On Orbital Elements of Extrasolar Planetary Candidates and Spectroscopic Binaries

NASA Technical Reports Server (NTRS)

Stepinski, T. F.; Black, D. C.

2001-01-01

We estimate probability densities of orbital elements, periods, and eccentricities, for the population of extrasolar planetary candidates (EPC) and, separately, for the population of spectroscopic binaries (SB) with solar-type primaries. We construct empirical cumulative distribution functions (CDFs) in order to infer probability distribution functions (PDFs) for orbital periods and eccentricities. We also derive a joint probability density for period-eccentricity pairs in each population. Comparison of respective distributions reveals that in all cases EPC and SB populations are, in the context of orbital elements, indistinguishable from each other to a high degree of statistical significance. Probability densities of orbital periods in both populations have P(exp -1) functional form, whereas the PDFs of eccentricities can he best characterized as a Gaussian with a mean of about 0.35 and standard deviation of about 0.2 turning into a flat distribution at small values of eccentricity. These remarkable similarities between EPC and SB must be taken into account by theories aimed at explaining the origin of extrasolar planetary candidates, and constitute an important clue us to their ultimate nature.

Boosting with Averaged Weight Vectors

NASA Technical Reports Server (NTRS)

Oza, Nikunj C.; Clancy, Daniel (Technical Monitor)

2002-01-01

AdaBoost is a well-known ensemble learning algorithm that constructs its constituent or base models in sequence. A key step in AdaBoost is constructing a distribution over the training examples to create each base model. This distribution, represented as a vector, is constructed to be orthogonal to the vector of mistakes made by the previous base model in the sequence. The idea is to make the next base model's errors uncorrelated with those of the previous model. Some researchers have pointed out the intuition that it is probably better to construct a distribution that is orthogonal to the mistake vectors of all the previous base models, but that this is not always possible. We present an algorithm that attempts to come as close as possible to this goal in an efficient manner. We present experimental results demonstrating significant improvement over AdaBoost and the Totally Corrective boosting algorithm, which also attempts to satisfy this goal.

Application of statistical distribution theory to launch-on-time for space construction logistic support

NASA Technical Reports Server (NTRS)

Morgenthaler, George W.

1989-01-01

The ability to launch-on-time and to send payloads into space has progressed dramatically since the days of the earliest missile and space programs. Causes for delay during launch, i.e., unplanned 'holds', are attributable to several sources: weather, range activities, vehicle conditions, human performance, etc. Recent developments in space program, particularly the need for highly reliable logistic support of space construction and the subsequent planned operation of space stations, large unmanned space structures, lunar and Mars bases, and the necessity of providing 'guaranteed' commercial launches have placed increased emphasis on understanding and mastering every aspect of launch vehicle operations. The Center of Space Construction has acquired historical launch vehicle data and is applying these data to the analysis of space launch vehicle logistic support of space construction. This analysis will include development of a better understanding of launch-on-time capability and simulation of required support systems for vehicle assembly and launch which are necessary to support national space program construction schedules. In this paper, the author presents actual launch data on unscheduled 'hold' distributions of various launch vehicles. The data have been supplied by industrial associate companies of the Center for Space Construction. The paper seeks to determine suitable probability models which describe these historical data and that can be used for several purposes such as: inputs to broader simulations of launch vehicle logistic space construction support processes and the determination of which launch operations sources cause the majority of the unscheduled 'holds', and hence to suggest changes which might improve launch-on-time. In particular, the paper investigates the ability of a compound distribution probability model to fit actual data, versus alternative models, and recommends the most productive avenues for future statistical work.

Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis

PubMed Central

Fancher, Chris M.; Han, Zhen; Levin, Igor; Page, Katharine; Reich, Brian J.; Smith, Ralph C.; Wilson, Alyson G.; Jones, Jacob L.

2016-01-01

A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method. PMID:27550221

Optimal minimal measurements of mixed states

NASA Astrophysics Data System (ADS)

Vidal, G.; Latorre, J. I.; Pascual, P.; Tarrach, R.

1999-07-01

The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized measurements, which turn out to be independent of the a priori probability distribution, obtaining the best guesses for the unknown state as well as a closed expression for the maximal mean-average fidelity. We do this for up to three copies of the unknown state in a way that leads to the generalization to any number of copies, which we then present and prove.

Percolation of spatially constrained Erdős-Rényi networks with degree correlations.

PubMed

Schmeltzer, C; Soriano, J; Sokolov, I M; Rüdiger, S

2014-01-01

Motivated by experiments on activity in neuronal cultures [ J. Soriano, M. Rodríguez Martínez, T. Tlusty and E. Moses Proc. Natl. Acad. Sci. 105 13758 (2008)], we investigate the percolation transition and critical exponents of spatially embedded Erdős-Rényi networks with degree correlations. In our model networks, nodes are randomly distributed in a two-dimensional spatial domain, and the connection probability depends on Euclidian link length by a power law as well as on the degrees of linked nodes. Generally, spatial constraints lead to higher percolation thresholds in the sense that more links are needed to achieve global connectivity. However, degree correlations favor or do not favor percolation depending on the connectivity rules. We employ two construction methods to introduce degree correlations. In the first one, nodes stay homogeneously distributed and are connected via a distance- and degree-dependent probability. We observe that assortativity in the resulting network leads to a decrease of the percolation threshold. In the second construction methods, nodes are first spatially segregated depending on their degree and afterwards connected with a distance-dependent probability. In this segregated model, we find a threshold increase that accompanies the rising assortativity. Additionally, when the network is constructed in a disassortative way, we observe that this property has little effect on the percolation transition.

Negative Binomial Process Count and Mixture Modeling.

PubMed

Zhou, Mingyuan; Carin, Lawrence

2015-02-01

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count- and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural, and computational advantages of the NB process. A variety of NB processes, including the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters.

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.

Lake bed classification using acoustic data

USGS Publications Warehouse

Yin, Karen K.; Li, Xing; Bonde, John; Richards, Carl; Cholwek, Gary

1998-01-01

As part of our effort to identify the lake bed surficial substrates using remote sensing data, this work designs pattern classifiers by multivariate statistical methods. Probability distribution of the preprocessed acoustic signal is analyzed first. A confidence region approach is then adopted to improve the design of the existing classifier. A technique for further isolation is proposed which minimizes the expected loss from misclassification. The devices constructed are applicable for real-time lake bed categorization. A mimimax approach is suggested to treat more general cases where the a priori probability distribution of the substrate types is unknown. Comparison of the suggested methods with the traditional likelihood ratio tests is discussed.

Species Distribution Models and Ecological Suitability Analysis for Potential Tick Vectors of Lyme Disease in Mexico

PubMed Central

Illoldi-Rangel, Patricia; Rivaldi, Chissa-Louise; Sissel, Blake; Trout Fryxell, Rebecca; Gordillo-Pérez, Guadalupe; Rodríguez-Moreno, Angel; Williamson, Phillip; Montiel-Parra, Griselda; Sánchez-Cordero, Víctor; Sarkar, Sahotra

2012-01-01

Species distribution models were constructed for ten Ixodes species and Amblyomma cajennense for a region including Mexico and Texas. The model was based on a maximum entropy algorithm that used environmental layers to predict the relative probability of presence for each taxon. For Mexico, species geographic ranges were predicted by restricting the models to cells which have a higher probability than the lowest probability of the cells in which a presence record was located. There was spatial nonconcordance between the distributions of Amblyomma cajennense and the Ixodes group with the former restricted to lowlands and mainly the eastern coast of Mexico and the latter to montane regions with lower temperature. The risk of Lyme disease is, therefore, mainly present in the highlands where some Ixodes species are known vectors; if Amblyomma cajennense turns out to be a competent vector, the area of risk also extends to the lowlands and the east coast. PMID:22518171

Species distribution models and ecological suitability analysis for potential tick vectors of lyme disease in Mexico.

PubMed

Illoldi-Rangel, Patricia; Rivaldi, Chissa-Louise; Sissel, Blake; Trout Fryxell, Rebecca; Gordillo-Pérez, Guadalupe; Rodríguez-Moreno, Angel; Williamson, Phillip; Montiel-Parra, Griselda; Sánchez-Cordero, Víctor; Sarkar, Sahotra

2012-01-01

Species distribution models were constructed for ten Ixodes species and Amblyomma cajennense for a region including Mexico and Texas. The model was based on a maximum entropy algorithm that used environmental layers to predict the relative probability of presence for each taxon. For Mexico, species geographic ranges were predicted by restricting the models to cells which have a higher probability than the lowest probability of the cells in which a presence record was located. There was spatial nonconcordance between the distributions of Amblyomma cajennense and the Ixodes group with the former restricted to lowlands and mainly the eastern coast of Mexico and the latter to montane regions with lower temperature. The risk of Lyme disease is, therefore, mainly present in the highlands where some Ixodes species are known vectors; if Amblyomma cajennense turns out to be a competent vector, the area of risk also extends to the lowlands and the east coast.

A discrimination method for the detection of pneumonia using chest radiograph.

PubMed

Noor, Norliza Mohd; Rijal, Omar Mohd; Yunus, Ashari; Abu-Bakar, S A R

2010-03-01

This paper presents a statistical method for the detection of lobar pneumonia when using digitized chest X-ray films. Each region of interest was represented by a vector of wavelet texture measures which is then multiplied by the orthogonal matrix Q(2). The first two elements of the transformed vectors were shown to have a bivariate normal distribution. Misclassification probabilities were estimated using probability ellipsoids and discriminant functions. The result of this study recommends the detection of pneumonia by constructing probability ellipsoids or discriminant function using maximum energy and maximum column sum energy texture measures where misclassification probabilities were less than 0.15. 2009 Elsevier Ltd. All rights reserved.

Emergence and stability of intermediate open vesicles in disk-to-vesicle transitions.

PubMed

Li, Jianfeng; Zhang, Hongdong; Qiu, Feng; Shi, An-Chang

2013-07-01

The transition between two basic structures, a disk and an enclosed vesicle, of a finite membrane is studied by examining the minimum energy path (MEP) connecting these two states. The MEP is constructed using the string method applied to continuum elastic membrane models. The results reveal that, besides the commonly observed disk and vesicle, open vesicles (bowl-shaped vesicles or vesicles with a pore) can become stable or metastable shapes. The emergence, stability, and probability distribution of these open vesicles are analyzed. It is demonstrated that open vesicles can be stabilized by higher-order elastic energies. The estimated probability distribution of the different structures is in good agreement with available experiments.

Quantum temporal probabilities in tunneling systems

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

Anastopoulos, Charis, E-mail: anastop@physics.upatras.gr; Savvidou, Ntina, E-mail: ksavvidou@physics.upatras.gr

We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal probabilities in tunneling systems that (i) defines ‘classical’ time observables for quantum systems and (ii) applies to relativistic particles interacting through quantum fields. We show that the relevant probabilities are defined in terms of specific correlation functions of the quantum field associated with tunneling particles. We construct a probability distribution with respect to the time of particle detection that contains all information about the temporal aspects ofmore » the tunneling process. In specific cases, this probability distribution leads to the definition of a delay time that, for parity-symmetric potentials, reduces to the phase time of Bohm and Wigner. We apply our results to piecewise constant potentials, by deriving the appropriate junction conditions on the points of discontinuity. For the double square potential, in particular, we demonstrate the existence of (at least) two physically relevant time parameters, the delay time and a decay rate that describes the escape of particles trapped in the inter-barrier region. Finally, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems. -- Highlights: •Present a general methodology for deriving temporal probabilities in tunneling systems. •Treatment applies to relativistic particles interacting through quantum fields. •Derive a new expression for tunneling time. •Identify new time parameters relevant to tunneling. •Propose a resolution of the superluminality paradox in tunneling.« less

Probabilistic seismic hazard in the San Francisco Bay area based on a simplified viscoelastic cycle model of fault interactions

USGS Publications Warehouse

Pollitz, F.F.; Schwartz, D.P.

2008-01-01

We construct a viscoelastic cycle model of plate boundary deformation that includes the effect of time-dependent interseismic strain accumulation, coseismic strain release, and viscoelastic relaxation of the substrate beneath the seismogenic crust. For a given fault system, time-averaged stress changes at any point (not on a fault) are constrained to zero; that is, kinematic consistency is enforced for the fault system. The dates of last rupture, mean recurrence times, and the slip distributions of the (assumed) repeating ruptures are key inputs into the viscoelastic cycle model. This simple formulation allows construction of stress evolution at all points in the plate boundary zone for purposes of probabilistic seismic hazard analysis (PSHA). Stress evolution is combined with a Coulomb failure stress threshold at representative points on the fault segments to estimate the times of their respective future ruptures. In our PSHA we consider uncertainties in a four-dimensional parameter space: the rupture peridocities, slip distributions, time of last earthquake (for prehistoric ruptures) and Coulomb failure stress thresholds. We apply this methodology to the San Francisco Bay region using a recently determined fault chronology of area faults. Assuming single-segment rupture scenarios, we find that fature rupture probabilities of area faults in the coming decades are the highest for the southern Hayward, Rodgers Creek, and northern Calaveras faults. This conclusion is qualitatively similar to that of Working Group on California Earthquake Probabilities, but the probabilities derived here are significantly higher. Given that fault rupture probabilities are highly model-dependent, no single model should be used to assess to time-dependent rupture probabilities. We suggest that several models, including the present one, be used in a comprehensive PSHA methodology, as was done by Working Group on California Earthquake Probabilities.

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

A functional model of sensemaking in a neurocognitive architecture.

PubMed

Lebiere, Christian; Pirolli, Peter; Thomson, Robert; Paik, Jaehyon; Rutledge-Taylor, Matthew; Staszewski, James; Anderson, John R

2013-01-01

Sensemaking is the active process of constructing a meaningful representation (i.e., making sense) of some complex aspect of the world. In relation to intelligence analysis, sensemaking is the act of finding and interpreting relevant facts amongst the sea of incoming reports, images, and intelligence. We present a cognitive model of core information-foraging and hypothesis-updating sensemaking processes applied to complex spatial probability estimation and decision-making tasks. While the model was developed in a hybrid symbolic-statistical cognitive architecture, its correspondence to neural frameworks in terms of both structure and mechanisms provided a direct bridge between rational and neural levels of description. Compared against data from two participant groups, the model correctly predicted both the presence and degree of four biases: confirmation, anchoring and adjustment, representativeness, and probability matching. It also favorably predicted human performance in generating probability distributions across categories, assigning resources based on these distributions, and selecting relevant features given a prior probability distribution. This model provides a constrained theoretical framework describing cognitive biases as arising from three interacting factors: the structure of the task environment, the mechanisms and limitations of the cognitive architecture, and the use of strategies to adapt to the dual constraints of cognition and the environment.

A Functional Model of Sensemaking in a Neurocognitive Architecture

PubMed Central

Lebiere, Christian; Paik, Jaehyon; Rutledge-Taylor, Matthew; Staszewski, James; Anderson, John R.

2013-01-01

Sensemaking is the active process of constructing a meaningful representation (i.e., making sense) of some complex aspect of the world. In relation to intelligence analysis, sensemaking is the act of finding and interpreting relevant facts amongst the sea of incoming reports, images, and intelligence. We present a cognitive model of core information-foraging and hypothesis-updating sensemaking processes applied to complex spatial probability estimation and decision-making tasks. While the model was developed in a hybrid symbolic-statistical cognitive architecture, its correspondence to neural frameworks in terms of both structure and mechanisms provided a direct bridge between rational and neural levels of description. Compared against data from two participant groups, the model correctly predicted both the presence and degree of four biases: confirmation, anchoring and adjustment, representativeness, and probability matching. It also favorably predicted human performance in generating probability distributions across categories, assigning resources based on these distributions, and selecting relevant features given a prior probability distribution. This model provides a constrained theoretical framework describing cognitive biases as arising from three interacting factors: the structure of the task environment, the mechanisms and limitations of the cognitive architecture, and the use of strategies to adapt to the dual constraints of cognition and the environment. PMID:24302930

Effects of the financial crisis on the wealth distribution of Korea's companies

NASA Astrophysics Data System (ADS)

Lim, Kyuseong; Kim, Soo Yong; Swanson, Todd; Kim, Jooyun

2017-02-01

We investigated the distribution functions of Korea's top-rated companies during two financial crises. A power-law scaling for rank distribution, as well as cumulative probability distribution, was found and observed as a general pattern. Similar distributions can be shown in other studies of wealth and income distributions. In our study, the Pareto exponents designating the distribution differed before and after the crisis. The companies covered in this research are divided into two subgroups during a period when the subprime mortgage crisis occurred. Various industrial sectors of Korea's companies were found to respond differently during the two financial crises, especially the construction sector, financial sectors, and insurance groups.

The Geothermal Probabilistic Cost Model with an Application to a Geothermal Reservoir at Heber, California

NASA Technical Reports Server (NTRS)

Orren, L. H.; Ziman, G. M.; Jones, S. C.

1981-01-01

A financial accounting model that incorporates physical and institutional uncertainties was developed for geothermal projects. Among the uncertainties it can handle are well depth, flow rate, fluid temperature, and permit and construction times. The outputs of the model are cumulative probability distributions of financial measures such as capital cost, levelized cost, and profit. These outputs are well suited for use in an investment decision incorporating risk. The model has the powerful feature that conditional probability distribution can be used to account for correlations among any of the input variables. The model has been applied to a geothermal reservoir at Heber, California, for a 45-MW binary electric plant. Under the assumptions made, the reservoir appears to be economically viable.

DNS of moderate-temperature gaseous mixing layers laden with multicomponent-fuel drops

NASA Technical Reports Server (NTRS)

Clercq, P. C. Le; Bellan, J.

2004-01-01

A formulation representing multicomponent-fuel (MC-fuel) composition as a Probability Distribution Function (PDF) depending on the molar weight is used to construct a model of a large number of MC-fuel drops evaporating in a gas flow, so as to assess the extent of fuel specificity on the vapor composition.

Restoration of STORM images from sparse subset of localizations (Conference Presentation)

NASA Astrophysics Data System (ADS)

Moiseev, Alexander A.; Gelikonov, Grigory V.; Gelikonov, Valentine M.

2016-02-01

To construct a Stochastic Optical Reconstruction Microscopy (STORM) image one should collect sufficient number of localized fluorophores to satisfy Nyquist criterion. This requirement limits time resolution of the method. In this work we propose a probabalistic approach to construct STORM images from a subset of localized fluorophores 3-4 times sparser than required from Nyquist criterion. Using a set of STORM images constructed from number of localizations sufficient for Nyquist criterion we derive a model which allows us to predict the probability for every location to be occupied by a fluorophore at the end of hypothetical acquisition, having as an input parameters distribution of already localized fluorophores in the proximity of this location. We show that probability map obtained from number of fluorophores 3-4 times less than required by Nyquist criterion may be used as superresolution image itself. Thus we are able to construct STORM image from a subset of localized fluorophores 3-4 times sparser than required from Nyquist criterion, proportionaly decreasing STORM data acquisition time. This method may be used complementary with other approaches desined for increasing STORM time resolution.

Paleodemographic age-at-death distributions of two Mexican skeletal collections: a comparison of transition analysis and traditional aging methods.

PubMed

Bullock, Meggan; Márquez, Lourdes; Hernández, Patricia; Ruíz, Fernando

2013-09-01

Traditional methods of aging adult skeletons suffer from the problem of age mimicry of the reference collection, as described by Bocquet-Appel and Masset (1982). Transition analysis (Boldsen et al., 2002) is a method of aging adult skeletons that addresses the problem of age mimicry of the reference collection by allowing users to select an appropriate prior probability. In order to evaluate whether transition analysis results in significantly different age estimates for adults, the method was applied to skeletal collections from Postclassic Cholula and Contact-Period Xochimilco. The resulting age-at-death distributions were then compared with age-at-death distributions for the two populations constructed using traditional aging methods. Although the traditional aging methods result in age-at-death distributions with high young adult mortality and few individuals living past the age of 50, the age-at-death distributions constructed using transition analysis indicate that most individuals who lived into adulthood lived past the age of 50. Copyright © 2013 Wiley Periodicals, Inc.

Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2016-12-01

In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posterior distribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, prior construction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In this paper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.

Precipitation intensity probability distribution modelling for hydrological and construction design purposes

NASA Astrophysics Data System (ADS)

Koshinchanov, Georgy; Dimitrov, Dobri

2008-11-01

The characteristics of rainfall intensity are important for many purposes, including design of sewage and drainage systems, tuning flood warning procedures, etc. Those estimates are usually statistical estimates of the intensity of precipitation realized for certain period of time (e.g. 5, 10 min., etc) with different return period (e.g. 20, 100 years, etc). The traditional approach in evaluating the mentioned precipitation intensities is to process the pluviometer's records and fit probability distribution to samples of intensities valid for certain locations ore regions. Those estimates further become part of the state regulations to be used for various economic activities. Two problems occur using the mentioned approach: 1. Due to various factors the climate conditions are changed and the precipitation intensity estimates need regular update; 2. As far as the extremes of the probability distribution are of particular importance for the practice, the methodology of the distribution fitting needs specific attention to those parts of the distribution. The aim of this paper is to make review of the existing methodologies for processing the intensive rainfalls and to refresh some of the statistical estimates for the studied areas. The methodologies used in Bulgaria for analyzing the intensive rainfalls and produce relevant statistical estimates: The method of the maximum intensity, used in the National Institute of Meteorology and Hydrology to process and decode the pluviometer's records, followed by distribution fitting for each precipitation duration period; As the above, but with separate modeling of probability distribution for the middle and high probability quantiles. Method is similar to the first one, but with a threshold of 0,36 mm/min of intensity; Another method proposed by the Russian hydrologist G. A. Aleksiev for regionalization of estimates over some territory, improved and adapted by S. Gerasimov for Bulgaria; Next method is considering only the intensive rainfalls (if any) during the day with the maximal annual daily precipitation total for a given year; Conclusions are drown on the relevance and adequacy of the applied methods.

VLSI Design, Parallel Computation and Distributed Computing

DTIC Science & Technology

1991-09-30

I U1 TA 3 Daniel Mleitman U. : C ..( -_. .. .s .. . . . . Tom Leighton David Shmoys . ........A ,~i ;.t , 77 Michael Sipser , Di.,t a-., Eva Tardos...Leighton and Plaxton on the construction of a sim- ple c log .- depth circuit (where c < 7.5) that sorts a random permutation with very high probability...puting iPOD( ). Aug-ust 1992. Vancouver. British Columbia (to appear). 20. B 1Xti~ c .. U(.ii. 1. Gopal. M. [Kaplan and S. Kutten, "Distributed Control for

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.

Regionalization of precipitation characteristics in Montana using L-moments

USGS Publications Warehouse

Parrett, C.

1998-01-01

Dimensionless precipitation-frequency curves for estimating precipitation depths having small exceedance probabilities were developed for 2-, 6-, and 24-hour storm durations for three homogeneous regions in Montana. L-moment statistics were used to help define the homogeneous regions. The generalized extreme value distribution was used to construct the frequency curves for each duration within each region. The effective record length for each duration in each region was estimated using a graphical method and was found to range from 500 years for 6-hour duration data in Region 2 to 5,100 years for 24-hour duration data in Region 3. The temporal characteristics of storms were analyzed, and methods for estimating synthetic storm hyetographs were developed. Dimensionless depth-duration data were grouped by independent duration (2,6, and 24 hours) and by region, and the beta distribution was fit to dimensionless depth data for various incremental time intervals. Ordinary least-squares regression was used to develop relations between dimensionless depths for a key, short duration - termed the kernel duration - and dimensionless depths for other durations. The regression relations were used, together with the probabilistic dimensionless depth data for the kernel duration, to calculate dimensionless depth-duration curves for exceedance probabilities from .1 to .9. Dimensionless storm hyetographs for each independent duration in each region were constructed for median value conditions based on an exceedance probability of .5.

In vitro culture increases mechanical stability of human tissue engineered cartilage constructs by prevention of microscale scaffold buckling.

PubMed

Middendorf, Jill M; Shortkroff, Sonya; Dugopolski, Caroline; Kennedy, Stephen; Siemiatkoski, Joseph; Bartell, Lena R; Cohen, Itai; Bonassar, Lawrence J

2017-11-07

Many studies have measured the global compressive properties of tissue engineered (TE) cartilage grown on porous scaffolds. Such scaffolds are known to exhibit strain softening due to local buckling under loading. As matrix is deposited onto these scaffolds, the global compressive properties increase. However the relationship between the amount and distribution of matrix in the scaffold and local buckling is unknown. To address this knowledge gap, we studied how local strain and construct buckling in human TE constructs changes over culture times and GAG content. Confocal elastography techniques and digital image correlation (DIC) were used to measure and record buckling modes and local strains. Receiver operating characteristic (ROC) curves were used to quantify construct buckling. The results from the ROC analysis were placed into Kaplan-Meier survival function curves to establish the probability that any point in a construct buckled. These analysis techniques revealed the presence of buckling at early time points, but bending at later time points. An inverse correlation was observed between the probability of buckling and the total GAG content of each construct. This data suggests that increased GAG content prevents the onset of construct buckling and improves the microscale compressive tissue properties. This increase in GAG deposition leads to enhanced global compressive properties by prevention of microscale buckling. Copyright © 2017 Elsevier Ltd. All rights reserved.

Technical report. The application of probability-generating functions to linear-quadratic radiation survival curves.

PubMed

Kendal, W S

2000-04-01

To illustrate how probability-generating functions (PGFs) can be employed to derive a simple probabilistic model for clonogenic survival after exposure to ionizing irradiation. Both repairable and irreparable radiation damage to DNA were assumed to occur by independent (Poisson) processes, at intensities proportional to the irradiation dose. Also, repairable damage was assumed to be either repaired or further (lethally) injured according to a third (Bernoulli) process, with the probability of lethal conversion being directly proportional to dose. Using the algebra of PGFs, these three processes were combined to yield a composite PGF that described the distribution of lethal DNA lesions in irradiated cells. The composite PGF characterized a Poisson distribution with mean, chiD+betaD2, where D was dose and alpha and beta were radiobiological constants. This distribution yielded the conventional linear-quadratic survival equation. To test the composite model, the derived distribution was used to predict the frequencies of multiple chromosomal aberrations in irradiated human lymphocytes. The predictions agreed well with observation. This probabilistic model was consistent with single-hit mechanisms, but it was not consistent with binary misrepair mechanisms. A stochastic model for radiation survival has been constructed from elementary PGFs that exactly yields the linear-quadratic relationship. This approach can be used to investigate other simple probabilistic survival models.

Evidence reasoning method for constructing conditional probability tables in a Bayesian network of multimorbidity.

PubMed

Du, Yuanwei; Guo, Yubin

2015-01-01

The intrinsic mechanism of multimorbidity is difficult to recognize and prediction and diagnosis are difficult to carry out accordingly. Bayesian networks can help to diagnose multimorbidity in health care, but it is difficult to obtain the conditional probability table (CPT) because of the lack of clinically statistical data. Today, expert knowledge and experience are increasingly used in training Bayesian networks in order to help predict or diagnose diseases, but the CPT in Bayesian networks is usually irrational or ineffective for ignoring realistic constraints especially in multimorbidity. In order to solve these problems, an evidence reasoning (ER) approach is employed to extract and fuse inference data from experts using a belief distribution and recursive ER algorithm, based on which evidence reasoning method for constructing conditional probability tables in Bayesian network of multimorbidity is presented step by step. A multimorbidity numerical example is used to demonstrate the method and prove its feasibility and application. Bayesian network can be determined as long as the inference assessment is inferred by each expert according to his/her knowledge or experience. Our method is more effective than existing methods for extracting expert inference data accurately and is fused effectively for constructing CPTs in a Bayesian network of multimorbidity.

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.

Lattice Duality: The Origin of Probability and Entropy

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.

2004-01-01

Bayesian probability theory is an inference calculus, which originates from a generalization of inclusion on the Boolean lattice of logical assertions to a degree of inclusion represented by a real number. Dual to this lattice is the distributive lattice of questions constructed from the ordered set of down-sets of assertions, which forms the foundation of the calculus of inquiry-a generalization of information theory. In this paper we introduce this novel perspective on these spaces in which machine learning is performed and discuss the relationship between these results and several proposed generalizations of information theory in the literature.

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.

An information diffusion technique to assess integrated hazard risks.

PubMed

Huang, Chongfu; Huang, Yundong

2018-02-01

An integrated risk is a scene in the future associated with some adverse incident caused by multiple hazards. An integrated probability risk is the expected value of disaster. Due to the difficulty of assessing an integrated probability risk with a small sample, weighting methods and copulas are employed to avoid this obstacle. To resolve the problem, in this paper, we develop the information diffusion technique to construct a joint probability distribution and a vulnerability surface. Then, an integrated risk can be directly assessed by using a small sample. A case of an integrated risk caused by flood and earthquake is given to show how the suggested technique is used to assess the integrated risk of annual property loss. Copyright © 2017 Elsevier Inc. All rights reserved.

Use of the Digamma Function in Statistical Astrophysics Distributions

NASA Astrophysics Data System (ADS)

Cahill, Michael

2017-06-01

Relaxed astrophysical statistical distributions may be constructed by using the inverse of a most probable energy distribution equation giving the energy ei of each particle in cell i in terms of the cell’s particle population Ni. The digamma mediated equation is A + Bei = Ψ(1+ Ni), where the constants A & B are Lagrange multipliers and Ψ is the digamma function given by Ψ(1+x) = dln(x!)/dx. Results are discussed for a Monatomic Ideal Gas, Atmospheres of Spherical Planets or Satellites and for Spherical Globular Clusters. These distributions are self-terminating even if other factors do not cause a cutoff. The examples are discussed classically but relativistic extensions are possible.

The 6dFGS Peculiar Velocity Field

NASA Astrophysics Data System (ADS)

Springob, Chris M.; Magoulas, C.; Colless, M.; Mould, J.; Erdogdu, P.; Jones, D. H.; Lucey, J.; Campbell, L.; Merson, A.; Jarrett, T.

2012-01-01

The 6dF Galaxy Survey (6dFGS) is an all southern sky galaxy survey, including 125,000 redshifts and a Fundamental Plane (FP) subsample of 10,000 peculiar velocities, making it the largest peculiar velocity sample to date. We have fit the FP using a maximum likelihood fit to a tri-variate Gaussian. We subsequently compute a Bayesian probability distribution for every possible peculiar velocity for each of the 10,000 galaxies, derived from the tri-variate Gaussian probability density distribution, accounting for our selection effects and measurement errors. We construct a predicted peculiar velocity field from the 2MASS redshift survey, and compare our observed 6dFGS velocity field to the predicted field. We discuss the resulting agreement between the observed and predicted fields, and the implications for measurements of the bias parameter and bulk flow.

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.

Modeling of magnitude distributions by the generalized truncated exponential distribution

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2015-01-01

The probability distribution of the magnitude can be modeled by an exponential distribution according to the Gutenberg-Richter relation. Two alternatives are the truncated exponential distribution (TED) and the cutoff exponential distribution (CED). The TED is frequently used in seismic hazard analysis although it has a weak point: when two TEDs with equal parameters except the upper bound magnitude are mixed, then the resulting distribution is not a TED. Inversely, it is also not possible to split a TED of a seismic region into TEDs of subregions with equal parameters except the upper bound magnitude. This weakness is a principal problem as seismic regions are constructed scientific objects and not natural units. We overcome it by the generalization of the abovementioned exponential distributions: the generalized truncated exponential distribution (GTED). Therein, identical exponential distributions are mixed by the probability distribution of the correct cutoff points. This distribution model is flexible in the vicinity of the upper bound magnitude and is equal to the exponential distribution for smaller magnitudes. Additionally, the exponential distributions TED and CED are special cases of the GTED. We discuss the possible ways of estimating its parameters and introduce the normalized spacing for this purpose. Furthermore, we present methods for geographic aggregation and differentiation of the GTED and demonstrate the potential and universality of our simple approach by applying it to empirical data. The considerable improvement by the GTED in contrast to the TED is indicated by a large difference between the corresponding values of the Akaike information criterion.

Integrated drought risk assessment of multi-hazard-affected bodies based on copulas in the Taoerhe Basin, China

NASA Astrophysics Data System (ADS)

Wang, Rui; Zhang, Jiquan; Guo, Enliang; Alu, Si; Li, Danjun; Ha, Si; Dong, Zhenhua

2018-02-01

Along with global warming, drought disasters are occurring more frequently and are seriously affecting normal life and food security in China. Drought risk assessments are necessary to provide support for local governments. This study aimed to establish an integrated drought risk model based on the relation curve of drought joint probabilities and drought losses of multi-hazard-affected bodies. First, drought characteristics, including duration and severity, were classified using the 1953-2010 precipitation anomaly in the Taoerhe Basin based on run theory, and their marginal distributions were identified by exponential and Gamma distributions, respectively. Then, drought duration and severity were related to construct a joint probability distribution based on the copula function. We used the EPIC (Environmental Policy Integrated Climate) model to simulate maize yield and historical data to calculate the loss rates of agriculture, industry, and animal husbandry in the study area. Next, we constructed vulnerability curves. Finally, the spatial distributions of drought risk for 10-, 20-, and 50-year return periods were expressed using inverse distance weighting. Our results indicate that the spatial distributions of the three return periods are consistent. The highest drought risk is in Ulanhot, and the duration and severity there were both highest. This means that higher drought risk corresponds to longer drought duration and larger drought severity, thus providing useful information for drought and water resource management. For 10-, 20-, and 50-year return periods, the drought risk values ranged from 0.41 to 0.53, 0.45 to 0.59, and 0.50 to 0.67, respectively. Therefore, when the return period increases, the drought risk increases.

Impact assessment of a high-speed railway line on species distribution: application to the European tree frog (Hyla arborea) in Franche-Comté.

PubMed

Clauzel, Céline; Girardet, Xavier; Foltête, Jean-Christophe

2013-09-30

The aim of the present work is to assess the potential long-distance effect of a high-speed railway line on the distribution of the European tree frog (Hyla arborea) in eastern France by combining graph-based analysis and species distribution models. This combination is a way to integrate patch-level connectivity metrics on different scales into a predictive model. The approach used is put in place before the construction of the infrastructure and allows areas potentially affected by isolation to be mapped. Through a diachronic analysis, comparing species distribution before and after the construction of the infrastructure, we identify changes in the probability of species presence and we determine the maximum distance of impact. The results show that the potential impact decreases with distance from the high-speed railway line and the largest disturbances occur within the first 500 m. Between 500 m and 3500 m, the infrastructure generates a moderate decrease in the probability of presence with maximum values close to -40%. Beyond 3500 m the average disturbance is less than -10%. The spatial extent of the impact is greater than the dispersal distance of the tree frog, confirming the assumption of the long-distance effect of the infrastructure. This predictive modelling approach appears to be a useful tool for environmental impact assessment and strategic environmental assessment. The results of the species distribution assessment may provide guidance for field surveys and support for conservation decisions by identifying the areas most affected. Copyright © 2013 Elsevier Ltd. All rights reserved.

Applications of physics to economics and finance: Money, income, wealth, and the stock market

NASA Astrophysics Data System (ADS)

Dragulescu, Adrian Antoniu

Several problems arising in Economics and Finance are analyzed using concepts and quantitative methods from Physics. The dissertation is organized as follows: In the first chapter it is argued that in a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann-Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. The emergence of Boltzmann-Gibbs distribution is demonstrated through computer simulations of economic models. A thermal machine which extracts a monetary profit can be constructed between two economic systems with different temperatures. The role of debt and models with broken time-reversal symmetry for which the Boltzmann-Gibbs law does not hold, are discussed. In the second chapter, using data from several sources, it is found that the distribution of income is described for the great majority of population by an exponential distribution, whereas the high-end tail follows a power law. From the individual income distribution, the probability distribution of income for families with two earners is derived and it is shown that it also agrees well with the data. Data on wealth is presented and it is found that the distribution of wealth has a structure similar to the distribution of income. The Lorenz curve and Gini coefficient were calculated and are shown to be in good agreement with both income and wealth data sets. In the third chapter, the stock-market fluctuations at different time scales are investigated. A model where stock-price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance is proposed. The corresponding Fokker-Planck equation can be solved exactly. Integrating out the variance, an analytic formula for the time-dependent probability distribution of stock price changes (returns) is found. The formula is in excellent agreement with the Dow-Jones index for the time lags from 1 to 250 trading days. For time lags longer than the relaxation time of variance, the probability distribution can be expressed in a scaling form using a Bessel function. The Dow-Jones data follow the scaling function for seven orders of magnitude.

Performance Probability Distributions for Sediment Control Best Management Practices

NASA Astrophysics Data System (ADS)

Ferrell, L.; Beighley, R.; Walsh, K.

2007-12-01

Controlling soil erosion and sediment transport can be a significant challenge during the construction process due to the extent and conditions of bare, disturbed soils. Best Management Practices (BMPs) are used as the framework for the design of sediment discharge prevention systems in stormwater pollution prevention plans which are typically required for construction sites. This research focuses on commonly-used BMP systems for perimeter control of sediment export: silt fences and fiber rolls. Although these systems are widely used, the physical and engineering parameters describing their performance are not well understood. Performance expectations are based on manufacturer results, but due to the dynamic conditions that exist on a construction site performance expectations are not always achievable in the field. Based on experimental results product performance is shown to be highly variable. Experiments using the same installation procedures show inconsistent sediment removal performances ranging from (>)85 percent to zero. The goal of this research is to improve the determination of off-site sediment yield based on probabilistic performance results of perimeter control BMPs. BMPs are evaluated in the Soil Erosion Research Laboratory (SERL) in the Civil and Environmental Engineering department at San Diego State University. SERL experiments are performed on a 3-m by 10-m tilting soil bed with a soil depth of 0.5 meters and a slope of 33 percent. The simulated storm event consists of 17 mm/hr for 20 minutes followed by 51 mm/hr for 30 minutes. The storm event is based on an ASTM design storm intended to simulate BMP failures. BMP performance is assessed based on experiments where BMPs are installed per manufacture specifications, less than optimal installations, and no treatment conditions. Preliminary results from 30 experiments are presented and used to develop probability distributions for BMP sediment removal efficiencies. The results are then combined with spatial and temporal distributions of perimeter sediment loadings for a construction site to estimate the time dependent risk of off-site sediment discharge over the duration of a project (ex., 0, 25, 50, 75 and 100 percent complete). The results are used to highlight the importance of considering all phases of construction when developing stormwater pollution prevention plans.

Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

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

Gamel, Omar E.; Fleming, Graham R.

Noncommuting observables cannot be simultaneously measured; however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fréchet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits.more » These inequalities place limits on the local hidden variable models that define joint probabilities for noncommuting observables. We also found that the Quasi-Bell inequalities have a quantum to classical violation as high as 3/2 on two qubit, higher than conventional Bell inequalities. Our result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics and provides an insightful generalization of Bell inequalities.« less

Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

DOE PAGES

Gamel, Omar E.; Fleming, Graham R.

2017-05-01

Noncommuting observables cannot be simultaneously measured; however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fréchet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits.more » These inequalities place limits on the local hidden variable models that define joint probabilities for noncommuting observables. We also found that the Quasi-Bell inequalities have a quantum to classical violation as high as 3/2 on two qubit, higher than conventional Bell inequalities. Our result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics and provides an insightful generalization of Bell inequalities.« less

Statistical thermodynamics of clustered populations.

PubMed

Matsoukas, Themis

2014-08-01

We present a thermodynamic theory for a generic population of M individuals distributed into N groups (clusters). We construct the ensemble of all distributions with fixed M and N, introduce a selection functional that embodies the physics that governs the population, and obtain the distribution that emerges in the scaling limit as the most probable among all distributions consistent with the given physics. We develop the thermodynamics of the ensemble and establish a rigorous mapping to regular thermodynamics. We treat the emergence of a so-called giant component as a formal phase transition and show that the criteria for its emergence are entirely analogous to the equilibrium conditions in molecular systems. We demonstrate the theory by an analytic model and confirm the predictions by Monte Carlo simulation.

Characterization of intermittency in renewal processes: Application to earthquakes

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

Akimoto, Takuma; Hasumi, Tomohiro; Aizawa, Yoji

2010-03-15

We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the piecewise linear intermittent map. Thus, we provide a framework to understand a unified characterization of intermittency and also present the Lyapunov exponent for renewal processes. This method is applied to the occurrence of earthquakes using the Japan Meteorological Agency and the National Earthquake Information Center catalog. By analyzing the return map of interevent times, we find that interevent times are not independent and identically distributed random variablesmore » but that the conditional probability distribution functions in the tail obey the Weibull distribution.« less

Generalized monogamy of contextual inequalities from the no-disturbance principle.

PubMed

Ramanathan, Ravishankar; Soeda, Akihito; Kurzyński, Paweł; Kaszlikowski, Dagomir

2012-08-03

In this Letter, we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs admit a joint probability distribution, we formulate a precise graph-theoretic condition that gives rise to the monogamy of contextuality. We also show how such monogamies arise within quantum theory for a single four-dimensional system and interpret violation of these relations in terms of a violation of causality. These monogamies can be tested with current experimental techniques.

Diversification and biogeography of Juniperus (Cupressaceae): variable diversification rates and multiple intercontinental dispersals.

PubMed

Mao, Kangshan; Hao, Gang; Liu, Jianquan; Adams, Robert P; Milne, Richard I

2010-10-01

• A central aim of biogeography is to understand when and how modern patterns of species diversity and distribution developed. Many plant groups have disjunct distributions within the Northern Hemisphere, but among these very few have been studied that prefer warm semi-arid habitats. • Here we examine the biogeography and diversification history of Juniperus, which occurs in semi-arid habitats through much of the Northern Hemisphere. A phylogeny was generated based on > 10,000 bp of cpDNA for 51 Juniperus species plus many outgroups. Phylogenies based on fewer species were also constructed based on nuclear internal transcribed spacer (nrITS) and combined nrITS/cpDNA data sets to check for congruence. Divergence time-scales and ancestral distributions were further inferred. • Both long dispersal and migration across land bridges probably contributed to the modern range of Juniperus, while long-term climatic changes and the uplift of the Qinghai-Tibetan plateau probably drove its diversification. Diversification apparently slowed down during climate-stable period of the Oligocene, and then speeded up from the Miocene onwards. • Juniperus probably originated in Eurasia, and was a part of the south Eurasian Tethyan vegetation of the Eocene to Oligocene. It reached America once at this time, once in the Miocene and once more recently.

Reliability Estimation of Parameters of Helical Wind Turbine with Vertical Axis

PubMed Central

Dumitrascu, Adela-Eliza; Lepadatescu, Badea; Dumitrascu, Dorin-Ion; Nedelcu, Anisor; Ciobanu, Doina Valentina

2015-01-01

Due to the prolonged use of wind turbines they must be characterized by high reliability. This can be achieved through a rigorous design, appropriate simulation and testing, and proper construction. The reliability prediction and analysis of these systems will lead to identifying the critical components, increasing the operating time, minimizing failure rate, and minimizing maintenance costs. To estimate the produced energy by the wind turbine, an evaluation approach based on the Monte Carlo simulation model is developed which enables us to estimate the probability of minimum and maximum parameters. In our simulation process we used triangular distributions. The analysis of simulation results has been focused on the interpretation of the relative frequency histograms and cumulative distribution curve (ogive diagram), which indicates the probability of obtaining the daily or annual energy output depending on wind speed. The experimental researches consist in estimation of the reliability and unreliability functions and hazard rate of the helical vertical axis wind turbine designed and patented to climatic conditions for Romanian regions. Also, the variation of power produced for different wind speeds, the Weibull distribution of wind probability, and the power generated were determined. The analysis of experimental results indicates that this type of wind turbine is efficient at low wind speed. PMID:26167524

Reliability Estimation of Parameters of Helical Wind Turbine with Vertical Axis.

PubMed

Dumitrascu, Adela-Eliza; Lepadatescu, Badea; Dumitrascu, Dorin-Ion; Nedelcu, Anisor; Ciobanu, Doina Valentina

2015-01-01

Due to the prolonged use of wind turbines they must be characterized by high reliability. This can be achieved through a rigorous design, appropriate simulation and testing, and proper construction. The reliability prediction and analysis of these systems will lead to identifying the critical components, increasing the operating time, minimizing failure rate, and minimizing maintenance costs. To estimate the produced energy by the wind turbine, an evaluation approach based on the Monte Carlo simulation model is developed which enables us to estimate the probability of minimum and maximum parameters. In our simulation process we used triangular distributions. The analysis of simulation results has been focused on the interpretation of the relative frequency histograms and cumulative distribution curve (ogive diagram), which indicates the probability of obtaining the daily or annual energy output depending on wind speed. The experimental researches consist in estimation of the reliability and unreliability functions and hazard rate of the helical vertical axis wind turbine designed and patented to climatic conditions for Romanian regions. Also, the variation of power produced for different wind speeds, the Weibull distribution of wind probability, and the power generated were determined. The analysis of experimental results indicates that this type of wind turbine is efficient at low wind speed.

Cortical Dynamics in Presence of Assemblies of Densely Connected Weight-Hub Neurons

PubMed Central

Setareh, Hesam; Deger, Moritz; Petersen, Carl C. H.; Gerstner, Wulfram

2017-01-01

Experimental measurements of pairwise connection probability of pyramidal neurons together with the distribution of synaptic weights have been used to construct randomly connected model networks. However, several experimental studies suggest that both wiring and synaptic weight structure between neurons show statistics that differ from random networks. Here we study a network containing a subset of neurons which we call weight-hub neurons, that are characterized by strong inward synapses. We propose a connectivity structure for excitatory neurons that contain assemblies of densely connected weight-hub neurons, while the pairwise connection probability and synaptic weight distribution remain consistent with experimental data. Simulations of such a network with generalized integrate-and-fire neurons display regular and irregular slow oscillations akin to experimentally observed up/down state transitions in the activity of cortical neurons with a broad distribution of pairwise spike correlations. Moreover, stimulation of a model network in the presence or absence of assembly structure exhibits responses similar to light-evoked responses of cortical layers in optogenetically modified animals. We conclude that a high connection probability into and within assemblies of excitatory weight-hub neurons, as it likely is present in some but not all cortical layers, changes the dynamics of a layer of cortical microcircuitry significantly. PMID:28690508

Probability distribution functions for intermittent scrape-off layer plasma fluctuations

NASA Astrophysics Data System (ADS)

Theodorsen, A.; Garcia, O. E.

2018-03-01

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribution to be exponentially distributed. Second, exponentially distributed amplitudes leads to a positive definite signal which cannot capture fluctuations in for example electric potential and radial velocity. Assuming pulse amplitudes which are not positive definite often make finding a closed form for the probability density function (PDF) difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the PDF. In this contribution, the effect of changing the amplitude distribution on the moments, PDF and characteristic function of the process is investigated and a parameter estimation method using the empirical characteristic function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations of all plasma parameters in the boundary region of magnetized plasmas.

Unstable density distribution associated with equatorial plasma bubble

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

Kherani, E. A., E-mail: esfhan.kherani@inpe.br; Meneses, F. Carlos de; Bharuthram, R.

2016-04-15

In this work, we present a simulation study of equatorial plasma bubble (EPB) in the evening time ionosphere. The fluid simulation is performed with a high grid resolution, enabling us to probe the steepened updrafting density structures inside EPB. Inside the density depletion that eventually evolves as EPB, both density and updraft are functions of space from which the density as implicit function of updraft velocity or the density distribution function is constructed. In the present study, this distribution function and the corresponding probability distribution function are found to evolve from Maxwellian to non-Maxwellian as the initial small depletion growsmore » to EPB. This non-Maxwellian distribution is of a gentle-bump type, in confirmation with the recently reported distribution within EPB from space-borne measurements that offer favorable condition for small scale kinetic instabilities.« less

Explosion probability of unexploded ordnance: expert beliefs.

PubMed

MacDonald, Jacqueline Anne; Small, Mitchell J; Morgan, M G

2008-08-01

This article reports on a study to quantify expert beliefs about the explosion probability of unexploded ordnance (UXO). Some 1,976 sites at closed military bases in the United States are contaminated with UXO and are slated for cleanup, at an estimated cost of $15-140 billion. Because no available technology can guarantee 100% removal of UXO, information about explosion probability is needed to assess the residual risks of civilian reuse of closed military bases and to make decisions about how much to invest in cleanup. This study elicited probability distributions for the chance of UXO explosion from 25 experts in explosive ordnance disposal, all of whom have had field experience in UXO identification and deactivation. The study considered six different scenarios: three different types of UXO handled in two different ways (one involving children and the other involving construction workers). We also asked the experts to rank by sensitivity to explosion 20 different kinds of UXO found at a case study site at Fort Ord, California. We found that the experts do not agree about the probability of UXO explosion, with significant differences among experts in their mean estimates of explosion probabilities and in the amount of uncertainty that they express in their estimates. In three of the six scenarios, the divergence was so great that the average of all the expert probability distributions was statistically indistinguishable from a uniform (0, 1) distribution-suggesting that the sum of expert opinion provides no information at all about the explosion risk. The experts' opinions on the relative sensitivity to explosion of the 20 UXO items also diverged. The average correlation between rankings of any pair of experts was 0.41, which, statistically, is barely significant (p= 0.049) at the 95% confidence level. Thus, one expert's rankings provide little predictive information about another's rankings. The lack of consensus among experts suggests that empirical studies are needed to better understand the explosion risks of UXO.

SAS procedures for designing and analyzing sample surveys

USGS Publications Warehouse

Stafford, Joshua D.; Reinecke, Kenneth J.; Kaminski, Richard M.

2003-01-01

Complex surveys often are necessary to estimate occurrence (or distribution), density, and abundance of plants and animals for purposes of re-search and conservation. Most scientists are familiar with simple random sampling, where sample units are selected from a population of interest (sampling frame) with equal probability. However, the goal of ecological surveys often is to make inferences about populations over large or complex spatial areas where organisms are not homogeneously distributed or sampling frames are in-convenient or impossible to construct. Candidate sampling strategies for such complex surveys include stratified,multistage, and adaptive sampling (Thompson 1992, Buckland 1994).

Entropy and wigner functions

PubMed

Manfredi; Feix

2000-10-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.

Wireless Sensor Network Metrics for Real-Time Systems

DTIC Science & Technology

2009-05-20

to compute the probability of end-to-end packet delivery as a function of latency, the expected radio energy consumption on the nodes from relaying... schedules for WSNs. Particularly, we focus on the impact scheduling has on path diversity, using short repeating schedules and Greedy Maximal Matching...a greedy algorithm for constructing a mesh routing topology. Finally, we study the implications of using distributed scheduling schemes to generate

Daniel Goodman’s empirical approach to Bayesian statistics

USGS Publications Warehouse

Gerrodette, Tim; Ward, Eric; Taylor, Rebecca L.; Schwarz, Lisa K.; Eguchi, Tomoharu; Wade, Paul; Himes Boor, Gina

2016-01-01

Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.

2dFLenS and KiDS: determining source redshift distributions with cross-correlations

NASA Astrophysics Data System (ADS)

Johnson, Andrew; Blake, Chris; Amon, Alexandra; Erben, Thomas; Glazebrook, Karl; Harnois-Deraps, Joachim; Heymans, Catherine; Hildebrandt, Hendrik; Joudaki, Shahab; Klaes, Dominik; Kuijken, Konrad; Lidman, Chris; Marin, Felipe A.; McFarland, John; Morrison, Christopher B.; Parkinson, David; Poole, Gregory B.; Radovich, Mario; Wolf, Christian

2017-03-01

We develop a statistical estimator to infer the redshift probability distribution of a photometric sample of galaxies from its angular cross-correlation in redshift bins with an overlapping spectroscopic sample. This estimator is a minimum-variance weighted quadratic function of the data: a quadratic estimator. This extends and modifies the methodology presented by McQuinn & White. The derived source redshift distribution is degenerate with the source galaxy bias, which must be constrained via additional assumptions. We apply this estimator to constrain source galaxy redshift distributions in the Kilo-Degree imaging survey through cross-correlation with the spectroscopic 2-degree Field Lensing Survey, presenting results first as a binned step-wise distribution in the range z < 0.8, and then building a continuous distribution using a Gaussian process model. We demonstrate the robustness of our methodology using mock catalogues constructed from N-body simulations, and comparisons with other techniques for inferring the redshift distribution.

Splitting nodes and linking channels: A method for assembling biocircuits from stochastic elementary units

NASA Astrophysics Data System (ADS)

Ferwerda, Cameron; Lipan, Ovidiu

2016-11-01

Akin to electric circuits, we construct biocircuits that are manipulated by cutting and assembling channels through which stochastic information flows. This diagrammatic manipulation allows us to create a method which constructs networks by joining building blocks selected so that (a) they cover only basic processes; (b) it is scalable to large networks; (c) the mean and variance-covariance from the Pauli master equation form a closed system; and (d) given the initial probability distribution, no special boundary conditions are necessary to solve the master equation. The method aims to help with both designing new synthetic signaling pathways and quantifying naturally existing regulatory networks.

On the Empirical Importance of the Conditional Skewness Assumption in Modelling the Relationship between Risk and Return

NASA Astrophysics Data System (ADS)

Pipień, M.

2008-09-01

We present the results of an application of Bayesian inference in testing the relation between risk and return on the financial instruments. On the basis of the Intertemporal Capital Asset Pricing Model, proposed by Merton we built a general sampling distribution suitable in analysing this relationship. The most important feature of our assumptions is that the skewness of the conditional distribution of returns is used as an alternative source of relation between risk and return. This general specification relates to Skewed Generalized Autoregressive Conditionally Heteroscedastic-in-Mean model. In order to make conditional distribution of financial returns skewed we considered the unified approach based on the inverse probability integral transformation. In particular, we applied hidden truncation mechanism, inverse scale factors, order statistics concept, Beta and Bernstein distribution transformations and also a constructive method. Based on the daily excess returns on the Warsaw Stock Exchange Index we checked the empirical importance of the conditional skewness assumption on the relation between risk and return on the Warsaw Stock Market. We present posterior probabilities of all competing specifications as well as the posterior analysis of the positive sign of the tested relationship.

Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, paranoid personality disorder diagnosis: a unitary or a two-dimensional construct?

PubMed

Falkum, Erik; Pedersen, Geir; Karterud, Sigmund

2009-01-01

This article examines reliability and validity aspects of the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV) paranoid personality disorder (PPD) diagnosis. Patients with personality disorders (n = 930) from the Norwegian network of psychotherapeutic day hospitals, of which 114 had PPD, were included in the study. Frequency distribution, chi(2), correlations, reliability statistics, exploratory, and confirmatory factor analyses were performed. The distribution of PPD criteria revealed no distinct boundary between patients with and without PPD. Diagnostic category membership was obtained in 37 of 64 theoretically possible ways. The PPD criteria formed a separate factor in a principal component analysis, whereas a confirmatory factor analysis indicated that the DSM-IV PPD construct consists of 2 separate dimensions as follows: suspiciousness and hostility. The reliability of the unitary PPD scale was only 0.70, probably partly due to the apparent 2-dimensionality of the construct. Persistent unwarranted doubts about the loyalty of friends had the highest diagnostic efficiency, whereas unwarranted accusations of infidelity of partner had particularly poor indicator properties. The reliability and validity of the unitary PPD construct may be questioned. The 2-dimensional PPD model should be further explored.

A computational framework to empower probabilistic protein design

PubMed Central

Fromer, Menachem; Yanover, Chen

2008-01-01

Motivation: The task of engineering a protein to perform a target biological function is known as protein design. A commonly used paradigm casts this functional design problem as a structural one, assuming a fixed backbone. In probabilistic protein design, positional amino acid probabilities are used to create a random library of sequences to be simultaneously screened for biological activity. Clearly, certain choices of probability distributions will be more successful in yielding functional sequences. However, since the number of sequences is exponential in protein length, computational optimization of the distribution is difficult. Results: In this paper, we develop a computational framework for probabilistic protein design following the structural paradigm. We formulate the distribution of sequences for a structure using the Boltzmann distribution over their free energies. The corresponding probabilistic graphical model is constructed, and we apply belief propagation (BP) to calculate marginal amino acid probabilities. We test this method on a large structural dataset and demonstrate the superiority of BP over previous methods. Nevertheless, since the results obtained by BP are far from optimal, we thoroughly assess the paradigm using high-quality experimental data. We demonstrate that, for small scale sub-problems, BP attains identical results to those produced by exact inference on the paradigmatic model. However, quantitative analysis shows that the distributions predicted significantly differ from the experimental data. These findings, along with the excellent performance we observed using BP on the smaller problems, suggest potential shortcomings of the paradigm. We conclude with a discussion of how it may be improved in the future. Contact: fromer@cs.huji.ac.il PMID:18586717

An intelligent system based on fuzzy probabilities for medical diagnosis– a study in aphasia diagnosis*

PubMed Central

Moshtagh-Khorasani, Majid; Akbarzadeh-T, Mohammad-R; Jahangiri, Nader; Khoobdel, Mehdi

2009-01-01

BACKGROUND: Aphasia diagnosis is particularly challenging due to the linguistic uncertainty and vagueness, inconsistencies in the definition of aphasic syndromes, large number of measurements with imprecision, natural diversity and subjectivity in test objects as well as in opinions of experts who diagnose the disease. METHODS: Fuzzy probability is proposed here as the basic framework for handling the uncertainties in medical diagnosis and particularly aphasia diagnosis. To efficiently construct this fuzzy probabilistic mapping, statistical analysis is performed that constructs input membership functions as well as determines an effective set of input features. RESULTS: Considering the high sensitivity of performance measures to different distribution of testing/training sets, a statistical t-test of significance is applied to compare fuzzy approach results with NN results as well as author's earlier work using fuzzy logic. The proposed fuzzy probability estimator approach clearly provides better diagnosis for both classes of data sets. Specifically, for the first and second type of fuzzy probability classifiers, i.e. spontaneous speech and comprehensive model, P-values are 2.24E-08 and 0.0059, respectively, strongly rejecting the null hypothesis. CONCLUSIONS: The technique is applied and compared on both comprehensive and spontaneous speech test data for diagnosis of four Aphasia types: Anomic, Broca, Global and Wernicke. Statistical analysis confirms that the proposed approach can significantly improve accuracy using fewer Aphasia features. PMID:21772867

Complementarity between entanglement-assisted and quantum distributed random access code

NASA Astrophysics Data System (ADS)

Hameedi, Alley; Saha, Debashis; Mironowicz, Piotr; Pawłowski, Marcin; Bourennane, Mohamed

2017-05-01

Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the entanglement-assisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific cases where one outperforms the other. In this article, we study a family of 3 →1 distributed RACs [J. Bowles, N. Brunner, and M. Pawłowski, Phys. Rev. A 92, 022351 (2015), 10.1103/PhysRevA.92.022351] and present its general construction of both the QRAC and the EARAC. We demonstrate that, depending on the function of inputs that is sought, if QRAC achieves the maximal success probability then EARAC fails to do so and vice versa. Moreover, a tripartite Bell-type inequality associated with the EARAC variants reveals the genuine multipartite nonlocality exhibited by our protocol. We conclude with an experimental realization of the 3 →1 distributed QRAC that achieves higher success probabilities than the maximum possible with EARACs for a number of tasks.

Bound entangled states with a private key and their classical counterpart.

PubMed

Ozols, Maris; Smith, Graeme; Smolin, John A

2014-03-21

Entanglement is a fundamental resource for quantum information processing. In its pure form, it allows quantum teleportation and sharing classical secrets. Realistic quantum states are noisy and their usefulness is only partially understood. Bound-entangled states are central to this question--they have no distillable entanglement, yet sometimes still have a private classical key. We present a construction of bound-entangled states with a private key based on classical probability distributions. From this emerge states possessing a new classical analogue of bound entanglement, distinct from the long-sought bound information. We also find states of smaller dimensions and higher key rates than previously known. Our construction has implications for classical cryptography: we show that existing protocols are insufficient for extracting private key from our distributions due to their "bound-entangled" nature. We propose a simple extension of existing protocols that can extract a key from them.

The Statistics of Urban Scaling and Their Connection to Zipf’s Law

PubMed Central

Gomez-Lievano, Andres; Youn, HyeJin; Bettencourt, Luís M. A.

2012-01-01

Urban scaling relations characterizing how diverse properties of cities vary on average with their population size have recently been shown to be a general quantitative property of many urban systems around the world. However, in previous studies the statistics of urban indicators were not analyzed in detail, raising important questions about the full characterization of urban properties and how scaling relations may emerge in these larger contexts. Here, we build a self-consistent statistical framework that characterizes the joint probability distributions of urban indicators and city population sizes across an urban system. To develop this framework empirically we use one of the most granular and stochastic urban indicators available, specifically measuring homicides in cities of Brazil, Colombia and Mexico, three nations with high and fast changing rates of violent crime. We use these data to derive the conditional probability of the number of homicides per year given the population size of a city. To do this we use Bayes’ rule together with the estimated conditional probability of city size given their number of homicides and the distribution of total homicides. We then show that scaling laws emerge as expectation values of these conditional statistics. Knowledge of these distributions implies, in turn, a relationship between scaling and population size distribution exponents that can be used to predict Zipf’s exponent from urban indicator statistics. Our results also suggest how a general statistical theory of urban indicators may be constructed from the stochastic dynamics of social interaction processes in cities. PMID:22815745

Flow-duration-frequency behaviour of British rivers based on annual minima data

NASA Astrophysics Data System (ADS)

Zaidman, Maxine D.; Keller, Virginie; Young, Andrew R.; Cadman, Daniel

2003-06-01

A comparison of different probability distribution models for describing the flow-duration-frequency behaviour of annual minima flow events in British rivers is reported. Twenty-five catchments were included in the study, each having stable and natural flow records of at least 30 years in length. Time series of annual minima D-day average flows were derived for each record using durations ( D) of 1, 7, 30, 60, 90, and 365 days and used to construct low flow frequency curves. In each case the Gringorten plotting position formula was used to determine probabilities (of non-exceedance). Four distribution types—Generalised Extreme Value (GEV), Generalised Logistic (GL), Pearson Type-3 (PE3) and Generalised Pareto (GP)—were used to model the probability distribution function for each site. L-moments were used to parameterise individual models, whilst goodness-of-fit tests were used to assess their match to the sample data. The study showed that where short durations (i.e. 60 days or less) were considered, high storage catchments tended to be best represented by GL and GEV distribution models whilst low storage catchments were best described by PE3 or GEV models. However, these models produced reasonable results only within a limited range (e.g. models for high storage catchments did not produce sensible estimates of return periods where the prescribed flow was less than 10% of the mean flow). For annual minima series derived using long duration flow averages (e.g. more than 90 days), GP and GEV models were generally more applicable. The study suggests that longer duration minima do not conform to the same distribution types as short durations, and that catchment properties can influence the type of distribution selected.

Phase relations in iron-rich systems and implications for the earth's core

NASA Technical Reports Server (NTRS)

Anderson, William W.; Svendsen, Bob; Ahrens, Thomas J.

1987-01-01

Recent experimental data concerning the properties of iron, iron sulfide, and iron oxide at high pressures are combined with theoretical arguments to constrain the probable behavior of the Fe-rich portions of the Fe-O and Fe-S phase diagrams. Phase diagrams are constructed for the Fe-S-O system at core pressures and temperatures. These properties are used to evaluate the current temperature distribution and composition of the core.

A stochastic differential equation model for the foraging behavior of fish schools.

PubMed

Tạ, Tôn Việt; Nguyen, Linh Thi Hoai

2018-03-15

Constructing models of living organisms locating food sources has important implications for understanding animal behavior and for the development of distribution technologies. This paper presents a novel simple model of stochastic differential equations for the foraging behavior of fish schools in a space including obstacles. The model is studied numerically. Three configurations of space with various food locations are considered. In the first configuration, fish swim in free but limited space. All individuals can find food with large probability while keeping their school structure. In the second and third configurations, they move in limited space with one and two obstacles, respectively. Our results reveal that the probability of foraging success is highest in the first configuration, and smallest in the third one. Furthermore, when school size increases up to an optimal value, the probability of foraging success tends to increase. When it exceeds an optimal value, the probability tends to decrease. The results agree with experimental observations.

A stochastic differential equation model for the foraging behavior of fish schools

NASA Astrophysics Data System (ADS)

Tạ, Tôn ệt, Vi; Hoai Nguyen, Linh Thi

2018-05-01

Constructing models of living organisms locating food sources has important implications for understanding animal behavior and for the development of distribution technologies. This paper presents a novel simple model of stochastic differential equations for the foraging behavior of fish schools in a space including obstacles. The model is studied numerically. Three configurations of space with various food locations are considered. In the first configuration, fish swim in free but limited space. All individuals can find food with large probability while keeping their school structure. In the second and third configurations, they move in limited space with one and two obstacles, respectively. Our results reveal that the probability of foraging success is highest in the first configuration, and smallest in the third one. Furthermore, when school size increases up to an optimal value, the probability of foraging success tends to increase. When it exceeds an optimal value, the probability tends to decrease. The results agree with experimental observations.

SUGGEL: A Program Suggesting the Orbital Angular Momentum of a Neutron Resonance from the Magnitude of its Neutron Width

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

Oh, S.Y.

2001-02-02

The SUGGEL computer code has been developed to suggest a value for the orbital angular momentum of a neutron resonance that is consistent with the magnitude of its neutron width. The suggestion is based on the probability that a resonance having a certain value of g{Gamma}{sub n} is an l-wave resonance. The probability is calculated by using Bayes' theorem on the conditional probability. The probability density functions (pdf's) of g{Gamma}{sub n} for up to d-wave (l=2) have been derived from the {chi}{sup 2} distribution of Porter and Thomas. The pdf's take two possible channel spins into account. This code ismore » a tool which evaluators will use to construct resonance parameters and help to assign resonance spin. The use of this tool is expected to reduce time and effort in the evaluation procedure, since the number of repeated runs of the fitting code (e.g., SAMMY) may be reduced.« less

Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise

NASA Astrophysics Data System (ADS)

Zhou, Wei-Xing; Sornette, Didier

We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) is found in a time series. The solution of this problem is already known for independent Gaussian distributed noise. We investigate more general situations with non-Gaussian correlated noises and present synthetic tests on the detectability and statistical significance of periodic components. A periodic component of a time series is usually detected by some sort of Fourier analysis. Here, we use the Lomb periodogram analysis, which is suitable and outperforms Fourier transforms for unevenly sampled time series. We examine the false-alarm probability of the largest spectral peak of the Lomb periodogram in the presence of power-law distributed noises, of short-range and of long-range fractional-Gaussian noises. Increasing heavy-tailness (respectively correlations describing persistence) tends to decrease (respectively increase) the false-alarm probability of finding a large spurious Lomb peak. Increasing anti-persistence tends to decrease the false-alarm probability. We also study the interplay between heavy-tailness and long-range correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should in principle characterize the Lomb peak height, its width and its relations to other peaks in the complete spectrum. As a step towards this full characterization, we construct the joint-distribution of the frequency position (relative to other peaks) and of the height of the highest peak of the power spectrum. We also provide the distributions of the ratio of the highest Lomb peak to the second highest one. Using the insight obtained by the present statistical study, we re-examine previously reported claims of ``log-periodicity'' and find that the credibility for log-periodicity in 2D-freely decaying turbulence is weakened while it is strengthened for fracture, for the ion-signature prior to the Kobe earthquake and for financial markets.

Is Einsteinian no-signalling violated in Bell tests?

NASA Astrophysics Data System (ADS)

Kupczynski, Marian

2017-11-01

Relativistic invariance is a physical law verified in several domains of physics. The impossibility of faster than light influences is not questioned by quantum theory. In quantum electrodynamics, in quantum field theory and in the standard model relativistic invariance is incorporated by construction. Quantum mechanics predicts strong long range correlations between outcomes of spin projection measurements performed in distant laboratories. In spite of these strong correlations marginal probability distributions should not depend on what was measured in the other laboratory what is called shortly: non-signalling. In several experiments, performed to test various Bell-type inequalities, some unexplained dependence of empirical marginal probability distributions on distant settings was observed. In this paper we demonstrate how a particular identification and selection procedure of paired distant outcomes is the most probable cause for this apparent violation of no-signalling principle. Thus this unexpected setting dependence does not prove the existence of superluminal influences and Einsteinian no-signalling principle has to be tested differently in dedicated experiments. We propose a detailed protocol telling how such experiments should be designed in order to be conclusive. We also explain how magical quantum correlations may be explained in a locally causal way.

Hantavirus reservoir Oligoryzomys longicaudatus spatial distribution sensitivity to climate change scenarios in Argentine Patagonia

PubMed Central

Carbajo, Aníbal E; Vera, Carolina; González, Paula LM

2009-01-01

Background Oligoryzomys longicaudatus (colilargo) is the rodent responsible for hantavirus pulmonary syndrome (HPS) in Argentine Patagonia. In past decades (1967–1998), trends of precipitation reduction and surface air temperature increase have been observed in western Patagonia. We explore how the potential distribution of the hantavirus reservoir would change under different climate change scenarios based on the observed trends. Methods Four scenarios of potential climate change were constructed using temperature and precipitation changes observed in Argentine Patagonia between 1967 and 1998: Scenario 1 assumed no change in precipitation but a temperature trend as observed; scenario 2 assumed no changes in temperature but a precipitation trend as observed; Scenario 3 included changes in both temperature and precipitation trends as observed; Scenario 4 assumed changes in both temperature and precipitation trends as observed but doubled. We used a validated spatial distribution model of O. longicaudatus as a function of temperature and precipitation. From the model probability of the rodent presence was calculated for each scenario. Results If changes in precipitation follow previous trends, the probability of the colilargo presence would fall in the HPS transmission zone of northern Patagonia. If temperature and precipitation trends remain at current levels for 60 years or double in the future 30 years, the probability of the rodent presence and the associated total area of potential distribution would diminish throughout Patagonia; the areas of potential distribution for colilargos would shift eastwards. These results suggest that future changes in Patagonia climate may lower transmission risk through a reduction in the potential distribution of the rodent reservoir. Conclusion According to our model the rates of temperature and precipitation changes observed between 1967 and 1998 may produce significant changes in the rodent distribution in an equivalent period of time only in certain areas. Given that changes maintain for 60 years or double in 30 years, the hantavirus reservoir Oligoryzomys longicaudatus may contract its distribution in Argentine Patagonia extensively. PMID:19607707

Habitat suitability criteria via parametric distributions: estimation, model selection and uncertainty

USGS Publications Warehouse

Som, Nicholas A.; Goodman, Damon H.; Perry, Russell W.; Hardy, Thomas B.

2016-01-01

Previous methods for constructing univariate habitat suitability criteria (HSC) curves have ranged from professional judgement to kernel-smoothed density functions or combinations thereof. We present a new method of generating HSC curves that applies probability density functions as the mathematical representation of the curves. Compared with previous approaches, benefits of our method include (1) estimation of probability density function parameters directly from raw data, (2) quantitative methods for selecting among several candidate probability density functions, and (3) concise methods for expressing estimation uncertainty in the HSC curves. We demonstrate our method with a thorough example using data collected on the depth of water used by juvenile Chinook salmon (Oncorhynchus tschawytscha) in the Klamath River of northern California and southern Oregon. All R code needed to implement our example is provided in the appendix. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

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

A multi-agent intelligent environment for medical knowledge.

PubMed

Vicari, Rosa M; Flores, Cecilia D; Silvestre, André M; Seixas, Louise J; Ladeira, Marcelo; Coelho, Helder

2003-03-01

AMPLIA is a multi-agent intelligent learning environment designed to support training of diagnostic reasoning and modelling of domains with complex and uncertain knowledge. AMPLIA focuses on the medical area. It is a system that deals with uncertainty under the Bayesian network approach, where learner-modelling tasks will consist of creating a Bayesian network for a problem the system will present. The construction of a network involves qualitative and quantitative aspects. The qualitative part concerns the network topology, that is, causal relations among the domain variables. After it is ready, the quantitative part is specified. It is composed of the distribution of conditional probability of the variables represented. A negotiation process (managed by an intelligent MediatorAgent) will treat the differences of topology and probability distribution between the model the learner built and the one built-in in the system. That negotiation process occurs between the agents that represent the expert knowledge domain (DomainAgent) and the agent that represents the learner knowledge (LearnerAgent).

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

Decisions with Uncertain Consequences—A Total Ordering on Loss-Distributions

PubMed Central

König, Sandra; Schauer, Stefan

2016-01-01

Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action can be modeled by a random variable, then the decision problem boils down to comparing different effects (random variables) by comparing their distribution functions. Although the full space of probability distributions cannot be ordered, a properly restricted subset of distributions can be totally ordered in a practically meaningful way. We call these loss-distributions, since they provide a substitute for the concept of loss-functions in decision theory. This article introduces the theory behind the necessary restrictions and the hereby constructible total ordering on random loss variables, which enables decisions under uncertainty of consequences. Using data obtained from simulations, we demonstrate the practical applicability of our approach. PMID:28030572

Funnel plot control limits to identify poorly performing healthcare providers when there is uncertainty in the value of the benchmark.

PubMed

Manktelow, Bradley N; Seaton, Sarah E; Evans, T Alun

2016-12-01

There is an increasing use of statistical methods, such as funnel plots, to identify poorly performing healthcare providers. Funnel plots comprise the construction of control limits around a benchmark and providers with outcomes falling outside the limits are investigated as potential outliers. The benchmark is usually estimated from observed data but uncertainty in this estimate is usually ignored when constructing control limits. In this paper, the use of funnel plots in the presence of uncertainty in the value of the benchmark is reviewed for outcomes from a Binomial distribution. Two methods to derive the control limits are shown: (i) prediction intervals; (ii) tolerance intervals Tolerance intervals formally include the uncertainty in the value of the benchmark while prediction intervals do not. The probability properties of 95% control limits derived using each method were investigated through hypothesised scenarios. Neither prediction intervals nor tolerance intervals produce funnel plot control limits that satisfy the nominal probability characteristics when there is uncertainty in the value of the benchmark. This is not necessarily to say that funnel plots have no role to play in healthcare, but that without the development of intervals satisfying the nominal probability characteristics they must be interpreted with care. © The Author(s) 2014.

Stochastic theory of fatigue corrosion

NASA Astrophysics Data System (ADS)

Hu, Haiyun

1999-10-01

A stochastic theory of corrosion has been constructed. The stochastic equations are described giving the transportation corrosion rate and fluctuation corrosion coefficient. In addition the pit diameter distribution function, the average pit diameter and the most probable pit diameter including other related empirical formula have been derived. In order to clarify the effect of stress range on the initiation and growth behaviour of pitting corrosion, round smooth specimen were tested under cyclic loading in 3.5% NaCl solution.

The influence of coordinated defects on inhomogeneous broadening in cubic lattices

NASA Astrophysics Data System (ADS)

Matheson, P. L.; Sullivan, Francis P.; Evenson, William E.

2016-12-01

The joint probability distribution function (JPDF) of electric field gradient (EFG) tensor components in cubic materials is dominated by coordinated pairings of defects in shells near probe nuclei. The contributions from these inner shell combinations and their surrounding structures contain the essential physics that determine the PAC-relevant quantities derived from them. The JPDF can be used to predict the nature of inhomogeneous broadening (IHB) in perturbed angular correlation (PAC) experiments by modeling the G 2 spectrum and finding expectation values for V zz and η. The ease with which this can be done depends upon the representation of the JPDF. Expanding on an earlier work by Czjzek et al. (Hyperfine Interact. 14, 189-194, 1983), Evenson et al. (Hyperfine Interact. 237, 119, 2016) provide a set of coordinates constructed from the EFG tensor invariants they named W 1 and W 2. Using this parameterization, the JPDF in cubic structures was constructed using a point charge model in which a single trapped defect (TD) is the nearest neighbor to a probe nucleus. Individual defects on nearby lattice sites pair with the TD to provide a locus of points in the W 1- W 2 plane around which an amorphous-like distribution of probability density grows. Interestingly, however, marginal, separable PDFs appear adequate to model IHB relevant cases. We present cases from simulations in cubic materials illustrating the importance of these near-shell coordinations.

Combined risk assessment of nonstationary monthly water quality based on Markov chain and time-varying copula.

PubMed

Shi, Wei; Xia, Jun

2017-02-01

Water quality risk management is a global hot research linkage with the sustainable water resource development. Ammonium nitrogen (NH 3 -N) and permanganate index (COD Mn ) as the focus indicators in Huai River Basin, are selected to reveal their joint transition laws based on Markov theory. The time-varying moments model with either time or land cover index as explanatory variables is applied to build the time-varying marginal distributions of water quality time series. Time-varying copula model, which takes the non-stationarity in the marginal distribution and/or the time variation in dependence structure between water quality series into consideration, is constructed to describe a bivariate frequency analysis for NH 3 -N and COD Mn series at the same monitoring gauge. The larger first-order Markov joint transition probability indicates water quality state Class V w , Class IV and Class III will occur easily in the water body of Bengbu Sluice. Both marginal distribution and copula models are nonstationary, and the explanatory variable time yields better performance than land cover index in describing the non-stationarities in the marginal distributions. In modelling the dependence structure changes, time-varying copula has a better fitting performance than the copula with the constant or the time-trend dependence parameter. The largest synchronous encounter risk probability of NH 3 -N and COD Mn simultaneously reaching Class V is 50.61%, while the asynchronous encounter risk probability is largest when NH 3 -N and COD Mn is inferior to class V and class IV water quality standards, respectively.

An Optimization-Based Framework for the Transformation of Incomplete Biological Knowledge into a Probabilistic Structure and Its Application to the Utilization of Gene/Protein Signaling Pathways in Discrete Phenotype Classification.

PubMed

Esfahani, Mohammad Shahrokh; Dougherty, Edward R

2015-01-01

Phenotype classification via genomic data is hampered by small sample sizes that negatively impact classifier design. Utilization of prior biological knowledge in conjunction with training data can improve both classifier design and error estimation via the construction of the optimal Bayesian classifier. In the genomic setting, gene/protein signaling pathways provide a key source of biological knowledge. Although these pathways are neither complete, nor regulatory, with no timing associated with them, they are capable of constraining the set of possible models representing the underlying interaction between molecules. The aim of this paper is to provide a framework and the mathematical tools to transform signaling pathways to prior probabilities governing uncertainty classes of feature-label distributions used in classifier design. Structural motifs extracted from the signaling pathways are mapped to a set of constraints on a prior probability on a Multinomial distribution. Being the conjugate prior for the Multinomial distribution, we propose optimization paradigms to estimate the parameters of a Dirichlet distribution in the Bayesian setting. The performance of the proposed methods is tested on two widely studied pathways: mammalian cell cycle and a p53 pathway model.

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.

2016-01-01

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

Climate Change Impact Assessment in Pacific North West Using Copula based Coupling of Temperature and Precipitation variables

NASA Astrophysics Data System (ADS)

Qin, Y.; Rana, A.; Moradkhani, H.

2014-12-01

The multi downscaled-scenario products allow us to better assess the uncertainty of the changes/variations of precipitation and temperature in the current and future periods. Joint Probability distribution functions (PDFs), of both the climatic variables, might help better understand the interdependence of the two, and thus in-turn help in accessing the future with confidence. Using the joint distribution of temperature and precipitation is also of significant importance in hydrological applications and climate change studies. In the present study, we have used multi-modelled statistically downscaled-scenario ensemble of precipitation and temperature variables using 2 different statistically downscaled climate dataset. The datasets used are, 10 Global Climate Models (GCMs) downscaled products from CMIP5 daily dataset, namely, those from the Bias Correction and Spatial Downscaling (BCSD) technique generated at Portland State University and from the Multivariate Adaptive Constructed Analogs (MACA) technique, generated at University of Idaho, leading to 2 ensemble time series from 20 GCM products. Thereafter the ensemble PDFs of both precipitation and temperature is evaluated for summer, winter, and yearly periods for all the 10 sub-basins across Columbia River Basin (CRB). Eventually, Copula is applied to establish the joint distribution of two variables enabling users to model the joint behavior of the variables with any level of correlation and dependency. Moreover, the probabilistic distribution helps remove the limitations on marginal distributions of variables in question. The joint distribution is then used to estimate the change trends of the joint precipitation and temperature in the current and future, along with estimation of the probabilities of the given change. Results have indicated towards varied change trends of the joint distribution of, summer, winter, and yearly time scale, respectively in all 10 sub-basins. Probabilities of changes, as estimated by the joint precipitation and temperature, will provide useful information/insights for hydrological and climate change predictions.

On the degree distribution of horizontal visibility graphs associated with Markov processes and dynamical systems: diagrammatic and variational approaches

NASA Astrophysics Data System (ADS)

Lacasa, Lucas

2014-09-01

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical time series analysis and signal processing and (ii) characterizing classes of dynamical systems and stochastic processes using the tools of graph theory. Recent works show that the degree distribution of these graphs encapsulates much information on the signals' variability, and therefore constitutes a fundamental feature for statistical learning purposes. However, exact solutions for the degree distributions are only known in a few cases, such as for uncorrelated random processes. Here we analytically explore these distributions in a list of situations. We present a diagrammatic formalism which computes for all degrees their corresponding probability as a series expansion in a coupling constant which is the number of hidden variables. We offer a constructive solution for general Markovian stochastic processes and deterministic maps. As case tests we focus on Ornstein-Uhlenbeck processes, fully chaotic and quasiperiodic maps. Whereas only for certain degree probabilities can all diagrams be summed exactly, in the general case we show that the perturbation theory converges. In a second part, we make use of a variational technique to predict the complete degree distribution for special classes of Markovian dynamics with fast-decaying correlations. In every case we compare the theory with numerical experiments.

Evolutionary squeaky wheel optimization: a new framework for analysis.

PubMed

Li, Jingpeng; Parkes, Andrew J; Burke, Edmund K

2011-01-01

Squeaky wheel optimization (SWO) is a relatively new metaheuristic that has been shown to be effective for many real-world problems. At each iteration SWO does a complete construction of a solution starting from the empty assignment. Although the construction uses information from previous iterations, the complete rebuilding does mean that SWO is generally effective at diversification but can suffer from a relatively weak intensification. Evolutionary SWO (ESWO) is a recent extension to SWO that is designed to improve the intensification by keeping the good components of solutions and only using SWO to reconstruct other poorer components of the solution. In such algorithms a standard challenge is to understand how the various parameters affect the search process. In order to support the future study of such issues, we propose a formal framework for the analysis of ESWO. The framework is based on Markov chains, and the main novelty arises because ESWO moves through the space of partial assignments. This makes it significantly different from the analyses used in local search (such as simulated annealing) which only move through complete assignments. Generally, the exact details of ESWO will depend on various heuristics; so we focus our approach on a case of ESWO that we call ESWO-II and that has probabilistic as opposed to heuristic selection and construction operators. For ESWO-II, we study a simple problem instance and explicitly compute the stationary distribution probability over the states of the search space. We find interesting properties of the distribution. In particular, we find that the probabilities of states generally, but not always, increase with their fitness. This nonmonotonocity is quite different from the monotonicity expected in algorithms such as simulated annealing.

A framework for performing comparative LCA between repairing flooded houses and construction of dikes in non-stationary climate with changing risk of flooding.

PubMed

Hennequin, Thomas; Sørup, Hjalte Jomo Danielsen; Dong, Yan; Arnbjerg-Nielsen, Karsten

2018-06-13

Sustainable flood management is a basic societal need. In this article, life cycle assessment is used to compare two ways to maintain the state of a coastal urban area in a changing climate with increasing flood risk. On one side, the construction of a dike, a hard and proactive scenario, is modelled using a bottom up approach. On the other, the systematic repair of houses flooded by sea surges, a post-disaster measure, is assessed using a Monte Carlo simulation allowing for aleatory uncertainties in predicting future sea level rise and occurrences of extreme events. Two metrics are identified, normalized mean impacts and probability of dike being most efficient. The methodology is applied to three case studies in Denmark representing three contrasting areas, Copenhagen, Frederiksværk, and Esbjerg. For all case studies the distribution of the calculated impact of repairing houses is highly right skewed, which in some cases has implications for the comparative LCA. The results show that, in Copenhagen, the scenario of the dike is overwhelmingly favorable for the environment, with a 43 times higher impact for repairing houses and only 0% probability of the repairs being favorable. For Frederiksværk and Esbjerg the corresponding numbers are 5 and 0.9 times and 85% and 32%, respectively. Hence constructing a dike at this point in time is highly recommended in Copenhagen, preferable in Frederiksværk, and probably not recommendable in Esbjerg. Copyright © 2018 Elsevier B.V. All rights reserved.

Probability Forecasting Using Monte Carlo Simulation

NASA Astrophysics Data System (ADS)

Duncan, M.; Frisbee, J.; Wysack, J.

2014-09-01

Space Situational Awareness (SSA) is defined as the knowledge and characterization of all aspects of space. SSA is now a fundamental and critical component of space operations. Increased dependence on our space assets has in turn lead to a greater need for accurate, near real-time knowledge of all space activities. With the growth of the orbital debris population, satellite operators are performing collision avoidance maneuvers more frequently. Frequent maneuver execution expends fuel and reduces the operational lifetime of the spacecraft. Thus the need for new, more sophisticated collision threat characterization methods must be implemented. The collision probability metric is used operationally to quantify the collision risk. The collision probability is typically calculated days into the future, so that high risk and potential high risk conjunction events are identified early enough to develop an appropriate course of action. As the time horizon to the conjunction event is reduced, the collision probability changes. A significant change in the collision probability will change the satellite mission stakeholder's course of action. So constructing a method for estimating how the collision probability will evolve improves operations by providing satellite operators with a new piece of information, namely an estimate or 'forecast' of how the risk will change as time to the event is reduced. Collision probability forecasting is a predictive process where the future risk of a conjunction event is estimated. The method utilizes a Monte Carlo simulation that produces a likelihood distribution for a given collision threshold. Using known state and state uncertainty information, the simulation generates a set possible trajectories for a given space object pair. Each new trajectory produces a unique event geometry at the time of close approach. Given state uncertainty information for both objects, a collision probability value can be computed for every trail. This yields a collision probability distribution given known, predicted uncertainty. This paper presents the details of the collision probability forecasting method. We examine various conjunction event scenarios and numerically demonstrate the utility of this approach in typical event scenarios. We explore the utility of a probability-based track scenario simulation that models expected tracking data frequency as the tasking levels are increased. The resulting orbital uncertainty is subsequently used in the forecasting algorithm.

Mean Excess Function as a method of identifying sub-exponential tails: Application to extreme daily rainfall

NASA Astrophysics Data System (ADS)

Nerantzaki, Sofia; Papalexiou, Simon Michael

2017-04-01

Identifying precisely the distribution tail of a geophysical variable is tough, or, even impossible. First, the tail is the part of the distribution for which we have the less empirical information available; second, a universally accepted definition of tail does not and cannot exist; and third, a tail may change over time due to long-term changes. Unfortunately, the tail is the most important part of the distribution as it dictates the estimates of exceedance probabilities or return periods. Fortunately, based on their tail behavior, probability distributions can be generally categorized into two major families, i.e., sub-exponentials (heavy-tailed) and hyper-exponentials (light-tailed). This study aims to update the Mean Excess Function (MEF), providing a useful tool in order to asses which type of tail better describes empirical data. The MEF is based on the mean value of a variable over a threshold and results in a zero slope regression line when applied for the Exponential distribution. Here, we construct slope confidence intervals for the Exponential distribution as functions of sample size. The validation of the method using Monte Carlo techniques on four theoretical distributions covering major tail cases (Pareto type II, Log-normal, Weibull and Gamma) revealed that it performs well especially for large samples. Finally, the method is used to investigate the behavior of daily rainfall extremes; thousands of rainfall records were examined, from all over the world and with sample size over 100 years, revealing that heavy-tailed distributions can describe more accurately rainfall extremes.

An estimation method of the direct benefit of a waterlogging control project applicable to the changing environment

NASA Astrophysics Data System (ADS)

Zengmei, L.; Guanghua, Q.; Zishen, C.

2015-05-01

The direct benefit of a waterlogging control project is reflected by the reduction or avoidance of waterlogging loss. Before and after the construction of a waterlogging control project, the disaster-inducing environment in the waterlogging-prone zone is generally different. In addition, the category, quantity and spatial distribution of the disaster-bearing bodies are also changed more or less. Therefore, under the changing environment, the direct benefit of a waterlogging control project should be the reduction of waterlogging losses compared to conditions with no control project. Moreover, the waterlogging losses with or without the project should be the mathematical expectations of the waterlogging losses when rainstorms of all frequencies meet various water levels in the drainage-accepting zone. So an estimation model of the direct benefit of waterlogging control is proposed. Firstly, on the basis of a Copula function, the joint distribution of the rainstorms and the water levels are established, so as to obtain their joint probability density function. Secondly, according to the two-dimensional joint probability density distribution, the dimensional domain of integration is determined, which is then divided into small domains so as to calculate the probability for each of the small domains and the difference between the average waterlogging loss with and without a waterlogging control project, called the regional benefit of waterlogging control project, under the condition that rainstorms in the waterlogging-prone zone meet the water level in the drainage-accepting zone. Finally, it calculates the weighted mean of the project benefit of all small domains, with probability as the weight, and gets the benefit of the waterlogging control project. Taking the estimation of benefit of a waterlogging control project in Yangshan County, Guangdong Province, as an example, the paper briefly explains the procedures in waterlogging control project benefit estimation. The results show that the waterlogging control benefit estimation model constructed is applicable to the changing conditions that occur in both the disaster-inducing environment of the waterlogging-prone zone and disaster-bearing bodies, considering all conditions when rainstorms of all frequencies meet different water levels in the drainage-accepting zone. Thus, the estimation method of waterlogging control benefit can reflect the actual situation more objectively, and offer a scientific basis for rational decision-making for waterlogging control projects.

Laplacian normalization and random walk on heterogeneous networks for disease-gene prioritization.

PubMed

Zhao, Zhi-Qin; Han, Guo-Sheng; Yu, Zu-Guo; Li, Jinyan

2015-08-01

Random walk on heterogeneous networks is a recently emerging approach to effective disease gene prioritization. Laplacian normalization is a technique capable of normalizing the weight of edges in a network. We use this technique to normalize the gene matrix and the phenotype matrix before the construction of the heterogeneous network, and also use this idea to define the transition matrices of the heterogeneous network. Our method has remarkably better performance than the existing methods for recovering known gene-phenotype relationships. The Shannon information entropy of the distribution of the transition probabilities in our networks is found to be smaller than the networks constructed by the existing methods, implying that a higher number of top-ranked genes can be verified as disease genes. In fact, the most probable gene-phenotype relationships ranked within top 3 or top 5 in our gene lists can be confirmed by the OMIM database for many cases. Our algorithms have shown remarkably superior performance over the state-of-the-art algorithms for recovering gene-phenotype relationships. All Matlab codes can be available upon email request. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

Will current probabilistic climate change information, as such, improve adaptation?

NASA Astrophysics Data System (ADS)

Lopez, A.; Smith, L. A.

2012-04-01

Probabilistic climate scenarios are currently being provided to end users, to employ as probabilities in adaptation decision making, with the explicit suggestion that they quantify the impacts of climate change relevant to a variety of sectors. These "probabilities" are, however, rather sensitive to the assumptions in, and the structure of the modelling approaches used to generate them. It is often argued that stakeholders require probabilistic climate change information to adequately evaluate and plan adaptation pathways. On the other hand, some circumstantial evidence suggests that on the ground decision making rarely uses well defined probability distributions of climate change as inputs. Nevertheless it is within this context of probability distributions of climate change that we discuss possible drawbacks of supplying information that, while presented as robust and decision relevant, , is in fact unlikely to be so due to known flaws both in the underlying models and in the methodology used to "account for" those known flaws. How might one use a probability forecast that is expected to change in the future, not due to a refinement in our information but due to fundamental flaws in its construction? What then are the alternatives? While the answer will depend on the context of the problem at hand, a good approach will be strongly informed by the timescale of the given planning decision, and the consideration of all the non-climatic factors that have to be taken into account in the corresponding risk assessment. Using a water resources system as an example, we illustrate an alternative approach to deal with these challenges and make robust adaptation decisions today.

A Bayesian connectivity-based approach to constructing probabilistic gene regulatory networks.

PubMed

Zhou, Xiaobo; Wang, Xiaodong; Pal, Ranadip; Ivanov, Ivan; Bittner, Michael; Dougherty, Edward R

2004-11-22

We have hypothesized that the construction of transcriptional regulatory networks using a method that optimizes connectivity would lead to regulation consistent with biological expectations. A key expectation is that the hypothetical networks should produce a few, very strong attractors, highly similar to the original observations, mimicking biological state stability and determinism. Another central expectation is that, since it is expected that the biological control is distributed and mutually reinforcing, interpretation of the observations should lead to a very small number of connection schemes. We propose a fully Bayesian approach to constructing probabilistic gene regulatory networks (PGRNs) that emphasizes network topology. The method computes the possible parent sets of each gene, the corresponding predictors and the associated probabilities based on a nonlinear perceptron model, using a reversible jump Markov chain Monte Carlo (MCMC) technique, and an MCMC method is employed to search the network configurations to find those with the highest Bayesian scores to construct the PGRN. The Bayesian method has been used to construct a PGRN based on the observed behavior of a set of genes whose expression patterns vary across a set of melanoma samples exhibiting two very different phenotypes with respect to cell motility and invasiveness. Key biological features have been faithfully reflected in the model. Its steady-state distribution contains attractors that are either identical or very similar to the states observed in the data, and many of the attractors are singletons, which mimics the biological propensity to stably occupy a given state. Most interestingly, the connectivity rules for the most optimal generated networks constituting the PGRN are remarkably similar, as would be expected for a network operating on a distributed basis, with strong interactions between the components.

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

Zhu, Lin; Dai, Zhenxue; Gong, Huili

Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in anmore » accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.« less

A Brownian model for recurrent earthquakes

USGS Publications Warehouse

Matthews, M.V.; Ellsworth, W.L.; Reasenberg, P.A.

2002-01-01

We construct a probability model for rupture times on a recurrent earthquake source. Adding Brownian perturbations to steady tectonic loading produces a stochastic load-state process. Rupture is assumed to occur when this process reaches a critical-failure threshold. An earthquake relaxes the load state to a characteristic ground level and begins a new failure cycle. The load-state process is a Brownian relaxation oscillator. Intervals between events have a Brownian passage-time distribution that may serve as a temporal model for time-dependent, long-term seismic forecasting. This distribution has the following noteworthy properties: (1) the probability of immediate rerupture is zero; (2) the hazard rate increases steadily from zero at t = 0 to a finite maximum near the mean recurrence time and then decreases asymptotically to a quasi-stationary level, in which the conditional probability of an event becomes time independent; and (3) the quasi-stationary failure rate is greater than, equal to, or less than the mean failure rate because the coefficient of variation is less than, equal to, or greater than 1/???2 ??? 0.707. In addition, the model provides expressions for the hazard rate and probability of rupture on faults for which only a bound can be placed on the time of the last rupture. The Brownian relaxation oscillator provides a connection between observable event times and a formal state variable that reflects the macromechanics of stress and strain accumulation. Analysis of this process reveals that the quasi-stationary distance to failure has a gamma distribution, and residual life has a related exponential distribution. It also enables calculation of "interaction" effects due to external perturbations to the state, such as stress-transfer effects from earthquakes outside the target source. The influence of interaction effects on recurrence times is transient and strongly dependent on when in the loading cycle step pertubations occur. Transient effects may be much stronger than would be predicted by the "clock change" method and characteristically decay inversely with elapsed time after the perturbation.

Wavelet analysis to decompose a vibration simulation signal to improve pre-distribution testing of packaging

NASA Astrophysics Data System (ADS)

Griffiths, K. R.; Hicks, B. J.; Keogh, P. S.; Shires, D.

2016-08-01

In general, vehicle vibration is non-stationary and has a non-Gaussian probability distribution; yet existing testing methods for packaging design employ Gaussian distributions to represent vibration induced by road profiles. This frequently results in over-testing and/or over-design of the packaging to meet a specification and correspondingly leads to wasteful packaging and product waste, which represent 15bn per year in the USA and €3bn per year in the EU. The purpose of the paper is to enable a measured non-stationary acceleration signal to be replaced by a constructed signal that includes as far as possible any non-stationary characteristics from the original signal. The constructed signal consists of a concatenation of decomposed shorter duration signals, each having its own kurtosis level. Wavelet analysis is used for the decomposition process into inner and outlier signal components. The constructed signal has a similar PSD to the original signal, without incurring excessive acceleration levels. This allows an improved and more representative simulated input signal to be generated that can be used on the current generation of shaker tables. The wavelet decomposition method is also demonstrated experimentally through two correlation studies. It is shown that significant improvements over current international standards for packaging testing are achievable; hence the potential for more efficient packaging system design is possible.

Bayesian image reconstruction - The pixon and optimal image modeling

NASA Technical Reports Server (NTRS)

Pina, R. K.; Puetter, R. C.

1993-01-01

In this paper we describe the optimal image model, maximum residual likelihood method (OptMRL) for image reconstruction. OptMRL is a Bayesian image reconstruction technique for removing point-spread function blurring. OptMRL uses both a goodness-of-fit criterion (GOF) and an 'image prior', i.e., a function which quantifies the a priori probability of the image. Unlike standard maximum entropy methods, which typically reconstruct the image on the data pixel grid, OptMRL varies the image model in order to find the optimal functional basis with which to represent the image. We show how an optimal basis for image representation can be selected and in doing so, develop the concept of the 'pixon' which is a generalized image cell from which this basis is constructed. By allowing both the image and the image representation to be variable, the OptMRL method greatly increases the volume of solution space over which the image is optimized. Hence the likelihood of the final reconstructed image is greatly increased. For the goodness-of-fit criterion, OptMRL uses the maximum residual likelihood probability distribution introduced previously by Pina and Puetter (1992). This GOF probability distribution, which is based on the spatial autocorrelation of the residuals, has the advantage that it ensures spatially uncorrelated image reconstruction residuals.

Deep Learning Role in Early Diagnosis of Prostate Cancer

PubMed Central

Reda, Islam; Khalil, Ashraf; Elmogy, Mohammed; Abou El-Fetouh, Ahmed; Shalaby, Ahmed; Abou El-Ghar, Mohamed; Elmaghraby, Adel; Ghazal, Mohammed; El-Baz, Ayman

2018-01-01

The objective of this work is to develop a computer-aided diagnostic system for early diagnosis of prostate cancer. The presented system integrates both clinical biomarkers (prostate-specific antigen) and extracted features from diffusion-weighted magnetic resonance imaging collected at multiple b values. The presented system performs 3 major processing steps. First, prostate delineation using a hybrid approach that combines a level-set model with nonnegative matrix factorization. Second, estimation and normalization of diffusion parameters, which are the apparent diffusion coefficients of the delineated prostate volumes at different b values followed by refinement of those apparent diffusion coefficients using a generalized Gaussian Markov random field model. Then, construction of the cumulative distribution functions of the processed apparent diffusion coefficients at multiple b values. In parallel, a K-nearest neighbor classifier is employed to transform the prostate-specific antigen results into diagnostic probabilities. Finally, those prostate-specific antigen–based probabilities are integrated with the initial diagnostic probabilities obtained using stacked nonnegativity constraint sparse autoencoders that employ apparent diffusion coefficient–cumulative distribution functions for better diagnostic accuracy. Experiments conducted on 18 diffusion-weighted magnetic resonance imaging data sets achieved 94.4% diagnosis accuracy (sensitivity = 88.9% and specificity = 100%), which indicate the promising results of the presented computer-aided diagnostic system. PMID:29804518

Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans

DOE PAGES

Zhu, Lin; Dai, Zhenxue; Gong, Huili; ...

2015-06-12

Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in anmore » accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.« less

Numerical analysis of the accuracy of bivariate quantile distributions utilizing copulas compared to the GUM supplement 2 for oil pressure balance uncertainties

NASA Astrophysics Data System (ADS)

Ramnath, Vishal

2017-11-01

In the field of pressure metrology the effective area is Ae = A0 (1 + λP) where A0 is the zero-pressure area and λ is the distortion coefficient and the conventional practise is to construct univariate probability density functions (PDFs) for A0 and λ. As a result analytical generalized non-Gaussian bivariate joint PDFs has not featured prominently in pressure metrology. Recently extended lambda distribution based quantile functions have been successfully utilized for summarizing univariate arbitrary PDF distributions of gas pressure balances. Motivated by this development we investigate the feasibility and utility of extending and applying quantile functions to systems which naturally exhibit bivariate PDFs. Our approach is to utilize the GUM Supplement 1 methodology to solve and generate Monte Carlo based multivariate uncertainty data for an oil based pressure balance laboratory standard that is used to generate known high pressures, and which are in turn cross-floated against another pressure balance transfer standard in order to deduce the transfer standard's respective area. We then numerically analyse the uncertainty data by formulating and constructing an approximate bivariate quantile distribution that directly couples A0 and λ in order to compare and contrast its accuracy to an exact GUM Supplement 2 based uncertainty quantification analysis.

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.

Valid statistical inference methods for a case-control study with missing data.

PubMed

Tian, Guo-Liang; Zhang, Chi; Jiang, Xuejun

2018-04-01

The main objective of this paper is to derive the valid sampling distribution of the observed counts in a case-control study with missing data under the assumption of missing at random by employing the conditional sampling method and the mechanism augmentation method. The proposed sampling distribution, called the case-control sampling distribution, can be used to calculate the standard errors of the maximum likelihood estimates of parameters via the Fisher information matrix and to generate independent samples for constructing small-sample bootstrap confidence intervals. Theoretical comparisons of the new case-control sampling distribution with two existing sampling distributions exhibit a large difference. Simulations are conducted to investigate the influence of the three different sampling distributions on statistical inferences. One finding is that the conclusion by the Wald test for testing independency under the two existing sampling distributions could be completely different (even contradictory) from the Wald test for testing the equality of the success probabilities in control/case groups under the proposed distribution. A real cervical cancer data set is used to illustrate the proposed statistical methods.

Arterial tree tracking from anatomical landmarks in magnetic resonance angiography scans

NASA Astrophysics Data System (ADS)

O'Neil, Alison; Beveridge, Erin; Houston, Graeme; McCormick, Lynne; Poole, Ian

2014-03-01

This paper reports on arterial tree tracking in fourteen Contrast Enhanced MRA volumetric scans, given the positions of a predefined set of vascular landmarks, by using the A* algorithm to find the optimal path for each vessel based on voxel intensity and a learnt vascular probability atlas. The algorithm is intended for use in conjunction with an automatic landmark detection step, to enable fully automatic arterial tree tracking. The scan is filtered to give two further images using the top-hat transform with 4mm and 8mm cubic structuring elements. Vessels are then tracked independently on the scan in which the vessel of interest is best enhanced, as determined from knowledge of typical vessel diameter and surrounding structures. A vascular probability atlas modelling expected vessel location and orientation is constructed by non-rigidly registering the training scans to the test scan using a 3D thin plate spline to match landmark correspondences, and employing kernel density estimation with the ground truth center line points to form a probability density distribution. Threshold estimation by histogram analysis is used to segment background from vessel intensities. The A* algorithm is run using a linear cost function constructed from the threshold and the vascular atlas prior. Tracking results are presented for all major arteries excluding those in the upper limbs. An improvement was observed when tracking was informed by contextual information, with particular benefit for peripheral vessels.

Learning multivariate distributions by competitive assembly of marginals.

PubMed

Sánchez-Vega, Francisco; Younes, Laurent; Geman, Donald

2013-02-01

We present a new framework for learning high-dimensional multivariate probability distributions from estimated marginals. The approach is motivated by compositional models and Bayesian networks, and designed to adapt to small sample sizes. We start with a large, overlapping set of elementary statistical building blocks, or "primitives," which are low-dimensional marginal distributions learned from data. Each variable may appear in many primitives. Subsets of primitives are combined in a Lego-like fashion to construct a probabilistic graphical model; only a small fraction of the primitives will participate in any valid construction. Since primitives can be precomputed, parameter estimation and structure search are separated. Model complexity is controlled by strong biases; we adapt the primitives to the amount of training data and impose rules which restrict the merging of them into allowable compositions. The likelihood of the data decomposes into a sum of local gains, one for each primitive in the final structure. We focus on a specific subclass of networks which are binary forests. Structure optimization corresponds to an integer linear program and the maximizing composition can be computed for reasonably large numbers of variables. Performance is evaluated using both synthetic data and real datasets from natural language processing and computational biology.

Degradation data analysis based on a generalized Wiener process subject to measurement error

NASA Astrophysics Data System (ADS)

Li, Junxing; Wang, Zhihua; Zhang, Yongbo; Fu, Huimin; Liu, Chengrui; Krishnaswamy, Sridhar

2017-09-01

Wiener processes have received considerable attention in degradation modeling over the last two decades. In this paper, we propose a generalized Wiener process degradation model that takes unit-to-unit variation, time-correlated structure and measurement error into considerations simultaneously. The constructed methodology subsumes a series of models studied in the literature as limiting cases. A simple method is given to determine the transformed time scale forms of the Wiener process degradation model. Then model parameters can be estimated based on a maximum likelihood estimation (MLE) method. The cumulative distribution function (CDF) and the probability distribution function (PDF) of the Wiener process with measurement errors are given based on the concept of the first hitting time (FHT). The percentiles of performance degradation (PD) and failure time distribution (FTD) are also obtained. Finally, a comprehensive simulation study is accomplished to demonstrate the necessity of incorporating measurement errors in the degradation model and the efficiency of the proposed model. Two illustrative real applications involving the degradation of carbon-film resistors and the wear of sliding metal are given. The comparative results show that the constructed approach can derive a reasonable result and an enhanced inference precision.

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

PubMed Central

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

2007-01-01

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

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

PubMed

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

2007-06-01

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

Risk-based decision making to manage water quality failures caused by combined sewer overflows

NASA Astrophysics Data System (ADS)

Sriwastava, A. K.; Torres-Matallana, J. A.; Tait, S.; Schellart, A.

2017-12-01

Regulatory authorities set certain environmental permit for water utilities such that the combined sewer overflows (CSO) managed by these companies conform to the regulations. These utility companies face the risk of paying penalty or negative publicity in case they breach the environmental permit. These risks can be addressed by designing appropriate solutions such as investing in additional infrastructure which improve the system capacity and reduce the impact of CSO spills. The performance of these solutions is often estimated using urban drainage models. Hence, any uncertainty in these models can have a significant effect on the decision making process. This study outlines a risk-based decision making approach to address water quality failure caused by CSO spills. A calibrated lumped urban drainage model is used to simulate CSO spill quality in Haute-Sûre catchment in Luxembourg. Uncertainty in rainfall and model parameters is propagated through Monte Carlo simulations to quantify uncertainty in the concentration of ammonia in the CSO spill. A combination of decision alternatives such as the construction of a storage tank at the CSO and the reduction in the flow contribution of catchment surfaces are selected as planning measures to avoid the water quality failure. Failure is defined as exceedance of a concentration-duration based threshold based on Austrian emission standards for ammonia (De Toffol, 2006) with a certain frequency. For each decision alternative, uncertainty quantification results into a probability distribution of the number of annual CSO spill events which exceed the threshold. For each alternative, a buffered failure probability as defined in Rockafellar & Royset (2010), is estimated. Buffered failure probability (pbf) is a conservative estimate of failure probability (pf), however, unlike failure probability, it includes information about the upper tail of the distribution. A pareto-optimal set of solutions is obtained by performing mean- pbf optimization. The effectiveness of using buffered failure probability compared to the failure probability is tested by comparing the solutions obtained by using mean-pbf and mean-pf optimizations.

Modeling marine oily wastewater treatment by a probabilistic agent-based approach.

PubMed

Jing, Liang; Chen, Bing; Zhang, Baiyu; Ye, Xudong

2018-02-01

This study developed a novel probabilistic agent-based approach for modeling of marine oily wastewater treatment processes. It begins first by constructing a probability-based agent simulation model, followed by a global sensitivity analysis and a genetic algorithm-based calibration. The proposed modeling approach was tested through a case study of the removal of naphthalene from marine oily wastewater using UV irradiation. The removal of naphthalene was described by an agent-based simulation model using 8 types of agents and 11 reactions. Each reaction was governed by a probability parameter to determine its occurrence. The modeling results showed that the root mean square errors between modeled and observed removal rates were 8.73 and 11.03% for calibration and validation runs, respectively. Reaction competition was analyzed by comparing agent-based reaction probabilities, while agents' heterogeneity was visualized by plotting their real-time spatial distribution, showing a strong potential for reactor design and process optimization. Copyright © 2017 Elsevier Ltd. All rights reserved.

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).

Multi-Scale Particle Size Distributions of Mars, Moon and Itokawa based on a time-maturation dependent fragmentation model

NASA Astrophysics Data System (ADS)

Charalambous, C. A.; Pike, W. T.

2013-12-01

We present the development of a soil evolution framework and multiscale modelling of the surface of Mars, Moon and Itokawa thus providing an atlas of extra-terrestrial Particle Size Distributions (PSD). These PSDs are profoundly based on a tailoring method which interconnects several datasets from different sites captured by the various missions. The final integrated product is then fully justified through a soil evolution analysis model mathematically constructed via fundamental physical principles (Charalambous, 2013). The construction of the PSD takes into account the macroscale fresh primary impacts and their products, the mesoscale distributions obtained by the in-situ data of surface missions (Golombek et al., 1997, 2012) and finally the microscopic scale distributions provided by Curiosity and Phoenix Lander (Pike, 2011). The distribution naturally extends at the magnitudinal scales at which current data does not exist due to the lack of scientific instruments capturing the populations at these data absent scales. The extension is based on the model distribution (Charalambous, 2013) which takes as parameters known values of material specific probabilities of fragmentation and grinding limits. Additionally, the establishment of a closed-form statistical distribution provides a quantitative description of the soil's structure. Consequently, reverse engineering of the model distribution allows the synthesis of soil that faithfully represents the particle population at the studied sites (Charalambous, 2011). Such representation essentially delivers a virtual soil environment to work with for numerous applications. A specific application demonstrated here will be the information that can directly be extracted for the successful drilling probability as a function of distance in an effort to aid the HP3 instrument of the 2016 Insight Mission to Mars. Pike, W. T., et al. "Quantification of the dry history of the Martian soil inferred from in situ microscopy." Geophysical Research Letters 38.24 (2011). C. A. Charalambous and W. T. Pike (2013). 'Evolution of Particle Size Distributions in Fragmentation Over Time' Abstract Submitted to the AGU 46th Fall Meeting. Charalambous, C., Pike, W. T., Goetz, W., Hecht, M. H., & Staufer, U. (2011, December). 'A Digital Martian Soil based on In-Situ Data.' In AGU Fall Meeting Abstracts (Vol. 1, p. 1669). Golombek, M., & Rapp, D. (1997). 'Size-frequency distributions of rocks on Mars and Earth analog sites: Implications for future landed missions.' Journal of Geophysical Research, 102(E2), 4117-4129. Golombek, M., Huertas, A., Kipp, D., & Calef, F. (2012). 'Detection and characterization of rocks and rock size-frequency distributions at the final four Mars Science Laboratory landing sites.' Mars, 7, 1-22.

Design of high temperature ceramic components against fast fracture and time-dependent failure using cares/life

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

Jadaan, O.M.; Powers, L.M.; Nemeth, N.N.

1995-08-01

A probabilistic design methodology which predicts the fast fracture and time-dependent failure behavior of thermomechanically loaded ceramic components is discussed using the CARES/LIFE integrated design computer program. Slow crack growth (SCG) is assumed to be the mechanism responsible for delayed failure behavior. Inert strength and dynamic fatigue data obtained from testing coupon specimens (O-ring and C-ring specimens) are initially used to calculate the fast fracture and SCG material parameters as a function of temperature using the parameter estimation techniques available with the CARES/LIFE code. Finite element analysis (FEA) is used to compute the stress distributions for the tube as amore » function of applied pressure. Knowing the stress and temperature distributions and the fast fracture and SCG material parameters, the life time for a given tube can be computed. A stress-failure probability-time to failure (SPT) diagram is subsequently constructed for these tubes. Such a diagram can be used by design engineers to estimate the time to failure at a given failure probability level for a component subjected to a given thermomechanical load.« less

An analytical model for regular respiratory signals derived from the probability density function of Rayleigh distribution.

PubMed

Li, Xin; Li, Ye

2015-01-01

Regular respiratory signals (RRSs) acquired with physiological sensing systems (e.g., the life-detection radar system) can be used to locate survivors trapped in debris in disaster rescue, or predict the breathing motion to allow beam delivery under free breathing conditions in external beam radiotherapy. Among the existing analytical models for RRSs, the harmonic-based random model (HRM) is shown to be the most accurate, which, however, is found to be subject to considerable error if the RRS has a slowly descending end-of-exhale (EOE) phase. The defect of the HRM motivates us to construct a more accurate analytical model for the RRS. In this paper, we derive a new analytical RRS model from the probability density function of Rayleigh distribution. We evaluate the derived RRS model by using it to fit a real-life RRS in the sense of least squares, and the evaluation result shows that, our presented model exhibits lower error and fits the slowly descending EOE phases of the real-life RRS better than the HRM.

The Effect of Velocity Correlation on the Spatial Evolution of Breakthrough Curves in Heterogeneous Media

NASA Astrophysics Data System (ADS)

Massoudieh, A.; Dentz, M.; Le Borgne, T.

2017-12-01

In heterogeneous media, the velocity distribution and the spatial correlation structure of velocity for solute particles determine the breakthrough curves and how they evolve as one moves away from the solute source. The ability to predict such evolution can help relating the spatio-statistical hydraulic properties of the media to the transport behavior and travel time distributions. While commonly used non-local transport models such as anomalous dispersion and classical continuous time random walk (CTRW) can reproduce breakthrough curve successfully by adjusting the model parameter values, they lack the ability to relate model parameters to the spatio-statistical properties of the media. This in turns limits the transferability of these models. In the research to be presented, we express concentration or flux of solutes as a distribution over their velocity. We then derive an integrodifferential equation that governs the evolution of the particle distribution over velocity at given times and locations for a particle ensemble, based on a presumed velocity correlation structure and an ergodic cross-sectional velocity distribution. This way, the spatial evolution of breakthrough curves away from the source is predicted based on cross-sectional velocity distribution and the connectivity, which is expressed by the velocity transition probability density. The transition probability is specified via a copula function that can help construct a joint distribution with a given correlation and given marginal velocities. Using this approach, we analyze the breakthrough curves depending on the velocity distribution and correlation properties. The model shows how the solute transport behavior evolves from ballistic transport at small spatial scales to Fickian dispersion at large length scales relative to the velocity correlation length.

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.

Invasion resistance arises in strongly interacting species-rich model competition communities.

PubMed Central

Case, T J

1990-01-01

I assemble stable multispecies Lotka-Volterra competition communities that differ in resident species number and average strength (and variance) of species interactions. These are then invaded with randomly constructed invaders drawn from the same distribution as the residents. The invasion success rate and the fate of the residents are determined as a function of community-and species-level properties. I show that the probability of colonization success for an invader decreases with community size and the average strength of competition (alpha). Communities composed of many strongly interacting species limit the invasion possibilities of most similar species. These communities, even for a superior invading competitor, set up a sort of "activation barrier" that repels invaders when they invade at low numbers. This "priority effect" for residents is not assumed a priori in my description for the individual population dynamics of these species; rather it emerges because species-rich and strongly interacting species sets have alternative stable states that tend to disfavor species at low densities. These models point to community-level rather than invader-level properties as the strongest determinant of differences in invasion success. The probability of extinction for a resident species increases with community size, and the probability of successful colonization by the invader decreases. Thus an equilibrium community size results wherein the probability of a resident species' extinction just balances the probability of an invader's addition. Given the distribution of alpha it is now possible to predict the equilibrium species number. The results provide a logical framework for an island-biogeographic theory in which species turnover is low even in the face of persistent invasions and for the protection of fragile native species from invading exotics. PMID:11607132

Information Density and Syntactic Repetition.

PubMed

Temperley, David; Gildea, Daniel

2015-11-01

In noun phrase (NP) coordinate constructions (e.g., NP and NP), there is a strong tendency for the syntactic structure of the second conjunct to match that of the first; the second conjunct in such constructions is therefore low in syntactic information. The theory of uniform information density predicts that low-information syntactic constructions will be counterbalanced by high information in other aspects of that part of the sentence, and high-information constructions will be counterbalanced by other low-information components. Three predictions follow: (a) lexical probabilities (measured by N-gram probabilities and head-dependent probabilities) will be lower in second conjuncts than first conjuncts; (b) lexical probabilities will be lower in matching second conjuncts (those whose syntactic expansions match the first conjunct) than nonmatching ones; and (c) syntactic repetition should be especially common for low-frequency NP expansions. Corpus analysis provides support for all three of these predictions. Copyright © 2015 Cognitive Science Society, Inc.

Measurement of the top quark mass using template methods on dilepton events in p anti-p collisions at s**(1/2) = 1.96-TeV

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

Abulencia, A.; Acosta, D.; Adelman, Jahred A.

2006-02-01

The authors describe a measurement of the top quark mass from events produced in p{bar p} collisions at a center-of-mass energy of 1.96 TeV, using the Collider Detector at Fermilab. They identify t{bar t} candidates where both W bosons from the top quarks decay into leptons (e{nu}, {mu}{nu}, or {tau}{nu}) from a data sample of 360 pb{sup -1}. The top quark mass is reconstructed in each event separately by three different methods, which draw upon simulated distributions of the neutrino pseudorapidity, t{bar t} longitudinal momentum, or neutrino azimuthal angle in order to extract probability distributions for the top quark mass.more » For each method, representative mass distributions, or templates, are constructed from simulated samples of signal and background events, and parameterized to form continuous probability density functions. A likelihood fit incorporating these parameterized templates is then performed on the data sample masses in order to derive a final top quark mass. Combining the three template methods, taking into account correlations in their statistical and systematic uncertainties, results in a top quark mass measurement of 170.1 {+-} 6.0(stat.) {+-} 4.1(syst.) GeV/c{sup 2}.« less

A Tensile Specimen of Tailor Rolled Blanks with Equal Probability in Yield and Its Mechanical Behavior Analysis

PubMed Central

Zhang, Sijia; Liu, Xianghua; Liu, Lizhong

2018-01-01

In this paper, the microstructure and mechanical properties that distribute regulation along the rolling direction of tailor rolled blanks (TRB) were investigated. A tensile specimen with equal probability in yield (EYS) was first designed considering variation both in thickness and in material strength. The uniaxial tension test was carried out with a digital image correlation method to analyze the mechanical behaviors. The results showed that the strain distribution of EYS was homogeneous. From the results, it can be known that a new design philosophy for a TRB tensile specimen is reasonable and EYS is suitable to characterize the mechanical behavior of TRB. The true stress-strain curves of metal in different cross sections of TRB were calculated. On the basis of the true stress-strain curves, a material model of TRB was constructed and then implemented into finite element simulations of TRB uniaxial tensile tests. The strain distribution of numerical and experimental results was similar and the error between the elongation of the specimen after fracture obtained by experiment and FE ranged from 9.51% to 13.06%. Therefore, the simulation results match well with the experimental results and the material model has high accuracy and as well as practicability. PMID:29710772

Efficient quantum repeater with respect to both entanglement-concentration rate and complexity of local operations and classical communication

NASA Astrophysics Data System (ADS)

Su, Zhaofeng; Guan, Ji; Li, Lvzhou

2018-01-01

Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. However, in practice, it is difficult to distribute quantum entanglement over a long distance, due to the absorption and noise in quantum channels. A solution to this challenge is a quantum repeater, which can extend the distance of entanglement distribution. In this scheme, the time consumption of classical communication and local operations takes an important place with respect to time efficiency. Motivated by this observation, we consider a basic quantum repeater scheme that focuses on not only the optimal rate of entanglement concentration but also the complexity of local operations and classical communication. First, we consider the case where two different two-qubit pure states are initially distributed in the scenario. We construct a protocol with the optimal entanglement-concentration rate and less consumption of local operations and classical communication. We also find a criterion for the projective measurements to achieve the optimal probability of creating a maximally entangled state between the two ends. Second, we consider the case in which two general pure states are prepared and general measurements are allowed. We get an upper bound on the probability for a successful measurement operation to produce a maximally entangled state without any further local operations.

Intra-Urban Human Mobility and Activity Transition: Evidence from Social Media Check-In Data

PubMed Central

Wu, Lun; Zhi, Ye; Sui, Zhengwei; Liu, Yu

2014-01-01

Most existing human mobility literature focuses on exterior characteristics of movements but neglects activities, the driving force that underlies human movements. In this research, we combine activity-based analysis with a movement-based approach to model the intra-urban human mobility observed from about 15 million check-in records during a yearlong period in Shanghai, China. The proposed model is activity-based and includes two parts: the transition of travel demands during a specific time period and the movement between locations. For the first part, we find the transition probability between activities varies over time, and then we construct a temporal transition probability matrix to represent the transition probability of travel demands during a time interval. For the second part, we suggest that the travel demands can be divided into two classes, locationally mandatory activity (LMA) and locationally stochastic activity (LSA), according to whether the demand is associated with fixed location or not. By judging the combination of predecessor activity type and successor activity type we determine three trip patterns, each associated with a different decay parameter. To validate the model, we adopt the mechanism of an agent-based model and compare the simulated results with the observed pattern from the displacement distance distribution, the spatio-temporal distribution of activities, and the temporal distribution of travel demand transitions. The results show that the simulated patterns fit the observed data well, indicating that these findings open new directions for combining activity-based analysis with a movement-based approach using social media check-in data. PMID:24824892

Effect of thermal noise on vesicles and capsules in shear flow.

PubMed

Abreu, David; Seifert, Udo

2012-07-01

We add thermal noise consistently to reduced models of undeformable vesicles and capsules in shear flow and derive analytically the corresponding stochastic equations of motion. We calculate the steady-state probability distribution function and construct the corresponding phase diagrams for the different dynamical regimes. For fluid vesicles, we predict that at small shear rates thermal fluctuations induce a tumbling motion for any viscosity contrast. For elastic capsules, due to thermal mixing, an intermittent regime appears in regions where deterministic models predict only pure tank treading or tumbling.

Optimal Universal Uncertainty Relations

PubMed Central

Li, Tao; Xiao, Yunlong; Ma, Teng; Fei, Shao-Ming; Jing, Naihuan; Li-Jost, Xianqing; Wang, Zhi-Xi

2016-01-01

We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002 (2013)]. The results give rise to state independent uncertainty relations satisfied by any nonnegative Schur-concave functions. On the other hand, a remarkable recent result of entropic uncertainty relation is the direct-sum majorization relation. In this paper, we illustrate our bounds by showing how they provide a complement to that in [Phys. Rev. A. 89, 052115 (2014)]. PMID:27775010

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.

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.

Measuring public opinion on alcohol policy: a factor analytic study of a US probability sample.

PubMed

Latimer, William W; Harwood, Eileen M; Newcomb, Michael D; Wagenaar, Alexander C

2003-03-01

Public opinion has been one factor affecting change in policies designed to reduce underage alcohol use. Extant research, however, has been criticized for using single survey items of unknown reliability to define adult attitudes on alcohol policy issues. The present investigation addresses a critical gap in the literature by deriving scales on public attitudes, knowledge, and concerns pertinent to alcohol policies designed to reduce underage drinking using a US probability sample survey of 7021 adults. Five attitudinal scales were derived from exploratory and confirmatory factor analyses addressing policies to: (1) regulate alcohol marketing, (2) regulate alcohol consumption in public places, (3) regulate alcohol distribution, (4) increase alcohol taxes, and (5) regulate youth access. The scales exhibited acceptable psychometric properties and were largely consistent with a rational framework which guided the survey construction.

Constructions of secure entanglement channels assisted by quantum dots inside single-sided optical cavities

NASA Astrophysics Data System (ADS)

Heo, Jino; Kang, Min-Sung; Hong, Chang-Ho; Choi, Seong-Gon; Hong, Jong-Phil

2017-08-01

We propose quantum information processing schemes to generate and swap entangled states based on the interactions between flying photons and quantum dots (QDs) confined within optical cavities for quantum communication. To produce and distribute entangled states (Bell and Greenberger-Horne-Zeilinger [GHZ] states) between the photonic qubits of flying photons of consumers (Alice and Bob) and electron-spin qubits of a provider (trust center, or TC), the TC employs the interactions of the QD-cavity system, which is composed of a charged QD (negatively charged exciton) inside a single-sided cavity. Subsequently, the TC constructs an entanglement channel (Bell state and 4-qubit GHZ state) to link one consumer with another through entanglement swapping, which can be realized to exploit a probe photon with interactions of the QD-cavity systems and single-qubit measurements without Bell state measurement, for quantum communication between consumers. Consequently, the TC, which has quantum nodes (QD-cavity systems), can accomplish constructing the entanglement channel (authenticated channel) between two separated consumers from the distributions of entangled states and entanglement swapping. Furthermore, our schemes using QD-cavity systems, which are feasible with a certain probability of success and high fidelity, can be experimentally implemented with technology currently in use.

Distributed Synchronization Technique for OFDMA-Based Wireless Mesh Networks Using a Bio-Inspired Algorithm

PubMed Central

Kim, Mi Jeong; Maeng, Sung Joon; Cho, Yong Soo

2015-01-01

In this paper, a distributed synchronization technique based on a bio-inspired algorithm is proposed for an orthogonal frequency division multiple access (OFDMA)-based wireless mesh network (WMN) with a time difference of arrival. The proposed time- and frequency-synchronization technique uses only the signals received from the neighbor nodes, by considering the effect of the propagation delay between the nodes. It achieves a fast synchronization with a relatively low computational complexity because it is operated in a distributed manner, not requiring any feedback channel for the compensation of the propagation delays. In addition, a self-organization scheme that can be effectively used to construct 1-hop neighbor nodes is proposed for an OFDMA-based WMN with a large number of nodes. The performance of the proposed technique is evaluated with regard to the convergence property and synchronization success probability using a computer simulation. PMID:26225974

Distributed Synchronization Technique for OFDMA-Based Wireless Mesh Networks Using a Bio-Inspired Algorithm.

PubMed

Kim, Mi Jeong; Maeng, Sung Joon; Cho, Yong Soo

2015-07-28

In this paper, a distributed synchronization technique based on a bio-inspired algorithm is proposed for an orthogonal frequency division multiple access (OFDMA)-based wireless mesh network (WMN) with a time difference of arrival. The proposed time- and frequency-synchronization technique uses only the signals received from the neighbor nodes, by considering the effect of the propagation delay between the nodes. It achieves a fast synchronization with a relatively low computational complexity because it is operated in a distributed manner, not requiring any feedback channel for the compensation of the propagation delays. In addition, a self-organization scheme that can be effectively used to construct 1-hop neighbor nodes is proposed for an OFDMA-based WMN with a large number of nodes. The performance of the proposed technique is evaluated with regard to the convergence property and synchronization success probability using a computer simulation.

Proposal for optimal placement platform of bikes using queueing networks.

PubMed

Mizuno, Shinya; Iwamoto, Shogo; Seki, Mutsumi; Yamaki, Naokazu

2016-01-01

In recent social experiments, rental motorbikes and rental bicycles have been arranged at nodes, and environments where users can ride these bikes have been improved. When people borrow bikes, they return them to nearby nodes. Some experiments have been conducted using the models of Hamachari of Yokohama, the Niigata Rental Cycle, and Bicing. However, from these experiments, the effectiveness of distributing bikes was unclear, and many models were discontinued midway. Thus, we need to consider whether these models are effectively designed to represent the distribution system. Therefore, we construct a model to arrange the nodes for distributing bikes using a queueing network. To adopt realistic values for our model, we use the Google Maps application program interface. Thus, we can easily obtain values of distance and transit time between nodes in various places in the world. Moreover, we apply the distribution of a population to a gravity model and we compute the effective transition probability for this queueing network. If the arrangement of the nodes and number of bikes at each node is known, we can precisely design the system. We illustrate our system using convenience stores as nodes and optimize the node configuration. As a result, we can optimize simultaneously the number of nodes, node places, and number of bikes for each node, and we can construct a base for a rental cycle business to use our system.

Optimal designs based on the maximum quasi-likelihood estimator

PubMed Central

Shen, Gang; Hyun, Seung Won; Wong, Weng Kee

2016-01-01

We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just as well or better than optimal designs based on any other asymptotically linear unbiased estimators such as the least square estimator (LSE). In addition, we show current algorithms for finding optimal designs can be directly used to find optimal designs based on the MqLE. As an illustrative application, we construct a variety of locally optimal designs based on the MqLE for the 4-parameter logistic (4PL) model and study their robustness properties to misspecifications in the model using asymptotic relative efficiency. The results suggest that optimal designs based on the MqLE can be easily generated and they are quite robust to mis-specification in the probability distribution of the responses. PMID:28163359

Real-Time Safety Risk Assessment Based on a Real-Time Location System for Hydropower Construction Sites

PubMed Central

Fan, Qixiang; Qiang, Maoshan

2014-01-01

The concern for workers' safety in construction industry is reflected in many studies focusing on static safety risk identification and assessment. However, studies on real-time safety risk assessment aimed at reducing uncertainty and supporting quick response are rare. A method for real-time safety risk assessment (RTSRA) to implement a dynamic evaluation of worker safety states on construction site has been proposed in this paper. The method provides construction managers who are in charge of safety with more abundant information to reduce the uncertainty of the site. A quantitative calculation formula, integrating the influence of static and dynamic hazards and that of safety supervisors, is established to link the safety risk of workers with the locations of on-site assets. By employing the hidden Markov model (HMM), the RTSRA provides a mechanism for processing location data provided by the real-time location system (RTLS) and analyzing the probability distributions of different states in terms of false positives and negatives. Simulation analysis demonstrated the logic of the proposed method and how it works. Application case shows that the proposed RTSRA is both feasible and effective in managing construction project safety concerns. PMID:25114958

Real-time safety risk assessment based on a real-time location system for hydropower construction sites.

PubMed

Jiang, Hanchen; Lin, Peng; Fan, Qixiang; Qiang, Maoshan

2014-01-01

The concern for workers' safety in construction industry is reflected in many studies focusing on static safety risk identification and assessment. However, studies on real-time safety risk assessment aimed at reducing uncertainty and supporting quick response are rare. A method for real-time safety risk assessment (RTSRA) to implement a dynamic evaluation of worker safety states on construction site has been proposed in this paper. The method provides construction managers who are in charge of safety with more abundant information to reduce the uncertainty of the site. A quantitative calculation formula, integrating the influence of static and dynamic hazards and that of safety supervisors, is established to link the safety risk of workers with the locations of on-site assets. By employing the hidden Markov model (HMM), the RTSRA provides a mechanism for processing location data provided by the real-time location system (RTLS) and analyzing the probability distributions of different states in terms of false positives and negatives. Simulation analysis demonstrated the logic of the proposed method and how it works. Application case shows that the proposed RTSRA is both feasible and effective in managing construction project safety concerns.

Machine health prognostics using the Bayesian-inference-based probabilistic indication and high-order particle filtering framework

NASA Astrophysics Data System (ADS)

Yu, Jianbo

2015-12-01

Prognostics is much efficient to achieve zero-downtime performance, maximum productivity and proactive maintenance of machines. Prognostics intends to assess and predict the time evolution of machine health degradation so that machine failures can be predicted and prevented. A novel prognostics system is developed based on the data-model-fusion scheme using the Bayesian inference-based self-organizing map (SOM) and an integration of logistic regression (LR) and high-order particle filtering (HOPF). In this prognostics system, a baseline SOM is constructed to model the data distribution space of healthy machine under an assumption that predictable fault patterns are not available. Bayesian inference-based probability (BIP) derived from the baseline SOM is developed as a quantification indication of machine health degradation. BIP is capable of offering failure probability for the monitored machine, which has intuitionist explanation related to health degradation state. Based on those historic BIPs, the constructed LR and its modeling noise constitute a high-order Markov process (HOMP) to describe machine health propagation. HOPF is used to solve the HOMP estimation to predict the evolution of the machine health in the form of a probability density function (PDF). An on-line model update scheme is developed to adapt the Markov process changes to machine health dynamics quickly. The experimental results on a bearing test-bed illustrate the potential applications of the proposed system as an effective and simple tool for machine health prognostics.

Probabilistic Tsunami Hazard Assessment along Nankai Trough (1) An assessment based on the information of the forthcoming earthquake that Earthquake Research Committee(2013) evaluated

NASA Astrophysics Data System (ADS)

Hirata, K.; Fujiwara, H.; Nakamura, H.; Osada, M.; Morikawa, N.; Kawai, S.; Ohsumi, T.; Aoi, S.; Yamamoto, N.; Matsuyama, H.; Toyama, N.; Kito, T.; Murashima, Y.; Murata, Y.; Inoue, T.; Saito, R.; Takayama, J.; Akiyama, S.; Korenaga, M.; Abe, Y.; Hashimoto, N.

2015-12-01

The Earthquake Research Committee(ERC)/HERP, Government of Japan (2013) revised their long-term evaluation of the forthcoming large earthquake along the Nankai Trough; the next earthquake is estimated M8 to 9 class, and the probability (P30) that the next earthquake will occur within the next 30 years (from Jan. 1, 2013) is 60% to 70%. In this study, we assess tsunami hazards (maximum coastal tsunami heights) in the near future, in terms of a probabilistic approach, from the next earthquake along Nankai Trough, on the basis of ERC(2013)'s report. The probabilistic tsunami hazard assessment that we applied is as follows; (1) Characterized earthquake fault models (CEFMs) are constructed on each of the 15 hypothetical source areas (HSA) that ERC(2013) showed. The characterization rule follows Toyama et al.(2015, JpGU). As results, we obtained total of 1441 CEFMs. (2) We calculate tsunamis due to CEFMs by solving nonlinear, finite-amplitude, long-wave equations with advection and bottom friction terms by finite-difference method. Run-up computation on land is included. (3) A time predictable model predicts the recurrent interval of the present seismic cycle is T=88.2 years (ERC,2013). We fix P30 = 67% by applying the renewal process based on BPT distribution with T and alpha=0.24 as its aperiodicity. (4) We divide the probability P30 into P30(i) for i-th subgroup consisting of the earthquakes occurring in each of 15 HSA by following a probability re-distribution concept (ERC,2014). Then each earthquake (CEFM) in i-th subgroup is assigned a probability P30(i)/N where N is the number of CEFMs in each sub-group. Note that such re-distribution concept of the probability is nothing but tentative because the present seismology cannot give deep knowledge enough to do it. Epistemic logic-tree approach may be required in future. (5) We synthesize a number of tsunami hazard curves at every evaluation points on coasts by integrating the information about 30 years occurrence probabilities P30(i) for all earthquakes (CEFMs) and calculated maximum coastal tsunami heights. In the synthesis, aleatory uncertainties relating to incompleteness of governing equations, CEFM modeling, bathymetry and topography data, etc, are modeled assuming a log-normal probabilistic distribution. Examples of tsunami hazard curves will be presented.

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

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

Research on efficiency evaluation model of integrated energy system based on hybrid multi-attribute decision-making.

PubMed

Li, Yan

2017-05-25

The efficiency evaluation model of integrated energy system, involving many influencing factors, and the attribute values are heterogeneous and non-deterministic, usually cannot give specific numerical or accurate probability distribution characteristics, making the final evaluation result deviation. According to the characteristics of the integrated energy system, a hybrid multi-attribute decision-making model is constructed. The evaluation model considers the decision maker's risk preference. In the evaluation of the efficiency of the integrated energy system, the evaluation value of some evaluation indexes is linguistic value, or the evaluation value of the evaluation experts is not consistent. These reasons lead to ambiguity in the decision information, usually in the form of uncertain linguistic values and numerical interval values. In this paper, the risk preference of decision maker is considered when constructing the evaluation model. Interval-valued multiple-attribute decision-making method and fuzzy linguistic multiple-attribute decision-making model are proposed. Finally, the mathematical model of efficiency evaluation of integrated energy system is constructed.

An economic evaluation of home management of malaria in Uganda: an interactive Markov model.

PubMed

Lubell, Yoel; Mills, Anne J; Whitty, Christopher J M; Staedke, Sarah G

2010-08-27

Home management of malaria (HMM), promoting presumptive treatment of febrile children in the community, is advocated to improve prompt appropriate treatment of malaria in Africa. The cost-effectiveness of HMM is likely to vary widely in different settings and with the antimalarial drugs used. However, no data on the cost-effectiveness of HMM programmes are available. A Markov model was constructed to estimate the cost-effectiveness of HMM as compared to conventional care for febrile illnesses in children without HMM. The model was populated with data from Uganda, but is designed to be interactive, allowing the user to adjust certain parameters, including the antimalarials distributed. The model calculates the cost per disability adjusted life year averted and presents the incremental cost-effectiveness ratio compared to a threshold value. Model output is stratified by level of malaria transmission and the probability that a child would receive appropriate care from a health facility, to indicate the circumstances in which HMM is likely to be cost-effective. The model output suggests that the cost-effectiveness of HMM varies with malaria transmission, the probability of appropriate care, and the drug distributed. Where transmission is high and the probability of appropriate care is limited, HMM is likely to be cost-effective from a provider perspective. Even with the most effective antimalarials, HMM remains an attractive intervention only in areas of high malaria transmission and in medium transmission areas with a lower probability of appropriate care. HMM is generally not cost-effective in low transmission areas, regardless of which antimalarial is distributed. Considering the analysis from the societal perspective decreases the attractiveness of HMM. Syndromic HMM for children with fever may be a useful strategy for higher transmission settings with limited health care and diagnosis, but is not appropriate for all settings. HMM may need to be tailored to specific settings, accounting for local malaria transmission intensity and availability of health services.

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

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.

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks.

PubMed

Meng, X Flora; Baetica, Ania-Ariadna; Singhal, Vipul; Murray, Richard M

2017-05-01

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. © 2017 The Author(s).

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks

PubMed Central

Baetica, Ania-Ariadna; Singhal, Vipul; Murray, Richard M.

2017-01-01

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. PMID:28566513

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.

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.

Assessment of accident severity in the construction industry using the Bayesian theorem.

PubMed

Alizadeh, Seyed Shamseddin; Mortazavi, Seyed Bagher; Mehdi Sepehri, Mohammad

2015-01-01

Construction is a major source of employment in many countries. In construction, workers perform a great diversity of activities, each one with a specific associated risk. The aim of this paper is to identify workers who are at risk of accidents with severe consequences and classify these workers to determine appropriate control measures. We defined 48 groups of workers and used the Bayesian theorem to estimate posterior probabilities about the severity of accidents at the level of individuals in construction sector. First, the posterior probabilities of injuries based on four variables were provided. Then the probabilities of injury for 48 groups of workers were determined. With regard to marginal frequency of injury, slight injury (0.856), fatal injury (0.086) and severe injury (0.058) had the highest probability of occurrence. It was observed that workers with <1 year's work experience (0.168) had the highest probability of injury occurrence. The first group of workers, who were extensively exposed to risk of severe and fatal accidents, involved workers ≥ 50 years old, married, with 1-5 years' work experience, who had no past accident experience. The findings provide a direction for more effective safety strategies and occupational accident prevention and emergency programmes.

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.

Quadratic RK shooting solution for a environmental parameter prediction boundary value problem

NASA Astrophysics Data System (ADS)

Famelis, Ioannis Th.; Tsitouras, Ch.

2014-10-01

Using tools of Information Geometry, the minimum distance between two elements of a statistical manifold is defined by the corresponding geodesic, e.g. the minimum length curve that connects them. Such a curve, where the probability distribution functions in the case of our meteorological data are two parameter Weibull distributions, satisfies a 2nd order Boundary Value (BV) system. We study the numerical treatment of the resulting special quadratic form system using Shooting method. We compare the solutions of the problem when we employ a classical Singly Diagonally Implicit Runge Kutta (SDIRK) 4(3) pair of methods and a quadratic SDIRK 5(3) pair . Both pairs have the same computational costs whereas the second one attains higher order as it is specially constructed for quadratic problems.

A Maximum Entropy Method for Particle Filtering

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Kim, Sangil

2006-06-01

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.

MaxEnt-Based Ecological Theory: A Template for Integrated Catchment Theory

NASA Astrophysics Data System (ADS)

Harte, J.

2017-12-01

The maximum information entropy procedure (MaxEnt) is both a powerful tool for inferring least-biased probability distributions from limited data and a framework for the construction of complex systems theory. The maximum entropy theory of ecology (METE) describes remarkably well widely observed patterns in the distribution, abundance and energetics of individuals and taxa in relatively static ecosystems. An extension to ecosystems undergoing change in response to disturbance or natural succession (DynaMETE) is in progress. I describe the structure of both the static and the dynamic theory and show a range of comparisons with census data. I then propose a generalization of the MaxEnt approach that could provide a framework for a predictive theory of both static and dynamic, fully-coupled, eco-socio-hydrological catchment systems.

Distribution of selenium, molybdenum and uranium in sediment cores from the Colorado River delta, Baja California, Mexico.

PubMed

Orozco-Durán, A; Daesslé, L W; Gutiérrez-Galindo, E A; Muñoz-Barbosa, A

2012-01-01

The distribution of selenium, molybdenum and uranium was studied in ~1.5 m sediment cores from the Colorado River delta, at the Colorado (CR) and Hardy (HR) riverbeds. Core HR2 showed highest Se, Mo and U concentrations at its bottom (2.3, 0.95 and 1.8 μg g(-1)) within a sandy-silt layer deposited prior to dam construction. In CR5 the highest concentrations of these elements (0.9, 1.4 and 1.7 μg g(-1) respectively) were located at the top of the core within a surface layer enriched in organic carbon. A few samples from HR2 had Se above the probable toxic effect level guidelines.

Efficient cooperative compressive spectrum sensing by identifying multi-candidate and exploiting deterministic matrix

NASA Astrophysics Data System (ADS)

Li, Jia; Wang, Qiang; Yan, Wenjie; Shen, Yi

2015-12-01

Cooperative spectrum sensing exploits the spatial diversity to improve the detection of occupied channels in cognitive radio networks (CRNs). Cooperative compressive spectrum sensing (CCSS) utilizing the sparsity of channel occupancy further improves the efficiency by reducing the number of reports without degrading detection performance. In this paper, we firstly and mainly propose the referred multi-candidate orthogonal matrix matching pursuit (MOMMP) algorithms to efficiently and effectively detect occupied channels at fusion center (FC), where multi-candidate identification and orthogonal projection are utilized to respectively reduce the number of required iterations and improve the probability of exact identification. Secondly, two common but different approaches based on threshold and Gaussian distribution are introduced to realize the multi-candidate identification. Moreover, to improve the detection accuracy and energy efficiency, we propose the matrix construction based on shrinkage and gradient descent (MCSGD) algorithm to provide a deterministic filter coefficient matrix of low t-average coherence. Finally, several numerical simulations validate that our proposals provide satisfactory performance with higher probability of detection, lower probability of false alarm and less detection time.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

DOE PAGES

Hagos, Samson; Feng, Zhe; Plant, Robert S.; ...

2018-02-20

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

NASA Astrophysics Data System (ADS)

Hagos, Samson; Feng, Zhe; Plant, Robert S.; Houze, Robert A.; Xiao, Heng

2018-02-01

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.

Scheduling of House Development Projects with CPM and PERT Method for Time Efficiency (Case Study: House Type 36)

NASA Astrophysics Data System (ADS)

Kholil, Muhammad; Nurul Alfa, Bonitasari; Hariadi, Madjumsyah

2018-04-01

Network planning is one of the management techniques used to plan and control the implementation of a project, which shows the relationship between activities. The objective of this research is to arrange network planning on house construction project on CV. XYZ and to know the role of network planning in increasing the efficiency of time so that can be obtained the optimal project completion period. This research uses descriptive method, where the data collected by direct observation to the company, interview, and literature study. The result of this research is optimal time planning in project work. Based on the results of the research, it can be concluded that the use of the both methods in scheduling of house construction project gives very significant effect on the completion time of the project. The company’s CPM (Critical Path Method) method can complete the project with 131 days, PERT (Program Evaluation Review and Technique) Method takes 136 days. Based on PERT calculation obtained Z = -0.66 or 0,2546 (from normal distribution table), and also obtained the value of probability or probability is 74,54%. This means that the possibility of house construction project activities can be completed on time is high enough. While without using both methods the project completion time takes 173 days. So using the CPM method, the company can save time up to 42 days and has time efficiency by using network planning.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

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

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less

Where and When: Optimal Scheduling of the Electromagnetic Follow-up of Gravitational-wave Events Based on Counterpart Light-curve Models

NASA Astrophysics Data System (ADS)

Salafia, Om Sharan; Colpi, Monica; Branchesi, Marica; Chassande-Mottin, Eric; Ghirlanda, Giancarlo; Ghisellini, Gabriele; Vergani, Susanna D.

2017-09-01

The electromagnetic (EM) follow-up of a gravitational-wave (GW) event requires scanning a wide sky region, defined by the so-called “skymap,” to detect and identify a transient counterpart. We propose a novel method that exploits the information encoded in the GW signal to construct a “detectability map,” which represents the time-dependent (“when”) probability of detecting the transient at each position of the skymap (“where”). Focusing on the case of a neutron star binary inspiral, we model the associated short gamma-ray burst afterglow and macronova emission using the probability distributions of binary parameters (sky position, distance, orbit inclination, mass ratio) extracted from the GW signal as inputs. The resulting family of possible light curves is the basis for constructing the detectability map. As a practical example, we apply the method to a simulated GW signal produced by a neutron star merger at 75 Mpc whose localization uncertainty is very large (˜1500 deg2). We construct observing strategies for optical, infrared, and radio facilities based on the detectability maps, taking VST, VISTA, and MeerKAT as prototypes. Assuming limiting fluxes of r˜ 24.5, J˜ 22.4 (AB magnitudes), and 500 μ {Jy} (1.4 {GHz}) for ˜1000 s of exposure each, the afterglow and macronova emissions are successfully detected with a minimum observing time of 7, 15, and 5 hr respectively.

Intrinsic Bayesian Active Contours for Extraction of Object Boundaries in Images

PubMed Central

Srivastava, Anuj

2010-01-01

We present a framework for incorporating prior information about high-probability shapes in the process of contour extraction and object recognition in images. Here one studies shapes as elements of an infinite-dimensional, non-linear quotient space, and statistics of shapes are defined and computed intrinsically using differential geometry of this shape space. Prior models on shapes are constructed using probability distributions on tangent bundles of shape spaces. Similar to the past work on active contours, where curves are driven by vector fields based on image gradients and roughness penalties, we incorporate the prior shape knowledge in the form of vector fields on curves. Through experimental results, we demonstrate the use of prior shape models in the estimation of object boundaries, and their success in handling partial obscuration and missing data. Furthermore, we describe the use of this framework in shape-based object recognition or classification. PMID:21076692

Stochastic Car-Following Model for Explaining Nonlinear Traffic Phenomena

NASA Astrophysics Data System (ADS)

Meng, Jianping; Song, Tao; Dong, Liyun; Dai, Shiqiang

There is a common time parameter for representing the sensitivity or the lag (response) time of drivers in many car-following models. In the viewpoint of traffic psychology, this parameter could be considered as the perception-response time (PRT). Generally, this parameter is set to be a constant in previous models. However, PRT is actually not a constant but a random variable described by the lognormal distribution. Thus the probability can be naturally introduced into car-following models by recovering the probability of PRT. For demonstrating this idea, a specific stochastic model is constructed based on the optimal velocity model. By conducting simulations under periodic boundary conditions, it is found that some important traffic phenomena, such as the hysteresis and phantom traffic jams phenomena, can be reproduced more realistically. Especially, an interesting experimental feature of traffic jams, i.e., two moving jams propagating in parallel with constant speed stably and sustainably, is successfully captured by the present model.

Expert Knowledge-Based Automatic Sleep Stage Determination by Multi-Valued Decision Making Method

NASA Astrophysics Data System (ADS)

Wang, Bei; Sugi, Takenao; Kawana, Fusae; Wang, Xingyu; Nakamura, Masatoshi

In this study, an expert knowledge-based automatic sleep stage determination system working on a multi-valued decision making method is developed. Visual inspection by a qualified clinician is adopted to obtain the expert knowledge database. The expert knowledge database consists of probability density functions of parameters for various sleep stages. Sleep stages are determined automatically according to the conditional probability. Totally, four subjects were participated. The automatic sleep stage determination results showed close agreements with the visual inspection on sleep stages of awake, REM (rapid eye movement), light sleep and deep sleep. The constructed expert knowledge database reflects the distributions of characteristic parameters which can be adaptive to variable sleep data in hospitals. The developed automatic determination technique based on expert knowledge of visual inspection can be an assistant tool enabling further inspection of sleep disorder cases for clinical practice.

Improved estimation of hydraulic conductivity by combining stochastically simulated hydrofacies with geophysical data.

PubMed

Zhu, Lin; Gong, Huili; Chen, Yun; Li, Xiaojuan; Chang, Xiang; Cui, Yijiao

2016-03-01

Hydraulic conductivity is a major parameter affecting the output accuracy of groundwater flow and transport models. The most commonly used semi-empirical formula for estimating conductivity is Kozeny-Carman equation. However, this method alone does not work well with heterogeneous strata. Two important parameters, grain size and porosity, often show spatial variations at different scales. This study proposes a method for estimating conductivity distributions by combining a stochastic hydrofacies model with geophysical methods. The Markov chain model with transition probability matrix was adopted to re-construct structures of hydrofacies for deriving spatial deposit information. The geophysical and hydro-chemical data were used to estimate the porosity distribution through the Archie's law. Results show that the stochastic simulated hydrofacies model reflects the sedimentary features with an average model accuracy of 78% in comparison with borehole log data in the Chaobai alluvial fan. The estimated conductivity is reasonable and of the same order of magnitude of the outcomes of the pumping tests. The conductivity distribution is consistent with the sedimentary distributions. This study provides more reliable spatial distributions of the hydraulic parameters for further numerical modeling.

A mathematical model for generating bipartite graphs and its application to protein networks

NASA Astrophysics Data System (ADS)

Nacher, J. C.; Ochiai, T.; Hayashida, M.; Akutsu, T.

2009-12-01

Complex systems arise in many different contexts from large communication systems and transportation infrastructures to molecular biology. Most of these systems can be organized into networks composed of nodes and interacting edges. Here, we present a theoretical model that constructs bipartite networks with the particular feature that the degree distribution can be tuned depending on the probability rate of fundamental processes. We then use this model to investigate protein-domain networks. A protein can be composed of up to hundreds of domains. Each domain represents a conserved sequence segment with specific functional tasks. We analyze the distribution of domains in Homo sapiens and Arabidopsis thaliana organisms and the statistical analysis shows that while (a) the number of domain types shared by k proteins exhibits a power-law distribution, (b) the number of proteins composed of k types of domains decays as an exponential distribution. The proposed mathematical model generates bipartite graphs and predicts the emergence of this mixing of (a) power-law and (b) exponential distributions. Our theoretical and computational results show that this model requires (1) growth process and (2) copy mechanism.

Why Are Product Prices in Online Markets Not Converging?

PubMed Central

Mizuno, Takayuki; Watanabe, Tsutomu

2013-01-01

Why are product prices in online markets dispersed in spite of very small search costs? To address this question, we construct a unique dataset from a Japanese price comparison site, which records price quotes offered by e-retailers as well as customers’ clicks on products, which occur when they proceed to purchase the product. The novelty of our approach is that we seek to extract useful information on the source of price dispersion from the shape of price distributions rather than focusing merely on the standard deviation or the coefficient of variation of prices, as previous studies have done. We find that the distribution of prices retailers quote for a particular product at a particular point in time (divided by the lowest price) follows an exponential distribution, showing the presence of substantial price dispersion. For example, 20 percent of all retailers quote prices that are more than 50 percent higher than the lowest price. Next, comparing the probability that customers click on a retailer with a particular rank and the probability that retailers post prices at a particular rank, we show that both decline exponentially with price rank and that the exponents associated with the probabilities are quite close. This suggests that the reason why some retailers set prices at a level substantially higher than the lowest price is that they know that some customers will choose them even at that high price. Based on these findings, we hypothesize that price dispersion in online markets stems from heterogeneity in customers’ preferences over retailers; that is, customers choose a set of candidate retailers based on their preferences, which are heterogeneous across customers, and then pick a particular retailer among the candidates based on the price ranking. PMID:24015219

Why are product prices in online markets not converging?

PubMed

Mizuno, Takayuki; Watanabe, Tsutomu

2013-01-01

Why are product prices in online markets dispersed in spite of very small search costs? To address this question, we construct a unique dataset from a Japanese price comparison site, which records price quotes offered by e-retailers as well as customers' clicks on products, which occur when they proceed to purchase the product. The novelty of our approach is that we seek to extract useful information on the source of price dispersion from the shape of price distributions rather than focusing merely on the standard deviation or the coefficient of variation of prices, as previous studies have done. We find that the distribution of prices retailers quote for a particular product at a particular point in time (divided by the lowest price) follows an exponential distribution, showing the presence of substantial price dispersion. For example, 20 percent of all retailers quote prices that are more than 50 percent higher than the lowest price. Next, comparing the probability that customers click on a retailer with a particular rank and the probability that retailers post prices at a particular rank, we show that both decline exponentially with price rank and that the exponents associated with the probabilities are quite close. This suggests that the reason why some retailers set prices at a level substantially higher than the lowest price is that they know that some customers will choose them even at that high price. Based on these findings, we hypothesize that price dispersion in online markets stems from heterogeneity in customers' preferences over retailers; that is, customers choose a set of candidate retailers based on their preferences, which are heterogeneous across customers, and then pick a particular retailer among the candidates based on the price ranking.

Expert Elicitations of 2100 Emission of CO2

NASA Astrophysics Data System (ADS)

Ho, Emily; Bosetti, Valentina; Budescu, David; Keller, Klaus; van Vuuren, Detlef

2017-04-01

Emission scenarios such as Shared Socioeconomic Pathways (SSPs) and Representative Concentration Pathways (RCPs) are used intensively for climate research (e.g. climate change projections) and policy analysis. While the range of these scenarios provides an indication of uncertainty, these scenarios are typically not associated with probability values. Some studies (e.g. Vuuren et al, 2007; Gillingham et al., 2015) took a different approach associating baseline emission pathways (conditionally) with probability distributions. This paper summarizes three studies where climate change experts were asked to conduct pair-wise comparisons of possible ranges of 2100 greenhouse gas emissions and rate the relative likelihood of the ranges. The elicitation was performed under two sets of assumptions: 1) a situation where no climate policies are introduced beyond the ones already in place (baseline scenario), and 2) a situation in which countries have ratified the voluntary policies in line with the long term target embedded in the 2015 Paris Agreement. These indirect relative judgments were used to construct subjective cumulative distribution functions. We show that by using a ratio scaling method that invokes relative likelihoods of scenarios, a subjective probability distribution can be derived for each expert that expresses their beliefs in the projected greenhouse gas emissions range in 2100. This method is shown to elicit stable estimates that require minimal adjustment and is relatively invariant to the partition of the domain of interest. Experts also rated the method as being easy and intuitive to use. We also report results of a study that allowed participants to choose their own ranges of greenhouse gas emissions to remove potential anchoring bias. We discuss the implications of the use of this method for facilitating comparison and communication of beliefs among diverse users of climate science research.

A Multivariate and Probabilistic Assessment of Drought in the Pacific Northwest under Observed and Future Climate.

NASA Astrophysics Data System (ADS)

Mortuza, M. R.; Demissie, Y. K.

2015-12-01

In lieu with the recent and anticipated more server and frequently droughts incidences in Yakima River Basin (YRB), a reliable and comprehensive drought assessment is deemed necessary to avoid major crop production loss and better manage the water right issues in the region during low precipitation and/or snow accumulation years. In this study, we have conducted frequency analysis of hydrological droughts and quantified associated uncertainty in the YRB under both historical and changing climate. Streamflow drought index (SDI) was employed to identify mutually correlated drought characteristics (e.g., severity, duration and peak). The historical and future characteristics of drought were estimated by applying tri-variate copulas probability distribution, which effectively describe the joint distribution and dependence of drought severity, duration, and peak. The associated prediction uncertainty, related to parameters of the joint probability and climate projections, were evaluated using the Bayesian approach with bootstrap resampling. For the climate change scenarios, two future representative pathways (RCP4.5 and RCP8.5) from University of Idaho's Multivariate Adaptive Constructed Analogs (MACA) database were considered. The results from the study are expected to provide useful information towards drought risk management in YRB under anticipated climate changes.

On weak lensing shape noise

NASA Astrophysics Data System (ADS)

Niemi, Sami-Matias; Kitching, Thomas D.; Cropper, Mark

2015-12-01

One of the most powerful techniques to study the dark sector of the Universe is weak gravitational lensing. In practice, to infer the reduced shear, weak lensing measures galaxy shapes, which are the consequence of both the intrinsic ellipticity of the sources and of the integrated gravitational lensing effect along the line of sight. Hence, a very large number of galaxies is required in order to average over their individual properties and to isolate the weak lensing cosmic shear signal. If this `shape noise' can be reduced, significant advances in the power of a weak lensing surveys can be expected. This paper describes a general method for extracting the probability distributions of parameters from catalogues of data using Voronoi cells, which has several applications, and has synergies with Bayesian hierarchical modelling approaches. This allows us to construct a probability distribution for the variance of the intrinsic ellipticity as a function of galaxy property using only photometric data, allowing a reduction of shape noise. As a proof of concept the method is applied to the CFHTLenS survey data. We use this approach to investigate trends of galaxy properties in the data and apply this to the case of weak lensing power spectra.

Comments on {open_quotes}interpretations of quantum mechanics, joint measurement of incompatible observables, and counterfactual definiteness{close_quotes}

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

Stapp, H.P.

1994-12-01

Some seeming logical deficiencies in a recent paper are described. The author responds to the arguments of the work by de Muynck, De Baere, and Martens (MDM), who argue it is widely accepted today that some sort of nonlocal effect is needed to resolve the problems raised by the works of Einstein, Podolsky, and Rosen (EPR) and John Bell. In MBM a variety of arguments are set forth that aim to invalidate the existing purported proofs of nonlocality and to provide, moreover, a local solution to the problems uncovered by EPR and Bell. Much of the argumentation in MBM ismore » based on the idea of introducing `nonideal` measurements, which, according to MBM, allow one to construct joint probability distributions for incompatible observables. The existence of a bona fide joint probability distribution for the incompatible observables occurring in the EPRB experiments would entail that Bell`s inequalities can be satisfied, and hence that the mathematical basis for the nonlocal effects would disappear. This relult would apparently allow one to eliminate the need for nonlocal effects by considering experiments of this new kind.« less

On Applying the Prognostic Performance Metrics

NASA Technical Reports Server (NTRS)

Saxena, Abhinav; Celaya, Jose; Saha, Bhaskar; Saha, Sankalita; Goebel, Kai

2009-01-01

Prognostics performance evaluation has gained significant attention in the past few years. As prognostics technology matures and more sophisticated methods for prognostic uncertainty management are developed, a standardized methodology for performance evaluation becomes extremely important to guide improvement efforts in a constructive manner. This paper is in continuation of previous efforts where several new evaluation metrics tailored for prognostics were introduced and were shown to effectively evaluate various algorithms as compared to other conventional metrics. Specifically, this paper presents a detailed discussion on how these metrics should be interpreted and used. Several shortcomings identified, while applying these metrics to a variety of real applications, are also summarized along with discussions that attempt to alleviate these problems. Further, these metrics have been enhanced to include the capability of incorporating probability distribution information from prognostic algorithms as opposed to evaluation based on point estimates only. Several methods have been suggested and guidelines have been provided to help choose one method over another based on probability distribution characteristics. These approaches also offer a convenient and intuitive visualization of algorithm performance with respect to some of these new metrics like prognostic horizon and alpha-lambda performance, and also quantify the corresponding performance while incorporating the uncertainty information.

A Novel Multiobjective Evolutionary Algorithm Based on Regression Analysis

PubMed Central

Song, Zhiming; Wang, Maocai; Dai, Guangming; Vasile, Massimiliano

2015-01-01

As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m − 1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m − 1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper. PMID:25874246

Electromigration Mechanism of Failure in Flip-Chip Solder Joints Based on Discrete Void Formation.

PubMed

Chang, Yuan-Wei; Cheng, Yin; Helfen, Lukas; Xu, Feng; Tian, Tian; Scheel, Mario; Di Michiel, Marco; Chen, Chih; Tu, King-Ning; Baumbach, Tilo

2017-12-20

In this investigation, SnAgCu and SN100C solders were electromigration (EM) tested, and the 3D laminography imaging technique was employed for in-situ observation of the microstructure evolution during testing. We found that discrete voids nucleate, grow and coalesce along the intermetallic compound/solder interface during EM testing. A systematic analysis yields quantitative information on the number, volume, and growth rate of voids, and the EM parameter of DZ*. We observe that fast intrinsic diffusion in SnAgCu solder causes void growth and coalescence, while in the SN100C solder this coalescence was not significant. To deduce the current density distribution, finite-element models were constructed on the basis of the laminography images. The discrete voids do not change the global current density distribution, but they induce the local current crowding around the voids: this local current crowding enhances the lateral void growth and coalescence. The correlation between the current density and the probability of void formation indicates that a threshold current density exists for the activation of void formation. There is a significant increase in the probability of void formation when the current density exceeds half of the maximum value.

Diagnostic accuracy of enzyme-linked immunosorbent assay (ELISA) and immunoblot (IB) for the detection of antibodies against Neospora caninum in milk from dairy cows.

PubMed

Chatziprodromidou, I P; Apostolou, T

2018-04-01

The aim of the study was to estimate the sensitivity and specificity of enzyme-linked immunosorbent assay (ELISA) and immunoblot (IB) for detecting antibodies of Neospora caninum in dairy cows, in the absence of a gold standard. The study complies with STRADAS-paratuberculosis guidelines for reporting the accuracy of the test. We tried to apply Bayesian models that do not require conditional independence of the tests under evaluation, but as convergence problems appeared, we used Bayesian methodology, that does not assume conditional dependence of the tests. Informative prior probability distributions were constructed, based on scientific inputs regarding sensitivity and specificity of the IB test and the prevalence of disease in the studied populations. IB sensitivity and specificity were estimated to be 98.8% and 91.3%, respectively, while the respective estimates for ELISA were 60% and 96.7%. A sensitivity analysis, where modified prior probability distributions concerning IB diagnostic accuracy applied, showed a limited effect in posterior assessments. We concluded that ELISA can be used to screen the bulk milk and secondly, IB can be used whenever needed.

Location Prediction Based on Transition Probability Matrices Constructing from Sequential Rules for Spatial-Temporal K-Anonymity Dataset

PubMed Central

Liu, Zhao; Zhu, Yunhong; Wu, Chenxue

2016-01-01

Spatial-temporal k-anonymity has become a mainstream approach among techniques for protection of users’ privacy in location-based services (LBS) applications, and has been applied to several variants such as LBS snapshot queries and continuous queries. Analyzing large-scale spatial-temporal anonymity sets may benefit several LBS applications. In this paper, we propose two location prediction methods based on transition probability matrices constructing from sequential rules for spatial-temporal k-anonymity dataset. First, we define single-step sequential rules mined from sequential spatial-temporal k-anonymity datasets generated from continuous LBS queries for multiple users. We then construct transition probability matrices from mined single-step sequential rules, and normalize the transition probabilities in the transition matrices. Next, we regard a mobility model for an LBS requester as a stationary stochastic process and compute the n-step transition probability matrices by raising the normalized transition probability matrices to the power n. Furthermore, we propose two location prediction methods: rough prediction and accurate prediction. The former achieves the probabilities of arriving at target locations along simple paths those include only current locations, target locations and transition steps. By iteratively combining the probabilities for simple paths with n steps and the probabilities for detailed paths with n-1 steps, the latter method calculates transition probabilities for detailed paths with n steps from current locations to target locations. Finally, we conduct extensive experiments, and correctness and flexibility of our proposed algorithm have been verified. PMID:27508502

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.

Stability metrics for multi-source biomedical data based on simplicial projections from probability distribution distances.

PubMed

Sáez, Carlos; Robles, Montserrat; García-Gómez, Juan M

2017-02-01

Biomedical data may be composed of individuals generated from distinct, meaningful sources. Due to possible contextual biases in the processes that generate data, there may exist an undesirable and unexpected variability among the probability distribution functions (PDFs) of the source subsamples, which, when uncontrolled, may lead to inaccurate or unreproducible research results. Classical statistical methods may have difficulties to undercover such variabilities when dealing with multi-modal, multi-type, multi-variate data. This work proposes two metrics for the analysis of stability among multiple data sources, robust to the aforementioned conditions, and defined in the context of data quality assessment. Specifically, a global probabilistic deviation and a source probabilistic outlyingness metrics are proposed. The first provides a bounded degree of the global multi-source variability, designed as an estimator equivalent to the notion of normalized standard deviation of PDFs. The second provides a bounded degree of the dissimilarity of each source to a latent central distribution. The metrics are based on the projection of a simplex geometrical structure constructed from the Jensen-Shannon distances among the sources PDFs. The metrics have been evaluated and demonstrated their correct behaviour on a simulated benchmark and with real multi-source biomedical data using the UCI Heart Disease data set. The biomedical data quality assessment based on the proposed stability metrics may improve the efficiency and effectiveness of biomedical data exploitation and research.

Nuclear Ensemble Approach with Importance Sampling.

PubMed

Kossoski, Fábris; Barbatti, Mario

2018-06-12

We show that the importance sampling technique can effectively augment the range of problems where the nuclear ensemble approach can be applied. A sampling probability distribution function initially determines the collection of initial conditions for which calculations are performed, as usual. Then, results for a distinct target distribution are computed by introducing compensating importance sampling weights for each sampled point. This mapping between the two probability distributions can be performed whenever they are both explicitly constructed. Perhaps most notably, this procedure allows for the computation of temperature dependent observables. As a test case, we investigated the UV absorption spectra of phenol, which has been shown to have a marked temperature dependence. Application of the proposed technique to a range that covers 500 K provides results that converge to those obtained with conventional sampling. We further show that an overall improved rate of convergence is obtained when sampling is performed at intermediate temperatures. The comparison between calculated and the available measured cross sections is very satisfactory, as the main features of the spectra are correctly reproduced. As a second test case, one of Tully's classical models was revisited, and we show that the computation of dynamical observables also profits from the importance sampling technique. In summary, the strategy developed here can be employed to assess the role of temperature for any property calculated within the nuclear ensemble method, with the same computational cost as doing so for a single temperature.

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

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

Hou, Z; Terry, N; Hubbard, S S

2013-02-12

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability distribution functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSim) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

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.

The oilspill risk analysis model of the U. S. Geological Survey

USGS Publications Warehouse

Smith, R.A.; Slack, J.R.; Wyant, Timothy; Lanfear, K.J.

1982-01-01

The U.S. Geological Survey has developed an oilspill risk analysis model to aid in estimating the environmental hazards of developing oil resources in Outer Continental Shelf (OCS) lease areas. The large, computerized model analyzes the probability of spill occurrence, as well as the likely paths or trajectories of spills in relation to the locations of recreational and biological resources which may be vulnerable. The analytical methodology can easily incorporate estimates of weathering rates , slick dispersion, and possible mitigating effects of cleanup. The probability of spill occurrence is estimated from information on the anticipated level of oil production and method of route of transport. Spill movement is modeled in Monte Carlo fashion with a sample of 500 spills per season, each transported by monthly surface current vectors and wind velocities sampled from 3-hour wind transition matrices. Transition matrices are based on historic wind records grouped in 41 wind velocity classes, and are constructed seasonally for up to six wind stations. Locations and monthly vulnerabilities of up to 31 categories of environmental resources are digitized within an 800,000 square kilometer study area. Model output includes tables of conditional impact probabilities (that is, the probability of hitting a target, given that a spill has occured), as well as probability distributions for oilspills occurring and contacting environmental resources within preselected vulnerability time horizons. (USGS)

The oilspill risk analysis model of the U. S. Geological Survey

USGS Publications Warehouse

Smith, R.A.; Slack, J.R.; Wyant, T.; Lanfear, K.J.

1980-01-01

The U.S. Geological Survey has developed an oilspill risk analysis model to aid in estimating the environmental hazards of developing oil resources in Outer Continental Shelf (OCS) lease areas. The large, computerized model analyzes the probability of spill occurrence, as well as the likely paths or trajectories of spills in relation to the locations of recreational and biological resources which may be vulnerable. The analytical methodology can easily incorporate estimates of weathering rates , slick dispersion, and possible mitigating effects of cleanup. The probability of spill occurrence is estimated from information on the anticipated level of oil production and method and route of transport. Spill movement is modeled in Monte Carlo fashion with a sample of 500 spills per season, each transported by monthly surface current vectors and wind velocities sampled from 3-hour wind transition matrices. Transition matrices are based on historic wind records grouped in 41 wind velocity classes, and are constructed seasonally for up to six wind stations. Locations and monthly vulnerabilities of up to 31 categories of environmental resources are digitized within an 800,000 square kilometer study area. Model output includes tables of conditional impact probabilities (that is, the probability of hitting a target, given that a spill has occurred), as well as probability distributions for oilspills occurring and contacting environmental resources within preselected vulnerability time horizons. (USGS)

Mixture distributions of wind speed in the UAE

NASA Astrophysics Data System (ADS)

Shin, J.; Ouarda, T.; Lee, T. S.

2013-12-01

Wind speed probability distribution is commonly used to estimate potential wind energy. The 2-parameter Weibull distribution has been most widely used to characterize the distribution of wind speed. However, it is unable to properly model wind speed regimes when wind speed distribution presents bimodal and kurtotic shapes. Several studies have concluded that the Weibull distribution should not be used for frequency analysis of wind speed without investigation of wind speed distribution. Due to these mixture distributional characteristics of wind speed data, the application of mixture distributions should be further investigated in the frequency analysis of wind speed. A number of studies have investigated the potential wind energy in different parts of the Arabian Peninsula. Mixture distributional characteristics of wind speed were detected from some of these studies. Nevertheless, mixture distributions have not been employed for wind speed modeling in the Arabian Peninsula. In order to improve our understanding of wind energy potential in Arabian Peninsula, mixture distributions should be tested for the frequency analysis of wind speed. The aim of the current study is to assess the suitability of mixture distributions for the frequency analysis of wind speed in the UAE. Hourly mean wind speed data at 10-m height from 7 stations were used in the current study. The Weibull and Kappa distributions were employed as representatives of the conventional non-mixture distributions. 10 mixture distributions are used and constructed by mixing four probability distributions such as Normal, Gamma, Weibull and Extreme value type-one (EV-1) distributions. Three parameter estimation methods such as Expectation Maximization algorithm, Least Squares method and Meta-Heuristic Maximum Likelihood (MHML) method were employed to estimate the parameters of the mixture distributions. In order to compare the goodness-of-fit of tested distributions and parameter estimation methods for sample wind data, the adjusted coefficient of determination, Bayesian Information Criterion (BIC) and Chi-squared statistics were computed. Results indicate that MHML presents the best performance of parameter estimation for the used mixture distributions. In most of the employed 7 stations, mixture distributions give the best fit. When the wind speed regime shows mixture distributional characteristics, most of these regimes present the kurtotic statistical characteristic. Particularly, applications of mixture distributions for these stations show a significant improvement in explaining the whole wind speed regime. In addition, the Weibull-Weibull mixture distribution presents the best fit for the wind speed data in the UAE.

Evaluation of statistical models for forecast errors from the HBV model

NASA Astrophysics Data System (ADS)

Engeland, Kolbjørn; Renard, Benjamin; Steinsland, Ingelin; Kolberg, Sjur

2010-04-01

SummaryThree statistical models for the forecast errors for inflow into the Langvatn reservoir in Northern Norway have been constructed and tested according to the agreement between (i) the forecast distribution and the observations and (ii) median values of the forecast distribution and the observations. For the first model observed and forecasted inflows were transformed by the Box-Cox transformation before a first order auto-regressive model was constructed for the forecast errors. The parameters were conditioned on weather classes. In the second model the Normal Quantile Transformation (NQT) was applied on observed and forecasted inflows before a similar first order auto-regressive model was constructed for the forecast errors. For the third model positive and negative errors were modeled separately. The errors were first NQT-transformed before conditioning the mean error values on climate, forecasted inflow and yesterday's error. To test the three models we applied three criterions: we wanted (a) the forecast distribution to be reliable; (b) the forecast intervals to be narrow; (c) the median values of the forecast distribution to be close to the observed values. Models 1 and 2 gave almost identical results. The median values improved the forecast with Nash-Sutcliffe R eff increasing from 0.77 for the original forecast to 0.87 for the corrected forecasts. Models 1 and 2 over-estimated the forecast intervals but gave the narrowest intervals. Their main drawback was that the distributions are less reliable than Model 3. For Model 3 the median values did not fit well since the auto-correlation was not accounted for. Since Model 3 did not benefit from the potential variance reduction that lies in bias estimation and removal it gave on average wider forecasts intervals than the two other models. At the same time Model 3 on average slightly under-estimated the forecast intervals, probably explained by the use of average measures to evaluate the fit.

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.

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

Modeling of Abrasion and Crushing of Unbound Granular Materials During Compaction

NASA Astrophysics Data System (ADS)

Ocampo, Manuel S.; Caicedo, Bernardo

2009-06-01

Unbound compacted granular materials are commonly used in engineering structures as layers in road pavements, railroad beds, highway embankments, and foundations. These structures are generally subjected to dynamic loading by construction operations, traffic and wheel loads. These repeated or cyclic loads cause abrasion and crushing of the granular materials. Abrasion changes a particle's shape, and crushing divides the particle into a mixture of many small particles of varying sizes. Particle breakage is important because the mechanical and hydraulic properties of these materials depend upon their grain size distribution. Therefore, it is important to evaluate the evolution of the grain size distribution of these materials. In this paper an analytical model for unbound granular materials is proposed in order to evaluate particle crushing of gravels and soils subjected to cyclic loads. The model is based on a Markov chain which describes the development of grading changes in the material as a function of stress levels. In the model proposed, each particle size is a state in the system, and the evolution of the material is the movement of particles from one state to another in n steps. Each step is a load cycle, and movement between states is possible with a transition probability. The crushing of particles depends on the mechanical properties of each grain and the packing density of the granular material. The transition probability was calculated using both the survival probability defined by Weibull and the compressible packing model developed by De Larrard. Material mechanical properties are considered using the Weibull probability theory. The size and shape of the grains, as well as the method of processing the packing density are considered using De Larrard's model. Results of the proposed analytical model show a good agreement with the experimental tests carried out using the gyratory compaction test.

A Riemannian framework for orientation distribution function computing.

PubMed

Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid

2009-01-01

Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy H1/2 of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation.

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.

The Efficacy of Consensus Tree Methods for Summarizing Phylogenetic Relationships from a Posterior Sample of Trees Estimated from Morphological Data.

PubMed

O'Reilly, Joseph E; Donoghue, Philip C J

2018-03-01

Consensus trees are required to summarize trees obtained through MCMC sampling of a posterior distribution, providing an overview of the distribution of estimated parameters such as topology, branch lengths, and divergence times. Numerous consensus tree construction methods are available, each presenting a different interpretation of the tree sample. The rise of morphological clock and sampled-ancestor methods of divergence time estimation, in which times and topology are coestimated, has increased the popularity of the maximum clade credibility (MCC) consensus tree method. The MCC method assumes that the sampled, fully resolved topology with the highest clade credibility is an adequate summary of the most probable clades, with parameter estimates from compatible sampled trees used to obtain the marginal distributions of parameters such as clade ages and branch lengths. Using both simulated and empirical data, we demonstrate that MCC trees, and trees constructed using the similar maximum a posteriori (MAP) method, often include poorly supported and incorrect clades when summarizing diffuse posterior samples of trees. We demonstrate that the paucity of information in morphological data sets contributes to the inability of MCC and MAP trees to accurately summarise of the posterior distribution. Conversely, majority-rule consensus (MRC) trees represent a lower proportion of incorrect nodes when summarizing the same posterior samples of trees. Thus, we advocate the use of MRC trees, in place of MCC or MAP trees, in attempts to summarize the results of Bayesian phylogenetic analyses of morphological data.

The Efficacy of Consensus Tree Methods for Summarizing Phylogenetic Relationships from a Posterior Sample of Trees Estimated from Morphological Data

PubMed Central

O’Reilly, Joseph E; Donoghue, Philip C J

2018-01-01

Abstract Consensus trees are required to summarize trees obtained through MCMC sampling of a posterior distribution, providing an overview of the distribution of estimated parameters such as topology, branch lengths, and divergence times. Numerous consensus tree construction methods are available, each presenting a different interpretation of the tree sample. The rise of morphological clock and sampled-ancestor methods of divergence time estimation, in which times and topology are coestimated, has increased the popularity of the maximum clade credibility (MCC) consensus tree method. The MCC method assumes that the sampled, fully resolved topology with the highest clade credibility is an adequate summary of the most probable clades, with parameter estimates from compatible sampled trees used to obtain the marginal distributions of parameters such as clade ages and branch lengths. Using both simulated and empirical data, we demonstrate that MCC trees, and trees constructed using the similar maximum a posteriori (MAP) method, often include poorly supported and incorrect clades when summarizing diffuse posterior samples of trees. We demonstrate that the paucity of information in morphological data sets contributes to the inability of MCC and MAP trees to accurately summarise of the posterior distribution. Conversely, majority-rule consensus (MRC) trees represent a lower proportion of incorrect nodes when summarizing the same posterior samples of trees. Thus, we advocate the use of MRC trees, in place of MCC or MAP trees, in attempts to summarize the results of Bayesian phylogenetic analyses of morphological data. PMID:29106675

The perception of probability.

PubMed

Gallistel, C R; Krishan, Monika; Liu, Ye; Miller, Reilly; Latham, Peter E

2014-01-01

We present a computational model to explain the results from experiments in which subjects estimate the hidden probability parameter of a stepwise nonstationary Bernoulli process outcome by outcome. The model captures the following results qualitatively and quantitatively, with only 2 free parameters: (a) Subjects do not update their estimate after each outcome; they step from one estimate to another at irregular intervals. (b) The joint distribution of step widths and heights cannot be explained on the assumption that a threshold amount of change must be exceeded in order for them to indicate a change in their perception. (c) The mapping of observed probability to the median perceived probability is the identity function over the full range of probabilities. (d) Precision (how close estimates are to the best possible estimate) is good and constant over the full range. (e) Subjects quickly detect substantial changes in the hidden probability parameter. (f) The perceived probability sometimes changes dramatically from one observation to the next. (g) Subjects sometimes have second thoughts about a previous change perception, after observing further outcomes. (h) The frequency with which they perceive changes moves in the direction of the true frequency over sessions. (Explaining this finding requires 2 additional parametric assumptions.) The model treats the perception of the current probability as a by-product of the construction of a compact encoding of the experienced sequence in terms of its change points. It illustrates the why and the how of intermittent Bayesian belief updating and retrospective revision in simple perception. It suggests a reinterpretation of findings in the recent literature on the neurobiology of decision making. (PsycINFO Database Record (c) 2014 APA, all rights reserved).

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

Vertical changes in the probability distribution of downward irradiance within the near-surface ocean under sunny conditions

NASA Astrophysics Data System (ADS)

Gernez, Pierre; Stramski, Dariusz; Darecki, Miroslaw

2011-07-01

Time series measurements of fluctuations in underwater downward irradiance, Ed, within the green spectral band (532 nm) show that the probability distribution of instantaneous irradiance varies greatly as a function of depth within the near-surface ocean under sunny conditions. Because of intense light flashes caused by surface wave focusing, the near-surface probability distributions are highly skewed to the right and are heavy tailed. The coefficients of skewness and excess kurtosis at depths smaller than 1 m can exceed 3 and 20, respectively. We tested several probability models, such as lognormal, Gumbel, Fréchet, log-logistic, and Pareto, which are potentially suited to describe the highly skewed heavy-tailed distributions. We found that the models cannot approximate with consistently good accuracy the high irradiance values within the right tail of the experimental distribution where the probability of these values is less than 10%. This portion of the distribution corresponds approximately to light flashes with Ed > 1.5?, where ? is the time-averaged downward irradiance. However, the remaining part of the probability distribution covering all irradiance values smaller than the 90th percentile can be described with a reasonable accuracy (i.e., within 20%) with a lognormal model for all 86 measurements from the top 10 m of the ocean included in this analysis. As the intensity of irradiance fluctuations decreases with depth, the probability distribution tends toward a function symmetrical around the mean like the normal distribution. For the examined data set, the skewness and excess kurtosis assumed values very close to zero at a depth of about 10 m.

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.

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.

Method of estimating flood-frequency parameters for streams in Idaho

USGS Publications Warehouse

Kjelstrom, L.C.; Moffatt, R.L.

1981-01-01

Skew coefficients for the log-Pearson type III distribution are generalized on the basis of some similarity of floods in the Snake River basin and other parts of Idaho. Generalized skew coefficients aid in shaping flood-frequency curves because skew coefficients computed from gaging stations having relatively short periods of peak flow records can be unreliable. Generalized skew coefficients can be obtained for a gaging station from one of three maps in this report. The map to be used depends on whether (1) snowmelt floods are domiant (generally when more than 20 percent of the drainage area is above 6,000 feet altitude), (2) rainstorm floods are dominant (generally when the mean altitude is less than 3,000 feet), or (3) either snowmelt or rainstorm floods can be the annual miximum discharge. For the latter case, frequency curves constructed using separate arrays of each type of runoff can be combined into one curve, which, for some stations, is significantly different than the frequency curve constructed using only annual maximum discharges. For 269 gaging stations, flood-frequency curves that include the generalized skew coefficients in the computation of the log-Pearson type III equation tend to fit the data better than previous analyses. Frequency curves for ungaged sites can be derived by estimating three statistics of the log-Pearson type III distribution. The mean and standard deviation of logarithms of annual maximum discharges are estimated by regression equations that use basin characteristics as independent variables. Skew coefficient estimates are the generalized skews. The log-Pearson type III equation is then applied with the three estimated statistics to compute the discharge at selected exceedance probabilities. Standard errors at the 2-percent exceedance probability range from 41 to 90 percent. (USGS)

PULSAR SIGNAL DENOISING METHOD BASED ON LAPLACE DISTRIBUTION IN NO-SUBSAMPLING WAVELET PACKET DOMAIN

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

Wenbo, Wang; Yanchao, Zhao; Xiangli, Wang

2016-11-01

In order to improve the denoising effect of the pulsar signal, a new denoising method is proposed in the no-subsampling wavelet packet domain based on the local Laplace prior model. First, we count the true noise-free pulsar signal’s wavelet packet coefficient distribution characteristics and construct the true signal wavelet packet coefficients’ Laplace probability density function model. Then, we estimate the denosied wavelet packet coefficients by using the noisy pulsar wavelet coefficients based on maximum a posteriori criteria. Finally, we obtain the denoisied pulsar signal through no-subsampling wavelet packet reconstruction of the estimated coefficients. The experimental results show that the proposed method performs better when calculating the pulsar time of arrival than the translation-invariant wavelet denoising method.

Volatility smile as relativistic effect

NASA Astrophysics Data System (ADS)

Kakushadze, Zura

2017-06-01

We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution (1) is properly normalized and (2) obeys the tower law (semigroup property), so we can construct martingales and self-financing hedging strategies and price claims (options). This model is a 1-constant-parameter extension of the Black-Scholes-Merton model. The new parameter is the analog of the speed of light in Special Relativity. However, in the financial context there is no ;speed limit; and the new parameter has the meaning of a characteristic diffusion speed at which relativistic effects become important and lead to a much softer asymptotic behavior, i.e., fat tails, giving rise to volatility smiles. We argue that a nonlocal stochastic description of such (Lévy) processes is inadequate and discuss a local description from physics. The presentation is intended to be pedagogical.

An updated climatology of explosive cyclones using alternative measures of cyclone intensity

NASA Astrophysics Data System (ADS)

Hanley, J.; Caballero, R.

2009-04-01

Using a novel cyclone tracking and identification method, we compute a climatology of explosively intensifying cyclones or ‘bombs' using the ERA-40 and ERA-Interim datasets. Traditionally, ‘bombs' have been identified using a central pressure deepening rate criterion (Sanders and Gyakum, 1980). We investigate alternative methods of capturing such extreme cyclones. These methods include using the maximum wind contained within the cyclone, and using a potential vorticity column measure within such systems, as a measure of intensity. Using the different measures of cyclone intensity, we construct and intercompare maps of peak cyclone intensity. We also compute peak intensity probability distributions, and assess the evidence for the bi-modal distribution found by Roebber (1984). Finally, we address the question of the relationship between storm intensification rate and storm destructiveness: are ‘bombs' the most destructive storms?

The Effects of Construction Probability on Word Durations during Spontaneous Incremental Sentence Production

ERIC Educational Resources Information Center

Kuperman, Victor; Bresnan, Joan

2012-01-01

In a series of seven studies, this paper examines acoustic characteristics of the spontaneous speech production of the English dative alternation ("gave the book to the boy/ the boy the book") as a function of the probability of the choice between alternating constructions. Probabilistic effects on the acoustic duration were observed in the…

Three paths toward the quantum angle operator

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

Gazeau, Jean Pierre, E-mail: gazeau@apc.univ-paris7.fr; Szafraniec, Franciszek Hugon, E-mail: franciszek.szafraniec@uj.edu.pl

2016-12-15

We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin–Klauder approaches. One method pertains to Weyl–Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of “weight”more » functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line.« less

Symmetric weak ternary quantum homomorphic encryption schemes

NASA Astrophysics Data System (ADS)

Wang, Yuqi; She, Kun; Luo, Qingbin; Yang, Fan; Zhao, Chao

2016-03-01

Based on a ternary quantum logic circuit, four symmetric weak ternary quantum homomorphic encryption (QHE) schemes were proposed. First, for a one-qutrit rotation gate, a QHE scheme was constructed. Second, in view of the synthesis of a general 3 × 3 unitary transformation, another one-qutrit QHE scheme was proposed. Third, according to the one-qutrit scheme, the two-qutrit QHE scheme about generalized controlled X (GCX(m,n)) gate was constructed and further generalized to the n-qutrit unitary matrix case. Finally, the security of these schemes was analyzed in two respects. It can be concluded that the attacker can correctly guess the encryption key with a maximum probability pk = 1/33n, thus it can better protect the privacy of users’ data. Moreover, these schemes can be well integrated into the future quantum remote server architecture, and thus the computational security of the users’ private quantum information can be well protected in a distributed computing environment.

Cross over of recurrence networks to random graphs and random geometric graphs

NASA Astrophysics Data System (ADS)

Jacob, Rinku; Harikrishnan, K. P.; Misra, R.; Ambika, G.

2017-02-01

Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability density variations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measures and show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to the time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics.

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.

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.

[Sequential sampling plans to Orthezia praelonga Douglas (Hemiptera: Sternorrhyncha, Ortheziidae) in citrus].

PubMed

Costa, Marilia G; Barbosa, José C; Yamamoto, Pedro T

2007-01-01

The sequential sampling is characterized by using samples of variable sizes, and has the advantage of reducing sampling time and costs if compared to fixed-size sampling. To introduce an adequate management for orthezia, sequential sampling plans were developed for orchards under low and high infestation. Data were collected in Matão, SP, in commercial stands of the orange variety 'Pêra Rio', at five, nine and 15 years of age. Twenty samplings were performed in the whole area of each stand by observing the presence or absence of scales on plants, being plots comprised of ten plants. After observing that in all of the three stands the scale population was distributed according to the contagious model, fitting the Negative Binomial Distribution in most samplings, two sequential sampling plans were constructed according to the Sequential Likelihood Ratio Test (SLRT). To construct these plans an economic threshold of 2% was adopted and the type I and II error probabilities were fixed in alpha = beta = 0.10. Results showed that the maximum numbers of samples expected to determine control need were 172 and 76 samples for stands with low and high infestation, respectively.

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.

The exact probability distribution of the rank product statistics for replicated experiments.

PubMed

Eisinga, Rob; Breitling, Rainer; Heskes, Tom

2013-03-18

The rank product method is a widely accepted technique for detecting differentially regulated genes in replicated microarray experiments. To approximate the sampling distribution of the rank product statistic, the original publication proposed a permutation approach, whereas recently an alternative approximation based on the continuous gamma distribution was suggested. However, both approximations are imperfect for estimating small tail probabilities. In this paper we relate the rank product statistic to number theory and provide a derivation of its exact probability distribution and the true tail probabilities. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Sampling Assumptions Affect Use of Indirect Negative Evidence in Language Learning.

PubMed

Hsu, Anne; Griffiths, Thomas L

2016-01-01

A classic debate in cognitive science revolves around understanding how children learn complex linguistic patterns, such as restrictions on verb alternations and contractions, without negative evidence. Recently, probabilistic models of language learning have been applied to this problem, framing it as a statistical inference from a random sample of sentences. These probabilistic models predict that learners should be sensitive to the way in which sentences are sampled. There are two main types of sampling assumptions that can operate in language learning: strong and weak sampling. Strong sampling, as assumed by probabilistic models, assumes the learning input is drawn from a distribution of grammatical samples from the underlying language and aims to learn this distribution. Thus, under strong sampling, the absence of a sentence construction from the input provides evidence that it has low or zero probability of grammaticality. Weak sampling does not make assumptions about the distribution from which the input is drawn, and thus the absence of a construction from the input as not used as evidence of its ungrammaticality. We demonstrate in a series of artificial language learning experiments that adults can produce behavior consistent with both sets of sampling assumptions, depending on how the learning problem is presented. These results suggest that people use information about the way in which linguistic input is sampled to guide their learning.

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

PubMed Central

Tribello, Gareth A.; Ceriotti, Michele; Parrinello, Michele

2012-01-01

When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about the process of interest, serve this purpose. Because finding these CVs is the most difficult part of any investigation, we recently developed a dimensionality reduction algorithm, sketch-map, that can be used to build a low-dimensional map of a phase space of high-dimensionality. In this paper we discuss how these machine-generated CVs can be used to accelerate the exploration of phase space and to reconstruct free-energy landscapes. To do so, we develop a formalism in which high-dimensional configurations are no longer represented by low-dimensional position vectors. Instead, for each configuration we calculate a probability distribution, which has a domain that encompasses the entirety of the low-dimensional space. To construct a biasing potential, we exploit an analogy with metadynamics and use the trajectory to adaptively construct a repulsive, history-dependent bias from the distributions that correspond to the previously visited configurations. This potential forces the system to explore more of phase space by making it desirable to adopt configurations whose distributions do not overlap with the bias. We apply this algorithm to a small model protein and succeed in reproducing the free-energy surface that we obtain from a parallel tempering calculation. PMID:22427357

Sampling Assumptions Affect Use of Indirect Negative Evidence in Language Learning

PubMed Central

2016-01-01

A classic debate in cognitive science revolves around understanding how children learn complex linguistic patterns, such as restrictions on verb alternations and contractions, without negative evidence. Recently, probabilistic models of language learning have been applied to this problem, framing it as a statistical inference from a random sample of sentences. These probabilistic models predict that learners should be sensitive to the way in which sentences are sampled. There are two main types of sampling assumptions that can operate in language learning: strong and weak sampling. Strong sampling, as assumed by probabilistic models, assumes the learning input is drawn from a distribution of grammatical samples from the underlying language and aims to learn this distribution. Thus, under strong sampling, the absence of a sentence construction from the input provides evidence that it has low or zero probability of grammaticality. Weak sampling does not make assumptions about the distribution from which the input is drawn, and thus the absence of a construction from the input as not used as evidence of its ungrammaticality. We demonstrate in a series of artificial language learning experiments that adults can produce behavior consistent with both sets of sampling assumptions, depending on how the learning problem is presented. These results suggest that people use information about the way in which linguistic input is sampled to guide their learning. PMID:27310576

Statistical mechanics of economics I

NASA Astrophysics Data System (ADS)

Kusmartsev, F. V.

2011-02-01

We show that statistical mechanics is useful in the description of financial crisis and economics. Taking a large amount of instant snapshots of a market over an interval of time we construct their ensembles and study their statistical interference. This results in a probability description of the market and gives capital, money, income, wealth and debt distributions, which in the most cases takes the form of the Bose-Einstein distribution. In addition, statistical mechanics provides the main market equations and laws which govern the correlations between the amount of money, debt, product, prices and number of retailers. We applied the found relations to a study of the evolution of the economics in USA between the years 1996 to 2008 and observe that over that time the income of a major population is well described by the Bose-Einstein distribution which parameters are different for each year. Each financial crisis corresponds to a peak in the absolute activity coefficient. The analysis correctly indicates the past crises and predicts the future one.

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.

Factorization of Observables

NASA Astrophysics Data System (ADS)

Eliaš, Peter; Frič, Roman

2017-12-01

Categorical approach to probability leads to better understanding of basic notions and constructions in generalized (fuzzy, operational, quantum) probability, where observables—dual notions to generalized random variables (statistical maps)—play a major role. First, to avoid inconsistencies, we introduce three categories L, S, and P, the objects and morphisms of which correspond to basic notions of fuzzy probability theory and operational probability theory, and describe their relationships. To illustrate the advantages of categorical approach, we show that two categorical constructions involving observables (related to the representation of generalized random variables via products, or smearing of sharp observables, respectively) can be described as factorizing a morphism into composition of two morphisms having desired properties. We close with a remark concerning products.

Bayesian network representing system dynamics in risk analysis of nuclear systems

NASA Astrophysics Data System (ADS)

Varuttamaseni, Athi

2011-12-01

A dynamic Bayesian network (DBN) model is used in conjunction with the alternating conditional expectation (ACE) regression method to analyze the risk associated with the loss of feedwater accident coupled with a subsequent initiation of the feed and bleed operation in the Zion-1 nuclear power plant. The use of the DBN allows the joint probability distribution to be factorized, enabling the analysis to be done on many simpler network structures rather than on one complicated structure. The construction of the DBN model assumes conditional independence relations among certain key reactor parameters. The choice of parameter to model is based on considerations of the macroscopic balance statements governing the behavior of the reactor under a quasi-static assumption. The DBN is used to relate the peak clad temperature to a set of independent variables that are known to be important in determining the success of the feed and bleed operation. A simple linear relationship is then used to relate the clad temperature to the core damage probability. To obtain a quantitative relationship among different nodes in the DBN, surrogates of the RELAP5 reactor transient analysis code are used. These surrogates are generated by applying the ACE algorithm to output data obtained from about 50 RELAP5 cases covering a wide range of the selected independent variables. These surrogates allow important safety parameters such as the fuel clad temperature to be expressed as a function of key reactor parameters such as the coolant temperature and pressure together with important independent variables such as the scram delay time. The time-dependent core damage probability is calculated by sampling the independent variables from their probability distributions and propagate the information up through the Bayesian network to give the clad temperature. With the knowledge of the clad temperature and the assumption that the core damage probability has a one-to-one relationship to it, we have calculated the core damage probably as a function of transient time. The use of the DBN model in combination with ACE allows risk analysis to be performed with much less effort than if the analysis were done using the standard techniques.

State-space modeling to support management of brucellosis in the Yellowstone bison population

USGS Publications Warehouse

Hobbs, N. Thompson; Geremia, Chris; Treanor, John; Wallen, Rick; White, P.J.; Hooten, Mevin B.; Rhyan, Jack C.

2015-01-01

The bison (Bison bison) of the Yellowstone ecosystem, USA, exemplify the difficulty of conserving large mammals that migrate across the boundaries of conservation areas. Bison are infected with brucellosis (Brucella abortus) and their seasonal movements can expose livestock to infection. Yellowstone National Park has embarked on a program of adaptive management of bison, which requires a model that assimilates data to support management decisions. We constructed a Bayesian state-space model to reveal the influence of brucellosis on the Yellowstone bison population. A frequency-dependent model of brucellosis transmission was superior to a density-dependent model in predicting out-of-sample observations of horizontal transmission probability. A mixture model including both transmission mechanisms converged on frequency dependence. Conditional on the frequency-dependent model, brucellosis median transmission rate was 1.87 yr−1. The median of the posterior distribution of the basic reproductive ratio (R0) was 1.75. Seroprevalence of adult females varied around 60% over two decades, but only 9.6 of 100 adult females were infectious. Brucellosis depressed recruitment; estimated population growth rate λ averaged 1.07 for an infected population and 1.11 for a healthy population. We used five-year forecasting to evaluate the ability of different actions to meet management goals relative to no action. Annually removing 200 seropositive female bison increased by 30-fold the probability of reducing seroprevalence below 40% and increased by a factor of 120 the probability of achieving a 50% reduction in transmission probability relative to no action. Annually vaccinating 200 seronegative animals increased the likelihood of a 50% reduction in transmission probability by fivefold over no action. However, including uncertainty in the ability to implement management by representing stochastic variation in the number of accessible bison dramatically reduced the probability of achieving goals using interventions relative to no action. Because the width of the posterior predictive distributions of future population states expands rapidly with increases in the forecast horizon, managers must accept high levels of uncertainty. These findings emphasize the necessity of iterative, adaptive management with relatively short-term commitment to action and frequent reevaluation in response to new data and model forecasts. We believe our approach has broad applications.

Efficient Bayesian parameter estimation with implicit sampling and surrogate modeling for a vadose zone hydrological problem

NASA Astrophysics Data System (ADS)

Liu, Y.; Pau, G. S. H.; Finsterle, S.

2015-12-01

Parameter inversion involves inferring the model parameter values based on sparse observations of some observables. To infer the posterior probability distributions of the parameters, Markov chain Monte Carlo (MCMC) methods are typically used. However, the large number of forward simulations needed and limited computational resources limit the complexity of the hydrological model we can use in these methods. In view of this, we studied the implicit sampling (IS) method, an efficient importance sampling technique that generates samples in the high-probability region of the posterior distribution and thus reduces the number of forward simulations that we need to run. For a pilot-point inversion of a heterogeneous permeability field based on a synthetic ponded infiltration experiment simu­lated with TOUGH2 (a subsurface modeling code), we showed that IS with linear map provides an accurate Bayesian description of the parameterized permeability field at the pilot points with just approximately 500 forward simulations. We further studied the use of surrogate models to improve the computational efficiency of parameter inversion. We implemented two reduced-order models (ROMs) for the TOUGH2 forward model. One is based on polynomial chaos expansion (PCE), of which the coefficients are obtained using the sparse Bayesian learning technique to mitigate the "curse of dimensionality" of the PCE terms. The other model is Gaussian process regression (GPR) for which different covariance, likelihood and inference models are considered. Preliminary results indicate that ROMs constructed based on the prior parameter space perform poorly. It is thus impractical to replace this hydrological model by a ROM directly in a MCMC method. However, the IS method can work with a ROM constructed for parameters in the close vicinity of the maximum a posteriori probability (MAP) estimate. We will discuss the accuracy and computational efficiency of using ROMs in the implicit sampling procedure for the hydrological problem considered. This work was supported, in part, by the U.S. Dept. of Energy under Contract No. DE-AC02-05CH11231

How might Model-based Probabilities Extracted from Imperfect Models Guide Rational Decisions: The Case for non-probabilistic odds

NASA Astrophysics Data System (ADS)

Smith, Leonard A.

2010-05-01

This contribution concerns "deep" or "second-order" uncertainty, such as the uncertainty in our probability forecasts themselves. It asks the question: "Is it rational to take (or offer) bets using model-based probabilities as if they were objective probabilities?" If not, what alternative approaches for determining odds, perhaps non-probabilistic odds, might prove useful in practice, given the fact we know our models are imperfect? We consider the case where the aim is to provide sustainable odds: not to produce a profit but merely to rationally expect to break even in the long run. In other words, to run a quantified risk of ruin that is relatively small. Thus the cooperative insurance schemes of coastal villages provide a more appropriate parallel than a casino. A "better" probability forecast would lead to lower premiums charged and less volatile fluctuations in the cash reserves of the village. Note that the Bayesian paradigm does not constrain one to interpret model distributions as subjective probabilities, unless one believes the model to be empirically adequate for the task at hand. In geophysics, this is rarely the case. When a probability forecast is interpreted as the objective probability of an event, the odds on that event can be easily computed as one divided by the probability of the event, and one need not favour taking either side of the wager. (Here we are using "odds-for" not "odds-to", the difference being whether of not the stake is returned; odds of one to one are equivalent to odds of two for one.) The critical question is how to compute sustainable odds based on information from imperfect models. We suggest that this breaks the symmetry between the odds-on an event and the odds-against it. While a probability distribution can always be translated into odds, interpreting the odds on a set of events might result in "implied-probabilities" that sum to more than one. And/or the set of odds may be incomplete, not covering all events. We ask whether or not probabilities based on imperfect models can be expected to yield probabilistic odds which are sustainable. Evidence is provided that suggest this is not the case. Even with very good models (good in an Root-Mean-Square sense), the risk of ruin of probabilistic odds is significantly higher than might be expected. Methods for constructing model-based non-probabilistic odds which are sustainable are discussed. The aim here is to be relevant to real world decision support, and so unrealistic assumptions of equal knowledge, equal compute power, or equal access to information are to be avoided. Finally, the use of non-probabilistic odds as a method for communicating deep uncertainty (uncertainty in a probability forecast itself) is discussed in the context of other methods, such as stating one's subjective probability that the models will prove inadequate in each particular instance (that is, the Probability of a "Big Surprise").

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 use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

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

Rupšys, P.

A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.

Bayesian approach for peak detection in two-dimensional chromatography.

PubMed

Vivó-Truyols, Gabriel

2012-03-20

A new method for peak detection in two-dimensional chromatography is presented. In a first step, the method starts with a conventional one-dimensional peak detection algorithm to detect modulated peaks. In a second step, a sophisticated algorithm is constructed to decide which of the individual one-dimensional peaks have been originated from the same compound and should then be arranged in a two-dimensional peak. The merging algorithm is based on Bayesian inference. The user sets prior information about certain parameters (e.g., second-dimension retention time variability, first-dimension band broadening, chromatographic noise). On the basis of these priors, the algorithm calculates the probability of myriads of peak arrangements (i.e., ways of merging one-dimensional peaks), finding which of them holds the highest value. Uncertainty in each parameter can be accounted by adapting conveniently its probability distribution function, which in turn may change the final decision of the most probable peak arrangement. It has been demonstrated that the Bayesian approach presented in this paper follows the chromatographers' intuition. The algorithm has been applied and tested with LC × LC and GC × GC data and takes around 1 min to process chromatograms with several thousands of peaks.

A constrained multinomial Probit route choice model in the metro network: Formulation, estimation and application

PubMed Central

Zhang, Yongsheng; Wei, Heng; Zheng, Kangning

2017-01-01

Considering that metro network expansion brings us with more alternative routes, it is attractive to integrate the impacts of routes set and the interdependency among alternative routes on route choice probability into route choice modeling. Therefore, the formulation, estimation and application of a constrained multinomial probit (CMNP) route choice model in the metro network are carried out in this paper. The utility function is formulated as three components: the compensatory component is a function of influencing factors; the non-compensatory component measures the impacts of routes set on utility; following a multivariate normal distribution, the covariance of error component is structured into three parts, representing the correlation among routes, the transfer variance of route, and the unobserved variance respectively. Considering multidimensional integrals of the multivariate normal probability density function, the CMNP model is rewritten as Hierarchical Bayes formula and M-H sampling algorithm based Monte Carlo Markov Chain approach is constructed to estimate all parameters. Based on Guangzhou Metro data, reliable estimation results are gained. Furthermore, the proposed CMNP model also shows a good forecasting performance for the route choice probabilities calculation and a good application performance for transfer flow volume prediction. PMID:28591188

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.

Signatures of a conical intersection in photofragment distributions and absorption spectra: Photodissociation in the Hartley band of ozone

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

Picconi, David; Grebenshchikov, Sergy Yu., E-mail: Sergy.Grebenshchikov@ch.tum.de

Photodissociation of ozone in the near UV is studied quantum mechanically in two excited electronic states coupled at a conical intersection located outside the Franck-Condon zone. The calculations, performed using recent ab initio PESs, provide an accurate description of the photodissociation dynamics across the Hartley/Huggins absorption bands. The observed photofragment distributions are reproduced in the two electronic dissociation channels. The room temperature absorption spectrum, constructed as a Boltzmann average of many absorption spectra of rotationally excited parent ozone, agrees with experiment in terms of widths and intensities of diffuse structures. The exit channel conical intersection contributes to the coherent broadeningmore » of the absorption spectrum and directly affects the product vibrational and translational distributions. The photon energy dependences of these distributions are strikingly different for fragments created along the adiabatic and the diabatic paths through the intersection. They can be used to reverse engineer the most probable geometry of the non-adiabatic transition. The angular distributions, quantified in terms of the anisotropy parameter β, are substantially different in the two channels due to a strong anticorrelation between β and the rotational angular momentum of the fragment O{sub 2}.« less

Improved estimation of hydraulic conductivity by combining stochastically simulated hydrofacies with geophysical data

PubMed Central

Zhu, Lin; Gong, Huili; Chen, Yun; Li, Xiaojuan; Chang, Xiang; Cui, Yijiao

2016-01-01

Hydraulic conductivity is a major parameter affecting the output accuracy of groundwater flow and transport models. The most commonly used semi-empirical formula for estimating conductivity is Kozeny-Carman equation. However, this method alone does not work well with heterogeneous strata. Two important parameters, grain size and porosity, often show spatial variations at different scales. This study proposes a method for estimating conductivity distributions by combining a stochastic hydrofacies model with geophysical methods. The Markov chain model with transition probability matrix was adopted to re-construct structures of hydrofacies for deriving spatial deposit information. The geophysical and hydro-chemical data were used to estimate the porosity distribution through the Archie’s law. Results show that the stochastic simulated hydrofacies model reflects the sedimentary features with an average model accuracy of 78% in comparison with borehole log data in the Chaobai alluvial fan. The estimated conductivity is reasonable and of the same order of magnitude of the outcomes of the pumping tests. The conductivity distribution is consistent with the sedimentary distributions. This study provides more reliable spatial distributions of the hydraulic parameters for further numerical modeling. PMID:26927886

Comparison of Deterministic and Probabilistic Radial Distribution Systems Load Flow

NASA Astrophysics Data System (ADS)

Gupta, Atma Ram; Kumar, Ashwani

2017-12-01

Distribution system network today is facing the challenge of meeting increased load demands from the industrial, commercial and residential sectors. The pattern of load is highly dependent on consumer behavior and temporal factors such as season of the year, day of the week or time of the day. For deterministic radial distribution load flow studies load is taken as constant. But, load varies continually with a high degree of uncertainty. So, there is a need to model probable realistic load. Monte-Carlo Simulation is used to model the probable realistic load by generating random values of active and reactive power load from the mean and standard deviation of the load and for solving a Deterministic Radial Load Flow with these values. The probabilistic solution is reconstructed from deterministic data obtained for each simulation. The main contribution of the work is: Finding impact of probable realistic ZIP load modeling on balanced radial distribution load flow. Finding impact of probable realistic ZIP load modeling on unbalanced radial distribution load flow. Compare the voltage profile and losses with probable realistic ZIP load modeling for balanced and unbalanced radial distribution load flow.

Characterization of the Ionospheric Scintillations at High Latitude using GPS Signal

NASA Astrophysics Data System (ADS)

Mezaoui, H.; Hamza, A. M.; Jayachandran, P. T.

2013-12-01

Transionospheric radio signals experience both amplitude and phase variations as a result of propagation through a turbulent ionosphere; this phenomenon is known as ionospheric scintillations. As a result of these fluctuations, Global Positioning System (GPS) receivers lose track of signals and consequently induce position and navigational errors. Therefore, there is a need to study these scintillations and their causes in order to not only resolve the navigational problem but in addition develop analytical and numerical radio propagation models. In order to quantify and qualify these scintillations, we analyze the probability distribution functions (PDFs) of L1 GPS signals at 50 Hz sampling rate using the Canadian High arctic Ionospheric Network (CHAIN) measurements. The raw GPS signal is detrended using a wavelet-based technique and the detrended amplitude and phase of the signal are used to construct probability distribution functions (PDFs) of the scintillating signal. The resulting PDFs are non-Gaussian. From the PDF functional fits, the moments are estimated. The results reveal a general non-trivial parabolic relationship between the normalized fourth and third moments for both the phase and amplitude of the signal. The calculated higher-order moments of the amplitude and phase distribution functions will help quantify some of the scintillation characteristics and in the process provide a base for forecasting, i.e. develop a scintillation climatology model. This statistical analysis, including power spectra, along with a numerical simulation will constitute the backbone of a high latitude scintillation model.

Probability density functions characterizing PSC particle size distribution parameters for NAT and STS derived from in situ measurements between 1989 and 2010 above McMurdo Station, Antarctica, and between 1991-2004 above Kiruna, Sweden

NASA Astrophysics Data System (ADS)

Deshler, Terry

2016-04-01

Balloon-borne optical particle counters were used to make in situ size resolved particle concentration measurements within polar stratospheric clouds (PSCs) over 20 years in the Antarctic and over 10 years in the Arctic. The measurements were made primarily during the late winter in the Antarctic and in the early and mid-winter in the Arctic. Measurements in early and mid-winter were also made during 5 years in the Antarctic. For the analysis bimodal lognormal size distributions are fit to 250 meter averages of the particle concentration data. The characteristics of these fits, along with temperature, water and nitric acid vapor mixing ratios, are used to classify the PSC observations as either NAT, STS, ice, or some mixture of these. The vapor mixing ratios are obtained from satellite when possible, otherwise assumptions are made. This classification of the data is used to construct probability density functions for NAT, STS, and ice number concentration, median radius and distribution width for mid and late winter clouds in the Antarctic and for early and mid-winter clouds in the Arctic. Additional analysis is focused on characterizing the temperature histories associated with the particle classes and the different time periods. The results from theses analyses will be presented, and should be useful to set bounds for retrievals of PSC properties from remote measurements, and to constrain model representations of PSCs.

Statistical deprojection of galaxy pairs

NASA Astrophysics Data System (ADS)

Nottale, Laurent; Chamaraux, Pierre

2018-06-01

Aims: The purpose of the present paper is to provide methods of statistical analysis of the physical properties of galaxy pairs. We perform this study to apply it later to catalogs of isolated pairs of galaxies, especially two new catalogs we recently constructed that contain ≈1000 and ≈13 000 pairs, respectively. We are particularly interested by the dynamics of those pairs, including the determination of their masses. Methods: We could not compute the dynamical parameters directly since the necessary data are incomplete. Indeed, we only have at our disposal one component of the intervelocity between the members, namely along the line of sight, and two components of their interdistance, i.e., the projection on the sky-plane. Moreover, we know only one point of each galaxy orbit. Hence we need statistical methods to find the probability distribution of 3D interdistances and 3D intervelocities from their projections; we designed those methods under the term deprojection. Results: We proceed in two steps to determine and use the deprojection methods. First we derive the probability distributions expected for the various relevant projected quantities, namely intervelocity vz, interdistance rp, their ratio, and the product rp v_z^2, which is involved in mass determination. In a second step, we propose various methods of deprojection of those parameters based on the previous analysis. We start from a histogram of the projected data and we apply inversion formulae to obtain the deprojected distributions; lastly, we test the methods by numerical simulations, which also allow us to determine the uncertainties involved.

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.

Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Ocean: Observations and Approximations

NASA Astrophysics Data System (ADS)

Lozovatsky, I.; Fernando, H. J. S.; Planella-Morato, J.; Liu, Zhiyu; Lee, J.-H.; Jinadasa, S. U. P.

2017-10-01

The probability distribution of turbulent kinetic energy dissipation rate in stratified ocean usually deviates from the classic lognormal distribution that has been formulated for and often observed in unstratified homogeneous layers of atmospheric and oceanic turbulence. Our measurements of vertical profiles of micro-scale shear, collected in the East China Sea, northern Bay of Bengal, to the south and east of Sri Lanka, and in the Gulf Stream region, show that the probability distributions of the dissipation rate ɛ˜r in the pycnoclines (r ˜ 1.4 m is the averaging scale) can be successfully modeled by the Burr (type XII) probability distribution. In weakly stratified boundary layers, lognormal distribution of ɛ˜r is preferable, although the Burr is an acceptable alternative. The skewness Skɛ and the kurtosis Kɛ of the dissipation rate appear to be well correlated in a wide range of Skɛ and Kɛ variability.

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.

Dynamic Uncertain Causality Graph for Knowledge Representation and Probabilistic Reasoning: Directed Cyclic Graph and Joint Probability Distribution.

PubMed

Zhang, Qin

2015-07-01

Probabilistic graphical models (PGMs) such as Bayesian network (BN) have been widely applied in uncertain causality representation and probabilistic reasoning. Dynamic uncertain causality graph (DUCG) is a newly presented model of PGMs, which can be applied to fault diagnosis of large and complex industrial systems, disease diagnosis, and so on. The basic methodology of DUCG has been previously presented, in which only the directed acyclic graph (DAG) was addressed. However, the mathematical meaning of DUCG was not discussed. In this paper, the DUCG with directed cyclic graphs (DCGs) is addressed. In contrast, BN does not allow DCGs, as otherwise the conditional independence will not be satisfied. The inference algorithm for the DUCG with DCGs is presented, which not only extends the capabilities of DUCG from DAGs to DCGs but also enables users to decompose a large and complex DUCG into a set of small, simple sub-DUCGs, so that a large and complex knowledge base can be easily constructed, understood, and maintained. The basic mathematical definition of a complete DUCG with or without DCGs is proved to be a joint probability distribution (JPD) over a set of random variables. The incomplete DUCG as a part of a complete DUCG may represent a part of JPD. Examples are provided to illustrate the methodology.

Comparison of Bootstrapping and Markov Chain Monte Carlo for Copula Analysis of Hydrological Droughts

NASA Astrophysics Data System (ADS)

Yang, P.; Ng, T. L.; Yang, W.

2015-12-01

Effective water resources management depends on the reliable estimation of the uncertainty of drought events. Confidence intervals (CIs) are commonly applied to quantify this uncertainty. A CI seeks to be at the minimal length necessary to cover the true value of the estimated variable with the desired probability. In drought analysis where two or more variables (e.g., duration and severity) are often used to describe a drought, copulas have been found suitable for representing the joint probability behavior of these variables. However, the comprehensive assessment of the parameter uncertainties of copulas of droughts has been largely ignored, and the few studies that have recognized this issue have not explicitly compared the various methods to produce the best CIs. Thus, the objective of this study to compare the CIs generated using two widely applied uncertainty estimation methods, bootstrapping and Markov Chain Monte Carlo (MCMC). To achieve this objective, (1) the marginal distributions lognormal, Gamma, and Generalized Extreme Value, and the copula functions Clayton, Frank, and Plackett are selected to construct joint probability functions of two drought related variables. (2) The resulting joint functions are then fitted to 200 sets of simulated realizations of drought events with known distribution and extreme parameters and (3) from there, using bootstrapping and MCMC, CIs of the parameters are generated and compared. The effect of an informative prior on the CIs generated by MCMC is also evaluated. CIs are produced for different sample sizes (50, 100, and 200) of the simulated drought events for fitting the joint probability functions. Preliminary results assuming lognormal marginal distributions and the Clayton copula function suggest that for cases with small or medium sample sizes (~50-100), MCMC to be superior method if an informative prior exists. Where an informative prior is unavailable, for small sample sizes (~50), both bootstrapping and MCMC yield the same level of performance, and for medium sample sizes (~100), bootstrapping is better. For cases with a large sample size (~200), there is little difference between the CIs generated using bootstrapping and MCMC regardless of whether or not an informative prior exists.

Bayesian analysis of multimodal data and brain imaging

NASA Astrophysics Data System (ADS)

Assadi, Amir H.; Eghbalnia, Hamid; Backonja, Miroslav; Wakai, Ronald T.; Rutecki, Paul; Haughton, Victor

2000-06-01

It is often the case that information about a process can be obtained using a variety of methods. Each method is employed because of specific advantages over the competing alternatives. An example in medical neuro-imaging is the choice between fMRI and MEG modes where fMRI can provide high spatial resolution in comparison to the superior temporal resolution of MEG. The combination of data from varying modes provides the opportunity to infer results that may not be possible by means of any one mode alone. We discuss a Bayesian and learning theoretic framework for enhanced feature extraction that is particularly suited to multi-modal investigations of massive data sets from multiple experiments. In the following Bayesian approach, acquired knowledge (information) regarding various aspects of the process are all directly incorporated into the formulation. This information can come from a variety of sources. In our case, it represents statistical information obtained from other modes of data collection. The information is used to train a learning machine to estimate a probability distribution, which is used in turn by a second machine as a prior, in order to produce a more refined estimation of the distribution of events. The computational demand of the algorithm is handled by proposing a distributed parallel implementation on a cluster of workstations that can be scaled to address real-time needs if required. We provide a simulation of these methods on a set of synthetically generated MEG and EEG data. We show how spatial and temporal resolutions improve by using prior distributions. The method on fMRI signals permits one to construct the probability distribution of the non-linear hemodynamics of the human brain (real data). These computational results are in agreement with biologically based measurements of other labs, as reported to us by researchers from UK. We also provide preliminary analysis involving multi-electrode cortical recording that accompanies behavioral data in pain experiments on freely moving mice subjected to moderate heat delivered by an electric bulb. Summary of new or breakthrough ideas: (1) A new method to estimate probability distribution for measurement of nonlinear hemodynamics of brain from a multi- modal neuronal data. This is the first time that such an idea is tried, to our knowledge. (2) Breakthrough in improvement of time resolution of fMRI signals using (1) above.

A New Bond Albedo for Performing Orbital Debris Brightness to Size Transformations

NASA Technical Reports Server (NTRS)

Mulrooney, Mark K.; Matney, Mark J.

2008-01-01

We have developed a technique for estimating the intrinsic size distribution of orbital debris objects via optical measurements alone. The process is predicated on the empirically observed power-law size distribution of debris (as indicated by radar RCS measurements) and the log-normal probability distribution of optical albedos as ascertained from phase (Lambertian) and range-corrected telescopic brightness measurements. Since the observed distribution of optical brightness is the product integral of the size distribution of the parent [debris] population with the albedo probability distribution, it is a straightforward matter to transform a given distribution of optical brightness back to a size distribution by the appropriate choice of a single albedo value. This is true because the integration of a powerlaw with a log-normal distribution (Fredholm Integral of the First Kind) yields a Gaussian-blurred power-law distribution with identical power-law exponent. Application of a single albedo to this distribution recovers a simple power-law [in size] which is linearly offset from the original distribution by a constant whose value depends on the choice of the albedo. Significantly, there exists a unique Bond albedo which, when applied to an observed brightness distribution, yields zero offset and therefore recovers the original size distribution. For physically realistic powerlaws of negative slope, the proper choice of albedo recovers the parent size distribution by compensating for the observational bias caused by the large number of small objects that appear anomalously large (bright) - and thereby skew the small population upward by rising above the detection threshold - and the lower number of large objects that appear anomalously small (dim). Based on this comprehensive analysis, a value of 0.13 should be applied to all orbital debris albedo-based brightness-to-size transformations regardless of data source. Its prima fascia genesis, derived and constructed from the current RCS to size conversion methodology (SiBAM Size-Based Estimation Model) and optical data reduction standards, assures consistency in application with the prior canonical value of 0.1. Herein we present the empirical and mathematical arguments for this approach and by example apply it to a comprehensive set of photometric data acquired via NASA's Liquid Mirror Telescopes during the 2000-2001 observing season.

Evaluation of the Three Parameter Weibull Distribution Function for Predicting Fracture Probability in Composite Materials

DTIC Science & Technology

1978-03-01

for the risk of rupture for a unidirectionally laminat - ed composite subjected to pure bending. (5D This equation can be simplified further by use of...C EVALUATION OF THE THREE PARAMETER WEIBULL DISTRIBUTION FUNCTION FOR PREDICTING FRACTURE PROBABILITY IN COMPOSITE MATERIALS. THESIS / AFIT/GAE...EVALUATION OF THE THREE PARAMETER WE1BULL DISTRIBUTION FUNCTION FOR PREDICTING FRACTURE PROBABILITY IN COMPOSITE MATERIALS THESIS Presented

Modeling exotic highly pathogenic avian influenza virus entrance risk through air passenger violations.

PubMed

Lai, Jyh-Mirn; Hwang, Yi-Ting; Chou, Chin-Cheng

2012-06-01

The highly pathogenic avian influenza virus (HPAIV) is able to survive in poultry products and could be carried into a country by air travelers. An assessment model was constructed to estimate the probability of the exotic viable HPAIV entering Taiwan from two neighboring areas through poultry products carried illegally by air passengers at Taiwan's main airports. The entrance risk was evaluated based on HPAIV-related factors (the prevalence and the incubation period of HPAIV; the manufacturing process of poultry products; and the distribution-storage-transportation factor event) and the passenger event. Distribution functions were adopted to simulate the probabilities of each HPAIV factor. The odds of passengers being intercepted with illegal poultry products were estimated by logistic regression. The Monte Carlo simulation established that the risk caused by HPAIV-related factors from area A was lower than area B, whereas the entrance risk by the passenger event from area A was similar to area B. Sensitivity analysis showed that the incubation period of HPAIV and the interception of passenger violations were major determinants. Although the result showed viable HPAIV was unlikely to enter Taiwan through meat illegally carried by air passengers, this low probability could be caused by incomplete animal disease data and modeling uncertainties. Considering the negative socioeconomic impacts of HPAIV outbreaks, strengthening airport quarantine measures is still necessary. This assessment provides a profile of HPAIV entrance risk through air travelers arriving from endemic areas and a feasible direction for quarantine and public health measures. © 2011 Society for Risk Analysis.

Maximum caliber inference of nonequilibrium processes

NASA Astrophysics Data System (ADS)

Otten, Moritz; Stock, Gerhard

2010-07-01

Thirty years ago, Jaynes suggested a general theoretical approach to nonequilibrium statistical mechanics, called maximum caliber (MaxCal) [Annu. Rev. Phys. Chem. 31, 579 (1980)]. MaxCal is a variational principle for dynamics in the same spirit that maximum entropy is a variational principle for equilibrium statistical mechanics. Motivated by the success of maximum entropy inference methods for equilibrium problems, in this work the MaxCal formulation is applied to the inference of nonequilibrium processes. That is, given some time-dependent observables of a dynamical process, one constructs a model that reproduces these input data and moreover, predicts the underlying dynamics of the system. For example, the observables could be some time-resolved measurements of the folding of a protein, which are described by a few-state model of the free energy landscape of the system. MaxCal then calculates the probabilities of an ensemble of trajectories such that on average the data are reproduced. From this probability distribution, any dynamical quantity of the system can be calculated, including population probabilities, fluxes, or waiting time distributions. After briefly reviewing the formalism, the practical numerical implementation of MaxCal in the case of an inference problem is discussed. Adopting various few-state models of increasing complexity, it is demonstrated that the MaxCal principle indeed works as a practical method of inference: The scheme is fairly robust and yields correct results as long as the input data are sufficient. As the method is unbiased and general, it can deal with any kind of time dependency such as oscillatory transients and multitime decays.

Data-driven probability concentration and sampling on manifold

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

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

2016-09-15

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation methodmore » for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.« less

Bivariate extreme value distributions

NASA Technical Reports Server (NTRS)

Elshamy, M.

1992-01-01

In certain engineering applications, such as those occurring in the analyses of ascent structural loads for the Space Transportation System (STS), some of the load variables have a lower bound of zero. Thus, the need for practical models of bivariate extreme value probability distribution functions with lower limits was identified. We discuss the Gumbel models and present practical forms of bivariate extreme probability distributions of Weibull and Frechet types with two parameters. Bivariate extreme value probability distribution functions can be expressed in terms of the marginal extremel distributions and a 'dependence' function subject to certain analytical conditions. Properties of such bivariate extreme distributions, sums and differences of paired extremals, as well as the corresponding forms of conditional distributions, are discussed. Practical estimation techniques are also given.

H∞ control for uncertain linear system over networks with Bernoulli data dropout and actuator saturation.

PubMed

Yu, Jimin; Yang, Chenchen; Tang, Xiaoming; Wang, Ping

2018-03-01

This paper investigates the H ∞ control problems for uncertain linear system over networks with random communication data dropout and actuator saturation. The random data dropout process is modeled by a Bernoulli distributed white sequence with a known conditional probability distribution and the actuator saturation is confined in a convex hull by introducing a group of auxiliary matrices. By constructing a quadratic Lyapunov function, effective conditions for the state feedback-based H ∞ controller and the observer-based H ∞ controller are proposed in the form of non-convex matrix inequalities to take the random data dropout and actuator saturation into consideration simultaneously, and the problem of non-convex feasibility is solved by applying cone complementarity linearization (CCL) procedure. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed new design techniques. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Characteristics of white LED transmission through a smoke screen

NASA Astrophysics Data System (ADS)

Zheng, Yunfei; Yang, Aiying; Feng, Lihui; Guo, Peng

2018-01-01

The characteristics of white LED transmission through a smoke screen is critical for visible light communication through a smoke screen. Based on the Mie scattering theory, the Monte Carlo transmission model is established. Based on the probability density function, the white LED sampling model is established according to the measured spectrum of a white LED and the distribution angle of the lambert model. The sampling model of smoke screen particle diameter is also established according to its distribution. We simulate numerically the influence the smoke thickness, the smoke concentration and the angle of irradiance of white LED on transmittance of the white LED. We construct a white LED smoke transmission experiment system. The measured result on the light transmittance and the smoke concentration agreed with the simulated result, and demonstrated the validity of simulation model for visible light transmission channel through a smoke screen.

The H2 + + He proton transfer reaction: quantum reactive differential cross sections to be linked with future velocity mapping experiments

NASA Astrophysics Data System (ADS)

Hernández Vera, Mario; Wester, Roland; Gianturco, Francesco Antonio

2018-01-01

We construct the velocity map images of the proton transfer reaction between helium and molecular hydrogen ion {{{H}}}2+. We perform simulations of imaging experiments at one representative total collision energy taking into account the inherent aberrations of the velocity mapping in order to explore the feasibility of direct comparisons between theory and future experiments planned in our laboratory. The asymptotic angular distributions of the fragments in a 3D velocity space is determined from the quantum state-to-state differential reactive cross sections and reaction probabilities which are computed by using the time-independent coupled channel hyperspherical coordinate method. The calculations employ an earlier ab initio potential energy surface computed at the FCI/cc-pVQZ level of theory. The present simulations indicate that the planned experiments would be selective enough to differentiate between product distributions resulting from different initial internal states of the reactants.

Uncertainty quantification for accident management using ACE surrogates

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

Varuttamaseni, A.; Lee, J. C.; Youngblood, R. W.

The alternating conditional expectation (ACE) regression method is used to generate RELAP5 surrogates which are then used to determine the distribution of the peak clad temperature (PCT) during the loss of feedwater accident coupled with a subsequent initiation of the feed and bleed (F and B) operation in the Zion-1 nuclear power plant. The construction of the surrogates assumes conditional independence relations among key reactor parameters. The choice of parameters to model is based on the macroscopic balance statements governing the behavior of the reactor. The peak clad temperature is calculated based on the independent variables that are known tomore » be important in determining the success of the F and B operation. The relationship between these independent variables and the plant parameters such as coolant pressure and temperature is represented by surrogates that are constructed based on 45 RELAP5 cases. The time-dependent PCT for different values of F and B parameters is calculated by sampling the independent variables from their probability distributions and propagating the information through two layers of surrogates. The results of our analysis show that the ACE surrogates are able to satisfactorily reproduce the behavior of the plant parameters even though a quasi-static assumption is primarily used in their construction. The PCT is found to be lower in cases where the F and B operation is initiated, compared to the case without F and B, regardless of the F and B parameters used. (authors)« less

Mapping Wildfire Ignition Probability Using Sentinel 2 and LiDAR (Jerte Valley, Cáceres, Spain)

PubMed Central

Sánchez Sánchez, Yolanda; Mateos Picado, Marina

2018-01-01

Wildfire is a major threat to the environment, and this threat is aggravated by different climatic and socioeconomic factors. The availability of detailed, reliable mapping and periodic and immediate updates makes wildfire prevention and extinction work more effective. An analyst protocol has been generated that allows the precise updating of high-resolution thematic maps. For this protocol, images obtained through the Sentinel 2A satellite, with a return time of five days, have been merged with Light Detection and Ranging (LiDAR) data with a density of 0.5 points/m2 in order to obtain vegetation mapping with an accuracy of 88% (kappa = 0.86), which is then extrapolated to fuel model mapping through a decision tree. This process, which is fast and reliable, serves as a cartographic base for the later calculation of ignition-probability mapping. The generated cartography is a fundamental tool to be used in the decision making involved in the planning of preventive silvicultural treatments, extinguishing media distribution, infrastructure construction, etc. PMID:29522460

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.

Thermodynamics and signatures of criticality in a network of neurons.

PubMed

Tkačik, Gašper; Mora, Thierry; Marre, Olivier; Amodei, Dario; Palmer, Stephanie E; Berry, Michael J; Bialek, William

2015-09-15

The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance.

Mapping Wildfire Ignition Probability Using Sentinel 2 and LiDAR (Jerte Valley, Cáceres, Spain).

PubMed

Sánchez Sánchez, Yolanda; Martínez-Graña, Antonio; Santos Francés, Fernando; Mateos Picado, Marina

2018-03-09

Wildfire is a major threat to the environment, and this threat is aggravated by different climatic and socioeconomic factors. The availability of detailed, reliable mapping and periodic and immediate updates makes wildfire prevention and extinction work more effective. An analyst protocol has been generated that allows the precise updating of high-resolution thematic maps. For this protocol, images obtained through the Sentinel 2A satellite, with a return time of five days, have been merged with Light Detection and Ranging (LiDAR) data with a density of 0.5 points/m² in order to obtain vegetation mapping with an accuracy of 88% (kappa = 0.86), which is then extrapolated to fuel model mapping through a decision tree. This process, which is fast and reliable, serves as a cartographic base for the later calculation of ignition-probability mapping. The generated cartography is a fundamental tool to be used in the decision making involved in the planning of preventive silvicultural treatments, extinguishing media distribution, infrastructure construction, etc.

7 CFR 1726.51 - Distribution line construction.

Code of Federal Regulations, 2010 CFR

2010-01-01

... of net utility plant (NUP), whichever is greater, per calendar year of distribution line construction... 7 Agriculture 11 2010-01-01 2010-01-01 false Distribution line construction. 1726.51 Section 1726..., DEPARTMENT OF AGRICULTURE ELECTRIC SYSTEM CONSTRUCTION POLICIES AND PROCEDURES Distribution Facilities § 1726...

Eruption probabilities for the Lassen Volcanic Center and regional volcanism, northern California, and probabilities for large explosive eruptions in the Cascade Range

USGS Publications Warehouse

Nathenson, Manuel; Clynne, Michael A.; Muffler, L.J. Patrick

2012-01-01

Chronologies for eruptive activity of the Lassen Volcanic Center and for eruptions from the regional mafic vents in the surrounding area of the Lassen segment of the Cascade Range are here used to estimate probabilities of future eruptions. For the regional mafic volcanism, the ages of many vents are known only within broad ranges, and two models are developed that should bracket the actual eruptive ages. These chronologies are used with exponential, Weibull, and mixed-exponential probability distributions to match the data for time intervals between eruptions. For the Lassen Volcanic Center, the probability of an eruption in the next year is 1.4x10-4 for the exponential distribution and 2.3x10-4 for the mixed exponential distribution. For the regional mafic vents, the exponential distribution gives a probability of an eruption in the next year of 6.5x10-4, but the mixed exponential distribution indicates that the current probability, 12,000 years after the last event, could be significantly lower. For the exponential distribution, the highest probability is for an eruption from a regional mafic vent. Data on areas and volumes of lava flows and domes of the Lassen Volcanic Center and of eruptions from the regional mafic vents provide constraints on the probable sizes of future eruptions. Probabilities of lava-flow coverage are similar for the Lassen Volcanic Center and for regional mafic vents, whereas the probable eruptive volumes for the mafic vents are generally smaller. Data have been compiled for large explosive eruptions (>≈ 5 km3 in deposit volume) in the Cascade Range during the past 1.2 m.y. in order to estimate probabilities of eruption. For erupted volumes >≈5 km3, the rate of occurrence since 13.6 ka is much higher than for the entire period, and we use these data to calculate the annual probability of a large eruption at 4.6x10-4. For erupted volumes ≥10 km3, the rate of occurrence has been reasonably constant from 630 ka to the present, giving more confidence in the estimate, and we use those data to calculate the annual probability of a large eruption in the next year at 1.4x10-5.

Burst wait time simulation of CALIBAN reactor at delayed super-critical state

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

Humbert, P.; Authier, N.; Richard, B.

2012-07-01

In the past, the super prompt critical wait time probability distribution was measured on CALIBAN fast burst reactor [4]. Afterwards, these experiments were simulated with a very good agreement by solving the non-extinction probability equation [5]. Recently, the burst wait time probability distribution has been measured at CEA-Valduc on CALIBAN at different delayed super-critical states [6]. However, in the delayed super-critical case the non-extinction probability does not give access to the wait time distribution. In this case it is necessary to compute the time dependent evolution of the full neutron count number probability distribution. In this paper we present themore » point model deterministic method used to calculate the probability distribution of the wait time before a prescribed count level taking into account prompt neutrons and delayed neutron precursors. This method is based on the solution of the time dependent adjoint Kolmogorov master equations for the number of detections using the generating function methodology [8,9,10] and inverse discrete Fourier transforms. The obtained results are then compared to the measurements and Monte-Carlo calculations based on the algorithm presented in [7]. (authors)« less

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

NASA Astrophysics Data System (ADS)

Malakar, Kanaya; Jemseena, V.; Kundu, Anupam; Vijay Kumar, K.; Sabhapandit, Sanjib; Majumdar, Satya N.; Redner, S.; Dhar, Abhishek

2018-04-01

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady-state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady-state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain with an absorbing boundary condition at the origin. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verification of our analytical results.

Fitness Probability Distribution of Bit-Flip Mutation.

PubMed

Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

2015-01-01

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.

Multinomial Logistic Regression Predicted Probability Map To Visualize The Influence Of Socio-Economic Factors On Breast Cancer Occurrence in Southern Karnataka

NASA Astrophysics Data System (ADS)

Madhu, B.; Ashok, N. C.; Balasubramanian, S.

2014-11-01

Multinomial logistic regression analysis was used to develop statistical model that can predict the probability of breast cancer in Southern Karnataka using the breast cancer occurrence data during 2007-2011. Independent socio-economic variables describing the breast cancer occurrence like age, education, occupation, parity, type of family, health insurance coverage, residential locality and socioeconomic status of each case was obtained. The models were developed as follows: i) Spatial visualization of the Urban- rural distribution of breast cancer cases that were obtained from the Bharat Hospital and Institute of Oncology. ii) Socio-economic risk factors describing the breast cancer occurrences were complied for each case. These data were then analysed using multinomial logistic regression analysis in a SPSS statistical software and relations between the occurrence of breast cancer across the socio-economic status and the influence of other socio-economic variables were evaluated and multinomial logistic regression models were constructed. iii) the model that best predicted the occurrence of breast cancer were identified. This multivariate logistic regression model has been entered into a geographic information system and maps showing the predicted probability of breast cancer occurrence in Southern Karnataka was created. This study demonstrates that Multinomial logistic regression is a valuable tool for developing models that predict the probability of breast cancer Occurrence in Southern Karnataka.

The Impact of an Instructional Intervention Designed to Support Development of Stochastic Understanding of Probability Distribution

ERIC Educational Resources Information Center

Conant, Darcy Lynn

2013-01-01

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…

Multi-model ensembles for assessment of flood losses and associated uncertainty

NASA Astrophysics Data System (ADS)

Figueiredo, Rui; Schröter, Kai; Weiss-Motz, Alexander; Martina, Mario L. V.; Kreibich, Heidi

2018-05-01

Flood loss modelling is a crucial part of risk assessments. However, it is subject to large uncertainty that is often neglected. Most models available in the literature are deterministic, providing only single point estimates of flood loss, and large disparities tend to exist among them. Adopting any one such model in a risk assessment context is likely to lead to inaccurate loss estimates and sub-optimal decision-making. In this paper, we propose the use of multi-model ensembles to address these issues. This approach, which has been applied successfully in other scientific fields, is based on the combination of different model outputs with the aim of improving the skill and usefulness of predictions. We first propose a model rating framework to support ensemble construction, based on a probability tree of model properties, which establishes relative degrees of belief between candidate models. Using 20 flood loss models in two test cases, we then construct numerous multi-model ensembles, based both on the rating framework and on a stochastic method, differing in terms of participating members, ensemble size and model weights. We evaluate the performance of ensemble means, as well as their probabilistic skill and reliability. Our results demonstrate that well-designed multi-model ensembles represent a pragmatic approach to consistently obtain more accurate flood loss estimates and reliable probability distributions of model uncertainty.

Probability distributions of the electroencephalogram envelope of preterm infants.

PubMed

Saji, Ryoya; Hirasawa, Kyoko; Ito, Masako; Kusuda, Satoshi; Konishi, Yukuo; Taga, Gentaro

2015-06-01

To determine the stationary characteristics of electroencephalogram (EEG) envelopes for prematurely born (preterm) infants and investigate the intrinsic characteristics of early brain development in preterm infants. Twenty neurologically normal sets of EEGs recorded in infants with a post-conceptional age (PCA) range of 26-44 weeks (mean 37.5 ± 5.0 weeks) were analyzed. Hilbert transform was applied to extract the envelope. We determined the suitable probability distribution of the envelope and performed a statistical analysis. It was found that (i) the probability distributions for preterm EEG envelopes were best fitted by lognormal distributions at 38 weeks PCA or less, and by gamma distributions at 44 weeks PCA; (ii) the scale parameter of the lognormal distribution had positive correlations with PCA as well as a strong negative correlation with the percentage of low-voltage activity; (iii) the shape parameter of the lognormal distribution had significant positive correlations with PCA; (iv) the statistics of mode showed significant linear relationships with PCA, and, therefore, it was considered a useful index in PCA prediction. These statistics, including the scale parameter of the lognormal distribution and the skewness and mode derived from a suitable probability distribution, may be good indexes for estimating stationary nature in developing brain activity in preterm infants. The stationary characteristics, such as discontinuity, asymmetry, and unimodality, of preterm EEGs are well indicated by the statistics estimated from the probability distribution of the preterm EEG envelopes. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Flood Frequency Curves - Use of information on the likelihood of extreme floods

NASA Astrophysics Data System (ADS)

Faber, B.

2011-12-01

Investment in the infrastructure that reduces flood risk for flood-prone communities must incorporate information on the magnitude and frequency of flooding in that area. Traditionally, that information has been a probability distribution of annual maximum streamflows developed from the historical gaged record at a stream site. Practice in the United States fits a Log-Pearson type3 distribution to the annual maximum flows of an unimpaired streamflow record, using the method of moments to estimate distribution parameters. The procedure makes the assumptions that annual peak streamflow events are (1) independent, (2) identically distributed, and (3) form a representative sample of the overall probability distribution. Each of these assumptions can be challenged. We rarely have enough data to form a representative sample, and therefore must compute and display the uncertainty in the estimated flood distribution. But, is there a wet/dry cycle that makes precipitation less than independent between successive years? Are the peak flows caused by different types of events from different statistical populations? How does the watershed or climate changing over time (non-stationarity) affect the probability distribution floods? Potential approaches to avoid these assumptions vary from estimating trend and shift and removing them from early data (and so forming a homogeneous data set), to methods that estimate statistical parameters that vary with time. A further issue in estimating a probability distribution of flood magnitude (the flood frequency curve) is whether a purely statistical approach can accurately capture the range and frequency of floods that are of interest. A meteorologically-based analysis produces "probable maximum precipitation" (PMP) and subsequently a "probable maximum flood" (PMF) that attempts to describe an upper bound on flood magnitude in a particular watershed. This analysis can help constrain the upper tail of the probability distribution, well beyond the range of gaged data or even historical or paleo-flood data, which can be very important in risk analyses performed for flood risk management and dam and levee safety studies.

Distributed decision-making in electric power system transmission maintenance scheduling using multi-agent systems (MAS)

NASA Astrophysics Data System (ADS)

Zhang, Zhong

In this work, motivated by the need to coordinate transmission maintenance scheduling among a multiplicity of self-interested entities in restructured power industry, a distributed decision support framework based on multiagent negotiation systems (MANS) is developed. An innovative risk-based transmission maintenance optimization procedure is introduced. Several models for linking condition monitoring information to the equipment's instantaneous failure probability are presented, which enable quantitative evaluation of the effectiveness of maintenance activities in terms of system cumulative risk reduction. Methodologies of statistical processing, equipment deterioration evaluation and time-dependent failure probability calculation are also described. A novel framework capable of facilitating distributed decision-making through multiagent negotiation is developed. A multiagent negotiation model is developed and illustrated that accounts for uncertainty and enables social rationality. Some issues of multiagent negotiation convergence and scalability are discussed. The relationships between agent-based negotiation and auction systems are also identified. A four-step MAS design methodology for constructing multiagent systems for power system applications is presented. A generic multiagent negotiation system, capable of inter-agent communication and distributed decision support through inter-agent negotiations, is implemented. A multiagent system framework for facilitating the automated integration of condition monitoring information and maintenance scheduling for power transformers is developed. Simulations of multiagent negotiation-based maintenance scheduling among several independent utilities are provided. It is shown to be a viable alternative solution paradigm to the traditional centralized optimization approach in today's deregulated environment. This multiagent system framework not only facilitates the decision-making among competing power system entities, but also provides a tool to use in studying competitive industry relative to monopolistic industry.

Technology-enhanced Interactive Teaching of Marginal, Joint and Conditional Probabilities: The Special Case of Bivariate Normal Distribution

PubMed Central

Dinov, Ivo D.; Kamino, Scott; Bhakhrani, Bilal; Christou, Nicolas

2014-01-01

Summary Data analysis requires subtle probability reasoning to answer questions like What is the chance of event A occurring, given that event B was observed? This generic question arises in discussions of many intriguing scientific questions such as What is the probability that an adolescent weighs between 120 and 140 pounds given that they are of average height? and What is the probability of (monetary) inflation exceeding 4% and housing price index below 110? To address such problems, learning some applied, theoretical or cross-disciplinary probability concepts is necessary. Teaching such courses can be improved by utilizing modern information technology resources. Students’ understanding of multivariate distributions, conditional probabilities, correlation and causation can be significantly strengthened by employing interactive web-based science educational resources. Independent of the type of a probability course (e.g. majors, minors or service probability course, rigorous measure-theoretic, applied or statistics course) student motivation, learning experiences and knowledge retention may be enhanced by blending modern technological tools within the classical conceptual pedagogical models. We have designed, implemented and disseminated a portable open-source web-application for teaching multivariate distributions, marginal, joint and conditional probabilities using the special case of bivariate Normal distribution. A real adolescent height and weight dataset is used to demonstrate the classroom utilization of the new web-application to address problems of parameter estimation, univariate and multivariate inference. PMID:25419016

Technology-enhanced Interactive Teaching of Marginal, Joint and Conditional Probabilities: The Special Case of Bivariate Normal Distribution.

PubMed

Dinov, Ivo D; Kamino, Scott; Bhakhrani, Bilal; Christou, Nicolas

2013-01-01

Data analysis requires subtle probability reasoning to answer questions like What is the chance of event A occurring, given that event B was observed? This generic question arises in discussions of many intriguing scientific questions such as What is the probability that an adolescent weighs between 120 and 140 pounds given that they are of average height? and What is the probability of (monetary) inflation exceeding 4% and housing price index below 110? To address such problems, learning some applied, theoretical or cross-disciplinary probability concepts is necessary. Teaching such courses can be improved by utilizing modern information technology resources. Students' understanding of multivariate distributions, conditional probabilities, correlation and causation can be significantly strengthened by employing interactive web-based science educational resources. Independent of the type of a probability course (e.g. majors, minors or service probability course, rigorous measure-theoretic, applied or statistics course) student motivation, learning experiences and knowledge retention may be enhanced by blending modern technological tools within the classical conceptual pedagogical models. We have designed, implemented and disseminated a portable open-source web-application for teaching multivariate distributions, marginal, joint and conditional probabilities using the special case of bivariate Normal distribution. A real adolescent height and weight dataset is used to demonstrate the classroom utilization of the new web-application to address problems of parameter estimation, univariate and multivariate inference.

75 FR 13342 - Pipeline Safety: Workshop on Distribution Pipeline Construction

Federal Register 2010, 2011, 2012, 2013, 2014

2010-03-19

... DEPARTMENT OF TRANSPORTATION Pipeline and Hazardous Materials Safety Administration [Docket ID... natural gas distribution construction. Natural gas distribution pipelines are subject to a unique subset... distribution pipeline construction practices. This workshop will focus solely on natural gas distribution...

Stylized facts in internal rates of return on stock index and its derivative transactions

NASA Astrophysics Data System (ADS)

Pichl, Lukáš; Kaizoji, Taisei; Yamano, Takuya

2007-08-01

Universal features in stock markets and their derivative markets are studied by means of probability distributions in internal rates of return on buy and sell transaction pairs. Unlike the stylized facts in normalized log returns, the probability distributions for such single asset encounters incorporate the time factor by means of the internal rate of return, defined as the continuous compound interest. Resulting stylized facts are shown in the probability distributions derived from the daily series of TOPIX, S & P 500 and FTSE 100 index close values. The application of the above analysis to minute-tick data of NIKKEI 225 and its futures market, respectively, reveals an interesting difference in the behavior of the two probability distributions, in case a threshold on the minimal duration of the long position is imposed. It is therefore suggested that the probability distributions of the internal rates of return could be used for causality mining between the underlying and derivative stock markets. The highly specific discrete spectrum, which results from noise trader strategies as opposed to the smooth distributions observed for fundamentalist strategies in single encounter transactions may be useful in deducing the type of investment strategy from trading revenues of small portfolio investors.

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.

Mathematical Model to estimate the wind power using four-parameter Burr distribution

NASA Astrophysics Data System (ADS)

Liu, Sanming; Wang, Zhijie; Pan, Zhaoxu

2018-03-01

When the real probability of wind speed in the same position needs to be described, the four-parameter Burr distribution is more suitable than other distributions. This paper introduces its important properties and characteristics. Also, the application of the four-parameter Burr distribution in wind speed prediction is discussed, and the expression of probability distribution of output power of wind turbine is deduced.

Identifying optimal threshold statistics for elimination of hookworm using a stochastic simulation model.

PubMed

Truscott, James E; Werkman, Marleen; Wright, James E; Farrell, Sam H; Sarkar, Rajiv; Ásbjörnsdóttir, Kristjana; Anderson, Roy M

2017-06-30

There is an increased focus on whether mass drug administration (MDA) programmes alone can interrupt the transmission of soil-transmitted helminths (STH). Mathematical models can be used to model these interventions and are increasingly being implemented to inform investigators about expected trial outcome and the choice of optimum study design. One key factor is the choice of threshold for detecting elimination. However, there are currently no thresholds defined for STH regarding breaking transmission. We develop a simulation of an elimination study, based on the DeWorm3 project, using an individual-based stochastic disease transmission model in conjunction with models of MDA, sampling, diagnostics and the construction of study clusters. The simulation is then used to analyse the relationship between the study end-point elimination threshold and whether elimination is achieved in the long term within the model. We analyse the quality of a range of statistics in terms of the positive predictive values (PPV) and how they depend on a range of covariates, including threshold values, baseline prevalence, measurement time point and how clusters are constructed. End-point infection prevalence performs well in discriminating between villages that achieve interruption of transmission and those that do not, although the quality of the threshold is sensitive to baseline prevalence and threshold value. Optimal post-treatment prevalence threshold value for determining elimination is in the range 2% or less when the baseline prevalence range is broad. For multiple clusters of communities, both the probability of elimination and the ability of thresholds to detect it are strongly dependent on the size of the cluster and the size distribution of the constituent communities. Number of communities in a cluster is a key indicator of probability of elimination and PPV. Extending the time, post-study endpoint, at which the threshold statistic is measured improves PPV value in discriminating between eliminating clusters and those that bounce back. The probability of elimination and PPV are very sensitive to baseline prevalence for individual communities. However, most studies and programmes are constructed on the basis of clusters. Since elimination occurs within smaller population sub-units, the construction of clusters introduces new sensitivities for elimination threshold values to cluster size and the underlying population structure. Study simulation offers an opportunity to investigate key sources of sensitivity for elimination studies and programme designs in advance and to tailor interventions to prevailing local or national conditions.

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.

Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations

NASA Astrophysics Data System (ADS)

Bhattacharjee, J. K.; Kirkpatrick, T. R.; Sengers, J. V.

2018-04-01

Work fluctuations and work probability distributions are fundamentally different in systems with short-ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with short-ranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet, well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behavior of the work probability distribution and the associated fluctuations is presented.

Methods to elicit probability distributions from experts: a systematic review of reported practice in health technology assessment.

PubMed

Grigore, Bogdan; Peters, Jaime; Hyde, Christopher; Stein, Ken

2013-11-01

Elicitation is a technique that can be used to obtain probability distribution from experts about unknown quantities. We conducted a methodology review of reports where probability distributions had been elicited from experts to be used in model-based health technology assessments. Databases including MEDLINE, EMBASE and the CRD database were searched from inception to April 2013. Reference lists were checked and citation mapping was also used. Studies describing their approach to the elicitation of probability distributions were included. Data was abstracted on pre-defined aspects of the elicitation technique. Reports were critically appraised on their consideration of the validity, reliability and feasibility of the elicitation exercise. Fourteen articles were included. Across these studies, the most marked features were heterogeneity in elicitation approach and failure to report key aspects of the elicitation method. The most frequently used approaches to elicitation were the histogram technique and the bisection method. Only three papers explicitly considered the validity, reliability and feasibility of the elicitation exercises. Judged by the studies identified in the review, reports of expert elicitation are insufficient in detail and this impacts on the perceived usability of expert-elicited probability distributions. In this context, the wider credibility of elicitation will only be improved by better reporting and greater standardisation of approach. Until then, the advantage of eliciting probability distributions from experts may be lost.

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

Bartram, Bart W.; Vaughan, Frank R.; Englehart, Richard W., Dr.

1991-01-01

The use of a radioisotope thermoelectric generator fueled with plutonium-238 dioxide on the Space Shuttle-launched Ulysses mission implies some level of risk due to potential accidents. This paper describes the method used to quantify risks in the Ulysses mission Final Safety Analysis Report prepared for the U.S. Department of Energy. The starting point for the analysis described herein is following input of source term probability distributions from the General Electric Company. A Monte Carlo technique is used to develop probability distributions of radiological consequences for a range of accident scenarios thoughout the mission. Factors affecting radiological consequences are identified, the probability distribution of the effect of each factor determined, and the functional relationship among all the factors established. The probability distributions of all the factor effects are then combined using a Monte Carlo technique. The results of the analysis are presented in terms of complementary cumulative distribution functions (CCDF) by mission sub-phase, phase, and the overall mission. The CCDFs show the total probability that consequences (calculated health effects) would be equal to or greater than a given value.

Force Density Function Relationships in 2-D Granular Media

NASA Technical Reports Server (NTRS)

Youngquist, Robert C.; Metzger, Philip T.; Kilts, Kelly N.

2004-01-01

An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms

An evaluation of procedures to estimate monthly precipitation probabilities

NASA Astrophysics Data System (ADS)

Legates, David R.

1991-01-01

Many frequency distributions have been used to evaluate monthly precipitation probabilities. Eight of these distributions (including Pearson type III, extreme value, and transform normal probability density functions) are comparatively examined to determine their ability to represent accurately variations in monthly precipitation totals for global hydroclimatological analyses. Results indicate that a modified version of the Box-Cox transform-normal distribution more adequately describes the 'true' precipitation distribution than does any of the other methods. This assessment was made using a cross-validation procedure for a global network of 253 stations for which at least 100 years of monthly precipitation totals were available.

"Intelligent Ensemble" Projections of Precipitation and Surface Radiation in Support of Agricultural Climate Change Adaptation

NASA Technical Reports Server (NTRS)

Taylor, Patrick C.; Baker, Noel C.

2015-01-01

Earth's climate is changing and will continue to change into the foreseeable future. Expected changes in the climatological distribution of precipitation, surface temperature, and surface solar radiation will significantly impact agriculture. Adaptation strategies are, therefore, required to reduce the agricultural impacts of climate change. Climate change projections of precipitation, surface temperature, and surface solar radiation distributions are necessary input for adaption planning studies. These projections are conventionally constructed from an ensemble of climate model simulations (e.g., the Coupled Model Intercomparison Project 5 (CMIP5)) as an equal weighted average, one model one vote. Each climate model, however, represents the array of climate-relevant physical processes with varying degrees of fidelity influencing the projection of individual climate variables differently. Presented here is a new approach, termed the "Intelligent Ensemble, that constructs climate variable projections by weighting each model according to its ability to represent key physical processes, e.g., precipitation probability distribution. This approach provides added value over the equal weighted average method. Physical process metrics applied in the "Intelligent Ensemble" method are created using a combination of NASA and NOAA satellite and surface-based cloud, radiation, temperature, and precipitation data sets. The "Intelligent Ensemble" method is applied to the RCP4.5 and RCP8.5 anthropogenic climate forcing simulations within the CMIP5 archive to develop a set of climate change scenarios for precipitation, temperature, and surface solar radiation in each USDA Farm Resource Region for use in climate change adaptation studies.

q-Gaussian distributions of leverage returns, first stopping times, and default risk valuations

NASA Astrophysics Data System (ADS)

Katz, Yuri A.; Tian, Li

2013-10-01

We study the probability distributions of daily leverage returns of 520 North American industrial companies that survive de-listing during the financial crisis, 2006-2012. We provide evidence that distributions of unbiased leverage returns of all individual firms belong to the class of q-Gaussian distributions with the Tsallis entropic parameter within the interval 1

Multi-level bandwidth efficient block modulation codes

NASA Technical Reports Server (NTRS)

Lin, Shu

1989-01-01

The multilevel technique is investigated for combining block coding and modulation. There are four parts. In the first part, a formulation is presented for signal sets on which modulation codes are to be constructed. Distance measures on a signal set are defined and their properties are developed. In the second part, a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate Euclidean distances. The distance properties, Euclidean weight distribution and linear structure of multilevel modulation codes are investigated. In the third part, several specific methods for constructing multilevel block modulation codes with interdependency among component codes are proposed. Given a multilevel block modulation code C with no interdependency among the binary component codes, the proposed methods give a multilevel block modulation code C which has the same rate as C, a minimum squared Euclidean distance not less than that of code C, a trellis diagram with the same number of states as that of C and a smaller number of nearest neighbor codewords than that of C. In the last part, error performance of block modulation codes is analyzed for an AWGN channel based on soft-decision maximum likelihood decoding. Error probabilities of some specific codes are evaluated based on their Euclidean weight distributions and simulation results.

Spatial distribution of organic pollutants in industrial construction and demolition waste and their mutual interaction on an abandoned pesticide manufacturing plant.

PubMed

Huang, Sheng; Zhao, Xin; Sun, Yanqiu; Ma, Jianli; Gao, Xiaofeng; Xie, Tian; Xu, Dongsheng; Yu, Yi; Zhao, Youcai

2016-04-01

A comprehensive field investigation of organic pollutants was examined in industrial construction and demolition waste (ICDW) inside an abandoned pesticide manufacturing plant. Concentrations of eight types of pesticides, a metabolite and two intermediates were studied. The ICDW was under severe and long-term contamination by organophosphorus, intermediates and pyrethroid pesticide with mean concentrations of 23,429, 3538 and 179.4 mg kg(-1), respectively. FT-IR analysis suggested that physical absorption and chemical bonding were their mutual interaction forms. Patterns of total pesticide spatial distribution showed good correlations with manufacturing processes spreading all over the plant both in enclosed workshops and in residues randomly dumped outside, while bricks and coatings were the most vulnerable to pollutants. Ultimately the fate of the OPPs was diversified as the immersion of ICDW in water largely transferred the pollutants into aquatic systems while exposure outside did not largely lead to pesticide degradation. The adoption of centralized collections for the disposal of wastes could only eliminate part of the contaminated ICDW, probably due to lack of knowledge and criteria. Correlation matrix and cluster analysis indicated that regulated disposal and management of polluted ICDW was effective, thus presenting the requirement for its appropriate disposal.

Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form

USGS Publications Warehouse

Greenwood, J. Arthur; Landwehr, J. Maciunas; Matalas, N.C.; Wallis, J.R.

1979-01-01

Distributions whose inverse forms are explicitly defined, such as Tukey's lambda, may present problems in deriving their parameters by more conventional means. Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions.

Univariate Probability Distributions

ERIC Educational Resources Information Center

Leemis, Lawrence M.; Luckett, Daniel J.; Powell, Austin G.; Vermeer, Peter E.

2012-01-01

We describe a web-based interactive graphic that can be used as a resource in introductory classes in mathematical statistics. This interactive graphic presents 76 common univariate distributions and gives details on (a) various features of the distribution such as the functional form of the probability density function and cumulative distribution…

[«All of a sudden…» preventability and priorities of construction fatalities: an experience in Piedmont].

PubMed

Pasqualini, Osvaldo; Libener, Marcello; Farina, Elena; Bena, Antonella

2011-01-01

To examine the usefulness for prevention of the National Surveillance System on occupational fatalities, which is based on the narrative description of the work accident collected by OSH inspectors and on the subsequent classification of the injury dynamics by means of a standardized model of analysis. The system ability of providing useful recommendations for prevention was evaluated on one hand by analyzing the effectiveness of inspections in preventing fatalities, on the other hand by identifying the most frequent accident mechanisms. Data analyzed consisted of investigation reports of construction fatalities occurred during 2002-2008 in the Piedmont Region, collected by surveillance system. The injury narrative description was used to assess whether the fatality would have been preventable by an inspection hypothetically conducted the day before the event; injuries were classified as probably preventable, probably not preventable, and uncertain. A standardized model of classification of injury dynamics was employed to identify mechanisms and circumstances related to the construction fatalities, and particularly those caused by falls from height. Among 122 construction fatalities occurred, 25%were considered probably preventable and 60%probably not preventable. Half of the construction fatalities was caused by fall from height, most of which were caused by sudden breaking of a surface walkway, and almost 20% by fall of objects, including burial. The analysis of the preventability of construction fatalities in Piedmont seems partly to rebut the assumption that more inspections are necessarily associated with a reduction in fatalities. The interpretation of the injury narrative descriptions, which are implemented by OHS inspectors as part of their usual activity, through a standardized model of analysis allows to identify the breaking of surface walkways as the most important mechanism of fatality among falls from height.

Regional probability distribution of the annual reference evapotranspiration and its effective parameters in Iran

NASA Astrophysics Data System (ADS)

Khanmohammadi, Neda; Rezaie, Hossein; Montaseri, Majid; Behmanesh, Javad

2017-10-01

The reference evapotranspiration (ET0) plays an important role in water management plans in arid or semi-arid countries such as Iran. For this reason, the regional analysis of this parameter is important. But, ET0 process is affected by several meteorological parameters such as wind speed, solar radiation, temperature and relative humidity. Therefore, the effect of distribution type of effective meteorological variables on ET0 distribution was analyzed. For this purpose, the regional probability distribution of the annual ET0 and its effective parameters were selected. Used data in this research was recorded data at 30 synoptic stations of Iran during 1960-2014. Using the probability plot correlation coefficient (PPCC) test and the L-moment method, five common distributions were compared and the best distribution was selected. The results of PPCC test and L-moment diagram indicated that the Pearson type III distribution was the best probability distribution for fitting annual ET0 and its four effective parameters. The results of RMSE showed that the ability of the PPCC test and L-moment method for regional analysis of reference evapotranspiration and its effective parameters was similar. The results also showed that the distribution type of the parameters which affected ET0 values can affect the distribution of reference evapotranspiration.

Probabilistic reasoning in data analysis.

PubMed

Sirovich, Lawrence

2011-09-20

This Teaching Resource provides lecture notes, slides, and a student assignment for a lecture on probabilistic reasoning in the analysis of biological data. General probabilistic frameworks are introduced, and a number of standard probability distributions are described using simple intuitive ideas. Particular attention is focused on random arrivals that are independent of prior history (Markovian events), with an emphasis on waiting times, Poisson processes, and Poisson probability distributions. The use of these various probability distributions is applied to biomedical problems, including several classic experimental studies.

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

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

Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

7 CFR 1710.251 - Construction work plans-distribution borrowers.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 11 2010-01-01 2010-01-01 false Construction work plans-distribution borrowers. 1710...—distribution borrowers. (a) All distribution borrowers must maintain a current CWP approved by their board of directors covering all new construction, improvements, replacements, and retirements of distribution and...

Almost conserved operators in nearly many-body localized systems

NASA Astrophysics Data System (ADS)

Pancotti, Nicola; Knap, Michael; Huse, David A.; Cirac, J. Ignacio; Bañuls, Mari Carmen

2018-03-01

We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase.

Methodology for assessment of undiscovered oil and gas resources for the 2008 Circum-Arctic Resource Appraisal

USGS Publications Warehouse

Charpentier, Ronald R.; Moore, Thomas E.; Gautier, D.L.

2017-11-15

The methodological procedures used in the geologic assessments of the 2008 Circum-Arctic Resource Appraisal (CARA) were based largely on the methodology developed for the 2000 U.S. Geological Survey World Petroleum Assessment. The main variables were probability distributions for numbers and sizes of undiscovered accumulations with an associated risk of occurrence. The CARA methodology expanded on the previous methodology in providing additional tools and procedures more applicable to the many Arctic basins that have little or no exploration history. Most importantly, geologic analogs from a database constructed for this study were used in many of the assessments to constrain numbers and sizes of undiscovered oil and gas accumulations.

Two protostar candidates in the bright-rimmed dark cloud LDN 1206

NASA Technical Reports Server (NTRS)

Ressler, Michael E.; Shure, Mark

1991-01-01

The discovery of several near IR objects associated with two IRAS point sources in the LDN 1206 region is reported. IRAS 22272 + 6358A is probably a 'protostar' which is seen only in scattered light at near-IR wavelengths because of heavy obscuration by an almost edge-on circumstellar disk. In contrast, IRAS 22272 + 6358B is directly visible at these wavelengths and is perhaps an object which lies between protostars and T-Tauri stars in its evolution. Both direct and polarimetric K-band images of the region are presented, as well as spectral energy distributions constructed from J, H, K, L, L-prime, and M data and published far-IR and mm data.

Hybrid computer technique yields random signal probability distributions

NASA Technical Reports Server (NTRS)

Cameron, W. D.

1965-01-01

Hybrid computer determines the probability distributions of instantaneous and peak amplitudes of random signals. This combined digital and analog computer system reduces the errors and delays of manual data analysis.

Fast Reliability Assessing Method for Distribution Network with Distributed Renewable Energy Generation

NASA Astrophysics Data System (ADS)

Chen, Fan; Huang, Shaoxiong; Ding, Jinjin; Ding, Jinjin; Gao, Bo; Xie, Yuguang; Wang, Xiaoming

2018-01-01

This paper proposes a fast reliability assessing method for distribution grid with distributed renewable energy generation. First, the Weibull distribution and the Beta distribution are used to describe the probability distribution characteristics of wind speed and solar irradiance respectively, and the models of wind farm, solar park and local load are built for reliability assessment. Then based on power system production cost simulation probability discretization and linearization power flow, a optimal power flow objected with minimum cost of conventional power generation is to be resolved. Thus a reliability assessment for distribution grid is implemented fast and accurately. The Loss Of Load Probability (LOLP) and Expected Energy Not Supplied (EENS) are selected as the reliability index, a simulation for IEEE RBTS BUS6 system in MATLAB indicates that the fast reliability assessing method calculates the reliability index much faster with the accuracy ensured when compared with Monte Carlo method.

40 CFR Appendix C to Part 191 - Guidance for Implementation of Subpart B

Code of Federal Regulations, 2014 CFR

2014-07-01

... that the remaining probability distribution of cumulative releases would not be significantly changed... with § 191.13 into a “complementary cumulative distribution function” that indicates the probability of... distribution function for each disposal system considered. The Agency assumes that a disposal system can be...

40 CFR Appendix C to Part 191 - Guidance for Implementation of Subpart B

Code of Federal Regulations, 2011 CFR

2011-07-01

... that the remaining probability distribution of cumulative releases would not be significantly changed... with § 191.13 into a “complementary cumulative distribution function” that indicates the probability of... distribution function for each disposal system considered. The Agency assumes that a disposal system can be...

Drilling High Precision Holes in Ti6Al4V Using Rotary Ultrasonic Machining and Uncertainties Underlying Cutting Force, Tool Wear, and Production Inaccuracies.

PubMed

Chowdhury, M A K; Sharif Ullah, A M M; Anwar, Saqib

2017-09-12

Ti6Al4V alloys are difficult-to-cut materials that have extensive applications in the automotive and aerospace industry. A great deal of effort has been made to develop and improve the machining operations of Ti6Al4V alloys. This paper presents an experimental study that systematically analyzes the effects of the machining conditions (ultrasonic power, feed rate, spindle speed, and tool diameter) on the performance parameters (cutting force, tool wear, overcut error, and cylindricity error), while drilling high precision holes on the workpiece made of Ti6Al4V alloys using rotary ultrasonic machining (RUM). Numerical results were obtained by conducting experiments following the design of an experiment procedure. The effects of the machining conditions on each performance parameter have been determined by constructing a set of possibility distributions (i.e., trapezoidal fuzzy numbers) from the experimental data. A possibility distribution is a probability-distribution-neural representation of uncertainty, and is effective in quantifying the uncertainty underlying physical quantities when there is a limited number of data points which is the case here. Lastly, the optimal machining conditions have been identified using these possibility distributions.

Monte Carlo decision curve analysis using aggregate data.

PubMed

Hozo, Iztok; Tsalatsanis, Athanasios; Djulbegovic, Benjamin

2017-02-01

Decision curve analysis (DCA) is an increasingly used method for evaluating diagnostic tests and predictive models, but its application requires individual patient data. The Monte Carlo (MC) method can be used to simulate probabilities and outcomes of individual patients and offers an attractive option for application of DCA. We constructed a MC decision model to simulate individual probabilities of outcomes of interest. These probabilities were contrasted against the threshold probability at which a decision-maker is indifferent between key management strategies: treat all, treat none or use predictive model to guide treatment. We compared the results of DCA with MC simulated data against the results of DCA based on actual individual patient data for three decision models published in the literature: (i) statins for primary prevention of cardiovascular disease, (ii) hospice referral for terminally ill patients and (iii) prostate cancer surgery. The results of MC DCA and patient data DCA were identical. To the extent that patient data DCA were used to inform decisions about statin use, referral to hospice or prostate surgery, the results indicate that MC DCA could have also been used. As long as the aggregate parameters on distribution of the probability of outcomes and treatment effects are accurately described in the published reports, the MC DCA will generate indistinguishable results from individual patient data DCA. We provide a simple, easy-to-use model, which can facilitate wider use of DCA and better evaluation of diagnostic tests and predictive models that rely only on aggregate data reported in the literature. © 2017 Stichting European Society for Clinical Investigation Journal Foundation.

Optimal methods for fitting probability distributions to propagule retention time in studies of zoochorous dispersal.

PubMed

Viana, Duarte S; Santamaría, Luis; Figuerola, Jordi

2016-02-01

Propagule retention time is a key factor in determining propagule dispersal distance and the shape of "seed shadows". Propagules dispersed by animal vectors are either ingested and retained in the gut until defecation or attached externally to the body until detachment. Retention time is a continuous variable, but it is commonly measured at discrete time points, according to pre-established sampling time-intervals. Although parametric continuous distributions have been widely fitted to these interval-censored data, the performance of different fitting methods has not been evaluated. To investigate the performance of five different fitting methods, we fitted parametric probability distributions to typical discretized retention-time data with known distribution using as data-points either the lower, mid or upper bounds of sampling intervals, as well as the cumulative distribution of observed values (using either maximum likelihood or non-linear least squares for parameter estimation); then compared the estimated and original distributions to assess the accuracy of each method. We also assessed the robustness of these methods to variations in the sampling procedure (sample size and length of sampling time-intervals). Fittings to the cumulative distribution performed better for all types of parametric distributions (lognormal, gamma and Weibull distributions) and were more robust to variations in sample size and sampling time-intervals. These estimated distributions had negligible deviations of up to 0.045 in cumulative probability of retention times (according to the Kolmogorov-Smirnov statistic) in relation to original distributions from which propagule retention time was simulated, supporting the overall accuracy of this fitting method. In contrast, fitting the sampling-interval bounds resulted in greater deviations that ranged from 0.058 to 0.273 in cumulative probability of retention times, which may introduce considerable biases in parameter estimates. We recommend the use of cumulative probability to fit parametric probability distributions to propagule retention time, specifically using maximum likelihood for parameter estimation. Furthermore, the experimental design for an optimal characterization of unimodal propagule retention time should contemplate at least 500 recovered propagules and sampling time-intervals not larger than the time peak of propagule retrieval, except in the tail of the distribution where broader sampling time-intervals may also produce accurate fits.

How Can Histograms Be Useful for Introducing Continuous Probability Distributions?

ERIC Educational Resources Information Center

Derouet, Charlotte; Parzysz, Bernard

2016-01-01

The teaching of probability has changed a great deal since the end of the last century. The development of technologies is indeed part of this evolution. In France, continuous probability distributions began to be studied in 2002 by scientific 12th graders, but this subject was marginal and appeared only as an application of integral calculus.…

Pseudo Bayes Estimates for Test Score Distributions and Chained Equipercentile Equating. Research Report. ETS RR-09-47

ERIC Educational Resources Information Center

Moses, Tim; Oh, Hyeonjoo J.

2009-01-01

Pseudo Bayes probability estimates are weighted averages of raw and modeled probabilities; these estimates have been studied primarily in nonpsychometric contexts. The purpose of this study was to evaluate pseudo Bayes probability estimates as applied to the estimation of psychometric test score distributions and chained equipercentile equating…

A synthetic seismicity model for the Middle America Trench

NASA Technical Reports Server (NTRS)

Ward, Steven N.

1991-01-01

A novel iterative technique, based on the concept of fault segmentation and computed using 2D static dislocation theory, for building models of seismicity and fault interaction which are physically acceptable and geometrically and kinematically correct, is presented. The technique is applied in two steps to seismicity observed at the Middle America Trench. The first constructs generic models which randomly draw segment strengths and lengths from a 2D probability distribution. The second constructs predictive models in which segment lengths and strengths are adjusted to mimic the actual geography and timing of large historical earthquakes. Both types of models reproduce the statistics of seismicity over five units of magnitude and duplicate other aspects including foreshock and aftershock sequences, migration of foci, and the capacity to produce both characteristic and noncharacteristic earthquakes. Over a period of about 150 yr the complex interaction of fault segments and the nonlinear failure conditions conspire to transform an apparently deterministic model into a chaotic one.

Development of a statistical oil spill model for risk assessment.

PubMed

Guo, Weijun

2017-11-01

To gain a better understanding of the impacts from potential risk sources, we developed an oil spill model using probabilistic method, which simulates numerous oil spill trajectories under varying environmental conditions. The statistical results were quantified from hypothetical oil spills under multiple scenarios, including area affected probability, mean oil slick thickness, and duration of water surface exposed to floating oil. The three sub-indices together with marine area vulnerability are merged to compute the composite index, characterizing the spatial distribution of risk degree. Integral of the index can be used to identify the overall risk from an emission source. The developed model has been successfully applied in comparison to and selection of an appropriate oil port construction location adjacent to a marine protected area for Phoca largha in China. The results highlight the importance of selection of candidates before project construction, since that risk estimation from two adjacent potential sources may turn out to be significantly different regarding hydrodynamic conditions and eco-environmental sensitivity. Copyright © 2017. Published by Elsevier Ltd.

Failure probability under parameter uncertainty.

PubMed

Gerrard, R; Tsanakas, A

2011-05-01

In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decisionmaker is able to set the threshold at an appropriate level. This abstract situation applies, for example, to environmental risks with infrastructure controls; to supply chain risks with inventory controls; and to insurance solvency risks with capital controls. However, uncertainty around the distribution of the risk factor implies that parameter error will be present and the measures taken to control failure probabilities may not be effective. We show that parameter uncertainty increases the probability (understood as expected frequency) of failures. For a large class of loss distributions, arising from increasing transformations of location-scale families (including the log-normal, Weibull, and Pareto distributions), the article shows that failure probabilities can be exactly calculated, as they are independent of the true (but unknown) parameters. Hence it is possible to obtain an explicit measure of the effect of parameter uncertainty on failure probability. Failure probability can be controlled in two different ways: (1) by reducing the nominal required failure probability, depending on the size of the available data set, and (2) by modifying of the distribution itself that is used to calculate the risk control. Approach (1) corresponds to a frequentist/regulatory view of probability, while approach (2) is consistent with a Bayesian/personalistic view. We furthermore show that the two approaches are consistent in achieving the required failure probability. Finally, we briefly discuss the effects of data pooling and its systemic risk implications. © 2010 Society for Risk Analysis.

Comparison of three-parameter probability distributions for representing annual extreme and partial duration precipitation series

NASA Astrophysics Data System (ADS)

Wilks, Daniel S.

1993-10-01

Performance of 8 three-parameter probability distributions for representing annual extreme and partial duration precipitation data at stations in the northeastern and southeastern United States is investigated. Particular attention is paid to fidelity on the right tail, through use of a bootstrap procedure simulating extrapolation on the right tail beyond the data. It is found that the beta-κ distribution best describes the extreme right tail of annual extreme series, and the beta-P distribution is best for the partial duration data. The conventionally employed two-parameter Gumbel distribution is found to substantially underestimate probabilities associated with the larger precipitation amounts for both annual extreme and partial duration data. Fitting the distributions using left-censored data did not result in improved fits to the right tail.

What's in a name? Intolerance of uncertainty, other uncertainty-relevant constructs, and their differential relations to worry and generalized anxiety disorder.

PubMed

Koerner, Naomi; Mejia, Teresa; Kusec, Andrea

2017-03-01

A number of studies have examined the association of intolerance of uncertainty (IU) to trait worry and generalized anxiety disorder (GAD). However, few studies have examined the extent of overlap between IU and other psychological constructs that bear conceptual resemblance to IU, despite the fact that IU-type constructs have been discussed and examined extensively within psychology and other disciplines. The present study investigated (1) the associations of IU, trait worry, and GAD status to a negative risk orientation, trait curiosity, indecisiveness, perceived constraints, self-oriented and socially prescribed perfectionism, intolerance of ambiguity, the need for predictability, and the need for order and structure and (2) whether IU is a unique correlate of trait worry and of the presence versus absence of Probable GAD, when overlap with other uncertainty-relevant constructs is accounted for. N = 255 adults completed self-report measures of the aforementioned constructs. Each of the constructs was significantly associated with IU. Only IU, and a subset of the other uncertainty-relevant constructs were correlated with trait worry or distinguished the Probable GAD group from the Non-GAD group. IU was the strongest unique correlate of trait worry and of the presence versus absence of Probable GAD. Indecisiveness, self-oriented perfectionism and the need for predictability were also unique correlates of trait worry or GAD status. Implications of the findings are discussed, in particular as they pertain to the definition, conceptualization, and cognitive-behavioral treatment of IU in GAD.

Martian crater counts on Elysium Mons

NASA Technical Reports Server (NTRS)

Mcbride, Kathleen; Barlow, Nadine G.

1990-01-01

Without returned samples from the Martian surface, relative age chronologies and stratigraphic relationships provide the best information for determining the ages of geomorphic features and surface regions. Crater-size frequency distributions of six recently mapped geological units of Elysium Mons were measured to establish their relative ages. Most of the craters on Elysium Mons and the adjacent plains units are between 500 and 1000 meters in diameter. However, only craters 1 km in diameter or larger were used because of inadequate spatial resolution of some of the Viking images and to reduce probability of counting secondary craters. The six geologic units include all of the Elysium Mons construct and a portion of the plains units west of the volcano. The surface area of the units studied is approximately 128,000 sq km. Four of the geologic units were used to create crater distribution curves. There are no craters larger than 1 km within the Elysium Mons caldera. Craters that lacked raised rims, were irregularly shaped, or were arranged in a linear pattern were assumed to be endogenic in origin and not counted. A crater frequency distribution analysis is presented.

The estimation of tree posterior probabilities using conditional clade probability distributions.

PubMed

Larget, Bret

2013-07-01

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.

Quantum Spectra and Dynamics

NASA Astrophysics Data System (ADS)

Arce, Julio Cesar

1992-01-01

This work focuses on time-dependent quantum theory and methods for the study of the spectra and dynamics of atomic and molecular systems. Specifically, we have addressed the following two problems: (i) Development of a time-dependent spectral method for the construction of spectra of simple quantum systems--This includes the calculation of eigenenergies, the construction of bound and continuum eigenfunctions, and the calculation of photo cross-sections. Computational applications include the quadrupole photoabsorption spectra and dissociation cross-sections of molecular hydrogen from various vibrational states in its ground electronic potential -energy curve. This method is seen to provide an advantageous alternative, both from the computational and conceptual point of view, to existing standard methods. (ii) Explicit time-dependent formulation of photoabsorption processes --Analytical solutions of the time-dependent Schrodinger equation are constructed and employed for the calculation of probability densities, momentum distributions, fluxes, transition rates, expectation values and correlation functions. These quantities are seen to establish the link between the dynamics and the calculated, or measured, spectra and cross-sections, and to clarify the dynamical nature of the excitation, transition and ejection processes. Numerical calculations on atomic and molecular hydrogen corroborate and complement the previous results, allowing the identification of different regimes during the photoabsorption process.

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.

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.

Using Quilt Blocks to Construct Understanding

ERIC Educational Resources Information Center

Westegaard, Susanne K.

2008-01-01

The article documents student experiences with quilt blocks in a mathematics classroom. Using blocks as tools, students construct their understanding of perimeter, area, probability, and transformations. (Contains 9 figures.)

Confidence as Bayesian Probability: From Neural Origins to Behavior.

PubMed

Meyniel, Florent; Sigman, Mariano; Mainen, Zachary F

2015-10-07

Research on confidence spreads across several sub-fields of psychology and neuroscience. Here, we explore how a definition of confidence as Bayesian probability can unify these viewpoints. This computational view entails that there are distinct forms in which confidence is represented and used in the brain, including distributional confidence, pertaining to neural representations of probability distributions, and summary confidence, pertaining to scalar summaries of those distributions. Summary confidence is, normatively, derived or "read out" from distributional confidence. Neural implementations of readout will trade off optimality versus flexibility of routing across brain systems, allowing confidence to serve diverse cognitive functions. Copyright © 2015 Elsevier Inc. All rights reserved.

Exact probability distribution functions for Parrondo's games

NASA Astrophysics Data System (ADS)

Zadourian, Rubina; Saakian, David B.; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

Exact probability distribution functions for Parrondo's games.

PubMed

Zadourian, Rubina; Saakian, David B; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

Incompleteness and limit of security theory of quantum key distribution

NASA Astrophysics Data System (ADS)

Hirota, Osamu; Murakami, Dan; Kato, Kentaro; Futami, Fumio

2012-10-01

It is claimed in the many papers that a trace distance: d guarantees the universal composition security in quantum key distribution (QKD) like BB84 protocol. In this introduction paper, at first, it is explicitly explained what is the main misconception in the claim of the unconditional security for QKD theory. In general terms, the cause of the misunderstanding on the security claim is the Lemma in the paper of Renner. It suggests that the generation of the perfect random key is assured by the probability (1-d), and its failure probability is d. Thus, it concludes that the generated key provides the perfect random key sequence when the protocol is success. So the QKD provides perfect secrecy to the one time pad. This is the reason for the composition claim. However, the quantity of the trace distance (or variational distance) is not the probability for such an event. If d is not small enough, always the generated key sequence is not uniform. Now one needs the reconstruction of the evaluation of the trace distance if one wants to use it. One should first go back to the indistinguishability theory in the computational complexity based, and to clarify the meaning of the value of the variational distance. In addition, the same analysis for the information theoretic case is necessary. The recent serial papers by H.P.Yuen have given the answer on such questions. In this paper, we show more concise description of Yuen's theory, and clarify that the upper bound theories for the trace distance by Tomamichel et al and Hayashi et al are constructed by the wrong reasoning of Renner and it is unsuitable as the security analysis. Finally, we introduce a new macroscopic quantum communication to replace Q-bit QKD.

Discrimination of coherent features in turbulent boundary layers by the entropy method

NASA Technical Reports Server (NTRS)

Corke, T. C.; Guezennec, Y. G.

1984-01-01

Entropy in information theory is defined as the expected or mean value of the measure of the amount of self-information contained in the ith point of a distribution series x sub i, based on its probability of occurrence p(x sub i). If p(x sub i) is the probability of the ith state of the system in probability space, then the entropy, E(X) = - sigma p(x sub i) logp (x sub i), is a measure of the disorder in the system. Based on this concept, a method was devised which sought to minimize the entropy in a time series in order to construct the signature of the most coherent motions. The constrained minimization was performed using a Lagrange multiplier approach which resulted in the solution of a simultaneous set of non-linear coupled equations to obtain the coherent time series. The application of the method to space-time data taken by a rake of sensors in the near-wall region of a turbulent boundary layer was presented. The results yielded coherent velocity motions made up of locally decelerated or accelerated fluid having a streamwise scale of approximately 100 nu/u(tau), which is in qualitative agreement with the results from other less objective discrimination methods.

Predicting the probability of elevated nitrate concentrations in the Puget Sound Basin: Implications for aquifer susceptibility and vulnerability

USGS Publications Warehouse

Tesoriero, A.J.; Voss, F.D.

1997-01-01

The occurrence and distribution of elevated nitrate concentrations (≥ 3 mg/l) in ground water in the Puget Sound Basin, Washington, were determined by examining existing data from more than 3000 wells. Models that estimate the probability that a well has an elevated nitrate concentration were constructed by relating the occurrence of elevated nitrate concentrations to both natural and anthropogenic variables using logistic regression. The variables that best explain the occurrence of elevated nitrate concentrations were well depth, surficial geology, and the percentage of urban and agricultural land within a radius of 3.2 kilometers of the well. From these relations, logistic regression models were developed to assess aquifer susceptibility (relative ease with which contaminants will reach aquifer) and ground-water vulnerability (relative ease with which contaminants will reach aquifer for a given set of land-use practices). Both models performed well at predicting the probability of elevated nitrate concentrations in an independent data set. This approach to assessing aquifer susceptibility and ground-water vulnerability has the advantages of having both model variables and coefficient values determined on the basis of existing water quality information and does not depend on the assignment of variables and weighting factors based on qualitative criteria.

What Can Quantum Optics Say about Computational Complexity Theory?

NASA Astrophysics Data System (ADS)

Rahimi-Keshari, Saleh; Lund, Austin P.; Ralph, Timothy C.

2015-02-01

Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPPNP complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output.

X{sub max}{sup μ} vs. N{sup μ} from extensive air showers as estimator for the mass of primary UHECR's. Application for the Pierre Auger Observatory

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

Arsene, Nicusor; Sima, Octavian

2015-02-24

We study the possibility of primary mass estimation for Ultra High Energy Cosmic Rays (UHECR's) using the X{sub max}{sup μ} (the height where the number of muons produced on the core of Extensive Air Showers (EAS) is maximum) and the number N{sup μ} of muons detected on ground. We use the 2D distribution - X{sub max}{sup μ} against N{sup μ} in order to find its sensitivity to the mass of the primary particle. For that, we construct a 2D Probability Function Prob(p,Fe | X{sub max}{sup μ}, N{sup μ}) which estimates the probability that a certain point from the plane (X{submore » max}{sup μ}, N{sup μ}) corresponds to a shower induced by a proton, respectively an iron nucleus. To test the procedure, we analyze a set of simulated EAS induced by protons and iron nuclei at energies of 10{sup 19}eV and 20° zenith angle with CORSIKA. Using the Bayesian approach and taking into account the geometry of the infill detectors from the Pierre Auger Observatory, we observe an improvement in the accuracy of the primary mass reconstruction in comparison with the results obtained using only the X{sub max}{sup μ} distributions.« less

Evolution of a Modified Binomial Random Graph by Agglomeration

NASA Astrophysics Data System (ADS)

Kang, Mihyun; Pachon, Angelica; Rodríguez, Pablo M.

2018-02-01

In the classical Erdős-Rényi random graph G( n, p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G( n, p) is homogeneous in the sense that all vertices have the same characteristics. On the other hand, numerous real-world networks are inhomogeneous in this respect. Such an inhomogeneity of vertices may influence the connection probability between pairs of vertices. The purpose of this paper is to propose a new inhomogeneous random graph model which is obtained in a constructive way from the Erdős-Rényi random graph G( n, p). Given a configuration of n vertices arranged in N subsets of vertices (we call each subset a super-vertex), we define a random graph with N super-vertices by letting two super-vertices be connected if and only if there is at least one edge between them in G( n, p). Our main result concerns the threshold for connectedness. We also analyze the phase transition for the emergence of the giant component and the degree distribution. Even though our model begins with G( n, p), it assumes the existence of some community structure encoded in the configuration. Furthermore, under certain conditions it exhibits a power law degree distribution. Both properties are important for real-world applications.

Vacuum quantum stress tensor fluctuations: A diagonalization approach

NASA Astrophysics Data System (ADS)

Schiappacasse, Enrico D.; Fewster, Christopher J.; Ford, L. H.

2018-01-01

Large vacuum fluctuations of a quantum stress tensor can be described by the asymptotic behavior of its probability distribution. Here we focus on stress tensor operators which have been averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we study a specific operator that contributes to the stress-energy tensor of a massless scalar field in Minkowski spacetime, namely, the normal ordered square of the time derivative of the field. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lend additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.

Measurements of gas hydrate formation probability distributions on a quasi-free water droplet

NASA Astrophysics Data System (ADS)

Maeda, Nobuo

2014-06-01

A High Pressure Automated Lag Time Apparatus (HP-ALTA) can measure gas hydrate formation probability distributions from water in a glass sample cell. In an HP-ALTA gas hydrate formation originates near the edges of the sample cell and gas hydrate films subsequently grow across the water-guest gas interface. It would ideally be desirable to be able to measure gas hydrate formation probability distributions of a single water droplet or mist that is freely levitating in a guest gas, but this is technically challenging. The next best option is to let a water droplet sit on top of a denser, immiscible, inert, and wall-wetting hydrophobic liquid to avoid contact of a water droplet with the solid walls. Here we report the development of a second generation HP-ALTA which can measure gas hydrate formation probability distributions of a water droplet which sits on a perfluorocarbon oil in a container that is coated with 1H,1H,2H,2H-Perfluorodecyltriethoxysilane. It was found that the gas hydrate formation probability distributions of such a quasi-free water droplet were significantly lower than those of water in a glass sample cell.

Intervals for posttest probabilities: a comparison of 5 methods.

PubMed

Mossman, D; Berger, J O

2001-01-01

Several medical articles discuss methods of constructing confidence intervals for single proportions and the likelihood ratio, but scant attention has been given to the systematic study of intervals for the posterior odds, or the positive predictive value, of a test. The authors describe 5 methods of constructing confidence intervals for posttest probabilities when estimates of sensitivity, specificity, and the pretest probability of a disorder are derived from empirical data. They then evaluate each method to determine how well the intervals' coverage properties correspond to their nominal value. When the estimates of pretest probabilities, sensitivity, and specificity are derived from more than 80 subjects and are not close to 0 or 1, all methods generate intervals with appropriate coverage properties. When these conditions are not met, however, the best-performing method is an objective Bayesian approach implemented by a simple simulation using a spreadsheet. Physicians and investigators can generate accurate confidence intervals for posttest probabilities in small-sample situations using the objective Bayesian approach.

Extending GIS Technology to Study Karst Features of Southeastern Minnesota

NASA Astrophysics Data System (ADS)

Gao, Y.; Tipping, R. G.; Alexander, E. C.; Alexander, S. C.

2001-12-01

This paper summarizes ongoing research on karst feature distribution of southeastern Minnesota. The main goals of this interdisciplinary research are: 1) to look for large-scale patterns in the rate and distribution of sinkhole development; 2) to conduct statistical tests of hypotheses about the formation of sinkholes; 3) to create management tools for land-use managers and planners; and 4) to deliver geomorphic and hydrogeologic criteria for making scientifically valid land-use policies and ethical decisions in karst areas of southeastern Minnesota. Existing county and sub-county karst feature datasets of southeastern Minnesota have been assembled into a large GIS-based database capable of analyzing the entire data set. The central database management system (DBMS) is a relational GIS-based system interacting with three modules: GIS, statistical and hydrogeologic modules. ArcInfo and ArcView were used to generate a series of 2D and 3D maps depicting karst feature distributions in southeastern Minnesota. IRIS ExplorerTM was used to produce satisfying 3D maps and animations using data exported from GIS-based database. Nearest-neighbor analysis has been used to test sinkhole distributions in different topographic and geologic settings. All current nearest-neighbor analyses testify that sinkholes in southeastern Minnesota are not evenly distributed in this area (i.e., they tend to be clustered). More detailed statistical methods such as cluster analysis, histograms, probability estimation, correlation and regression have been used to study the spatial distributions of some mapped karst features of southeastern Minnesota. A sinkhole probability map for Goodhue County has been constructed based on sinkhole distribution, bedrock geology, depth to bedrock, GIS buffer analysis and nearest-neighbor analysis. A series of karst features for Winona County including sinkholes, springs, seeps, stream sinks and outcrop has been mapped and entered into the Karst Feature Database of Southeastern Minnesota. The Karst Feature Database of Winona County is being expanded to include all the mapped karst features of southeastern Minnesota. Air photos from 1930s to 1990s of Spring Valley Cavern Area in Fillmore County were scanned and geo-referenced into our GIS system. This technology has been proved to be very useful to identify sinkholes and study the rate of sinkhole development.

Fragment size distribution in viscous bag breakup of a drop

NASA Astrophysics Data System (ADS)

Kulkarni, Varun; Bulusu, Kartik V.; Plesniak, Michael W.; Sojka, Paul E.

2015-11-01

In this study we examine the drop size distribution resulting from the fragmentation of a single drop in the presence of a continuous air jet. Specifically, we study the effect of Weber number, We, and Ohnesorge number, Oh on the disintegration process. The regime of breakup considered is observed between 12 <= We <= 16 for Oh <= 0.1. Experiments are conducted using phase Doppler anemometry. Both the number and volume fragment size probability distributions are plotted. The volume probability distribution revealed a bi-modal behavior with two distinct peaks: one corresponding to the rim fragments and the other to the bag fragments. This behavior was suppressed in the number probability distribution. Additionally, we employ an in-house particle detection code to isolate the rim fragment size distribution from the total probability distributions. Our experiments showed that the bag fragments are smaller in diameter and larger in number, while the rim fragments are larger in diameter and smaller in number. Furthermore, with increasing We for a given Ohwe observe a large number of small-diameter drops and small number of large-diameter drops. On the other hand, with increasing Oh for a fixed We the opposite is seen.

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

Bartram, Bart W.; Vaughan, Frank R.; Englehart, Richard W.

An account is given of the method used to quantify the risks accruing to the use of a radioisotope thermoelectric generator fueled by Pu-238 dioxide aboard the Space Shuttle-launched Ulysses mission. After using a Monte Carlo technique to develop probability distributions for the radiological consequences of a range of accident scenarios throughout the mission, factors affecting those consequences are identified in conjunction with their probability distributions. The functional relationship among all the factors is then established, and probability distributions for all factor effects are combined by means of a Monte Carlo technique.

Application of BIM technology in construction bidding

NASA Astrophysics Data System (ADS)

wei, Li

2017-12-01

bidding is a very important step of construction project. For the owners, bidding is the key link of selecting the best construction plan and saving the project cost to the maximum extent. For Construction Corporation, it is the key to show their construction technology which can improve the probability of winning the bid. this paper researches on the application of BIM technology in bidding process of construction project in detail, and discussesthe application of BIM technology in construction field comprehensively.

Score distributions of gapped multiple sequence alignments down to the low-probability tail

NASA Astrophysics Data System (ADS)

Fieth, Pascal; Hartmann, Alexander K.

2016-08-01

Assessing the significance of alignment scores of optimally aligned DNA or amino acid sequences can be achieved via the knowledge of the score distribution of random sequences. But this requires obtaining the distribution in the biologically relevant high-scoring region, where the probabilities are exponentially small. For gapless local alignments of infinitely long sequences this distribution is known analytically to follow a Gumbel distribution. Distributions for gapped local alignments and global alignments of finite lengths can only be obtained numerically. To obtain result for the small-probability region, specific statistical mechanics-based rare-event algorithms can be applied. In previous studies, this was achieved for pairwise alignments. They showed that, contrary to results from previous simple sampling studies, strong deviations from the Gumbel distribution occur in case of finite sequence lengths. Here we extend the studies to multiple sequence alignments with gaps, which are much more relevant for practical applications in molecular biology. We study the distributions of scores over a large range of the support, reaching probabilities as small as 10-160, for global and local (sum-of-pair scores) multiple alignments. We find that even after suitable rescaling, eliminating the sequence-length dependence, the distributions for multiple alignment differ from the pairwise alignment case. Furthermore, we also show that the previously discussed Gaussian correction to the Gumbel distribution needs to be refined, also for the case of pairwise alignments.

Site occupancy models with heterogeneous detection probabilities

USGS Publications Warehouse

Royle, J. Andrew

2006-01-01

Models for estimating the probability of occurrence of a species in the presence of imperfect detection are important in many ecological disciplines. In these ?site occupancy? models, the possibility of heterogeneity in detection probabilities among sites must be considered because variation in abundance (and other factors) among sampled sites induces variation in detection probability (p). In this article, I develop occurrence probability models that allow for heterogeneous detection probabilities by considering several common classes of mixture distributions for p. For any mixing distribution, the likelihood has the general form of a zero-inflated binomial mixture for which inference based upon integrated likelihood is straightforward. A recent paper by Link (2003, Biometrics 59, 1123?1130) demonstrates that in closed population models used for estimating population size, different classes of mixture distributions are indistinguishable from data, yet can produce very different inferences about population size. I demonstrate that this problem can also arise in models for estimating site occupancy in the presence of heterogeneous detection probabilities. The implications of this are discussed in the context of an application to avian survey data and the development of animal monitoring programs.

Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

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

Li Yupeng, E-mail: yupeng@ualberta.ca; Deutsch, Clayton V.

2012-06-15

In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells.more » In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.« less

A direct approach to estimating the number of potential fatalities from an eruption: Application to the Central Volcanic Complex of Tenerife Island

NASA Astrophysics Data System (ADS)

Marrero, J. M.; García, A.; Llinares, A.; Rodriguez-Losada, J. A.; Ortiz, R.

2012-03-01

One of the critical issues in managing volcanic crises is making the decision to evacuate a densely-populated region. In order to take a decision of such importance it is essential to estimate the cost in lives for each of the expected eruptive scenarios. One of the tools that assist in estimating the number of potential fatalities for such decision-making is the calculation of the FN-curves. In this case the FN-curve is a graphical representation that relates the frequency of the different hazards to be expected for a particular volcano or volcanic area, and the number of potential fatalities expected for each event if the zone of impact is not evacuated. In this study we propose a method for assessing the impact that a possible eruption from the Tenerife Central Volcanic Complex (CVC) would have on the population at risk. Factors taken into account include the spatial probability of the eruptive scenarios (susceptibility) and the temporal probability of the magnitudes of the eruptive scenarios. For each point or cell of the susceptibility map with greater probability, a series of probability-scaled hazard maps is constructed for the whole range of magnitudes expected. The number of potential fatalities is obtained from the intersection of the hazard maps with the spatial map of population distribution. The results show that the Emergency Plan for Tenerife must provide for the evacuation of more than 100,000 persons.

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.

Modeling highway travel time distribution with conditional probability models

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

Oliveira Neto, Francisco Moraes; Chin, Shih-Miao; Hwang, Ho-Ling

ABSTRACT Under the sponsorship of the Federal Highway Administration's Office of Freight Management and Operations, the American Transportation Research Institute (ATRI) has developed performance measures through the Freight Performance Measures (FPM) initiative. Under this program, travel speed information is derived from data collected using wireless based global positioning systems. These telemetric data systems are subscribed and used by trucking industry as an operations management tool. More than one telemetric operator submits their data dumps to ATRI on a regular basis. Each data transmission contains truck location, its travel time, and a clock time/date stamp. Data from the FPM program providesmore » a unique opportunity for studying the upstream-downstream speed distributions at different locations, as well as different time of the day and day of the week. This research is focused on the stochastic nature of successive link travel speed data on the continental United States Interstates network. Specifically, a method to estimate route probability distributions of travel time is proposed. This method uses the concepts of convolution of probability distributions and bivariate, link-to-link, conditional probability to estimate the expected distributions for the route travel time. Major contribution of this study is the consideration of speed correlation between upstream and downstream contiguous Interstate segments through conditional probability. The established conditional probability distributions, between successive segments, can be used to provide travel time reliability measures. This study also suggests an adaptive method for calculating and updating route travel time distribution as new data or information is added. This methodology can be useful to estimate performance measures as required by the recent Moving Ahead for Progress in the 21st Century Act (MAP 21).« less

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

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

Hou, Zhangshuan; Terry, Neil C.; Hubbard, Susan S.

2013-02-22

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability density functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSIM) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

Probability of success for phase III after exploratory biomarker analysis in phase II.

PubMed

Götte, Heiko; Kirchner, Marietta; Sailer, Martin Oliver

2017-05-01

The probability of success or average power describes the potential of a future trial by weighting the power with a probability distribution of the treatment effect. The treatment effect estimate from a previous trial can be used to define such a distribution. During the development of targeted therapies, it is common practice to look for predictive biomarkers. The consequence is that the trial population for phase III is often selected on the basis of the most extreme result from phase II biomarker subgroup analyses. In such a case, there is a tendency to overestimate the treatment effect. We investigate whether the overestimation of the treatment effect estimate from phase II is transformed into a positive bias for the probability of success for phase III. We simulate a phase II/III development program for targeted therapies. This simulation allows to investigate selection probabilities and allows to compare the estimated with the true probability of success. We consider the estimated probability of success with and without subgroup selection. Depending on the true treatment effects, there is a negative bias without selection because of the weighting by the phase II distribution. In comparison, selection increases the estimated probability of success. Thus, selection does not lead to a bias in probability of success if underestimation due to the phase II distribution and overestimation due to selection cancel each other out. We recommend to perform similar simulations in practice to get the necessary information about the risk and chances associated with such subgroup selection designs. Copyright © 2017 John Wiley & Sons, Ltd.

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.

Effect of inhomogeneities on high precision measurements of cosmological distances

NASA Astrophysics Data System (ADS)

Peel, Austin; Troxel, M. A.; Ishak, Mustapha

2014-12-01

We study effects of inhomogeneities on distance measures in an exact relativistic Swiss-cheese model of the Universe, focusing on the distance modulus. The model has Λ CDM background dynamics, and the "holes" are nonsymmetric structures described by the Szekeres metric. The Szekeres exact solution of Einstein's equations, which is inhomogeneous and anisotropic, allows us to capture potentially relevant effects on light propagation due to nontrivial evolution of structures in an exact framework. Light beams traversing a single Szekeres structure in different ways can experience either magnification or demagnification, depending on the particular path. Consistent with expectations, we find a shift in the distance modulus μ to distant sources due to demagnification when the light beam travels primarily through the void regions of our model. Conversely, beams are magnified when they propagate mainly through the overdense regions of the structures, and we explore a small additional effect due to time evolution of the structures. We then study the probability distributions of Δ μ =μΛ CDM-μSC for sources at different redshifts in various Swiss-cheese constructions, where the light beams travel through a large number of randomly oriented Szekeres holes with random impact parameters. We find for Δ μ the dispersions 0.004 ≤σΔ μ≤0.008 mag for sources with redshifts 1.0 ≤z ≤1.5 , which are smaller than the intrinsic dispersion of, for example, magnitudes of type Ia supernovae. The shapes of the distributions we obtain for our Swiss-cheese constructions are peculiar in the sense that they are not consistently skewed toward the demagnification side, as they are in analyses of lensing in cosmological simulations. Depending on the source redshift, the distributions for our models can be skewed to either the demagnification or the magnification side, reflecting a limitation of these constructions. This could be the result of requiring the continuity of Einstein's equations throughout the overall spacetime patchwork, which imposes the condition that compensating overdense shells must accompany the underdense void regions in the holes. The possibility to explore other uses of these constructions that could circumvent this limitation and lead to different statistics remains open.

Stochastic analysis of particle movement over a dune bed

USGS Publications Warehouse

Lee, Baum K.; Jobson, Harvey E.

1977-01-01

Stochastic models are available that can be used to predict the transport and dispersion of bed-material sediment particles in an alluvial channel. These models are based on the proposition that the movement of a single bed-material sediment particle consists of a series of steps of random length separated by rest periods of random duration and, therefore, application of the models requires a knowledge of the probability distributions of the step lengths, the rest periods, the elevation of particle deposition, and the elevation of particle erosion. The procedure was tested by determining distributions from bed profiles formed in a large laboratory flume with a coarse sand as the bed material. The elevation of particle deposition and the elevation of particle erosion can be considered to be identically distributed, and their distribution can be described by either a ' truncated Gaussian ' or a ' triangular ' density function. The conditional probability distribution of the rest period given the elevation of particle deposition closely followed the two-parameter gamma distribution. The conditional probability distribution of the step length given the elevation of particle erosion and the elevation of particle deposition also closely followed the two-parameter gamma density function. For a given flow, the scale and shape parameters describing the gamma probability distributions can be expressed as functions of bed-elevation. (Woodard-USGS)

14 CFR 33.17 - Fire protection.

Code of Federal Regulations, 2011 CFR

2011-01-01

... STANDARDS: AIRCRAFT ENGINES Design and Construction; General § 33.17 Fire protection. (a) The design and... addition, the design and construction of turbine engines must minimize the probability of the occurrence of...

Using type IV Pearson distribution to calculate the probabilities of underrun and overrun of lists of multiple cases.

PubMed

Wang, Jihan; Yang, Kai

2014-07-01

An efficient operating room needs both little underutilised and overutilised time to achieve optimal cost efficiency. The probabilities of underrun and overrun of lists of cases can be estimated by a well defined duration distribution of the lists. To propose a method of predicting the probabilities of underrun and overrun of lists of cases using Type IV Pearson distribution to support case scheduling. Six years of data were collected. The first 5 years of data were used to fit distributions and estimate parameters. The data from the last year were used as testing data to validate the proposed methods. The percentiles of the duration distribution of lists of cases were calculated by Type IV Pearson distribution and t-distribution. Monte Carlo simulation was conducted to verify the accuracy of percentiles defined by the proposed methods. Operating rooms in John D. Dingell VA Medical Center, United States, from January 2005 to December 2011. Differences between the proportion of lists of cases that were completed within the percentiles of the proposed duration distribution of the lists and the corresponding percentiles. Compared with the t-distribution, the proposed new distribution is 8.31% (0.38) more accurate on average and 14.16% (0.19) more accurate in calculating the probabilities at the 10th and 90th percentiles of the distribution, which is a major concern of operating room schedulers. The absolute deviations between the percentiles defined by Type IV Pearson distribution and those from Monte Carlo simulation varied from 0.20  min (0.01) to 0.43  min (0.03). Operating room schedulers can rely on the most recent 10 cases with the same combination of surgeon and procedure(s) for distribution parameter estimation to plan lists of cases. Values are mean (SEM). The proposed Type IV Pearson distribution is more accurate than t-distribution to estimate the probabilities of underrun and overrun of lists of cases. However, as not all the individual case durations followed log-normal distributions, there was some deviation from the true duration distribution of the lists.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

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

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The approach used follows the non-equilibrium statistical mechanical approach through a master equation. The aim is to represent the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and mass flux is a non-linear function of convective cell area, mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated mass flux variability under diurnally varying forcing. Besides its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to be capable of providing alternative, non-equilibrium, closure formulations for spectral mass flux parameterizations.« less

A tool for simulating collision probabilities of animals with marine renewable energy devices.

PubMed

Schmitt, Pál; Culloch, Ross; Lieber, Lilian; Molander, Sverker; Hammar, Linus; Kregting, Louise

2017-01-01

The mathematical problem of establishing a collision probability distribution is often not trivial. The shape and motion of the animal as well as of the the device must be evaluated in a four-dimensional space (3D motion over time). Earlier work on wind and tidal turbines was limited to a simplified two-dimensional representation, which cannot be applied to many new structures. We present a numerical algorithm to obtain such probability distributions using transient, three-dimensional numerical simulations. The method is demonstrated using a sub-surface tidal kite as an example. Necessary pre- and post-processing of the data created by the model is explained, numerical details and potential issues and limitations in the application of resulting probability distributions are highlighted.

Lognormal Approximations of Fault Tree Uncertainty Distributions.

PubMed

El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P

2018-01-26

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.

Quantum key distribution without the wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key distribution allows a much more general and abstract access than commonly thought. The results include some generalizations of the Hilbert space version of quantum key distribution, but are based upon a general nonclassical extension of conditional probability. A special state-independent conditional probability is identified as origin of the superior security of quantum key distribution; this is a purely algebraic property of the quantum logic and represents the transition probability between the outcomes of two consecutive quantum measurements.

The complexity of divisibility.

PubMed

Bausch, Johannes; Cubitt, Toby

2016-09-01

We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive trace-preserving maps, i.e. the quantum analogue of stochastic matrices. We further prove a complexity hierarchy for the divisibility and decomposability of probability distributions, showing that finite distribution divisibility is in P, but decomposability is NP-hard. For the former, we give an explicit polynomial-time algorithm. All results on distributions extend to weak-membership formulations, proving that the complexity of these problems is robust to perturbations.

Probability distributions of hydraulic conductivity for the hydrogeologic units of the Death Valley regional ground-water flow system, Nevada and California

USGS Publications Warehouse

Belcher, Wayne R.; Sweetkind, Donald S.; Elliott, Peggy E.

2002-01-01

The use of geologic information such as lithology and rock properties is important to constrain conceptual and numerical hydrogeologic models. This geologic information is difficult to apply explicitly to numerical modeling and analyses because it tends to be qualitative rather than quantitative. This study uses a compilation of hydraulic-conductivity measurements to derive estimates of the probability distributions for several hydrogeologic units within the Death Valley regional ground-water flow system, a geologically and hydrologically complex region underlain by basin-fill sediments, volcanic, intrusive, sedimentary, and metamorphic rocks. Probability distributions of hydraulic conductivity for general rock types have been studied previously; however, this study provides more detailed definition of hydrogeologic units based on lithostratigraphy, lithology, alteration, and fracturing and compares the probability distributions to the aquifer test data. Results suggest that these probability distributions can be used for studies involving, for example, numerical flow modeling, recharge, evapotranspiration, and rainfall runoff. These probability distributions can be used for such studies involving the hydrogeologic units in the region, as well as for similar rock types elsewhere. Within the study area, fracturing appears to have the greatest influence on the hydraulic conductivity of carbonate bedrock hydrogeologic units. Similar to earlier studies, we find that alteration and welding in the Tertiary volcanic rocks greatly influence hydraulic conductivity. As alteration increases, hydraulic conductivity tends to decrease. Increasing degrees of welding appears to increase hydraulic conductivity because welding increases the brittleness of the volcanic rocks, thus increasing the amount of fracturing.

Identification, prediction, and mitigation of sinkhole hazards in evaporite karst areas

USGS Publications Warehouse

Gutierrez, F.; Cooper, A.H.; Johnson, K.S.

2008-01-01

Sinkholes usually have a higher probability of occurrence and a greater genetic diversity in evaporite terrains than in carbonate karst areas. This is because evaporites have a higher solubility and, commonly, a lower mechanical strength. Subsidence damage resulting from evaporite dissolution generates substantial losses throughout the world, but the causes are only well understood in a few areas. To deal with these hazards, a phased approach is needed for sinkhole identification, investigation, prediction, and mitigation. Identification techniques include field surveys and geomorphological mapping combined with accounts from local people and historical sources. Detailed sinkhole maps can be constructed from sequential historical maps, recent topographical maps, and digital elevation models (DEMs) complemented with building-damage surveying, remote sensing, and high-resolution geodetic surveys. On a more detailed level, information from exposed paleosubsidence features (paleokarst), speleological explorations, geophysical investigations, trenching, dating techniques, and boreholes may help in investigating dissolution and subsidence features. Information on the hydrogeological pathways including caves, springs, and swallow holes are particularly important especially when corroborated by tracer tests. These diverse data sources make a valuable database-the karst inventory. From this dataset, sinkhole susceptibility zonations (relative probability) may be produced based on the spatial distribution of the features and good knowledge of the local geology. Sinkhole distribution can be investigated by spatial distribution analysis techniques including studies of preferential elongation, alignment, and nearest neighbor analysis. More objective susceptibility models may be obtained by analyzing the statistical relationships between the known sinkholes and the conditioning factors. Chronological information on sinkhole formation is required to estimate the probability of occurrence of sinkholes (number of sinkholes/km2 year). Such spatial and temporal predictions, frequently derived from limited records and based on the assumption that past sinkhole activity may be extrapolated to the future, are non-corroborated hypotheses. Validation methods allow us to assess the predictive capability of the susceptibility maps and to transform them into probability maps. Avoiding the most hazardous areas by preventive planning is the safest strategy for development in sinkhole-prone areas. Corrective measures could be applied to reduce the dissolution activity and subsidence processes. A more practical solution for safe development is to reduce the vulnerability of the structures by using subsidence-proof designs. ?? 2007 Springer-Verlag.

The statistics of Pearce element diagrams and the Chayes closure problem

NASA Astrophysics Data System (ADS)

Nicholls, J.

1988-05-01

Pearce element ratios are defined as having a constituent in their denominator that is conserved in a system undergoing change. The presence of a conserved element in the denominator simplifies the statistics of such ratios and renders them subject to statistical tests, especially tests of significance of the correlation coefficient between Pearce element ratios. Pearce element ratio diagrams provide unambigous tests of petrologic hypotheses because they are based on the stoichiometry of rock-forming minerals. There are three ways to recognize a conserved element: 1. The petrologic behavior of the element can be used to select conserved ones. They are usually the incompatible elements. 2. The ratio of two conserved elements will be constant in a comagmatic suite. 3. An element ratio diagram that is not constructed with a conserved element in the denominator will have a trend with a near zero intercept. The last two criteria can be tested statistically. The significance of the slope, intercept and correlation coefficient can be tested by estimating the probability of obtaining the observed values from a random population of arrays. This population of arrays must satisfy two criteria: 1. The population must contain at least one array that has the means and variances of the array of analytical data for the rock suite. 2. Arrays with the means and variances of the data must not be so abundant in the population that nearly every array selected at random has the properties of the data. The population of random closed arrays can be obtained from a population of open arrays whose elements are randomly selected from probability distributions. The means and variances of these probability distributions are themselves selected from probability distributions which have means and variances equal to a hypothetical open array that would give the means and variances of the data on closure. This hypothetical open array is called the Chayes array. Alternatively, the population of random closed arrays can be drawn from the compositional space available to rock-forming processes. The minerals comprising the available space can be described with one additive component per mineral phase and a small number of exchange components. This space is called Thompson space. Statistics based on either space lead to the conclusion that Pearce element ratios are statistically valid and that Pearce element diagrams depict the processes that create chemical inhomogeneities in igneous rock suites.

Algorithmic universality in F-theory compactifications

NASA Astrophysics Data System (ADS)

Halverson, James; Long, Cody; Sung, Benjamin

2017-12-01

We study universality of geometric gauge sectors in the string landscape in the context of F-theory compactifications. A finite time construction algorithm is presented for 4/3 ×2.96 ×10755 F-theory geometries that are connected by a network of topological transitions in a connected moduli space. High probability geometric assumptions uncover universal structures in the ensemble without explicitly constructing it. For example, non-Higgsable clusters of seven-branes with intricate gauge sectors occur with a probability above 1 - 1.01 ×10-755 , and the geometric gauge group rank is above 160 with probability 0.999995. In the latter case there are at least 10 E8 factors, the structure of which fixes the gauge groups on certain nearby seven-branes. Visible sectors may arise from E6 or S U (3 ) seven-branes, which occur in certain random samples with probability ≃1 /200 .

Bayesian alternative to the ISO-GUM's use of the Welch Satterthwaite formula

NASA Astrophysics Data System (ADS)

Kacker, Raghu N.

2006-02-01

In certain disciplines, uncertainty is traditionally expressed as an interval about an estimate for the value of the measurand. Development of such uncertainty intervals with a stated coverage probability based on the International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) requires a description of the probability distribution for the value of the measurand. The ISO-GUM propagates the estimates and their associated standard uncertainties for various input quantities through a linear approximation of the measurement equation to determine an estimate and its associated standard uncertainty for the value of the measurand. This procedure does not yield a probability distribution for the value of the measurand. The ISO-GUM suggests that under certain conditions motivated by the central limit theorem the distribution for the value of the measurand may be approximated by a scaled-and-shifted t-distribution with effective degrees of freedom obtained from the Welch-Satterthwaite (W-S) formula. The approximate t-distribution may then be used to develop an uncertainty interval with a stated coverage probability for the value of the measurand. We propose an approximate normal distribution based on a Bayesian uncertainty as an alternative to the t-distribution based on the W-S formula. A benefit of the approximate normal distribution based on a Bayesian uncertainty is that it greatly simplifies the expression of uncertainty by eliminating altogether the need for calculating effective degrees of freedom from the W-S formula. In the special case where the measurand is the difference between two means, each evaluated from statistical analyses of independent normally distributed measurements with unknown and possibly unequal variances, the probability distribution for the value of the measurand is known to be a Behrens-Fisher distribution. We compare the performance of the approximate normal distribution based on a Bayesian uncertainty and the approximate t-distribution based on the W-S formula with respect to the Behrens-Fisher distribution. The approximate normal distribution is simpler and better in this case. A thorough investigation of the relative performance of the two approximate distributions would require comparison for a range of measurement equations by numerical methods.

Does Litter Size Variation Affect Models of Terrestrial Carnivore Extinction Risk and Management?

PubMed Central

Devenish-Nelson, Eleanor S.; Stephens, Philip A.; Harris, Stephen; Soulsbury, Carl; Richards, Shane A.

2013-01-01

Background Individual variation in both survival and reproduction has the potential to influence extinction risk. Especially for rare or threatened species, reliable population models should adequately incorporate demographic uncertainty. Here, we focus on an important form of demographic stochasticity: variation in litter sizes. We use terrestrial carnivores as an example taxon, as they are frequently threatened or of economic importance. Since data on intraspecific litter size variation are often sparse, it is unclear what probability distribution should be used to describe the pattern of litter size variation for multiparous carnivores. Methodology/Principal Findings We used litter size data on 32 terrestrial carnivore species to test the fit of 12 probability distributions. The influence of these distributions on quasi-extinction probabilities and the probability of successful disease control was then examined for three canid species – the island fox Urocyon littoralis, the red fox Vulpes vulpes, and the African wild dog Lycaon pictus. Best fitting probability distributions differed among the carnivores examined. However, the discretised normal distribution provided the best fit for the majority of species, because variation among litter-sizes was often small. Importantly, however, the outcomes of demographic models were generally robust to the distribution used. Conclusion/Significance These results provide reassurance for those using demographic modelling for the management of less studied carnivores in which litter size variation is estimated using data from species with similar reproductive attributes. PMID:23469140

Does litter size variation affect models of terrestrial carnivore extinction risk and management?

PubMed

Devenish-Nelson, Eleanor S; Stephens, Philip A; Harris, Stephen; Soulsbury, Carl; Richards, Shane A

2013-01-01

Individual variation in both survival and reproduction has the potential to influence extinction risk. Especially for rare or threatened species, reliable population models should adequately incorporate demographic uncertainty. Here, we focus on an important form of demographic stochasticity: variation in litter sizes. We use terrestrial carnivores as an example taxon, as they are frequently threatened or of economic importance. Since data on intraspecific litter size variation are often sparse, it is unclear what probability distribution should be used to describe the pattern of litter size variation for multiparous carnivores. We used litter size data on 32 terrestrial carnivore species to test the fit of 12 probability distributions. The influence of these distributions on quasi-extinction probabilities and the probability of successful disease control was then examined for three canid species - the island fox Urocyon littoralis, the red fox Vulpes vulpes, and the African wild dog Lycaon pictus. Best fitting probability distributions differed among the carnivores examined. However, the discretised normal distribution provided the best fit for the majority of species, because variation among litter-sizes was often small. Importantly, however, the outcomes of demographic models were generally robust to the distribution used. These results provide reassurance for those using demographic modelling for the management of less studied carnivores in which litter size variation is estimated using data from species with similar reproductive attributes.

Neighbor-Dependent Ramachandran Probability Distributions of Amino Acids Developed from a Hierarchical Dirichlet Process Model

PubMed Central

Mitra, Rajib; Jordan, Michael I.; Dunbrack, Roland L.

2010-01-01

Distributions of the backbone dihedral angles of proteins have been studied for over 40 years. While many statistical analyses have been presented, only a handful of probability densities are publicly available for use in structure validation and structure prediction methods. The available distributions differ in a number of important ways, which determine their usefulness for various purposes. These include: 1) input data size and criteria for structure inclusion (resolution, R-factor, etc.); 2) filtering of suspect conformations and outliers using B-factors or other features; 3) secondary structure of input data (e.g., whether helix and sheet are included; whether beta turns are included); 4) the method used for determining probability densities ranging from simple histograms to modern nonparametric density estimation; and 5) whether they include nearest neighbor effects on the distribution of conformations in different regions of the Ramachandran map. In this work, Ramachandran probability distributions are presented for residues in protein loops from a high-resolution data set with filtering based on calculated electron densities. Distributions for all 20 amino acids (with cis and trans proline treated separately) have been determined, as well as 420 left-neighbor and 420 right-neighbor dependent distributions. The neighbor-independent and neighbor-dependent probability densities have been accurately estimated using Bayesian nonparametric statistical analysis based on the Dirichlet process. In particular, we used hierarchical Dirichlet process priors, which allow sharing of information between densities for a particular residue type and different neighbor residue types. The resulting distributions are tested in a loop modeling benchmark with the program Rosetta, and are shown to improve protein loop conformation prediction significantly. The distributions are available at http://dunbrack.fccc.edu/hdp. PMID:20442867

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.

Comparative analysis through probability distributions of a data set

NASA Astrophysics Data System (ADS)

Cristea, Gabriel; Constantinescu, Dan Mihai

2018-02-01

In practice, probability distributions are applied in such diverse fields as risk analysis, reliability engineering, chemical engineering, hydrology, image processing, physics, market research, business and economic research, customer support, medicine, sociology, demography etc. This article highlights important aspects of fitting probability distributions to data and applying the analysis results to make informed decisions. There are a number of statistical methods available which can help us to select the best fitting model. Some of the graphs display both input data and fitted distributions at the same time, as probability density and cumulative distribution. The goodness of fit tests can be used to determine whether a certain distribution is a good fit. The main used idea is to measure the "distance" between the data and the tested distribution, and compare that distance to some threshold values. Calculating the goodness of fit statistics also enables us to order the fitted distributions accordingly to how good they fit to data. This particular feature is very helpful for comparing the fitted models. The paper presents a comparison of most commonly used goodness of fit tests as: Kolmogorov-Smirnov, Anderson-Darling, and Chi-Squared. A large set of data is analyzed and conclusions are drawn by visualizing the data, comparing multiple fitted distributions and selecting the best model. These graphs should be viewed as an addition to the goodness of fit tests.

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.

Semi-automatic segmentation of brain tumors using population and individual information.

PubMed

Wu, Yao; Yang, Wei; Jiang, Jun; Li, Shuanqian; Feng, Qianjin; Chen, Wufan

2013-08-01

Efficient segmentation of tumors in medical images is of great practical importance in early diagnosis and radiation plan. This paper proposes a novel semi-automatic segmentation method based on population and individual statistical information to segment brain tumors in magnetic resonance (MR) images. First, high-dimensional image features are extracted. Neighborhood components analysis is proposed to learn two optimal distance metrics, which contain population and patient-specific information, respectively. The probability of each pixel belonging to the foreground (tumor) and the background is estimated by the k-nearest neighborhood classifier under the learned optimal distance metrics. A cost function for segmentation is constructed through these probabilities and is optimized using graph cuts. Finally, some morphological operations are performed to improve the achieved segmentation results. Our dataset consists of 137 brain MR images, including 68 for training and 69 for testing. The proposed method overcomes segmentation difficulties caused by the uneven gray level distribution of the tumors and even can get satisfactory results if the tumors have fuzzy edges. Experimental results demonstrate that the proposed method is robust to brain tumor segmentation.

Predicting the Distribution of Vibrio spp. in the Chesapeake Bay: A Vibrio cholerae Case Study

PubMed Central

Magny, Guillaume Constantin de; Long, Wen; Brown, Christopher W.; Hood, Raleigh R.; Huq, Anwar; Murtugudde, Raghu; Colwell, Rita R.

2010-01-01

Vibrio cholerae, the causative agent of cholera, is a naturally occurring inhabitant of the Chesapeake Bay and serves as a predictor for other clinically important vibrios, including Vibrio parahaemolyticus and Vibrio vulnificus. A system was constructed to predict the likelihood of the presence of V. cholerae in surface waters of the Chesapeake Bay, with the goal to provide forecasts of the occurrence of this and related pathogenic Vibrio spp. Prediction was achieved by driving an available multivariate empirical habitat model estimating the probability of V. cholerae within a range of temperatures and salinities in the Bay, with hydrodynamically generated predictions of ambient temperature and salinity. The experimental predictions provided both an improved understanding of the in situ variability of V. cholerae, including identification of potential hotspots of occurrence, and usefulness as an early warning system. With further development of the system, prediction of the probability of the occurrence of related pathogenic vibrios in the Chesapeake Bay, notably V. parahaemolyticus and V. vulnificus, will be possible, as well as its transport to any geographical location where sufficient relevant data are available. PMID:20145974

Optimizing DNA assembly based on statistical language modelling.

PubMed

Fang, Gang; Zhang, Shemin; Dong, Yafei

2017-12-15

By successively assembling genetic parts such as BioBrick according to grammatical models, complex genetic constructs composed of dozens of functional blocks can be built. However, usually every category of genetic parts includes a few or many parts. With increasing quantity of genetic parts, the process of assembling more than a few sets of these parts can be expensive, time consuming and error prone. At the last step of assembling it is somewhat difficult to decide which part should be selected. Based on statistical language model, which is a probability distribution P(s) over strings S that attempts to reflect how frequently a string S occurs as a sentence, the most commonly used parts will be selected. Then, a dynamic programming algorithm was designed to figure out the solution of maximum probability. The algorithm optimizes the results of a genetic design based on a grammatical model and finds an optimal solution. In this way, redundant operations can be reduced and the time and cost required for conducting biological experiments can be minimized. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

Transient Properties of Probability Distribution for a Markov Process with Size-dependent Additive Noise

NASA Astrophysics Data System (ADS)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

This study considered a stochastic model for cluster growth in a Markov process with a cluster size dependent additive noise. According to this model, the probability distribution of the cluster size transiently becomes an exponential or a log-normal distribution depending on the initial condition of the growth. In this letter, a master equation is obtained for this model, and derivation of the distributions is discussed.

q-Gaussian distributions and multiplicative stochastic processes for analysis of multiple financial time series

NASA Astrophysics Data System (ADS)

Sato, Aki-Hiro

2010-12-01

This study considers q-Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a q-Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both mutually independent multiplicative and additive noises. By using the proposed stochastic differential equation a method to evaluate a default probability under a given risk buffer is proposed.

Net present value probability distributions from decline curve reserves estimates

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

Simpson, D.E.; Huffman, C.H.; Thompson, R.S.

1995-12-31

This paper demonstrates how reserves probability distributions can be used to develop net present value (NPV) distributions. NPV probability distributions were developed from the rate and reserves distributions presented in SPE 28333. This real data study used practicing engineer`s evaluations of production histories. Two approaches were examined to quantify portfolio risk. The first approach, the NPV Relative Risk Plot, compares the mean NPV with the NPV relative risk ratio for the portfolio. The relative risk ratio is the NPV standard deviation (a) divided the mean ({mu}) NPV. The second approach, a Risk - Return Plot, is a plot of themore » {mu} discounted cash flow rate of return (DCFROR) versus the {sigma} for the DCFROR distribution. This plot provides a risk-return relationship for comparing various portfolios. These methods may help evaluate property acquisition and divestiture alternatives and assess the relative risk of a suite of wells or fields for bank loans.« less

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.

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

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

Thapliyal, Kishore, E-mail: tkishore36@yahoo.com; Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in; Pathak, Anirban, E-mail: anirban.pathak@gmail.com

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained frommore » experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.« less

Making sense of sparse rating data in collaborative filtering via topographic organization of user preference patterns.

PubMed

Polcicová, Gabriela; Tino, Peter

2004-01-01

We introduce topographic versions of two latent class models (LCM) for collaborative filtering. Latent classes are topologically organized on a square grid. Topographic organization of latent classes makes orientation in rating/preference patterns captured by the latent classes easier and more systematic. The variation in film rating patterns is modelled by multinomial and binomial distributions with varying independence assumptions. In the first stage of topographic LCM construction, self-organizing maps with neural field organized according to the LCM topology are employed. We apply our system to a large collection of user ratings for films. The system can provide useful visualization plots unveiling user preference patterns buried in the data, without loosing potential to be a good recommender model. It appears that multinomial distribution is most adequate if the model is regularized by tight grid topologies. Since we deal with probabilistic models of the data, we can readily use tools from probability and information theories to interpret and visualize information extracted by our system.

Deriving photometric redshifts using fuzzy archetypes and self-organizing maps - I. Methodology

NASA Astrophysics Data System (ADS)

Speagle, Joshua S.; Eisenstein, Daniel J.

2017-07-01

We propose a method to substantially increase the flexibility and power of template fitting-based photometric redshifts by transforming a large number of galaxy spectral templates into a corresponding collection of 'fuzzy archetypes' using a suitable set of perturbative priors designed to account for empirical variation in dust attenuation and emission-line strengths. To bypass widely separated degeneracies in parameter space (e.g. the redshift-reddening degeneracy), we train self-organizing maps (SOMs) on large 'model catalogues' generated from Monte Carlo sampling of our fuzzy archetypes to cluster the predicted observables in a topologically smooth fashion. Subsequent sampling over the SOM then allows full reconstruction of the relevant probability distribution functions (PDFs). This combined approach enables the multimodal exploration of known variation among galaxy spectral energy distributions with minimal modelling assumptions. We demonstrate the power of this approach to recover full redshift PDFs using discrete Markov chain Monte Carlo sampling methods combined with SOMs constructed from Large Synoptic Survey Telescope ugrizY and Euclid YJH mock photometry.

Order-restricted inference for means with missing values.

PubMed

Wang, Heng; Zhong, Ping-Shou

2017-09-01

Missing values appear very often in many applications, but the problem of missing values has not received much attention in testing order-restricted alternatives. Under the missing at random (MAR) assumption, we impute the missing values nonparametrically using kernel regression. For data with imputation, the classical likelihood ratio test designed for testing the order-restricted means is no longer applicable since the likelihood does not exist. This article proposes a novel method for constructing test statistics for assessing means with an increasing order or a decreasing order based on jackknife empirical likelihood (JEL) ratio. It is shown that the JEL ratio statistic evaluated under the null hypothesis converges to a chi-bar-square distribution, whose weights depend on missing probabilities and nonparametric imputation. Simulation study shows that the proposed test performs well under various missing scenarios and is robust for normally and nonnormally distributed data. The proposed method is applied to an Alzheimer's disease neuroimaging initiative data set for finding a biomarker for the diagnosis of the Alzheimer's disease. © 2017, The International Biometric Society.

Correlation between friction and thickness of vanadium-pentoxide nanowires

NASA Astrophysics Data System (ADS)

Kim, Taekyeong

2015-11-01

We investigated the correlation between friction and thickness of vanadium-pentoxide nanowires (V2O5 NWs) by using friction/atomic force microscopy (FFM/AFM). We observed that the friction signal generally increased with thickness in the FFM/AFM image of the V2O5 NWs. We constructed a two-dimensional (2D) correlation distribution of the frictional force and the thickness of the V2O5 NWs and found that they are strongly correlated; i.e., thicker NWs had higher friction. We also generated a histogram for the correlation factors obtained from each distribution and found that the most probable factor is ~0.45. Furthermore, we found that the adhesion force between the tip and the V2O5 NWs was about -3 nN, and that the friction increased with increasing applied load for different thicknesses of V2O5 NWs. Our results provide an understanding of tribological and nanomechanical studies of various one-dimensional NWs for future fundamental research.

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

The applicability of ordinary least squares to consistently short distances between taxa in phylogenetic tree construction and the normal distribution test consequences.

PubMed

Roux, C Z

2009-05-01

Short phylogenetic distances between taxa occur, for example, in studies on ribosomal RNA-genes with slow substitution rates. For consistently short distances, it is proved that in the completely singular limit of the covariance matrix ordinary least squares (OLS) estimates are minimum variance or best linear unbiased (BLU) estimates of phylogenetic tree branch lengths. Although OLS estimates are in this situation equal to generalized least squares (GLS) estimates, the GLS chi-square likelihood ratio test will be inapplicable as it is associated with zero degrees of freedom. Consequently, an OLS normal distribution test or an analogous bootstrap approach will provide optimal branch length tests of significance for consistently short phylogenetic distances. As the asymptotic covariances between branch lengths will be equal to zero, it follows that the product rule can be used in tree evaluation to calculate an approximate simultaneous confidence probability that all interior branches are positive.

Generalized Entanglement Entropy and Holography

NASA Astrophysics Data System (ADS)

Obregón, O.

2018-04-01

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ 2) distribution that depends on β and also on pl . The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2dCFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV (for c = 1) ones and also than those due to the area dependent AdS 3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS 3 area dependent entropy.

Pricing foreign equity option under stochastic volatility tempered stable Lévy processes

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2017-10-01

Considering that financial assets returns exhibit leptokurtosis, asymmetry properties as well as clustering and heteroskedasticity effect, this paper substitutes the logarithm normal jumps in Heston stochastic volatility model by the classical tempered stable (CTS) distribution and normal tempered stable (NTS) distribution to construct stochastic volatility tempered stable Lévy processes (TSSV) model. The TSSV model framework permits infinite activity jump behaviors of return dynamics and time varying volatility consistently observed in financial markets through subordinating tempered stable process to stochastic volatility process, capturing leptokurtosis, fat tailedness and asymmetry features of returns. By employing the analytical characteristic function and fast Fourier transform (FFT) technique, the formula for probability density function (PDF) of TSSV returns is derived, making the analytical formula for foreign equity option (FEO) pricing available. High frequency financial returns data are employed to verify the effectiveness of proposed models in reflecting the stylized facts of financial markets. Numerical analysis is performed to investigate the relationship between the corresponding parameters and the implied volatility of foreign equity option.

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.

Development and application of an empirical probability distribution for the prediction error of re-entry body maximum dynamic pressure

NASA Technical Reports Server (NTRS)

Lanzi, R. James; Vincent, Brett T.

1993-01-01

The relationship between actual and predicted re-entry maximum dynamic pressure is characterized using a probability density function and a cumulative distribution function derived from sounding rocket flight data. This paper explores the properties of this distribution and demonstrates applications of this data with observed sounding rocket re-entry body damage characteristics to assess probabilities of sustaining various levels of heating damage. The results from this paper effectively bridge the gap existing in sounding rocket reentry analysis between the known damage level/flight environment relationships and the predicted flight environment.

Probability and the changing shape of response distributions for orientation.

PubMed

Anderson, Britt

2014-11-18

Spatial attention and feature-based attention are regarded as two independent mechanisms for biasing the processing of sensory stimuli. Feature attention is held to be a spatially invariant mechanism that advantages a single feature per sensory dimension. In contrast to the prediction of location independence, I found that participants were able to report the orientation of a briefly presented visual grating better for targets defined by high probability conjunctions of features and locations even when orientations and locations were individually uniform. The advantage for high-probability conjunctions was accompanied by changes in the shape of the response distributions. High-probability conjunctions had error distributions that were not normally distributed but demonstrated increased kurtosis. The increase in kurtosis could be explained as a change in the variances of the component tuning functions that comprise a population mixture. By changing the mixture distribution of orientation-tuned neurons, it is possible to change the shape of the discrimination function. This prompts the suggestion that attention may not "increase" the quality of perceptual processing in an absolute sense but rather prioritizes some stimuli over others. This results in an increased number of highly accurate responses to probable targets and, simultaneously, an increase in the number of very inaccurate responses. © 2014 ARVO.

Vector wind and vector wind shear models 0 to 27 km altitude for Cape Kennedy, Florida, and Vandenberg AFB, California

NASA Technical Reports Server (NTRS)

Smith, O. E.

1976-01-01

The techniques are presented to derive several statistical wind models. The techniques are from the properties of the multivariate normal probability function. Assuming that the winds can be considered as bivariate normally distributed, then (1) the wind components and conditional wind components are univariate normally distributed, (2) the wind speed is Rayleigh distributed, (3) the conditional distribution of wind speed given a wind direction is Rayleigh distributed, and (4) the frequency of wind direction can be derived. All of these distributions are derived from the 5-sample parameter of wind for the bivariate normal distribution. By further assuming that the winds at two altitudes are quadravariate normally distributed, then the vector wind shear is bivariate normally distributed and the modulus of the vector wind shear is Rayleigh distributed. The conditional probability of wind component shears given a wind component is normally distributed. Examples of these and other properties of the multivariate normal probability distribution function as applied to Cape Kennedy, Florida, and Vandenberg AFB, California, wind data samples are given. A technique to develop a synthetic vector wind profile model of interest to aerospace vehicle applications is presented.

Joint probabilities and quantum cognition

NASA Astrophysics Data System (ADS)

de Barros, J. Acacio

2012-12-01

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

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

Bradonjic, Milan; Elsasser, Robert; Friedrich, Tobias

A Randon Geometric Graph (RGG) is constructed by distributing n nodes uniformly at random in the unit square and connecting two nodes if their Euclidean distance is at most r, for some prescribed r. They analyze the following randomized broadcast algorithm on RGGs. At the beginning, there is only one informed node. Then in each round, each informed node chooses a neighbor uniformly at random and informs it. They prove that this algorithm informs every node in the largest component of a RGG in {Omicron}({radical}n/r) rounds with high probability. This holds for any value of r larger than the criticalmore » value for the emergence of a giant component. In particular, the result implies that the diameter of the giant component is {Theta}({radical}n/r).« less

Stochastic foundations in nonlinear density-regulation growth

NASA Astrophysics Data System (ADS)

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

2017-08-01

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for population extinction and calculate the mean time to extinction. If the population does not become extinct, we obtain analytical expressions for the population abundance distribution. Our theoretical results are based on WKB theory and the probability generating function formalism and are verified by numerical simulations.

Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks.

PubMed

Zhuang, Jiancang; Ogata, Yosihiko

2006-04-01

The space-time epidemic-type aftershock sequence model is a stochastic branching process in which earthquake activity is classified into background and clustering components and each earthquake triggers other earthquakes independently according to certain rules. This paper gives the probability distributions associated with the largest event in a cluster and their properties for all three cases when the process is subcritical, critical, and supercritical. One of the direct uses of these probability distributions is to evaluate the probability of an earthquake to be a foreshock, and magnitude distributions of foreshocks and nonforeshock earthquakes. To verify these theoretical results, the Japan Meteorological Agency earthquake catalog is analyzed. The proportion of events that have 1 or more larger descendants in total events is found to be as high as about 15%. When the differences between background events and triggered event in the behavior of triggering children are considered, a background event has a probability about 8% to be a foreshock. This probability decreases when the magnitude of the background event increases. These results, obtained from a complicated clustering model, where the characteristics of background events and triggered events are different, are consistent with the results obtained in [Ogata, Geophys. J. Int. 127, 17 (1996)] by using the conventional single-linked cluster declustering method.

Winter habitat selection of mule deer before and during development of a natural gas field

USGS Publications Warehouse

Sawyer, H.; Nielson, R.M.; Lindzey, F.; McDonald, L.L.

2006-01-01

Increased levels of natural gas exploration, development, and production across the Intermountain West have created a variety of concerns for mule deer (Odocoileus hemionus) populations, including direct habitat loss to road and well-pad construction and indirect habitat losses that may occur if deer use declines near roads or well pads. We examined winter habitat selection patterns of adult female mule deer before and during the first 3 years of development in a natural gas field in western Wyoming. We used global positioning system (GPS) locations collected from a sample of adult female mule deer to model relative frequency or probability of use as a function of habitat variables. Model coefficients and predictive maps suggested mule deer were less likely to occupy areas in close proximity to well pads than those farther away. Changes in habitat selection appeared to be immediate (i.e., year 1 of development), and no evidence of well-pad acclimation occurred through the course of the study; rather, mule deer selected areas farther from well pads as development progressed. Lower predicted probabilities of use within 2.7 to 3.7 km of well pads suggested indirect habitat losses may be substantially larger than direct habitat losses. Additionally, some areas classified as high probability of use by mule deer before gas field development changed to areas of low use following development, and others originally classified as low probability of use were used more frequently as the field developed. If areas with high probability of use before development were those preferred by the deer, observed shifts in their distribution as development progressed were toward less-preferred and presumably less-suitable habitats.

Does Breast Cancer Drive the Building of Survival Probability Models among States? An Assessment of Goodness of Fit for Patient Data from SEER Registries

PubMed

Khan, Hafiz; Saxena, Anshul; Perisetti, Abhilash; Rafiq, Aamrin; Gabbidon, Kemesha; Mende, Sarah; Lyuksyutova, Maria; Quesada, Kandi; Blakely, Summre; Torres, Tiffany; Afesse, Mahlet

2016-12-01

Background: Breast cancer is a worldwide public health concern and is the most prevalent type of cancer in women in the United States. This study concerned the best fit of statistical probability models on the basis of survival times for nine state cancer registries: California, Connecticut, Georgia, Hawaii, Iowa, Michigan, New Mexico, Utah, and Washington. Materials and Methods: A probability random sampling method was applied to select and extract records of 2,000 breast cancer patients from the Surveillance Epidemiology and End Results (SEER) database for each of the nine state cancer registries used in this study. EasyFit software was utilized to identify the best probability models by using goodness of fit tests, and to estimate parameters for various statistical probability distributions that fit survival data. Results: Statistical analysis for the summary of statistics is reported for each of the states for the years 1973 to 2012. Kolmogorov-Smirnov, Anderson-Darling, and Chi-squared goodness of fit test values were used for survival data, the highest values of goodness of fit statistics being considered indicative of the best fit survival model for each state. Conclusions: It was found that California, Connecticut, Georgia, Iowa, New Mexico, and Washington followed the Burr probability distribution, while the Dagum probability distribution gave the best fit for Michigan and Utah, and Hawaii followed the Gamma probability distribution. These findings highlight differences between states through selected sociodemographic variables and also demonstrate probability modeling differences in breast cancer survival times. The results of this study can be used to guide healthcare providers and researchers for further investigations into social and environmental factors in order to reduce the occurrence of and mortality due to breast cancer. Creative Commons Attribution License

Role of the site of synaptic competition and the balance of learning forces for Hebbian encoding of probabilistic Markov sequences

PubMed Central

Bouchard, Kristofer E.; Ganguli, Surya; Brainard, Michael S.

2015-01-01

The majority of distinct sensory and motor events occur as temporally ordered sequences with rich probabilistic structure. Sequences can be characterized by the probability of transitioning from the current state to upcoming states (forward probability), as well as the probability of having transitioned to the current state from previous states (backward probability). Despite the prevalence of probabilistic sequencing of both sensory and motor events, the Hebbian mechanisms that mold synapses to reflect the statistics of experienced probabilistic sequences are not well understood. Here, we show through analytic calculations and numerical simulations that Hebbian plasticity (correlation, covariance, and STDP) with pre-synaptic competition can develop synaptic weights equal to the conditional forward transition probabilities present in the input sequence. In contrast, post-synaptic competition can develop synaptic weights proportional to the conditional backward probabilities of the same input sequence. We demonstrate that to stably reflect the conditional probability of a neuron's inputs and outputs, local Hebbian plasticity requires balance between competitive learning forces that promote synaptic differentiation and homogenizing learning forces that promote synaptic stabilization. The balance between these forces dictates a prior over the distribution of learned synaptic weights, strongly influencing both the rate at which structure emerges and the entropy of the final distribution of synaptic weights. Together, these results demonstrate a simple correspondence between the biophysical organization of neurons, the site of synaptic competition, and the temporal flow of information encoded in synaptic weights by Hebbian plasticity while highlighting the utility of balancing learning forces to accurately encode probability distributions, and prior expectations over such probability distributions. PMID:26257637

A method to deconvolve stellar rotational velocities II. The probability distribution function via Tikhonov regularization

NASA Astrophysics Data System (ADS)

Christen, Alejandra; Escarate, Pedro; Curé, Michel; Rial, Diego F.; Cassetti, Julia

2016-10-01

Aims: Knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. Because we measure the projected rotational speed v sin I, we need to solve an ill-posed problem given by a Fredholm integral of the first kind to recover the "true" rotational velocity distribution. Methods: After discretization of the Fredholm integral we apply the Tikhonov regularization method to obtain directly the probability distribution function for stellar rotational velocities. We propose a simple and straightforward procedure to determine the Tikhonov parameter. We applied Monte Carlo simulations to prove that the Tikhonov method is a consistent estimator and asymptotically unbiased. Results: This method is applied to a sample of cluster stars. We obtain confidence intervals using a bootstrap method. Our results are in close agreement with those obtained using the Lucy method for recovering the probability density distribution of rotational velocities. Furthermore, Lucy estimation lies inside our confidence interval. Conclusions: Tikhonov regularization is a highly robust method that deconvolves the rotational velocity probability density function from a sample of v sin I data directly without the need for any convergence criteria.

Redshift-space distortions with the halo occupation distribution - II. Analytic model

NASA Astrophysics Data System (ADS)

Tinker, Jeremy L.

2007-01-01

We present an analytic model for the galaxy two-point correlation function in redshift space. The cosmological parameters of the model are the matter density Ωm, power spectrum normalization σ8, and velocity bias of galaxies αv, circumventing the linear theory distortion parameter β and eliminating nuisance parameters for non-linearities. The model is constructed within the framework of the halo occupation distribution (HOD), which quantifies galaxy bias on linear and non-linear scales. We model one-halo pairwise velocities by assuming that satellite galaxy velocities follow a Gaussian distribution with dispersion proportional to the virial dispersion of the host halo. Two-halo velocity statistics are a combination of virial motions and host halo motions. The velocity distribution function (DF) of halo pairs is a complex function with skewness and kurtosis that vary substantially with scale. Using a series of collisionless N-body simulations, we demonstrate that the shape of the velocity DF is determined primarily by the distribution of local densities around a halo pair, and at fixed density the velocity DF is close to Gaussian and nearly independent of halo mass. We calibrate a model for the conditional probability function of densities around halo pairs on these simulations. With this model, the full shape of the halo velocity DF can be accurately calculated as a function of halo mass, radial separation, angle and cosmology. The HOD approach to redshift-space distortions utilizes clustering data from linear to non-linear scales to break the standard degeneracies inherent in previous models of redshift-space clustering. The parameters of the occupation function are well constrained by real-space clustering alone, separating constraints on bias and cosmology. We demonstrate the ability of the model to separately constrain Ωm,σ8 and αv in models that are constructed to have the same value of β at large scales as well as the same finger-of-god distortions at small scales.

Receiver Operating Characteristic Analysis for Classification Based on Various Prior Probabilities of Groups with an Application to Breath Analysis

NASA Astrophysics Data System (ADS)

Cimermanová, K.

2009-01-01

In this paper we illustrate the influence of prior probabilities of diseases on diagnostic reasoning. For various prior probabilities of classified groups characterized by volatile organic compounds of breath profile, smokers and non-smokers, we constructed the ROC curve and the Youden index with related asymptotic pointwise confidence intervals.

Quantitative assessment of building fire risk to life safety.

PubMed

Guanquan, Chu; Jinhua, Sun

2008-06-01

This article presents a quantitative risk assessment framework for evaluating fire risk to life safety. Fire risk is divided into two parts: probability and corresponding consequence of every fire scenario. The time-dependent event tree technique is used to analyze probable fire scenarios based on the effect of fire protection systems on fire spread and smoke movement. To obtain the variation of occurrence probability with time, Markov chain is combined with a time-dependent event tree for stochastic analysis on the occurrence probability of fire scenarios. To obtain consequences of every fire scenario, some uncertainties are considered in the risk analysis process. When calculating the onset time to untenable conditions, a range of fires are designed based on different fire growth rates, after which uncertainty of onset time to untenable conditions can be characterized by probability distribution. When calculating occupant evacuation time, occupant premovement time is considered as a probability distribution. Consequences of a fire scenario can be evaluated according to probability distribution of evacuation time and onset time of untenable conditions. Then, fire risk to life safety can be evaluated based on occurrence probability and consequences of every fire scenario. To express the risk assessment method in detail, a commercial building is presented as a case study. A discussion compares the assessment result of the case study with fire statistics.

Competing risk models in reliability systems, an exponential distribution model with Bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, I.

2018-03-01

The exponential distribution is the most widely used reliability analysis. This distribution is very suitable for representing the lengths of life of many cases and is available in a simple statistical form. The characteristic of this distribution is a constant hazard rate. The exponential distribution is the lower rank of the Weibull distributions. In this paper our effort is to introduce the basic notions that constitute an exponential competing risks model in reliability analysis using Bayesian analysis approach and presenting their analytic methods. The cases are limited to the models with independent causes of failure. A non-informative prior distribution is used in our analysis. This model describes the likelihood function and follows with the description of the posterior function and the estimations of the point, interval, hazard function, and reliability. The net probability of failure if only one specific risk is present, crude probability of failure due to a specific risk in the presence of other causes, and partial crude probabilities are also included.

On probability-possibility transformations

NASA Technical Reports Server (NTRS)

Klir, George J.; Parviz, Behzad

1992-01-01

Several probability-possibility transformations are compared in terms of the closeness of preserving second-order properties. The comparison is based on experimental results obtained by computer simulation. Two second-order properties are involved in this study: noninteraction of two distributions and projections of a joint distribution.

Theoretical size distribution of fossil taxa: analysis of a null model.

PubMed

Reed, William J; Hughes, Barry D

2007-03-22

This article deals with the theoretical size distribution (of number of sub-taxa) of a fossil taxon arising from a simple null model of macroevolution. New species arise through speciations occurring independently and at random at a fixed probability rate, while extinctions either occur independently and at random (background extinctions) or cataclysmically. In addition new genera are assumed to arise through speciations of a very radical nature, again assumed to occur independently and at random at a fixed probability rate. The size distributions of the pioneering genus (following a cataclysm) and of derived genera are determined. Also the distribution of the number of genera is considered along with a comparison of the probability of a monospecific genus with that of a monogeneric family.

Newton/Poisson-Distribution Program

NASA Technical Reports Server (NTRS)

Bowerman, Paul N.; Scheuer, Ernest M.

1990-01-01

NEWTPOIS, one of two computer programs making calculations involving cumulative Poisson distributions. NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714) used independently of one another. NEWTPOIS determines Poisson parameter for given cumulative probability, from which one obtains percentiles for gamma distributions with integer shape parameters and percentiles for X(sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Program written in C.

Leads Detection Using Mixture Statistical Distribution Based CRF Algorithm from Sentinel-1 Dual Polarization SAR Imagery

NASA Astrophysics Data System (ADS)

Zhang, Yu; Li, Fei; Zhang, Shengkai; Zhu, Tingting

2017-04-01

Synthetic Aperture Radar (SAR) is significantly important for polar remote sensing since it can provide continuous observations in all days and all weather. SAR can be used for extracting the surface roughness information characterized by the variance of dielectric properties and different polarization channels, which make it possible to observe different ice types and surface structure for deformation analysis. In November, 2016, Chinese National Antarctic Research Expedition (CHINARE) 33rd cruise has set sails in sea ice zone in Antarctic. Accurate leads spatial distribution in sea ice zone for routine planning of ship navigation is essential. In this study, the semantic relationship between leads and sea ice categories has been described by the Conditional Random Fields (CRF) model, and leads characteristics have been modeled by statistical distributions in SAR imagery. In the proposed algorithm, a mixture statistical distribution based CRF is developed by considering the contexture information and the statistical characteristics of sea ice for improving leads detection in Sentinel-1A dual polarization SAR imagery. The unary potential and pairwise potential in CRF model is constructed by integrating the posteriori probability estimated from statistical distributions. For mixture statistical distribution parameter estimation, Method of Logarithmic Cumulants (MoLC) is exploited for single statistical distribution parameters estimation. The iteration based Expectation Maximal (EM) algorithm is investigated to calculate the parameters in mixture statistical distribution based CRF model. In the posteriori probability inference, graph-cut energy minimization method is adopted in the initial leads detection. The post-processing procedures including aspect ratio constrain and spatial smoothing approaches are utilized to improve the visual result. The proposed method is validated on Sentinel-1A SAR C-band Extra Wide Swath (EW) Ground Range Detected (GRD) imagery with a pixel spacing of 40 meters near Prydz Bay area, East Antarctica. Main work is listed as follows: 1) A mixture statistical distribution based CRF algorithm has been developed for leads detection from Sentinel-1A dual polarization images. 2) The assessment of the proposed mixture statistical distribution based CRF method and single distribution based CRF algorithm has been presented. 3) The preferable parameters sets including statistical distributions, the aspect ratio threshold and spatial smoothing window size have been provided. In the future, the proposed algorithm will be developed for the operational Sentinel series data sets processing due to its less time consuming cost and high accuracy in leads detection.

Probability theory for 3-layer remote sensing radiative transfer model: univariate case.

PubMed

Ben-David, Avishai; Davidson, Charles E

2012-04-23

A probability model for a 3-layer radiative transfer model (foreground layer, cloud layer, background layer, and an external source at the end of line of sight) has been developed. The 3-layer model is fundamentally important as the primary physical model in passive infrared remote sensing. The probability model is described by the Johnson family of distributions that are used as a fit for theoretically computed moments of the radiative transfer model. From the Johnson family we use the SU distribution that can address a wide range of skewness and kurtosis values (in addition to addressing the first two moments, mean and variance). In the limit, SU can also describe lognormal and normal distributions. With the probability model one can evaluate the potential for detecting a target (vapor cloud layer), the probability of observing thermal contrast, and evaluate performance (receiver operating characteristics curves) in clutter-noise limited scenarios. This is (to our knowledge) the first probability model for the 3-layer remote sensing geometry that treats all parameters as random variables and includes higher-order statistics. © 2012 Optical Society of America

Sampling probability distributions of lesions in mammograms

NASA Astrophysics Data System (ADS)

Looney, P.; Warren, L. M.; Dance, D. R.; Young, K. C.

2015-03-01

One approach to image perception studies in mammography using virtual clinical trials involves the insertion of simulated lesions into normal mammograms. To facilitate this, a method has been developed that allows for sampling of lesion positions across the cranio-caudal and medio-lateral radiographic projections in accordance with measured distributions of real lesion locations. 6825 mammograms from our mammography image database were segmented to find the breast outline. The outlines were averaged and smoothed to produce an average outline for each laterality and radiographic projection. Lesions in 3304 mammograms with malignant findings were mapped on to a standardised breast image corresponding to the average breast outline using piecewise affine transforms. A four dimensional probability distribution function was found from the lesion locations in the cranio-caudal and medio-lateral radiographic projections for calcification and noncalcification lesions. Lesion locations sampled from this probability distribution function were mapped on to individual mammograms using a piecewise affine transform which transforms the average outline to the outline of the breast in the mammogram. The four dimensional probability distribution function was validated by comparing it to the two dimensional distributions found by considering each radiographic projection and laterality independently. The correlation of the location of the lesions sampled from the four dimensional probability distribution function across radiographic projections was shown to match the correlation of the locations of the original mapped lesion locations. The current system has been implemented as a web-service on a server using the Python Django framework. The server performs the sampling, performs the mapping and returns the results in a javascript object notation format.

Deriving Laws from Ordering Relations

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.

2003-01-01

It took much effort in the early days of non-Euclidean geometry to break away from the mindset that all spaces are flat and that two distinct parallel lines do not cross. Up to that point, all that was known was Euclidean geometry, and it was difficult to imagine anything else. We have suffered a similar handicap brought on by the enormous relevance of Boolean algebra to the problems of our age-logic and set theory. Previously, I demonstrated that the algebra of questions is not Boolean, but rather is described by the free distributive algebra. To get to this stage took much effort, as many obstacles-most self-placed-had to be overcome. As Boolean algebras were all I had ever known, it was almost impossible for me to imagine working with an algebra where elements do not have complements. With this realization, it became very clear that the sum and product rules of probability theory at the most basic level had absolutely nothing to do with the Boolean algebra of logical statements. Instead, a measure of degree of inclusion can be invented for many different partially ordered sets, and the sum and product rules fall out of the associativity and distributivity of the algebra. To reinforce this very important idea, this paper will go over how these constructions are made, while focusing on the underlying assumptions. I will derive the sum and product rules for a distributive lattice in general and demonstrate how this leads to probability theory on the Boolean lattice and is related to the calculus of quantum mechanical amplitudes on the partially ordered set of experimental setups. I will also discuss the rules that can be derived from modular lattices and their relevance to the cross-ratio of projective geometry.

Correlated evolution between mode of larval development and habitat in muricid gastropods.

PubMed

Pappalardo, Paula; Rodríguez-Serrano, Enrique; Fernández, Miriam

2014-01-01

Larval modes of development affect evolutionary processes and influence the distribution of marine invertebrates in the ocean. The decrease in pelagic development toward higher latitudes is one of the patterns of distribution most frequently discussed in marine organisms (Thorson's rule), which has been related to increased larval mortality associated with long pelagic durations in colder waters. However, the type of substrate occupied by adults has been suggested to influence the generality of the latitudinal patterns in larval development. To help understand how the environment affects the evolution of larval types we evaluated the association between larval development and habitat using gastropods of the Muricidae family as a model group. To achieve this goal, we collected information on latitudinal distribution, sea water temperature, larval development and type of substrate occupied by adults. We constructed a molecular phylogeny for 45 species of muricids to estimate the ancestral character states and to assess the relationship between traits using comparative methods in a Bayesian framework. Our results showed high probability for a common ancestor of the muricids with nonpelagic (and nonfeeding) development, that lived in hard bottoms and cold temperatures. From this ancestor, a pelagic feeding larva evolved three times, and some species shifted to warmer temperatures or sand bottoms. The evolution of larval development was not independent of habitat; the most probable evolutionary route reconstructed in the analysis of correlated evolution showed that type of larval development may change in soft bottoms but in hard bottoms this change is highly unlikely. Lower sea water temperatures were associated with nonpelagic modes of development, supporting Thorson's rule. We show how environmental pressures can favor a particular mode of larval development or transitions between larval modes and discuss the reacquisition of feeding larva in muricids gastropods.

Probable effects on ground-water resources from construction of the proposed Grand River cut-off channel west of Lansing, Mich.

USGS Publications Warehouse

Ferris, John G.

1950-01-01

This memorandum summarize information brought out in correspondence between the office of the District Engineer of the Milwaukee District, U.S. Corps of Engineers, and the District Office of the Ground Water Branch of the U.S. Geological Survey at Lansing, Mich., concerning the probable effects on the ground-water resources of the Lansing area from the construction of a proposed flood-water cut-off channel for the Grand River to extend from Millett to Delta Mills, in Eaton County, Mich.

How to model a negligible probability under the WTO sanitary and phytosanitary agreement?

PubMed

Powell, Mark R

2013-06-01

Since the 1997 EC--Hormones decision, World Trade Organization (WTO) Dispute Settlement Panels have wrestled with the question of what constitutes a negligible risk under the Sanitary and Phytosanitary Agreement. More recently, the 2010 WTO Australia--Apples Panel focused considerable attention on the appropriate quantitative model for a negligible probability in a risk assessment. The 2006 Australian Import Risk Analysis for Apples from New Zealand translated narrative probability statements into quantitative ranges. The uncertainty about a "negligible" probability was characterized as a uniform distribution with a minimum value of zero and a maximum value of 10(-6) . The Australia - Apples Panel found that the use of this distribution would tend to overestimate the likelihood of "negligible" events and indicated that a triangular distribution with a most probable value of zero and a maximum value of 10⁻⁶ would correct the bias. The Panel observed that the midpoint of the uniform distribution is 5 × 10⁻⁷ but did not consider that the triangular distribution has an expected value of 3.3 × 10⁻⁷. Therefore, if this triangular distribution is the appropriate correction, the magnitude of the bias found by the Panel appears modest. The Panel's detailed critique of the Australian risk assessment, and the conclusions of the WTO Appellate Body about the materiality of flaws found by the Panel, may have important implications for the standard of review for risk assessments under the WTO SPS Agreement. © 2012 Society for Risk Analysis.

Fourier Method for Calculating Fission Chain Neutron Multiplicity Distributions

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

Chambers, David H.; Chandrasekaran, Hema; Walston, Sean E.

Here, a new way of utilizing the fast Fourier transform is developed to compute the probability distribution for a fission chain to create n neutrons. We then extend this technique to compute the probability distributions for detecting n neutrons. Lastly, our technique can be used for fission chains initiated by either a single neutron inducing a fission or by the spontaneous fission of another isotope.

Fourier Method for Calculating Fission Chain Neutron Multiplicity Distributions

DOE PAGES

Chambers, David H.; Chandrasekaran, Hema; Walston, Sean E.

2017-03-27

Here, a new way of utilizing the fast Fourier transform is developed to compute the probability distribution for a fission chain to create n neutrons. We then extend this technique to compute the probability distributions for detecting n neutrons. Lastly, our technique can be used for fission chains initiated by either a single neutron inducing a fission or by the spontaneous fission of another isotope.

Teaching Uncertainties

ERIC Educational Resources Information Center

Duerdoth, Ian

2009-01-01

The subject of uncertainties (sometimes called errors) is traditionally taught (to first-year science undergraduates) towards the end of a course on statistics that defines probability as the limit of many trials, and discusses probability distribution functions and the Gaussian distribution. We show how to introduce students to the concepts of…

Robust approaches to quantification of margin and uncertainty for sparse data

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

Hund, Lauren; Schroeder, Benjamin B.; Rumsey, Kelin

Characterizing the tails of probability distributions plays a key role in quantification of margins and uncertainties (QMU), where the goal is characterization of low probability, high consequence events based on continuous measures of performance. When data are collected using physical experimentation, probability distributions are typically fit using statistical methods based on the collected data, and these parametric distributional assumptions are often used to extrapolate about the extreme tail behavior of the underlying probability distribution. In this project, we character- ize the risk associated with such tail extrapolation. Specifically, we conducted a scaling study to demonstrate the large magnitude of themore » risk; then, we developed new methods for communicat- ing risk associated with tail extrapolation from unvalidated statistical models; lastly, we proposed a Bayesian data-integration framework to mitigate tail extrapolation risk through integrating ad- ditional information. We conclude that decision-making using QMU is a complex process that cannot be achieved using statistical analyses alone.« less

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

Chen, Hang, E-mail: hangchen@mit.edu; Thill, Peter; Cao, Jianshu

In biochemical systems, intrinsic noise may drive the system switch from one stable state to another. We investigate how kinetic switching between stable states in a bistable network is influenced by dynamic disorder, i.e., fluctuations in the rate coefficients. Using the geometric minimum action method, we first investigate the optimal transition paths and the corresponding minimum actions based on a genetic toggle switch model in which reaction coefficients draw from a discrete probability distribution. For the continuous probability distribution of the rate coefficient, we then consider two models of dynamic disorder in which reaction coefficients undergo different stochastic processes withmore » the same stationary distribution. In one, the kinetic parameters follow a discrete Markov process and in the other they follow continuous Langevin dynamics. We find that regulation of the parameters modulating the dynamic disorder, as has been demonstrated to occur through allosteric control in bistable networks in the immune system, can be crucial in shaping the statistics of optimal transition paths, transition probabilities, and the stationary probability distribution of the network.« less

Detecting background changes in environments with dynamic foreground by separating probability distribution function mixtures using Pearson's method of moments

NASA Astrophysics Data System (ADS)

Jenkins, Colleen; Jordan, Jay; Carlson, Jeff

2007-02-01

This paper presents parameter estimation techniques useful for detecting background changes in a video sequence with extreme foreground activity. A specific application of interest is automated detection of the covert placement of threats (e.g., a briefcase bomb) inside crowded public facilities. We propose that a histogram of pixel intensity acquired from a fixed mounted camera over time for a series of images will be a mixture of two Gaussian functions: the foreground probability distribution function and background probability distribution function. We will use Pearson's Method of Moments to separate the two probability distribution functions. The background function can then be "remembered" and changes in the background can be detected. Subsequent comparisons of background estimates are used to detect changes. Changes are flagged to alert security forces to the presence and location of potential threats. Results are presented that indicate the significant potential for robust parameter estimation techniques as applied to video surveillance.

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.

p-adic stochastic hidden variable model

NASA Astrophysics Data System (ADS)

Khrennikov, Andrew

1998-03-01

We propose stochastic hidden variables model in which hidden variables have a p-adic probability distribution ρ(λ) and at the same time conditional probabilistic distributions P(U,λ), U=A,A',B,B', are ordinary probabilities defined on the basis of the Kolmogorov measure-theoretical axiomatics. A frequency definition of p-adic probability is quite similar to the ordinary frequency definition of probability. p-adic frequency probability is defined as the limit of relative frequencies νn but in the p-adic metric. We study a model with p-adic stochastics on the level of the hidden variables description. But, of course, responses of macroapparatuses have to be described by ordinary stochastics. Thus our model describes a mixture of p-adic stochastics of the microworld and ordinary stochastics of macroapparatuses. In this model probabilities for physical observables are the ordinary probabilities. At the same time Bell's inequality is violated.

Competing contact processes in the Watts-Strogatz network

NASA Astrophysics Data System (ADS)

Rybak, Marcin; Malarz, Krzysztof; Kułakowski, Krzysztof

2016-06-01

We investigate two competing contact processes on a set of Watts-Strogatz networks with the clustering coefficient tuned by rewiring. The base for network construction is one-dimensional chain of N sites, where each site i is directly linked to nodes labelled as i ± 1 and i ± 2. So initially, each node has the same degree k i = 4. The periodic boundary conditions are assumed as well. For each node i the links to sites i + 1 and i + 2 are rewired to two randomly selected nodes so far not-connected to node i. An increase of the rewiring probability q influences the nodes degree distribution and the network clusterization coefficient 𝓒. For given values of rewiring probability q the set 𝓝(q)={𝓝1,𝓝2,...,𝓝 M } of M networks is generated. The network's nodes are decorated with spin-like variables s i ∈ { S,D }. During simulation each S node having a D-site in its neighbourhood converts this neighbour from D to S state. Conversely, a node in D state having at least one neighbour also in state D-state converts all nearest-neighbours of this pair into D-state. The latter is realized with probability p. We plot the dependence of the nodes S final density n S T on initial nodes S fraction n S 0. Then, we construct the surface of the unstable fixed points in (𝓒, p, n S 0) space. The system evolves more often toward n S T for (𝓒, p, n S 0) points situated above this surface while starting simulation with (𝓒, p, n S 0) parameters situated below this surface leads system to n S T =0. The points on this surface correspond to such value of initial fraction n S * of S nodes (for fixed values 𝓒 and p) for which their final density is n S T=1/2.

Stationary properties of maximum-entropy random walks.

PubMed

Dixit, Purushottam D

2015-10-01

Maximum-entropy (ME) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic systems, how state space topology and path-dependent constraints affect ME-inferred state probabilities remains unknown. To that end, we derive the transition probabilities and the stationary distribution of a maximum path entropy Markov process subject to state- and path-dependent constraints. A main finding is that the stationary distribution over states differs significantly from the Boltzmann distribution and reflects a competition between path multiplicity and imposed constraints. We illustrate our results with particle diffusion on a two-dimensional landscape. Connections with the path integral approach to diffusion are discussed.

Estimation and prediction of maximum daily rainfall at Sagar Island using best fit probability models

NASA Astrophysics Data System (ADS)

Mandal, S.; Choudhury, B. U.

2015-07-01

Sagar Island, setting on the continental shelf of Bay of Bengal, is one of the most vulnerable deltas to the occurrence of extreme rainfall-driven climatic hazards. Information on probability of occurrence of maximum daily rainfall will be useful in devising risk management for sustaining rainfed agrarian economy vis-a-vis food and livelihood security. Using six probability distribution models and long-term (1982-2010) daily rainfall data, we studied the probability of occurrence of annual, seasonal and monthly maximum daily rainfall (MDR) in the island. To select the best fit distribution models for annual, seasonal and monthly time series based on maximum rank with minimum value of test statistics, three statistical goodness of fit tests, viz. Kolmogorove-Smirnov test (K-S), Anderson Darling test ( A 2 ) and Chi-Square test ( X 2) were employed. The fourth probability distribution was identified from the highest overall score obtained from the three goodness of fit tests. Results revealed that normal probability distribution was best fitted for annual, post-monsoon and summer seasons MDR, while Lognormal, Weibull and Pearson 5 were best fitted for pre-monsoon, monsoon and winter seasons, respectively. The estimated annual MDR were 50, 69, 86, 106 and 114 mm for return periods of 2, 5, 10, 20 and 25 years, respectively. The probability of getting an annual MDR of >50, >100, >150, >200 and >250 mm were estimated as 99, 85, 40, 12 and 03 % level of exceedance, respectively. The monsoon, summer and winter seasons exhibited comparatively higher probabilities (78 to 85 %) for MDR of >100 mm and moderate probabilities (37 to 46 %) for >150 mm. For different recurrence intervals, the percent probability of MDR varied widely across intra- and inter-annual periods. In the island, rainfall anomaly can pose a climatic threat to the sustainability of agricultural production and thus needs adequate adaptation and mitigation measures.

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.

Computer routines for probability distributions, random numbers, and related functions

USGS Publications Warehouse

Kirby, W.

1983-01-01

Use of previously coded and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main progress. The probability distributions provided include the beta, chi-square, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F. Other mathematical functions include the Bessel function, I sub o, gamma and log-gamma functions, error functions, and exponential integral. Auxiliary services include sorting and printer-plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

Computer routines for probability distributions, random numbers, and related functions

USGS Publications Warehouse

Kirby, W.H.

1980-01-01

Use of previously codes and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main programs. The probability distributions provided include the beta, chisquare, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F tests. Other mathematical functions include the Bessel function I (subzero), gamma and log-gamma functions, error functions and exponential integral. Auxiliary services include sorting and printer plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

Universal laws of human society's income distribution

NASA Astrophysics Data System (ADS)

Tao, Yong

2015-10-01

General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system. Since Arrow's Impossibility Theorem and Rawls' principle of social fairness will provide a powerful support for the hypothesis of equal probability, then the principle of maximum entropy is available in a just and equilibrium economy so that an income distribution will occur spontaneously (with the largest probability). Remarkably, some scholars have observed such an income distribution in some democratic countries, e.g. USA. This result implies that the hypothesis of equal probability may be only suitable for some "fair" systems (economic or physical systems). From this meaning, the non-equilibrium systems may be "unfair" so that the hypothesis of equal probability is unavailable.

Gravitational lensing, time delay, and gamma-ray bursts

NASA Technical Reports Server (NTRS)

Mao, Shude

1992-01-01

The probability distributions of time delay in gravitational lensing by point masses and isolated galaxies (modeled as singular isothermal spheres) are studied. For point lenses (all with the same mass) the probability distribution is broad, and with a peak at delta(t) of about 50 S; for singular isothermal spheres, the probability distribution is a rapidly decreasing function with increasing time delay, with a median delta(t) equals about 1/h month, and its behavior depends sensitively on the luminosity function of galaxies. The present simplified calculation is particularly relevant to the gamma-ray bursts if they are of cosmological origin. The frequency of 'recurrent' bursts due to gravitational lensing by galaxies is probably between 0.05 and 0.4 percent. Gravitational lensing can be used as a test of the cosmological origin of gamma-ray bursts.

Entropy of network ensembles

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra

2009-03-01

In this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach. This framework is able to describe undirected and directed network ensembles as well as weighted network ensembles. These networks might have nontrivial community structure or, in the case of networks embedded in a given space, they might have a link probability with a nontrivial dependence on the distance between the nodes. These ensembles are characterized by their entropy, which evaluates the cardinality of networks in the ensemble. In particular, in this paper we define and evaluate the structural entropy, i.e., the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence. We stress the apparent paradox that scale-free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural, social, and technological complex systems. We propose a solution to the paradox by proving that scale-free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy. Finally, the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden-variable network ensembles with significant implications for the formulation of network-constructing algorithms.

Inferring the three-dimensional distribution of dust in the Galaxy with a non-parametric method . Preparing for Gaia

NASA Astrophysics Data System (ADS)

Rezaei Kh., S.; Bailer-Jones, C. A. L.; Hanson, R. J.; Fouesneau, M.

2017-02-01

We present a non-parametric model for inferring the three-dimensional (3D) distribution of dust density in the Milky Way. Our approach uses the extinction measured towards stars at different locations in the Galaxy at approximately known distances. Each extinction measurement is proportional to the integrated dust density along its line of sight (LoS). Making simple assumptions about the spatial correlation of the dust density, we can infer the most probable 3D distribution of dust across the entire observed region, including along sight lines which were not observed. This is possible because our model employs a Gaussian process to connect all LoS. We demonstrate the capability of our model to capture detailed dust density variations using mock data and simulated data from the Gaia Universe Model Snapshot. We then apply our method to a sample of giant stars observed by APOGEE and Kepler to construct a 3D dust map over a small region of the Galaxy. Owing to our smoothness constraint and its isotropy, we provide one of the first maps which does not show the "fingers of God" effect.

Stimulus-dependent Maximum Entropy Models of Neural Population Codes

PubMed Central

Segev, Ronen; Schneidman, Elad

2013-01-01

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model—a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population. PMID:23516339

Reconciling Streamflow Uncertainty Estimation and River Bed Morphology Dynamics. Insights from a Probabilistic Assessment of Streamflow Uncertainties Using a Reliability Diagram

NASA Astrophysics Data System (ADS)

Morlot, T.; Mathevet, T.; Perret, C.; Favre Pugin, A. C.

2014-12-01

Streamflow uncertainty estimation has recently received a large attention in the literature. A dynamic rating curve assessment method has been introduced (Morlot et al., 2014). This dynamic method allows to compute a rating curve for each gauging and a continuous streamflow time-series, while calculating streamflow uncertainties. Streamflow uncertainty takes into account many sources of uncertainty (water level, rating curve interpolation and extrapolation, gauging aging, etc.) and produces an estimated distribution of streamflow for each days. In order to caracterise streamflow uncertainty, a probabilistic framework has been applied on a large sample of hydrometric stations of the Division Technique Générale (DTG) of Électricité de France (EDF) hydrometric network (>250 stations) in France. A reliability diagram (Wilks, 1995) has been constructed for some stations, based on the streamflow distribution estimated for a given day and compared to a real streamflow observation estimated via a gauging. To build a reliability diagram, we computed the probability of an observed streamflow (gauging), given the streamflow distribution. Then, the reliability diagram allows to check that the distribution of probabilities of non-exceedance of the gaugings follows a uniform law (i.e., quantiles should be equipropables). Given the shape of the reliability diagram, the probabilistic calibration is caracterised (underdispersion, overdispersion, bias) (Thyer et al., 2009). In this paper, we present case studies where reliability diagrams have different statistical properties for different periods. Compared to our knowledge of river bed morphology dynamic of these hydrometric stations, we show how reliability diagram gives us invaluable information on river bed movements, like a continuous digging or backfilling of the hydraulic control due to erosion or sedimentation processes. Hence, the careful analysis of reliability diagrams allows to reconcile statistics and long-term river bed morphology processes. This knowledge improves our real-time management of hydrometric stations, given a better caracterisation of erosion/sedimentation processes and the stability of hydrometric station hydraulic control.

Fit to predict? Eco-informatics for predicting the catchability of a pelagic fish in near real time.

PubMed

Scales, Kylie L; Hazen, Elliott L; Maxwell, Sara M; Dewar, Heidi; Kohin, Suzanne; Jacox, Michael G; Edwards, Christopher A; Briscoe, Dana K; Crowder, Larry B; Lewison, Rebecca L; Bograd, Steven J

2017-12-01

The ocean is a dynamic environment inhabited by a diverse array of highly migratory species, many of which are under direct exploitation in targeted fisheries. The timescales of variability in the marine realm coupled with the extreme mobility of ocean-wandering species such as tuna and billfish complicates fisheries management. Developing eco-informatics solutions that allow for near real-time prediction of the distributions of highly mobile marine species is an important step towards the maturation of dynamic ocean management and ecological forecasting. Using 25 yr (1990-2014) of NOAA fisheries' observer data from the California drift gillnet fishery, we model relative probability of occurrence (presence-absence) and catchability (total catch per gillnet set) of broadbill swordfish Xiphias gladius in the California Current System. Using freely available environmental data sets and open source software, we explore the physical drivers of regional swordfish distribution. Comparing models built upon remotely sensed data sets with those built upon a data-assimilative configuration of the Regional Ocean Modelling System (ROMS), we explore trade-offs in model construction, and address how physical data can affect predictive performance and operational capacity. Swordfish catchability was found to be highest in deeper waters (>1,500 m) with surface temperatures in the 14-20°C range, isothermal layer depth (ILD) of 20-40 m, positive sea surface height (SSH) anomalies, and during the new moon (<20% lunar illumination). We observed a greater influence of mesoscale variability (SSH, wind speed, isothermal layer depth, eddy kinetic energy) in driving swordfish catchability (total catch) than was evident in predicting the relative probability of presence (presence-absence), confirming the utility of generating spatiotemporally dynamic predictions. Data-assimilative ROMS circumvent the limitations of satellite remote sensing in providing physical data fields for species distribution models (e.g., cloud cover, variable resolution, subsurface data), and facilitate broad-scale prediction of dynamic species distributions in near real time. © 2017 by the Ecological Society of America.

A spatial risk assessment of bighorn sheep extirpation by grazing domestic sheep on public lands.

PubMed

Carpenter, Tim E; Coggins, Victor L; McCarthy, Clinton; O'Brien, Chans S; O'Brien, Joshua M; Schommer, Timothy J

2014-04-01

Bighorn sheep currently occupy just 30% of their historic distribution, and persist in populations less than 5% as abundant overall as their early 19th century counterparts. Present-day recovery of bighorn sheep populations is in large part limited by periodic outbreaks of respiratory disease, which can be transmitted to bighorn sheep via contact with domestic sheep grazing in their vicinity. In order to assess the viability of bighorn sheep populations on the Payette National Forest (PNF) under several alternative proposals for domestic sheep grazing, we developed a series of interlinked models. Using telemetry and habitat data, we characterized herd home ranges and foray movements of bighorn sheep from their home ranges. Combining foray model movement estimates with known domestic sheep grazing areas (allotments), a Risk of Contact Model estimated bighorn sheep contact rates with domestic sheep allotments. Finally, we used demographic and epidemiologic data to construct population and disease transmission models (Disease Model), which we used to estimate bighorn sheep persistence under each alternative grazing scenario. Depending on the probability of disease transmission following interspecies contact, extirpation probabilities for the seven bighorn sheep herds examined here ranged from 20% to 100%. The Disease Model allowed us to assess the probabilities that varied domestic sheep management scenarios would support persistent populations of free-ranging bighorn sheep. Copyright © 2014 Elsevier B.V. All rights reserved.

A general formula for computing maximum proportion correct scores in various psychophysical paradigms with arbitrary probability distributions of stimulus observations.

PubMed

Dai, Huanping; Micheyl, Christophe

2015-05-01

Proportion correct (Pc) is a fundamental measure of task performance in psychophysics. The maximum Pc score that can be achieved by an optimal (maximum-likelihood) observer in a given task is of both theoretical and practical importance, because it sets an upper limit on human performance. Within the framework of signal detection theory, analytical solutions for computing the maximum Pc score have been established for several common experimental paradigms under the assumption of Gaussian additive internal noise. However, as the scope of applications of psychophysical signal detection theory expands, the need is growing for psychophysicists to compute maximum Pc scores for situations involving non-Gaussian (internal or stimulus-induced) noise. In this article, we provide a general formula for computing the maximum Pc in various psychophysical experimental paradigms for arbitrary probability distributions of sensory activity. Moreover, easy-to-use MATLAB code implementing the formula is provided. Practical applications of the formula are illustrated, and its accuracy is evaluated, for two paradigms and two types of probability distributions (uniform and Gaussian). The results demonstrate that Pc scores computed using the formula remain accurate even for continuous probability distributions, as long as the conversion from continuous probability density functions to discrete probability mass functions is supported by a sufficiently high sampling resolution. We hope that the exposition in this article, and the freely available MATLAB code, facilitates calculations of maximum performance for a wider range of experimental situations, as well as explorations of the impact of different assumptions concerning internal-noise distributions on maximum performance in psychophysical experiments.

Atom counting in HAADF STEM using a statistical model-based approach: methodology, possibilities, and inherent limitations.

PubMed

De Backer, A; Martinez, G T; Rosenauer, A; Van Aert, S

2013-11-01

In the present paper, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. In order to count the number of atoms, it is assumed that the total scattered intensity scales with the number of atoms per atom column. These intensities are quantitatively determined using model-based statistical parameter estimation theory. The distribution describing the probability that intensity values are generated by atomic columns containing a specific number of atoms is inferred on the basis of the experimental scattered intensities. Finally, the number of atoms per atom column is quantified using this estimated probability distribution. The number of atom columns available in the observed STEM image, the number of components in the estimated probability distribution, the width of the components of the probability distribution, and the typical shape of a criterion to assess the number of components in the probability distribution directly affect the accuracy and precision with which the number of atoms in a particular atom column can be estimated. It is shown that single atom sensitivity is feasible taking the latter aspects into consideration. © 2013 Elsevier B.V. All rights reserved.

Theoretical size distribution of fossil taxa: analysis of a null model

PubMed Central

Reed, William J; Hughes, Barry D

2007-01-01

Background This article deals with the theoretical size distribution (of number of sub-taxa) of a fossil taxon arising from a simple null model of macroevolution. Model New species arise through speciations occurring independently and at random at a fixed probability rate, while extinctions either occur independently and at random (background extinctions) or cataclysmically. In addition new genera are assumed to arise through speciations of a very radical nature, again assumed to occur independently and at random at a fixed probability rate. Conclusion The size distributions of the pioneering genus (following a cataclysm) and of derived genera are determined. Also the distribution of the number of genera is considered along with a comparison of the probability of a monospecific genus with that of a monogeneric family. PMID:17376249

Bragg peak prediction from quantitative proton computed tomography using different path estimates

PubMed Central

Wang, Dongxu; Mackie, T Rockwell

2015-01-01

This paper characterizes the performance of the straight-line path (SLP) and cubic spline path (CSP) as path estimates used in reconstruction of proton computed tomography (pCT). The GEANT4 Monte Carlo simulation toolkit is employed to simulate the imaging phantom and proton projections. SLP, CSP and the most-probable path (MPP) are constructed based on the entrance and exit information of each proton. The physical deviations of SLP, CSP and MPP from the real path are calculated. Using a conditional proton path probability map, the relative probability of SLP, CSP and MPP are calculated and compared. The depth dose and Bragg peak are predicted on the pCT images reconstructed using SLP, CSP, and MPP and compared with the simulation result. The root-mean-square physical deviations and the cumulative distribution of the physical deviations show that the performance of CSP is comparable to MPP while SLP is slightly inferior. About 90% of the SLP pixels and 99% of the CSP pixels lie in the 99% relative probability envelope of the MPP. Even at an imaging dose of ~0.1 mGy the proton Bragg peak for a given incoming energy can be predicted on the pCT image reconstructed using SLP, CSP, or MPP with 1 mm accuracy. This study shows that SLP and CSP, like MPP, are adequate path estimates for pCT reconstruction, and therefore can be chosen as the path estimation method for pCT reconstruction, which can aid the treatment planning and range prediction of proton radiation therapy. PMID:21212472

Entropy for quantum pure states and quantum H theorem

NASA Astrophysics Data System (ADS)

Han, Xizhi; Wu, Biao

2015-06-01

We construct a complete set of Wannier functions that are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability distribution in quantum phase space, we define an entropy for a quantum pure state. We prove an inequality regarding the long-time behavior of our entropy's fluctuation. For a typical initial state, this inequality indicates that our entropy can relax dynamically to a maximized value and stay there most of time with small fluctuations. This result echoes the quantum H theorem proved by von Neumann [Zeitschrift für Physik 57, 30 (1929), 10.1007/BF01339852]. Our entropy is different from the standard von Neumann entropy, which is always zero for quantum pure states. According to our definition, a system always has bigger entropy than its subsystem even when the system is described by a pure state. As the construction of the Wannier basis can be implemented numerically, the dynamical evolution of our entropy is illustrated with an example.

Photoacoustic diagnosis of burns in rats: two-dimensional photo-acoustic imaging of burned tissue

NASA Astrophysics Data System (ADS)

Yamazaki, Mutsuo; Sato, Shunichi; Saito, Daizo; Okada, Yoshiaki; Kurita, Akira; Kikuchi, Makoto; Ashida, Hiroshi; Obara, Minoru

2003-06-01

We previously reported that for rat burn models, deep dermal burns and deep burns can be well differentiated by measuring the propagation time of the photoacoustic signals originated from the blood in the healthy skin tissue under the damaged tissue layer. However, the diagnosis was based on point measurement in the wound, and therefore site-dependent information on the injuries was not obtained; such information is very important for diagnosis of extended burns. In the present study, we scanned a photoacoustic detector on the wound and constructed two-dimensional (2-D) images of the blood-originated photoacoustic signals for superficial dermal burns (SDB), deep dermal burns (DDB), deep burns (DB), and healthy skins (control) in rats. For each burn model, site-dependent variation of the signal was observed; the variation probably reflects the distribution of blood vessels in the skin tissue. In spite of the variation, clear differentiation was obtained between SDB, DDB, and DB from the 2D images. The images were constructed as a function of post burn time. Temporal signal variation will be also presented.

Modelling of wildlife migrations and its economic impacts

NASA Astrophysics Data System (ADS)

Myšková, Kateřina; Žák, Jaroslav

2013-10-01

Natural wildlife migrations are often disrupted by the construction of line structures, especially freeways. Various overpasses and underpasses (migration objects) are being designed to enable species to pass through line structures. The newly developed original procedure for the quantification of the utility of migration objects (migration potentials) and sections of line structures retrieves the deficiencies of the previous ones. The procedure has been developed under bulk information obtained by monitoring migrations using camera system and spy games. The log-normal distribution functions are used. The procedure for the evaluation of the probability of the permeability of the line structures sectors is also presented. The above mentioned procedures and algorithms can be used while planning, preparing, constructing or verifying the measures to assure the permeability of line structures for selected feral species. Using the procedures can significantly reduce financial costs and improve the permeability. When the migration potentials are correctly determined and the whole sector is taken into account for the migrations, some originally designed objects may be found to be redundant and not building them will bring financial savings.

Maximum entropy approach to statistical inference for an ocean acoustic waveguide.

PubMed

Knobles, D P; Sagers, J D; Koch, R A

2012-02-01

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations. © 2012 Acoustical Society of America

Probability distributions of continuous measurement results for conditioned quantum evolution

NASA Astrophysics Data System (ADS)

Franquet, A.; Nazarov, Yuli V.

2017-02-01

We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the latter is achieved by the postselection in the end of the evolution. The statistics may drastically differ from the nonconditioned case, and the interference between initial and final states can be observed in the probability distributions of measurement outcomes as well as in the average values exceeding the conventional range of nonconditioned averages. We develop a proper formalism to compute the distributions of measurement outcomes, and evaluate and discuss the distributions in experimentally relevant setups. We demonstrate the manifestations of the interference between initial and final states in various regimes. We consider analytically simple examples of nontrivial probability distributions. We reveal peaks (or dips) at half-quantized values of the measurement outputs. We discuss in detail the case of zero overlap between initial and final states demonstrating anomalously big average outputs and sudden jump in time-integrated output. We present and discuss the numerical evaluation of the probability distribution aiming at extending the analytical results and describing a realistic experimental situation of a qubit in the regime of resonant fluorescence.

Shallow slip amplification and enhanced tsunami hazard unravelled by dynamic simulations of mega-thrust earthquakes

PubMed Central

Murphy, S.; Scala, A.; Herrero, A.; Lorito, S.; Festa, G.; Trasatti, E.; Tonini, R.; Romano, F.; Molinari, I.; Nielsen, S.

2016-01-01

The 2011 Tohoku earthquake produced an unexpected large amount of shallow slip greatly contributing to the ensuing tsunami. How frequent are such events? How can they be efficiently modelled for tsunami hazard? Stochastic slip models, which can be computed rapidly, are used to explore the natural slip variability; however, they generally do not deal specifically with shallow slip features. We study the systematic depth-dependence of slip along a thrust fault with a number of 2D dynamic simulations using stochastic shear stress distributions and a geometry based on the cross section of the Tohoku fault. We obtain a probability density for the slip distribution, which varies both with depth, earthquake size and whether the rupture breaks the surface. We propose a method to modify stochastic slip distributions according to this dynamically-derived probability distribution. This method may be efficiently applied to produce large numbers of heterogeneous slip distributions for probabilistic tsunami hazard analysis. Using numerous M9 earthquake scenarios, we demonstrate that incorporating the dynamically-derived probability distribution does enhance the conditional probability of exceedance of maximum estimated tsunami wave heights along the Japanese coast. This technique for integrating dynamic features in stochastic models can be extended to any subduction zone and faulting style. PMID:27725733

A discussion on the origin of quantum probabilities

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

Holik, Federico, E-mail: olentiev2@gmail.com; Departamento de Matemática - Ciclo Básico Común, Universidad de Buenos Aires - Pabellón III, Ciudad Universitaria, Buenos Aires; Sáenz, Manuel

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case). -- Highlights: •Several recent works use a derivation similar to that of R.T. Cox to obtain quantum probabilities. •We apply Cox’s method to the lattice of subspaces of the Hilbert space. •We obtain a derivationmore » of quantum probabilities which includes mixed states. •The method presented in this work is susceptible to generalization. •It includes quantum mechanics and classical mechanics as particular cases.« less

Probability Weighting Functions Derived from Hyperbolic Time Discounting: Psychophysical Models and Their Individual Level Testing.

PubMed

Takemura, Kazuhisa; Murakami, Hajime

2016-01-01

A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 - k log p)(-1). Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a geometric distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

Hybrid Approaches and Industrial Applications of Pattern Recognition,

DTIC Science & Technology

1980-10-01

emphasized that the probability distribution in (9) is correct only under the assumption that P( wIx ) is known exactly. In practice this assumption will...sufficient precision. The alternative would be to take the probability distribution of estimates of P( wix ) into account in the analysis. However, from the

Generalized Success-Breeds-Success Principle Leading to Time-Dependent Informetric Distributions.

ERIC Educational Resources Information Center

Egghe, Leo; Rousseau, Ronald

1995-01-01

Reformulates the success-breeds-success (SBS) principle in informetrics in order to generate a general theory of source-item relationships. Topics include a time-dependent probability, a new model for the expected probability that is compared with the SBS principle with exact combinatorial calculations, classical frequency distributions, and…

The beta distribution: A statistical model for world cloud cover

NASA Technical Reports Server (NTRS)

Falls, L. W.

1973-01-01

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

Gas Hydrate Formation Probability Distributions: The Effect of Shear and Comparisons with Nucleation Theory.

PubMed

May, Eric F; Lim, Vincent W; Metaxas, Peter J; Du, Jianwei; Stanwix, Paul L; Rowland, Darren; Johns, Michael L; Haandrikman, Gert; Crosby, Daniel; Aman, Zachary M

2018-03-13

Gas hydrate formation is a stochastic phenomenon of considerable significance for any risk-based approach to flow assurance in the oil and gas industry. In principle, well-established results from nucleation theory offer the prospect of predictive models for hydrate formation probability in industrial production systems. In practice, however, heuristics are relied on when estimating formation risk for a given flowline subcooling or when quantifying kinetic hydrate inhibitor (KHI) performance. Here, we present statistically significant measurements of formation probability distributions for natural gas hydrate systems under shear, which are quantitatively compared with theoretical predictions. Distributions with over 100 points were generated using low-mass, Peltier-cooled pressure cells, cycled in temperature between 40 and -5 °C at up to 2 K·min -1 and analyzed with robust algorithms that automatically identify hydrate formation and initial growth rates from dynamic pressure data. The application of shear had a significant influence on the measured distributions: at 700 rpm mass-transfer limitations were minimal, as demonstrated by the kinetic growth rates observed. The formation probability distributions measured at this shear rate had mean subcoolings consistent with theoretical predictions and steel-hydrate-water contact angles of 14-26°. However, the experimental distributions were substantially wider than predicted, suggesting that phenomena acting on macroscopic length scales are responsible for much of the observed stochastic formation. Performance tests of a KHI provided new insights into how such chemicals can reduce the risk of hydrate blockage in flowlines. Our data demonstrate that the KHI not only reduces the probability of formation (by both shifting and sharpening the distribution) but also reduces hydrate growth rates by a factor of 2.

Multinomial Logistic Regression & Bootstrapping for Bayesian Estimation of Vertical Facies Prediction in Heterogeneous Sandstone Reservoirs

NASA Astrophysics Data System (ADS)

Al-Mudhafar, W. J.

2013-12-01

Precisely prediction of rock facies leads to adequate reservoir characterization by improving the porosity-permeability relationships to estimate the properties in non-cored intervals. It also helps to accurately identify the spatial facies distribution to perform an accurate reservoir model for optimal future reservoir performance. In this paper, the facies estimation has been done through Multinomial logistic regression (MLR) with respect to the well logs and core data in a well in upper sandstone formation of South Rumaila oil field. The entire independent variables are gamma rays, formation density, water saturation, shale volume, log porosity, core porosity, and core permeability. Firstly, Robust Sequential Imputation Algorithm has been considered to impute the missing data. This algorithm starts from a complete subset of the dataset and estimates sequentially the missing values in an incomplete observation by minimizing the determinant of the covariance of the augmented data matrix. Then, the observation is added to the complete data matrix and the algorithm continues with the next observation with missing values. The MLR has been chosen to estimate the maximum likelihood and minimize the standard error for the nonlinear relationships between facies & core and log data. The MLR is used to predict the probabilities of the different possible facies given each independent variable by constructing a linear predictor function having a set of weights that are linearly combined with the independent variables by using a dot product. Beta distribution of facies has been considered as prior knowledge and the resulted predicted probability (posterior) has been estimated from MLR based on Baye's theorem that represents the relationship between predicted probability (posterior) with the conditional probability and the prior knowledge. To assess the statistical accuracy of the model, the bootstrap should be carried out to estimate extra-sample prediction error by randomly drawing datasets with replacement from the training data. Each sample has the same size of the original training set and it can be conducted N times to produce N bootstrap datasets to re-fit the model accordingly to decrease the squared difference between the estimated and observed categorical variables (facies) leading to decrease the degree of uncertainty.

Using satellite remote sensing to model and map the distribution of Bicknell's thrush (Catharus bicknelli) in the White Mountains of New Hampshire

NASA Astrophysics Data System (ADS)

Hale, Stephen Roy

Landsat-7 Enhanced Thematic Mapper satellite imagery was used to model Bicknell's Thrush (Catharus bicknelli) distribution in the White Mountains of New Hampshire. The proof-of-concept was established for using satellite imagery in species-habitat modeling, where for the first time imagery spectral features were used to estimate a species-habitat model variable. The model predicted rising probabilities of thrush presence with decreasing dominant vegetation height, increasing elevation, and decreasing distance to nearest Fir Sapling cover type. To solve the model at all locations required regressor estimates at every pixel, which were not available for the dominant vegetation height and elevation variables. Topographically normalized imagery features Normalized Difference Vegetation Index and Band 1 (blue) were used to estimate dominant vegetation height using multiple linear regression; and a Digital Elevation Model was used to estimate elevation. Distance to nearest Fir Sapling cover type was obtained for each pixel from a land cover map specifically constructed for this project. The Bicknell's Thrush habitat model was derived using logistic regression, which produced the probability of detecting a singing male based on the pattern of model covariates. Model validation using Bicknell's Thrush data not used in model calibration, revealed that the model accurately estimated thrush presence at probabilities ranging from 0 to <0.40 and from 0.50 to <0.60. Probabilities from 0.40 to <0.50 and greater than 0.60 significantly underestimated and overestimated presence, respectively. Applying the model to the study area illuminated an important implication for Bicknell's Thrush conservation. The model predicted increasing numbers of presences and increasing relative density with rising elevation, with which exists a concomitant decrease in land area. Greater land area of lower density habitats may account for more total individuals and reproductive output than higher density less abundant land area. Efforts to conserve areas of highest individual density under the assumption that density reflects habitat quality could target the smallest fraction of the total population.

Applying the log-normal distribution to target detection

NASA Astrophysics Data System (ADS)

Holst, Gerald C.

1992-09-01

Holst and Pickard experimentally determined that MRT responses tend to follow a log-normal distribution. The log normal distribution appeared reasonable because nearly all visual psychological data is plotted on a logarithmic scale. It has the additional advantage that it is bounded to positive values; an important consideration since probability of detection is often plotted in linear coordinates. Review of published data suggests that the log-normal distribution may have universal applicability. Specifically, the log-normal distribution obtained from MRT tests appears to fit the target transfer function and the probability of detection of rectangular targets.

Tsunami Size Distributions at Far-Field Locations from Aggregated Earthquake Sources

NASA Astrophysics Data System (ADS)

Geist, E. L.; Parsons, T.

2015-12-01

The distribution of tsunami amplitudes at far-field tide gauge stations is explained by aggregating the probability of tsunamis derived from individual subduction zones and scaled by their seismic moment. The observed tsunami amplitude distributions of both continental (e.g., San Francisco) and island (e.g., Hilo) stations distant from subduction zones are examined. Although the observed probability distributions nominally follow a Pareto (power-law) distribution, there are significant deviations. Some stations exhibit varying degrees of tapering of the distribution at high amplitudes and, in the case of the Hilo station, there is a prominent break in slope on log-log probability plots. There are also differences in the slopes of the observed distributions among stations that can be significant. To explain these differences we first estimate seismic moment distributions of observed earthquakes for major subduction zones. Second, regression models are developed that relate the tsunami amplitude at a station to seismic moment at a subduction zone, correcting for epicentral distance. The seismic moment distribution is then transformed to a site-specific tsunami amplitude distribution using the regression model. Finally, a mixture distribution is developed, aggregating the transformed tsunami distributions from all relevant subduction zones. This mixture distribution is compared to the observed distribution to assess the performance of the method described above. This method allows us to estimate the largest tsunami that can be expected in a given time period at a station.

Thermodynamic method for generating random stress distributions on an earthquake fault

USGS Publications Warehouse

Barall, Michael; Harris, Ruth A.

2012-01-01

This report presents a new method for generating random stress distributions on an earthquake fault, suitable for use as initial conditions in a dynamic rupture simulation. The method employs concepts from thermodynamics and statistical mechanics. A pattern of fault slip is considered to be analogous to a micro-state of a thermodynamic system. The energy of the micro-state is taken to be the elastic energy stored in the surrounding medium. Then, the Boltzmann distribution gives the probability of a given pattern of fault slip and stress. We show how to decompose the system into independent degrees of freedom, which makes it computationally feasible to select a random state. However, due to the equipartition theorem, straightforward application of the Boltzmann distribution leads to a divergence which predicts infinite stress. To avoid equipartition, we show that the finite strength of the fault acts to restrict the possible states of the system. By analyzing a set of earthquake scaling relations, we derive a new formula for the expected power spectral density of the stress distribution, which allows us to construct a computer algorithm free of infinities. We then present a new technique for controlling the extent of the rupture by generating a random stress distribution thousands of times larger than the fault surface, and selecting a portion which, by chance, has a positive stress perturbation of the desired size. Finally, we present a new two-stage nucleation method that combines a small zone of forced rupture with a larger zone of reduced fracture energy.

The Mass Distribution of Companions to Low-mass White Dwarfs

NASA Astrophysics Data System (ADS)

Andrews, Jeff J.; Price-Whelan, Adrian M.; Agüeros, Marcel A.

2014-12-01

Measuring the masses of companions to single-line spectroscopic binary stars is (in general) not possible because of the unknown orbital plane inclination. Even when the mass of the visible star can be measured, only a lower limit can be placed on the mass of the unseen companion. However, since these inclination angles should be isotropically distributed, for a large enough, unbiased sample, the companion mass distribution can be deconvolved from the distribution of observables. In this work, we construct a hierarchical probabilistic model to infer properties of unseen companion stars given observations of the orbital period and projected radial velocity of the primary star. We apply this model to three mock samples of low-mass white dwarfs (LMWDs; M <~ 0.45 M ⊙) and a sample of post-common-envelope binaries. We use a mixture of two Gaussians to model the WD and neutron star (NS) companion mass distributions. Our model successfully recovers the initial parameters of these test data sets. We then apply our model to 55 WDs in the extremely low-mass (ELM) WD Survey. Our maximum a posteriori model for the WD companion population has a mean mass μWD = 0.74 M ⊙, with a standard deviation σWD = 0.24 M ⊙. Our model constrains the NS companion fraction f NS to be <16% at 68% confidence. We make samples from the posterior distribution publicly available so that future observational efforts may compute the NS probability for newly discovered LMWDs.

Large Scale Groundwater Flow Model for Ho Chi Minh City and its Catchment Area, Southern Vietnam

NASA Astrophysics Data System (ADS)

Sigrist, M.; Tokunaga, T.; Takizawa, S.

2005-12-01

Ho Chi Minh City (HCMC) has become a fast growing city in recent decades and is still growing at a high pace. The water demand for more than 7 million people has increased tremendously, too. Beside surface water, groundwater is used in big amounts to satisfy the need of water. By now, more than 200,000 wells have been developed with very little control. To investigate the sustainability of the water abstraction, a model had been built for the HCMC area and its surrounding. On the catchment scale (around 24,000km2); however, many questions have remained unsolved. In this study, we first gathered and complied geological and hydrogeological information as well as data on groundwater quality to get an idea on regional groundwater flow pattern and problems related to the temporal change of the groundwater situation. Two problems have been depicted by this study. One is the construction of a water reservoir upstream of the Saigon River. This construction has probably changed the water table of the unconfined aquifer, and hence, has significantly changed the properties of soils in some areas. The other problem is the distribution of salty groundwater. Despite the distance of more than 40km from the seashore, groundwater from some wells in and around HCMC shows high concentrations of chloride. Several wells started to produce non-potable water. The chloride concentrations show a complicated and patchy distribution below HCMC, suggesting the possibility of the remnant saltwater at the time of sediment deposition. On the other hand, seawater invades along the streams far beyond HCMC during the dry season and this might be one of the possible sources of salty groundwater by vertical infiltration. A large-scale geological model was constructed and transformed into a hydrogeological model to better understand and quantify the groundwater flow system and the origin of saltwater. Based on the constructed model and numerical calculation, we discuss the influence of reservoir construction on the groundwater situation at the upstream Saigon River, and possible factors for the existence of salty groundwater underneath HCMC.

ON THE EVOLUTIONARY AND PULSATION MASS OF CLASSICAL CEPHEIDS. III. THE CASE OF THE ECLIPSING BINARY CEPHEID CEP0227 IN THE LARGE MAGELLANIC CLOUD

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

Prada Moroni, P. G.; Gennaro, M.; Bono, G.

2012-04-20

We present a new Bayesian approach to constrain the intrinsic parameters (stellar mass and age) of the eclipsing binary system-CEP0227-in the Large Magellanic Cloud (LMC). We computed several sets of evolutionary models covering a broad range in chemical compositions and in stellar mass. Independent sets of models were also constructed either by neglecting or by including a moderate convective core overshooting ({beta}{sub ov} = 0.2) during central hydrogen-burning phases. Sets of models were also constructed either by neglecting or by assuming a canonical ({eta} = 0.4, 0.8) or an enhanced ({eta} = 4) mass-loss rate. The most probable solutions weremore » computed in three different planes: luminosity-temperature, mass-radius, and gravity-temperature. By using the Bayes factor, we found that the most probable solutions were obtained in the gravity-temperature plane with a Gaussian mass prior distribution. The evolutionary models constructed by assuming a moderate convective core overshooting ({beta}{sub ov} = 0.2) and a canonical mass-loss rate ({eta} = 0.4) give stellar masses for the primary (Cepheid)-M = 4.14{sup +0.04}{sub -0.05} M{sub Sun }-and for the secondary-M = 4.15{sup +0.04}{sub -0.05} M{sub Sun }-that agree at the 1% level with dynamical measurements. Moreover, we found ages for the two components and for the combined system-t = 151{sup +4}{sub -3} Myr-that agree at the 5% level. The solutions based on evolutionary models that neglect the mass loss attain similar parameters, while those ones based on models that either account for an enhanced mass loss or neglect convective core overshooting have lower Bayes factors and larger confidence intervals. The dependence on the mass-loss rate might be the consequence of the crude approximation we use to mimic this phenomenon. By using the isochrone of the most probable solution and a Gaussian prior on the LMC distance, we found a true distance modulus-18.53{sup +0.02}{sub -0.02} mag-and a reddening value-E(B - V) = 0.142{sup +0.005}{sub -0.010} mag-that agree quite well with similar estimates in the literature.« less

Application of at-site peak-streamflow frequency analyses for very low annual exceedance probabilities

USGS Publications Warehouse

Asquith, William H.; Kiang, Julie E.; Cohn, Timothy A.

2017-07-17

The U.S. Geological Survey (USGS), in cooperation with the U.S. Nuclear Regulatory Commission, has investigated statistical methods for probabilistic flood hazard assessment to provide guidance on very low annual exceedance probability (AEP) estimation of peak-streamflow frequency and the quantification of corresponding uncertainties using streamgage-specific data. The term “very low AEP” implies exceptionally rare events defined as those having AEPs less than about 0.001 (or 1 × 10–3 in scientific notation or for brevity 10–3). Such low AEPs are of great interest to those involved with peak-streamflow frequency analyses for critical infrastructure, such as nuclear power plants. Flood frequency analyses at streamgages are most commonly based on annual instantaneous peak streamflow data and a probability distribution fit to these data. The fitted distribution provides a means to extrapolate to very low AEPs. Within the United States, the Pearson type III probability distribution, when fit to the base-10 logarithms of streamflow, is widely used, but other distribution choices exist. The USGS-PeakFQ software, implementing the Pearson type III within the Federal agency guidelines of Bulletin 17B (method of moments) and updates to the expected moments algorithm (EMA), was specially adapted for an “Extended Output” user option to provide estimates at selected AEPs from 10–3 to 10–6. Parameter estimation methods, in addition to product moments and EMA, include L-moments, maximum likelihood, and maximum product of spacings (maximum spacing estimation). This study comprehensively investigates multiple distributions and parameter estimation methods for two USGS streamgages (01400500 Raritan River at Manville, New Jersey, and 01638500 Potomac River at Point of Rocks, Maryland). The results of this study specifically involve the four methods for parameter estimation and up to nine probability distributions, including the generalized extreme value, generalized log-normal, generalized Pareto, and Weibull. Uncertainties in streamflow estimates for corresponding AEP are depicted and quantified as two primary forms: quantile (aleatoric [random sampling] uncertainty) and distribution-choice (epistemic [model] uncertainty). Sampling uncertainties of a given distribution are relatively straightforward to compute from analytical or Monte Carlo-based approaches. Distribution-choice uncertainty stems from choices of potentially applicable probability distributions for which divergence among the choices increases as AEP decreases. Conventional goodness-of-fit statistics, such as Cramér-von Mises, and L-moment ratio diagrams are demonstrated in order to hone distribution choice. The results generally show that distribution choice uncertainty is larger than sampling uncertainty for very low AEP values.

Polynomial probability distribution estimation using the method of moments

PubMed Central

Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram–Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation. PMID:28394949

Polynomial probability distribution estimation using the method of moments.

PubMed

Munkhammar, Joakim; Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram-Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

[Application of decision curve on evaluation of MRI predictive model for early assessing pathological complete response to neoadjuvant therapy in breast cancer].

PubMed

He, Y J; Li, X T; Fan, Z Q; Li, Y L; Cao, K; Sun, Y S; Ouyang, T

2018-01-23

Objective: To construct a dynamic enhanced MR based predictive model for early assessing pathological complete response (pCR) to neoadjuvant therapy in breast cancer, and to evaluate the clinical benefit of the model by using decision curve. Methods: From December 2005 to December 2007, 170 patients with breast cancer treated with neoadjuvant therapy were identified and their MR images before neoadjuvant therapy and at the end of the first cycle of neoadjuvant therapy were collected. Logistic regression model was used to detect independent factors for predicting pCR and construct the predictive model accordingly, then receiver operating characteristic (ROC) curve and decision curve were used to evaluate the predictive model. Results: ΔArea(max) and Δslope(max) were independent predictive factors for pCR, OR =0.942 (95% CI : 0.918-0.967) and 0.961 (95% CI : 0.940-0.987), respectively. The area under ROC curve (AUC) for the constructed model was 0.886 (95% CI : 0.820-0.951). Decision curve showed that in the range of the threshold probability above 0.4, the predictive model presented increased net benefit as the threshold probability increased. Conclusions: The constructed predictive model for pCR is of potential clinical value, with an AUC>0.85. Meanwhile, decision curve analysis indicates the constructed predictive model has net benefit from 3 to 8 percent in the likely range of probability threshold from 80% to 90%.

The Spiral of Life

NASA Astrophysics Data System (ADS)

Cajiao Vélez, F.; Kamiński, J. Z.; Krajewska, K.

2018-04-01

High-energy photoionization driven by short and circularly-polarized laser pulses is studied in the framework of the relativistic strong-field approximation. The saddle-point analysis of the integrals defining the probability amplitude is used to determine the general properties of the probability distributions. Additionally, an approximate solution to the saddle-point equation is derived. This leads to the concept of the three-dimensional spiral of life in momentum space, around which the ionization probability distribution is maximum. We demonstrate that such spiral is also obtained from a classical treatment.

Towards a Fuzzy Bayesian Network Based Approach for Safety Risk Analysis of Tunnel-Induced Pipeline Damage.

PubMed

Zhang, Limao; Wu, Xianguo; Qin, Yawei; Skibniewski, Miroslaw J; Liu, Wenli

2016-02-01

Tunneling excavation is bound to produce significant disturbances to surrounding environments, and the tunnel-induced damage to adjacent underground buried pipelines is of considerable importance for geotechnical practice. A fuzzy Bayesian networks (FBNs) based approach for safety risk analysis is developed in this article with detailed step-by-step procedures, consisting of risk mechanism analysis, the FBN model establishment, fuzzification, FBN-based inference, defuzzification, and decision making. In accordance with the failure mechanism analysis, a tunnel-induced pipeline damage model is proposed to reveal the cause-effect relationships between the pipeline damage and its influential variables. In terms of the fuzzification process, an expert confidence indicator is proposed to reveal the reliability of the data when determining the fuzzy probability of occurrence of basic events, with both the judgment ability level and the subjectivity reliability level taken into account. By means of the fuzzy Bayesian inference, the approach proposed in this article is capable of calculating the probability distribution of potential safety risks and identifying the most likely potential causes of accidents under both prior knowledge and given evidence circumstances. A case concerning the safety analysis of underground buried pipelines adjacent to the construction of the Wuhan Yangtze River Tunnel is presented. The results demonstrate the feasibility of the proposed FBN approach and its application potential. The proposed approach can be used as a decision tool to provide support for safety assurance and management in tunnel construction, and thus increase the likelihood of a successful project in a complex project environment. © 2015 Society for Risk Analysis.

A novel approach for detecting heat waves: the Standardized Heat-Wave Index.

NASA Astrophysics Data System (ADS)

Cucchi, Marco; Petitta, Marcello; Calmanti, Sandro

2016-04-01

Extreme temperatures have an impact on the energy balance of any living organism and on the operational capabilities of critical infrastructures. The ability to capture the occurrence of extreme temperature events is therefore an essential property of a multi-hazard extreme climate indicator. In this paper we introduce a new index for the detection of such extreme temperature events called SHI (Standardized Heat-Wave Index), developed in the context of XCF project for the construction of a multi-hazard extreme climate indicator (ECI). SHI is a probabilistic index based on the analysis of maximum daily temperatures time series; it is standardized, enabling comparisons overs space/time and with other indices, and it is capable of describing both extreme cold and hot events. Given a particular location, SHI is constructed using the time series of local maximum daily temperatures with the following procedure: three-days cumulated maximum daily temperatures are assigned to each day of the time series; probabilities of occurrence in the same months the reference days belong to are computed for each of the previous calculated values; such probability values are thus projected on a standard normal distribution, obtaining our standardized indices. In this work we present results obtained using NCEP Reanalysis dataset for air temperature at sigma 0.995 level, which timespan ranges from 1948 to 2014. Given the specific framework of this work, the geographical focus of this study is limited to the African continent. We present a validation of the index by showing its use for monitoring heat-waves under different climate regimes.

Association of earthquakes and faults in the San Francisco Bay area using Bayesian inference

USGS Publications Warehouse

Wesson, R.L.; Bakun, W.H.; Perkins, D.M.

2003-01-01

Bayesian inference provides a method to use seismic intensity data or instrumental locations, together with geologic and seismologic data, to make quantitative estimates of the probabilities that specific past earthquakes are associated with specific faults. Probability density functions are constructed for the location of each earthquake, and these are combined with prior probabilities through Bayes' theorem to estimate the probability that an earthquake is associated with a specific fault. Results using this method are presented here for large, preinstrumental, historical earthquakes and for recent earthquakes with instrumental locations in the San Francisco Bay region. The probabilities for individual earthquakes can be summed to construct a probabilistic frequency-magnitude relationship for a fault segment. Other applications of the technique include the estimation of the probability of background earthquakes, that is, earthquakes not associated with known or considered faults, and the estimation of the fraction of the total seismic moment associated with earthquakes less than the characteristic magnitude. Results for the San Francisco Bay region suggest that potentially damaging earthquakes with magnitudes less than the characteristic magnitudes should be expected. Comparisons of earthquake locations and the surface traces of active faults as determined from geologic data show significant disparities, indicating that a complete understanding of the relationship between earthquakes and faults remains elusive.

Count data, detection probabilities, and the demography, dynamics, distribution, and decline of amphibians.

PubMed

Schmidt, Benedikt R

2003-08-01

The evidence for amphibian population declines is based on count data that were not adjusted for detection probabilities. Such data are not reliable even when collected using standard methods. The formula C = Np (where C is a count, N the true parameter value, and p is a detection probability) relates count data to demography, population size, or distributions. With unadjusted count data, one assumes a linear relationship between C and N and that p is constant. These assumptions are unlikely to be met in studies of amphibian populations. Amphibian population data should be based on methods that account for detection probabilities.

Bayesian data analysis tools for atomic physics

NASA Astrophysics Data System (ADS)

Trassinelli, Martino

2017-10-01

We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes' theorem and its applications. In particular we discuss about how to calculate simple and joint probability distributions and the Bayesian evidence, a model dependent quantity that allows to assign probabilities to different hypotheses from the analysis of a same data set. To give some practical examples, these methods are applied to two concrete cases. In the first example, the presence or not of a satellite line in an atomic spectrum is investigated. In the second example, we determine the most probable model among a set of possible profiles from the analysis of a statistically poor spectrum. We show also how to calculate the probability distribution of the main spectral component without having to determine uniquely the spectrum modeling. For these two studies, we implement the program Nested_fit to calculate the different probability distributions and other related quantities. Nested_fit is a Fortran90/Python code developed during the last years for analysis of atomic spectra. As indicated by the name, it is based on the nested algorithm, which is presented in details together with the program itself.

Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

NASA Astrophysics Data System (ADS)

Batac, Rene C.; Paguirigan, Antonino A., Jr.; Tarun, Anjali B.; Longjas, Anthony G.

2017-04-01

We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of self-organized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy distributions closely follow power-law probability density functions (PDFs) with a scaling exponent of around -1. 6, consistent with the expectations of the Gutenberg-Richter (GR) law, for a wide range of the targeted triggering probability values. Additionally, for targeted triggering probabilities within the range 0.004-0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, the foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, while introducing minimal parameters in the simple rules of the sandpile. We believe that the critical targeting probability parameterizes the memory that is inherently present in earthquake-generating regions.

Assessment of impact of urbanisation on background radiation exposure and human health risk estimation in Kuala Lumpur, Malaysia.

PubMed

Sanusi, M S M; Ramli, A T; Hassan, W M S W; Lee, M H; Izham, A; Said, M N; Wagiran, H; Heryanshah, A

2017-07-01

Kuala Lumpur has been undergoing rapid urbanisation process, mainly in infrastructure development. The opening of new township and residential in former tin mining areas, particularly in the heavy mineral- or tin-bearing alluvial soil in Kuala Lumpur, is a contentious subject in land-use regulation. Construction practices, i.e. reclamation and dredging in these areas are potential to enhance the radioactivity levels of soil and subsequently, increase the existing background gamma radiation levels. This situation is worsened with the utilisation of tin tailings as construction materials apart from unavoidable soil pollutions due to naturally occurring radioactive materials in construction materials, e.g. granitic aggregate, cement and red clay brick. This study was conducted to assess the urbanisation impacts on background gamma radiation in Kuala Lumpur. The study found that the mean value of measured dose rate was 251±6nGyh -1 (156-392nGyh -1 ) and 4 times higher than the world average value. High radioactivity levels of 238 U (95±12Bqkg -1 ), 232 Th (191±23Bqkg -1 ,) and 40 K (727±130Bqkg -1 ) in soil were identified as the major source of high radiation exposure. Based on statistical ANOVA, t-test, and analyses of cumulative probability distribution, this study has statistically verified the dose enhancements in the background radiation. The effective dose was estimated to be 0.31±0.01mSvy -1 per man. The recommended ICRP reference level (1-20mSvy -1 ) is applicable to the involved existing exposure situation in this study. The estimated effective dose in this study is lower than the ICRP reference level and too low to cause deterministic radiation effects. Nevertheless based on estimations of lifetime radiation exposure risks, this study found that there was small probability for individual in Kuala Lumpur being diagnosed with cancer and dying of cancer. Copyright © 2017 Elsevier Ltd. All rights reserved.

An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling

NASA Astrophysics Data System (ADS)

Zhang, Guannan; Lu, Dan; Ye, Ming; Gunzburger, Max; Webster, Clayton

2013-10-01

Bayesian analysis has become vital to uncertainty quantification in groundwater modeling, but its application has been hindered by the computational cost associated with numerous model executions required by exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, a new approach is developed to improve the computational efficiency of Bayesian inference by constructing a surrogate of the PPDF, using an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, this paper utilizes a compactly supported higher-order hierarchical basis to construct the surrogate system, resulting in a significant reduction in the number of required model executions. In addition, using the hierarchical surplus as an error indicator allows locally adaptive refinement of sparse grids in the parameter space, which further improves computational efficiency. To efficiently build the surrogate system for the PPDF with multiple significant modes, optimization techniques are used to identify the modes, for which high-probability regions are defined and components of the aSG-hSC approximation are constructed. After the surrogate is determined, the PPDF can be evaluated by sampling the surrogate system directly without model execution, resulting in improved efficiency of the surrogate-based MCMC compared with conventional MCMC. The developed method is evaluated using two synthetic groundwater reactive transport models. The first example involves coupled linear reactions and demonstrates the accuracy of our high-order hierarchical basis approach in approximating high-dimensional posteriori distribution. The second example is highly nonlinear because of the reactions of uranium surface complexation, and demonstrates how the iterative aSG-hSC method is able to capture multimodal and non-Gaussian features of PPDF caused by model nonlinearity. Both experiments show that aSG-hSC is an effective and efficient tool for Bayesian inference.

Characterising RNA secondary structure space using information entropy

PubMed Central

2013-01-01

Comparative methods for RNA secondary structure prediction use evolutionary information from RNA alignments to increase prediction accuracy. The model is often described in terms of stochastic context-free grammars (SCFGs), which generate a probability distribution over secondary structures. It is, however, unclear how this probability distribution changes as a function of the input alignment. As prediction programs typically only return a single secondary structure, better characterisation of the underlying probability space of RNA secondary structures is of great interest. In this work, we show how to efficiently compute the information entropy of the probability distribution over RNA secondary structures produced for RNA alignments by a phylo-SCFG, and implement it for the PPfold model. We also discuss interpretations and applications of this quantity, including how it can clarify reasons for low prediction reliability scores. PPfold and its source code are available from http://birc.au.dk/software/ppfold/. PMID:23368905

The probability distribution of side-chain conformations in [Leu] and [Met]enkephalin determines the potency and selectivity to mu and delta opiate receptors.

PubMed

Nielsen, Bjørn G; Jensen, Morten Ø; Bohr, Henrik G

2003-01-01

The structure of enkephalin, a small neuropeptide with five amino acids, has been simulated on computers using molecular dynamics. Such simulations exhibit a few stable conformations, which also have been identified experimentally. The simulations provide the possibility to perform cluster analysis in the space defined by potentially pharmacophoric measures such as dihedral angles, side-chain orientation, etc. By analyzing the statistics of the resulting clusters, the probability distribution of the side-chain conformations may be determined. These probabilities allow us to predict the selectivity of [Leu]enkephalin and [Met]enkephalin to the known mu- and delta-type opiate receptors to which they bind as agonists. Other plausible consequences of these probability distributions are discussed in relation to the way in which they may influence the dynamics of the synapse. Copyright 2003 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 71: 577-592, 2003

A Single Camera Motion Capture System for Human-Computer Interaction

NASA Astrophysics Data System (ADS)

Okada, Ryuzo; Stenger, Björn

This paper presents a method for markerless human motion capture using a single camera. It uses tree-based filtering to efficiently propagate a probability distribution over poses of a 3D body model. The pose vectors and associated shapes are arranged in a tree, which is constructed by hierarchical pairwise clustering, in order to efficiently evaluate the likelihood in each frame. Anew likelihood function based on silhouette matching is proposed that improves the pose estimation of thinner body parts, i. e. the limbs. The dynamic model takes self-occlusion into account by increasing the variance of occluded body-parts, thus allowing for recovery when the body part reappears. We present two applications of our method that work in real-time on a Cell Broadband Engine™: a computer game and a virtual clothing application.

Towards an information geometric characterization/classification of complex systems. I. Use of generalized entropies

NASA Astrophysics Data System (ADS)

Ghikas, Demetris P. K.; Oikonomou, Fotios D.

2018-04-01

Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is to construct first some fundamental geometric objects which will be used in the development of our geometrical framework. We first establish the existence of a two-parameter family of probability distributions. Then using this family we derive the associated metric and we state a generalized Cramer-Rao Inequality. This gives a first two-parameter classification of complex systems. Finally computing the scalar curvature of the information manifold we obtain a further discrimination of the corresponding classes. Our analysis is based on the two-parameter family of generalized entropies of Hanel and Thurner (2011).

Predictive Modeling of Risk Associated with Temperature Extremes over Continental US

NASA Astrophysics Data System (ADS)

Kravtsov, S.; Roebber, P.; Brazauskas, V.

2016-12-01

We build an extremely statistically accurate, essentially bias-free empirical emulator of atmospheric surface temperature and apply it for meteorological risk assessment over the domain of continental US. The resulting prediction scheme achieves an order-of-magnitude or larger gain of numerical efficiency compared with the schemes based on high-resolution dynamical atmospheric models, leading to unprecedented accuracy of the estimated risk distributions. The empirical model construction methodology is based on our earlier work, but is further modified to account for the influence of large-scale, global climate change on regional US weather and climate. The resulting estimates of the time-dependent, spatially extended probability of temperature extremes over the simulation period can be used as a risk management tool by insurance companies and regulatory governmental agencies.

The returns and risks of investment portfolio in a financial market

NASA Astrophysics Data System (ADS)

Li, Jiang-Cheng; Mei, Dong-Cheng

2014-07-01

The returns and risks of investment portfolio in a financial system was investigated by constructing a theoretical model based on the Heston model. After the theoretical model and analysis of portfolio were calculated and analyzed, we find the following: (i) The statistical properties (i.e., the probability distribution, the variance and loss rate of equity portfolio return) between simulation results of the theoretical model and the real financial data obtained from Dow Jones Industrial Average are in good agreement; (ii) The maximum dispersion of the investment portfolio is associated with the maximum stability of the equity portfolio return and minimal investment risks; (iii) An increase of the investment period and a worst investment period are associated with a decrease of stability of the equity portfolio return and a maximum investment risk, respectively.

Non-Gaussian statistics and optical rogue waves in stimulated Raman scattering.

PubMed

Monfared, Yashar E; Ponomarenko, Sergey A

2017-03-20

We explore theoretically and numerically optical rogue wave formation in stimulated Raman scattering inside a hydrogen filled hollow core photonic crystal fiber. We assume a weak noisy Stokes pulse input and explicitly construct the input Stokes pulse ensemble using the coherent mode representation of optical coherence theory, thereby providing a link between optical coherence and rogue wave theories. We show that the Stokes pulse peak power probability distribution function (PDF) acquires a long tail in the limit of nearly incoherent input Stokes pulses. We demonstrate a clear link between the PDF tail magnitude and the source coherence time. Thus, the latter can serve as a convenient parameter to control the former. We explain our findings qualitatively using the concepts of statistical granularity and global degree of coherence.

Rényi and Tsallis formulations of separability conditions in finite dimensions

NASA Astrophysics Data System (ADS)

Rastegin, Alexey E.

2017-12-01

Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of Rényi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach based on the convolution of discrete probability distributions. Measurements on a total system are constructed of local ones according to the convolution scheme. Separability conditions are derived on the base of uncertainty relations of the Maassen-Uffink type as well as majorization relations. On each of subsystems, we use a pair of sets of subnormalized vectors that form rank-one POVMs. We also obtain entropic separability conditions for local measurements with a special structure, such as mutually unbiased bases and symmetric informationally complete measurements. The relevance of the derived separability conditions is demonstrated with several examples.

Simulation of noisy dynamical system by Deep Learning

NASA Astrophysics Data System (ADS)

Yeo, Kyongmin

2017-11-01

Deep learning has attracted huge attention due to its powerful representation capability. However, most of the studies on deep learning have been focused on visual analytics or language modeling and the capability of the deep learning in modeling dynamical systems is not well understood. In this study, we use a recurrent neural network to model noisy nonlinear dynamical systems. In particular, we use a long short-term memory (LSTM) network, which constructs internal nonlinear dynamics systems. We propose a cross-entropy loss with spatial ridge regularization to learn a non-stationary conditional probability distribution from a noisy nonlinear dynamical system. A Monte Carlo procedure to perform time-marching simulations by using the LSTM is presented. The behavior of the LSTM is studied by using noisy, forced Van der Pol oscillator and Ikeda equation.

Statistical behavior of ten million experimental detection limits

NASA Astrophysics Data System (ADS)

Voigtman, Edward; Abraham, Kevin T.

2011-02-01

Using a lab-constructed laser-excited fluorimeter, together with bootstrapping methodology, the authors have generated many millions of experimental linear calibration curves for the detection of rhodamine 6G tetrafluoroborate in ethanol solutions. The detection limits computed from them are in excellent agreement with both previously published theory and with comprehensive Monte Carlo computer simulations. Currie decision levels and Currie detection limits, each in the theoretical, chemical content domain, were found to be simply scaled reciprocals of the non-centrality parameter of the non-central t distribution that characterizes univariate linear calibration curves that have homoscedastic, additive Gaussian white noise. Accurate and precise estimates of the theoretical, content domain Currie detection limit for the experimental system, with 5% (each) probabilities of false positives and false negatives, are presented.

Exact probability distribution function for the volatility of cumulative production

NASA Astrophysics Data System (ADS)

Zadourian, Rubina; Klümper, Andreas

2018-04-01

In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in Lafond et al. (2017), which addressed the effects of normally distributed noise in the production process. Due to its wide applicability in industrial and technological activities we present here the mathematical foundation for an arbitrary distribution function of the process, which we expect will pave the future research on forecasting of the production process.

Statistics of intensity in adaptive-optics images and their usefulness for detection and photometry of exoplanets.

PubMed

Gladysz, Szymon; Yaitskova, Natalia; Christou, Julian C

2010-11-01

This paper is an introduction to the problem of modeling the probability density function of adaptive-optics speckle. We show that with the modified Rician distribution one cannot describe the statistics of light on axis. A dual solution is proposed: the modified Rician distribution for off-axis speckle and gamma-based distribution for the core of the point spread function. From these two distributions we derive optimal statistical discriminators between real sources and quasi-static speckles. In the second part of the paper the morphological difference between the two probability density functions is used to constrain a one-dimensional, "blind," iterative deconvolution at the position of an exoplanet. Separation of the probability density functions of signal and speckle yields accurate differential photometry in our simulations of the SPHERE planet finder instrument.

Small-Scale Spatio-Temporal Distribution of Bactrocera minax (Enderlein) (Diptera: Tephritidae) Using Probability Kriging.

PubMed

Wang, S Q; Zhang, H Y; Li, Z L

2016-10-01

Understanding spatio-temporal distribution of pest in orchards can provide important information that could be used to design monitoring schemes and establish better means for pest control. In this study, the spatial and temporal distribution of Bactrocera minax (Enderlein) (Diptera: Tephritidae) was assessed, and activity trends were evaluated by using probability kriging. Adults of B. minax were captured in two successive occurrences in a small-scale citrus orchard by using food bait traps, which were placed both inside and outside the orchard. The weekly spatial distribution of B. minax within the orchard and adjacent woods was examined using semivariogram parameters. The edge concentration was discovered during the most weeks in adult occurrence, and the population of the adults aggregated with high probability within a less-than-100-m-wide band on both of the sides of the orchard and the woods. The sequential probability kriged maps showed that the adults were estimated in the marginal zone with higher probability, especially in the early and peak stages. The feeding, ovipositing, and mating behaviors of B. minax are possible explanations for these spatio-temporal patterns. Therefore, spatial arrangement and distance to the forest edge of traps or spraying spot should be considered to enhance pest control on B. minax in small-scale orchards.

L1-norm locally linear representation regularization multi-source adaptation learning.

PubMed

Tao, Jianwen; Wen, Shiting; Hu, Wenjun

2015-09-01

In most supervised domain adaptation learning (DAL) tasks, one has access only to a small number of labeled examples from target domain. Therefore the success of supervised DAL in this "small sample" regime needs the effective utilization of the large amounts of unlabeled data to extract information that is useful for generalization. Toward this end, we here use the geometric intuition of manifold assumption to extend the established frameworks in existing model-based DAL methods for function learning by incorporating additional information about the target geometric structure of the marginal distribution. We would like to ensure that the solution is smooth with respect to both the ambient space and the target marginal distribution. In doing this, we propose a novel L1-norm locally linear representation regularization multi-source adaptation learning framework which exploits the geometry of the probability distribution, which has two techniques. Firstly, an L1-norm locally linear representation method is presented for robust graph construction by replacing the L2-norm reconstruction measure in LLE with L1-norm one, which is termed as L1-LLR for short. Secondly, considering the robust graph regularization, we replace traditional graph Laplacian regularization with our new L1-LLR graph Laplacian regularization and therefore construct new graph-based semi-supervised learning framework with multi-source adaptation constraint, which is coined as L1-MSAL method. Moreover, to deal with the nonlinear learning problem, we also generalize the L1-MSAL method by mapping the input data points from the input space to a high-dimensional reproducing kernel Hilbert space (RKHS) via a nonlinear mapping. Promising experimental results have been obtained on several real-world datasets such as face, visual video and object. Copyright © 2015 Elsevier Ltd. All rights reserved.

A comparison of confidence interval methods for the concordance correlation coefficient and intraclass correlation coefficient with small number of raters.

PubMed

Feng, Dai; Svetnik, Vladimir; Coimbra, Alexandre; Baumgartner, Richard

2014-01-01

The intraclass correlation coefficient (ICC) with fixed raters or, equivalently, the concordance correlation coefficient (CCC) for continuous outcomes is a widely accepted aggregate index of agreement in settings with small number of raters. Quantifying the precision of the CCC by constructing its confidence interval (CI) is important in early drug development applications, in particular in qualification of biomarker platforms. In recent years, there have been several new methods proposed for construction of CIs for the CCC, but their comprehensive comparison has not been attempted. The methods consisted of the delta method and jackknifing with and without Fisher's Z-transformation, respectively, and Bayesian methods with vague priors. In this study, we carried out a simulation study, with data simulated from multivariate normal as well as heavier tailed distribution (t-distribution with 5 degrees of freedom), to compare the state-of-the-art methods for assigning CI to the CCC. When the data are normally distributed, the jackknifing with Fisher's Z-transformation (JZ) tended to provide superior coverage and the difference between it and the closest competitor, the Bayesian method with the Jeffreys prior was in general minimal. For the nonnormal data, the jackknife methods, especially the JZ method, provided the coverage probabilities closest to the nominal in contrast to the others which yielded overly liberal coverage. Approaches based upon the delta method and Bayesian method with conjugate prior generally provided slightly narrower intervals and larger lower bounds than others, though this was offset by their poor coverage. Finally, we illustrated the utility of the CIs for the CCC in an example of a wake after sleep onset (WASO) biomarker, which is frequently used in clinical sleep studies of drugs for treatment of insomnia.

The Detection of Signals in Impulsive Noise.

DTIC Science & Technology

1983-06-01

ASSI FICATION/ DOWN GRADING SCHEOUL1E * I1S. DISTRIBUTION STATEMENT (of th0i0 Rhport) Approved for Public Release; Distribucion Unlimited * 17...has a symmetric distribution, sgn(x i) will be -1 with probability 1/2 and +1 with probability 1/2. Considering the sum of observations as 0 binomial