPA are well defined whereas those in ABC are not. NCPA can analyze a large number of locations, but ABC cannot. Finally, the dimensionality of tested hypothesis is known in NCPA, but not for ABC. As a consequence, the “probabilities” generated by ABC are not true probabilities and are statistically non-interpretable. Accordingly, ABC should not be used for hypothesis testing, but simulation approaches are valuable when used in conjunction with NCPA or other methods that do not rely on highly parameterized models. PMID:19192182

Daily tornado frequency distributions in the United States

NASA Astrophysics Data System (ADS)

Elsner, J. B.; Jagger, T. H.; Widen, H. M.; Chavas, D. R.

2014-01-01

The authors examine daily tornado counts in the United States over the period 1994-2012 and find strong evidence for a power-law relationship in the distribution frequency. The scaling exponent is estimated at 1.64 (0.019 s.e.) giving a per tornado-day probability of 0.014% (return period of 71 years) that a tornado day produces 145 tornadoes as was observed on 27 April 2011. They also find that the total number of tornadoes by damage category on days with at least one violent tornado follows an exponential rule. On average, the daily number of tornadoes in the next lowest damage category is approximately twice the number in the current category. These findings are important and timely for tornado hazard models and for seasonal and sub-seasonal forecasts of tornado activity.

A seismological model for earthquakes induced by fluid extraction from a subsurface reservoir

NASA Astrophysics Data System (ADS)

Bourne, S. J.; Oates, S. J.; van Elk, J.; Doornhof, D.

2014-12-01

A seismological model is developed for earthquakes induced by subsurface reservoir volume changes. The approach is based on the work of Kostrov () and McGarr () linking total strain to the summed seismic moment in an earthquake catalog. We refer to the fraction of the total strain expressed as seismic moment as the strain partitioning function, α. A probability distribution for total seismic moment as a function of time is derived from an evolving earthquake catalog. The moment distribution is taken to be a Pareto Sum Distribution with confidence bounds estimated using approximations given by Zaliapin et al. (). In this way available seismic moment is expressed in terms of reservoir volume change and hence compaction in the case of a depleting reservoir. The Pareto Sum Distribution for moment and the Pareto Distribution underpinning the Gutenberg-Richter Law are sampled using Monte Carlo methods to simulate synthetic earthquake catalogs for subsequent estimation of seismic ground motion hazard. We demonstrate the method by applying it to the Groningen gas field. A compaction model for the field calibrated using various geodetic data allows reservoir strain due to gas extraction to be expressed as a function of both spatial position and time since the start of production. Fitting with a generalized logistic function gives an empirical expression for the dependence of α on reservoir compaction. Probability density maps for earthquake event locations can then be calculated from the compaction maps. Predicted seismic moment is shown to be strongly dependent on planned gas production.

Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

NASA Astrophysics Data System (ADS)

Massiot, Cécile; Townend, John; Nicol, Andrew; McNamara, David D.

2017-08-01

Acoustic borehole televiewer (BHTV) logs provide measurements of fracture attributes (orientations, thickness, and spacing) at depth. Orientation, censoring, and truncation sampling biases similar to those described for one-dimensional outcrop scanlines, and other logging or drilling artifacts specific to BHTV logs, can affect the interpretation of fracture attributes from BHTV logs. K-means, fuzzy K-means, and agglomerative clustering methods provide transparent means of separating fracture groups on the basis of their orientation. Fracture spacing is calculated for each of these fracture sets. Maximum likelihood estimation using truncated distributions permits the fitting of several probability distributions to the fracture attribute data sets within truncation limits, which can then be extrapolated over the entire range where they naturally occur. Akaike Information Criterion (AIC) and Schwartz Bayesian Criterion (SBC) statistical information criteria rank the distributions by how well they fit the data. We demonstrate these attribute analysis methods with a data set derived from three BHTV logs acquired from the high-temperature Rotokawa geothermal field, New Zealand. Varying BHTV log quality reduces the number of input data points, but careful selection of the quality levels where fractures are deemed fully sampled increases the reliability of the analysis. Spacing data analysis comprising up to 300 data points and spanning three orders of magnitude can be approximated similarly well (similar AIC rankings) with several distributions. Several clustering configurations and probability distributions can often characterize the data at similar levels of statistical criteria. Thus, several scenarios should be considered when using BHTV log data to constrain numerical fracture models.

Analytic Neutrino Oscillation Probabilities in Matter: Revisited

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

Parke, Stephen J.; Denton, Peter B.; Minakata, Hisakazu

2018-01-02

We summarize our recent paper on neutrino oscillation probabilities in matter, explaining the importance, relevance and need for simple, highly accurate approximations to the neutrino oscillation probabilities in matter.

Reliability estimation of a N- M-cold-standby redundancy system in a multicomponent stress-strength model with generalized half-logistic distribution

NASA Astrophysics Data System (ADS)

Liu, Yiming; Shi, Yimin; Bai, Xuchao; Zhan, Pei

2018-01-01

In this paper, we study the estimation for the reliability of a multicomponent system, named N- M-cold-standby redundancy system, based on progressive Type-II censoring sample. In the system, there are N subsystems consisting of M statistically independent distributed strength components, and only one of these subsystems works under the impact of stresses at a time and the others remain as standbys. Whenever the working subsystem fails, one from the standbys takes its place. The system fails when the entire subsystems fail. It is supposed that the underlying distributions of random strength and stress both belong to the generalized half-logistic distribution with different shape parameter. The reliability of the system is estimated by using both classical and Bayesian statistical inference. Uniformly minimum variance unbiased estimator and maximum likelihood estimator for the reliability of the system are derived. Under squared error loss function, the exact expression of the Bayes estimator for the reliability of the system is developed by using the Gauss hypergeometric function. The asymptotic confidence interval and corresponding coverage probabilities are derived based on both the Fisher and the observed information matrices. The approximate highest probability density credible interval is constructed by using Monte Carlo method. Monte Carlo simulations are performed to compare the performances of the proposed reliability estimators. A real data set is also analyzed for an illustration of the findings.

Kilauea summit overflows: Their ages and distribution in the Puna District, Hawai'i

USGS Publications Warehouse

Clague, D.A.; Hagstrum, J.T.; Beeson, M.H.; Champion, D.E.

1999-01-01

The tube-fed pahoehoe lava flows covering much of the northeast flank of Kilauea Volcano are named the 'Aila'au flows. Their eruption age, based on published and six new radiocarbon dates, is approximately AD 1445. The flows have distinctive paleomagnetic directions with steep inclinations (40??-50??) and easterly declinations (0??-10??E). The lava was transported ~40 km from the vent to the coast in long, large-diameter lava tubes; the longest tube (Kazumura Cave) reaches from near the summit to within several kilometers of the coast near Kaloli Point. The estimated volume of the 'Aila'au flow field is 5.2 ?? 0.8 km3, and the eruption that formed it probably lasted for approximately 50 years. Summit overflows from Kilauea may have been nearly continuous between approximately AD 1290 and 1470, during which time a series of shields formed at and around the summit. The 'Aila'au shield was either the youngest or the next to youngest in this series of shields. Site-mean paleomagnetic directions for lava flows underlying the 'Aila'au flows form only six groups. These older pahoehoe flows range in age from 2750 to 2200 years. Lava flows from most of these summit eruptions also reached the coast, but none appears as extensive as the 'Aila'au flow field. The chemistry of the melts erupted during each of these summit overflow events is remarkably similar, averaging approximately 6.3 wt.% MgO near the coast and 6.8 wt.% MgO near the summit. The present-day caldera probably formed more recently than the eruption that formed the 'Aila'au flows (estimated termination ca. AD 1470). The earliest explosive eruptions that formed the Keanakako'i Ash, which is stratigraphically above the 'Aila'au flows, cannot be older than this age.

Objectified quantification of uncertainties in Bayesian atmospheric inversions

NASA Astrophysics Data System (ADS)

Berchet, A.; Pison, I.; Chevallier, F.; Bousquet, P.; Bonne, J.-L.; Paris, J.-D.

2015-05-01

Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. When data pieces are sparse, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results to enhance the classical Bayesian inversion framework through a marginalization on a large set of plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurrence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is not explicitly describable. As a consequence, we carry out a Monte Carlo sampling based on an approximation of the probability of occurrence of the error distributions. This approximation is deduced from the well-tested method of the maximum likelihood estimation. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly accounts for the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of an emission aggregation pattern and of a sampling protocol in order to reduce the computation cost. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the mesoscale with virtual observations on a realistic network in Eurasia. Observing system simulation experiments are carried out with different transport patterns, flux distributions and total prior amounts of emitted methane. The method proves to consistently reproduce the known "truth" in most cases, with satisfactory tolerance intervals. Additionally, the method explicitly provides influence scores and posterior correlation matrices. An in-depth interpretation of the inversion results is then possible. The more objective quantification of the influence of the observations on the fluxes proposed here allows us to evaluate the impact of the observation network on the characterization of the surface fluxes. The explicit correlations between emission aggregates reveal the mis-separated regions, hence the typical temporal and spatial scales the inversion can analyse. These scales are consistent with the chosen aggregation patterns.

Microgrid Optimal Scheduling With Chance-Constrained Islanding Capability

DOE PAGES

Liu, Guodong; Starke, Michael R.; Xiao, B.; ...

2017-01-13

To facilitate the integration of variable renewable generation and improve the resilience of electricity sup-ply in a microgrid, this paper proposes an optimal scheduling strategy for microgrid operation considering constraints of islanding capability. A new concept, probability of successful islanding (PSI), indicating the probability that a microgrid maintains enough spinning reserve (both up and down) to meet local demand and accommodate local renewable generation after instantaneously islanding from the main grid, is developed. The PSI is formulated as mixed-integer linear program using multi-interval approximation taking into account the probability distributions of forecast errors of wind, PV and load. With themore » goal of minimizing the total operating cost while preserving user specified PSI, a chance-constrained optimization problem is formulated for the optimal scheduling of mirogrids and solved by mixed integer linear programming (MILP). Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator and a battery demonstrate the effectiveness of the proposed scheduling strategy. Lastly, we verify the relationship between PSI and various factors.« less

Log-Linear Models for Gene Association

PubMed Central

Hu, Jianhua; Joshi, Adarsh; Johnson, Valen E.

2009-01-01

We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data that have been reduced to contingency tables using ranks of observations within subjects, and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on Ewens’ sampling distribution is used to restrict the number of interacting components assigned high posterior probability, and the calculation of posterior model probabilities is expedited by approximations based on the likelihood ratio statistic. Simulation studies are used to evaluate the efficiency of the resulting algorithm for known interaction structures. Finally, the algorithm is validated in a microarray study for which it was possible to obtain biological confirmation of detected interactions. PMID:19655032

Delay-induced stochastic bifurcations in a bistable system under white noise

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

Sun, Zhongkui, E-mail: sunzk@nwpu.edu.cn; Fu, Jin; Xu, Wei

2015-08-15

In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochasticmore » P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.« less

Probabilistic vs. non-probabilistic approaches to the neurobiology of perceptual decision-making

PubMed Central

Drugowitsch, Jan; Pouget, Alexandre

2012-01-01

Optimal binary perceptual decision making requires accumulation of evidence in the form of a probability distribution that specifies the probability of the choices being correct given the evidence so far. Reward rates can then be maximized by stopping the accumulation when the confidence about either option reaches a threshold. Behavioral and neuronal evidence suggests that humans and animals follow such a probabilitistic decision strategy, although its neural implementation has yet to be fully characterized. Here we show that that diffusion decision models and attractor network models provide an approximation to the optimal strategy only under certain circumstances. In particular, neither model type is sufficiently flexible to encode the reliability of both the momentary and the accumulated evidence, which is a pre-requisite to accumulate evidence of time-varying reliability. Probabilistic population codes, in contrast, can encode these quantities and, as a consequence, have the potential to implement the optimal strategy accurately. PMID:22884815

Uncertainty and Surprise: Ideas from the Open Discussion

NASA Astrophysics Data System (ADS)

Jordan, Michelle E.

Approximately one hundred participants met for three days at a conference entitled "Uncertainty and Surprise: Questions on Working with the Unexpected and Unknowable." There were a diversity of conference participants ranging from researchers in the natural sciences and researchers in the social sciences (business professors, physicists, ethnographers, nursing school deans) to practitioners and executives in public policy and management (business owners, health care managers, high tech executives), all of whom had varying levels of experience and expertise in dealing with uncertainty and surprise. One group held the traditional, statistical view that uncertainty comes from variance and events that are described by usually unimodal probability law. A second group was comfortable on the one hand with phase diagrams and the phase transitions that come from systems with multi-modal distributions, and on the other hand, with deterministic chaos. A third group was comfortable with the emergent events from evolutionary processes that may not have any probability laws at all.

Human dynamics scaling characteristics for aerial inbound logistics operation

NASA Astrophysics Data System (ADS)

Wang, Qing; Guo, Jin-Li

2010-05-01

In recent years, the study of power-law scaling characteristics of real-life networks has attracted much interest from scholars; it deviates from the Poisson process. In this paper, we take the whole process of aerial inbound operation in a logistics company as the empirical object. The main aim of this work is to study the statistical scaling characteristics of the task-restricted work patterns. We found that the statistical variables have the scaling characteristics of unimodal distribution with a power-law tail in five statistical distributions - that is to say, there obviously exists a peak in each distribution, the shape of the left part closes to a Poisson distribution, and the right part has a heavy-tailed scaling statistics. Furthermore, to our surprise, there is only one distribution where the right parts can be approximated by the power-law form with exponent α=1.50. Others are bigger than 1.50 (three of four are about 2.50, one of four is about 3.00). We then obtain two inferences based on these empirical results: first, the human behaviors probably both close to the Poisson statistics and power-law distributions on certain levels, and the human-computer interaction behaviors may be the most common in the logistics operational areas, even in the whole task-restricted work pattern areas. Second, the hypothesis in Vázquez et al. (2006) [A. Vázquez, J. G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási. Modeling burst and heavy tails in human dynamics, Phys. Rev. E 73 (2006) 036127] is probably not sufficient; it claimed that human dynamics can be classified as two discrete university classes. There may be a new human dynamics mechanism that is different from the classical Barabási models.

Approximating Integrals Using Probability

ERIC Educational Resources Information Center

Maruszewski, Richard F., Jr.; Caudle, Kyle A.

2005-01-01

As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…

Series approximation to probability densities

NASA Astrophysics Data System (ADS)

Cohen, L.

2018-04-01

One of the historical and fundamental uses of the Edgeworth and Gram-Charlier series is to "correct" a Gaussian density when it is determined that the probability density under consideration has moments that do not correspond to the Gaussian [5, 6]. There is a fundamental difficulty with these methods in that if the series are truncated, then the resulting approximate density is not manifestly positive. The aim of this paper is to attempt to expand a probability density so that if it is truncated it will still be manifestly positive.

Approximation of the ruin probability using the scaled Laplace transform inversion

PubMed Central

Mnatsakanov, Robert M.; Sarkisian, Khachatur; Hakobyan, Artak

2015-01-01

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen–Weideman–Schmelzer and maximum entropy methods are presented via a simulation study. PMID:26752796

Atmospheric Quantum Channels with Weak and Strong Turbulence.

PubMed

Vasylyev, D; Semenov, A A; Vogel, W

2016-08-26

The free-space transfer of high-fidelity optical signals between remote locations has many applications, including both classical and quantum communication, precision navigation, clock synchronization, etc. The physical processes that contribute to signal fading and loss need to be carefully analyzed in the theory of light propagation through the atmospheric turbulence. Here we derive the probability distribution for the atmospheric transmittance including beam wandering, beam shape deformation, and beam-broadening effects. Our model, referred to as the elliptic beam approximation, applies to weak, weak-to-moderate, and strong turbulence and hence to the most important regimes in atmospheric communication scenarios.

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

NASA Astrophysics Data System (ADS)

Zverev, V. V.; Rubinstein, B. Ya.

1991-04-01

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.

Scale matters

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

Margolin, L. G.

The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.

Scale matters

DOE PAGES

Margolin, L. G.

2018-03-19

The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.

Minimal entropy probability paths between genome families.

PubMed

Ahlbrandt, Calvin; Benson, Gary; Casey, William

2004-05-01

We develop a metric for probability distributions with applications to biological sequence analysis. Our distance metric is obtained by minimizing a functional defined on the class of paths over probability measures on N categories. The underlying mathematical theory is connected to a constrained problem in the calculus of variations. The solution presented is a numerical solution, which approximates the true solution in a set of cases called rich paths where none of the components of the path is zero. The functional to be minimized is motivated by entropy considerations, reflecting the idea that nature might efficiently carry out mutations of genome sequences in such a way that the increase in entropy involved in transformation is as small as possible. We characterize sequences by frequency profiles or probability vectors, in the case of DNA where N is 4 and the components of the probability vector are the frequency of occurrence of each of the bases A, C, G and T. Given two probability vectors a and b, we define a distance function based as the infimum of path integrals of the entropy function H( p) over all admissible paths p(t), 0 < or = t< or =1, with p(t) a probability vector such that p(0)=a and p(1)=b. If the probability paths p(t) are parameterized as y(s) in terms of arc length s and the optimal path is smooth with arc length L, then smooth and "rich" optimal probability paths may be numerically estimated by a hybrid method of iterating Newton's method on solutions of a two point boundary value problem, with unknown distance L between the abscissas, for the Euler-Lagrange equations resulting from a multiplier rule for the constrained optimization problem together with linear regression to improve the arc length estimate L. Matlab code for these numerical methods is provided which works only for "rich" optimal probability vectors. These methods motivate a definition of an elementary distance function which is easier and faster to calculate, works on non-rich vectors, does not involve variational theory and does not involve differential equations, but is a better approximation of the minimal entropy path distance than the distance //b-a//(2). We compute minimal entropy distance matrices for examples of DNA myostatin genes and amino-acid sequences across several species. Output tree dendograms for our minimal entropy metric are compared with dendograms based on BLAST and BLAST identity scores.

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

NASA Astrophysics Data System (ADS)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Emission Depth Distribution Function of Al 2s Photoelectrons in Al2O3

NASA Astrophysics Data System (ADS)

Hucek, S.; Zemek, J.; Jablonski, A.; Tilinin, I. S.

The escape probability of Al 2s photoelectrons leaving an aluminum oxide sample (Al2O3) has been studied as a function of depth of origin. It has been found that the escape probability (the so-called emission depth distribution function - DDF) depends strongly on the photoelectron emission direction with respect to that of the incident X-ray beam. In particular, in the emission direction close to that of photon propagation, the DDF differs substantially from the simple Beer-Lambert law and exhibits a nonmonotonic behavior with a maximum in the near-surface region at a depth of about 10 Å. Experimental results are in good agreement with theoretical predictions based on Monte Carlo simulations of the electron transport and with analytical solution of the linearized Boltzmann kinetic equation with appropriate boundary conditions. Both theoretical approaches take into account multiple elastic scattering of photoelectrons on their way out of the sample. It is shown that the commonly used straight line approximation (SLA), which neglects elastic scattering effects, fails to describe adequately experimental data at emission directions close to minima of the differential photoelectric cross section.

3D-modelling of radon-induced cellular radiobiological effects in bronchial airway bifurcations: direct versus bystander effects.

PubMed

Szőke, István; Farkas, Arpád; Balásházy, Imre; Hofmann, Werner; Madas, Balázs G; Szőke, Réka

2012-06-01

The primary objective of this paper was to investigate the distribution of radiation doses and the related biological responses in cells of a central airway bifurcation of the human lung of a hypothetical worker of the New Mexico uranium mines during approximately 12 hours of exposure to short-lived radon progenies. State-of-the-art computational modelling techniques were applied to simulate the relevant biophysical and biological processes in a central human airway bifurcation. The non-uniform deposition pattern of inhaled radon daughters caused a non-uniform distribution of energy deposition among cells, and of related cell inactivation and cell transformation probabilities. When damage propagation via bystander signalling was assessed, it produced more cell killing and cell transformation events than did direct effects. If bystander signalling was considered, variations of the average probabilities of cell killing and cell transformation were supra-linear over time. Our results are very sensitive to the radiobiological parameters, derived from in vitro experiments (e.g., range of bystander signalling), applied in this work and suggest that these parameters may not be directly applicable to realistic three-dimensional (3D) epithelium models.

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.

Multiple transmitter performance with appropriate amplitude modulation for free-space optical communication.

PubMed

Tellez, Jason A; Schmidt, Jason D

2011-08-20

The propagation of a free-space optical communications signal through atmospheric turbulence experiences random fluctuations in intensity, including signal fades, which negatively impact the performance of the communications link. The gamma-gamma probability density function is commonly used to model the scintillation of a single beam. One proposed method to reduce the occurrence of scintillation-induced fades at the receiver plane involves the use of multiple beams propagating through independent paths, resulting in a sum of independent gamma-gamma random variables. Recently an analytical model for the probability distribution of irradiance from the sum of multiple independent beams was developed. Because truly independent beams are practically impossible to create, we present here a more general but approximate model for the distribution of beams traveling through partially correlated paths. This model compares favorably with wave-optics simulations and highlights the reduced scintillation as the number of transmitted beams is increased. Additionally, a pulse-position modulation scheme is used to reduce the impact of signal fades when they occur. Analytical and simulated results showed significantly improved performance when compared to fixed threshold on/off keying. © 2011 Optical Society of America

Dynamical Response of Networks Under External Perturbations: Exact Results

NASA Astrophysics Data System (ADS)

Chinellato, David D.; Epstein, Irving R.; Braha, Dan; Bar-Yam, Yaneer; de Aguiar, Marcus A. M.

2015-04-01

We give exact statistical distributions for the dynamic response of influence networks subjected to external perturbations. We consider networks whose nodes have two internal states labeled 0 and 1. We let nodes be frozen in state 0, in state 1, and the remaining nodes change by adopting the state of a connected node with a fixed probability per time step. The frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes. Analytically extending and to be smaller than 1 enables modeling the case of weak coupling. We solve the dynamical equations exactly for fully connected networks, obtaining the equilibrium distribution, transition probabilities between any two states and the characteristic time to equilibration. Our exact results are excellent approximations for other topologies, including random, regular lattice, scale-free and small world networks, when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment. This model can describe a variety of complex systems, from magnetic spins to social networks to population genetics, and was recently applied as a framework for early warning signals for real-world self-organized economic market crises.

Autoregressive processes with exponentially decaying probability distribution functions: applications to daily variations of a stock market index.

PubMed

Porto, Markus; Roman, H Eduardo

2002-04-01

We consider autoregressive conditional heteroskedasticity (ARCH) processes in which the variance sigma(2)(y) depends linearly on the absolute value of the random variable y as sigma(2)(y) = a+b absolute value of y. While for the standard model, where sigma(2)(y) = a + b y(2), the corresponding probability distribution function (PDF) P(y) decays as a power law for absolute value of y-->infinity, in the linear case it decays exponentially as P(y) approximately exp(-alpha absolute value of y), with alpha = 2/b. We extend these results to the more general case sigma(2)(y) = a+b absolute value of y(q), with 0 < q < 2. We find stretched exponential decay for 1 < q < 2 and stretched Gaussian behavior for 0 < q < 1. As an application, we consider the case q=1 as our starting scheme for modeling the PDF of daily (logarithmic) variations in the Dow Jones stock market index. When the history of the ARCH process is taken into account, the resulting PDF becomes a stretched exponential even for q = 1, with a stretched exponent beta = 2/3, in a much better agreement with the empirical data.

Orders of Magnitude Extension of the Effective Dynamic Range of TDC-Based TOFMS Data Through Maximum Likelihood Estimation

NASA Astrophysics Data System (ADS)

Ipsen, Andreas; Ebbels, Timothy M. D.

2014-10-01

In a recent article, we derived a probability distribution that was shown to closely approximate that of the data produced by liquid chromatography time-of-flight mass spectrometry (LC/TOFMS) instruments employing time-to-digital converters (TDCs) as part of their detection system. The approach of formulating detailed and highly accurate mathematical models of LC/MS data via probability distributions that are parameterized by quantities of analytical interest does not appear to have been fully explored before. However, we believe it could lead to a statistically rigorous framework for addressing many of the data analytical problems that arise in LC/MS studies. In this article, we present new procedures for correcting for TDC saturation using such an approach and demonstrate that there is potential for significant improvements in the effective dynamic range of TDC-based mass spectrometers, which could make them much more competitive with the alternative analog-to-digital converters (ADCs). The degree of improvement depends on our ability to generate mass and chromatographic peaks that conform to known mathematical functions and our ability to accurately describe the state of the detector dead time—tasks that may be best addressed through engineering efforts.

Distribution of the largest aftershocks in branching models of triggered seismicity: theory of the universal Båth law.

PubMed

Saichev, A; Sornette, D

2005-05-01

Using the epidemic-type aftershock sequence (ETAS) branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all generations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Båth's law. Our theory shows that Båth's law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars +/- 0.1 for Båth's constant value around 1.2, our exact analytical treatment of Båth's law provides new constraints on the productivity exponent alpha and the branching ratio n: 0.9 approximately < alpha < or =1. We propose a method for measuring alpha based on the predicted renormalization of the Gutenberg-Richter distribution of the magnitudes of the largest aftershock. We also introduce the "second Båth law for foreshocks:" the probability that a main earthquake turns out to be the foreshock does not depend on its magnitude rho.

Soft context clustering for F0 modeling in HMM-based speech synthesis

NASA Astrophysics Data System (ADS)

Khorram, Soheil; Sameti, Hossein; King, Simon

2015-12-01

This paper proposes the use of a new binary decision tree, which we call a soft decision tree, to improve generalization performance compared to the conventional `hard' decision tree method that is used to cluster context-dependent model parameters in statistical parametric speech synthesis. We apply the method to improve the modeling of fundamental frequency, which is an important factor in synthesizing natural-sounding high-quality speech. Conventionally, hard decision tree-clustered hidden Markov models (HMMs) are used, in which each model parameter is assigned to a single leaf node. However, this `divide-and-conquer' approach leads to data sparsity, with the consequence that it suffers from poor generalization, meaning that it is unable to accurately predict parameters for models of unseen contexts: the hard decision tree is a weak function approximator. To alleviate this, we propose the soft decision tree, which is a binary decision tree with soft decisions at the internal nodes. In this soft clustering method, internal nodes select both their children with certain membership degrees; therefore, each node can be viewed as a fuzzy set with a context-dependent membership function. The soft decision tree improves model generalization and provides a superior function approximator because it is able to assign each context to several overlapped leaves. In order to use such a soft decision tree to predict the parameters of the HMM output probability distribution, we derive the smoothest (maximum entropy) distribution which captures all partial first-order moments and a global second-order moment of the training samples. Employing such a soft decision tree architecture with maximum entropy distributions, a novel speech synthesis system is trained using maximum likelihood (ML) parameter re-estimation and synthesis is achieved via maximum output probability parameter generation. In addition, a soft decision tree construction algorithm optimizing a log-likelihood measure is developed. Both subjective and objective evaluations were conducted and indicate a considerable improvement over the conventional method.

Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model.

PubMed

Fasoli, Diego; Cattani, Anna; Panzeri, Stefano

2018-05-01

Despite their biological plausibility, neural network models with asymmetric weights are rarely solved analytically, and closed-form solutions are available only in some limiting cases or in some mean-field approximations. We found exact analytical solutions of an asymmetric spin model of neural networks with arbitrary size without resorting to any approximation, and we comprehensively studied its dynamical and statistical properties. The network had discrete time evolution equations and binary firing rates, and it could be driven by noise with any distribution. We found analytical expressions of the conditional and stationary joint probability distributions of the membrane potentials and the firing rates. By manipulating the conditional probability distribution of the firing rates, we extend to stochastic networks the associating learning rule previously introduced by Personnaz and coworkers. The new learning rule allowed the safe storage, under the presence of noise, of point and cyclic attractors, with useful implications for content-addressable memories. Furthermore, we studied the bifurcation structure of the network dynamics in the zero-noise limit. We analytically derived examples of the codimension 1 and codimension 2 bifurcation diagrams of the network, which describe how the neuronal dynamics changes with the external stimuli. This showed that the network may undergo transitions among multistable regimes, oscillatory behavior elicited by asymmetric synaptic connections, and various forms of spontaneous symmetry breaking. We also calculated analytically groupwise correlations of neural activity in the network in the stationary regime. This revealed neuronal regimes where, statistically, the membrane potentials and the firing rates are either synchronous or asynchronous. Our results are valid for networks with any number of neurons, although our equations can be realistically solved only for small networks. For completeness, we also derived the network equations in the thermodynamic limit of infinite network size and we analytically studied their local bifurcations. All the analytical results were extensively validated by numerical simulations.

A novel multitarget model of radiation-induced cell killing based on the Gaussian distribution.

PubMed

Zhao, Lei; Mi, Dong; Sun, Yeqing

2017-05-07

The multitarget version of the traditional target theory based on the Poisson distribution is still used to describe the dose-survival curves of cells after ionizing radiation in radiobiology and radiotherapy. However, noting that the usual ionizing radiation damage is the result of two sequential stochastic processes, the probability distribution of the damage number per cell should follow a compound Poisson distribution, like e.g. Neyman's distribution of type A (N. A.). In consideration of that the Gaussian distribution can be considered as the approximation of the N. A. in the case of high flux, a multitarget model based on the Gaussian distribution is proposed to describe the cell inactivation effects in low linear energy transfer (LET) radiation with high dose-rate. Theoretical analysis and experimental data fitting indicate that the present theory is superior to the traditional multitarget model and similar to the Linear - Quadratic (LQ) model in describing the biological effects of low-LET radiation with high dose-rate, and the parameter ratio in the present model can be used as an alternative indicator to reflect the radiation damage and radiosensitivity of the cells. Copyright © 2017 Elsevier Ltd. All rights reserved.

Fossil preservation and the stratigraphic ranges of taxa

NASA Technical Reports Server (NTRS)

Foote, M.; Raup, D. M.

1996-01-01

The incompleteness of the fossil record hinders the inference of evolutionary rates and patterns. Here, we derive relationships among true taxonomic durations, preservation probability, and observed taxonomic ranges. We use these relationships to estimate original distributions of taxonomic durations, preservation probability, and completeness (proportion of taxa preserved), given only the observed ranges. No data on occurrences within the ranges of taxa are required. When preservation is random and the original distribution of durations is exponential, the inference of durations, preservability, and completeness is exact. However, reasonable approximations are possible given non-exponential duration distributions and temporal and taxonomic variation in preservability. Thus, the approaches we describe have great potential in studies of taphonomy, evolutionary rates and patterns, and genealogy. Analyses of Upper Cambrian-Lower Ordovician trilobite species, Paleozoic crinoid genera, Jurassic bivalve species, and Cenozoic mammal species yield the following results: (1) The preservation probability inferred from stratigraphic ranges alone agrees with that inferred from the analysis of stratigraphic gaps when data on the latter are available. (2) Whereas median durations based on simple tabulations of observed ranges are biased by stratigraphic resolution, our estimates of median duration, extinction rate, and completeness are not biased.(3) The shorter geologic ranges of mammalian species relative to those of bivalves cannot be attributed to a difference in preservation potential. However, we cannot rule out the contribution of taxonomic practice to this difference. (4) In the groups studied, completeness (proportion of species [trilobites, bivalves, mammals] or genera [crinoids] preserved) ranges from 60% to 90%. The higher estimates of completeness at smaller geographic scales support previous suggestions that the incompleteness of the fossil record reflects loss of fossiliferous rock more than failure of species to enter the fossil record in the first place.

A simulator for evaluating methods for the detection of lesion-deficit associations

NASA Technical Reports Server (NTRS)

Megalooikonomou, V.; Davatzikos, C.; Herskovits, E. H.

2000-01-01

Although much has been learned about the functional organization of the human brain through lesion-deficit analysis, the variety of statistical and image-processing methods developed for this purpose precludes a closed-form analysis of the statistical power of these systems. Therefore, we developed a lesion-deficit simulator (LDS), which generates artificial subjects, each of which consists of a set of functional deficits, and a brain image with lesions; the deficits and lesions conform to predefined distributions. We used probability distributions to model the number, sizes, and spatial distribution of lesions, to model the structure-function associations, and to model registration error. We used the LDS to evaluate, as examples, the effects of the complexities and strengths of lesion-deficit associations, and of registration error, on the power of lesion-deficit analysis. We measured the numbers of recovered associations from these simulated data, as a function of the number of subjects analyzed, the strengths and number of associations in the statistical model, the number of structures associated with a particular function, and the prior probabilities of structures being abnormal. The number of subjects required to recover the simulated lesion-deficit associations was found to have an inverse relationship to the strength of associations, and to the smallest probability in the structure-function model. The number of structures associated with a particular function (i.e., the complexity of associations) had a much greater effect on the performance of the analysis method than did the total number of associations. We also found that registration error of 5 mm or less reduces the number of associations discovered by approximately 13% compared to perfect registration. The LDS provides a flexible framework for evaluating many aspects of lesion-deficit analysis.

Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions.

PubMed

Dinov, Ivo D; Siegrist, Kyle; Pearl, Dennis K; Kalinin, Alexandr; Christou, Nicolas

2016-06-01

Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, the Distributome , which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the learning assessment protocols.

Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions

PubMed Central

Dinov, Ivo D.; Siegrist, Kyle; Pearl, Dennis K.; Kalinin, Alexandr; Christou, Nicolas

2015-01-01

Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, the Distributome, which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the learning assessment protocols. PMID:27158191

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: I. Theoretical study

NASA Astrophysics Data System (ADS)

Bourlier, C.; Berginc, G.

2004-07-01

In this paper the first- and second-order Kirchhoff approximation is applied to study the backscattering enhancement phenomenon, which appears when the surface rms slope is greater than 0.5. The formulation is reduced to the geometric optics approximation in which the second-order illumination function is taken into account. This study is developed for a two-dimensional (2D) anisotropic stationary rough dielectric surface and for any surface slope and height distributions assumed to be statistically even. Using the Weyl representation of the Green function (which introduces an absolute value over the surface elevation in the phase term), the incoherent scattering coefficient under the stationary phase assumption is expressed as the sum of three terms. The incoherent scattering coefficient then requires the numerical computation of a ten- dimensional integral. To reduce the number of numerical integrations, the geometric optics approximation is applied, which assumes that the correlation between two adjacent points is very strong. The model is then proportional to two surface slope probabilities, for which the slopes would specularly reflect the beams in the double scattering process. In addition, the slope distributions are related with each other by a propagating function, which accounts for the second-order illumination function. The companion paper is devoted to the simulation of this model and comparisons with an 'exact' numerical method.

Probabilistic inference using linear Gaussian importance sampling for hybrid Bayesian networks

NASA Astrophysics Data System (ADS)

Sun, Wei; Chang, K. C.

2005-05-01

Probabilistic inference for Bayesian networks is in general NP-hard using either exact algorithms or approximate methods. However, for very complex networks, only the approximate methods such as stochastic sampling could be used to provide a solution given any time constraint. There are several simulation methods currently available. They include logic sampling (the first proposed stochastic method for Bayesian networks, the likelihood weighting algorithm) the most commonly used simulation method because of its simplicity and efficiency, the Markov blanket scoring method, and the importance sampling algorithm. In this paper, we first briefly review and compare these available simulation methods, then we propose an improved importance sampling algorithm called linear Gaussian importance sampling algorithm for general hybrid model (LGIS). LGIS is aimed for hybrid Bayesian networks consisting of both discrete and continuous random variables with arbitrary distributions. It uses linear function and Gaussian additive noise to approximate the true conditional probability distribution for continuous variable given both its parents and evidence in a Bayesian network. One of the most important features of the newly developed method is that it can adaptively learn the optimal important function from the previous samples. We test the inference performance of LGIS using a 16-node linear Gaussian model and a 6-node general hybrid model. The performance comparison with other well-known methods such as Junction tree (JT) and likelihood weighting (LW) shows that LGIS-GHM is very promising.

The Chandra M10l Megasecond: Diffuse Emission

NASA Technical Reports Server (NTRS)

Kuntz, K. D.; Snowden, S. L.

2009-01-01

Because MIOl is nearly face-on, it provides an excellent laboratory in which to study the distribution of X-ray emitting gas in a typical late-type spiral galaxy. We obtained a Chandra observation with a cumulative exposure of roughly 1 Ms to study the diffuse X-ray emission in MlOl. The bulk of the X-ray emission is correlated with the star formation traced by the FUV emission. The global FUV/Xray correlation is non-linear (the X-ray surface brightness is roughly proportional to the square root of the FUV surface brightness) and the small-scale correlation is poor, probably due to the delay between the FUV emission and the X-ray production ill star-forming regions. The X-ray emission contains only minor contributions from unresolved stars (approximates less than 3%), unresolved X-ray point sources (approximates less than 4%), and individual supernova remnants (approximates 3%). The global spectrum of the diffuse emission can be reasonably well fitted with a three component thermal model, but the fitted temperatures are not unique; many distributions of emission measure can produce the same temperatures when observed with the current CCD energy resolution. The spectrum of the diffuse emission depends on the environment; regions with higher X-ray surface brightnesses have relatively stronger hard components, but there is no significant evidence that the temperatures of the emitting components increase with surface brightness.

Random Partition Distribution Indexed by Pairwise Information

PubMed Central

Dahl, David B.; Day, Ryan; Tsai, Jerry W.

2017-01-01

We propose a random partition distribution indexed by pairwise similarity information such that partitions compatible with the similarities are given more probability. The use of pairwise similarities, in the form of distances, is common in some clustering algorithms (e.g., hierarchical clustering), but we show how to use this type of information to define a prior partition distribution for flexible Bayesian modeling. A defining feature of the distribution is that it allocates probability among partitions within a given number of subsets, but it does not shift probability among sets of partitions with different numbers of subsets. Our distribution places more probability on partitions that group similar items yet keeps the total probability of partitions with a given number of subsets constant. The distribution of the number of subsets (and its moments) is available in closed-form and is not a function of the similarities. Our formulation has an explicit probability mass function (with a tractable normalizing constant) so the full suite of MCMC methods may be used for posterior inference. We compare our distribution with several existing partition distributions, showing that our formulation has attractive properties. We provide three demonstrations to highlight the features and relative performance of our distribution. PMID:29276318

Master equations and the theory of stochastic path integrals

NASA Astrophysics Data System (ADS)

Weber, Markus F.; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

On a Solar Origin for the Cosmogenic Nuclide Event of 775 A.D.

NASA Technical Reports Server (NTRS)

Cliver, E. W.; Tylka, A. J.; Dietrich, W. F.; Ling, A. G.

2014-01-01

We explore requirements for a solar particle event (SPE) and flare capable of producing the cosmogenic nuclide event of 775 A.D., and review solar circumstances at that time. A solar source for 775 would require a greater than 1 GV spectrum approximately 45 times stronger than that of the intense high-energy SPE of 1956 February 23. This implies a greater than 30 MeV proton fluence (F(sub 30)) of approximately 8 × 10(exp 10) proton cm(exp -2), approximately 10 times larger than that of the strongest 3 month interval of SPE activity in the modern era. This inferred F(sub 30) value for the 775 SPE is inconsistent with the occurrence probability distribution for greater than 30 MeV solar proton events. The best guess value for the soft X-ray classification (total energy) of an associated flare is approximately X230 (approximately 9 × 10(exp 33) erg). For comparison, the flares on 2003 November 4 and 1859 September 1 had observed/inferred values of approximately X35 (approximately 10(exp 33) erg) and approximately X45 (approximately 2 × 10(exp 33) erg), respectively. The estimated size of the source active region for a approximately 10(exp 34) erg flare is approximately 2.5 times that of the largest region yet recorded. The 775 event occurred during a period of relatively low solar activity, with a peak smoothed amplitude about half that of the second half of the 20th century. The approximately 1945-1995 interval, the most active of the last approximately 2000 yr, failed to witness a SPE comparable to that required for the proposed solar event in 775. These considerations challenge a recent suggestion that the 775 event is likely of solar origin.

Using probabilistic modeling to evaluate human exposure to organotin in drinking water transported by polyvinyl chloride pipe.

PubMed

Fristachi, Anthony; Xu, Ying; Rice, Glenn; Impellitteri, Christopher A; Carlson-Lynch, Heather; Little, John C

2009-11-01

The leaching of organotin (OT) heat stabilizers from polyvinyl chloride (PVC) pipes used in residential drinking water systems may affect the quality of drinking water. These OTs, principally mono- and di-substituted species of butyltins and methyltins, are a potential health concern because they belong to a broad class of compounds that may be immune, nervous, and reproductive system toxicants. In this article, we develop probability distributions of U.S. population exposures to mixtures of OTs encountered in drinking water transported by PVC pipes. We employed a family of mathematical models to estimate OT leaching rates from PVC pipe as a function of both surface area and time. We then integrated the distribution of estimated leaching rates into an exposure model that estimated the probability distribution of OT concentrations in tap waters and the resulting potential human OT exposures via tap water consumption. Our study results suggest that human OT exposures through tap water consumption are likely to be considerably lower than the World Health Organization (WHO) "safe" long-term concentration in drinking water (150 microg/L) for dibutyltin (DBT)--the most toxic of the OT considered in this article. The 90th percentile average daily dose (ADD) estimate of 0.034 +/- 2.92 x 10(-4)microg/kg day is approximately 120 times lower than the WHO-based ADD for DBT (4.2 microg/kg day).

A brief introduction to probability.

PubMed

Di Paola, Gioacchino; Bertani, Alessandro; De Monte, Lavinia; Tuzzolino, Fabio

2018-02-01

The theory of probability has been debated for centuries: back in 1600, French mathematics used the rules of probability to place and win bets. Subsequently, the knowledge of probability has significantly evolved and is now an essential tool for statistics. In this paper, the basic theoretical principles of probability will be reviewed, with the aim of facilitating the comprehension of statistical inference. After a brief general introduction on probability, we will review the concept of the "probability distribution" that is a function providing the probabilities of occurrence of different possible outcomes of a categorical or continuous variable. Specific attention will be focused on normal distribution that is the most relevant distribution applied to statistical analysis.

Singular solution of the Feller diffusion equation via a spectral decomposition.

PubMed

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

Singular solution of the Feller diffusion equation via a spectral decomposition

NASA Astrophysics Data System (ADS)

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

Planar measurements of soot volume fraction and OH in a JP-8 pool fire

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

Henriksen, Tara L.; Ring, Terry A.; Eddings, Eric G.

2009-07-15

The simultaneous measurement of soot volume fraction by laser induced incandescence (LII) and qualitative imaging of OH by laser induced fluorescence (LIF) was performed in a JP-8 pool fire contained in a 152 mm diameter pan. Line of sight extinction was used to calibrate the LII system in a laminar flame, and to provide an independent method of measuring average soot volume fraction in the turbulent flame. The presence of soot in the turbulent flame was found to be approximately 50% probable, resulting in high levels of optical extinction, which increased slightly through the flame from approximately 30% near themore » base, to approximately 50% at the tip. This high soot loading pushes both techniques toward their detection limit. Nevertheless, useful accuracy was obtained, with the LII measurement of apparent extinction in the turbulent flame being approximately 21% lower than a direct measurement, consistent with the influence of signal trapping. The axial and radial distributions of soot volume fraction are presented, along with PDFs of volume fraction, and new insight into the behavior of soot sheets in pool fires are sought from the simultaneous measurements of OH and LII. (author)« less

[Study on the matching of the shade between beverage and modifying porcelain shade guide].

PubMed

Yao, Jiang-wu; Li, Shui-gen; Lin, Jin-ying

2007-10-01

To evaluate the matching of the shade between beverage and modifying porcelain shade guide according to Munsell color order system, thus to provide the reference basis for selecting modifying porcelain to mimic the stain of natural tooth by technician. The shade of Vita Akzent, Vita Interno, Shofu Vintage & Unibond and Noritake Super Porcelain EX-3 shade tabs as well as 15 kinds of beverage were measured according to Munsell color order system on Color-Eye 7000A spectrophotometer. The difference of the frequency of approximate hue, value, and chroma between shade tabs and beverage were compared by calculating the Fisher exact probabilities. The frequency of approximate hue between 4 kinds of shade tabs and 15 kinds of bev-erage was significant different (P<0.05), while the frequency of approximate value, and chroma was not significant different (P>0.05). Except the hue, the color distribution of 4 kinds of shade tabs was similar to that of 15 kinds of beverage. But the color of beverage also can be approximately matched by any kind of modifying porcelain by mixing porcelain powder of appropriate hue, value, and chroma.

Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions.

PubMed

Yura, Harold T; Hanson, Steen G

2012-04-01

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative examples with relevance for optics are given.

The global impact distribution of Near-Earth objects

NASA Astrophysics Data System (ADS)

Rumpf, Clemens; Lewis, Hugh G.; Atkinson, Peter M.

2016-02-01

Asteroids that could collide with the Earth are listed on the publicly available Near-Earth object (NEO) hazard web sites maintained by the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA). The impact probability distribution of 69 potentially threatening NEOs from these lists that produce 261 dynamically distinct impact instances, or Virtual Impactors (VIs), were calculated using the Asteroid Risk Mitigation and Optimization Research (ARMOR) tool in conjunction with OrbFit. ARMOR projected the impact probability of each VI onto the surface of the Earth as a spatial probability distribution. The projection considers orbit solution accuracy and the global impact probability. The method of ARMOR is introduced and the tool is validated against two asteroid-Earth collision cases with objects 2008 TC3 and 2014 AA. In the analysis, the natural distribution of impact corridors is contrasted against the impact probability distribution to evaluate the distributions' conformity with the uniform impact distribution assumption. The distribution of impact corridors is based on the NEO population and orbital mechanics. The analysis shows that the distribution of impact corridors matches the common assumption of uniform impact distribution and the result extends the evidence base for the uniform assumption from qualitative analysis of historic impact events into the future in a quantitative way. This finding is confirmed in a parallel analysis of impact points belonging to a synthetic population of 10,006 VIs. Taking into account the impact probabilities introduced significant variation into the results and the impact probability distribution, consequently, deviates markedly from uniformity. The concept of impact probabilities is a product of the asteroid observation and orbit determination technique and, thus, represents a man-made component that is largely disconnected from natural processes. It is important to consider impact probabilities because such information represents the best estimate of where an impact might occur.

Bayesian ionospheric multi-instrument 3D tomography

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Vierinen, Juha; Roininen, Lassi

2017-04-01

The tomographic reconstruction of ionospheric electron densities is an inverse problem that cannot be solved without relatively strong regularising additional information. % Especially the vertical electron density profile is determined predominantly by the regularisation. % %Often utilised regularisations in ionospheric tomography include smoothness constraints and iterative methods with initial ionospheric models. % Despite its crucial role, the regularisation is often hidden in the algorithm as a numerical procedure without physical understanding. % % The Bayesian methodology provides an interpretative approach for the problem, as the regularisation can be given in a physically meaningful and quantifiable prior probability distribution. % The prior distribution can be based on ionospheric physics, other available ionospheric measurements and their statistics. % Updating the prior with measurements results as the posterior distribution that carries all the available information combined. % From the posterior distribution, the most probable state of the ionosphere can then be solved with the corresponding probability intervals. % Altogether, the Bayesian methodology provides understanding on how strong the given regularisation is, what is the information gained with the measurements and how reliable the final result is. % In addition, the combination of different measurements and temporal development can be taken into account in a very intuitive way. However, a direct implementation of the Bayesian approach requires inversion of large covariance matrices resulting in computational infeasibility. % In the presented method, Gaussian Markov random fields are used to form a sparse matrix approximations for the covariances. % The approach makes the problem computationally feasible while retaining the probabilistic and physical interpretation. Here, the Bayesian method with Gaussian Markov random fields is applied for ionospheric 3D tomography over Northern Europe. % Multi-instrument measurements are utilised from TomoScand receiver network for Low Earth orbit beacon satellite signals, GNSS receiver networks, as well as from EISCAT ionosondes and incoherent scatter radars. % %The performance is demonstrated in three-dimensional spatial domain with temporal development also taken into account.

Measurement of Plutonium-240 Angular Momentum Dependent Fission Probabilities Using the Alpha-Alpha' Reaction

NASA Astrophysics Data System (ADS)

Koglin, Johnathon

Accurate nuclear reaction data from a few keV to tens of MeV and across the table of nuclides is essential to a number of applications of nuclear physics, including national security, nuclear forensics, nuclear astrophysics, and nuclear energy. Precise determination of (n, f) and neutron capture cross sections for reactions in high- ux environments are particularly important for a proper understanding of nuclear reactor performance and stellar nucleosynthesis. In these extreme environments reactions on short-lived and otherwise difficult-to-produce isotopes play a significant role in system evolution and provide insights into the types of nuclear processes taking place; a detailed understanding of these processes is necessary to properly determine cross sections far from stability. Indirect methods are often attempted to measure cross sections on isotopes that are difficult to separate in a laboratory setting. Using the surrogate approach, the same compound nucleus from the reaction of interest is created through a "surrogate" reaction on a different isotope and the resulting decay is measured. This result is combined with appropriate reaction theory for compound nucleus population, from which the desired cross sections can be inferred. This method has shown promise, but the theoretical framework often lacks necessary experimental data to constrain models. In this work, dual arrays of silicon telescope particle identification detectors and photovoltaic (solar) cell fission fragment detectors have been used to measure the fission probability of the 240Pu(alpha, alpha'f) reaction - a surrogate for the 239Pu(n, f) - and fission of 35.9(2)MeV at eleven scattering angles from 40° to 140° in 10° intervals and at nuclear excitation energies up to 16MeV. Within experimental uncertainty, the maximum fission probability was observed at the neutron separation energy for each alpha scattering angle. Fission probabilities were separated into five 500 keV bins from 5:5MeV to 8:0MeV and one bin from 4:5MeV to 5:5MeV. Across energy bins the fission probability increases approximately linearly with increasing alpha' scattering angle. At 90° the fission probability increases from 0:069(6) in the lowest energy bin to 0:59(2) in the highest. Likewise, within a single energy bin the fission probability increases with alpha' scattering angle. Within the 6:5MeV and 7:0MeV energy bin, the fission probability increased from 0:41(1) at 60° to 0:81(10) at 140°. Fission fragment angular distributions were also measured integrated over each energy bin. These distributions were fit to theoretical distributions based on combinations of transitional nuclear vibrational and rotational excitations at the saddle point. Contributions from specific K vibrational states were extracted and combined with fission probability measurements to determine the relative fission probability of each state as a function of nuclear excitation energy. Within a given excitation energy bin, it is found that contributions from K states greater than the minimum K = 0 state tend to increase with the increasing alpha' scattering angle. This is attributed to an increase in the transferred angular momentum associated with larger scattering angles. The 90° alpha' scattering angle produced the highest quality results. The relative contributions of K states do not show a discernible trend across the energy spectrum. The energy-binned results confirm existing measurements that place a K = 2 state in the first energy bin with the opening of K = 1 and K = 4 states at energies above 5:5MeV. This experiment represents the first of its kind in which fission probabilities and angular distributions are simultaneously measured at a large number of scattering angles. The acquired fission probability, angular distribution, and K state contribution provide a diverse dataset against which microscopic fission models can be constrained and further the understanding of the properties of the 240Pu fission.

Inverse estimation of the spheroidal particle size distribution using Ant Colony Optimization algorithms in multispectral extinction technique

NASA Astrophysics Data System (ADS)

He, Zhenzong; Qi, Hong; Wang, Yuqing; Ruan, Liming

2014-10-01

Four improved Ant Colony Optimization (ACO) algorithms, i.e. the probability density function based ACO (PDF-ACO) algorithm, the Region ACO (RACO) algorithm, Stochastic ACO (SACO) algorithm and Homogeneous ACO (HACO) algorithm, are employed to estimate the particle size distribution (PSD) of the spheroidal particles. The direct problems are solved by the extended Anomalous Diffraction Approximation (ADA) and the Lambert-Beer law. Three commonly used monomodal distribution functions i.e. the Rosin-Rammer (R-R) distribution function, the normal (N-N) distribution function, and the logarithmic normal (L-N) distribution function are estimated under dependent model. The influence of random measurement errors on the inverse results is also investigated. All the results reveal that the PDF-ACO algorithm is more accurate than the other three ACO algorithms and can be used as an effective technique to investigate the PSD of the spheroidal particles. Furthermore, the Johnson's SB (J-SB) function and the modified beta (M-β) function are employed as the general distribution functions to retrieve the PSD of spheroidal particles using PDF-ACO algorithm. The investigation shows a reasonable agreement between the original distribution function and the general distribution function when only considering the variety of the length of the rotational semi-axis.

An improved multilevel Monte Carlo method for estimating probability distribution functions in stochastic oil reservoir simulations

DOE PAGES

Lu, Dan; Zhang, Guannan; Webster, Clayton G.; ...

2016-12-30

In this paper, we develop an improved multilevel Monte Carlo (MLMC) method for estimating cumulative distribution functions (CDFs) of a quantity of interest, coming from numerical approximation of large-scale stochastic subsurface simulations. Compared with Monte Carlo (MC) methods, that require a significantly large number of high-fidelity model executions to achieve a prescribed accuracy when computing statistical expectations, MLMC methods were originally proposed to significantly reduce the computational cost with the use of multifidelity approximations. The improved performance of the MLMC methods depends strongly on the decay of the variance of the integrand as the level increases. However, the main challengemore » in estimating CDFs is that the integrand is a discontinuous indicator function whose variance decays slowly. To address this difficult task, we approximate the integrand using a smoothing function that accelerates the decay of the variance. In addition, we design a novel a posteriori optimization strategy to calibrate the smoothing function, so as to balance the computational gain and the approximation error. The combined proposed techniques are integrated into a very general and practical algorithm that can be applied to a wide range of subsurface problems for high-dimensional uncertainty quantification, such as a fine-grid oil reservoir model considered in this effort. The numerical results reveal that with the use of the calibrated smoothing function, the improved MLMC technique significantly reduces the computational complexity compared to the standard MC approach. Finally, we discuss several factors that affect the performance of the MLMC method and provide guidance for effective and efficient usage in practice.« less

Performance Analysis of Direct-Sequence Code-Division Multiple-Access Communications with Asymmetric Quadrature Phase-Shift-Keying Modulation

NASA Technical Reports Server (NTRS)

Wang, C.-W.; Stark, W.

2005-01-01

This article considers a quaternary direct-sequence code-division multiple-access (DS-CDMA) communication system with asymmetric quadrature phase-shift-keying (AQPSK) modulation for unequal error protection (UEP) capability. Both time synchronous and asynchronous cases are investigated. An expression for the probability distribution of the multiple-access interference is derived. The exact bit-error performance and the approximate performance using a Gaussian approximation and random signature sequences are evaluated by extending the techniques used for uniform quadrature phase-shift-keying (QPSK) and binary phase-shift-keying (BPSK) DS-CDMA systems. Finally, a general system model with unequal user power and the near-far problem is considered and analyzed. The results show that, for a system with UEP capability, the less protected data bits are more sensitive to the near-far effect that occurs in a multiple-access environment than are the more protected bits.

A B-B-G-K-Y framework for fluid turbulence

NASA Technical Reports Server (NTRS)

Montgomery, D.

1975-01-01

A kinetic theory for fluid turbulence is developed from the Liouville equation and the associated BBGKY hierarchy. Real and imaginary parts of Fourier coefficients of fluid variables play the roles of particles. Closure is achieved by the assumption of negligible five-coefficient correlation functions and probability distributions of Fourier coefficients are the basic variables of the theory. An additional approximation leads to a closed-moment description similar to the so-called eddy-damped Markovian approximation. A kinetic equation is derived for which conservation laws and an H-theorem can be rigorously established, the H-theorem implying relaxation of the absolute equilibrium of Kraichnan. The equation can be cast in the Fokker-Planck form, and relaxation times estimated from its friction and diffusion coefficients. An undetermined parameter in the theory is the free decay time for triplet correlations. Some attention is given to the inclusion of viscous damping and external driving forces.

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

Quantum Walks on the Line with Phase Parameters

NASA Astrophysics Data System (ADS)

Villagra, Marcos; Nakanishi, Masaki; Yamashita, Shigeru; Nakashima, Yasuhiko

In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step toward this objective, the following question is being addressed: Given a graph, what is the probability that a quantum walk arrives at a given vertex after some number of steps? This is a very natural question, and for random walks it can be answered by several different combinatorial arguments. For quantum walks this is a highly non-trivial task. Furthermore, this was only achieved before for one specific coin operator (Hadamard operator) for walks on the line. Even considering only walks on lines, generalizing these computations to a general SU(2) coin operator is a complex task. The main contribution is a closed-form formula for the amplitudes of the state of the walk (which includes the question above) for a general symmetric SU(2) operator for walks on the line. To this end, a coin operator with parameters that alters the phase of the state of the walk is defined. Then, closed-form solutions are computed by means of Fourier analysis and asymptotic approximation methods. We also present some basic properties of the walk which can be deducted using weak convergence theorems for quantum walks. In particular, the support of the induced probability distribution of the walk is calculated. Then, it is shown how changing the parameters in the coin operator affects the resulting probability distribution.

Tensor distribution function

NASA Astrophysics Data System (ADS)

Leow, Alex D.; Zhu, Siwei

2008-03-01

Diffusion weighted MR imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitizing gradients along a minimum of 6 directions, second-order tensors (represetnted by 3-by-3 positive definiite matrices) can be computed to model dominant diffusion processes. However, it has been shown that conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g. crossing fiber tracts. More recently, High Angular Resolution Diffusion Imaging (HARDI) seeks to address this issue by employing more than 6 gradient directions. To account for fiber crossing when analyzing HARDI data, several methodologies have been introduced. For example, q-ball imaging was proposed to approximate Orientation Diffusion Function (ODF). Similarly, the PAS method seeks to reslove the angular structure of displacement probability functions using the maximum entropy principle. Alternatively, deconvolution methods extract multiple fiber tracts by computing fiber orientations using a pre-specified single fiber response function. In this study, we introduce Tensor Distribution Function (TDF), a probability function defined on the space of symmetric and positive definite matrices. Using calculus of variations, we solve for the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, ODF can easily be computed by analytical integration of the resulting displacement probability function. Moreover, principle fiber directions can also be directly derived from the TDF.

Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

DOE PAGES

Clerkin, L.; Kirk, D.; Manera, M.; ...

2016-08-30

It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (kappa_WL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the Counts in Cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey (DES) Science Verification data over 139 deg^2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirmmore » that the galaxy density contrast distribution is well modeled by a lognormal PDF convolved with Poisson noise at angular scales from 10-40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as kappa_WL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the kappa_WL distribution is well modeled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fit chi^2/DOF of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07 respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.« less

Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

NASA Astrophysics Data System (ADS)

Clerkin, L.; Kirk, D.; Manera, M.; Lahav, O.; Abdalla, F.; Amara, A.; Bacon, D.; Chang, C.; Gaztañaga, E.; Hawken, A.; Jain, B.; Joachimi, B.; Vikram, V.; Abbott, T.; Allam, S.; Armstrong, R.; Benoit-Lévy, A.; Bernstein, G. M.; Bernstein, R. A.; Bertin, E.; Brooks, D.; Burke, D. L.; Rosell, A. Carnero; Carrasco Kind, M.; Crocce, M.; Cunha, C. E.; D'Andrea, C. B.; da Costa, L. N.; Desai, S.; Diehl, H. T.; Dietrich, J. P.; Eifler, T. F.; Evrard, A. E.; Flaugher, B.; Fosalba, P.; Frieman, J.; Gerdes, D. W.; Gruen, D.; Gruendl, R. A.; Gutierrez, G.; Honscheid, K.; James, D. J.; Kent, S.; Kuehn, K.; Kuropatkin, N.; Lima, M.; Melchior, P.; Miquel, R.; Nord, B.; Plazas, A. A.; Romer, A. K.; Roodman, A.; Sanchez, E.; Schubnell, M.; Sevilla-Noarbe, I.; Smith, R. C.; Soares-Santos, M.; Sobreira, F.; Suchyta, E.; Swanson, M. E. C.; Tarle, G.; Walker, A. R.

2017-04-01

It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (κWL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the counts-in-cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey Science Verification data over 139 deg2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modelled by a lognormal PDF convolved with Poisson noise at angular scales from 10 to 40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as κWL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the κWL distribution is well modelled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fitting χ2/dof of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07, respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check, we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.

Maximum Entropy Methods as the Bridge Between Microscopic and Macroscopic Theory

NASA Astrophysics Data System (ADS)

Taylor, Jamie M.

2016-09-01

This paper is concerned with an investigation into a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability distributions on a state space, defined so that it corresponds to the maximum possible entropy given known observed statistical averages, although non-classical entropy-like objective functions will also be considered. First the set of admissible moments must be established, and under the conditions presented in this work the set is open, bounded and convex allowing a description in terms of supporting hyperplanes, which provides estimates on the development of singularities for related probability distributions. Under appropriate conditions it is shown that the singular potential is strictly convex, as differentiable as the microscopic entropy, and blows up uniformly as the macroscopic variable tends to the boundary of the set of admissible moments. Applications of the singular potential are then discussed, and particular consideration will be given to certain free-energy functionals typical in mean-field theory, demonstrating an equivalence between certain microscopic and macroscopic free-energy functionals. This allows statements about L^1-local minimisers of Onsager's free energy to be obtained which cannot be given by two-sided variations, and overcomes the need to ensure local minimisers are bounded away from zero and +∞ before taking L^∞ variations. The analysis also permits the definition of a dual order parameter for which Onsager's free energy allows an explicit representation. Also, the difficulties in approximating the singular potential by everywhere defined functions, in particular by polynomial functions, are addressed, with examples demonstrating the failure of the Taylor approximation to preserve relevant shape properties of the singular potential.

Optimizing Retransmission Threshold in Wireless Sensor Networks

PubMed Central

Bi, Ran; Li, Yingshu; Tan, Guozhen; Sun, Liang

2016-01-01

The retransmission threshold in wireless sensor networks is critical to the latency of data delivery in the networks. However, existing works on data transmission in sensor networks did not consider the optimization of the retransmission threshold, and they simply set the same retransmission threshold for all sensor nodes in advance. The method did not take link quality and delay requirement into account, which decreases the probability of a packet passing its delivery path within a given deadline. This paper investigates the problem of finding optimal retransmission thresholds for relay nodes along a delivery path in a sensor network. The object of optimizing retransmission thresholds is to maximize the summation of the probability of the packet being successfully delivered to the next relay node or destination node in time. A dynamic programming-based distributed algorithm for finding optimal retransmission thresholds for relay nodes along a delivery path in the sensor network is proposed. The time complexity is OnΔ·max1≤i≤n{ui}, where ui is the given upper bound of the retransmission threshold of sensor node i in a given delivery path, n is the length of the delivery path and Δ is the given upper bound of the transmission delay of the delivery path. If Δ is greater than the polynomial, to reduce the time complexity, a linear programming-based (1+pmin)-approximation algorithm is proposed. Furthermore, when the ranges of the upper and lower bounds of retransmission thresholds are big enough, a Lagrange multiplier-based distributed O(1)-approximation algorithm with time complexity O(1) is proposed. Experimental results show that the proposed algorithms have better performance. PMID:27171092

Weibull-Based Design Methodology for Rotating Aircraft Engine Structures

NASA Technical Reports Server (NTRS)

Zaretsky, Erwin; Hendricks, Robert C.; Soditus, Sherry

2002-01-01

The NASA Energy Efficient Engine (E(sup 3)-Engine) is used as the basis of a Weibull-based life and reliability analysis. Each component's life and thus the engine's life is defined by high-cycle fatigue (HCF) or low-cycle fatigue (LCF). Knowing the cumulative life distribution of each of the components making up the engine as represented by a Weibull slope is a prerequisite to predicting the life and reliability of the entire engine. As the engine Weibull slope increases, the predicted lives decrease. The predicted engine lives L(sub 5) (95 % probability of survival) of approximately 17,000 and 32,000 hr do correlate with current engine maintenance practices without and with refurbishment. respectively. The individual high pressure turbine (HPT) blade lives necessary to obtain a blade system life L(sub 0.1) (99.9 % probability of survival) of 9000 hr for Weibull slopes of 3, 6 and 9, are 47,391 and 20,652 and 15,658 hr, respectively. For a design life of the HPT disks having probable points of failure equal to or greater than 36,000 hr at a probability of survival of 99.9 %, the predicted disk system life L(sub 0.1) can vary from 9,408 to 24,911 hr.

Tangled nature model of evolutionary dynamics reconsidered: Structural and dynamical effects of trait inheritance

NASA Astrophysics Data System (ADS)

Andersen, Christian Walther; Sibani, Paolo

2016-05-01

Based on the stochastic dynamics of interacting agents which reproduce, mutate, and die, the tangled nature model (TNM) describes key emergent features of biological and cultural ecosystems' evolution. While trait inheritance is not included in many applications, i.e., the interactions of an agent and those of its mutated offspring are taken to be uncorrelated, in the family of TNMs introduced in this work correlations of varying strength are parametrized by a positive integer K . We first show that the interactions generated by our rule are nearly independent of K . Consequently, the structural and dynamical effects of trait inheritance can be studied independently of effects related to the form of the interactions. We then show that changing K strengthens the core structure of the ecology, leads to population abundance distributions better approximated by log-normal probability densities, and increases the probability that a species extant at time tw also survives at t >tw . Finally, survival probabilities of species are shown to decay as powers of the ratio t /tw , a so-called pure aging behavior usually seen in glassy systems of physical origin. We find a quantitative dynamical effect of trait inheritance, namely, that increasing the value of K numerically decreases the decay exponent of the species survival probability.

Tangled nature model of evolutionary dynamics reconsidered: Structural and dynamical effects of trait inheritance.

PubMed

Andersen, Christian Walther; Sibani, Paolo

2016-05-01

Based on the stochastic dynamics of interacting agents which reproduce, mutate, and die, the tangled nature model (TNM) describes key emergent features of biological and cultural ecosystems' evolution. While trait inheritance is not included in many applications, i.e., the interactions of an agent and those of its mutated offspring are taken to be uncorrelated, in the family of TNMs introduced in this work correlations of varying strength are parametrized by a positive integer K. We first show that the interactions generated by our rule are nearly independent of K. Consequently, the structural and dynamical effects of trait inheritance can be studied independently of effects related to the form of the interactions. We then show that changing K strengthens the core structure of the ecology, leads to population abundance distributions better approximated by log-normal probability densities, and increases the probability that a species extant at time t_{w} also survives at t>t_{w}. Finally, survival probabilities of species are shown to decay as powers of the ratio t/t_{w}, a so-called pure aging behavior usually seen in glassy systems of physical origin. We find a quantitative dynamical effect of trait inheritance, namely, that increasing the value of K numerically decreases the decay exponent of the species survival probability.

Characterisation of edge turbulence in relation to edge magnetic field configuration in L-mode plasmas in the Mega Amp Spherical Tokamak.

NASA Astrophysics Data System (ADS)

Dewhurst, J.; Hnat, B.; Dudson, B.; Dendy, R. O.; Counsell, G. F.; Kirk, A.

2007-12-01

Almost all astrophysical and magnetically confined fusion plasmas are turbulent. Here, we examine ion saturation current (Isat) measurements of edge plasma turbulence for three MAST L-mode plasmas that differ primarily in their edge magnetic field configurations. First, absolute moments of the coarse grained data are examined to obtain accurate values of scaling exponents. The dual scaling behaviour is identified in all samples, with the temporal scale τ ≍ 40-60 μs separating the two regimes. Strong universality is then identified in the functional form of the probability density function (PDF) for Isat fluctuations, which is well approximated by the Fréchet distribution on temporal scales τ ≤ 40μs. For temporal scales τ > 40μs, the PDFs appear to converge to the Gumbel distribution, which has been previously identified as a universal feature of many other complex phenomena. The optimal fitting parameters k=1.15 for Fréchet and a=1.35 for Gumbel provide a simple quantitative characterisation of the full spectrum of fluctuations. We conclude that, to good approximation, the properties of the edge turbulence are independent of the edge magnetic field configuration.

Characterization of edge turbulence in relation to edge magnetic field configuration in Ohmic L-mode plasmas in the Mega Amp Spherical Tokamak

NASA Astrophysics Data System (ADS)

Hnat, B.; Dudson, B. D.; Dendy, R. O.; Counsell, G. F.; Kirk, A.; MAST Team

2008-08-01

Ion saturation current (Isat) measurements of edge plasma turbulence are analysed for six MAST L-mode plasmas that differ primarily in their edge magnetic field configurations. The analysis techniques are designed to capture the strong nonlinearities of the datasets. First, absolute moments of the data are examined to obtain accurate values of scaling exponents. This confirms dual scaling behaviour in all samples, with the temporal scale τ ≈ 40-60 µs separating the two regimes. Strong universality is then identified in the functional form of the probability density function (PDF) for Isat fluctuations, which is well approximated by the Fréchet distribution on temporal scales τ <= 40 µs. For temporal scales τ > 40 µs, the PDFs appear to converge to the Gumbel distribution, which has been previously identified as a universal feature of many other complex phenomena. The optimal fitting parameters k = 1.15 for Fréchet and a = 1.35 for Gumbel provide a simple quantitative characterization of the full spectrum of fluctuations. It is concluded that, to good approximation, the properties of the edge turbulence are independent of the edge magnetic field configuration.

Bayesian Inference and Online Learning in Poisson Neuronal Networks.

PubMed

Huang, Yanping; Rao, Rajesh P N

2016-08-01

Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.

Distributed Storage Algorithm for Geospatial Image Data Based on Data Access Patterns.

PubMed

Pan, Shaoming; Li, Yongkai; Xu, Zhengquan; Chong, Yanwen

2015-01-01

Declustering techniques are widely used in distributed environments to reduce query response time through parallel I/O by splitting large files into several small blocks and then distributing those blocks among multiple storage nodes. Unfortunately, however, many small geospatial image data files cannot be further split for distributed storage. In this paper, we propose a complete theoretical system for the distributed storage of small geospatial image data files based on mining the access patterns of geospatial image data using their historical access log information. First, an algorithm is developed to construct an access correlation matrix based on the analysis of the log information, which reveals the patterns of access to the geospatial image data. Then, a practical heuristic algorithm is developed to determine a reasonable solution based on the access correlation matrix. Finally, a number of comparative experiments are presented, demonstrating that our algorithm displays a higher total parallel access probability than those of other algorithms by approximately 10-15% and that the performance can be further improved by more than 20% by simultaneously applying a copy storage strategy. These experiments show that the algorithm can be applied in distributed environments to help realize parallel I/O and thereby improve system performance.

Decision analysis with approximate probabilities

NASA Technical Reports Server (NTRS)

Whalen, Thomas

1992-01-01

This paper concerns decisions under uncertainty in which the probabilities of the states of nature are only approximately known. Decision problems involving three states of nature are studied. This is due to the fact that some key issues do not arise in two-state problems, while probability spaces with more than three states of nature are essentially impossible to graph. The primary focus is on two levels of probabilistic information. In one level, the three probabilities are separately rounded to the nearest tenth. This can lead to sets of rounded probabilities which add up to 0.9, 1.0, or 1.1. In the other level, probabilities are rounded to the nearest tenth in such a way that the rounded probabilities are forced to sum to 1.0. For comparison, six additional levels of probabilistic information, previously analyzed, were also included in the present analysis. A simulation experiment compared four criteria for decisionmaking using linearly constrained probabilities (Maximin, Midpoint, Standard Laplace, and Extended Laplace) under the eight different levels of information about probability. The Extended Laplace criterion, which uses a second order maximum entropy principle, performed best overall.

Root location in random trees: a polarity property of all sampling consistent phylogenetic models except one.

PubMed

Steel, Mike

2012-10-01

Neutral macroevolutionary models, such as the Yule model, give rise to a probability distribution on the set of discrete rooted binary trees over a given leaf set. Such models can provide a signal as to the approximate location of the root when only the unrooted phylogenetic tree is known, and this signal becomes relatively more significant as the number of leaves grows. In this short note, we show that among models that treat all taxa equally, and are sampling consistent (i.e. the distribution on trees is not affected by taxa yet to be included), all such models, except one (the so-called PDA model), convey some information as to the location of the ancestral root in an unrooted tree. Copyright © 2012 Elsevier Inc. All rights reserved.

Optical model calculations of heavy-ion target fragmentation

NASA Technical Reports Server (NTRS)

Townsend, L. W.; Wilson, J. W.; Cucinotta, F. A.; Norbury, J. W.

1986-01-01

The fragmentation of target nuclei by relativistic protons and heavy ions is described within the context of a simple abrasion-ablation-final-state interaction model. Abrasion is described by a quantum mechanical formalism utilizing an optical model potential approximation. Nuclear charge distributions of the excited prefragments are calculated by both a hypergeometric distribution and a method based upon the zero-point oscillations of the giant dipole resonance. Excitation energies are estimated from the excess surface energy resulting from the abrasion process and the additional energy deposited by frictional spectator interactions of the abraded nucleons. The ablation probabilities are obtained from the EVA-3 computer program. Isotope production cross sections for the spallation of copper targets by relativistic protons and for the fragmenting of carbon targets by relativistic carbon, neon, and iron projectiles are calculated and compared with available experimental data.

Average symbol error rate for M-ary quadrature amplitude modulation in generalized atmospheric turbulence and misalignment errors

NASA Astrophysics Data System (ADS)

Sharma, Prabhat Kumar

2016-11-01

A framework is presented for the analysis of average symbol error rate (SER) for M-ary quadrature amplitude modulation in a free-space optical communication system. The standard probability density function (PDF)-based approach is extended to evaluate the average SER by representing the Q-function through its Meijer's G-function equivalent. Specifically, a converging power series expression for the average SER is derived considering the zero-boresight misalignment errors in the receiver side. The analysis presented here assumes a unified expression for the PDF of channel coefficient which incorporates the M-distributed atmospheric turbulence and Rayleigh-distributed radial displacement for the misalignment errors. The analytical results are compared with the results obtained using Q-function approximation. Further, the presented results are supported by the Monte Carlo simulations.

Discrete hierarchy of sizes and performances in the exchange-traded fund universe

NASA Astrophysics Data System (ADS)

Vandermarliere, B.; Ryckebusch, J.; Schoors, K.; Cauwels, P.; Sornette, D.

2017-03-01

Using detailed statistical analyses of the size distribution of a universe of equity exchange-traded funds (ETFs), we discover a discrete hierarchy of sizes, which imprints a log-periodic structure on the probability distribution of ETF sizes that dominates the details of the asymptotic tail. This allows us to propose a classification of the studied universe of ETFs into seven size layers approximately organized according to a multiplicative ratio of 3.5 in their total market capitalization. Introducing a similarity metric generalizing the Herfindhal index, we find that the largest ETFs exhibit a significantly stronger intra-layer and inter-layer similarity compared with the smaller ETFs. Comparing the performance across the seven discerned ETF size layers, we find an inverse size effect, namely large ETFs perform significantly better than the small ones both in 2014 and 2015.

Fuzzy rationality and parameter elicitation in decision analysis

NASA Astrophysics Data System (ADS)

Nikolova, Natalia D.; Tenekedjiev, Kiril I.

2010-07-01

It is widely recognised by decision analysts that real decision-makers always make estimates in an interval form. An overview of techniques to find an optimal alternative among such with imprecise and interval probabilities is presented. Scalarisation methods are outlined as most appropriate. A proper continuation of such techniques is fuzzy rational (FR) decision analysis. A detailed representation of the elicitation process influenced by fuzzy rationality is given. The interval character of probabilities leads to the introduction of ribbon functions, whose general form and special cases are compared with the p-boxes. As demonstrated, approximation of utilities in FR decision analysis does not depend on the probabilities, but the approximation of probabilities is dependent on preferences.

A Stochastic Model For Extracting Sediment Delivery Timescales From Sediment Budgets

NASA Astrophysics Data System (ADS)

Pizzuto, J. E.; Benthem, A.; Karwan, D. L.; Keeler, J. J.; Skalak, K.

2015-12-01

Watershed managers need to quantify sediment storage and delivery timescales to understand the time required for best management practices to improve downstream water quality. To address this need, we route sediment downstream using a random walk through a series of valley compartments spaced at 1 km intervals. The probability of storage within each compartment, q, is specified from a sediment budget and is defined as the ratio of the volume deposited to the annual sediment flux. Within each compartment, the probability of sediment moving directly downstream without being stored is p=1-q. If sediment is stored within a compartment, its "resting time" is specified by a stochastic exponential waiting time distribution with a mean of 10 years. After a particle's waiting time is over, it moves downstream to the next compartment by fluvial transport. Over a distance of "n" compartments, a sediment particle may be stored from 0 to n times with the probability of each outcome (store or not store) specified by the binomial distribution. We assign q = 0.02, a stream velocity of 0.5 m/s, an event "intermittency "of 0.01, and assume a balanced sediment budget. Travel time probability density functions have a steep peak at the shortest times, representing rapid transport in the channel of the fraction of sediment that moves downstream without being stored. However, the probability of moving downstream "n" km without storage is pn (0.90 for 5 km, 0.36 for 50 km, 0.006 for 250 km), so travel times are increasingly dominated by storage with increasing distance. Median travel times for 5, 50, and 250 km are 0.03, 4.4, and 46.5 years. After a distance of approximately 2/q or 100 km (2/0.02/km), the median travel time is determined by storage timescales, and active fluvial transport is irrelevant. Our model extracts travel time statistics from sediment budgets, and can be cast as a differential equation and solved numerically for more complex systems.

Design of a sampling plan to detect ochratoxin A in green coffee.

PubMed

Vargas, E A; Whitaker, T B; Dos Santos, E A; Slate, A B; Lima, F B; Franca, R C A

2006-01-01

The establishment of maximum limits for ochratoxin A (OTA) in coffee by importing countries requires that coffee-producing countries develop scientifically based sampling plans to assess OTA contents in lots of green coffee before coffee enters the market thus reducing consumer exposure to OTA, minimizing the number of lots rejected, and reducing financial loss for producing countries. A study was carried out to design an official sampling plan to determine OTA in green coffee produced in Brazil. Twenty-five lots of green coffee (type 7 - approximately 160 defects) were sampled according to an experimental protocol where 16 test samples were taken from each lot (total of 16 kg) resulting in a total of 800 OTA analyses. The total, sampling, sample preparation, and analytical variances were 10.75 (CV = 65.6%), 7.80 (CV = 55.8%), 2.84 (CV = 33.7%), and 0.11 (CV = 6.6%), respectively, assuming a regulatory limit of 5 microg kg(-1) OTA and using a 1 kg sample, Romer RAS mill, 25 g sub-samples, and high performance liquid chromatography. The observed OTA distribution among the 16 OTA sample results was compared to several theoretical distributions. The 2 parameter-log normal distribution was selected to model OTA test results for green coffee as it gave the best fit across all 25 lot distributions. Specific computer software was developed using the variance and distribution information to predict the probability of accepting or rejecting coffee lots at specific OTA concentrations. The acceptation probability was used to compute an operating characteristic (OC) curve specific to a sampling plan design. The OC curve was used to predict the rejection of good lots (sellers' or exporters' risk) and the acceptance of bad lots (buyers' or importers' risk).

Nonadditive entropies yield probability distributions with biases not warranted by the data.

PubMed

Pressé, Steve; Ghosh, Kingshuk; Lee, Julian; Dill, Ken A

2013-11-01

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann-Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types of entropies that violate the Shore and Johnson axioms, including nonadditive entropies such as the Tsallis entropy, violate this basic consistency requirement. Here we use the axiomatic framework of Shore and Johnson to show how such nonadditive entropy functions generate biases in probability distributions that are not warranted by the underlying data.

ProbOnto: ontology and knowledge base of probability distributions.

PubMed

Swat, Maciej J; Grenon, Pierre; Wimalaratne, Sarala

2016-09-01

Probability distributions play a central role in mathematical and statistical modelling. The encoding, annotation and exchange of such models could be greatly simplified by a resource providing a common reference for the definition of probability distributions. Although some resources exist, no suitably detailed and complex ontology exists nor any database allowing programmatic access. ProbOnto, is an ontology-based knowledge base of probability distributions, featuring more than 80 uni- and multivariate distributions with their defining functions, characteristics, relationships and re-parameterization formulas. It can be used for model annotation and facilitates the encoding of distribution-based models, related functions and quantities. http://probonto.org mjswat@ebi.ac.uk Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press.

PRODIGEN: visualizing the probability landscape of stochastic gene regulatory networks in state and time space.

PubMed

Ma, Chihua; Luciani, Timothy; Terebus, Anna; Liang, Jie; Marai, G Elisabeta

2017-02-15

Visualizing the complex probability landscape of stochastic gene regulatory networks can further biologists' understanding of phenotypic behavior associated with specific genes. We present PRODIGEN (PRObability DIstribution of GEne Networks), a web-based visual analysis tool for the systematic exploration of probability distributions over simulation time and state space in such networks. PRODIGEN was designed in collaboration with bioinformaticians who research stochastic gene networks. The analysis tool combines in a novel way existing, expanded, and new visual encodings to capture the time-varying characteristics of probability distributions: spaghetti plots over one dimensional projection, heatmaps of distributions over 2D projections, enhanced with overlaid time curves to display temporal changes, and novel individual glyphs of state information corresponding to particular peaks. We demonstrate the effectiveness of the tool through two case studies on the computed probabilistic landscape of a gene regulatory network and of a toggle-switch network. Domain expert feedback indicates that our visual approach can help biologists: 1) visualize probabilities of stable states, 2) explore the temporal probability distributions, and 3) discover small peaks in the probability landscape that have potential relation to specific diseases.

Bit Error Probability for Maximum Likelihood Decoding of Linear Block Codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Fossorier, Marc P. C.; Rhee, Dojun

1996-01-01

In this paper, the bit error probability P(sub b) for maximum likelihood decoding of binary linear codes is investigated. The contribution of each information bit to P(sub b) is considered. For randomly generated codes, it is shown that the conventional approximation at high SNR P(sub b) is approximately equal to (d(sub H)/N)P(sub s), where P(sub s) represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P(sub b) when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for decoding methods which require a generator matrix with a particular structure such as trellis decoding or algebraic-based soft decision decoding, equivalent schemes that reduce the bit error probability are discussed.

Comparision of the different probability distributions for earthquake hazard assessment in the North Anatolian Fault Zone

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

Yilmaz, Şeyda, E-mail: seydayilmaz@ktu.edu.tr; Bayrak, Erdem, E-mail: erdmbyrk@gmail.com; Bayrak, Yusuf, E-mail: bayrak@ktu.edu.tr

In this study we examined and compared the three different probabilistic distribution methods for determining the best suitable model in probabilistic assessment of earthquake hazards. We analyzed a reliable homogeneous earthquake catalogue between a time period 1900-2015 for magnitude M ≥ 6.0 and estimated the probabilistic seismic hazard in the North Anatolian Fault zone (39°-41° N 30°-40° E) using three distribution methods namely Weibull distribution, Frechet distribution and three-parameter Weibull distribution. The distribution parameters suitability was evaluated Kolmogorov-Smirnov (K-S) goodness-of-fit test. We also compared the estimated cumulative probability and the conditional probabilities of occurrence of earthquakes for different elapsed timemore » using these three distribution methods. We used Easyfit and Matlab software to calculate these distribution parameters and plotted the conditional probability curves. We concluded that the Weibull distribution method was the most suitable than other distribution methods in this region.« less

Estimation of the diagnostic threshold accounting for decision costs and sampling uncertainty.

PubMed

Skaltsa, Konstantina; Jover, Lluís; Carrasco, Josep Lluís

2010-10-01

Medical diagnostic tests are used to classify subjects as non-diseased or diseased. The classification rule usually consists of classifying subjects using the values of a continuous marker that is dichotomised by means of a threshold. Here, the optimum threshold estimate is found by minimising a cost function that accounts for both decision costs and sampling uncertainty. The cost function is optimised either analytically in a normal distribution setting or empirically in a free-distribution setting when the underlying probability distributions of diseased and non-diseased subjects are unknown. Inference of the threshold estimates is based on approximate analytically standard errors and bootstrap-based approaches. The performance of the proposed methodology is assessed by means of a simulation study, and the sample size required for a given confidence interval precision and sample size ratio is also calculated. Finally, a case example based on previously published data concerning the diagnosis of Alzheimer's patients is provided in order to illustrate the procedure.

Assessing the Risk of a Canine Rabies Incursion in Northern Australia

PubMed Central

Hudson, Emily G.; Brookes, Victoria J.; Ward, Michael P.

2017-01-01

Rabies is a globally distributed virus that causes approximately 60,00 human deaths annually with >99% of cases caused by dog bites. Australia is currently canine rabies free. However, the recent eastward spread of rabies in the Indonesian archipelago has increased the probability of rabies entry into northern Australian communities. In addition, many northern Australian communities have large populations of free-roaming dogs, capable of maintaining rabies should an incursion occur. A risk assessment of rabies entry and transmission into these communities is needed to target control and surveillance measures. Illegal transportation of rabies-infected dogs via boat landings is a high-risk entry pathway and was the focus of the current study. A quantitative, stochastic, risk assessment model was developed to evaluate the risk of rabies entry into north-west Cape York Peninsula, Australia, and rabies introduction to resident dogs in one of the communities via transport of rabies-infected dogs on illegal Indonesian fishing boats. Parameter distributions were derived from expert opinion, literature, and analysis of field studies. The estimated median probability of rabies entry into north-west Cape York Peninsula and into Seisia from individual fishing boats was 1.9 × 10−4/boat and 8.7 × 10−6/boat, respectively. The estimated annual probability that at least one rabies-infected dog enters north-west Cape York Peninsula and into Seisia was 5.5 × 10−3 and 3.5 × 10−4, respectively. The estimated median probability of rabies introduction into Seisia was 4.7 × 10−8/boat, and the estimated annual probability that at least one rabies-infected dog causes rabies transmission in a resident Seisia dog was 8.3 × 10−5. Sensitivity analysis using the Sobol method highlighted some parameters as influential, including but not limited to the prevalence of rabies in Indonesia, the probability of a dog on board an Indonesian fishing boat, and the probability of a Seisia dog being on the beach. Overall, the probabilities of rabies entry into north-west Cape York Peninsula and rabies introduction into Seisia are low. However, the potential devastating consequences of a rabies incursion in this region make this a non-negligible risk. PMID:28913341

Incorporating Skew into RMS Surface Roughness Probability Distribution

NASA Technical Reports Server (NTRS)

Stahl, Mark T.; Stahl, H. Philip.

2013-01-01

The standard treatment of RMS surface roughness data is the application of a Gaussian probability distribution. This handling of surface roughness ignores the skew present in the surface and overestimates the most probable RMS of the surface, the mode. Using experimental data we confirm the Gaussian distribution overestimates the mode and application of an asymmetric distribution provides a better fit. Implementing the proposed asymmetric distribution into the optical manufacturing process would reduce the polishing time required to meet surface roughness specifications.

Closed-form solutions of performability. [in computer systems

NASA Technical Reports Server (NTRS)

Meyer, J. F.

1982-01-01

It is noted that if computing system performance is degradable then system evaluation must deal simultaneously with aspects of both performance and reliability. One approach is the evaluation of a system's performability which, relative to a specified performance variable Y, generally requires solution of the probability distribution function of Y. The feasibility of closed-form solutions of performability when Y is continuous are examined. In particular, the modeling of a degradable buffer/multiprocessor system is considered whose performance Y is the (normalized) average throughput rate realized during a bounded interval of time. Employing an approximate decomposition of the model, it is shown that a closed-form solution can indeed be obtained.

Flexible binding simulation by a novel and improved version of virtual-system coupled adaptive umbrella sampling

NASA Astrophysics Data System (ADS)

Dasgupta, Bhaskar; Nakamura, Haruki; Higo, Junichi

2016-10-01

Virtual-system coupled adaptive umbrella sampling (VAUS) enhances sampling along a reaction coordinate by using a virtual degree of freedom. However, VAUS and regular adaptive umbrella sampling (AUS) methods are yet computationally expensive. To decrease the computational burden further, improvements of VAUS for all-atom explicit solvent simulation are presented here. The improvements include probability distribution calculation by a Markov approximation; parameterization of biasing forces by iterative polynomial fitting; and force scaling. These when applied to study Ala-pentapeptide dimerization in explicit solvent showed advantage over regular AUS. By using improved VAUS larger biological systems are amenable.

Probabilistic brains: knowns and unknowns

PubMed Central

Pouget, Alexandre; Beck, Jeffrey M; Ma, Wei Ji; Latham, Peter E

2015-01-01

There is strong behavioral and physiological evidence that the brain both represents probability distributions and performs probabilistic inference. Computational neuroscientists have started to shed light on how these probabilistic representations and computations might be implemented in neural circuits. One particularly appealing aspect of these theories is their generality: they can be used to model a wide range of tasks, from sensory processing to high-level cognition. To date, however, these theories have only been applied to very simple tasks. Here we discuss the challenges that will emerge as researchers start focusing their efforts on real-life computations, with a focus on probabilistic learning, structural learning and approximate inference. PMID:23955561

Some Simple Formulas for Posterior Convergence Rates

PubMed Central

2014-01-01

We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a “penalized divergence” of the prior, which measures the ability of the prior distribution to propose a nonnegligible set of working models to approximate the true model and a “norm complexity” of the prior, which measures the complexity of the prior support, weighted by the prior probability masses. These formulas are explicit and involve no essential assumptions and are easy to apply. We apply this approach to the case with model averaging and derive some useful oracle inequalities that can optimize the performance adaptively without knowing the true model. PMID:27379278

Scale matters

NASA Astrophysics Data System (ADS)

Margolin, L. G.

2018-04-01

The applicability of Navier-Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman-Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics. This article is part of the theme issue `Hilbert's sixth problem'.

Probability Quantization for Multiplication-Free Binary Arithmetic Coding

NASA Technical Reports Server (NTRS)

Cheung, K. -M.

1995-01-01

A method has been developed to improve on Witten's binary arithmetic coding procedure of tracking a high value and a low value. The new method approximates the probability of the less probable symbol, which improves the worst-case coding efficiency.

The Estimation of Tree Posterior Probabilities Using Conditional Clade Probability Distributions

PubMed Central

Larget, Bret

2013-01-01

In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample. [Bayesian phylogenetics; conditional clade distributions; improved accuracy; posterior probabilities of trees.] PMID:23479066

Generalized Quantum Theory of Bianchi IX Cosmologies

NASA Astrophysics Data System (ADS)

Craig, David; Hartle, James

2003-04-01

We apply sum-over-histories generalized quantum theory to the closed homogeneous minisuperspace Bianchi IX cosmological model. We sketch how the probabilities in decoherent sets of alternative, coarse-grained histories of this model universe are calculated. We consider in particular, the probabilities for classical evolution in a suitable coarse-graining. For a restricted class of initial conditions and coarse grainings we exhibit the approximate decoherence of alternative histories in which the universe behaves classically and those in which it does not, illustrating the prediction that these universes will evolve in an approximately classical manner with a probability near unity.

Predicting the probability of slip in gait: methodology and distribution study.

PubMed

Gragg, Jared; Yang, James

2016-01-01

The likelihood of a slip is related to the available and required friction for a certain activity, here gait. Classical slip and fall analysis presumed that a walking surface was safe if the difference between the mean available and required friction coefficients exceeded a certain threshold. Previous research was dedicated to reformulating the classical slip and fall theory to include the stochastic variation of the available and required friction when predicting the probability of slip in gait. However, when predicting the probability of a slip, previous researchers have either ignored the variation in the required friction or assumed the available and required friction to be normally distributed. Also, there are no published results that actually give the probability of slip for various combinations of required and available frictions. This study proposes a modification to the equation for predicting the probability of slip, reducing the previous equation from a double-integral to a more convenient single-integral form. Also, a simple numerical integration technique is provided to predict the probability of slip in gait: the trapezoidal method. The effect of the random variable distributions on the probability of slip is also studied. It is shown that both the required and available friction distributions cannot automatically be assumed as being normally distributed. The proposed methods allow for any combination of distributions for the available and required friction, and numerical results are compared to analytical solutions for an error analysis. The trapezoidal method is shown to be highly accurate and efficient. The probability of slip is also shown to be sensitive to the input distributions of the required and available friction. Lastly, a critical value for the probability of slip is proposed based on the number of steps taken by an average person in a single day.

Integrated-Circuit Pseudorandom-Number Generator

NASA Technical Reports Server (NTRS)

Steelman, James E.; Beasley, Jeff; Aragon, Michael; Ramirez, Francisco; Summers, Kenneth L.; Knoebel, Arthur

1992-01-01

Integrated circuit produces 8-bit pseudorandom numbers from specified probability distribution, at rate of 10 MHz. Use of Boolean logic, circuit implements pseudorandom-number-generating algorithm. Circuit includes eight 12-bit pseudorandom-number generators, outputs are uniformly distributed. 8-bit pseudorandom numbers satisfying specified nonuniform probability distribution are generated by processing uniformly distributed outputs of eight 12-bit pseudorandom-number generators through "pipeline" of D flip-flops, comparators, and memories implementing conditional probabilities on zeros and ones.

Transformation of arbitrary distributions to the normal distribution with application to EEG test-retest reliability.

PubMed

van Albada, S J; Robinson, P A

2007-04-15

Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are often used. Box-Cox transformations or ad hoc methods are sometimes used for parameters for which no transformation is known to approximate normality. However, these methods do not always give good agreement with the Gaussian. A transformation is discussed that maps probability distributions as closely as possible to the normal distribution, with exact agreement for continuous distributions. To illustrate, the transformation is applied to a theoretical distribution, and to quantitative electroencephalographic (qEEG) measures from repeat recordings of 32 subjects which are highly non-normal. Agreement with the Gaussian was better than using logarithmic, logit, or Box-Cox transformations. Since normal data have previously been shown to have better test-retest reliability than non-normal data under fairly general circumstances, the implications of our transformation for the test-retest reliability of parameters were investigated. Reliability was shown to improve with the transformation, where the improvement was comparable to that using Box-Cox. An advantage of the general transformation is that it does not require laborious optimization over a range of parameters or a case-specific choice of form.

Characteristics of service requests and service processes of fire and rescue service dispatch centers: analysis of real world data and the underlying probability distributions.

PubMed

Krueger, Ute; Schimmelpfeng, Katja

2013-03-01

A sufficient staffing level in fire and rescue dispatch centers is crucial for saving lives. Therefore, it is important to estimate the expected workload properly. For this purpose, we analyzed whether a dispatch center can be considered as a call center. Current call center publications very often model call arrivals as a non-homogeneous Poisson process. This bases on the underlying assumption of the caller's independent decision to call or not to call. In case of an emergency, however, there are often calls from more than one person reporting the same incident and thus, these calls are not independent. Therefore, this paper focuses on the dependency of calls in a fire and rescue dispatch center. We analyzed and evaluated several distributions in this setting. Results are illustrated using real-world data collected from a typical German dispatch center in Cottbus ("Leitstelle Lausitz"). We identified the Pólya distribution as being superior to the Poisson distribution in describing the call arrival rate and the Weibull distribution to be more suitable than the exponential distribution for interarrival times and service times. However, the commonly used distributions offer acceptable approximations. This is important for estimating a sufficient staffing level in practice using, e.g., the Erlang-C model.

Monitoring of styrene oligomers as indicators of polystyrene plastic pollution in the North-West Pacific Ocean.

PubMed

Kwon, Bum Gun; Amamiya, Keiji; Sato, Hideto; Chung, Seon-Yong; Kodera, Yoichi; Kim, Seung-Kyu; Lee, Eung Jae; Saido, Katsuhiko

2017-08-01

Styrene oligomers (SOs) as global contaminants are an environmental concern. However, little is known on the distribution of SOs in the ocean. Here, we show the distribution of anthropogenic SOs generated from discarded polystyrene (PS) plastic monitored from the coastal ocean surface waters (horizontal distribution) and deep seawaters (vertical distribution) in the North-West Pacific Ocean. SOs concentrations in surface seawater and deep seawater ranged from 0.17 to 4.26 μg L -1 (total mean: 1.48 ± 1.23 μg L -1 ) and from 0.31 to 4.31 μg L -1 (total mean: 1.32 ± 0.87 μg L -1 ), respectively. Since there is no significant difference in the mean concentrations, SOs seems to be spread across marine environment selected in this study. Nevertheless, regional SOs appears to persist to varying degrees with their broad horizontal and vertical distribution in the ocean. Each horizontal and vertical distribution of SOs differs by approximately 1.95-2.57 times, probably depending on the events of weather and global ocean circulation. These results provide the distribution pattern of SOs for assessing environmental pollution arising from PS plastic. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

Prentice, John K.; Gardner, David Randall

A methodology was developed for computing the probability that the sensor dart for the 'Near Real-Time Site Characterization for Assured HDBT Defeat' Grand-Challenge LDRD project will survive deployment over a forested region. The probability can be decomposed into three approximately independent probabilities that account for forest coverage, branch density and the physics of an impact between the dart and a tree branch. The probability that a dart survives an impact with a tree branch was determined from the deflection induced by the impact. If a dart that was deflected so that it impacted the ground at an angle of attackmore » exceeding a user-specified, threshold value, the dart was assumed to not survive the impact with the branch; otherwise it was assumed to have survived. A computer code was developed for calculating dart angle of attack at impact with the ground and a Monte Carlo scheme was used to calculate the probability distribution of a sensor dart surviving an impact with a branch as a function of branch radius, length, and height from the ground. Both an early prototype design and the current dart design were used in these studies. As a general rule of thumb, it we observed that for reasonably generic trees and for a threshold angle of attack of 5{sup o} (which is conservative for dart survival), the probability of reaching the ground with an angle of attack less than the threshold is on the order of 30% for the prototype dart design and 60% for the current dart design, though these numbers should be treated with some caution.« less

On the probability of exceeding allowable leak rates through degraded steam generator tubes

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

Cizelj, L.; Sorsek, I.; Riesch-Oppermann, H.

1997-02-01

This paper discusses some possible ways of predicting the behavior of the total leak rate through the damaged steam generator tubes. This failure mode is of special concern in cases where most through-wall defects may remain In operation. A particular example is the application of alternate (bobbin coil voltage) plugging criterion to Outside Diameter Stress Corrosion Cracking at the tube support plate intersections. It is the authors aim to discuss some possible modeling options that could be applied to solve the problem formulated as: Estimate the probability that the sum of all individual leak rates through degraded tubes exceeds themore » predefined acceptable value. The probabilistic approach is of course aiming at reliable and computationaly bearable estimate of the failure probability. A closed form solution is given for a special case of exponentially distributed individual leak rates. Also, some possibilities for the use of computationaly efficient First and Second Order Reliability Methods (FORM and SORM) are discussed. The first numerical example compares the results of approximate methods with closed form results. SORM in particular shows acceptable agreement. The second numerical example considers a realistic case of NPP in Krsko, Slovenia.« less

Quantum Inference on Bayesian Networks

NASA Astrophysics Data System (ADS)

Yoder, Theodore; Low, Guang Hao; Chuang, Isaac

2014-03-01

Because quantum physics is naturally probabilistic, it seems reasonable to expect physical systems to describe probabilities and their evolution in a natural fashion. Here, we use quantum computation to speedup sampling from a graphical probability model, the Bayesian network. A specialization of this sampling problem is approximate Bayesian inference, where the distribution on query variables is sampled given the values e of evidence variables. Inference is a key part of modern machine learning and artificial intelligence tasks, but is known to be NP-hard. Classically, a single unbiased sample is obtained from a Bayesian network on n variables with at most m parents per node in time (nmP(e) - 1 / 2) , depending critically on P(e) , the probability the evidence might occur in the first place. However, by implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking (n2m P(e) -1/2) time per sample. The speedup is the result of amplitude amplification, which is proving to be broadly applicable in sampling and machine learning tasks. In particular, we provide an explicit and efficient circuit construction that implements the algorithm without the need for oracle access.

Spatial distribution of the dagger nematode Xiphinema index and its associated Grapevine fanleaf virus in French vineyard.

PubMed

Villate, L; Fievet, V; Hanse, B; Delemarre, F; Plantard, O; Esmenjaud, D; van Helden, M

2008-08-01

The nematode Xiphinema index is, economically, the major virus vector in viticulture, transmitting specifically the Grapevine fanleaf virus (GFLV), the most severe grapevine virus disease worldwide. Increased knowledge of the spatial distribution of this nematode, both horizontally and vertically, and of correlative GFLV plant infections, is essential to efficiently control the disease. In two infested blocks of the Bordeaux vineyard, vertical distribution data showed that the highest numbers of individuals occurred at 40 to 110 cm depth, corresponding to the two layers where the highest densities of fine roots were observed. Horizontal distribution based on a 10 x 15 m grid sampling procedure revealed a significant aggregative pattern but no significant neighborhood structure of nematode densities. At a finer scale ( approximately 2 x 2 m), nematode sampling performed in a third block confirmed a significant aggregative pattern, with patches of 6 to 8 m diameter, together with a significant neighborhood structure of nematode densities, thus identifying the relevant sampling scale to describe the nematode distribution. Nematode patches correlate significantly with those of GFLV-infected grapevine plants. Finally, nematode and virus spread were shown to extend preferentially parallel to vine rows, probably due to tillage during mechanical weeding.

Tidal disruption and the appearance of periodic comet Shoemaker-Levy 9

NASA Technical Reports Server (NTRS)

Sekanina, Z.; Chodas, P. W.; Yeomans, D. K.

1994-01-01

A unified model is formulated to interpret quantitatively the observed characteristics of the nuclear train, the two dust trails, and the tail region of P/Shoemaker-Levy 9 in terms of a collisionally modified rotation velocity distribution of the comet's debris. Since there is no evidence for the comet's out-gassing, the model does not assume activity. The discruption of the parent comet was due primarily to tidal stesses during its extremely close approach to Juptier in July 1992. The original nucleus is found to have been most probably approximately 5 km in radius or, equivalently, approximately 10(exp 17) g in mass. The dynamical separation of the debris occurred apparently approximately 2.2 hr after the perijove passage, even though the actual fragmentation of the original mass is likely to have begun before closest approach. Physical breakp was accompanied by ubiquitous low-velocity collisions among the particulates, resulting in a rearrangement of the initial rotaional velocities into a rapidly 'thermalized' distribution, characterized by a long tail of relatively high velocities for the debris that populates the dust trails far from the nuclear train. Compelling evidence is presented for secondary fragmentation events, indicative of the comet's continuing disintegration. Secondary fragmentation may be caused by rotational bursting of the massive fragments that had been cracked but unbroken during the tidal disruption. Impact conditions and possible interactions of the comet's debris with the jovian system during the encounter in July 1994 are described.

APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RÉNYI DIVERGENCES.

PubMed

Han, Qiyang; Wellner, Jon A

2016-01-01

In this paper, we study the approximation and estimation of s -concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s -concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [ Ann. Statist. 38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show continuity of the divergence functional in Q : if Q n → Q in the Wasserstein metric, then the projected densities converge in weighted L 1 metrics and uniformly on closed subsets of the continuity set of the limit. Moreover, directional derivatives of the projected densities also enjoy local uniform convergence. This contains both on-the-model and off-the-model situations, and entails strong consistency of the divergence estimator of an s -concave density under mild conditions. One interesting and important feature for the Rényi divergence estimator of an s -concave density is that the estimator is intrinsically related with the estimation of log-concave densities via maximum likelihood methods. In fact, we show that for d = 1 at least, the Rényi divergence estimators for s -concave densities converge to the maximum likelihood estimator of a log-concave density as s ↗ 0. The Rényi divergence estimator shares similar characterizations as the MLE for log-concave distributions, which allows us to develop pointwise asymptotic distribution theory assuming that the underlying density is s -concave.

APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RÉNYI DIVERGENCES

PubMed Central

Han, Qiyang; Wellner, Jon A.

2017-01-01

In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist. 38 (2010) 2998–3027] if and only if Q admits full-dimensional support and a first moment. We also show continuity of the divergence functional in Q: if Qn → Q in the Wasserstein metric, then the projected densities converge in weighted L1 metrics and uniformly on closed subsets of the continuity set of the limit. Moreover, directional derivatives of the projected densities also enjoy local uniform convergence. This contains both on-the-model and off-the-model situations, and entails strong consistency of the divergence estimator of an s-concave density under mild conditions. One interesting and important feature for the Rényi divergence estimator of an s-concave density is that the estimator is intrinsically related with the estimation of log-concave densities via maximum likelihood methods. In fact, we show that for d = 1 at least, the Rényi divergence estimators for s-concave densities converge to the maximum likelihood estimator of a log-concave density as s ↗ 0. The Rényi divergence estimator shares similar characterizations as the MLE for log-concave distributions, which allows us to develop pointwise asymptotic distribution theory assuming that the underlying density is s-concave. PMID:28966410

Bivariate normal, conditional and rectangular probabilities: A computer program with applications

NASA Technical Reports Server (NTRS)

Swaroop, R.; Brownlow, J. D.; Ashwworth, G. R.; Winter, W. R.

1980-01-01

Some results for the bivariate normal distribution analysis are presented. Computer programs for conditional normal probabilities, marginal probabilities, as well as joint probabilities for rectangular regions are given: routines for computing fractile points and distribution functions are also presented. Some examples from a closed circuit television experiment are included.

Assessment of source probabilities for potential tsunamis affecting the U.S. Atlantic coast

USGS Publications Warehouse

Geist, E.L.; Parsons, T.

2009-01-01

Estimating the likelihood of tsunamis occurring along the U.S. Atlantic coast critically depends on knowledge of tsunami source probability. We review available information on both earthquake and landslide probabilities from potential sources that could generate local and transoceanic tsunamis. Estimating source probability includes defining both size and recurrence distributions for earthquakes and landslides. For the former distribution, source sizes are often distributed according to a truncated or tapered power-law relationship. For the latter distribution, sources are often assumed to occur in time according to a Poisson process, simplifying the way tsunami probabilities from individual sources can be aggregated. For the U.S. Atlantic coast, earthquake tsunami sources primarily occur at transoceanic distances along plate boundary faults. Probabilities for these sources are constrained from previous statistical studies of global seismicity for similar plate boundary types. In contrast, there is presently little information constraining landslide probabilities that may generate local tsunamis. Though there is significant uncertainty in tsunami source probabilities for the Atlantic, results from this study yield a comparative analysis of tsunami source recurrence rates that can form the basis for future probabilistic analyses.

A new model to predict weak-lensing peak counts. II. Parameter constraint strategies

NASA Astrophysics Data System (ADS)

Lin, Chieh-An; Kilbinger, Martin

2015-11-01

Context. Peak counts have been shown to be an excellent tool for extracting the non-Gaussian part of the weak lensing signal. Recently, we developed a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analysis. Aims: In this work, we explore and compare various strategies for constraining a parameter using our model, focusing on the matter density Ωm and the density fluctuation amplitude σ8. Methods: First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analysis with the copula likelihood, a technique that makes a weaker assumption than does the Gaussian likelihood. Third, direct, non-analytic parameter estimations are applied using the full information of the distribution. Fourth, we obtain constraints with approximate Bayesian computation (ABC), an efficient, robust, and likelihood-free algorithm based on accept-reject sampling. Results: We find that neglecting the CDC effect enlarges parameter contours by 22% and that the covariance-varying copula likelihood is a very good approximation to the true likelihood. The direct techniques work well in spite of noisier contours. Concerning ABC, the iterative process converges quickly to a posterior distribution that is in excellent agreement with results from our other analyses. The time cost for ABC is reduced by two orders of magnitude. Conclusions: The stochastic nature of our weak-lensing peak count model allows us to use various techniques that approach the true underlying probability distribution of observables, without making simplifying assumptions. Our work can be generalized to other observables where forward simulations provide samples of the underlying distribution.

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.

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

Friar, James Lewis; Goldman, Terrance J.; Pérez-Mercader, J.

In this paper, we apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdf's), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the scale-change distribution function is scale invariant then the constructed distribution will also be scale invariant. Repeated application of this construction on an arbitrary set of (normalizable) pdf's results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. Finally, we separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropymore » for size-class distributions with uniform bin sizes.« less

Positive phase space distributions and uncertainty relations

NASA Technical Reports Server (NTRS)

Kruger, Jan

1993-01-01

In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.

Extreme Statistics of Storm Surges in the Baltic Sea

NASA Astrophysics Data System (ADS)

Kulikov, E. A.; Medvedev, I. P.

2017-11-01

Statistical analysis of the extreme values of the Baltic Sea level has been performed for a series of observations for 15-125 years at 13 tide gauge stations. It is shown that the empirical relation between value of extreme sea level rises or ebbs (caused by storm events) and its return period in the Baltic Sea can be well approximated by the Gumbel probability distribution. The maximum values of extreme floods/ebbs of the 100-year recurrence were observed in the Gulf of Finland and the Gulf of Riga. The two longest data series, observed in Stockholm and Vyborg over 125 years, have shown a significant deviation from the Gumbel distribution for the rarest events. Statistical analysis of the hourly sea level data series reveals some asymmetry in the variability of the Baltic Sea level. The probability of rises proved higher than that of ebbs. As for the magnitude of the 100-year recurrence surge, it considerably exceeded the magnitude of ebbs almost everywhere. This asymmetry effect can be attributed to the influence of low atmospheric pressure during storms. A statistical study of extreme values has also been applied to sea level series for Narva over the period of 1994-2000, which were simulated by the ROMS numerical model. Comparisons of the "simulated" and "observed" extreme sea level distributions show that the model reproduces quite satisfactorily extreme floods of "moderate" magnitude; however, it underestimates sea level changes for the most powerful storm surges.

Ecological niche models reveal the importance of climate variability for the biogeography of protosteloid amoebae

PubMed Central

Aguilar, María; Lado, Carlos

2012-01-01

Habitat availability and environmental preferences of species are among the most important factors in determining the success of dispersal processes and therefore in shaping the distribution of protists. We explored the differences in fundamental niches and potential distributions of an ecological guild of slime moulds—protosteloid amoebae—in the Iberian Peninsula. A large set of samples collected in a north-east to south-west transect of approximately 1000 km along the peninsula was used to test the hypothesis that, together with the existence of suitable microhabitats, climate conditions may determine the probability of survival of species. Although protosteloid amoebae share similar morphologies and life history strategies, canonical correspondence analyses showed that they have varied ecological optima, and that climate conditions have an important effect in niche differentiation. Maxent environmental niche models provided consistent predictions of the probability of presence of the species based on climate data, and they were used to generate maps of potential distribution in an ‘everything is everywhere' scenario. The most important climatic factors were, in both analyses, variables that measure changes in conditions throughout the year, confirming that the alternation of fruiting bodies, cysts and amoeboid stages in the life cycles of protosteloid amoebae constitutes an advantage for surviving in a changing environment. Microhabitat affinity seems to be influenced by climatic conditions, which suggests that the micro-environment may vary at a local scale and change together with the external climate at a larger scale. PMID:22402402

Ecological niche models reveal the importance of climate variability for the biogeography of protosteloid amoebae.

PubMed

Aguilar, María; Lado, Carlos

2012-08-01

Habitat availability and environmental preferences of species are among the most important factors in determining the success of dispersal processes and therefore in shaping the distribution of protists. We explored the differences in fundamental niches and potential distributions of an ecological guild of slime moulds-protosteloid amoebae-in the Iberian Peninsula. A large set of samples collected in a north-east to south-west transect of approximately 1000 km along the peninsula was used to test the hypothesis that, together with the existence of suitable microhabitats, climate conditions may determine the probability of survival of species. Although protosteloid amoebae share similar morphologies and life history strategies, canonical correspondence analyses showed that they have varied ecological optima, and that climate conditions have an important effect in niche differentiation. Maxent environmental niche models provided consistent predictions of the probability of presence of the species based on climate data, and they were used to generate maps of potential distribution in an 'everything is everywhere' scenario. The most important climatic factors were, in both analyses, variables that measure changes in conditions throughout the year, confirming that the alternation of fruiting bodies, cysts and amoeboid stages in the life cycles of protosteloid amoebae constitutes an advantage for surviving in a changing environment. Microhabitat affinity seems to be influenced by climatic conditions, which suggests that the micro-environment may vary at a local scale and change together with the external climate at a larger scale.

Exact sampling hardness of Ising spin models

NASA Astrophysics Data System (ADS)

Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.

2017-09-01

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

Unified framework for information integration based on information geometry

PubMed Central

Oizumi, Masafumi; Amari, Shun-ichi

2016-01-01

Assessment of causal influences is a ubiquitous and important subject across diverse research fields. Drawn from consciousness studies, integrated information is a measure that defines integration as the degree of causal influences among elements. Whereas pairwise causal influences between elements can be quantified with existing methods, quantifying multiple influences among many elements poses two major mathematical difficulties. First, overestimation occurs due to interdependence among influences if each influence is separately quantified in a part-based manner and then simply summed over. Second, it is difficult to isolate causal influences while avoiding noncausal confounding influences. To resolve these difficulties, we propose a theoretical framework based on information geometry for the quantification of multiple causal influences with a holistic approach. We derive a measure of integrated information, which is geometrically interpreted as the divergence between the actual probability distribution of a system and an approximated probability distribution where causal influences among elements are statistically disconnected. This framework provides intuitive geometric interpretations harmonizing various information theoretic measures in a unified manner, including mutual information, transfer entropy, stochastic interaction, and integrated information, each of which is characterized by how causal influences are disconnected. In addition to the mathematical assessment of consciousness, our framework should help to analyze causal relationships in complex systems in a complete and hierarchical manner. PMID:27930289

The study of RMB exchange rate complex networks based on fluctuation mode

NASA Astrophysics Data System (ADS)

Yao, Can-Zhong; Lin, Ji-Nan; Zheng, Xu-Zhou; Liu, Xiao-Feng

2015-10-01

In the paper, we research on the characteristics of RMB exchange rate time series fluctuation with methods of symbolization and coarse gaining. First, based on fluctuation features of RMB exchange rate, we define the first type of fluctuation mode as one specific foreign currency against RMB in four days' fluctuating situations, and the second type as four different foreign currencies against RMB in one day's fluctuating situation. With the transforming method, we construct the unique-currency and multi-currency complex networks. Further, through analyzing the topological features including out-degree, betweenness centrality and clustering coefficient of fluctuation-mode complex networks, we find that the out-degree distribution of both types of fluctuation mode basically follows power-law distributions with exponents between 1 and 2. The further analysis reveals that the out-degree and the clustering coefficient generally obey the approximated negative correlation. With this result, we confirm previous observations showing that the RMB exchange rate exhibits a characteristic of long-range memory. Finally, we analyze the most probable transmission route of fluctuation modes, and provide probability prediction matrix. The transmission route for RMB exchange rate fluctuation modes exhibits the characteristics of partially closed loop, repeat and reversibility, which lays a solid foundation for predicting RMB exchange rate fluctuation patterns with large volume of data.

Estimating occupancy probability of moose using hunter survey data

USGS Publications Warehouse

Crum, Nathan J.; Fuller, Angela K.; Sutherland, Christopher S.; Cooch, Evan G.; Hurst, Jeremy E.

2017-01-01

Monitoring rare species can be difficult, especially across large spatial extents, making conventional methods of population monitoring costly and logistically challenging. Citizen science has the potential to produce observational data across large areas that can be used to monitor wildlife distributions using occupancy models. We used citizen science (i.e., hunter surveys) to facilitate monitoring of moose (Alces alces) populations, an especially important endeavor because of their recent apparent declines in the northeastern and upper midwestern regions of the United States. To better understand patterns of occurrence of moose in New York, we used data collected through an annual survey of approximately 11,000 hunters between 2012 and 2014 that recorded detection–non-detection data of moose and other species. We estimated patterns of occurrence of moose in relation to land cover characteristics, climate effects, and interspecific interactions using occupancy models to analyze spatially referenced moose observations. Coniferous and deciduous forest with low prevalence of white-tailed deer (Odocoileus virginianus) had the highest probability of moose occurrence. This study highlights the potential of data collected using citizen science for understanding the spatial distribution of low-density species across large spatial extents and providing key information regarding where and when future research and management activities should be focused.

Simulation and evaluation of phase noise for optical amplification using semiconductor optical amplifiers in DPSK applications

NASA Astrophysics Data System (ADS)

Hong, Wei; Huang, Dexiu; Zhang, Xinliang; Zhu, Guangxi

2008-01-01

A thorough simulation and evaluation of phase noise for optical amplification using semiconductor optical amplifier (SOA) is very important for predicting its performance in differential phase-shift keyed (DPSK) applications. In this paper, standard deviation and probability distribution of differential phase noise at the SOA output are obtained from the statistics of simulated differential phase noise. By using a full-wave model of SOA, the noise performance in the entire operation range can be investigated. It is shown that nonlinear phase noise substantially contributes to the total phase noise in case of a noisy signal amplified by a saturated SOA and the nonlinear contribution is larger with shorter SOA carrier lifetime. It is also shown that Gaussian distribution can be useful as a good approximation of the total differential phase noise statistics in the whole operation range. Power penalty due to differential phase noise is evaluated using a semi-analytical probability density function (PDF) of receiver noise. Obvious increase of power penalty at high signal input powers can be found for low input OSNR, which is due to both the large nonlinear differential phase noise and the dependence of BER vs. receiving power curvature on differential phase noise standard deviation.

Photographic mark-recapture analysis of local dynamics within an open population of dolphins.

PubMed

Fearnbach, H; Durban, J; Parsons, K; Claridge, D

2012-07-01

Identifying demographic changes is important for understanding population dynamics. However, this requires long-term studies of definable populations of distinct individuals, which can be particularly challenging when studying mobile cetaceans in the marine environment. We collected photo-identification data from 19 years (1992-2010) to assess the dynamics of a population of bottlenose dolphins (Tursiops truncatus) restricted to the shallow (<7 m) waters of Little Bahama Bank, northern Bahamas. This population was known to range beyond our study area, so we adopted a Bayesian mixture modeling approach to mark-recapture to identify clusters of individuals that used the area to different extents, and we specifically estimated trends in survival, recruitment, and abundance of a "resident" population with high probabilities of identification. There was a high probability (p= 0.97) of a long-term decrease in the size of this resident population from a maximum of 47 dolphins (95% highest posterior density intervals, HPDI = 29-61) in 1996 to a minimum of just 24 dolphins (95% HPDI = 14-37) in 2009, a decline of 49% (95% HPDI = approximately 5% to approximately 75%). This was driven by low per capita recruitment (average approximately 0.02) that could not compensate for relatively low apparent survival rates (average approximately 0.94). Notably, there was a significant increase in apparent mortality (approximately 5 apparent mortalities vs. approximately 2 on average) in 1999 when two intense hurricanes passed over the study area, with a high probability (p = 0.83) of a drop below the average survival probability (approximately 0.91 in 1999; approximately 0.94, on average). As such, our mark-recapture approach enabled us to make useful inference about local dynamics within an open population of bottlenose dolphins; this should be applicable to other studies challenged by sampling highly mobile individuals with heterogeneous space use.

Ubiquity of Benford's law and emergence of the reciprocal distribution

DOE PAGES

Friar, James Lewis; Goldman, Terrance J.; Pérez-Mercader, J.

2016-04-07

In this paper, we apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdf's), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the scale-change distribution function is scale invariant then the constructed distribution will also be scale invariant. Repeated application of this construction on an arbitrary set of (normalizable) pdf's results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. Finally, we separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropymore » for size-class distributions with uniform bin sizes.« less

Parametric vs. non-parametric statistics of low resolution electromagnetic tomography (LORETA).

PubMed

Thatcher, R W; North, D; Biver, C

2005-01-01

This study compared the relative statistical sensitivity of non-parametric and parametric statistics of 3-dimensional current sources as estimated by the EEG inverse solution Low Resolution Electromagnetic Tomography (LORETA). One would expect approximately 5% false positives (classification of a normal as abnormal) at the P < .025 level of probability (two tailed test) and approximately 1% false positives at the P < .005 level. EEG digital samples (2 second intervals sampled 128 Hz, 1 to 2 minutes eyes closed) from 43 normal adult subjects were imported into the Key Institute's LORETA program. We then used the Key Institute's cross-spectrum and the Key Institute's LORETA output files (*.lor) as the 2,394 gray matter pixel representation of 3-dimensional currents at different frequencies. The mean and standard deviation *.lor files were computed for each of the 2,394 gray matter pixels for each of the 43 subjects. Tests of Gaussianity and different transforms were computed in order to best approximate a normal distribution for each frequency and gray matter pixel. The relative sensitivity of parametric vs. non-parametric statistics were compared using a "leave-one-out" cross validation method in which individual normal subjects were withdrawn and then statistically classified as being either normal or abnormal based on the remaining subjects. Log10 transforms approximated Gaussian distribution in the range of 95% to 99% accuracy. Parametric Z score tests at P < .05 cross-validation demonstrated an average misclassification rate of approximately 4.25%, and range over the 2,394 gray matter pixels was 27.66% to 0.11%. At P < .01 parametric Z score cross-validation false positives were 0.26% and ranged from 6.65% to 0% false positives. The non-parametric Key Institute's t-max statistic at P < .05 had an average misclassification error rate of 7.64% and ranged from 43.37% to 0.04% false positives. The nonparametric t-max at P < .01 had an average misclassification rate of 6.67% and ranged from 41.34% to 0% false positives of the 2,394 gray matter pixels for any cross-validated normal subject. In conclusion, adequate approximation to Gaussian distribution and high cross-validation can be achieved by the Key Institute's LORETA programs by using a log10 transform and parametric statistics, and parametric normative comparisons had lower false positive rates than the non-parametric tests.

Methane bubbling from northern lakes: present and future contributions to the global methane budget.

PubMed

Walter, Katey M; Smith, Laurence C; Chapin, F Stuart

2007-07-15

Large uncertainties in the budget of atmospheric methane (CH4) limit the accuracy of climate change projections. Here we describe and quantify an important source of CH4 -- point-source ebullition (bubbling) from northern lakes -- that has not been incorporated in previous regional or global methane budgets. Employing a method recently introduced to measure ebullition more accurately by taking into account its spatial patchiness in lakes, we estimate point-source ebullition for 16 lakes in Alaska and Siberia that represent several common northern lake types: glacial, alluvial floodplain, peatland and thermokarst (thaw) lakes. Extrapolation of measured fluxes from these 16 sites to all lakes north of 45 degrees N using circumpolar databases of lake and permafrost distributions suggests that northern lakes are a globally significant source of atmospheric CH4, emitting approximately 24.2+/-10.5Tg CH4yr(-1). Thermokarst lakes have particularly high emissions because they release CH4 produced from organic matter previously sequestered in permafrost. A carbon mass balance calculation of CH4 release from thermokarst lakes on the Siberian yedoma ice complex suggests that these lakes alone would emit as much as approximately 49000Tg CH4 if this ice complex was to thaw completely. Using a space-for-time substitution based on the current lake distributions in permafrost-dominated and permafrost-free terrains, we estimate that lake emissions would be reduced by approximately 12% in a more probable transitional permafrost scenario and by approximately 53% in a 'permafrost-free' Northern Hemisphere. Long-term decline in CH4 ebullition from lakes due to lake area loss and permafrost thaw would occur only after the large release of CH4 associated thermokarst lake development in the zone of continuous permafrost.

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our method to others in the literature as well as the aforementioned TRW estimator.

Spatial Probability Distribution of Strata's Lithofacies and its Impacts on Land Subsidence in Huairou Emergency Water Resources Region of Beijing

NASA Astrophysics Data System (ADS)

Li, Y.; Gong, H.; Zhu, L.; Guo, L.; Gao, M.; Zhou, C.

2016-12-01

Continuous over-exploitation of groundwater causes dramatic drawdown, and leads to regional land subsidence in the Huairou Emergency Water Resources region, which is located in the up-middle part of the Chaobai river basin of Beijing. Owing to the spatial heterogeneity of strata's lithofacies of the alluvial fan, ground deformation has no significant positive correlation with groundwater drawdown, and one of the challenges ahead is to quantify the spatial distribution of strata's lithofacies. The transition probability geostatistics approach provides potential for characterizing the distribution of heterogeneous lithofacies in the subsurface. Combined the thickness of clay layer extracted from the simulation, with deformation field acquired from PS-InSAR technology, the influence of strata's lithofacies on land subsidence can be analyzed quantitatively. The strata's lithofacies derived from borehole data were generalized into four categories and their probability distribution in the observe space was mined by using the transition probability geostatistics, of which clay was the predominant compressible material. Geologically plausible realizations of lithofacies distribution were produced, accounting for complex heterogeneity in alluvial plain. At a particular probability level of more than 40 percent, the volume of clay defined was 55 percent of the total volume of strata's lithofacies. This level, equaling nearly the volume of compressible clay derived from the geostatistics, was thus chosen to represent the boundary between compressible and uncompressible material. The method incorporates statistical geological information, such as distribution proportions, average lengths and juxtaposition tendencies of geological types, mainly derived from borehole data and expert knowledge, into the Markov chain model of transition probability. Some similarities of patterns were indicated between the spatial distribution of deformation field and clay layer. In the area with roughly similar water table decline, locations in the subsurface having a higher probability for the existence of compressible material occur more than that in the location with a lower probability. Such estimate of spatial probability distribution is useful to analyze the uncertainty of land subsidence.

Aerosol-type retrieval and uncertainty quantification from OMI data

NASA Astrophysics Data System (ADS)

Kauppi, Anu; Kolmonen, Pekka; Laine, Marko; Tamminen, Johanna

2017-11-01

We discuss uncertainty quantification for aerosol-type selection in satellite-based atmospheric aerosol retrieval. The retrieval procedure uses precalculated aerosol microphysical models stored in look-up tables (LUTs) and top-of-atmosphere (TOA) spectral reflectance measurements to solve the aerosol characteristics. The forward model approximations cause systematic differences between the modelled and observed reflectance. Acknowledging this model discrepancy as a source of uncertainty allows us to produce more realistic uncertainty estimates and assists the selection of the most appropriate LUTs for each individual retrieval.This paper focuses on the aerosol microphysical model selection and characterisation of uncertainty in the retrieved aerosol type and aerosol optical depth (AOD). The concept of model evidence is used as a tool for model comparison. The method is based on Bayesian inference approach, in which all uncertainties are described as a posterior probability distribution. When there is no single best-matching aerosol microphysical model, we use a statistical technique based on Bayesian model averaging to combine AOD posterior probability densities of the best-fitting models to obtain an averaged AOD estimate. We also determine the shared evidence of the best-matching models of a certain main aerosol type in order to quantify how plausible it is that it represents the underlying atmospheric aerosol conditions.The developed method is applied to Ozone Monitoring Instrument (OMI) measurements using a multiwavelength approach for retrieving the aerosol type and AOD estimate with uncertainty quantification for cloud-free over-land pixels. Several larger pixel set areas were studied in order to investigate the robustness of the developed method. We evaluated the retrieved AOD by comparison with ground-based measurements at example sites. We found that the uncertainty of AOD expressed by posterior probability distribution reflects the difficulty in model selection. The posterior probability distribution can provide a comprehensive characterisation of the uncertainty in this kind of problem for aerosol-type selection. As a result, the proposed method can account for the model error and also include the model selection uncertainty in the total uncertainty budget.

Evolutionary dynamics of incubation periods

PubMed Central

Ottino-Loffler, Bertrand; Scott, Jacob G

2017-01-01

The incubation period for typhoid, polio, measles, leukemia and many other diseases follows a right-skewed, approximately lognormal distribution. Although this pattern was discovered more than sixty years ago, it remains an open question to explain its ubiquity. Here, we propose an explanation based on evolutionary dynamics on graphs. For simple models of a mutant or pathogen invading a network-structured population of healthy cells, we show that skewed distributions of incubation periods emerge for a wide range of assumptions about invader fitness, competition dynamics, and network structure. The skewness stems from stochastic mechanisms associated with two classic problems in probability theory: the coupon collector and the random walk. Unlike previous explanations that rely crucially on heterogeneity, our results hold even for homogeneous populations. Thus, we predict that two equally healthy individuals subjected to equal doses of equally pathogenic agents may, by chance alone, show remarkably different time courses of disease. PMID:29266000

The competitiveness versus the wealth of a country.

PubMed

Podobnik, Boris; Horvatić, Davor; Kenett, Dror Y; Stanley, H Eugene

2012-01-01

Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its per capita GDP (gdp) rank within a decade follows an exponential distribution with decay constant λ = 0.12. We use the Corruption Perceptions Index (CPI) and the Global Competitiveness Index (GCI) and find that the distribution of change in CPI (GCI) rank follows exponential functions with approximately the same exponent as λ, suggesting that the dynamics of gdp, CPI, and GCI may share the same origin. Using the GCI, we develop a new measure, which we call relative competitiveness, to evaluate an economy's competitiveness relative to its gdp. For all European and EU countries during the 2008-2011 economic downturn we find that the drop in gdp in more competitve countries relative to gdp was substantially smaller than in relatively less competitive countries, which is valuable information for policymakers.

The competitiveness versus the wealth of a country

PubMed Central

Podobnik, Boris; Horvatić, Davor; Kenett, Dror Y.; Stanley, H. Eugene

2012-01-01

Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its per capita GDP (gdp) rank within a decade follows an exponential distribution with decay constant λ = 0.12. We use the Corruption Perceptions Index (CPI) and the Global Competitiveness Index (GCI) and find that the distribution of change in CPI (GCI) rank follows exponential functions with approximately the same exponent as λ, suggesting that the dynamics of gdp, CPI, and GCI may share the same origin. Using the GCI, we develop a new measure, which we call relative competitiveness, to evaluate an economy's competitiveness relative to its gdp. For all European and EU countries during the 2008–2011 economic downturn we find that the drop in gdp in more competitve countries relative to gdp was substantially smaller than in relatively less competitive countries, which is valuable information for policymakers. PMID:22997552

Evolutionary dynamics of incubation periods.

PubMed

Ottino-Loffler, Bertrand; Scott, Jacob G; Strogatz, Steven H

2017-12-21

The incubation period for typhoid, polio, measles, leukemia and many other diseases follows a right-skewed, approximately lognormal distribution. Although this pattern was discovered more than sixty years ago, it remains an open question to explain its ubiquity. Here, we propose an explanation based on evolutionary dynamics on graphs. For simple models of a mutant or pathogen invading a network-structured population of healthy cells, we show that skewed distributions of incubation periods emerge for a wide range of assumptions about invader fitness, competition dynamics, and network structure. The skewness stems from stochastic mechanisms associated with two classic problems in probability theory: the coupon collector and the random walk. Unlike previous explanations that rely crucially on heterogeneity, our results hold even for homogeneous populations. Thus, we predict that two equally healthy individuals subjected to equal doses of equally pathogenic agents may, by chance alone, show remarkably different time courses of disease.

SER Analysis of MPPM-Coded MIMO-FSO System over Uncorrelated and Correlated Gamma-Gamma Atmospheric Turbulence Channels

NASA Astrophysics Data System (ADS)

Khallaf, Haitham S.; Garrido-Balsells, José M.; Shalaby, Hossam M. H.; Sampei, Seiichi

2015-12-01

The performance of multiple-input multiple-output free space optical (MIMO-FSO) communication systems, that adopt multipulse pulse position modulation (MPPM) techniques, is analyzed. Both exact and approximate symbol-error rates (SERs) are derived for both cases of uncorrelated and correlated channels. The effects of background noise, receiver shot-noise, and atmospheric turbulence are taken into consideration in our analysis. The random fluctuations of the received optical irradiance, produced by the atmospheric turbulence, is modeled by the widely used gamma-gamma statistical distribution. Uncorrelated MIMO channels are modeled by the α-μ distribution. A closed-form expression for the probability density function of the optical received irradiance is derived for the case of correlated MIMO channels. Using our analytical expressions, the degradation of the system performance with the increment of the correlation coefficients between MIMO channels is corroborated.

Distributed Adaptive Neural Network Output Tracking of Leader-Following High-Order Stochastic Nonlinear Multiagent Systems With Unknown Dead-Zone Input.

PubMed

Hua, Changchun; Zhang, Liuliu; Guan, Xinping

2017-01-01

This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.

The competitiveness versus the wealth of a country

NASA Astrophysics Data System (ADS)

Podobnik, Boris; Horvatić, Davor; Kenett, Dror Y.; Stanley, H. Eugene

2012-09-01

Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its per capita GDP (gdp) rank within a decade follows an exponential distribution with decay constant λ = 0.12. We use the Corruption Perceptions Index (CPI) and the Global Competitiveness Index (GCI) and find that the distribution of change in CPI (GCI) rank follows exponential functions with approximately the same exponent as λ, suggesting that the dynamics of gdp, CPI, and GCI may share the same origin. Using the GCI, we develop a new measure, which we call relative competitiveness, to evaluate an economy's competitiveness relative to its gdp. For all European and EU countries during the 2008-2011 economic downturn we find that the drop in gdp in more competitve countries relative to gdp was substantially smaller than in relatively less competitive countries, which is valuable information for policymakers.

Improved statistical fluctuation analysis for measurement-device-independent quantum key distribution with four-intensity decoy-state method.

PubMed

Mao, Chen-Chen; Zhou, Xing-Yu; Zhu, Jian-Rong; Zhang, Chun-Hui; Zhang, Chun-Mei; Wang, Qin

2018-05-14

Recently Zhang et al [ Phys. Rev. A95, 012333 (2017)] developed a new approach to estimate the failure probability for the decoy-state BB84 QKD system when taking finite-size key effect into account, which offers security comparable to Chernoff bound, while results in an improved key rate and transmission distance. Based on Zhang et al's work, now we extend this approach to the case of the measurement-device-independent quantum key distribution (MDI-QKD), and for the first time implement it onto the four-intensity decoy-state MDI-QKD system. Moreover, through utilizing joint constraints and collective error-estimation techniques, we can obviously increase the performance of practical MDI-QKD systems compared with either three- or four-intensity decoy-state MDI-QKD using Chernoff bound analysis, and achieve much higher level security compared with those applying Gaussian approximation analysis.

A fast algorithm for determining bounds and accurate approximate p-values of the rank product statistic for replicate experiments.

PubMed

Heskes, Tom; Eisinga, Rob; Breitling, Rainer

2014-11-21

The rank product method is a powerful statistical technique for identifying differentially expressed molecules in replicated experiments. A critical issue in molecule selection is accurate calculation of the p-value of the rank product statistic to adequately address multiple testing. Both exact calculation and permutation and gamma approximations have been proposed to determine molecule-level significance. These current approaches have serious drawbacks as they are either computationally burdensome or provide inaccurate estimates in the tail of the p-value distribution. We derive strict lower and upper bounds to the exact p-value along with an accurate approximation that can be used to assess the significance of the rank product statistic in a computationally fast manner. The bounds and the proposed approximation are shown to provide far better accuracy over existing approximate methods in determining tail probabilities, with the slightly conservative upper bound protecting against false positives. We illustrate the proposed method in the context of a recently published analysis on transcriptomic profiling performed in blood. We provide a method to determine upper bounds and accurate approximate p-values of the rank product statistic. The proposed algorithm provides an order of magnitude increase in throughput as compared with current approaches and offers the opportunity to explore new application domains with even larger multiple testing issue. The R code is published in one of the Additional files and is available at http://www.ru.nl/publish/pages/726696/rankprodbounds.zip .

Modeling the probability distribution of peak discharge for infiltrating hillslopes

NASA Astrophysics Data System (ADS)

Baiamonte, Giorgio; Singh, Vijay P.

2017-07-01

Hillslope response plays a fundamental role in the prediction of peak discharge at the basin outlet. The peak discharge for the critical duration of rainfall and its probability distribution are needed for designing urban infrastructure facilities. This study derives the probability distribution, denoted as GABS model, by coupling three models: (1) the Green-Ampt model for computing infiltration, (2) the kinematic wave model for computing discharge hydrograph from the hillslope, and (3) the intensity-duration-frequency (IDF) model for computing design rainfall intensity. The Hortonian mechanism for runoff generation is employed for computing the surface runoff hydrograph. Since the antecedent soil moisture condition (ASMC) significantly affects the rate of infiltration, its effect on the probability distribution of peak discharge is investigated. Application to a watershed in Sicily, Italy, shows that with the increase of probability, the expected effect of ASMC to increase the maximum discharge diminishes. Only for low values of probability, the critical duration of rainfall is influenced by ASMC, whereas its effect on the peak discharge seems to be less for any probability. For a set of parameters, the derived probability distribution of peak discharge seems to be fitted by the gamma distribution well. Finally, an application to a small watershed, with the aim to test the possibility to arrange in advance the rational runoff coefficient tables to be used for the rational method, and a comparison between peak discharges obtained by the GABS model with those measured in an experimental flume for a loamy-sand soil were carried out.

Multivariate moment closure techniques for stochastic kinetic models

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

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporallymore » evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.« less

Distribution of distances between DNA barcode labels in nanochannels close to the persistence length

NASA Astrophysics Data System (ADS)

Reinhart, Wesley F.; Reifenberger, Jeff G.; Gupta, Damini; Muralidhar, Abhiram; Sheats, Julian; Cao, Han; Dorfman, Kevin D.

2015-02-01

We obtained experimental extension data for barcoded E. coli genomic DNA molecules confined in nanochannels from 40 nm to 51 nm in width. The resulting data set consists of 1 627 779 measurements of the distance between fluorescent probes on 25 407 individual molecules. The probability density for the extension between labels is negatively skewed, and the magnitude of the skewness is relatively insensitive to the distance between labels. The two Odijk theories for DNA confinement bracket the mean extension and its variance, consistent with the scaling arguments underlying the theories. We also find that a harmonic approximation to the free energy, obtained directly from the probability density for the distance between barcode labels, leads to substantial quantitative error in the variance of the extension data. These results suggest that a theory for DNA confinement in such channels must account for the anharmonic nature of the free energy as a function of chain extension.

Quantum finance

NASA Astrophysics Data System (ADS)

Schaden, Martin

2002-12-01

Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding securities and cash is taken as the basis of the Hilbert space of market states. The temporal evolution of an isolated market is unitary in this space. Linear operators representing basic financial transactions such as cash transfer and the buying or selling of securities are constructed and simple model Hamiltonians that generate the temporal evolution due to cash flows and the trading of securities are proposed. The Hamiltonian describing financial transactions becomes local when the profit/loss from trading is small compared to the turnover. This approximation may describe a highly liquid and efficient stock market. The lognormal probability distribution for the price of a stock with a variance that is proportional to the elapsed time is reproduced for an equilibrium market. The asymptotic volatility of a stock in this case is related to the long-term probability that it is traded.

The difficulty of ultraviolet emssion from supernovae

NASA Technical Reports Server (NTRS)

Colgate, S. A.

1971-01-01

There are certain conceptual difficulties in the theory of the generation of ultraviolet radiation which is presumed for the creation of the optical fluorescence mechanism of supernova light emission and ionization of a nebula as large as the Gum nebula. Requirements concerning the energy distribution of the ultraviolet photons are: 1) The energy of the greater part of the photons must be sufficient to cause both helium fluorescence and hydrogen ionization. 2) If the photons are emitted in an approximate black body spectrum, the fraction of energy emitted in the optical must be no more than what is already observed. Ultraviolet black body emission depends primarily on the energy source. The probability that the wide mixture of elements present in the interstellar medium and supernova ejecta results in an emission localized in a limited region with less than 0.001 emission in the visible, for either ionization or fluorescence ultraviolet, is remote. Therefore transparent emission must be excluded as unlikely, and black body or at least quasi-black-body emission is more probable.

The escape problem for mortal walkers

NASA Astrophysics Data System (ADS)

Grebenkov, D. S.; Rupprecht, J.-F.

2017-02-01

We introduce and investigate the escape problem for random walkers that may eventually die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region on the boundary of a confining domain. In the case of a first-order kinetics (i.e., exponentially distributed lifetimes), we study the effect of the associated death rate onto the survival probability, the exit probability, and the mean first passage time. We derive the upper and lower bounds and some approximations for these quantities. We reveal three asymptotic regimes of small, intermediate, and large death rates. General estimates and asymptotics are compared to several explicit solutions for simple domains and to numerical simulations. These results allow one to account for stochastic photobleaching of fluorescent tracers in bio-imaging, degradation of mRNA molecules in genetic translation mechanisms, or high mortality rates of spermatozoa in the fertilization process. Our findings provide a mathematical ground for optimizing storage containers and materials to reduce the risk of leakage of dangerous chemicals or nuclear wastes.

Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle.

PubMed

Osche, G R

2000-08-20

Single- and multiple-pulse detection statistics are presented for aperture-averaged direct detection optical receivers operating against partially developed speckle fields. A partially developed speckle field arises when the probability density function of the received intensity does not follow negative exponential statistics. The case of interest here is the target surface that exhibits diffuse as well as specular components in the scattered radiation. An approximate expression is derived for the integrated intensity at the aperture, which leads to single- and multiple-pulse discrete probability density functions for the case of a Poisson signal in Poisson noise with an additive coherent component. In the absence of noise, the single-pulse discrete density function is shown to reduce to a generalized negative binomial distribution. The radar concept of integration loss is discussed in the context of direct detection optical systems where it is shown that, given an appropriate set of system parameters, multiple-pulse processing can be more efficient than single-pulse processing over a finite range of the integration parameter n.

FastSKAT: Sequence kernel association tests for very large sets of markers.

PubMed

Lumley, Thomas; Brody, Jennifer; Peloso, Gina; Morrison, Alanna; Rice, Kenneth

2018-06-22

The sequence kernel association test (SKAT) is widely used to test for associations between a phenotype and a set of genetic variants that are usually rare. Evaluating tail probabilities or quantiles of the null distribution for SKAT requires computing the eigenvalues of a matrix related to the genotype covariance between markers. Extracting the full set of eigenvalues of this matrix (an n×n matrix, for n subjects) has computational complexity proportional to n 3 . As SKAT is often used when n>104, this step becomes a major bottleneck in its use in practice. We therefore propose fastSKAT, a new computationally inexpensive but accurate approximations to the tail probabilities, in which the k largest eigenvalues of a weighted genotype covariance matrix or the largest singular values of a weighted genotype matrix are extracted, and a single term based on the Satterthwaite approximation is used for the remaining eigenvalues. While the method is not particularly sensitive to the choice of k, we also describe how to choose its value, and show how fastSKAT can automatically alert users to the rare cases where the choice may affect results. As well as providing faster implementation of SKAT, the new method also enables entirely new applications of SKAT that were not possible before; we give examples grouping variants by topologically associating domains, and comparing chromosome-wide association by class of histone marker. © 2018 WILEY PERIODICALS, INC.

Partial entrainment of gravel bars during floods

USGS Publications Warehouse

Konrad, Christopher P.; Booth, Derek B.; Burges, Stephen J.; Montgomery, David R.

2002-01-01

Spatial patterns of bed material entrainment by floods were documented at seven gravel bars using arrays of metal washers (bed tags) placed in the streambed. The observed patterns were used to test a general stochastic model that bed material entrainment is a spatially independent, random process where the probability of entrainment is uniform over a gravel bar and a function of the peak dimensionless shear stress τ0* of the flood. The fraction of tags missing from a gravel bar during a flood, or partial entrainment, had an approximately normal distribution with respect to τ0* with a mean value (50% of the tags entrained) of 0.085 and standard deviation of 0.022 (root‐mean‐square error of 0.09). Variation in partial entrainment for a given τ0* demonstrated the effects of flow conditioning on bed strength, with lower values of partial entrainment after intermediate magnitude floods (0.065 < τ0*< 0.08) than after higher magnitude floods. Although the probability of bed material entrainment was approximately uniform over a gravel bar during individual floods and independent from flood to flood, regions of preferential stability and instability emerged at some bars over the course of a wet season. Deviations from spatially uniform and independent bed material entrainment were most pronounced for reaches with varied flow and in consecutive floods with small to intermediate magnitudes.

Spatial pattern of groundwater arsenic occurrence and association with bedrock geology in greater Augusta, Maine.

PubMed

Yang, Qiang; Jung, Hun Bok; Culbertson, Charles W; Marvinney, Robert G; Loiselle, Marc C; Locke, Daniel B; Cheek, Heidi; Thibodeau, Hilary; Zheng, Yan

2009-04-15

In New England, groundwater arsenic occurrence has been linked to bedrock geology on regional scales. To ascertain and quantify this linkage at intermediate (10(0)-10(1) km) scales, 790 groundwater samples from fractured bedrock aquifers in the greater Augusta, Maine area are analyzed, and 31% of the sampled wells have arsenic concentrations >10 microg/L. The probability of [As] exceeding 10 microg/L mapped by indicator kriging is highest in Silurian pelite-sandstone and pelite-limestone units (approximately 40%). This probability differs significantly (p < 0.001) from those in the Silurian-Ordovician sandstone (24%),the Devonian granite (15%), and the Ordovician-Cambrian volcanic rocks (9%). The spatial pattern of groundwater arsenic distribution resembles the bedrock map. Thus, bedrock geology is associated with arsenic occurrence in fractured bedrock aquifers of the study area at intermediate scales relevant to water resources planning. The arsenic exceedance rate for each rock unit is considered robust because low, medium, and high arsenic occurrences in four cluster areas (3-20 km2) with a low sampling density of 1-6 wells per km2 are comparable to those with a greater density of 5-42 wells per km2. About 12,000 people (21% of the population) in the greater Augusta area (approximately 1135 km2) are at risk of exposure to >10 microg/L arsenic in groundwater.

Irradiation stratigraphy and depositional history of the Apollo 16 double drive tube 60009/10

NASA Technical Reports Server (NTRS)

Blanford, G. E.; Blanford, J.; Hawkins, J. A.

1979-01-01

We report track density frequency distributions, the fraction of high density grains and minimum track densities for 63, 1 mm wide locations in the Apollo 16 double drive tube 60009/10. From these data we conclude that there are seven irradiation strata in the core. Only one buried reworking zone extending from 50-52 cm was found and it was exposed near the surface from 4.5-9 times 10 to the 6th y with a most probable exposure period of 6 times 10 to the 6th y. There is lack of conclusive data that this zone represents a reworking zone in which case the material below 52 cm most probably was exposed in situ for 4.5 times 10 to the 6th y and developed a reworking zone approximately less than 0.5 cm. The present surface of the core has a reworking zone of 12-13 cm which was exposed from 1.3 times 10 to the 7th to 2.5 times 10 to the 8th y. The best estimate for this exposure period remains the value of approximately less than 1.25 times 10 to the 8th y determined by Bogard and Hirsch (1976). The other strata in the core appear to contain mixtures of various soil types and are not related to in situ depositional events.

Constructing inverse probability weights for continuous exposures: a comparison of methods.

PubMed

Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S

2014-03-01

Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.

Minimal entropy approximation for cellular automata

NASA Astrophysics Data System (ADS)

Fukś, Henryk

2014-02-01

We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim.

Probabilistic hindcasts and projections of the coupled climate, carbon cycle and Atlantic meridional overturning circulation system: a Bayesian fusion of century-scale observations with a simple model

NASA Astrophysics Data System (ADS)

Urban, Nathan M.; Keller, Klaus

2010-10-01

How has the Atlantic Meridional Overturning Circulation (AMOC) varied over the past centuries and what is the risk of an anthropogenic AMOC collapse? We report probabilistic projections of the future climate which improve on previous AMOC projection studies by (i) greatly expanding the considered observational constraints and (ii) carefully sampling the tail areas of the parameter probability distribution function (pdf). We use a Bayesian inversion to constrain a simple model of the coupled climate, carbon cycle and AMOC systems using observations to derive multicentury hindcasts and projections. Our hindcasts show considerable skill in representing the observational constraints. We show that robust AMOC risk estimates can require carefully sampling the parameter pdfs. We find a low probability of experiencing an AMOC collapse within the 21st century for a business-as-usual emissions scenario. The probability of experiencing an AMOC collapse within two centuries is 1/10. The probability of crossing a forcing threshold and triggering a future AMOC collapse (by 2300) is approximately 1/30 in the 21st century and over 1/3 in the 22nd. Given the simplicity of the model structure and uncertainty in the forcing assumptions, our analysis should be considered a proof of concept and the quantitative conclusions subject to severe caveats.

Finite element probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes

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

Bacvarov, D.C.

1981-01-01

A new method for probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes is presented. The utilized approach of applying the finite element method for probabilistic risk assessment is demonstrated to be very powerful. The reasons for this are two. First, the finite element method is inherently suitable for analysis of three dimensional spaces where the parameters, such as three variate probability densities of the lightning currents, are non-uniformly distributed. Second, the finite element method permits non-uniform discretization of the three dimensional probability spaces thus yielding high accuracy in critical regions, such as the area of themore » low probability events, while at the same time maintaining coarse discretization in the non-critical areas to keep the number of grid points and the size of the problem to a manageable low level. The finite element probabilistic risk assessment method presented here is based on a new multidimensional search algorithm. It utilizes an efficient iterative technique for finite element interpolation of the transmission line insulation flashover criteria computed with an electro-magnetic transients program. Compared to other available methods the new finite element probabilistic risk assessment method is significantly more accurate and approximately two orders of magnitude computationally more efficient. The method is especially suited for accurate assessment of rare, very low probability events.« less

Use of the negative binomial-truncated Poisson distribution in thunderstorm prediction

NASA Technical Reports Server (NTRS)

Cohen, A. C.

1971-01-01

A probability model is presented for the distribution of thunderstorms over a small area given that thunderstorm events (1 or more thunderstorms) are occurring over a larger area. The model incorporates the negative binomial and truncated Poisson distributions. Probability tables for Cape Kennedy for spring, summer, and fall months and seasons are presented. The computer program used to compute these probabilities is appended.

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)

A Time-Dependent Quantum Dynamics Study of the H2 + CH3 yields H + CH4 Reaction

NASA Technical Reports Server (NTRS)

Wang, Dunyou; Kwak, Dochan (Technical Monitor)

2002-01-01

We present a time-dependent wave-packet propagation calculation for the H2 + CH3 yields H + CH4 reaction in six degrees of freedom and for zero total angular momentum. Initial state selected reaction probability for different initial rotational-vibrational states are presented in this study. The cumulative reaction probability (CRP) is obtained by summing over initial-state-selected reaction probability. The energy-shift approximation to account for the contribution of degrees of freedom missing in the 6D calculation is employed to obtain an approximate full-dimensional CRP. Thermal rate constant is compared with different experiment results.

A Sensitivity Analysis of Circular Error Probable Approximation Techniques

DTIC Science & Technology

1992-03-01

SENSITIVITY ANALYSIS OF CIRCULAR ERROR PROBABLE APPROXIMATION TECHNIQUES THESIS Presented to the Faculty of the School of Engineering of the Air Force...programming skills. Major Paul Auclair patiently advised me in this endeavor, and Major Andy Howell added numerous insightful contributions. I thank my...techniques. The two ret(st accuratec techniiques require numerical integration and can take several hours to run ov a personal comlputer [2:1-2,4-6]. Some

A Modeling and Data Analysis of Laser Beam Propagation in the Maritime Domain

DTIC Science & Technology

2015-05-18

approach to computing pdfs is the Kernel Density Method (Reference [9] has an intro - duction to the method), which we will apply to compute the pdf of our...The project has two parts to it: 1) we present a computational analysis of different probability density function approximation techniques; and 2) we... computational analysis of different probability density function approximation techniques; and 2) we introduce preliminary steps towards developing a

Transition probabilities of Br II

NASA Technical Reports Server (NTRS)

Bengtson, R. D.; Miller, M. H.

1976-01-01

Absolute transition probabilities of the three most prominent visible Br II lines are measured in emission. Results compare well with Coulomb approximations and with line strengths extrapolated from trends in homologous atoms.