COVAL, Compound Probability Distribution for Function of Probability Distribution
International Nuclear Information System (INIS)
Astolfi, M.; Elbaz, J.
1979-01-01
1 - Nature of the physical problem solved: Computation of the probability distribution of a function of variables, given the probability distribution of the variables themselves. 'COVAL' has been applied to reliability analysis of a structure subject to random loads. 2 - Method of solution: Numerical transformation of probability distributions
Some applications of the fractional Poisson probability distribution
International Nuclear Information System (INIS)
Laskin, Nick
2009-01-01
Physical and mathematical applications of the recently invented fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we have developed the fractional generalization of Bell polynomials, Bell numbers, and Stirling numbers of the second kind. The appearance of fractional Bell polynomials is natural if one evaluates the diagonal matrix element of the evolution operator in the basis of newly introduced quantum coherent states. Fractional Stirling numbers of the second kind have been introduced and applied to evaluate the skewness and kurtosis of the fractional Poisson probability distribution function. A representation of the Bernoulli numbers in terms of fractional Stirling numbers of the second kind has been found. In the limit case when the fractional Poisson probability distribution becomes the Poisson probability distribution, all of the above listed developments and implementations turn into the well-known results of the quantum optics and the theory of combinatorial numbers.
Subjective Probabilities for State-Dependent Continuous Utility
P.P. Wakker (Peter)
1987-01-01
textabstractFor the expected utility model with state dependent utilities, Karni, Schmeidler and Vind (1983) have shown how to recover uniquely the involved subjective probabilities if the preferences, contingent on a hypothetical probability distribution over the state space, are known. This they
On the probability distribution of daily streamflow in the United States
Blum, Annalise G.; Archfield, Stacey A.; Vogel, Richard M.
2017-06-01
Daily streamflows are often represented by flow duration curves (FDCs), which illustrate the frequency with which flows are equaled or exceeded. FDCs have had broad applications across both operational and research hydrology for decades; however, modeling FDCs has proven elusive. Daily streamflow is a complex time series with flow values ranging over many orders of magnitude. The identification of a probability distribution that can approximate daily streamflow would improve understanding of the behavior of daily flows and the ability to estimate FDCs at ungaged river locations. Comparisons of modeled and empirical FDCs at nearly 400 unregulated, perennial streams illustrate that the four-parameter kappa distribution provides a very good representation of daily streamflow across the majority of physiographic regions in the conterminous United States (US). Further, for some regions of the US, the three-parameter generalized Pareto and lognormal distributions also provide a good approximation to FDCs. Similar results are found for the period of record FDCs, representing the long-term hydrologic regime at a site, and median annual FDCs, representing the behavior of flows in a typical year.
Wigner function and the probability representation of quantum states
Directory of Open Access Journals (Sweden)
Man’ko Margarita A.
2014-01-01
Full Text Available The relation of theWigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics with the integral Radon transform of the Wigner quasidistribution is discussed. The Wigner–Moyal equation for the Wigner function is presented in the form of kinetic equation for the tomographic probability distribution both in quantum mechanics and in the classical limit of the Liouville equation. The calculation of moments of physical observables in terms of integrals with the state tomographic probability distributions is constructed having a standard form of averaging in the probability theory. New uncertainty relations for the position and momentum are written in terms of optical tomograms suitable for directexperimental check. Some recent experiments on checking the uncertainty relations including the entropic uncertainty relations are discussed.
Pre-Aggregation with Probability Distributions
DEFF Research Database (Denmark)
Timko, Igor; Dyreson, Curtis E.; Pedersen, Torben Bach
2006-01-01
Motivated by the increasing need to analyze complex, uncertain multidimensional data this paper proposes probabilistic OLAP queries that are computed using probability distributions rather than atomic values. The paper describes how to create probability distributions from base data, and how...... the distributions can be subsequently used in pre-aggregation. Since the probability distributions can become large, we show how to achieve good time and space efficiency by approximating the distributions. We present the results of several experiments that demonstrate the effectiveness of our methods. The work...... is motivated with a real-world case study, based on our collaboration with a leading Danish vendor of location-based services. This paper is the first to consider the approximate processing of probabilistic OLAP queries over probability distributions....
Probability distributions for Markov chain based quantum walks
Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.
2018-01-01
We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.
A Probability Distribution over Latent Causes, in the Orbitofrontal Cortex.
Chan, Stephanie C Y; Niv, Yael; Norman, Kenneth A
2016-07-27
The orbitofrontal cortex (OFC) has been implicated in both the representation of "state," in studies of reinforcement learning and decision making, and also in the representation of "schemas," in studies of episodic memory. Both of these cognitive constructs require a similar inference about the underlying situation or "latent cause" that generates our observations at any given time. The statistically optimal solution to this inference problem is to use Bayes' rule to compute a posterior probability distribution over latent causes. To test whether such a posterior probability distribution is represented in the OFC, we tasked human participants with inferring a probability distribution over four possible latent causes, based on their observations. Using fMRI pattern similarity analyses, we found that BOLD activity in the OFC is best explained as representing the (log-transformed) posterior distribution over latent causes. Furthermore, this pattern explained OFC activity better than other task-relevant alternatives, such as the most probable latent cause, the most recent observation, or the uncertainty over latent causes. Our world is governed by hidden (latent) causes that we cannot observe, but which generate the observations we see. A range of high-level cognitive processes require inference of a probability distribution (or "belief distribution") over the possible latent causes that might be generating our current observations. This is true for reinforcement learning and decision making (where the latent cause comprises the true "state" of the task), and for episodic memory (where memories are believed to be organized by the inferred situation or "schema"). Using fMRI, we show that this belief distribution over latent causes is encoded in patterns of brain activity in the orbitofrontal cortex, an area that has been separately implicated in the representations of both states and schemas. Copyright © 2016 the authors 0270-6474/16/367817-12$15.00/0.
Probabilistic Cloning of Three Real States with Optimal Success Probabilities
Rui, Pin-shu
2017-06-01
We investigate the probabilistic quantum cloning (PQC) of three real states with average probability distribution. To get the analytic forms of the optimal success probabilities we assume that the three states have only two pairwise inner products. Based on the optimal success probabilities, we derive the explicit form of 1 →2 PQC for cloning three real states. The unitary operation needed in the PQC process is worked out too. The optimal success probabilities are also generalized to the M→ N PQC case.
Pre-aggregation for Probability Distributions
DEFF Research Database (Denmark)
Timko, Igor; Dyreson, Curtis E.; Pedersen, Torben Bach
Motivated by the increasing need to analyze complex uncertain multidimensional data (e.g., in order to optimize and personalize location-based services), this paper proposes novel types of {\\em probabilistic} OLAP queries that operate on aggregate values that are probability distributions...... and the techniques to process these queries. The paper also presents the methods for computing the probability distributions, which enables pre-aggregation, and for using the pre-aggregated distributions for further aggregation. In order to achieve good time and space efficiency, the methods perform approximate...... multidimensional data analysis that is considered in this paper (i.e., approximate processing of probabilistic OLAP queries over probability distributions)....
International Nuclear Information System (INIS)
Vinogradov, S.
2012-01-01
Silicon Photomultipliers (SiPM), also called Solid State Photomultipliers (SSPM), are based on Geiger mode avalanche breakdown that is limited by a strong negative feedback. An SSPM can detect and resolve single photons due to the high gain and ultra-low excess noise of avalanche multiplication in this mode. Crosstalk and afterpulsing processes associated with the high gain introduce specific excess noise and deteriorate the photon number resolution of the SSPM. The probabilistic features of these processes are widely studied because of its significance for the SSPM design, characterization, optimization and application, but the process modeling is mostly based on Monte Carlo simulations and numerical methods. In this study, crosstalk is considered to be a branching Poisson process, and analytical models of probability distribution and excess noise factor (ENF) of SSPM signals based on the Borel distribution as an advance on the geometric distribution models are presented and discussed. The models are found to be in a good agreement with the experimental probability distributions for dark counts and a few photon spectrums in a wide range of fired pixels number as well as with observed super-linear behavior of crosstalk ENF.
Feynman quasi probability distribution for spin-(1/2), and its generalizations
International Nuclear Information System (INIS)
Colucci, M.
1999-01-01
It has been examined the Feynman's paper Negative probability, in which, after a discussion about the possibility of attributing a real physical meaning to quasi probability distributions, he introduces a new kind of distribution for spin-(1/2), with a possible method of generalization to systems with arbitrary number of states. The principal aim of this article is to shed light upon the method of construction of these distributions, taking into consideration their application to some experiments, and discussing their positive and negative aspects
Evaluation of burst probability for tubes by Weibull distributions
International Nuclear Information System (INIS)
Kao, S.
1975-10-01
The investigations of candidate distributions that best describe the burst pressure failure probability characteristics of nuclear power steam generator tubes has been continued. To date it has been found that the Weibull distribution provides an acceptable fit for the available data from both the statistical and physical viewpoints. The reasons for the acceptability of the Weibull distribution are stated together with the results of tests for the suitability of fit. In exploring the acceptability of the Weibull distribution for the fitting, a graphical method to be called the ''density-gram'' is employed instead of the usual histogram. With this method a more sensible graphical observation on the empirical density may be made for cases where the available data is very limited. Based on these methods estimates of failure pressure are made for the left-tail probabilities
Probability distribution of long-run indiscriminate felling of trees in ...
African Journals Online (AJOL)
The study was undertaken to determine the probability distribution of Long-run indiscriminate felling of trees in northern senatorial district of Adamawa State. Specifically, the study focused on examining the future direction of indiscriminate felling of trees as well as its equilibrium distribution. A multi-stage and simple random ...
Modeling highway travel time distribution with conditional probability models
Energy Technology Data Exchange (ETDEWEB)
Oliveira Neto, Francisco Moraes [ORNL; Chin, Shih-Miao [ORNL; Hwang, Ho-Ling [ORNL; Han, Lee [University of Tennessee, Knoxville (UTK)
2014-01-01
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 provides 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).
Bayesian optimization for computationally extensive probability distributions.
Tamura, Ryo; Hukushima, Koji
2018-01-01
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribution. Our Bayesian optimization technique is applied to the posterior distribution in the effective physical model estimation, which is a computationally extensive probability distribution. Even when the number of sampling points on the posterior distributions is fixed to be small, the Bayesian optimization provides a better maximizer of the posterior distributions in comparison to those by the random search method, the steepest descent method, or the Monte Carlo method. Furthermore, the Bayesian optimization improves the results efficiently by combining the steepest descent method and thus it is a powerful tool to search for a better maximizer of computationally extensive probability distributions.
Assigning probability distributions to input parameters of performance assessment models
Energy Technology Data Exchange (ETDEWEB)
Mishra, Srikanta [INTERA Inc., Austin, TX (United States)
2002-02-01
This study presents an overview of various approaches for assigning probability distributions to input parameters and/or future states of performance assessment models. Specifically,three broad approaches are discussed for developing input distributions: (a) fitting continuous distributions to data, (b) subjective assessment of probabilities, and (c) Bayesian updating of prior knowledge based on new information. The report begins with a summary of the nature of data and distributions, followed by a discussion of several common theoretical parametric models for characterizing distributions. Next, various techniques are presented for fitting continuous distributions to data. These include probability plotting, method of moments, maximum likelihood estimation and nonlinear least squares analysis. The techniques are demonstrated using data from a recent performance assessment study for the Yucca Mountain project. Goodness of fit techniques are also discussed, followed by an overview of how distribution fitting is accomplished in commercial software packages. The issue of subjective assessment of probabilities is dealt with in terms of the maximum entropy distribution selection approach, as well as some common rules for codifying informal expert judgment. Formal expert elicitation protocols are discussed next, and are based primarily on the guidance provided by the US NRC. The Bayesian framework for updating prior distributions (beliefs) when new information becomes available is discussed. A simple numerical approach is presented for facilitating practical applications of the Bayes theorem. Finally, a systematic framework for assigning distributions is presented: (a) for the situation where enough data are available to define an empirical CDF or fit a parametric model to the data, and (b) to deal with the situation where only a limited amount of information is available.
Assigning probability distributions to input parameters of performance assessment models
International Nuclear Information System (INIS)
Mishra, Srikanta
2002-02-01
This study presents an overview of various approaches for assigning probability distributions to input parameters and/or future states of performance assessment models. Specifically,three broad approaches are discussed for developing input distributions: (a) fitting continuous distributions to data, (b) subjective assessment of probabilities, and (c) Bayesian updating of prior knowledge based on new information. The report begins with a summary of the nature of data and distributions, followed by a discussion of several common theoretical parametric models for characterizing distributions. Next, various techniques are presented for fitting continuous distributions to data. These include probability plotting, method of moments, maximum likelihood estimation and nonlinear least squares analysis. The techniques are demonstrated using data from a recent performance assessment study for the Yucca Mountain project. Goodness of fit techniques are also discussed, followed by an overview of how distribution fitting is accomplished in commercial software packages. The issue of subjective assessment of probabilities is dealt with in terms of the maximum entropy distribution selection approach, as well as some common rules for codifying informal expert judgment. Formal expert elicitation protocols are discussed next, and are based primarily on the guidance provided by the US NRC. The Bayesian framework for updating prior distributions (beliefs) when new information becomes available is discussed. A simple numerical approach is presented for facilitating practical applications of the Bayes theorem. Finally, a systematic framework for assigning distributions is presented: (a) for the situation where enough data are available to define an empirical CDF or fit a parametric model to the data, and (b) to deal with the situation where only a limited amount of information is available
Quantum probabilities of composite events in quantum measurements with multimode states
International Nuclear Information System (INIS)
Yukalov, V I; Sornette, D
2013-01-01
The problem of defining quantum probabilities of composite events is considered. This problem is of great importance for the theory of quantum measurements and for quantum decision theory, which is a part of measurement theory. We show that the Lüders probability of consecutive measurements is a transition probability between two quantum states and that this probability cannot be treated as a quantum extension of the classical conditional probability. The Wigner distribution is shown to be a weighted transition probability that cannot be accepted as a quantum extension of the classical joint probability. We suggest the definition of quantum joint probabilities by introducing composite events in multichannel measurements. The notion of measurements under uncertainty is defined. We demonstrate that the necessary condition for mode interference is the entanglement of the composite prospect together with the entanglement of the composite statistical state. As an illustration, we consider an example of a quantum game. Special attention is paid to the application of the approach to systems with multimode states, such as atoms, molecules, quantum dots, or trapped Bose-condensed atoms with several coherent modes. (paper)
Superthermal photon bunching in terms of simple probability distributions
Lettau, T.; Leymann, H. A. M.; Melcher, B.; Wiersig, J.
2018-05-01
We analyze the second-order photon autocorrelation function g(2 ) with respect to the photon probability distribution and discuss the generic features of a distribution that results in superthermal photon bunching [g(2 )(0 ) >2 ]. Superthermal photon bunching has been reported for a number of optical microcavity systems that exhibit processes such as superradiance or mode competition. We show that a superthermal photon number distribution cannot be constructed from the principle of maximum entropy if only the intensity and the second-order autocorrelation are given. However, for bimodal systems, an unbiased superthermal distribution can be constructed from second-order correlations and the intensities alone. Our findings suggest modeling superthermal single-mode distributions by a mixture of a thermal and a lasinglike state and thus reveal a generic mechanism in the photon probability distribution responsible for creating superthermal photon bunching. We relate our general considerations to a physical system, i.e., a (single-emitter) bimodal laser, and show that its statistics can be approximated and understood within our proposed model. Furthermore, the excellent agreement of the statistics of the bimodal laser and our model reveals that the bimodal laser is an ideal source of bunched photons, in the sense that it can generate statistics that contain no other features but the superthermal bunching.
Joint Probability Distributions for a Class of Non-Markovian Processes
Baule, A.; Friedrich, R.
2004-01-01
We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single time probability distributions to the case of N-time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fr...
Bayesian Analysis for EMP Survival Probability of Solid State Relay
International Nuclear Information System (INIS)
Sun Beiyun; Zhou Hui; Cheng Xiangyue; Mao Congguang
2009-01-01
The principle to estimate the parameter p of binomial distribution by Bayesian method and the several non-informative prior are introduced. The survival probability of DC solid state relay under current injection at certain amplitude is obtained by this method. (authors)
Fitness Probability Distribution of Bit-Flip Mutation.
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.
Joint probability distributions for a class of non-Markovian processes.
Baule, A; Friedrich, R
2005-02-01
We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H. C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single-time probability distributions to the case of N -time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.
Bayesian Prior Probability Distributions for Internal Dosimetry
Energy Technology Data Exchange (ETDEWEB)
Miller, G.; Inkret, W.C.; Little, T.T.; Martz, H.F.; Schillaci, M.E
2001-07-01
The problem of choosing a prior distribution for the Bayesian interpretation of measurements (specifically internal dosimetry measurements) is considered using a theoretical analysis and by examining historical tritium and plutonium urine bioassay data from Los Alamos. Two models for the prior probability distribution are proposed: (1) the log-normal distribution, when there is some additional information to determine the scale of the true result, and (2) the 'alpha' distribution (a simplified variant of the gamma distribution) when there is not. These models have been incorporated into version 3 of the Bayesian internal dosimetric code in use at Los Alamos (downloadable from our web site). Plutonium internal dosimetry at Los Alamos is now being done using prior probability distribution parameters determined self-consistently from population averages of Los Alamos data. (author)
Incorporating Skew into RMS Surface Roughness Probability Distribution
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.
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
Proposal for Modified Damage Probability Distribution Functions
DEFF Research Database (Denmark)
Pedersen, Preben Terndrup; Hansen, Peter Friis
1996-01-01
Immidiately following the Estonia disaster, the Nordic countries establishe a project entitled "Safety of Passenger/RoRo Vessels" As part of this project the present proposal for modified damage stability probability distribution functions has been developed. and submitted to "Sub-committee on st......Immidiately following the Estonia disaster, the Nordic countries establishe a project entitled "Safety of Passenger/RoRo Vessels" As part of this project the present proposal for modified damage stability probability distribution functions has been developed. and submitted to "Sub...
Converting dose distributions into tumour control probability
International Nuclear Information System (INIS)
Nahum, A.E.
1996-01-01
The endpoints in radiotherapy that are truly of relevance are not dose distributions but the probability of local control, sometimes known as the Tumour Control Probability (TCP) and the Probability of Normal Tissue Complications (NTCP). A model for the estimation of TCP based on simple radiobiological considerations is described. It is shown that incorporation of inter-patient heterogeneity into the radiosensitivity parameter a through s a can result in a clinically realistic slope for the dose-response curve. The model is applied to inhomogeneous target dose distributions in order to demonstrate the relationship between dose uniformity and s a . The consequences of varying clonogenic density are also explored. Finally the model is applied to the target-volume DVHs for patients in a clinical trial of conformal pelvic radiotherapy; the effect of dose inhomogeneities on distributions of TCP are shown as well as the potential benefits of customizing the target dose according to normal-tissue DVHs. (author). 37 refs, 9 figs
Converting dose distributions into tumour control probability
Energy Technology Data Exchange (ETDEWEB)
Nahum, A E [The Royal Marsden Hospital, London (United Kingdom). Joint Dept. of Physics
1996-08-01
The endpoints in radiotherapy that are truly of relevance are not dose distributions but the probability of local control, sometimes known as the Tumour Control Probability (TCP) and the Probability of Normal Tissue Complications (NTCP). A model for the estimation of TCP based on simple radiobiological considerations is described. It is shown that incorporation of inter-patient heterogeneity into the radiosensitivity parameter a through s{sub a} can result in a clinically realistic slope for the dose-response curve. The model is applied to inhomogeneous target dose distributions in order to demonstrate the relationship between dose uniformity and s{sub a}. The consequences of varying clonogenic density are also explored. Finally the model is applied to the target-volume DVHs for patients in a clinical trial of conformal pelvic radiotherapy; the effect of dose inhomogeneities on distributions of TCP are shown as well as the potential benefits of customizing the target dose according to normal-tissue DVHs. (author). 37 refs, 9 figs.
STADIC: a computer code for combining probability distributions
International Nuclear Information System (INIS)
Cairns, J.J.; Fleming, K.N.
1977-03-01
The STADIC computer code uses a Monte Carlo simulation technique for combining probability distributions. The specific function for combination of the input distribution is defined by the user by introducing the appropriate FORTRAN statements to the appropriate subroutine. The code generates a Monte Carlo sampling from each of the input distributions and combines these according to the user-supplied function to provide, in essence, a random sampling of the combined distribution. When the desired number of samples is obtained, the output routine calculates the mean, standard deviation, and confidence limits for the resultant distribution. This method of combining probability distributions is particularly useful in cases where analytical approaches are either too difficult or undefined
Joint probability distributions and fluctuation theorems
International Nuclear Information System (INIS)
García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien
2012-01-01
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators
Evidence for Truncated Exponential Probability Distribution of Earthquake Slip
Thingbaijam, Kiran Kumar; Mai, Paul Martin
2016-01-01
Earthquake ruptures comprise spatially varying slip on the fault surface, where slip represents the displacement discontinuity between the two sides of the rupture plane. In this study, we analyze the probability distribution of coseismic slip, which provides important information to better understand earthquake source physics. Although the probability distribution of slip is crucial for generating realistic rupture scenarios for simulation-based seismic and tsunami-hazard analysis, the statistical properties of earthquake slip have received limited attention so far. Here, we use the online database of earthquake source models (SRCMOD) to show that the probability distribution of slip follows the truncated exponential law. This law agrees with rupture-specific physical constraints limiting the maximum possible slip on the fault, similar to physical constraints on maximum earthquake magnitudes.We show the parameters of the best-fitting truncated exponential distribution scale with average coseismic slip. This scaling property reflects the control of the underlying stress distribution and fault strength on the rupture dimensions, which determines the average slip. Thus, the scale-dependent behavior of slip heterogeneity is captured by the probability distribution of slip. We conclude that the truncated exponential law accurately quantifies coseismic slip distribution and therefore allows for more realistic modeling of rupture scenarios. © 2016, Seismological Society of America. All rights reserverd.
Evidence for Truncated Exponential Probability Distribution of Earthquake Slip
Thingbaijam, Kiran K. S.
2016-07-13
Earthquake ruptures comprise spatially varying slip on the fault surface, where slip represents the displacement discontinuity between the two sides of the rupture plane. In this study, we analyze the probability distribution of coseismic slip, which provides important information to better understand earthquake source physics. Although the probability distribution of slip is crucial for generating realistic rupture scenarios for simulation-based seismic and tsunami-hazard analysis, the statistical properties of earthquake slip have received limited attention so far. Here, we use the online database of earthquake source models (SRCMOD) to show that the probability distribution of slip follows the truncated exponential law. This law agrees with rupture-specific physical constraints limiting the maximum possible slip on the fault, similar to physical constraints on maximum earthquake magnitudes.We show the parameters of the best-fitting truncated exponential distribution scale with average coseismic slip. This scaling property reflects the control of the underlying stress distribution and fault strength on the rupture dimensions, which determines the average slip. Thus, the scale-dependent behavior of slip heterogeneity is captured by the probability distribution of slip. We conclude that the truncated exponential law accurately quantifies coseismic slip distribution and therefore allows for more realistic modeling of rupture scenarios. © 2016, Seismological Society of America. All rights reserverd.
International Nuclear Information System (INIS)
Romain, P.; Duarte, H.; Morillon, B.
2012-01-01
The energy derivatives of probabilities are functions suited to a best understanding of certain mechanisms. Applied to compound nuclear reactions, they can bring information on fusion barrier distributions as originally introduced, and also, as presented here, on fission barrier distributions and heights. Extendedly, they permit to access the compound nucleus spin-parity states preferentially populated according to an entrance channel, at a given energy. (authors)
Characterizing single-molecule FRET dynamics with probability distribution analysis.
Santoso, Yusdi; Torella, Joseph P; Kapanidis, Achillefs N
2010-07-12
Probability distribution analysis (PDA) is a recently developed statistical tool for predicting the shapes of single-molecule fluorescence resonance energy transfer (smFRET) histograms, which allows the identification of single or multiple static molecular species within a single histogram. We used a generalized PDA method to predict the shapes of FRET histograms for molecules interconverting dynamically between multiple states. This method is tested on a series of model systems, including both static DNA fragments and dynamic DNA hairpins. By fitting the shape of this expected distribution to experimental data, the timescale of hairpin conformational fluctuations can be recovered, in good agreement with earlier published results obtained using different techniques. This method is also applied to studying the conformational fluctuations in the unliganded Klenow fragment (KF) of Escherichia coli DNA polymerase I, which allows both confirmation of the consistency of a simple, two-state kinetic model with the observed smFRET distribution of unliganded KF and extraction of a millisecond fluctuation timescale, in good agreement with rates reported elsewhere. We expect this method to be useful in extracting rates from processes exhibiting dynamic FRET, and in hypothesis-testing models of conformational dynamics against experimental data.
APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING MODELS
Directory of Open Access Journals (Sweden)
T. I. Aliev
2013-03-01
Full Text Available For probability distributions with variation coefficient, not equal to unity, mathematical dependences for approximating distributions on the basis of first two moments are derived by making use of multi exponential distributions. It is proposed to approximate distributions with coefficient of variation less than unity by using hypoexponential distribution, which makes it possible to generate random variables with coefficient of variation, taking any value in a range (0; 1, as opposed to Erlang distribution, having only discrete values of coefficient of variation.
International Nuclear Information System (INIS)
Koshinchanov, Georgy; Dimitrov, Dobri
2008-01-01
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
Probability distributions with truncated, log and bivariate extensions
Thomopoulos, Nick T
2018-01-01
This volume presents a concise and practical overview of statistical methods and tables not readily available in other publications. It begins with a review of the commonly used continuous and discrete probability distributions. Several useful distributions that are not so common and less understood are described with examples and applications in full detail: discrete normal, left-partial, right-partial, left-truncated normal, right-truncated normal, lognormal, bivariate normal, and bivariate lognormal. Table values are provided with examples that enable researchers to easily apply the distributions to real applications and sample data. The left- and right-truncated normal distributions offer a wide variety of shapes in contrast to the symmetrically shaped normal distribution, and a newly developed spread ratio enables analysts to determine which of the three distributions best fits a particular set of sample data. The book will be highly useful to anyone who does statistical and probability analysis. This in...
Fitting the Probability Distribution Functions to Model Particulate Matter Concentrations
International Nuclear Information System (INIS)
El-Shanshoury, Gh.I.
2017-01-01
The main objective of this study is to identify the best probability distribution and the plotting position formula for modeling the concentrations of Total Suspended Particles (TSP) as well as the Particulate Matter with an aerodynamic diameter<10 μm (PM 10 ). The best distribution provides the estimated probabilities that exceed the threshold limit given by the Egyptian Air Quality Limit value (EAQLV) as well the number of exceedance days is estimated. The standard limits of the EAQLV for TSP and PM 10 concentrations are 24-h average of 230 μg/m 3 and 70 μg/m 3 , respectively. Five frequency distribution functions with seven formula of plotting positions (empirical cumulative distribution functions) are compared to fit the average of daily TSP and PM 10 concentrations in year 2014 for Ain Sokhna city. The Quantile-Quantile plot (Q-Q plot) is used as a method for assessing how closely a data set fits a particular distribution. A proper probability distribution that represents the TSP and PM 10 has been chosen based on the statistical performance indicator values. The results show that Hosking and Wallis plotting position combined with Frechet distribution gave the highest fit for TSP and PM 10 concentrations. Burr distribution with the same plotting position follows Frechet distribution. The exceedance probability and days over the EAQLV are predicted using Frechet distribution. In 2014, the exceedance probability and days for TSP concentrations are 0.052 and 19 days, respectively. Furthermore, the PM 10 concentration is found to exceed the threshold limit by 174 days
Calculating Cumulative Binomial-Distribution Probabilities
Scheuer, Ernest M.; Bowerman, Paul N.
1989-01-01
Cumulative-binomial computer program, CUMBIN, one of set of three programs, calculates cumulative binomial probability distributions for arbitrary inputs. CUMBIN, NEWTONP (NPO-17556), and CROSSER (NPO-17557), used independently of one another. Reliabilities and availabilities of k-out-of-n systems analyzed. Used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. Used for calculations of reliability and availability. Program written in C.
Modeling the probability distribution of peak discharge for infiltrating hillslopes
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.
Most probable degree distribution at fixed structural entropy
Indian Academy of Sciences (India)
Here we derive the most probable degree distribution emerging ... the structural entropy of power-law networks is an increasing function of the expo- .... tition function Z of the network as the sum over all degree distributions, with given energy.
Non-LTE population probabilities of the excited ionic levels in a steady state plasma
International Nuclear Information System (INIS)
Salzmann, D.
1982-01-01
A Complete-Staedy-State (CSS) model for the charge state distribution and the ionic levels population probabilities of ions in hot non-LTE plasmas is described. The following properties of this model are described: (i) it is shown that CSS covers LTE and Corona Equilibrium (CE) in the high and low electron density regimes respectively, (ii) an explicit expression is found for the low electron density asymptotic behaviour of the population probabilities, (iii) it is shown that at intermediate density regions the CSS model predicts results similar to that of the Quasi-Steady-State model, (iv) new validity limits are derived for LTE and CE, (v) the population distribution of the excited levels is revised, (vi) an analytical expression is found for the high electron density asymptotic behaviour of the population distribution, (vii) the influence of the radiation reabsorption in a spherically symmetric CSS plasma is briefly described, and (viii) the effect of the inaccuracies in the rate-coefficients on the results of CSS calculations is evaluated. (author)
Geometry of q-Exponential Family of Probability Distributions
Directory of Open Access Journals (Sweden)
Shun-ichi Amari
2011-06-01
Full Text Available The Gibbs distribution of statistical physics is an exponential family of probability distributions, which has a mathematical basis of duality in the form of the Legendre transformation. Recent studies of complex systems have found lots of distributions obeying the power law rather than the standard Gibbs type distributions. The Tsallis q-entropy is a typical example capturing such phenomena. We treat the q-Gibbs distribution or the q-exponential family by generalizing the exponential function to the q-family of power functions, which is useful for studying various complex or non-standard physical phenomena. We give a new mathematical structure to the q-exponential family different from those previously given. It has a dually flat geometrical structure derived from the Legendre transformation and the conformal geometry is useful for understanding it. The q-version of the maximum entropy theorem is naturally induced from the q-Pythagorean theorem. We also show that the maximizer of the q-escort distribution is a Bayesian MAP (Maximum A posteriori Probability estimator.
Comparative analysis through probability distributions of a data set
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.
Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks
International Nuclear Information System (INIS)
Xu, Xin-Ping; Ide, Yusuke
2016-01-01
In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.
Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks
Energy Technology Data Exchange (ETDEWEB)
Xu, Xin-Ping, E-mail: xuxp@mail.ihep.ac.cn [School of Physical Science and Technology, Soochow University, Suzhou 215006 (China); Ide, Yusuke [Department of Information Systems Creation, Faculty of Engineering, Kanagawa University, Yokohama, Kanagawa, 221-8686 (Japan)
2016-10-15
In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.
Probability and stochastic modeling
Rotar, Vladimir I
2012-01-01
Basic NotionsSample Space and EventsProbabilitiesCounting TechniquesIndependence and Conditional ProbabilityIndependenceConditioningThe Borel-Cantelli TheoremDiscrete Random VariablesRandom Variables and VectorsExpected ValueVariance and Other Moments. Inequalities for DeviationsSome Basic DistributionsConvergence of Random Variables. The Law of Large NumbersConditional ExpectationGenerating Functions. Branching Processes. Random Walk RevisitedBranching Processes Generating Functions Branching Processes Revisited More on Random WalkMarkov ChainsDefinitions and Examples. Probability Distributions of Markov ChainsThe First Step Analysis. Passage TimesVariables Defined on a Markov ChainErgodicity and Stationary DistributionsA Classification of States and ErgodicityContinuous Random VariablesContinuous DistributionsSome Basic Distributions Continuous Multivariate Distributions Sums of Independent Random Variables Conditional Distributions and ExpectationsDistributions in the General Case. SimulationDistribution F...
Predicting the probability of slip in gait: methodology and distribution study.
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.
Probability Distribution for Flowing Interval Spacing
International Nuclear Information System (INIS)
Kuzio, S.
2001-01-01
The purpose of this analysis is to develop a probability distribution for flowing interval spacing. A flowing interval is defined as a fractured zone that transmits flow in the Saturated Zone (SZ), as identified through borehole flow meter surveys (Figure 1). This analysis uses the term ''flowing interval spacing'' as opposed to fractured spacing, which is typically used in the literature. The term fracture spacing was not used in this analysis because the data used identify a zone (or a flowing interval) that contains fluid-conducting fractures but does not distinguish how many or which fractures comprise the flowing interval. The flowing interval spacing is measured between the midpoints of each flowing interval. Fracture spacing within the SZ is defined as the spacing between fractures, with no regard to which fractures are carrying flow. The Development Plan associated with this analysis is entitled, ''Probability Distribution for Flowing Interval Spacing'', (CRWMS M and O 2000a). The parameter from this analysis may be used in the TSPA SR/LA Saturated Zone Flow and Transport Work Direction and Planning Documents: (1) ''Abstraction of Matrix Diffusion for SZ Flow and Transport Analyses'' (CRWMS M and O 1999a) and (2) ''Incorporation of Heterogeneity in SZ Flow and Transport Analyses'', (CRWMS M and O 1999b). A limitation of this analysis is that the probability distribution of flowing interval spacing may underestimate the effect of incorporating matrix diffusion processes in the SZ transport model because of the possible overestimation of the flowing interval spacing. Larger flowing interval spacing results in a decrease in the matrix diffusion processes. This analysis may overestimate the flowing interval spacing because the number of fractures that contribute to a flowing interval cannot be determined from the data. Because each flowing interval probably has more than one fracture contributing to a flowing interval, the true flowing interval spacing could be
Information-theoretic methods for estimating of complicated probability distributions
Zong, Zhi
2006-01-01
Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neur
Confidence intervals for the lognormal probability distribution
International Nuclear Information System (INIS)
Smith, D.L.; Naberejnev, D.G.
2004-01-01
The present communication addresses the topic of symmetric confidence intervals for the lognormal probability distribution. This distribution is frequently utilized to characterize inherently positive, continuous random variables that are selected to represent many physical quantities in applied nuclear science and technology. The basic formalism is outlined herein and a conjured numerical example is provided for illustration. It is demonstrated that when the uncertainty reflected in a lognormal probability distribution is large, the use of a confidence interval provides much more useful information about the variable used to represent a particular physical quantity than can be had by adhering to the notion that the mean value and standard deviation of the distribution ought to be interpreted as best value and corresponding error, respectively. Furthermore, it is shown that if the uncertainty is very large a disturbing anomaly can arise when one insists on interpreting the mean value and standard deviation as the best value and corresponding error, respectively. Reliance on using the mode and median as alternative parameters to represent the best available knowledge of a variable with large uncertainties is also shown to entail limitations. Finally, a realistic physical example involving the decay of radioactivity over a time period that spans many half-lives is presented and analyzed to further illustrate the concepts discussed in this communication
Simulation of Daily Weather Data Using Theoretical Probability Distributions.
Bruhn, J. A.; Fry, W. E.; Fick, G. W.
1980-09-01
A computer simulation model was constructed to supply daily weather data to a plant disease management model for potato late blight. In the weather model Monte Carlo techniques were employed to generate daily values of precipitation, maximum temperature, minimum temperature, minimum relative humidity and total solar radiation. Each weather variable is described by a known theoretical probability distribution but the values of the parameters describing each distribution are dependent on the occurrence of rainfall. Precipitation occurrence is described by a first-order Markov chain. The amount of rain, given that rain has occurred, is described by a gamma probability distribution. Maximum and minimum temperature are simulated with a trivariate normal probability distribution involving maximum temperature on the previous day, maximum temperature on the current day and minimum temperature on the current day. Parameter values for this distribution are dependent on the occurrence of rain on the previous day. Both minimum relative humidity and total solar radiation are assumed to be normally distributed. The values of the parameters describing the distribution of minimum relative humidity is dependent on rainfall occurrence on the previous day and current day. Parameter values for total solar radiation are dependent on the occurrence of rain on the current day. The assumptions made during model construction were found to be appropriate for actual weather data from Geneva, New York. The performance of the weather model was evaluated by comparing the cumulative frequency distributions of simulated weather data with the distributions of actual weather data from Geneva, New York and Fort Collins, Colorado. For each location, simulated weather data were similar to actual weather data in terms of mean response, variability and autocorrelation. The possible applications of this model when used with models of other components of the agro-ecosystem are discussed.
Subjective probability appraisal of uranium resources in the state of New Mexico
International Nuclear Information System (INIS)
Ellis, J.R.; Harris, D.P.; VanWie, N.H.
1975-12-01
This report presents an estimate of undiscovered uranium resources in New Mexico of 226,681,000 tons of material containing 455,480 tons U 3 O 8 . The basis for this estimate was a survey of expectations of 36 geologists, in terms of subjective probabilities of number of deposits, ore tonnage, and grade. Weighting of the geologists' estimates to derive a mean value used a self-appraisal index of their knowledge within the field. Detailed estimates are presented for the state, for each of 62 subdivisions (cells), and for an aggregation of eight cells encompassing the San Juan Basin, which is estimated to contain 92 percent of the undiscovered uranium resources in New Mexico. Ore-body attributes stated as probability distributions enabled the application of Monte Carlo methods to the analysis of the data. Sampling of estimates of material and contained U 3 O 8 which are provided as probability distributions indicates a 10 percent probability of there being at least 600,000 tons U 3 O 8 remaining undiscovered in deposits virtually certain to number between 500 and 565. An indicated probability of 99.5 percent that the ore grade is greater than 0.12 percent U 3 O 8 suggests that this survey may not provide reliable estimates of the abundance of material in very low-grade categories. Extrapolation to examine the potential for such deposits indicates more than 1,000,000 tons U 3 O 8 may be available down to a grade of 0.05 percent U 3 O 8 . Supplemental point estimates of ore depth and thickness allowed derivative estimates of cost of development, extraction, and milling. 80 percent of the U 3 O 8 is estimated to be available at a cost less than dollars 15/lb (1974) and about 98 percent at less than dollars 30/lb
The probability representation as a new formulation of quantum mechanics
International Nuclear Information System (INIS)
Man'ko, Margarita A; Man'ko, Vladimir I
2012-01-01
We present a new formulation of conventional quantum mechanics, in which the notion of a quantum state is identified via a fair probability distribution of the position measured in a reference frame of the phase space with rotated axes. In this formulation, the quantum evolution equation as well as the equation for finding energy levels are expressed as linear equations for the probability distributions that determine the quantum states. We also give the integral transforms relating the probability distribution (called the tomographic-probability distribution or the state tomogram) to the density matrix and the Wigner function and discuss their connection with the Radon transform. Qudit states are considered and the invertible map of the state density operators onto the probability vectors is discussed. The tomographic entropies and entropic uncertainty relations are reviewed. We demonstrate the uncertainty relations for the position and momentum and the entropic uncertainty relations in the tomographic-probability representation, which is suitable for an experimental check of the uncertainty relations.
Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution
Energy Technology Data Exchange (ETDEWEB)
Hamadameen, Abdulqader Othman [Optimization, Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia); Zainuddin, Zaitul Marlizawati [Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia)
2014-06-19
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.
Martin A. Spetich; Zhaofei Fan; Zhen Sui; Michael Crosby; Hong S. He; Stephen R. Shifley; Theodor D. Leininger; W. Keith Moser
2017-01-01
Stresses to trees under a changing climate can lead to changes in forest tree survival, mortality and distribution.Â For instance, a study examining the effects of human-induced climate change on forest biodiversity by Hansen and others (2001) predicted a 32% reduction in loblollyâshortleaf pine habitat across the eastern United States.Â However, they also...
International Nuclear Information System (INIS)
Humbert, Ph.
2005-01-01
In this paper we consider the probability distribution of neutrons in a multiplying assembly. The problem is studied using a space independent one group neutron point reactor model without delayed neutrons. We recall the generating function methodology and analytical results obtained by G.I. Bell when the c 2 approximation is used and we present numerical solutions in the general case, without this approximation. The neutron source induced distribution is calculated using the single initial neutron distribution which satisfies a master (Kolmogorov backward) equation. This equation is solved using the generating function method. The generating function satisfies a differential equation and the probability distribution is derived by inversion of the generating function. Numerical results are obtained using the same methodology where the generating function is the Fourier transform of the probability distribution. Discrete Fourier transforms are used to calculate the discrete time dependent distributions and continuous Fourier transforms are used to calculate the asymptotic continuous probability distributions. Numerical applications are presented to illustrate the method. (author)
The exact probability distribution of the rank product statistics for replicated experiments.
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.
The estimated lifetime probability of acquiring human papillomavirus in the United States.
Chesson, Harrell W; Dunne, Eileen F; Hariri, Susan; Markowitz, Lauri E
2014-11-01
Estimates of the lifetime probability of acquiring human papillomavirus (HPV) can help to quantify HPV incidence, illustrate how common HPV infection is, and highlight the importance of HPV vaccination. We developed a simple model, based primarily on the distribution of lifetime numbers of sex partners across the population and the per-partnership probability of acquiring HPV, to estimate the lifetime probability of acquiring HPV in the United States in the time frame before HPV vaccine availability. We estimated the average lifetime probability of acquiring HPV among those with at least 1 opposite sex partner to be 84.6% (range, 53.6%-95.0%) for women and 91.3% (range, 69.5%-97.7%) for men. Under base case assumptions, more than 80% of women and men acquire HPV by age 45 years. Our results are consistent with estimates in the existing literature suggesting a high lifetime probability of HPV acquisition and are supported by cohort studies showing high cumulative HPV incidence over a relatively short period, such as 3 to 5 years.
International Nuclear Information System (INIS)
Wen Xiaoqiong; Li Qiang; Zhou Guangming; Li Wenjian; Wei Zengquan
2001-01-01
In order to estimate the influence of the un-uniform dose distribution on the clinical treatment result, the Influence of dose distribution homogeneity on the tumor control probability was investigated. Basing on the formula deduced previously for survival fraction of cells irradiated by the un-uniform heavy-ion irradiation field and the theory of tumor control probability, the tumor control probability was calculated for a tumor mode exposed to different dose distribution homogeneity. The results show that the tumor control probability responding to the same total dose will decrease if the dose distribution homogeneity gets worse. In clinical treatment, the dose distribution homogeneity should be better than 95%
Radtke, T.; Fritzsche, S.
2008-11-01
, quantum information science has contributed to our understanding of quantum mechanics and has provided also new and efficient protocols, based on the use of entangled quantum states. To determine the behavior and entanglement of n-qubit quantum registers, symbolic and numerical simulations need to be applied in order to analyze how these quantum information protocols work and which role the entanglement plays hereby. Solution method: Using the computer algebra system Maple, we have developed a set of procedures that support the definition, manipulation and analysis of n-qubit quantum registers. These procedures also help to deal with (unitary) logic gates and (nonunitary) quantum operations that act upon the quantum registers. With the parameterization of various frequently-applied objects, that are implemented in the present version, the program now facilitates a wider range of symbolic and numerical studies. All commands can be used interactively in order to simulate and analyze the evolution of n-qubit quantum systems, both in ideal and noisy quantum circuits. Reasons for new version: In the first version of the FEYNMAN program [1], we implemented the data structures and tools that are necessary to create, manipulate and to analyze the state of quantum registers. Later [2,3], support was added to deal with quantum operations (noisy channels) as an ingredient which is essential for studying the effects of decoherence. With the present extension, we add a number of parametrizations of objects frequently utilized in decoherence and entanglement studies, such that as hermitian and unitary matrices, probability distributions, or various kinds of quantum states. This extension therefore provides the basis, for example, for the optimization of a given function over the set of pure states or the simple generation of random objects. Running time: Most commands that act upon quantum registers with five or less qubits take ⩽10 seconds of processor time on a Pentium 4 processor
Separating the contributions of variability and parameter uncertainty in probability distributions
International Nuclear Information System (INIS)
Sankararaman, S.; Mahadevan, S.
2013-01-01
This paper proposes a computational methodology to quantify the individual contributions of variability and distribution parameter uncertainty to the overall uncertainty in a random variable. Even if the distribution type is assumed to be known, sparse or imprecise data leads to uncertainty about the distribution parameters. If uncertain distribution parameters are represented using probability distributions, then the random variable can be represented using a family of probability distributions. The family of distributions concept has been used to obtain qualitative, graphical inference of the contributions of natural variability and distribution parameter uncertainty. The proposed methodology provides quantitative estimates of the contributions of the two types of uncertainty. Using variance-based global sensitivity analysis, the contributions of variability and distribution parameter uncertainty to the overall uncertainty are computed. The proposed method is developed at two different levels; first, at the level of a variable whose distribution parameters are uncertain, and second, at the level of a model output whose inputs have uncertain distribution parameters
The distributed failure probability approach to dependent failure analysis, and its application
International Nuclear Information System (INIS)
Hughes, R.P.
1989-01-01
The Distributed Failure Probability (DFP) approach to the problem of dependent failures in systems is presented. The basis of the approach is that the failure probability of a component is a variable. The source of this variability is the change in the 'environment' of the component, where the term 'environment' is used to mean not only obvious environmental factors such as temperature etc., but also such factors as the quality of maintenance and manufacture. The failure probability is distributed among these various 'environments' giving rise to the Distributed Failure Probability method. Within the framework which this method represents, modelling assumptions can be made, based both on engineering judgment and on the data directly. As such, this DFP approach provides a soundly based and scrutable technique by which dependent failures can be quantitatively assessed. (orig.)
Stirk, Emily R; Lythe, Grant; van den Berg, Hugo A; Hurst, Gareth A D; Molina-París, Carmen
2010-04-01
The limiting conditional probability distribution (LCD) has been much studied in the field of mathematical biology, particularly in the context of epidemiology and the persistence of epidemics. However, it has not yet been applied to the immune system. One of the characteristic features of the T cell repertoire is its diversity. This diversity declines in old age, whence the concepts of extinction and persistence are also relevant to the immune system. In this paper we model T cell repertoire maintenance by means of a continuous-time birth and death process on the positive integers, where the origin is an absorbing state. We show that eventual extinction is guaranteed. The late-time behaviour of the process before extinction takes place is modelled by the LCD, which we prove always exists for the process studied here. In most cases, analytic expressions for the LCD cannot be computed but the probability distribution may be approximated by means of the stationary probability distributions of two related processes. We show how these approximations are related to the LCD of the original process and use them to study the LCD in two special cases. We also make use of the large N expansion to derive a further approximation to the LCD. The accuracy of the various approximations is then analysed. (c) 2009 Elsevier Inc. All rights reserved.
Generalization of Poisson distribution for the case of changing probability of consequential events
International Nuclear Information System (INIS)
Kushnirenko, E.
1995-01-01
The generalization of the Poisson distribution for the case of changing probabilities of the consequential events is done. It is shown that the classical Poisson distribution is the special case of this generalized distribution when the probabilities of the consequential events are constant. The using of the generalized Poisson distribution gives the possibility in some cases to obtain analytical result instead of making Monte-Carlo calculation
Sonnino, Giorgio; Steinbrecher, György; Cardinali, Alessandro; Sonnino, Alberto; Tlidi, Mustapha
2013-01-01
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, where the stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.
Study on probability distribution of fire scenarios in risk assessment to emergency evacuation
International Nuclear Information System (INIS)
Chu Guanquan; Wang Jinhui
2012-01-01
Event tree analysis (ETA) is a frequently-used technique to analyze the probability of probable fire scenario. The event probability is usually characterized by definite value. It is not appropriate to use definite value as these estimates may be the result of poor quality statistics and limited knowledge. Without addressing uncertainties, ETA will give imprecise results. The credibility of risk assessment will be undermined. This paper presents an approach to address event probability uncertainties and analyze probability distribution of probable fire scenario. ETA is performed to construct probable fire scenarios. The activation time of every event is characterized as stochastic variable by considering uncertainties of fire growth rate and other input variables. To obtain probability distribution of probable fire scenario, Markov Chain is proposed to combine with ETA. To demonstrate the approach, a case study is presented.
Energy Technology Data Exchange (ETDEWEB)
Sardeshmukh, Prashant D., E-mail: Prashant.D.Sardeshmukh@noaa.gov [CIRES, University of Colorado, Boulder, Colorado 80309 (United States); NOAA/Earth System Research Laboratory, Boulder, Colorado 80305 (United States); Penland, Cécile [NOAA/Earth System Research Laboratory, Boulder, Colorado 80305 (United States)
2015-03-15
The probability distributions of large-scale atmospheric and oceanic variables are generally skewed and heavy-tailed. We argue that their distinctive departures from Gaussianity arise fundamentally from the fact that in a quadratically nonlinear system with a quadratic invariant, the coupling coefficients between system components are not constant but depend linearly on the system state in a distinctive way. In particular, the skewness arises from a tendency of the system trajectory to linger near states of weak coupling. We show that the salient features of the observed non-Gaussianity can be captured in the simplest such nonlinear 2-component system. If the system is stochastically forced and linearly damped, with one component damped much more strongly than the other, then the strongly damped fast component becomes effectively decoupled from the weakly damped slow component, and its impact on the slow component can be approximated as a stochastic noise forcing plus an augmented nonlinear damping. In the limit of large time-scale separation, the nonlinear augmentation of the damping becomes small, and the noise forcing can be approximated as an additive noise plus a correlated additive and multiplicative noise (CAM noise) forcing. Much of the diversity of observed large-scale atmospheric and oceanic probability distributions can be interpreted in this minimal framework.
International Nuclear Information System (INIS)
Huang Zhifu; Lin Bihong; ChenJincan
2009-01-01
In order to overcome the limitations of the original expression of the probability distribution appearing in literature of Incomplete Statistics, a new expression of the probability distribution is derived, where the Lagrange multiplier β introduced here is proved to be identical with that introduced in the second and third choices for the internal energy constraint in Tsallis' statistics and to be just equal to the physical inverse temperature. It is expounded that the probability distribution described by the new expression is invariant through uniform translation of the energy spectrum. Moreover, several fundamental thermodynamic relations are given and the relationship between the new and the original expressions of the probability distribution is discussed.
Collective motions of globally coupled oscillators and some probability distributions on circle
Energy Technology Data Exchange (ETDEWEB)
Jaćimović, Vladimir [Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put, bb., 81000 Podgorica (Montenegro); Crnkić, Aladin, E-mail: aladin.crnkic@hotmail.com [Faculty of Technical Engineering, University of Bihać, Ljubijankićeva, bb., 77000 Bihać, Bosnia and Herzegovina (Bosnia and Herzegovina)
2017-06-28
In 2010 Kato and Jones described a new family of probability distributions on circle, obtained as Möbius transformation of von Mises distribution. We present the model demonstrating that these distributions appear naturally in study of populations of coupled oscillators. We use this opportunity to point out certain relations between Directional Statistics and collective motion of coupled oscillators. - Highlights: • We specify probability distributions on circle that arise in Kuramoto model. • We study how the mean-field coupling affects the shape of distribution of phases. • We discuss potential applications in some experiments on cell cycle. • We apply Directional Statistics to study collective dynamics of coupled oscillators.
How Can Histograms Be Useful for Introducing Continuous Probability Distributions?
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.…
Quantum operations, state transformations and probabilities
International Nuclear Information System (INIS)
Chefles, Anthony
2002-01-01
In quantum operations, probabilities characterize both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a unified treatment of pure→pure state transformations, covering both probabilistic and deterministic cases. We then discuss the role of majorization in describing the dynamics of mixing in quantum operations. The conditions for mixing enhancement for all initial states are derived. We show that mixing is monotonically decreasing for deterministic pure→pure transformations, and discuss the relationship between these transformations and deterministic local operations with classical communication entanglement transformations
Calculation of ruin probabilities for a dense class of heavy tailed distributions
DEFF Research Database (Denmark)
Bladt, Mogens; Nielsen, Bo Friis; Samorodnitsky, Gennady
2015-01-01
In this paper, we propose a class of infinite-dimensional phase-type distributions with finitely many parameters as models for heavy tailed distributions. The class of finite-dimensional phase-type distributions is dense in the class of distributions on the positive reals and may hence approximate...... any such distribution. We prove that formulas from renewal theory, and with a particular attention to ruin probabilities, which are true for common phase-type distributions also hold true for the infinite-dimensional case. We provide algorithms for calculating functionals of interest...... such as the renewal density and the ruin probability. It might be of interest to approximate a given heavy tailed distribution of some other type by a distribution from the class of infinite-dimensional phase-type distributions and to this end we provide a calibration procedure which works for the approximation...
Probability distribution of extreme share returns in Malaysia
Zin, Wan Zawiah Wan; Safari, Muhammad Aslam Mohd; Jaaman, Saiful Hafizah; Yie, Wendy Ling Shin
2014-09-01
The objective of this study is to investigate the suitable probability distribution to model the extreme share returns in Malaysia. To achieve this, weekly and monthly maximum daily share returns are derived from share prices data obtained from Bursa Malaysia over the period of 2000 to 2012. The study starts with summary statistics of the data which will provide a clue on the likely candidates for the best fitting distribution. Next, the suitability of six extreme value distributions, namely the Gumbel, Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA), the Lognormal (GNO) and the Pearson (PE3) distributions are evaluated. The method of L-moments is used in parameter estimation. Based on several goodness of fit tests and L-moment diagram test, the Generalized Pareto distribution and the Pearson distribution are found to be the best fitted distribution to represent the weekly and monthly maximum share returns in Malaysia stock market during the studied period, respectively.
International Nuclear Information System (INIS)
Helton, J.C.
1996-03-01
A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S st , S st , p st ) for stochastic uncertainty, a probability space (S su , S su , p su ) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S st , S st , p st ) and (S su , S su , p su ). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the U.S. Environmental Protection Agency's standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems
International Nuclear Information System (INIS)
Helton, J.C.
1996-01-01
A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S st , L st , P st ) for stochastic uncertainty, a probability space (S su , L su , P su ) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S st , L st , P st ) and (S su , L su , P su ). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the US Environmental Protection Agency's standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems
A formalism to generate probability distributions for performance-assessment modeling
International Nuclear Information System (INIS)
Kaplan, P.G.
1990-01-01
A formalism is presented for generating probability distributions of parameters used in performance-assessment modeling. The formalism is used when data are either sparse or nonexistent. The appropriate distribution is a function of the known or estimated constraints and is chosen to maximize a quantity known as Shannon's informational entropy. The formalism is applied to a parameter used in performance-assessment modeling. The functional form of the model that defines the parameter, data from the actual field site, and natural analog data are analyzed to estimate the constraints. A beta probability distribution of the example parameter is generated after finding four constraints. As an example of how the formalism is applied to the site characterization studies of Yucca Mountain, the distribution is generated for an input parameter in a performance-assessment model currently used to estimate compliance with disposal of high-level radioactive waste in geologic repositories, 10 CFR 60.113(a)(2), commonly known as the ground water travel time criterion. 8 refs., 2 figs
Statistical models based on conditional probability distributions
International Nuclear Information System (INIS)
Narayanan, R.S.
1991-10-01
We present a formulation of statistical mechanics models based on conditional probability distribution rather than a Hamiltonian. We show that it is possible to realize critical phenomena through this procedure. Closely linked with this formulation is a Monte Carlo algorithm, in which a configuration generated is guaranteed to be statistically independent from any other configuration for all values of the parameters, in particular near the critical point. (orig.)
Directory of Open Access Journals (Sweden)
Changhao Fan
2017-01-01
Full Text Available In modeling, only information from the deviation between the output of the support vector regression (SVR model and the training sample is considered, whereas the other prior information of the training sample, such as probability distribution information, is ignored. Probabilistic distribution information describes the overall distribution of sample data in a training sample that contains different degrees of noise and potential outliers, as well as helping develop a high-accuracy model. To mine and use the probability distribution information of a training sample, a new support vector regression model that incorporates probability distribution information weight SVR (PDISVR is proposed. In the PDISVR model, the probability distribution of each sample is considered as the weight and is then introduced into the error coefficient and slack variables of SVR. Thus, the deviation and probability distribution information of the training sample are both used in the PDISVR model to eliminate the influence of noise and outliers in the training sample and to improve predictive performance. Furthermore, examples with different degrees of noise were employed to demonstrate the performance of PDISVR, which was then compared with those of three SVR-based methods. The results showed that PDISVR performs better than the three other methods.
DEFF Research Database (Denmark)
Schjær-Jacobsen, Hans
2012-01-01
uncertainty can be calculated. The possibility approach is particular well suited for representation of uncertainty of a non-statistical nature due to lack of knowledge and requires less information than the probability approach. Based on the kind of uncertainty and knowledge present, these aspects...... to the understanding of similarities and differences of the two approaches as well as practical applications. The probability approach offers a good framework for representation of randomness and variability. Once the probability distributions of uncertain parameters and their correlations are known the resulting...... are thoroughly discussed in the case of rectangular representation of uncertainty by the uniform probability distribution and the interval, respectively. Also triangular representations are dealt with and compared. Calculation of monotonic as well as non-monotonic functions of variables represented...
WIENER-HOPF SOLVER WITH SMOOTH PROBABILITY DISTRIBUTIONS OF ITS COMPONENTS
Directory of Open Access Journals (Sweden)
Mr. Vladimir A. Smagin
2016-12-01
Full Text Available The Wiener – Hopf solver with smooth probability distributions of its component is presented. The method is based on hyper delta approximations of initial distributions. The use of Fourier series transformation and characteristic function allows working with the random variable method concentrated in transversal axis of absc.
Theoretical derivation of wind power probability distribution function and applications
International Nuclear Information System (INIS)
Altunkaynak, Abdüsselam; Erdik, Tarkan; Dabanlı, İsmail; Şen, Zekai
2012-01-01
Highlights: ► Derivation of wind power stochastic characteristics are standard deviation and the dimensionless skewness. ► The perturbation is expressions for the wind power statistics from Weibull probability distribution function (PDF). ► Comparisons with the corresponding characteristics of wind speed PDF abides by the Weibull PDF. ► The wind power abides with the Weibull-PDF. -- Abstract: The instantaneous wind power contained in the air current is directly proportional with the cube of the wind speed. In practice, there is a record of wind speeds in the form of a time series. It is, therefore, necessary to develop a formulation that takes into consideration the statistical parameters of such a time series. The purpose of this paper is to derive the general wind power formulation in terms of the statistical parameters by using the perturbation theory, which leads to a general formulation of the wind power expectation and other statistical parameter expressions such as the standard deviation and the coefficient of variation. The formulation is very general and can be applied specifically for any wind speed probability distribution function. Its application to two-parameter Weibull probability distribution of wind speeds is presented in full detail. It is concluded that provided wind speed is distributed according to a Weibull distribution, the wind power could be derived based on wind speed data. It is possible to determine wind power at any desired risk level, however, in practical studies most often 5% or 10% risk levels are preferred and the necessary simple procedure is presented for this purpose in this paper.
Numerical Loading of a Maxwellian Probability Distribution Function
International Nuclear Information System (INIS)
Lewandowski, J.L.V.
2003-01-01
A renormalization procedure for the numerical loading of a Maxwellian probability distribution function (PDF) is formulated. The procedure, which involves the solution of three coupled nonlinear equations, yields a numerically loaded PDF with improved properties for higher velocity moments. This method is particularly useful for low-noise particle-in-cell simulations with electron dynamics
Probability Distribution of Long-run Indiscriminate Felling of Trees in ...
African Journals Online (AJOL)
Bright
conditionally independent of every prior state given the current state (Obodos, ... of events or experiments in which the probability of occurrence for an event ... represent the exhaustive and mutually exclusive outcomes (states) of a system at.
On the probability distribution of the stochastic saturation scale in QCD
International Nuclear Information System (INIS)
Marquet, C.; Soyez, G.; Xiao Bowen
2006-01-01
It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation scales formed with all the events is distributed according to a probability law whose cumulants have been recently computed. In this work, we obtain the probability distribution from the cumulants. We prove that it can be considered as Gaussian over a large domain that we specify and our results are confirmed by numerical simulations
Calculation of magnetization curves and probability distribution for monoclinic and uniaxial systems
International Nuclear Information System (INIS)
Sobh, Hala A.; Aly, Samy H.; Yehia, Sherif
2013-01-01
We present the application of a simple classical statistical mechanics-based model to selected monoclinic and hexagonal model systems. In this model, we treat the magnetization as a classical vector whose angular orientation is dictated by the laws of equilibrium classical statistical mechanics. We calculate for these anisotropic systems, the magnetization curves, energy landscapes and probability distribution for different sets of relevant parameters and magnetic fields of different strengths and directions. Our results demonstrate a correlation between the most probable orientation of the magnetization vector, the system's parameters, and the external magnetic field. -- Highlights: ► We calculate magnetization curves and probability angular distribution of the magnetization. ► The magnetization curves are consistent with probability results for the studied systems. ► Monoclinic and hexagonal systems behave differently due to their different anisotropies
Energy Technology Data Exchange (ETDEWEB)
Helton, J.C. [Arizona State Univ., Tempe, AZ (United States)
1996-03-01
A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S{sub st}, S{sub st}, p{sub st}) for stochastic uncertainty, a probability space (S{sub su}, S{sub su}, p{sub su}) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S{sub st}, S{sub st}, p{sub st}) and (S{sub su}, S{sub su}, p{sub su}). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the U.S. Environmental Protection Agency`s standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems.
Quantum Fourier transform, Heisenberg groups and quasi-probability distributions
International Nuclear Information System (INIS)
Patra, Manas K; Braunstein, Samuel L
2011-01-01
This paper aims to explore the inherent connection between Heisenberg groups, quantum Fourier transform (QFT) and (quasi-probability) distribution functions. Distribution functions for continuous and finite quantum systems are examined from three perspectives and all of them lead to Weyl-Gabor-Heisenberg groups. The QFT appears as the intertwining operator of two equivalent representations arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of the Wigner function from the marginal distributions via inverse Radon transform giving explicit formulae. We consider some applications of our approach to quantum information processing and quantum process tomography.
New family of probability distributions with applications to Monte Carlo studies
International Nuclear Information System (INIS)
Johnson, M.E.; Tietjen, G.L.; Beckman, R.J.
1980-01-01
A new probability distribution is presented that offers considerable potential for providing stochastic inputs to Monte Carlo simulation studies. The distribution includes the exponential power family as a special case. An efficient computational strategy is proposed for random variate generation. An example for testing the hypothesis of unit variance illustrates the advantages of the proposed distribution
Fluctuating States: What is the Probability of a Thermodynamical Transition?
Directory of Open Access Journals (Sweden)
Álvaro M. Alhambra
2016-10-01
Full Text Available If the second law of thermodynamics forbids a transition from one state to another, then it is still possible to make the transition happen by using a sufficient amount of work. But if we do not have access to this amount of work, can the transition happen probabilistically? In the thermodynamic limit, this probability tends to zero, but here we find that for finite-sized and quantum systems it can be finite. We compute the maximum probability of a transition or a thermodynamical fluctuation from any initial state to any final state and show that this maximum can be achieved for any final state that is block diagonal in the energy eigenbasis. We also find upper and lower bounds on this transition probability, in terms of the work of transition. As a by-product, we introduce a finite set of thermodynamical monotones related to the thermomajorization criteria which governs state transitions and compute the work of transition in terms of them. The trade-off between the probability of a transition and any partial work added to aid in that transition is also considered. Our results have applications in entanglement theory, and we find the amount of entanglement required (or gained when transforming one pure entangled state into any other.
International Nuclear Information System (INIS)
Birchall, A.; Muirhead, C.R.; James, A.C.
1988-01-01
An analytical expression has been derived for the k-sum distribution, formed by summing k random variables from a lognormal population. Poisson statistics are used with this distribution to derive distribution of intake when breathing an atmosphere with a constant particle number concentration. Bayesian inference is then used to calculate the posterior probability distribution of concentrations from a given measurement. This is combined with the above intake distribution to give the probability distribution of intake resulting from a single measurement of activity made by an ideal sampler. It is shown that the probability distribution of intake is very dependent on the prior distribution used in Bayes' theorem. The usual prior assumption, that all number concentrations are equally probable, leads to an imbalance in the posterior intake distribution. This can be resolved if a new prior proportional to w -2/3 is used, where w is the expected number of particles collected. (author)
International Nuclear Information System (INIS)
Tutnov, A.; Alexeev, E.
2001-01-01
'PULSAR-2' and 'PULSAR+' codes make it possible to simulate thermo-mechanical and thermo-physical parameters of WWER fuel elements. The probabilistic approach is used instead of traditional deterministic one to carry out a sensitive study of fuel element behavior under steady-state operation mode. Fuel elements initial parameters are given as a density of the probability distributions. Calculations are provided for all possible combinations of initial data as fuel-cladding gap, fuel density and gas pressure. Dividing values of these parameters to intervals final variants for calculations are obtained . Intervals of permissible fuel-cladding gap size have been divided to 10 equal parts, fuel density and gas pressure - to 5 parts. Probability of each variant realization is determined by multiplying the probabilities of separate parameters, because the tolerances of these parameters are distributed independently. Simulation results are turn out in the probabilistic bar charts. The charts present probability distribution of the changes in fuel outer diameter, hoop stress kinetics and fuel temperature versus irradiation time. A normative safety factor is introduced for control of any criterion realization and for determination of a reserve to the criteria failure. A probabilistic analysis of fuel element behavior under Reactivity Initiating Accident (RIA) is also performed and probability fuel element depressurization under hypothetical RIA is presented
Wave functions and two-electron probability distributions of the Hooke's-law atom and helium
International Nuclear Information System (INIS)
O'Neill, Darragh P.; Gill, Peter M. W.
2003-01-01
The Hooke's-law atom (hookium) provides an exactly soluble model for a two-electron atom in which the nuclear-electron Coulombic attraction has been replaced by a harmonic one. Starting from the known exact position-space wave function for the ground state of hookium, we present the momentum-space wave function. We also look at the intracules, two-electron probability distributions, for hookium in position, momentum, and phase space. These are compared with the Hartree-Fock results and the Coulomb holes (the difference between the exact and Hartree-Fock intracules) in position, momentum, and phase space are examined. We then compare these results with analogous results for the ground state of helium using a simple, explicitly correlated wave function
Log-concave Probability Distributions: Theory and Statistical Testing
DEFF Research Database (Denmark)
An, Mark Yuing
1996-01-01
This paper studies the broad class of log-concave probability distributions that arise in economics of uncertainty and information. For univariate, continuous, and log-concave random variables we prove useful properties without imposing the differentiability of density functions. Discrete...... and multivariate distributions are also discussed. We propose simple non-parametric testing procedures for log-concavity. The test statistics are constructed to test one of the two implicati ons of log-concavity: increasing hazard rates and new-is-better-than-used (NBU) property. The test for increasing hazard...... rates are based on normalized spacing of the sample order statistics. The tests for NBU property fall into the category of Hoeffding's U-statistics...
Exact probability distribution function for the volatility of cumulative production
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.
Probability of collective excited state decay
International Nuclear Information System (INIS)
Manykin, Eh.A.; Ozhovan, M.I.; Poluehktov, P.P.
1987-01-01
Decay mechanisms of condensed excited state formed of highly excited (Rydberg) atoms are considered, i.e. stability of so-called Rydberg substance is analyzed. It is shown that Auger recombination and radiation transitions are the basic processes. The corresponding probabilities are calculated and compared. It is ascertained that the ''Rydberg substance'' possesses macroscopic lifetime (several seconds) and in a sense it is metastable
Bounds for the probability distribution function of the linear ACD process
Fernandes, Marcelo
2003-01-01
Rio de Janeiro This paper derives both lower and upper bounds for the probability distribution function of stationary ACD(p, q) processes. For the purpose of illustration, I specialize the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.
International Nuclear Information System (INIS)
El-Shanshoury, Gh. I.; El-Hemamy, S.T.
2013-01-01
The main objective of this paper is to identify an appropriate probability model and best plotting position formula which represent the maximum annual wind speed in east Cairo. This model can be used to estimate the extreme wind speed and return period at a particular site as well as to determine the radioactive release distribution in case of accident occurrence at a nuclear power plant. Wind speed probabilities can be estimated by using probability distributions. An accurate determination of probability distribution for maximum wind speed data is very important in expecting the extreme value . The probability plots of the maximum annual wind speed (MAWS) in east Cairo are fitted to six major statistical distributions namely: Gumbel, Weibull, Normal, Log-Normal, Logistic and Log- Logistic distribution, while eight plotting positions of Hosking and Wallis, Hazen, Gringorten, Cunnane, Blom, Filliben, Benard and Weibull are used for determining exceedance of their probabilities. A proper probability distribution for representing the MAWS is selected by the statistical test criteria in frequency analysis. Therefore, the best plotting position formula which can be used to select appropriate probability model representing the MAWS data must be determined. The statistical test criteria which represented in: the probability plot correlation coefficient (PPCC), the root mean square error (RMSE), the relative root mean square error (RRMSE) and the maximum absolute error (MAE) are used to select the appropriate probability position and distribution. The data obtained show that the maximum annual wind speed in east Cairo vary from 44.3 Km/h to 96.1 Km/h within duration of 39 years . Weibull plotting position combined with Normal distribution gave the highest fit, most reliable, accurate predictions and determination of the wind speed in the study area having the highest value of PPCC and lowest values of RMSE, RRMSE and MAE
Measurement of probability distributions for internal stresses in dislocated crystals
Energy Technology Data Exchange (ETDEWEB)
Wilkinson, Angus J.; Tarleton, Edmund; Vilalta-Clemente, Arantxa; Collins, David M. [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Jiang, Jun; Britton, T. Benjamin [Department of Materials, Imperial College London, Royal School of Mines, Exhibition Road, London SW7 2AZ (United Kingdom)
2014-11-03
Here, we analyse residual stress distributions obtained from various crystal systems using high resolution electron backscatter diffraction (EBSD) measurements. Histograms showing stress probability distributions exhibit tails extending to very high stress levels. We demonstrate that these extreme stress values are consistent with the functional form that should be expected for dislocated crystals. Analysis initially developed by Groma and co-workers for X-ray line profile analysis and based on the so-called “restricted second moment of the probability distribution” can be used to estimate the total dislocation density. The generality of the results are illustrated by application to three quite different systems, namely, face centred cubic Cu deformed in uniaxial tension, a body centred cubic steel deformed to larger strain by cold rolling, and hexagonal InAlN layers grown on misfitting sapphire and silicon carbide substrates.
Rank-Ordered Multifractal Analysis (ROMA of probability distributions in fluid turbulence
Directory of Open Access Journals (Sweden)
C. C. Wu
2011-04-01
Full Text Available Rank-Ordered Multifractal Analysis (ROMA was introduced by Chang and Wu (2008 to describe the multifractal characteristic of intermittent events. The procedure provides a natural connection between the rank-ordered spectrum and the idea of one-parameter scaling for monofractals. This technique has successfully been applied to MHD turbulence simulations and turbulence data observed in various space plasmas. In this paper, the technique is applied to the probability distributions in the inertial range of the turbulent fluid flow, as given in the vast Johns Hopkins University (JHU turbulence database. In addition, a new way of finding the continuous ROMA spectrum and the scaled probability distribution function (PDF simultaneously is introduced.
International Nuclear Information System (INIS)
Difilippo, F.C.
1994-01-01
For a mixture of two families of resonances, we found the probability distribution for the distance, as first neighbors, between resonances that belong to different families. Integration of this distribution gives the probability of accidental overlapping of resonances of one isotope by resonances of the other, provided that the resonances of each isotope belong to a single family. (author)
Diachronic changes in word probability distributions in daily press
Directory of Open Access Journals (Sweden)
Stanković Jelena
2006-01-01
Full Text Available Changes in probability distributions of individual words and word types were investigated within two samples of daily press in the span of fifty years. Two samples of daily press were used in this study. The one derived from the Corpus of Serbian Language (CSL /Kostić, Đ., 2001/ that covers period between 1945. and 1957. and the other derived from the Ebart Media Documentation (EBR that was complied from seven daily news and five weekly magazines from 2002. and 2003. Each sample consisted of about 1 million words. The obtained results indicate that nouns and adjectives were more frequent in the CSL, while verbs and prepositions are more frequent in the EBR sample, suggesting a decrease of sentence length in the last five decades. Conspicuous changes in probability distribution of individual words were observed for nouns and adjectives, while minimal or no changes were observed for verbs and prepositions. Such an outcome suggests that nouns and adjectives are most susceptible to diachronic changes, while verbs and prepositions appear to be resistant to such changes.
Jacobsen, J L; Saleur, H
2008-02-29
We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model.
Probability distributions in conservative energy exchange models of multiple interacting agents
International Nuclear Information System (INIS)
Scafetta, Nicola; West, Bruce J
2007-01-01
Herein we study energy exchange models of multiple interacting agents that conserve energy in each interaction. The models differ regarding the rules that regulate the energy exchange and boundary effects. We find a variety of stochastic behaviours that manifest energy equilibrium probability distributions of different types and interaction rules that yield not only the exponential distributions such as the familiar Maxwell-Boltzmann-Gibbs distribution of an elastically colliding ideal particle gas, but also uniform distributions, truncated exponential distributions, Gaussian distributions, Gamma distributions, inverse power law distributions, mixed exponential and inverse power law distributions, and evolving distributions. This wide variety of distributions should be of value in determining the underlying mechanisms generating the statistical properties of complex phenomena including those to be found in complex chemical reactions
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.
Directory of Open Access Journals (Sweden)
Stihi Nadjet
2012-01-01
Full Text Available For M/G/1 retrial queues with impatient customers, we review the results, concerning the steady state distribution of the system state, presented in the literature. Since the existing formulas are cumbersome (so their utilization in practice becomes delicate or the obtaining of these formulas is impossible, we apply the information theoretic techniques for estimating the above mentioned distribution. More concretely, we use the principle of maximum entropy which provides an adequate methodology for computing a unique estimate for an unknown probability distribution based on information expressed in terms of some given mean value constraints.
International Nuclear Information System (INIS)
Peschar, R.; Schenk, H.
1991-01-01
A method to derive joint probability distributions of structure factors is presented which incorporates anomalous-scattering and isomorphous-replacement data in a unified procedure. The structure factors F H and F -H , whose magnitudes are different due to anomalous scattering, are shown to be isomorphously related. This leads to a definition of isomorphism by means of which isomorphous-replacement and anomalous-scattering data can be handled simultaneously. The definition and calculation of the general term of the joint probability distribution for isomorphous structure factors turns out to be crucial. Its analytical form leads to an algorithm by means of which any particular joint probability distribution of structure factors can be constructed. The calculation of the general term is discussed for the case of four isomorphous structure factors in P1, assuming the atoms to be independently and uniformly distributed. A main result is the construction of the probability distribution of the 64 triplet phase sums present in space group P1 amongst four isomorphous structure factors F H , four isomorphous F K and four isomorphous F -H-K . The procedure is readily generalized in the case where an arbitrary number of isomorphous structure factors are available for F H , F K and F -H-K . (orig.)
Directory of Open Access Journals (Sweden)
A. B. Levina
2016-03-01
Full Text Available Error detection codes are mechanisms that enable robust delivery of data in unreliable communication channels and devices. Unreliable channels and devices are error-prone objects. Respectively, error detection codes allow detecting such errors. There are two classes of error detecting codes - classical codes and security-oriented codes. The classical codes have high percentage of detected errors; however, they have a high probability to miss an error in algebraic manipulation. In order, security-oriented codes are codes with a small Hamming distance and high protection to algebraic manipulation. The probability of error masking is a fundamental parameter of security-oriented codes. A detailed study of this parameter allows analyzing the behavior of the error-correcting code in the case of error injection in the encoding device. In order, the complexity of the encoding function plays an important role in the security-oriented codes. Encoding functions with less computational complexity and a low probability of masking are the best protection of encoding device against malicious acts. This paper investigates the influence of encoding function complexity on the error masking probability distribution. It will be shownthat the more complex encoding function reduces the maximum of error masking probability. It is also shown in the paper that increasing of the function complexity changes the error masking probability distribution. In particular, increasing of computational complexity decreases the difference between the maximum and average value of the error masking probability. Our resultshave shown that functions with greater complexity have smoothed maximums of error masking probability, which significantly complicates the analysis of error-correcting code by attacker. As a result, in case of complex encoding function the probability of the algebraic manipulation is reduced. The paper discusses an approach how to measure the error masking
International Nuclear Information System (INIS)
Marshman, Emily; Singh, Chandralekha
2017-01-01
A solid grasp of the probability distributions for measuring physical observables is central to connecting the quantum formalism to measurements. However, students often struggle with the probability distributions of measurement outcomes for an observable and have difficulty expressing this concept in different representations. Here we first describe the difficulties that upper-level undergraduate and PhD students have with the probability distributions for measuring physical observables in quantum mechanics. We then discuss how student difficulties found in written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of the probability distributions of measurement outcomes for physical observables. The QuILT strives to help students become proficient in expressing the probability distributions for the measurement of physical observables in Dirac notation and in the position representation and be able to convert from Dirac notation to position representation and vice versa. We describe the development and evaluation of the QuILT and findings about the effectiveness of the QuILT from in-class evaluations. (paper)
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).
Multimode Interference: Identifying Channels and Ridges in Quantum Probability Distributions
O'Connell, Ross C.; Loinaz, Will
2004-01-01
The multimode interference technique is a simple way to study the interference patterns found in many quantum probability distributions. We demonstrate that this analysis not only explains the existence of so-called "quantum carpets," but can explain the spatial distribution of channels and ridges in the carpets. With an understanding of the factors that govern these channels and ridges we have a limited ability to produce a particular pattern of channels and ridges by carefully choosing the ...
Influence of nucleon density distribution in nucleon emission probability
International Nuclear Information System (INIS)
Paul, Sabyasachi; Nandy, Maitreyee; Mohanty, A.K.; Sarkar, P.K.; Gambhir, Y.K.
2014-01-01
Different decay modes are observed in heavy ion reactions at low to intermediate energies. It is interesting to study total neutron emission in these reactions which may be contributed by all/many of these decay modes. In an attempt to understand the importance of mean field and the entrance channel angular momentum, we study their influence on the emission probability of nucleons in heavy ion reactions in this work. This study owes its significance to the fact that once population of different states are determined, emission probability governs the double differential neutron yield
Energy Technology Data Exchange (ETDEWEB)
Yilmaz, Şeyda, E-mail: seydayilmaz@ktu.edu.tr; Bayrak, Erdem, E-mail: erdmbyrk@gmail.com [Karadeniz Technical University, Trabzon (Turkey); Bayrak, Yusuf, E-mail: bayrak@ktu.edu.tr [Ağrı İbrahim Çeçen University, Ağrı (Turkey)
2016-04-18
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 time 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.
Probability distribution relationships
Directory of Open Access Journals (Sweden)
Yousry Abdelkader
2013-05-01
Full Text Available In this paper, we are interesting to show the most famous distributions and their relations to the other distributions in collected diagrams. Four diagrams are sketched as networks. The first one is concerned to the continuous distributions and their relations. The second one presents the discrete distributions. The third diagram is depicted the famous limiting distributions. Finally, the Balakrishnan skew-normal density and its relationship with the other distributions are shown in the fourth diagram.
The distribution function of a probability measure on a space with a fractal structure
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Granero, M.A.; Galvez-Rodriguez, J.F.
2017-07-01
In this work we show how to define a probability measure with the help of a fractal structure. One of the keys of this approach is to use the completion of the fractal structure. Then we use the theory of a cumulative distribution function on a Polish ultrametric space and describe it in this context. Finally, with the help of fractal structures, we prove that a function satisfying the properties of a cumulative distribution function on a Polish ultrametric space is a cumulative distribution function with respect to some probability measure on the space. (Author)
DEFF Research Database (Denmark)
Yura, Harold; Hanson, Steen Grüner
2012-01-01
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...
On the Meta Distribution of Coverage Probability in Uplink Cellular Networks
Elsawy, Hesham; Alouini, Mohamed-Slim
2017-01-01
This letter studies the meta distribution of coverage probability (CP), within a stochastic geometry framework, for cellular uplink transmission with fractional path-loss inversion power control. Using the widely accepted Poisson point process (PPP
The p-sphere and the geometric substratum of power-law probability distributions
International Nuclear Information System (INIS)
Vignat, C.; Plastino, A.
2005-01-01
Links between power law probability distributions and marginal distributions of uniform laws on p-spheres in R n show that a mathematical derivation of the Boltzmann-Gibbs distribution necessarily passes through power law ones. Results are also given that link parameters p and n to the value of the non-extensivity parameter q that characterizes these power laws in the context of non-extensive statistics
Landslide Probability Assessment by the Derived Distributions Technique
Muñoz, E.; Ochoa, A.; Martínez, H.
2012-12-01
Landslides are potentially disastrous events that bring along human and economic losses; especially in cities where an accelerated and unorganized growth leads to settlements on steep and potentially unstable areas. Among the main causes of landslides are geological, geomorphological, geotechnical, climatological, hydrological conditions and anthropic intervention. This paper studies landslides detonated by rain, commonly known as "soil-slip", which characterize by having a superficial failure surface (Typically between 1 and 1.5 m deep) parallel to the slope face and being triggered by intense and/or sustained periods of rain. This type of landslides is caused by changes on the pore pressure produced by a decrease in the suction when a humid front enters, as a consequence of the infiltration initiated by rain and ruled by the hydraulic characteristics of the soil. Failure occurs when this front reaches a critical depth and the shear strength of the soil in not enough to guarantee the stability of the mass. Critical rainfall thresholds in combination with a slope stability model are widely used for assessing landslide probability. In this paper we present a model for the estimation of the occurrence of landslides based on the derived distributions technique. Since the works of Eagleson in the 1970s the derived distributions technique has been widely used in hydrology to estimate the probability of occurrence of extreme flows. The model estimates the probability density function (pdf) of the Factor of Safety (FOS) from the statistical behavior of the rainfall process and some slope parameters. The stochastic character of the rainfall is transformed by means of a deterministic failure model into FOS pdf. Exceedance probability and return period estimation is then straightforward. The rainfall process is modeled as a Rectangular Pulses Poisson Process (RPPP) with independent exponential pdf for mean intensity and duration of the storms. The Philip infiltration model
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.
Load sharing in distributed real-time systems with state-change broadcasts
Shin, Kang G.; Chang, Yi-Chieh
1989-01-01
A decentralized dynamic load-sharing (LS) method based on state-change broadcasts is proposed for a distributed real-time system. Whenever the state of a node changes from underloaded to fully loaded and vice versa, the node broadcasts this change to a set of nodes, called a buddy set, in the system. The performance of the method is evaluated with both analytic modeling and simulation. It is modeled first by an embedded Markov chain for which numerical solutions are derived. The model solutions are then used to calculate the distribution of queue lengths at the nodes and the probability of meeting task deadlines. The analytical results show that buddy sets of 10 nodes outperform those of less than 10 nodes, and the incremental benefit gained from increasing the buddy set size beyond 15 nodes is insignificant. These and other analytical results are verified by simulation. The proposed LS method is shown to meet task deadlines with a very high probability.
Estimating probable flaw distributions in PWR steam generator tubes
International Nuclear Information System (INIS)
Gorman, J.A.; Turner, A.P.L.
1997-01-01
This paper describes methods for estimating the number and size distributions of flaws of various types in PWR steam generator tubes. These estimates are needed when calculating the probable primary to secondary leakage through steam generator tubes under postulated accidents such as severe core accidents and steam line breaks. The paper describes methods for two types of predictions: (1) the numbers of tubes with detectable flaws of various types as a function of time, and (2) the distributions in size of these flaws. Results are provided for hypothetical severely affected, moderately affected and lightly affected units. Discussion is provided regarding uncertainties and assumptions in the data and analyses
On the continuity of the stationary state distribution of DPCM
Naraghi-Pour, Morteza; Neuhoff, David L.
1990-03-01
Continuity and singularity properties of the stationary state distribution of differential pulse code modulation (DPCM) are explored. Two-level DPCM (i.e., delta modulation) operating on a first-order autoregressive source is considered, and it is shown that, when the magnitude of the DPCM prediciton coefficient is between zero and one-half, the stationary state distribution is singularly continuous; i.e., it is not discrete but concentrates on an uncountable set with a Lebesgue measure of zero. Consequently, it cannot be represented with a probability density function. For prediction coefficients with magnitude greater than or equal to one-half, the distribution is pure, i.e., either absolutely continuous and representable with a density function, or singular. This problem is compared to the well-known and still substantially unsolved problem of symmetric Bernoulli convolutions.
DEFF Research Database (Denmark)
Helles, Glennie; Fonseca, Rasmus
2009-01-01
residue in the input-window. The trained neural network shows a significant improvement (4-68%) in predicting the most probable bin (covering a 30°×30° area of the dihedral angle space) for all amino acids in the data set compared to first order statistics. An accuracy comparable to that of secondary...... seem to have a significant influence on the dihedral angles adopted by the individual amino acids in coil segments. In this work we attempt to predict a probability distribution of these dihedral angles based on the flanking residues. While attempts to predict dihedral angles of coil segments have been...... done previously, none have, to our knowledge, presented comparable results for the probability distribution of dihedral angles. Results: In this paper we develop an artificial neural network that uses an input-window of amino acids to predict a dihedral angle probability distribution for the middle...
A measure of mutual divergence among a number of probability distributions
Directory of Open Access Journals (Sweden)
J. N. Kapur
1987-01-01
major inequalities due to Shannon, Renyi and Holder. The inequalities are then used to obtain some useful results in information theory. In particular measures are obtained to measure the mutual divergence among two or more probability distributions.
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
Outage probability of distributed beamforming with co-channel interference
Yang, Liang
2012-03-01
In this letter, we consider a distributed beamforming scheme (DBF) in the presence of equal-power co-channel interferers for both amplify-and-forward and decode-and-forward relaying protocols over Rayleigh fading channels. We first derive outage probability expressions for the DBF systems. We then present a performance analysis for a scheme relying on source selection. Numerical results are finally presented to verify our analysis. © 2011 IEEE.
International Nuclear Information System (INIS)
Wasastjerna, F.; Lux, I.
1980-03-01
A transmission probability method implemented in the program TPHEX is described. This program was developed for the calculation of neutron flux distributions in hexagonal light water reactor fuel assemblies. The accuracy appears to be superior to diffusion theory, and the computation time is shorter than that of the collision probability method. (author)
Energy Technology Data Exchange (ETDEWEB)
Kanki, T [Osaka Univ., Toyonaka (Japan). Coll. of General Education
1976-12-01
We present a quark-gluon-parton model in which quark-partons and gluons make clusters corresponding to two or three constituent quarks (or anti-quarks) in the meson or in the baryon, respectively. We explicitly construct the constituent quark state (cluster), by employing the Kuti-Weisskopf theory and by requiring the scaling. The quark additivity of the hadronic total cross sections and the quark counting rules on the threshold powers of various distributions are satisfied. For small x (Feynman fraction), it is shown that the constituent quarks and quark-partons have quite different probability distributions. We apply our model to hadron-hadron inclusive reactions, and clarify that the fragmentation and the diffractive processes relate to the constituent quark distributions, while the processes in or near the central region are controlled by the quark-partons. Our model gives the reasonable interpretation for the experimental data and much improves the usual ''constituent interchange model'' result near and in the central region (x asymptotically equals x sub(T) asymptotically equals 0).
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.
Goldberg, Samuel
1960-01-01
Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, more. Includes 360 problems with answers for half.
Directory of Open Access Journals (Sweden)
Daniel Ting
2010-04-01
Full Text Available 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.
Transition probabilities of health states for workers in Malaysia using a Markov chain model
Samsuddin, Shamshimah; Ismail, Noriszura
2017-04-01
The aim of our study is to estimate the transition probabilities of health states for workers in Malaysia who contribute to the Employment Injury Scheme under the Social Security Organization Malaysia using the Markov chain model. Our study uses four states of health (active, temporary disability, permanent disability and death) based on the data collected from the longitudinal studies of workers in Malaysia for 5 years. The transition probabilities vary by health state, age and gender. The results show that men employees are more likely to have higher transition probabilities to any health state compared to women employees. The transition probabilities can be used to predict the future health of workers in terms of a function of current age, gender and health state.
Semiquantum-key distribution using less than four quantum states
International Nuclear Information System (INIS)
Zou Xiangfu; Qiu Daowen; Li Lvzhou; Wu Lihua; Li Lvjun
2009-01-01
Recently Boyer et al. [Phys. Rev. Lett. 99, 140501 (2007)] suggested the idea of semiquantum key distribution (SQKD) in which Bob is classical and they also proposed a semiquantum key distribution protocol (BKM2007). To discuss the security of the BKM2007 protocol, they proved that their protocol is completely robust. This means that nonzero information acquired by Eve on the information string implies the nonzero probability that the legitimate participants can find errors on the bits tested by this protocol. The BKM2007 protocol uses four quantum states to distribute a secret key. In this paper, we simplify their protocol by using less than four quantum states. In detail, we present five different SQKD protocols in which Alice sends three quantum states, two quantum states, and one quantum state, respectively. Also, we prove that all the five protocols are completely robust. In particular, we invent two completely robust SQKD protocols in which Alice sends only one quantum state. Alice uses a register in one SQKD protocol, but she does not use any register in the other. The information bit proportion of the SQKD protocol in which Alice sends only one quantum state but uses a register is the double as that in the BKM2007 protocol. Furthermore, the information bit rate of the SQKD protocol in which Alice sends only one quantum state and does not use any register is not lower than that of the BKM2007 protocol.
Probabilities of filaments in a Poissonian distribution of points -I
International Nuclear Information System (INIS)
Betancort-Rijo, J.
1989-01-01
Statistical techniques are devised to assess the likelihood of a Poisson sample of points in two and three dimensions, containing specific filamentary structures. For that purpose, the expression of Otto et al (1986. Astrophys. J., 304) for the probability density of clumps in a Poissonian distribution of points is generalized for any value of the density contrast. A way of counting filaments differing from that of Otto et al. is proposed, because at low density contrast the filaments counted by Otto et al. are distributed in a clumpy fashion, each clump of filaments corresponding to a distinct observed filament. (author)
Crovelli, R.A.; Balay, R.H.
1991-01-01
A general risk-analysis method was developed for petroleum-resource assessment and other applications. The triangular probability distribution is used as a model with an analytic aggregation methodology based on probability theory rather than Monte-Carlo simulation. Among the advantages of the analytic method are its computational speed and flexibility, and the saving of time and cost on a microcomputer. The input into the model consists of a set of components (e.g. geologic provinces) and, for each component, three potential resource estimates: minimum, most likely (mode), and maximum. Assuming a triangular probability distribution, the mean, standard deviation, and seven fractiles (F100, F95, F75, F50, F25, F5, and F0) are computed for each component, where for example, the probability of more than F95 is equal to 0.95. The components are aggregated by combining the means, standard deviations, and respective fractiles under three possible siutations (1) perfect positive correlation, (2) complete independence, and (3) any degree of dependence between these two polar situations. A package of computer programs named the TRIAGG system was written in the Turbo Pascal 4.0 language for performing the analytic probabilistic methodology. The system consists of a program for processing triangular probability distribution assessments and aggregations, and a separate aggregation routine for aggregating aggregations. The user's documentation and program diskette of the TRIAGG system are available from USGS Open File Services. TRIAGG requires an IBM-PC/XT/AT compatible microcomputer with 256kbyte of main memory, MS-DOS 3.1 or later, either two diskette drives or a fixed disk, and a 132 column printer. A graphics adapter and color display are optional. ?? 1991.
Idealized models of the joint probability distribution of wind speeds
Monahan, Adam H.
2018-05-01
The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.
Structure of states and reduced probabilities of electromagnetic transitions in 169Yb
International Nuclear Information System (INIS)
Bonch-Osmolovskaya, N.A.; Morozov, V.A.; Khudajberdyev, Eh.N.
1988-01-01
The effect of accounting the Pauli principle on the structure and energy of nonrotational states of 169 Yb deformed nucleus as well as on reduced probabilities of E2-transitions B(E2) is studied within the framework of the quasiparticle-phonon model (QPM). The amplitudes of states mixing due to Coriolis interaction and reduced probabilities of gamma transition within the framework of nonadiabatic rotation model are also calculated. The results are compared with calculations made within QPM with account of Coriolis interaction but excluding the Pauli principle in the wave state function. It is shown that to describe correctly both the level structure and reduced probabilities B(E2) it is necessary to include all types of interaction : quasiparticle interaction with phonons with account of the Pauli principle in the wave state functions and Coriolis interactions. Now no uniform theoretical approach exists
Probability distribution functions of turbulence in seepage-affected alluvial channel
Energy Technology Data Exchange (ETDEWEB)
Sharma, Anurag; Kumar, Bimlesh, E-mail: anurag.sharma@iitg.ac.in, E-mail: bimk@iitg.ac.in [Department of Civil Engineering, Indian Institute of Technology Guwahati, 781039 (India)
2017-02-15
The present experimental study is carried out on the probability distribution functions (PDFs) of turbulent flow characteristics within near-bed-surface and away-from-bed surfaces for both no seepage and seepage flow. Laboratory experiments were conducted in the plane sand bed for no seepage (NS), 10% seepage (10%S) and 15% seepage (15%) cases. The experimental calculation of the PDFs of turbulent parameters such as Reynolds shear stress, velocity fluctuations, and bursting events is compared with theoretical expression obtained by Gram–Charlier (GC)-based exponential distribution. Experimental observations follow the computed PDF distributions for both no seepage and seepage cases. Jensen-Shannon divergence (JSD) method is used to measure the similarity between theoretical and experimental PDFs. The value of JSD for PDFs of velocity fluctuation lies between 0.0005 to 0.003 while the JSD value for PDFs of Reynolds shear stress varies between 0.001 to 0.006. Even with the application of seepage, the PDF distribution of bursting events, sweeps and ejections are well characterized by the exponential distribution of the GC series, except that a slight deflection of inward and outward interactions is observed which may be due to weaker events. The value of JSD for outward and inward interactions ranges from 0.0013 to 0.032, while the JSD value for sweep and ejection events varies between 0.0001 to 0.0025. The theoretical expression for the PDF of turbulent intensity is developed in the present study, which agrees well with the experimental observations and JSD lies between 0.007 and 0.015. The work presented is potentially applicable to the probability distribution of mobile-bed sediments in seepage-affected alluvial channels typically characterized by the various turbulent parameters. The purpose of PDF estimation from experimental data is that it provides a complete numerical description in the areas of turbulent flow either at a single or finite number of points
Parametric Probability Distribution Functions for Axon Diameters of Corpus Callosum
Directory of Open Access Journals (Sweden)
Farshid eSepehrband
2016-05-01
Full Text Available Axon diameter is an important neuroanatomical characteristic of the nervous system that alters in the course of neurological disorders such as multiple sclerosis. Axon diameters vary, even within a fiber bundle, and are not normally distributed. An accurate distribution function is therefore beneficial, either to describe axon diameters that are obtained from a direct measurement technique (e.g., microscopy, or to infer them indirectly (e.g., using diffusion-weighted MRI. The gamma distribution is a common choice for this purpose (particularly for the inferential approach because it resembles the distribution profile of measured axon diameters which has been consistently shown to be non-negative and right-skewed. In this study we compared a wide range of parametric probability distribution functions against empirical data obtained from electron microscopy images. We observed that the gamma distribution fails to accurately describe the main characteristics of the axon diameter distribution, such as location and scale of the mode and the profile of distribution tails. We also found that the generalized extreme value distribution consistently fitted the measured distribution better than other distribution functions. This suggests that there may be distinct subpopulations of axons in the corpus callosum, each with their own distribution profiles. In addition, we observed that several other distributions outperformed the gamma distribution, yet had the same number of unknown parameters; these were the inverse Gaussian, log normal, log logistic and Birnbaum-Saunders distributions.
Universal Probability Distribution Function for Bursty Transport in Plasma Turbulence
International Nuclear Information System (INIS)
Sandberg, I.; Benkadda, S.; Garbet, X.; Ropokis, G.; Hizanidis, K.; Castillo-Negrete, D. del
2009-01-01
Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this Letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness S and kurtosis K. Similar statistical characteristics of variabilities have been also observed in other physical systems that are characterized by convection such as the x-ray fluctuations emitted by the Cygnus X-1 accretion disc plasmas and the sea surface temperature fluctuations.
Non-Gaussian probability distributions of solar wind fluctuations
Directory of Open Access Journals (Sweden)
E. Marsch
Full Text Available The probability distributions of field differences ∆x(τ=x(t+τ-x(t, where the variable x(t may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag τ, ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of ∆x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale τ by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of ∆x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.
A discussion on the origin of quantum probabilities
International Nuclear Information System (INIS)
Holik, Federico; Sáenz, Manuel; Plastino, Angel
2014-01-01
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 derivation 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
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.
Most probable mixing state of aerosols in Delhi NCR, northern India
Srivastava, Parul; Dey, Sagnik; Srivastava, Atul Kumar; Singh, Sachchidanand; Tiwari, Suresh
2018-02-01
Unknown mixing state is one of the major sources of uncertainty in estimating aerosol direct radiative forcing (DRF). Aerosol DRF in India is usually reported for external mixing and any deviation from this would lead to high bias and error. Limited information on aerosol composition hinders in resolving this issue in India. Here we use two years of aerosol chemical composition data measured at megacity Delhi to examine the most probable aerosol mixing state by comparing the simulated clear-sky downward surface flux with the measured flux. We consider external, internal, and four combinations of core-shell (black carbon, BC over dust; water-soluble, WS over dust; WS over water-insoluble, WINS and BC over WINS) mixing. Our analysis reveals that choice of external mixing (usually considered in satellite retrievals and climate models) seems reasonable in Delhi only in the pre-monsoon (Mar-Jun) season. During the winter (Dec-Feb) and monsoon (Jul-Sep) seasons, 'WS coating over dust' externally mixed with BC and WINS appears to be the most probable mixing state; while 'WS coating over WINS' externally mixed with BC and dust seems to be the most probable mixing state in the post-monsoon (Oct-Nov) season. Mean seasonal TOA (surface) aerosol DRF for the most probable mixing states are 4.4 ± 3.9 (- 25.9 ± 3.9), - 16.3 ± 5.7 (- 42.4 ± 10.5), 13.6 ± 11.4 (- 76.6 ± 16.6) and - 5.4 ± 7.7 (- 80.0 ± 7.2) W m- 2 respectively in the pre-monsoon, monsoon, post-monsoon and winter seasons. Our results highlight the importance of realistic mixing state treatment in estimating aerosol DRF to aid in policy making to combat climate change.
Charge state distribution of ionic kryptons after photoionization
International Nuclear Information System (INIS)
Cai Xiaohong
1992-01-01
Monochromatic X-rays from the 2.3 GeV synchrotron at University Bonn (Germany) are employed for inner shell excitation of krypton. Various ionic kryptons and a number of electrons are produced due to photoionization. In order to study the equilibrium charge state distribution of ionic kryptons, a time of flight mass spectrometer is set up and used to measure the resulting ionic charge spectra with photo energies near the L 1 - , L 2 - and L 3 - absorption edges of krypton. The energy dependence of relative probabilities is presented
Introduction to probability with Mathematica
Hastings, Kevin J
2009-01-01
Discrete ProbabilityThe Cast of Characters Properties of Probability Simulation Random SamplingConditional ProbabilityIndependenceDiscrete DistributionsDiscrete Random Variables, Distributions, and ExpectationsBernoulli and Binomial Random VariablesGeometric and Negative Binomial Random Variables Poisson DistributionJoint, Marginal, and Conditional Distributions More on ExpectationContinuous ProbabilityFrom the Finite to the (Very) Infinite Continuous Random Variables and DistributionsContinuous ExpectationContinuous DistributionsThe Normal Distribution Bivariate Normal DistributionNew Random Variables from OldOrder Statistics Gamma DistributionsChi-Square, Student's t, and F-DistributionsTransformations of Normal Random VariablesAsymptotic TheoryStrong and Weak Laws of Large Numbers Central Limit TheoremStochastic Processes and ApplicationsMarkov ChainsPoisson Processes QueuesBrownian MotionFinancial MathematicsAppendixIntroduction to Mathematica Glossary of Mathematica Commands for Probability Short Answers...
Extreme points of the convex set of joint probability distributions with ...
Indian Academy of Sciences (India)
Here we address the following problem: If G is a standard ... convex set of all joint probability distributions on the product Borel space (X1 ×X2, F1 ⊗. F2) which .... cannot be identically zero when X and Y vary in A1 and u and v vary in H2. Thus.
Flux-probability distributions from the master equation for radiation transport in stochastic media
International Nuclear Information System (INIS)
Franke, Brian C.; Prinja, Anil K.
2011-01-01
We present numerical investigations into the accuracy of approximations in the master equation for radiation transport in discrete binary random media. Our solutions of the master equation yield probability distributions of particle flux at each element of phase space. We employ the Levermore-Pomraning interface closure and evaluate the effectiveness of closures for the joint conditional flux distribution for estimating scattering integrals. We propose a parameterized model for this joint-pdf closure, varying between correlation neglect and a full-correlation model. The closure is evaluated for a variety of parameter settings. Comparisons are made with benchmark results obtained through suites of fixed-geometry realizations of random media in rod problems. All calculations are performed using Monte Carlo techniques. Accuracy of the approximations in the master equation is assessed by examining the probability distributions for reflection and transmission and by evaluating the moments of the pdfs. The results suggest the correlation-neglect setting in our model performs best and shows improved agreement in the atomic-mix limit. (author)
International Nuclear Information System (INIS)
Caldarola, L.
1976-01-01
A method is proposed for the analytical evaluation of the cumulative failure probability distribution of complex repairable systems. The method is based on a set of integral equations each one referring to a specific minimal cut set of the system. Each integral equation links the unavailability of a minimal cut set to its failure probability density distribution and to the probability that the minimal cut set is down at the time t under the condition that it was down at time t'(t'<=t). The limitations for the applicability of the method are also discussed. It has been concluded that the method is applicable if the process describing the failure of a minimal cut set is a 'delayed semi-regenerative process'. (Auth.)
The force distribution probability function for simple fluids by density functional theory.
Rickayzen, G; Heyes, D M
2013-02-28
Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.
Application of the Unbounded Probability Distribution of the Johnson System for Floods Estimation
Directory of Open Access Journals (Sweden)
Campos-Aranda Daniel Francisco
2015-09-01
Full Text Available Floods designs constitute a key to estimate the sizing of new water works and to review the hydrological security of existing ones. The most reliable method for estimating their magnitudes associated with certain return periods is to fit a probabilistic model to available records of maximum annual flows. Since such model is at first unknown, several models need to be tested in order to select the most appropriate one according to an arbitrary statistical index, commonly the standard error of fit. Several probability distributions have shown versatility and consistency of results when processing floods records and therefore, its application has been established as a norm or precept. The Johnson System has three families of distributions, one of which is the Log–Normal model with three parameters of fit, which is also the border between the bounded distributions and those with no upper limit. These families of distributions have four adjustment parameters and converge to the standard normal distribution, so that their predictions are obtained with such a model. Having contrasted the three probability distributions established by precept in 31 historical records of hydrological events, the Johnson system is applied to such data. The results of the unbounded distribution of the Johnson system (SJU are compared to the optimal results from the three distributions. It was found that the predictions of the SJU distribution are similar to those obtained with the other models in the low return periods ( 1000 years. Because of its theoretical support, the SJU model is recommended in flood estimation.
THREE-MOMENT BASED APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING SYSTEMS
Directory of Open Access Journals (Sweden)
T. I. Aliev
2014-03-01
Full Text Available The paper deals with the problem of approximation of probability distributions of random variables defined in positive area of real numbers with coefficient of variation different from unity. While using queueing systems as models for computer networks, calculation of characteristics is usually performed at the level of expectation and variance. At the same time, one of the main characteristics of multimedia data transmission quality in computer networks is delay jitter. For jitter calculation the function of packets time delay distribution should be known. It is shown that changing the third moment of distribution of packets delay leads to jitter calculation difference in tens or hundreds of percent, with the same values of the first two moments – expectation value and delay variation coefficient. This means that delay distribution approximation for the calculation of jitter should be performed in accordance with the third moment of delay distribution. For random variables with coefficients of variation greater than unity, iterative approximation algorithm with hyper-exponential two-phase distribution based on three moments of approximated distribution is offered. It is shown that for random variables with coefficients of variation less than unity, the impact of the third moment of distribution becomes negligible, and for approximation of such distributions Erlang distribution with two first moments should be used. This approach gives the possibility to obtain upper bounds for relevant characteristics, particularly, the upper bound of delay jitter.
International Nuclear Information System (INIS)
Gupta, S.S.; Panchapakesan, S.
1975-01-01
A quantile selection procedure in reliability problems pertaining to a restricted family of probability distributions is discussed. This family is assumed to be star-ordered with respect to the standard normal distribution folded at the origin. Motivation for this formulation of the problem is described. Both exact and asymptotic results dealing with the distribution of the maximum of ratios of order statistics from such a family are obtained and tables of the appropriate constants, percentiles of this statistic, are given in order to facilitate the use of the selection procedure
Analysis of the probability of channel satisfactory state in P2P live ...
African Journals Online (AJOL)
In this paper a model based on user behaviour of P2P live streaming systems was developed in order to analyse one of the key QoS parameter of such systems, i.e. the probability of channel-satisfactory state, the impact of upload bandwidths and channels' popularity on the probability of channel-satisfactory state was also ...
International Nuclear Information System (INIS)
Akashi, Masatsune; Kenjyo, Takao; Matsukura, Shinji; Kawamoto, Teruaki
1984-01-01
In order to discuss the probability distribution of intergranular stress corrsion carcking life for sensitized 304 stainless steels, a series of the creviced bent beem (CBB) and the uni-axial constant load tests were carried out in oxygenated high temperature, high purity water. The following concludions were resulted; (1) The initiation process of intergranular stress corrosion cracking has been assumed to be approximated by the Poisson stochastic process, based on the CBB test results. (2) The probability distribution of intergranular stress corrosion cracking life may consequently be approximated by the exponential probability distribution. (3) The experimental data could be fitted to the exponential probability distribution. (author)
A Semi-Continuous State-Transition Probability HMM-Based Voice Activity Detector
Directory of Open Access Journals (Sweden)
H. Othman
2007-02-01
Full Text Available We introduce an efficient hidden Markov model-based voice activity detection (VAD algorithm with time-variant state-transition probabilities in the underlying Markov chain. The transition probabilities vary in an exponential charge/discharge scheme and are softly merged with state conditional likelihood into a final VAD decision. Working in the domain of ITU-T G.729 parameters, with no additional cost for feature extraction, the proposed algorithm significantly outperforms G.729 Annex B VAD while providing a balanced tradeoff between clipping and false detection errors. The performance compares very favorably with the adaptive multirate VAD, option 2 (AMR2.
A Semi-Continuous State-Transition Probability HMM-Based Voice Activity Detector
Directory of Open Access Journals (Sweden)
Othman H
2007-01-01
Full Text Available We introduce an efficient hidden Markov model-based voice activity detection (VAD algorithm with time-variant state-transition probabilities in the underlying Markov chain. The transition probabilities vary in an exponential charge/discharge scheme and are softly merged with state conditional likelihood into a final VAD decision. Working in the domain of ITU-T G.729 parameters, with no additional cost for feature extraction, the proposed algorithm significantly outperforms G.729 Annex B VAD while providing a balanced tradeoff between clipping and false detection errors. The performance compares very favorably with the adaptive multirate VAD, option 2 (AMR2.
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.
On the issues of probability distribution of GPS carrier phase observations
Luo, X.; Mayer, M.; Heck, B.
2009-04-01
In common practice the observables related to Global Positioning System (GPS) are assumed to follow a Gauss-Laplace normal distribution. Actually, full knowledge of the observables' distribution is not required for parameter estimation by means of the least-squares algorithm based on the functional relation between observations and unknown parameters as well as the associated variance-covariance matrix. However, the probability distribution of GPS observations plays a key role in procedures for quality control (e.g. outlier and cycle slips detection, ambiguity resolution) and in reliability-related assessments of the estimation results. Under non-ideal observation conditions with respect to the factors impacting GPS data quality, for example multipath effects and atmospheric delays, the validity of the normal distribution postulate of GPS observations is in doubt. This paper presents a detailed analysis of the distribution properties of GPS carrier phase observations using double difference residuals. For this purpose 1-Hz observation data from the permanent SAPOS
E2 transition probabilities between Nilsson states in odd-A nuclei
International Nuclear Information System (INIS)
Krpic, D.K.; Savic, I.M.; Anicin, I.V.
1976-01-01
Presented here are the matrices needed for the calculation of E2 transition probabilities between all pairs of Nilsson states with ΔN = 0 and ΔK = 0, 1, 2. The needed coefficients of states are tabulated by Nilsson and by Davidson
Distribution of return point memory states for systems with stochastic inputs
International Nuclear Information System (INIS)
Amann, A; Brokate, M; Rachinskii, D; Temnov, G
2011-01-01
We consider the long term effect of stochastic inputs on the state of an open loop system which exhibits the so-called return point memory. An example of such a system is the Preisach model; more generally, systems with the Preisach type input-state relationship, such as in spin-interaction models, are considered. We focus on the characterisation of the expected memory configuration after the system has been effected by the input for sufficiently long period of time. In the case where the input is given by a discrete time random walk process, or the Wiener process, simple closed form expressions for the probability density of the vector of the main input extrema recorded by the memory state, and scaling laws for the dimension of this vector, are derived. If the input is given by a general continuous Markov process, we show that the distribution of previous memory elements can be obtained from a Markov chain scheme which is derived from the solution of an associated one-dimensional escape type problem. Formulas for transition probabilities defining this Markov chain scheme are presented. Moreover, explicit formulas for the conditional probability densities of previous main extrema are obtained for the Ornstein-Uhlenbeck input process. The analytical results are confirmed by numerical experiments.
Quantum probability measures and tomographic probability densities
Amosov, GG; Man'ko, [No Value
2004-01-01
Using a simple relation of the Dirac delta-function to generalized the theta-function, the relationship between the tomographic probability approach and the quantum probability measure approach with the description of quantum states is discussed. The quantum state tomogram expressed in terms of the
Salama, Paul
2008-02-01
Multi-photon microscopy has provided biologists with unprecedented opportunities for high resolution imaging deep into tissues. Unfortunately deep tissue multi-photon microscopy images are in general noisy since they are acquired at low photon counts. To aid in the analysis and segmentation of such images it is sometimes necessary to initially enhance the acquired images. One way to enhance an image is to find the maximum a posteriori (MAP) estimate of each pixel comprising an image, which is achieved by finding a constrained least squares estimate of the unknown distribution. In arriving at the distribution it is assumed that the noise is Poisson distributed, the true but unknown pixel values assume a probability mass function over a finite set of non-negative values, and since the observed data also assumes finite values because of low photon counts, the sum of the probabilities of the observed pixel values (obtained from the histogram of the acquired pixel values) is less than one. Experimental results demonstrate that it is possible to closely estimate the unknown probability mass function with these assumptions.
Probability distribution for the Gaussian curvature of the zero level surface of a random function
Hannay, J. H.
2018-04-01
A rather natural construction for a smooth random surface in space is the level surface of value zero, or ‘nodal’ surface f(x,y,z) = 0, of a (real) random function f; the interface between positive and negative regions of the function. A physically significant local attribute at a point of a curved surface is its Gaussian curvature (the product of its principal curvatures) because, when integrated over the surface it gives the Euler characteristic. Here the probability distribution for the Gaussian curvature at a random point on the nodal surface f = 0 is calculated for a statistically homogeneous (‘stationary’) and isotropic zero mean Gaussian random function f. Capitalizing on the isotropy, a ‘fixer’ device for axes supplies the probability distribution directly as a multiple integral. Its evaluation yields an explicit algebraic function with a simple average. Indeed, this average Gaussian curvature has long been known. For a non-zero level surface instead of the nodal one, the probability distribution is not fully tractable, but is supplied as an integral expression.
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…
A Bernstein-Von Mises Theorem for discrete probability distributions
Boucheron, S.; Gassiat, E.
2008-01-01
We investigate the asymptotic normality of the posterior distribution in the discrete setting, when model dimension increases with sample size. We consider a probability mass function θ0 on ℕ∖{0} and a sequence of truncation levels (kn)n satisfying kn3≤ninf i≤knθ0(i). Let θ̂ denote the maximum likelihood estimate of (θ0(i))i≤kn and let Δn(θ0) denote the kn-dimensional vector which i-th coordinate is defined by $\\sqrt{n}(\\hat{\\theta}_{n}(i)-\\theta_{0}(i))$ for 1≤i≤kn. We check that under mild ...
Ruin Probabilities and Aggregrate Claims Distributions for Shot Noise Cox Processes
DEFF Research Database (Denmark)
Albrecher, H.; Asmussen, Søren
claim size is investigated under these assumptions. For both light-tailed and heavy-tailed claim size distributions, asymptotic estimates for infinite-time and finite-time ruin probabilities are derived. Moreover, we discuss an extension of the model to an adaptive premium rule that is dynamically......We consider a risk process Rt where the claim arrival process is a superposition of a homogeneous Poisson process and a Cox process with a Poisson shot noise intensity process, capturing the effect of sudden increases of the claim intensity due to external events. The distribution of the aggregate...... adjusted according to past claims experience....
Convergence of Transition Probability Matrix in CLVMarkov Models
Permana, D.; Pasaribu, U. S.; Indratno, S. W.; Suprayogi, S.
2018-04-01
A transition probability matrix is an arrangement of transition probability from one states to another in a Markov chain model (MCM). One of interesting study on the MCM is its behavior for a long time in the future. The behavior is derived from one property of transition probabilty matrix for n steps. This term is called the convergence of the n-step transition matrix for n move to infinity. Mathematically, the convergence of the transition probability matrix is finding the limit of the transition matrix which is powered by n where n moves to infinity. The convergence form of the transition probability matrix is very interesting as it will bring the matrix to its stationary form. This form is useful for predicting the probability of transitions between states in the future. The method usually used to find the convergence of transition probability matrix is through the process of limiting the distribution. In this paper, the convergence of the transition probability matrix is searched using a simple concept of linear algebra that is by diagonalizing the matrix.This method has a higher level of complexity because it has to perform the process of diagonalization in its matrix. But this way has the advantage of obtaining a common form of power n of the transition probability matrix. This form is useful to see transition matrix before stationary. For example cases are taken from CLV model using MCM called Model of CLV-Markov. There are several models taken by its transition probability matrix to find its convergence form. The result is that the convergence of the matrix of transition probability through diagonalization has similarity with convergence with commonly used distribution of probability limiting method.
Probability distribution functions for intermittent scrape-off layer plasma fluctuations
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.
Audio feature extraction using probability distribution function
Suhaib, A.; Wan, Khairunizam; Aziz, Azri A.; Hazry, D.; Razlan, Zuradzman M.; Shahriman A., B.
2015-05-01
Voice recognition has been one of the popular applications in robotic field. It is also known to be recently used for biometric and multimedia information retrieval system. This technology is attained from successive research on audio feature extraction analysis. Probability Distribution Function (PDF) is a statistical method which is usually used as one of the processes in complex feature extraction methods such as GMM and PCA. In this paper, a new method for audio feature extraction is proposed which is by using only PDF as a feature extraction method itself for speech analysis purpose. Certain pre-processing techniques are performed in prior to the proposed feature extraction method. Subsequently, the PDF result values for each frame of sampled voice signals obtained from certain numbers of individuals are plotted. From the experimental results obtained, it can be seen visually from the plotted data that each individuals' voice has comparable PDF values and shapes.
Subspace Learning via Local Probability Distribution for Hyperspectral Image Classification
Directory of Open Access Journals (Sweden)
Huiwu Luo
2015-01-01
Full Text Available The computational procedure of hyperspectral image (HSI is extremely complex, not only due to the high dimensional information, but also due to the highly correlated data structure. The need of effective processing and analyzing of HSI has met many difficulties. It has been evidenced that dimensionality reduction has been found to be a powerful tool for high dimensional data analysis. Local Fisher’s liner discriminant analysis (LFDA is an effective method to treat HSI processing. In this paper, a novel approach, called PD-LFDA, is proposed to overcome the weakness of LFDA. PD-LFDA emphasizes the probability distribution (PD in LFDA, where the maximum distance is replaced with local variance for the construction of weight matrix and the class prior probability is applied to compute the affinity matrix. The proposed approach increases the discriminant ability of the transformed features in low dimensional space. Experimental results on Indian Pines 1992 data indicate that the proposed approach significantly outperforms the traditional alternatives.
Classical probabilities for Majorana and Weyl spinors
International Nuclear Information System (INIS)
Wetterich, C.
2011-01-01
Highlights: → Map of classical statistical Ising model to fermionic quantum field theory. → Lattice-regularized real Grassmann functional integral for single Weyl spinor. → Emerging complex structure characteristic for quantum physics. → A classical statistical ensemble describes a quantum theory. - Abstract: We construct a map between the quantum field theory of free Weyl or Majorana fermions and the probability distribution of a classical statistical ensemble for Ising spins or discrete bits. More precisely, a Grassmann functional integral based on a real Grassmann algebra specifies the time evolution of the real wave function q τ (t) for the Ising states τ. The time dependent probability distribution of a generalized Ising model obtains as p τ (t)=q τ 2 (t). The functional integral employs a lattice regularization for single Weyl or Majorana spinors. We further introduce the complex structure characteristic for quantum mechanics. Probability distributions of the Ising model which correspond to one or many propagating fermions are discussed explicitly. Expectation values of observables can be computed equivalently in the classical statistical Ising model or in the quantum field theory for fermions.
PHOTOMETRIC REDSHIFT PROBABILITY DISTRIBUTIONS FOR GALAXIES IN THE SDSS DR8
International Nuclear Information System (INIS)
Sheldon, Erin S.; Cunha, Carlos E.; Mandelbaum, Rachel; Brinkmann, J.; Weaver, Benjamin A.
2012-01-01
We present redshift probability distributions for galaxies in the Sloan Digital Sky Survey (SDSS) Data Release 8 imaging data. We used the nearest-neighbor weighting algorithm to derive the ensemble redshift distribution N(z), and individual redshift probability distributions P(z) for galaxies with r < 21.8 and u < 29.0. As part of this technique, we calculated weights for a set of training galaxies with known redshifts such that their density distribution in five-dimensional color-magnitude space was proportional to that of the photometry-only sample, producing a nearly fair sample in that space. We estimated the ensemble N(z) of the photometric sample by constructing a weighted histogram of the training-set redshifts. We derived P(z)'s for individual objects by using training-set objects from the local color-magnitude space around each photometric object. Using the P(z) for each galaxy can reduce the statistical error in measurements that depend on the redshifts of individual galaxies. The spectroscopic training sample is substantially larger than that used for the DR7 release. The newly added PRIMUS catalog is now the most important training set used in this analysis by a wide margin. We expect the primary sources of error in the N(z) reconstruction to be sample variance and spectroscopic failures: The training sets are drawn from relatively small volumes of space, and some samples have large incompleteness. Using simulations we estimated the uncertainty in N(z) due to sample variance at a given redshift to be ∼10%-15%. The uncertainty on calculations incorporating N(z) or P(z) depends on how they are used; we discuss the case of weak lensing measurements. The P(z) catalog is publicly available from the SDSS Web site.
Freund, John E
1993-01-01
Thorough, lucid coverage of permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, binomial distribution, geometric distribution, standard deviation, law of large numbers, and much more. Exercises with some solutions. Summary. Bibliography. Includes 42 black-and-white illustrations. 1973 edition.
A brief introduction to probability.
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.
Scoring Rules for Subjective Probability Distributions
DEFF Research Database (Denmark)
Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd
The theoretical literature has a rich characterization of scoring rules for eliciting the subjective beliefs that an individual has for continuous events, but under the restrictive assumption of risk neutrality. It is well known that risk aversion can dramatically affect the incentives to correctly...... report the true subjective probability of a binary event, even under Subjective Expected Utility. To address this one can “calibrate” inferences about true subjective probabilities from elicited subjective probabilities over binary events, recognizing the incentives that risk averse agents have...... to distort reports. We characterize the comparable implications of the general case of a risk averse agent when facing a popular scoring rule over continuous events, and find that these concerns do not apply with anything like the same force. For empirically plausible levels of risk aversion, one can...
Directory of Open Access Journals (Sweden)
Brian C. Houle
2010-01-01
Full Text Available Few studies consider obesity inequalities as a distributional property. This study uses relative distribution methods to explore inequalities in body mass index (BMI; kg/m2. Data from 1999–2006 from the National Health and Nutrition Examination Survey were used to compare BMI distributions by gender, Black/White race, and education subgroups in the United States. For men, comparisons between Whites and Blacks show a polarized relative distribution, with more Black men at increased risk of over or underweight. Comparisons by education (overall and within race/ethnic groups effects also show a polarized relative distribution, with more cases of the least educated men at the upper and lower tails of the BMI distribution. For women, Blacks have a greater probability of high BMI values largely due to a right-shifted BMI distribution relative to White women. Women with less education also have a BMI distribution shifted to the right compared to the most educated women.
Decoy State Quantum Key Distribution
Lo, Hoi-Kwong
2005-10-01
Quantum key distribution (QKD) allows two parties to communicate in absolute security based on the fundamental laws of physics. Up till now, it is widely believed that unconditionally secure QKD based on standard Bennett-Brassard (BB84) protocol is limited in both key generation rate and distance because of imperfect devices. Here, we solve these two problems directly by presenting new protocols that are feasible with only current technology. Surprisingly, our new protocols can make fiber-based QKD unconditionally secure at distances over 100km (for some experiments, such as GYS) and increase the key generation rate from O(η2) in prior art to O(η) where η is the overall transmittance. Our method is to develop the decoy state idea (first proposed by W.-Y. Hwang in "Quantum Key Distribution with High Loss: Toward Global Secure Communication", Phys. Rev. Lett. 91, 057901 (2003)) and consider simple extensions of the BB84 protocol. This part of work is published in "Decoy State Quantum Key Distribution", . We present a general theory of the decoy state protocol and propose a decoy method based on only one signal state and two decoy states. We perform optimization on the choice of intensities of the signal state and the two decoy states. Our result shows that a decoy state protocol with only two types of decoy states--a vacuum and a weak decoy state--asymptotically approaches the theoretical limit of the most general type of decoy state protocols (with an infinite number of decoy states). We also present a one-decoy-state protocol as a special case of Vacuum+Weak decoy method. Moreover, we provide estimations on the effects of statistical fluctuations and suggest that, even for long distance (larger than 100km) QKD, our two-decoy-state protocol can be implemented with only a few hours of experimental data. In conclusion, decoy state quantum key distribution is highly practical. This part of work is published in "Practical Decoy State for Quantum Key Distribution
Uncertainty about probability: a decision analysis perspective
International Nuclear Information System (INIS)
Howard, R.A.
1988-01-01
The issue of how to think about uncertainty about probability is framed and analyzed from the viewpoint of a decision analyst. The failure of nuclear power plants is used as an example. The key idea is to think of probability as describing a state of information on an uncertain event, and to pose the issue of uncertainty in this quantity as uncertainty about a number that would be definitive: it has the property that you would assign it as the probability if you knew it. Logical consistency requires that the probability to assign to a single occurrence in the absence of further information be the mean of the distribution of this definitive number, not the medium as is sometimes suggested. Any decision that must be made without the benefit of further information must also be made using the mean of the definitive number's distribution. With this formulation, they find further that the probability of r occurrences in n exchangeable trials will depend on the first n moments of the definitive number's distribution. In making decisions, the expected value of clairvoyance on the occurrence of the event must be at least as great as that on the definitive number. If one of the events in question occurs, then the increase in probability of another such event is readily computed. This means, in terms of coin tossing, that unless one is absolutely sure of the fairness of a coin, seeing a head must increase the probability of heads, in distinction to usual thought. A numerical example for nuclear power shows that the failure of one plant of a group with a low probability of failure can significantly increase the probability that must be assigned to failure of a second plant in the group
DEFF Research Database (Denmark)
Asmussen, Søren; Albrecher, Hansjörg
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities......, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially...... updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber–Shiu functions and dependence....
Oil spill contamination probability in the southeastern Levantine basin.
Goldman, Ron; Biton, Eli; Brokovich, Eran; Kark, Salit; Levin, Noam
2015-02-15
Recent gas discoveries in the eastern Mediterranean Sea led to multiple operations with substantial economic interest, and with them there is a risk of oil spills and their potential environmental impacts. To examine the potential spatial distribution of this threat, we created seasonal maps of the probability of oil spill pollution reaching an area in the Israeli coastal and exclusive economic zones, given knowledge of its initial sources. We performed simulations of virtual oil spills using realistic atmospheric and oceanic conditions. The resulting maps show dominance of the alongshore northerly current, which causes the high probability areas to be stretched parallel to the coast, increasing contamination probability downstream of source points. The seasonal westerly wind forcing determines how wide the high probability areas are, and may also restrict these to a small coastal region near source points. Seasonal variability in probability distribution, oil state, and pollution time is also discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.
Contributions to quantum probability
International Nuclear Information System (INIS)
Fritz, Tobias
2010-01-01
Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a finite set can occur as the outcome
Error Distributions on Large Entangled States with Non-Markovian Dynamics
DEFF Research Database (Denmark)
McCutcheon, Dara; Lindner, Netanel H.; Rudolph, Terry
2014-01-01
We investigate the distribution of errors on a computationally useful entangled state generated via the repeated emission from an emitter undergoing strongly non-Markovian evolution. For emitter-environment coupling of pure-dephasing form, we show that the probability that a particular patten...... of errors occurs has a bound of Markovian form, and thus, accuracy threshold theorems based on Markovian models should be just as effective. Beyond the pure-dephasing assumption, though complicated error structures can arise, they can still be qualitatively bounded by a Markovian error model....
Estimation and asymptotic theory for transition probabilities in Markov Renewal Multi–state models
Spitoni, C.; Verduijn, M.; Putter, H.
2012-01-01
In this paper we discuss estimation of transition probabilities for semi–Markov multi–state models. Non–parametric and semi–parametric estimators of the transition probabilities for a large class of models (forward going models) are proposed. Large sample theory is derived using the functional
Impact of spike train autostructure on probability distribution of joint spike events.
Pipa, Gordon; Grün, Sonja; van Vreeswijk, Carl
2013-05-01
The discussion whether temporally coordinated spiking activity really exists and whether it is relevant has been heated over the past few years. To investigate this issue, several approaches have been taken to determine whether synchronized events occur significantly above chance, that is, whether they occur more often than expected if the neurons fire independently. Most investigations ignore or destroy the autostructure of the spiking activity of individual cells or assume Poissonian spiking as a model. Such methods that ignore the autostructure can significantly bias the coincidence statistics. Here, we study the influence of the autostructure on the probability distribution of coincident spiking events between tuples of mutually independent non-Poisson renewal processes. In particular, we consider two types of renewal processes that were suggested as appropriate models of experimental spike trains: a gamma and a log-normal process. For a gamma process, we characterize the shape of the distribution analytically with the Fano factor (FFc). In addition, we perform Monte Carlo estimations to derive the full shape of the distribution and the probability for false positives if a different process type is assumed as was actually present. We also determine how manipulations of such spike trains, here dithering, used for the generation of surrogate data change the distribution of coincident events and influence the significance estimation. We find, first, that the width of the coincidence count distribution and its FFc depend critically and in a nontrivial way on the detailed properties of the structure of the spike trains as characterized by the coefficient of variation CV. Second, the dependence of the FFc on the CV is complex and mostly nonmonotonic. Third, spike dithering, even if as small as a fraction of the interspike interval, can falsify the inference on coordinated firing.
Capacity analysis in multi-state synaptic models: a retrieval probability perspective.
Huang, Yibi; Amit, Yali
2011-06-01
We define the memory capacity of networks of binary neurons with finite-state synapses in terms of retrieval probabilities of learned patterns under standard asynchronous dynamics with a predetermined threshold. The threshold is set to control the proportion of non-selective neurons that fire. An optimal inhibition level is chosen to stabilize network behavior. For any local learning rule we provide a computationally efficient and highly accurate approximation to the retrieval probability of a pattern as a function of its age. The method is applied to the sequential models (Fusi and Abbott, Nat Neurosci 10:485-493, 2007) and meta-plasticity models (Fusi et al., Neuron 45(4):599-611, 2005; Leibold and Kempter, Cereb Cortex 18:67-77, 2008). We show that as the number of synaptic states increases, the capacity, as defined here, either plateaus or decreases. In the few cases where multi-state models exceed the capacity of binary synapse models the improvement is small.
Probability Distribution and Projected Trends of Daily Precipitation in China
Institute of Scientific and Technical Information of China (English)
CAO; Li-Ge; ZHONG; Jun; SU; Bu-Da; ZHAI; Jian-Qing; Macro; GEMMER
2013-01-01
Based on observed daily precipitation data of 540 stations and 3,839 gridded data from the high-resolution regional climate model COSMO-Climate Limited-area Modeling(CCLM)for 1961–2000,the simulation ability of CCLM on daily precipitation in China is examined,and the variation of daily precipitation distribution pattern is revealed.By applying the probability distribution and extreme value theory to the projected daily precipitation(2011–2050)under SRES A1B scenario with CCLM,trends of daily precipitation series and daily precipitation extremes are analyzed.Results show that except for the western Qinghai-Tibetan Plateau and South China,distribution patterns of the kurtosis and skewness calculated from the simulated and observed series are consistent with each other;their spatial correlation coefcients are above 0.75.The CCLM can well capture the distribution characteristics of daily precipitation over China.It is projected that in some parts of the Jianghuai region,central-eastern Northeast China and Inner Mongolia,the kurtosis and skewness will increase significantly,and precipitation extremes will increase during 2011–2050.The projected increase of maximum daily rainfall and longest non-precipitation period during flood season in the aforementioned regions,also show increasing trends of droughts and floods in the next 40 years.
Comment on "Measurements without probabilities in the final state proposal"
Cohen, Eliahu; Nowakowski, Marcin
2018-04-01
The final state proposal [G. T. Horowitz and J. M. Maldacena, J. High Energy Phys. 04 (2004) 008, 10.1088/1126-6708/2004/04/008] is an attempt to relax the apparent tension between string theory and semiclassical arguments regarding the unitarity of black hole evaporation. Authors Bousso and Stanford [Phys. Rev. D 89, 044038 (2014), 10.1103/PhysRevD.89.044038] analyze thought experiments where an infalling observer first verifies the entanglement between early and late Hawking modes and then verifies the interior purification of the same Hawking particle. They claim that "probabilities for outcomes of these measurements are not defined" and therefore suggest that "the final state proposal does not offer a consistent alternative to the firewall hypothesis." We show, in contrast, that one may define all the relevant probabilities based on the so-called ABL rule [Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz, Phys. Rev. 134, B1410 (1964), 10.1103/PhysRev.134.B1410], which is better suited for this task than the decoherence functional. We thus assert that the analysis of Bousso and Stanford cannot yet rule out the final state proposal.
Dopkins, Stephen; Varner, Kaitlin; Hoyer, Darin
2017-10-01
In word recognition semantic priming of test words increased the false-alarm rate and the mean of confidence ratings to lures. Such priming also increased the standard deviation of confidence ratings to lures and the slope of the z-ROC function, suggesting that the priming increased the standard deviation of the lure evidence distribution. The Unequal Variance Signal Detection (UVSD) model interpreted the priming as increasing the standard deviation of the lure evidence distribution. Without additional parameters the Dual Process Signal Detection (DPSD) model could only accommodate the results by fitting the data for related and unrelated primes separately, interpreting the priming, implausibly, as decreasing the probability of target recollection (DPSD). With an additional parameter, for the probability of false (lure) recollection the model could fit the data for related and unrelated primes together, interpreting the priming as increasing the probability of false recollection. These results suggest that DPSD estimates of target recollection probability will decrease with increases in the lure confidence/evidence standard deviation unless a parameter is included for false recollection. Unfortunately the size of a given lure confidence/evidence standard deviation relative to other possible lure confidence/evidence standard deviations is often unspecified by context. Hence the model often has no way of estimating false recollection probability and thereby correcting its estimates of target recollection probability.
On the calculation of steady-state loss probabilities in the GI/G/2/0 queue
Directory of Open Access Journals (Sweden)
Igor N. Kovalenko
1994-01-01
Full Text Available This paper considers methods for calculating the steady-state loss probability in the GI/G/2/0 queue. A previous study analyzed this queue in discrete time and this led to an efficient, numerical approximation scheme for continuous-time systems. The primary aim of the present work is to provide an alternative approach by analyzing the GI/ME/2/0 queue; i.e., assuming that the service time can be represented by a matrix-exponential distribution. An efficient computational scheme based on this method is developed and some numerical examples are studied. Some comparisons are made with the discrete-time approach, and the two methods are seen to be complementary.
Quantum key distribution using three basis states
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 54; Issue 5. Quantum key distribution using three ... This note presents a method of public key distribution using quantum communication of photons that simultaneously provides a high probability that the bits have not been tampered. It is a variant of the quantum ...
Quantum key distribution with a single photon from a squeezed coherent state
International Nuclear Information System (INIS)
Matsuoka, Masahiro; Hirano, Takuya
2003-01-01
Squeezing of the coherent state by optical parametric amplifier is shown to efficiently produce single-photon states with reduced multiphoton probabilities compared with the weak coherent light. It can be a better source for a longer-distance quantum key distribution and also for other quantum optical experiments. The necessary condition for a secure quantum key distribution given by Brassard et al. is analyzed as functions of the coherent-state amplitude and squeeze parameter. Similarly, the rate of the gained secure bits G after error correction and privacy amplification given by Luetkenhaus is calculated. Compared with the weak coherent light, it is found that G is about ten times larger and its high level continues on about two times longer distance. By improvement of the detector efficiency it is shown that the distance extends further. Measurement of the intensity correlation function and the relation to photon antibunching are discussed for the experimental verification of the single-photon generation
Scarred resonances and steady probability distribution in a chaotic microcavity
International Nuclear Information System (INIS)
Lee, Soo-Young; Rim, Sunghwan; Kim, Chil-Min; Ryu, Jung-Wan; Kwon, Tae-Yoon
2005-01-01
We investigate scarred resonances of a stadium-shaped chaotic microcavity. It is shown that two components with different chirality of the scarring pattern are slightly rotated in opposite ways from the underlying unstable periodic orbit, when the incident angles of the scarring pattern are close to the critical angle for total internal reflection. In addition, the correspondence of emission pattern with the scarring pattern disappears when the incident angles are much larger than the critical angle. The steady probability distribution gives a consistent explanation about these interesting phenomena and makes it possible to expect the emission pattern in the latter case
Hameren, Andreas Ferdinand Willem van
2001-01-01
Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses point sets that are distributed more uniformly than sets of
The Probability Distribution for a Biased Spinner
Foster, Colin
2012-01-01
This article advocates biased spinners as an engaging context for statistics students. Calculating the probability of a biased spinner landing on a particular side makes valuable connections between probability and other areas of mathematics. (Contains 2 figures and 1 table.)
Yang, Dixiong; Liu, Zhenjun; Zhou, Jilei
2014-04-01
Chaos optimization algorithms (COAs) usually utilize the chaotic map like Logistic map to generate the pseudo-random numbers mapped as the design variables for global optimization. Many existing researches indicated that COA can more easily escape from the local minima than classical stochastic optimization algorithms. This paper reveals the inherent mechanism of high efficiency and superior performance of COA, from a new perspective of both the probability distribution property and search speed of chaotic sequences generated by different chaotic maps. The statistical property and search speed of chaotic sequences are represented by the probability density function (PDF) and the Lyapunov exponent, respectively. Meanwhile, the computational performances of hybrid chaos-BFGS algorithms based on eight one-dimensional chaotic maps with different PDF and Lyapunov exponents are compared, in which BFGS is a quasi-Newton method for local optimization. Moreover, several multimodal benchmark examples illustrate that, the probability distribution property and search speed of chaotic sequences from different chaotic maps significantly affect the global searching capability and optimization efficiency of COA. To achieve the high efficiency of COA, it is recommended to adopt the appropriate chaotic map generating the desired chaotic sequences with uniform or nearly uniform probability distribution and large Lyapunov exponent.
Hamiltonian theories quantization based on a probability operator
International Nuclear Information System (INIS)
Entral'go, E.E.
1986-01-01
The quantization method with a linear reflection of classical coordinate-momentum-time functions Λ(q,p,t) at quantum operators in a space of quantum states ψ, is considered. The probability operator satisfies a system of equations representing the principles of dynamical and canonical correspondences between the classical and quantum theories. The quantization based on a probability operator leads to a quantum theory with a nonnegative joint coordinate-momentum distribution function for any state ψ. The main consequences of quantum mechanics with a probability operator are discussed in comparison with the generally accepted quantum and classical theories. It is shown that a probability operator leads to an appearance of some new notions called ''subquantum'' ones. Hence the quantum theory with a probability operator does not pretend to any complete description of physical reality in terms of classical variables and by this reason contains no problems like Einstein-Podolsky-Rosen paradox. The results of some concrete problems are given: a free particle, a harmonic oscillator, an electron in the Coulomb field. These results give hope on the possibility of an experimental verification of the quantization based on a probability operator
Study of the SEMG probability distribution of the paretic tibialis anterior muscle
Energy Technology Data Exchange (ETDEWEB)
Cherniz, AnalIa S; Bonell, Claudia E; Tabernig, Carolina B [Laboratorio de Ingenieria de Rehabilitacion e Investigaciones Neuromusculares y Sensoriales, Facultad de Ingenieria, UNER, Oro Verde (Argentina)
2007-11-15
The surface electromyographic signal is a stochastic signal that has been modeled as a Gaussian process, with a zero mean. It has been experimentally proved that this probability distribution can be adjusted with less error to a Laplacian type distribution. The selection of estimators for the detection of changes in the amplitude of the muscular signal depends, among other things, on the type of distribution. In the case of subjects with lesions to the superior motor neuron, the lack of central control affects the muscular tone, the force and the patterns of muscular movement involved in activities such as the gait cycle. In this work, the distribution types of the SEMG signal amplitudes of the tibialis anterior muscle are evaluated during gait, both in two healthy subjects and in two hemiparetic ones in order to select the estimators that best characterize them. It was observed that the Laplacian distribution function would be the one that best adjusts to the experimental data in the studied subjects, although this largely depends on the subject and on the data segment analyzed.
Study of the SEMG probability distribution of the paretic tibialis anterior muscle
International Nuclear Information System (INIS)
Cherniz, AnalIa S; Bonell, Claudia E; Tabernig, Carolina B
2007-01-01
The surface electromyographic signal is a stochastic signal that has been modeled as a Gaussian process, with a zero mean. It has been experimentally proved that this probability distribution can be adjusted with less error to a Laplacian type distribution. The selection of estimators for the detection of changes in the amplitude of the muscular signal depends, among other things, on the type of distribution. In the case of subjects with lesions to the superior motor neuron, the lack of central control affects the muscular tone, the force and the patterns of muscular movement involved in activities such as the gait cycle. In this work, the distribution types of the SEMG signal amplitudes of the tibialis anterior muscle are evaluated during gait, both in two healthy subjects and in two hemiparetic ones in order to select the estimators that best characterize them. It was observed that the Laplacian distribution function would be the one that best adjusts to the experimental data in the studied subjects, although this largely depends on the subject and on the data segment analyzed
Spectral shaping of a randomized PWM DC-DC converter using maximum entropy probability distributions
CSIR Research Space (South Africa)
Dove, Albert
2017-01-01
Full Text Available maintaining constraints in a DC-DC converter is investigated. A probability distribution whose aim is to ensure maximal harmonic spreading and yet mainaint constraints is presented. The PDFs are determined from a direct application of the method of Maximum...
Contributions to quantum probability
Energy Technology Data Exchange (ETDEWEB)
Fritz, Tobias
2010-06-25
Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a
Institute of Scientific and Technical Information of China (English)
HAN Li-Bo; GONG Xiao-Long; CAO Li; WU Da-Jin
2007-01-01
An approximate Fokker-P1anck equation for the logistic growth model which is driven by coloured correlated noises is derived by applying the Novikov theorem and the Fox approximation. The steady-state probability distribution (SPD) and the mean of the tumour cell number are analysed. It is found that the SPD is the single extremum configuration when the degree of correlation between the multiplicative and additive noises, λ, is in -1＜λ ≤ 0 and can be the double extrema in 0＜λ＜1. A configuration transition occurs because of the variation of noise parameters. A minimum appears in the curve of the mean of the steady-state tumour cell number, 〈x〉, versus λ. The position and the value of the minimum are controlled by the noise-correlated times.
Performance Probability Distributions for Sediment Control Best Management Practices
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
Probability evolution method for exit location distribution
Zhu, Jinjie; Chen, Zhen; Liu, Xianbin
2018-03-01
The exit problem in the framework of the large deviation theory has been a hot topic in the past few decades. The most probable escape path in the weak-noise limit has been clarified by the Freidlin-Wentzell action functional. However, noise in real physical systems cannot be arbitrarily small while noise with finite strength may induce nontrivial phenomena, such as noise-induced shift and noise-induced saddle-point avoidance. Traditional Monte Carlo simulation of noise-induced escape will take exponentially large time as noise approaches zero. The majority of the time is wasted on the uninteresting wandering around the attractors. In this paper, a new method is proposed to decrease the escape simulation time by an exponentially large factor by introducing a series of interfaces and by applying the reinjection on them. This method can be used to calculate the exit location distribution. It is verified by examining two classical examples and is compared with theoretical predictions. The results show that the method performs well for weak noise while may induce certain deviations for large noise. Finally, some possible ways to improve our method are discussed.
International Nuclear Information System (INIS)
Tierney, M.S.
1990-12-01
A five-step procedure was used in the 1990 performance simulations to construct probability distributions of the uncertain variables appearing in the mathematical models used to simulate the Waste Isolation Pilot Plant's (WIPP's) performance. This procedure provides a consistent approach to the construction of probability distributions in cases where empirical data concerning a variable are sparse or absent and minimizes the amount of spurious information that is often introduced into a distribution by assumptions of nonspecialists. The procedure gives first priority to the professional judgment of subject-matter experts and emphasizes the use of site-specific empirical data for the construction of the probability distributions when such data are available. In the absence of sufficient empirical data, the procedure employs the Maximum Entropy Formalism and the subject-matter experts' subjective estimates of the parameters of the distribution to construct a distribution that can be used in a performance simulation. (author)
Energy Technology Data Exchange (ETDEWEB)
Tierney, M S
1990-12-15
A five-step procedure was used in the 1990 performance simulations to construct probability distributions of the uncertain variables appearing in the mathematical models used to simulate the Waste Isolation Pilot Plant's (WIPP's) performance. This procedure provides a consistent approach to the construction of probability distributions in cases where empirical data concerning a variable are sparse or absent and minimizes the amount of spurious information that is often introduced into a distribution by assumptions of nonspecialists. The procedure gives first priority to the professional judgment of subject-matter experts and emphasizes the use of site-specific empirical data for the construction of the probability distributions when such data are available. In the absence of sufficient empirical data, the procedure employs the Maximum Entropy Formalism and the subject-matter experts' subjective estimates of the parameters of the distribution to construct a distribution that can be used in a performance simulation. (author)
Directory of Open Access Journals (Sweden)
Fang Zheng
2013-04-01
Full Text Available Analysis of knee joint vibration or vibroarthrographic (VAG signals using signal processing and machine learning algorithms possesses high potential for the noninvasive detection of articular cartilage degeneration, which may reduce unnecessary exploratory surgery. Feature representation of knee joint VAG signals helps characterize the pathological condition of degenerative articular cartilages in the knee. This paper used the kernel-based probability density estimation method to model the distributions of the VAG signals recorded from healthy subjects and patients with knee joint disorders. The estimated densities of the VAG signals showed explicit distributions of the normal and abnormal signal groups, along with the corresponding contours in the bivariate feature space. The signal classifications were performed by using the Fisher’s linear discriminant analysis, support vector machine with polynomial kernels, and the maximal posterior probability decision criterion. The maximal posterior probability decision criterion was able to provide the total classification accuracy of 86.67% and the area (Az of 0.9096 under the receiver operating characteristics curve, which were superior to the results obtained by either the Fisher’s linear discriminant analysis (accuracy: 81.33%, Az: 0.8564 or the support vector machine with polynomial kernels (accuracy: 81.33%, Az: 0.8533. Such results demonstrated the merits of the bivariate feature distribution estimation and the superiority of the maximal posterior probability decision criterion for analysis of knee joint VAG signals.
International Nuclear Information System (INIS)
Monthus, Cécile
2011-01-01
Filyokov and Karpov (1967 Inzh.-Fiz. Zh. 13 624) have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states: the principle is to maximize the Shannon entropy associated with the probability distribution of dynamical trajectories in the presence of constraints, including the macroscopic current of interest, via the method of Lagrange multipliers. This maximization leads directly to the generalized Gibbs distribution for the probability distribution of dynamical trajectories, and to some fluctuation relation of the integrated current. The simplest stochastic dynamics where these ideas can be applied are discrete-time Markov chains, defined by transition probabilities W i→j between configurations i and j: instead of choosing the dynamical rules W i→j a priori, one determines the transition probabilities and the associate stationary state that maximize the entropy of dynamical trajectories with the other physical constraints that one wishes to impose. We give a self-contained and unified presentation of this type of approach, both for discrete-time Markov chains and for continuous-time master equations. The obtained results are in full agreement with the Bayesian approach introduced by Evans (2004 Phys. Rev. Lett. 92 150601) under the name 'Non-equilibrium Counterpart to detailed balance', and with the 'invariant quantities' derived by Baule and Evans (2008 Phys. Rev. Lett. 101 240601), but provide a slightly different perspective via the formulation in terms of an eigenvalue problem
International Nuclear Information System (INIS)
Zhuang Jiancang; Ogata, Yosihiko
2006-01-01
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 et al., Geophys. J. Int. 127, 17 (1996)] by using the conventional single-linked cluster declustering method
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.
Steeneveld, W.; Gaag, van der L.C.; Barkema, H.W.; Hogeveen, H.
2009-01-01
Clinical mastitis (CM) can be caused by a wide variety of pathogens and farmers must start treatment before the actual causal pathogen is known. By providing a probability distribution for the causal pathogen, naive Bayesian networks (NBN) can serve as a management tool for farmers to decide which
A methodology for more efficient tail area sampling with discrete probability distribution
International Nuclear Information System (INIS)
Park, Sang Ryeol; Lee, Byung Ho; Kim, Tae Woon
1988-01-01
Monte Carlo Method is commonly used to observe the overall distribution and to determine the lower or upper bound value in statistical approach when direct analytical calculation is unavailable. However, this method would not be efficient if the tail area of a distribution is concerned. A new method entitled 'Two Step Tail Area Sampling' is developed, which uses the assumption of discrete probability distribution and samples only the tail area without distorting the overall distribution. This method uses two step sampling procedure. First, sampling at points separated by large intervals is done and second, sampling at points separated by small intervals is done with some check points determined at first step sampling. Comparison with Monte Carlo Method shows that the results obtained from the new method converge to analytic value faster than Monte Carlo Method if the numbers of calculation of both methods are the same. This new method is applied to DNBR (Departure from Nucleate Boiling Ratio) prediction problem in design of the pressurized light water nuclear reactor
The probability distribution model of air pollution index and its dominants in Kuala Lumpur
AL-Dhurafi, Nasr Ahmed; Razali, Ahmad Mahir; Masseran, Nurulkamal; Zamzuri, Zamira Hasanah
2016-11-01
This paper focuses on the statistical modeling for the distributions of air pollution index (API) and its sub-indexes data observed at Kuala Lumpur in Malaysia. Five pollutants or sub-indexes are measured including, carbon monoxide (CO); sulphur dioxide (SO2); nitrogen dioxide (NO2), and; particulate matter (PM10). Four probability distributions are considered, namely log-normal, exponential, Gamma and Weibull in search for the best fit distribution to the Malaysian air pollutants data. In order to determine the best distribution for describing the air pollutants data, five goodness-of-fit criteria's are applied. This will help in minimizing the uncertainty in pollution resource estimates and improving the assessment phase of planning. The conflict in criterion results for selecting the best distribution was overcome by using the weight of ranks method. We found that the Gamma distribution is the best distribution for the majority of air pollutants data in Kuala Lumpur.
Foundations of quantization for probability distributions
Graf, Siegfried
2000-01-01
Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.
Directory of Open Access Journals (Sweden)
Tong Yifei
2014-01-01
Full Text Available Crane is a mechanical device, used widely to move materials in modern production. It is reported that the energy consumptions of China are at least 5–8 times of other developing countries. Thus, energy consumption becomes an unavoidable topic. There are several reasons influencing the energy loss, and the camber of the girder is the one not to be neglected. In this paper, the problem of the deflections induced by the moving payload in the girder of overhead travelling crane is examined. The evaluation of a camber giving a counterdeflection of the girder is proposed in order to get minimum energy consumptions for trolley to move along a nonstraight support. To this aim, probabilistic payload distributions are considered instead of fixed or rated loads involved in other researches. Taking 50/10 t bridge crane as a research object, the probability loads are determined by analysis of load distribution density functions. According to load distribution, camber design under different probability loads is discussed in detail as well as energy consumptions distribution. The research results provide the design reference of reasonable camber to obtain the least energy consumption for climbing corresponding to different P0; thus energy-saving design can be achieved.
State-to-state and state-to-all-states reactive scattering angular distributions: F+H 2→HF+H
International Nuclear Information System (INIS)
Emmons, R.W.; Suck, S.H.
1983-01-01
How each state-to-state reactive transition determines nonundulatory ''state-to-all-states'' angular distribution has not yet been investigated. Here we present a complete exposure of state-to-state distorted-wave Born-approximation angular distributions in order to examine how the nonoscillatory and backward-peaked state-to-all-states reactive scattering angular distribution occurs
Stationary Distribution and Thermodynamic Relation in Nonequilibrium Steady States
Komatsu, Teruhisa S.; Nakagawa, Naoko; Sasa, Shin-ichi; Tasaki, Hal; Ito, Nobuyasu
2010-01-01
We describe our recent attempts toward statistical mechanics and thermodynamics for nonequilibrium steady states (NESS) realized, e.g., in a heat conducting system. Our first result is a simple expression of the probability distribution (of microscopic states) of a NESS. Our second result is a natural extension of the thermodynamic Clausius relation and a definition of an accompanying entropy in NESS. This entropy coincides with the normalization constant appearing in the above mentioned microscopic expression of NESS, and has an expression similar to the Shannon entropy (with a further symmetrization). The NESS entropy proposed here is a clearly defined measurable quantity even in a system with a large degrees of freedom. We numerically measure the NESS entropy in hardsphere fluid systems with a heat current, by observing energy exchange between the system and the heat baths when the temperatures of the baths are changed according to specified protocols.
Tumour control probability (TCP) for non-uniform activity distribution in radionuclide therapy
International Nuclear Information System (INIS)
Uusijaervi, Helena; Bernhardt, Peter; Forssell-Aronsson, Eva
2008-01-01
Non-uniform radionuclide distribution in tumours will lead to a non-uniform absorbed dose. The aim of this study was to investigate how tumour control probability (TCP) depends on the radionuclide distribution in the tumour, both macroscopically and at the subcellular level. The absorbed dose in the cell nuclei of tumours was calculated for 90 Y, 177 Lu, 103m Rh and 211 At. The radionuclides were uniformly distributed within the subcellular compartment and they were uniformly, normally or log-normally distributed among the cells in the tumour. When all cells contain the same amount of activity, the cumulated activities required for TCP = 0.99 (A-tilde TCP=0.99 ) were 1.5-2 and 2-3 times higher when the activity was distributed on the cell membrane compared to in the cell nucleus for 103m Rh and 211 At, respectively. TCP for 90 Y was not affected by different radionuclide distributions, whereas for 177 Lu, it was slightly affected when the radionuclide was in the nucleus. TCP for 103m Rh and 211 At were affected by different radionuclide distributions to a great extent when the radionuclides were in the cell nucleus and to lesser extents when the radionuclides were distributed on the cell membrane or in the cytoplasm. When the activity was distributed in the nucleus, A-tilde TCP=0.99 increased when the activity distribution became more heterogeneous for 103m Rh and 211 At, and the increase was large when the activity was normally distributed compared to log-normally distributed. When the activity was distributed on the cell membrane, A-tilde TCP=0.99 was not affected for 103m Rh and 211 At when the activity distribution became more heterogeneous. A-tilde TCP=0.99 for 90 Y and 177 Lu were not affected by different activity distributions, neither macroscopic nor subcellular
Bayesian probability theory applications in the physical sciences
Linden, Wolfgang von der; Toussaint, Udo von
2014-01-01
From the basics to the forefront of modern research, this book presents all aspects of probability theory, statistics and data analysis from a Bayesian perspective for physicists and engineers. The book presents the roots, applications and numerical implementation of probability theory, and covers advanced topics such as maximum entropy distributions, stochastic processes, parameter estimation, model selection, hypothesis testing and experimental design. In addition, it explores state-of-the art numerical techniques required to solve demanding real-world problems. The book is ideal for students and researchers in physical sciences and engineering.
Random phenomena fundamentals of probability and statistics for engineers
Ogunnaike, Babatunde A
2009-01-01
PreludeApproach PhilosophyFour Basic PrinciplesI FoundationsTwo Motivating ExamplesYield Improvement in a Chemical ProcessQuality Assurance in a Glass Sheet Manufacturing ProcessOutline of a Systematic ApproachRandom Phenomena, Variability, and UncertaintyTwo Extreme Idealizations of Natural PhenomenaRandom Mass PhenomenaIntroducing ProbabilityThe Probabilistic FrameworkII ProbabilityFundamentals of Probability TheoryBuilding BlocksOperationsProbabilityConditional ProbabilityIndependenceRandom Variables and DistributionsDistributionsMathematical ExpectationCharacterizing DistributionsSpecial Derived Probability FunctionsMultidimensional Random VariablesDistributions of Several Random VariablesDistributional Characteristics of Jointly Distributed Random VariablesRandom Variable TransformationsSingle Variable TransformationsBivariate TransformationsGeneral Multivariate TransformationsApplication Case Studies I: ProbabilityMendel and HeredityWorld War II Warship Tactical Response Under AttackIII DistributionsIde...
Various models for pion probability distributions from heavy-ion collisions
International Nuclear Information System (INIS)
Mekjian, A.Z.; Mekjian, A.Z.; Schlei, B.R.; Strottman, D.; Schlei, B.R.
1998-01-01
Various models for pion multiplicity distributions produced in relativistic heavy ion collisions are discussed. The models include a relativistic hydrodynamic model, a thermodynamic description, an emitting source pion laser model, and a description which generates a negative binomial description. The approach developed can be used to discuss other cases which will be mentioned. The pion probability distributions for these various cases are compared. Comparison of the pion laser model and Bose-Einstein condensation in a laser trap and with the thermal model are made. The thermal model and hydrodynamic model are also used to illustrate why the number of pions never diverges and why the Bose-Einstein correction effects are relatively small. The pion emission strength η of a Poisson emitter and a critical density η c are connected in a thermal model by η/n c =e -m/T <1, and this fact reduces any Bose-Einstein correction effects in the number and number fluctuation of pions. Fluctuations can be much larger than Poisson in the pion laser model and for a negative binomial description. The clan representation of the negative binomial distribution due to Van Hove and Giovannini is discussed using the present description. Applications to CERN/NA44 and CERN/NA49 data are discussed in terms of the relativistic hydrodynamic model. copyright 1998 The American Physical Society
International Nuclear Information System (INIS)
Cheng, Tianjin; Pandey, Mahesh D.; Weide, J.A.M. van der
2012-01-01
The stochastic gamma process has been widely used to model uncertain degradation in engineering systems and structures. The optimization of the condition-based maintenance (CBM) policy is typically based on the minimization of the asymptotic cost rate. In the financial planning of a maintenance program, however, a more accurate prediction interval for the cost is needed for prudent decision making. The prediction interval cannot be estimated unless the probability distribution of cost is known. In this context, the asymptotic cost rate has a limited utility. This paper presents the derivation of the probability distribution of maintenance cost, when the system degradation is modelled as a stochastic gamma process. A renewal equation is formulated to derive the characteristic function, then the discrete Fourier transform of the characteristic function leads to the complete probability distribution of cost in a finite time setting. The proposed approach is useful for a precise estimation of prediction limits and optimization of the maintenance cost.
Nuijten, M J
1999-07-01
The aim of the present study is to describe a refinement of a previously presented method, based on the concept of point sensitivity, to deal with uncertainty in economic studies. The original method was refined by the incorporation of probability distributions which allow a more accurate assessment of the level of uncertainty in the model. In addition, a bootstrap method was used to create a probability distribution for a fixed input variable based on a limited number of data points. The original method was limited in that the sensitivity measurement was based on a uniform distribution of the variables and that the overall sensitivity measure was based on a subjectively chosen range which excludes the impact of values outside the range on the overall sensitivity. The concepts of the refined method were illustrated using a Markov model of depression. The application of the refined method substantially changed the ranking of the most sensitive variables compared with the original method. The response rate became the most sensitive variable instead of the 'per diem' for hospitalisation. The refinement of the original method yields sensitivity outcomes, which greater reflect the real uncertainty in economic studies.
Exploring non-signalling polytopes with negative probability
International Nuclear Information System (INIS)
Oas, G; Barros, J Acacio de; Carvalhaes, C
2014-01-01
Bipartite and tripartite EPR–Bell type systems are examined via joint quasi-probability distributions where probabilities are permitted to be negative. It is shown that such distributions exist only when the no-signalling condition is satisfied. A characteristic measure, the probability mass, is introduced and, via its minimization, limits the number of quasi-distributions describing a given marginal probability distribution. The minimized probability mass is shown to be an alternative way to characterize non-local systems. Non-signalling polytopes for two to eight settings in the bipartite scenario are examined and compared to prior work. Examining perfect cloning of non-local systems within the tripartite scenario suggests defining two categories of signalling. It is seen that many properties of non-local systems can be efficiently described by quasi-probability theory. (paper)
Distributed state estimation for multi-agent based active distribution networks
Nguyen, H.P.; Kling, W.L.
2010-01-01
Along with the large-scale implementation of distributed generators, the current distribution networks have changed gradually from passive to active operation. State estimation plays a vital role to facilitate this transition. In this paper, a suitable state estimation method for the active network
Conditional probabilities in Ponzano-Regge minisuperspace
International Nuclear Information System (INIS)
Petryk, Roman; Schleich, Kristin
2003-01-01
We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge formulation of gravity in three dimensions. We consider the behavior of conditional probabilities and expectation values for geometrical quantities in this initial state for a simple minisuperspace model consisting of a two-parameter set of anisotropic geometries on a 2-sphere boundary. We find dependence on the cutoff used in the construction of Ponzano-Regge amplitudes for expectation values of edge lengths. However, these expectation values are cutoff independent when computed in certain, but not all, conditional probability distributions. Conditions that yield cutoff independent expectation values are those that constrain the boundary geometry to a finite range of edge lengths. We argue that such conditions have a correspondence to fixing a range of local time, as classically associated with the area of a surface for spatially closed cosmologies. Thus these results may hint at how classical spacetime emerges from quantum amplitudes
International Nuclear Information System (INIS)
Lopez-Martens, A.P.; Doessing, T.; Khoo, T.L.; Korichi, A.; Hannachi, F.; Calderin, I.J.; Lauritsen, T.; Ahmad, I.; Carpenter, M.P.; Fischer, S.M.; Hackman, G.; Janssens, R.V.F.; Nisius, D.; Reiter, P.; Amro, H.; Moore, E.F.
1999-01-01
The strength distribution of the primary γ rays in the decay from superdeformed (SD) states is investigated by applying the maximum likelihood method. For the 194 Hg nucleus, 41 primary transitions are identified above 2600 keV. It is concluded that they represent the strongest 10% of the transitions selected stochastically from a Porter-Thomas distribution. This would support the scenario of a statistical decay of SD states via coupling to a compound state at normal deformation. However, the occurrence of several very strong 'one-step linking' transitions is found to have a very small probability. Based on the absence of strong primary transitions from SD states in adjacent nuclei, the situation in 194 Hg is viewed as a very lucky incidence
Serial Spike Time Correlations Affect Probability Distribution of Joint Spike Events.
Shahi, Mina; van Vreeswijk, Carl; Pipa, Gordon
2016-01-01
Detecting the existence of temporally coordinated spiking activity, and its role in information processing in the cortex, has remained a major challenge for neuroscience research. Different methods and approaches have been suggested to test whether the observed synchronized events are significantly different from those expected by chance. To analyze the simultaneous spike trains for precise spike correlation, these methods typically model the spike trains as a Poisson process implying that the generation of each spike is independent of all the other spikes. However, studies have shown that neural spike trains exhibit dependence among spike sequences, such as the absolute and relative refractory periods which govern the spike probability of the oncoming action potential based on the time of the last spike, or the bursting behavior, which is characterized by short epochs of rapid action potentials, followed by longer episodes of silence. Here we investigate non-renewal processes with the inter-spike interval distribution model that incorporates spike-history dependence of individual neurons. For that, we use the Monte Carlo method to estimate the full shape of the coincidence count distribution and to generate false positives for coincidence detection. The results show that compared to the distributions based on homogeneous Poisson processes, and also non-Poisson processes, the width of the distribution of joint spike events changes. Non-renewal processes can lead to both heavy tailed or narrow coincidence distribution. We conclude that small differences in the exact autostructure of the point process can cause large differences in the width of a coincidence distribution. Therefore, manipulations of the autostructure for the estimation of significance of joint spike events seem to be inadequate.
International Nuclear Information System (INIS)
Alavi, Omid; Mohammadi, Kasra; Mostafaeipour, Ali
2016-01-01
Highlights: • Suitability of different wind speed probability functions is assessed. • 5 stations distributed in east and south-east of Iran are considered as case studies. • Nakagami distribution is tested for first time and compared with 7 other functions. • Due to difference in wind features, best function is not similar for all stations. - Abstract: Precise information of wind speed probability distribution is truly significant for many wind energy applications. The objective of this study is to evaluate the suitability of different probability functions for estimating wind speed distribution at five stations, distributed in the east and southeast of Iran. Nakagami distribution function is utilized for the first time to estimate the distribution of wind speed. The performance of Nakagami function is compared with seven typically used distribution functions. The achieved results reveal that the more effective function is not similar among all stations. Wind speed characteristics, quantity and quality of the recorded wind speed data can be considered as influential parameters on the performance of the distribution functions. Also, the skewness of the recorded wind speed data may have influence on the accuracy of the Nakagami distribution. For Chabahar and Khaf stations the Nakagami distribution shows the highest performance while for Lutak, Rafsanjan and Zabol stations the Gamma, Generalized Extreme Value and Inverse-Gaussian distributions offer the best fits, respectively. Based on the analysis, the Nakagami distribution can generally be considered as an effective distribution since it provides the best fits in 2 stations and ranks 3rd to 5th in the remaining stations; however, due to the close performance of the Nakagami and Weibull distributions and also flexibility of the Weibull function as its widely proven feature, more assessments on the performance of the Nakagami distribution are required.
Failure probability under parameter uncertainty.
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.
Energy Technology Data Exchange (ETDEWEB)
Korhonen, Marko [Department of Mathematics and Statistics, University of Helsinki, FIN-00014 (Finland); Lee, Eunghyun [Centre de Recherches Mathématiques (CRM), Université de Montréal, Quebec H3C 3J7 (Canada)
2014-01-15
We treat the N-particle zero range process whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q-boson model by Sasamoto and Wadati [“Exact results for one-dimensional totally asymmetric diffusion models,” J. Phys. A 31, 6057–6071 (1998)] or the q-totally asymmetric zero range process (TAZRP) by Borodin and Corwin [“Macdonald processes,” Probab. Theory Relat. Fields (to be published)]. We find the explicit formula of the transition probability of the q-TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle's position at time t. To find the probability for the left-most particle's position we find a new identity corresponding to identity for the asymmetric simple exclusion process by Tracy and Widom [“Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys. 279, 815–844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle's position at time t is represented by the contour integral of a determinant.
New method for extracting tumors in PET/CT images based on the probability distribution
International Nuclear Information System (INIS)
Nitta, Shuhei; Hontani, Hidekata; Hukami, Tadanori
2006-01-01
In this report, we propose a method for extracting tumors from PET/CT images by referring to the probability distribution of pixel values in the PET image. In the proposed method, first, the organs that normally take up fluorodeoxyglucose (FDG) (e.g., the liver, kidneys, and brain) are extracted. Then, the tumors are extracted from the images. The distribution of pixel values in PET images differs in each region of the body. Therefore, the threshold for detecting tumors is adaptively determined by referring to the distribution. We applied the proposed method to 37 cases and evaluated its performance. This report also presents the results of experiments comparing the proposed method and another method in which the pixel values are normalized for extracting tumors. (author)
Weak value distributions for spin 1/2
Berry, M. V.; Dennis, M. R.; McRoberts, B.; Shukla, P.
2011-05-01
The simplest weak measurement is of a component of spin 1/2. For this observable, the probability distributions of the real and imaginary parts of the weak value, and their joint probability distribution, are calculated exactly for pre- and postselected states uniformly distributed over the surface of the Poincaré-Bloch sphere. The superweak probability, that the real part of the weak value lies outside the spectral range, is 1/3. This case, with just two eigenvalues, complements our previous calculation (Berry and Shukla 2010 J. Phys. A: Math. Theor. 43 354024) of the universal form of the weak value probability distribution for an operator with many eigenvalues.
Weak value distributions for spin 1/2
International Nuclear Information System (INIS)
Berry, M V; Dennis, M R; McRoberts, B; Shukla, P
2011-01-01
The simplest weak measurement is of a component of spin 1/2. For this observable, the probability distributions of the real and imaginary parts of the weak value, and their joint probability distribution, are calculated exactly for pre- and postselected states uniformly distributed over the surface of the Poincare-Bloch sphere. The superweak probability, that the real part of the weak value lies outside the spectral range, is 1/3. This case, with just two eigenvalues, complements our previous calculation (Berry and Shukla 2010 J. Phys. A: Math. Theor. 43 354024) of the universal form of the weak value probability distribution for an operator with many eigenvalues.
Statistical representation of quantum states
Energy Technology Data Exchange (ETDEWEB)
Montina, A [Dipartimento di Fisica, Universita di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (Italy)
2007-05-15
In the standard interpretation of quantum mechanics, the state is described by an abstract wave function in the representation space. Conversely, in a realistic interpretation, the quantum state is replaced by a probability distribution of physical quantities. Bohm mechanics is a consistent example of realistic theory, where the wave function and the particle positions are classically defined quantities. Recently, we proved that the probability distribution in a realistic theory cannot be a quadratic function of the quantum state, in contrast to the apparently obvious suggestion given by the Born rule for transition probabilities. Here, we provide a simplified version of this proof.
International Nuclear Information System (INIS)
Chen Libing; Jin Ruibo; Lu Hong
2008-01-01
Remote quantum-state discrimination is a critical step for the implementation of quantum communication network and distributed quantum computation. We present a protocol for remotely implementing the unambiguous discrimination between nonorthogonal states using quantum entanglements, local operations, and classical communications. This protocol consists of a remote generalized measurement described by a positive operator valued measurement (POVM). We explicitly construct the required remote POVM. The remote POVM can be realized by performing a nonlocal controlled-rotation operation on two spatially separated qubits, one is an ancillary qubit and the other is the qubit which is encoded by two nonorthogonal states to be distinguished, and a conventional local Von Neumann orthogonal measurement on the ancilla. The particular pair of states that can be remotely and unambiguously distinguished is specified by the state of the ancilla. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subset it can be very close to an optimal value in an ordinary local POVM
Directory of Open Access Journals (Sweden)
S. K. Morley
2007-11-01
Full Text Available We compare the probability distributions of substorm magnetic bay magnitudes from observations and a minimal substorm model. The observed distribution was derived previously and independently using the IL index from the IMAGE magnetometer network. The model distribution is derived from a synthetic AL index time series created using real solar wind data and a minimal substorm model, which was previously shown to reproduce observed substorm waiting times. There are two free parameters in the model which scale the contributions to AL from the directly-driven DP2 electrojet and loading-unloading DP1 electrojet, respectively. In a limited region of the 2-D parameter space of the model, the probability distribution of modelled substorm bay magnitudes is not significantly different to the observed distribution. The ranges of the two parameters giving acceptable (95% confidence level agreement are consistent with expectations using results from other studies. The approximately linear relationship between the two free parameters over these ranges implies that the substorm magnitude simply scales linearly with the solar wind power input at the time of substorm onset.
International Nuclear Information System (INIS)
Fraassen, B.C. van
1979-01-01
The interpretation of probabilities in physical theories are considered, whether quantum or classical. The following points are discussed 1) the functions P(μ, Q) in terms of which states and propositions can be represented, are classical (Kolmogoroff) probabilities, formally speaking, 2) these probabilities are generally interpreted as themselves conditional, and the conditions are mutually incompatible where the observables are maximal and 3) testing of the theory typically takes the form of confronting the expectation values of observable Q calculated with probability measures P(μ, Q) for states μ; hence, of comparing the probabilities P(μ, Q)(E) with the frequencies of occurrence of the corresponding events. It seems that even the interpretation of quantum mechanics, in so far as it concerns what the theory says about the empirical (i.e. actual, observable) phenomena, deals with the confrontation of classical probability measures with observable frequencies. This confrontation is studied. (Auth./C.F.)
Toward a generalized probability theory: conditional probabilities
International Nuclear Information System (INIS)
Cassinelli, G.
1979-01-01
The main mathematical object of interest in the quantum logic approach to the foundations of quantum mechanics is the orthomodular lattice and a set of probability measures, or states, defined by the lattice. This mathematical structure is studied per se, independently from the intuitive or physical motivation of its definition, as a generalized probability theory. It is thought that the building-up of such a probability theory could eventually throw light on the mathematical structure of Hilbert-space quantum mechanics as a particular concrete model of the generalized theory. (Auth.)
On the Meta Distribution of Coverage Probability in Uplink Cellular Networks
Elsawy, Hesham
2017-04-07
This letter studies the meta distribution of coverage probability (CP), within a stochastic geometry framework, for cellular uplink transmission with fractional path-loss inversion power control. Using the widely accepted Poisson point process (PPP) for modeling the spatial locations of base stations (BSs), we obtain the percentiles of users that achieve a target uplink CP over an arbitrary, but fixed, realization of the PPP. To this end, the effect of the users activity factor (p) and the path-loss compensation factor () on the uplink performance are analyzed. The results show that decreasing p and/or increasing reduce the CP variation around the spatially averaged value.
International Nuclear Information System (INIS)
Viana, R.S.; Yoriyaz, H.; Santos, A.
2011-01-01
The Expectation-Maximization (E-M) algorithm is an iterative computational method for maximum likelihood (M-L) estimates, useful in a variety of incomplete-data problems. Due to its stochastic nature, one of the most relevant applications of E-M algorithm is the reconstruction of emission tomography images. In this paper, the statistical formulation of the E-M algorithm was applied to the in vivo spectrographic imaging of stable isotopes called Neutron Stimulated Emission Computed Tomography (NSECT). In the process of E-M algorithm iteration, the conditional probability distribution plays a very important role to achieve high quality image. This present work proposes an alternative methodology for the generation of the conditional probability distribution associated to the E-M reconstruction algorithm, using the Monte Carlo code MCNP5 and with the application of the reciprocity theorem. (author)
Energy Technology Data Exchange (ETDEWEB)
Viana, R.S.; Yoriyaz, H.; Santos, A., E-mail: rodrigossviana@gmail.com, E-mail: hyoriyaz@ipen.br, E-mail: asantos@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2011-07-01
The Expectation-Maximization (E-M) algorithm is an iterative computational method for maximum likelihood (M-L) estimates, useful in a variety of incomplete-data problems. Due to its stochastic nature, one of the most relevant applications of E-M algorithm is the reconstruction of emission tomography images. In this paper, the statistical formulation of the E-M algorithm was applied to the in vivo spectrographic imaging of stable isotopes called Neutron Stimulated Emission Computed Tomography (NSECT). In the process of E-M algorithm iteration, the conditional probability distribution plays a very important role to achieve high quality image. This present work proposes an alternative methodology for the generation of the conditional probability distribution associated to the E-M reconstruction algorithm, using the Monte Carlo code MCNP5 and with the application of the reciprocity theorem. (author)
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.
The probability distribution of extreme precipitation
Korolev, V. Yu.; Gorshenin, A. K.
2017-12-01
On the basis of the negative binomial distribution of the duration of wet periods calculated per day, an asymptotic model is proposed for distributing the maximum daily rainfall volume during the wet period, having the form of a mixture of Frechet distributions and coinciding with the distribution of the positive degree of a random variable having the Fisher-Snedecor distribution. The method of proving the corresponding result is based on limit theorems for extreme order statistics in samples of a random volume with a mixed Poisson distribution. The adequacy of the models proposed and methods of their statistical analysis is demonstrated by the example of estimating the extreme distribution parameters based on real data.
Directory of Open Access Journals (Sweden)
Bogdan Ozga-Zielinski
2016-06-01
New hydrological insights for the region: The results indicated that the 2D normal probability distribution model gives a better probabilistic description of snowmelt floods characterized by the 2-dimensional random variable (Qmax,f, Vf compared to the elliptical Gaussian copula and Archimedean 1-parameter Gumbel–Hougaard copula models, in particular from the view point of probability of exceedance as well as complexity and time of computation. Nevertheless, the copula approach offers a new perspective in estimating the 2D probability distribution for multidimensional random variables. Results showed that the 2D model for snowmelt floods built using the Gumbel–Hougaard copula is much better than the model built using the Gaussian copula.
Directory of Open Access Journals (Sweden)
Alberto Cargnelutti Filho
2004-12-01
Full Text Available O objetivo deste trabalho foi verificar o ajuste das séries de dados de radiação solar global média decendial, de 22 municípios do Estado do Rio Grande do Sul, às funções de distribuições de probabilidade normal, log-normal, gama, gumbel e weibull. Aplicou-se o teste de aderência de Kolmogorov-Smirnov, nas 792 séries de dados (22 municípios x 36 decêndios de radiação solar global média decendial, para verificar o ajuste dos dados às distribuições normal, log-normal, gama, gumbel e weibull, totalizando 3.960 testes. Os dados decendiais de radiação solar global média se ajustam às funções de distribuições de probabilidade normal, log-normal, gama, gumbel e weibull, e apresentam melhor ajuste à função de distribuição de probabilidade normal.The objective of this work was to verify the adjustment of data series for average global solar radiation to the normal, log-normal, gamma, gumbel and weibull probability distribution functions. Data were collected from 22 cities in Rio Grande do Sul State, Brazil. The Kolmogorov-Smirnov test was applied in the 792 series of data (22 localities x 36 periods of ten days of average global solar radiation to verify the adjustment of the data to the normal, log-normal, gamma, gumbel and weibull probability distribution functions, totalizing 3,960 tests. The data of average global solar radiation adjust to the normal, log-normal, gamma, gumbel and weibull probability distribution functions, and present a better adjustment to the normal probability function.
Koglin, Johnathon
8:0MeV and one bin from 4:5MeV to 5:5MeV. Across energy bins the fission probability increases approximately linearly with increasing alpha' scattering angle. At 90° the fission probability increases from 0:069(6) in the lowest energy bin to 0:59(2) in the highest. Likewise, within a single energy bin the fission probability increases with alpha' scattering angle. Within the 6:5MeV and 7:0MeV energy bin, the fission probability increased from 0:41(1) at 60° to 0:81(10) at 140°. Fission fragment angular distributions were also measured integrated over each energy bin. These distributions were fit to theoretical distributions based on combinations of transitional nuclear vibrational and rotational excitations at the saddle point. Contributions from specific K vibrational states were extracted and combined with fission probability measurements to determine the relative fission probability of each state as a function of nuclear excitation energy. Within a given excitation energy bin, it is found that contributions from K states greater than the minimum K = 0 state tend to increase with the increasing alpha' scattering angle. This is attributed to an increase in the transferred angular momentum associated with larger scattering angles. The 90° alpha' scattering angle produced the highest quality results. The relative contributions of K states do not show a discernible trend across the energy spectrum. The energy-binned results confirm existing measurements that place a K = 2 state in the first energy bin with the opening of K = 1 and K = 4 states at energies above 5:5MeV. This experiment represents the first of its kind in which fission probabilities and angular distributions are simultaneously measured at a large number of scattering angles. The acquired fission probability, angular distribution, and K state contribution provide a diverse dataset against which microscopic fission models can be constrained and further the understanding of the properties of the 240Pu
Directory of Open Access Journals (Sweden)
Panpan Zhao
2017-05-01
Full Text Available This study investigates the sensitivity and uncertainty of hydrological droughts frequencies and severity in the Weihe Basin, China during 1960–2012, by using six commonly used univariate probability distributions and three Archimedean copulas to fit the marginal and joint distributions of drought characteristics. The Anderson-Darling method is used for testing the goodness-of-fit of the univariate model, and the Akaike information criterion (AIC is applied to select the best distribution and copula functions. The results demonstrate that there is a very strong correlation between drought duration and drought severity in three stations. The drought return period varies depending on the selected marginal distributions and copula functions and, with an increase of the return period, the differences become larger. In addition, the estimated return periods (both co-occurrence and joint from the best-fitted copulas are the closet to those from empirical distribution. Therefore, it is critical to select the appropriate marginal distribution and copula function to model the hydrological drought frequency and severity. The results of this study can not only help drought investigation to select a suitable probability distribution and copulas function, but are also useful for regional water resource management. However, a few limitations remain in this study, such as the assumption of stationary of runoff series.
International Nuclear Information System (INIS)
Rasin, I.M.; Sarapul'tsev, I.A.
1975-01-01
The probability distribution of tissue radiation doses in the skeleton were studied in experiments on swines and dogs. When introducing Sr-90 into the organism from the day of birth till 90 days dose rate probability distribution is characterized by one, or, for adult animals, by two independent aggregates. Each of these aggregates correspond to the normal distribution law
Shiryaev, A N
1996-01-01
This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter Many examples are discussed in detail, and there are a large number of exercises The book is accessible to advanced undergraduates and can be used as a text for self-study This new edition contains substantial revisions and updated references The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures Proofs for a number of some important results which were merely stated in the first edition have been added The author included new material on the probability of large deviations, and on the central limit theorem for sums of dependent random variables
International Nuclear Information System (INIS)
El-Shanshoury, Gh.I.
2015-01-01
Assessing the adequacy of probability distributions for estimating the extreme events of air temperature in Dabaa region is one of the pre-requisite s for any design purpose at Dabaa site which can be achieved by probability approach. In the present study, three extreme value distributions are considered and compared to estimate the extreme events of monthly and annual maximum and minimum temperature. These distributions include the Gumbel/Frechet distributions for estimating the extreme maximum values and Gumbel /Weibull distributions for estimating the extreme minimum values. Lieblein technique and Method of Moments are applied for estimating the distribution para meters. Subsequently, the required design values with a given return period of exceedance are obtained. Goodness-of-Fit tests involving Kolmogorov-Smirnov and Anderson-Darling are used for checking the adequacy of fitting the method/distribution for the estimation of maximum/minimum temperature. Mean Absolute Relative Deviation, Root Mean Square Error and Relative Mean Square Deviation are calculated, as the performance indicators, to judge which distribution and method of parameters estimation are the most appropriate one to estimate the extreme temperatures. The present study indicated that the Weibull distribution combined with Method of Moment estimators gives the highest fit, most reliable, accurate predictions for estimating the extreme monthly and annual minimum temperature. The Gumbel distribution combined with Method of Moment estimators showed the highest fit, accurate predictions for the estimation of the extreme monthly and annual maximum temperature except for July, August, October and November. The study shows that the combination of Frechet distribution with Method of Moment is the most accurate for estimating the extreme maximum temperature in July, August and November months while t he Gumbel distribution and Lieblein technique is the best for October
International Nuclear Information System (INIS)
Caleyo, F.; Velazquez, J.C.; Valor, A.; Hallen, J.M.
2009-01-01
The probability distributions of external-corrosion pit depth and pit growth rate were investigated in underground pipelines using Monte Carlo simulations. The study combines a predictive pit growth model developed by the authors with the observed distributions of the model variables in a range of soils. Depending on the pipeline age, any of the three maximal extreme value distributions, i.e. Weibull, Frechet or Gumbel, can arise as the best fit to the pitting depth and rate data. The Frechet distribution best fits the corrosion data for long exposure periods. This can be explained by considering the long-term stabilization of the diffusion-controlled pit growth. The findings of the study provide reliability analysts with accurate information regarding the stochastic characteristics of the pitting damage in underground pipelines.
Energy Technology Data Exchange (ETDEWEB)
Caleyo, F. [Departamento de Ingenieria Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, 07738 Mexico, D.F. (Mexico)], E-mail: fcaleyo@gmail.com; Velazquez, J.C. [Departamento de Ingenieria Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, 07738 Mexico, D.F. (Mexico); Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400, La Habana (Cuba); Hallen, J.M. [Departamento de Ingenieria Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, 07738 Mexico, D.F. (Mexico)
2009-09-15
The probability distributions of external-corrosion pit depth and pit growth rate were investigated in underground pipelines using Monte Carlo simulations. The study combines a predictive pit growth model developed by the authors with the observed distributions of the model variables in a range of soils. Depending on the pipeline age, any of the three maximal extreme value distributions, i.e. Weibull, Frechet or Gumbel, can arise as the best fit to the pitting depth and rate data. The Frechet distribution best fits the corrosion data for long exposure periods. This can be explained by considering the long-term stabilization of the diffusion-controlled pit growth. The findings of the study provide reliability analysts with accurate information regarding the stochastic characteristics of the pitting damage in underground pipelines.
A probability space for quantum models
Lemmens, L. F.
2017-06-01
A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.
Matrix-exponential distributions in applied probability
Bladt, Mogens
2017-01-01
This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution is obtained through replacing the intensity parameter in an exponential distribution by a matrix. The ME distributions can also be identified as the class of non-negative distributions with rational Laplace transforms. If the matrix has the structure of a sub-intensity matrix for a Markov jump process we obtain a PH distribution which allows for nice probabilistic interpretations facilitating the derivation of exact solutions and closed form formulas. The full potential of ME and PH unfolds in their use in stochastic modelling. Several chapters on generic applications, like renewal theory, random walks and regenerative processes, are included together with some specific examples from queueing theory and insurance risk. We emphasize our intention towards applications by including an extensive treatment on statistical methods for PH distribu...
Probability Distribution for Flowing Interval Spacing
International Nuclear Information System (INIS)
S. Kuzio
2004-01-01
Fracture spacing is a key hydrologic parameter in analyses of matrix diffusion. Although the individual fractures that transmit flow in the saturated zone (SZ) cannot be identified directly, it is possible to determine the fractured zones that transmit flow from flow meter survey observations. The fractured zones that transmit flow as identified through borehole flow meter surveys have been defined in this report as flowing intervals. The flowing interval spacing is measured between the midpoints of each flowing interval. The determination of flowing interval spacing is important because the flowing interval spacing parameter is a key hydrologic parameter in SZ transport modeling, which impacts the extent of matrix diffusion in the SZ volcanic matrix. The output of this report is input to the ''Saturated Zone Flow and Transport Model Abstraction'' (BSC 2004 [DIRS 170042]). Specifically, the analysis of data and development of a data distribution reported herein is used to develop the uncertainty distribution for the flowing interval spacing parameter for the SZ transport abstraction model. Figure 1-1 shows the relationship of this report to other model reports that also pertain to flow and transport in the SZ. Figure 1-1 also shows the flow of key information among the SZ reports. It should be noted that Figure 1-1 does not contain a complete representation of the data and parameter inputs and outputs of all SZ reports, nor does it show inputs external to this suite of SZ reports. Use of the developed flowing interval spacing probability distribution is subject to the limitations of the assumptions discussed in Sections 5 and 6 of this analysis report. The number of fractures in a flowing interval is not known. Therefore, the flowing intervals are assumed to be composed of one flowing zone in the transport simulations. This analysis may overestimate the flowing interval spacing because the number of fractures that contribute to a flowing interval cannot be
Nogawa, Tomoaki
2012-10-18
We examine the effectiveness of assuming an equal probability for states far from equilibrium. For this aim, we propose a method to construct a master equation for extensive variables describing nonstationary nonequilibrium dynamics. The key point of the method is the assumption that transient states are equivalent to the equilibrium state that has the same extensive variables, i.e., an equal probability holds for microscopic states in nonequilibrium. We demonstrate an application of this method to the critical relaxation of the two-dimensional Potts model by Monte Carlo simulations. While the one-variable description, which is adequate for equilibrium, yields relaxation dynamics that are very fast, the redundant two-variable description well reproduces the true dynamics quantitatively. These results suggest that some class of the nonequilibrium state can be described with a small extension of degrees of freedom, which may lead to an alternative way to understand nonequilibrium phenomena. © 2012 American Physical Society.
Nogawa, Tomoaki; Ito, Nobuyasu; Watanabe, Hiroshi
2012-01-01
We examine the effectiveness of assuming an equal probability for states far from equilibrium. For this aim, we propose a method to construct a master equation for extensive variables describing nonstationary nonequilibrium dynamics. The key point of the method is the assumption that transient states are equivalent to the equilibrium state that has the same extensive variables, i.e., an equal probability holds for microscopic states in nonequilibrium. We demonstrate an application of this method to the critical relaxation of the two-dimensional Potts model by Monte Carlo simulations. While the one-variable description, which is adequate for equilibrium, yields relaxation dynamics that are very fast, the redundant two-variable description well reproduces the true dynamics quantitatively. These results suggest that some class of the nonequilibrium state can be described with a small extension of degrees of freedom, which may lead to an alternative way to understand nonequilibrium phenomena. © 2012 American Physical Society.
p-adic probability interpretation of Bell's inequality
International Nuclear Information System (INIS)
Khrennikov, A.
1995-01-01
We study the violation of Bell's inequality using a p-adic generalization of the theory of probability. p-adic probability is introduced as a limit of relative frequencies but this limit exists with respect to a p-adic metric. In particular, negative probability distributions are well defined on the basis of the frequency definition. This new type of stochastics can be used to describe hidden-variables distributions of some quantum models. If the hidden variables have a p-adic probability distribution, Bell's inequality is not valid and it is not necessary to discuss the experimental violations of this inequality. ((orig.))
Measuring Robustness of Timetables at Stations using a Probability Distribution
DEFF Research Database (Denmark)
Jensen, Lars Wittrup; Landex, Alex
Stations are often the limiting capacity factor in a railway network. This induces interdependencies, especially at at-grade junctions, causing network effects. This paper presents three traditional methods that can be used to measure the complexity of a station, indicating the robustness...... of the station’s infrastructure layout and plan of operation. However, these three methods do not take the timetable at the station into consideration. Therefore, two methods are introduced in this paper, making it possible to estimate the robustness of different timetables at a station or different...... infrastructure layouts given a timetable. These two methods provide different precision at the expense of a more complex calculation process. The advanced and more precise method is based on a probability distribution that can describe the expected delay between two trains as a function of the buffer time...
Description of atomic burials in compact globular proteins by Fermi-Dirac probability distributions.
Gomes, Antonio L C; de Rezende, Júlia R; Pereira de Araújo, Antônio F; Shakhnovich, Eugene I
2007-02-01
We perform a statistical analysis of atomic distributions as a function of the distance R from the molecular geometrical center in a nonredundant set of compact globular proteins. The number of atoms increases quadratically for small R, indicating a constant average density inside the core, reaches a maximum at a size-dependent distance R(max), and falls rapidly for larger R. The empirical curves turn out to be consistent with the volume increase of spherical concentric solid shells and a Fermi-Dirac distribution in which the distance R plays the role of an effective atomic energy epsilon(R) = R. The effective chemical potential mu governing the distribution increases with the number of residues, reflecting the size of the protein globule, while the temperature parameter beta decreases. Interestingly, betamu is not as strongly dependent on protein size and appears to be tuned to maintain approximately half of the atoms in the high density interior and the other half in the exterior region of rapidly decreasing density. A normalized size-independent distribution was obtained for the atomic probability as a function of the reduced distance, r = R/R(g), where R(g) is the radius of gyration. The global normalized Fermi distribution, F(r), can be reasonably decomposed in Fermi-like subdistributions for different atomic types tau, F(tau)(r), with Sigma(tau)F(tau)(r) = F(r), which depend on two additional parameters mu(tau) and h(tau). The chemical potential mu(tau) affects a scaling prefactor and depends on the overall frequency of the corresponding atomic type, while the maximum position of the subdistribution is determined by h(tau), which appears in a type-dependent atomic effective energy, epsilon(tau)(r) = h(tau)r, and is strongly correlated to available hydrophobicity scales. Better adjustments are obtained when the effective energy is not assumed to be necessarily linear, or epsilon(tau)*(r) = h(tau)*r(alpha,), in which case a correlation with hydrophobicity
DEFF Research Database (Denmark)
Huang, Shaojun; Sun, Yuanzhang; Wu, Qiuwei
2018-01-01
This paper focuses on economic dispatch (ED) in power systems with intermittent wind power, which is a very critical issue in future power systems. A stochastic ED problem is formed based on the recently proposed versatile probability distribution (VPD) of wind power. The problem is then analyzed...
Park, Junehyeong; Sung, Jang Hyun; Lim, Yoon-Jin; Kang, Hyun-Suk
2018-05-01
The widely used meteorological drought index, the Standardized Precipitation Index (SPI), basically assumes stationarity, but recent changes in the climate have led to a need to review this hypothesis. In this study, a new non-stationary SPI that considers not only the modified probability distribution parameter but also the return period under the non-stationary process was proposed. The results were evaluated for two severe drought cases during the last 10 years in South Korea. As a result, SPIs considered that the non-stationary hypothesis underestimated the drought severity than the stationary SPI despite that these past two droughts were recognized as significantly severe droughts. It may be caused by that the variances of summer and autumn precipitation become larger over time then it can make the probability distribution wider than before. This implies that drought expressions by statistical index such as SPI can be distorted by stationary assumption and cautious approach is needed when deciding drought level considering climate changes.
International Nuclear Information System (INIS)
Biyajima, M.; Shirane, K.; Suzuki, N.
1988-01-01
Moments in pseudorapidity intervals at the CERN Sp-barpS collider (√s = 546 GeV) are analyzed by means of two probability distributions in the pure-birth stochastic process. Our results show that a probability distribution obtained from the Poisson distribution as an initial condition is more useful than that obtained from the Kronecker δ function. Analyses of moments by Koba-Nielsen-Olesen scaling functions derived from solutions of the pure-birth stochastic process are also made. Moreover, analyses of preliminary data at √s = 200 and 900 GeV are added
A Study of Probability Models in Monitoring Environmental Pollution in Nigeria
Directory of Open Access Journals (Sweden)
P. E. Oguntunde
2014-01-01
Full Text Available In Lagos State, Nigeria, pollutant emissions were monitored across the state to detect any significant change which may cause harm to human health and the environment at large. In this research, three theoretical distributions, Weibull, lognormal, and gamma distributions, were examined on the carbon monoxide observations to determine the best fit. The characteristics of the pollutant observation were established and the probabilities of exceeding the Lagos State Environmental Protection Agency (LASEPA and the Federal Environmental Protection Agency (FEPA acceptable limits have been successfully predicted. Increase in the use of vehicles and increase in the establishment of industries have been found not to contribute significantly to the high level of carbon monoxide concentration in Lagos State for the period studied.
Energy Technology Data Exchange (ETDEWEB)
Antal, T [Physics Department, Simon Fraser University, Burnaby, BC V5A 1S6 (Canada); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH 1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest, Pazmany setany 1/a (Hungary)
2004-02-06
Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T {yields} 0), the size of the system going to infinity (N {yields} {infinity}) while N[1 - tanh(J/k{sub B}T)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.
Zuluaga, Jorge I.; Sucerquia, Mario
2018-06-01
Tunguska and Chelyabinsk impact events occurred inside a geographical area of only 3.4 per cent of the Earth's surface. Although two events hardly constitute a statistically significant demonstration of a geographical pattern of impacts, their spatial coincidence is at least tantalizing. To understand if this concurrence reflects an underlying geographical and/or temporal pattern, we must aim at predicting the spatio-temporal distribution of meteoroid impacts on Earth. For this purpose we designed, implemented, and tested a novel numerical technique, the `Gravitational Ray Tracing' (GRT) designed to compute the relative impact probability (RIP) on the surface of any planet. GRT is inspired by the so-called ray-casting techniques used to render realistic images of complex 3D scenes. In this paper we describe the method and the results of testing it at the time of large impact events. Our findings suggest a non-trivial pattern of impact probabilities at any given time on the Earth. Locations at 60-90° from the apex are more prone to impacts, especially at midnight. Counterintuitively, sites close to apex direction have the lowest RIP, while in the antapex RIP are slightly larger than average. We present here preliminary maps of RIP at the time of Tunguska and Chelyabinsk events and found no evidence of a spatial or temporal pattern, suggesting that their coincidence was fortuitous. We apply the GRT method to compute theoretical RIP at the location and time of 394 large fireballs. Although the predicted spatio-temporal impact distribution matches marginally the observed events, we successfully predict their impact speed distribution.
Multiscale probability distribution of pressure fluctuations in fluidized beds
International Nuclear Information System (INIS)
Ghasemi, Fatemeh; Sahimi, Muhammad; Reza Rahimi Tabar, M; Peinke, Joachim
2012-01-01
Analysis of flow in fluidized beds, a common chemical reactor, is of much current interest due to its fundamental as well as industrial importance. Experimental data for the successive increments of the pressure fluctuations time series in a fluidized bed are analyzed by computing a multiscale probability density function (PDF) of the increments. The results demonstrate the evolution of the shape of the PDF from the short to long time scales. The deformation of the PDF across time scales may be modeled by the log-normal cascade model. The results are also in contrast to the previously proposed PDFs for the pressure fluctuations that include a Gaussian distribution and a PDF with a power-law tail. To understand better the properties of the pressure fluctuations, we also construct the shuffled and surrogate time series for the data and analyze them with the same method. It turns out that long-range correlations play an important role in the structure of the time series that represent the pressure fluctuation. (paper)
Fram, Miranda S.; Belitz, Kenneth
2011-01-01
We use data from 1626 groundwater samples collected in California, primarily from public drinking water supply wells, to investigate the distribution of perchlorate in deep groundwater under natural conditions. The wells were sampled for the California Groundwater Ambient Monitoring and Assessment Priority Basin Project. We develop a logistic regression model for predicting probabilities of detecting perchlorate at concentrations greater than multiple threshold concentrations as a function of climate (represented by an aridity index) and potential anthropogenic contributions of perchlorate (quantified as an anthropogenic score, AS). AS is a composite categorical variable including terms for nitrate, pesticides, and volatile organic compounds. Incorporating water-quality parameters in AS permits identification of perturbation of natural occurrence patterns by flushing of natural perchlorate salts from unsaturated zones by irrigation recharge as well as addition of perchlorate from industrial and agricultural sources. The data and model results indicate low concentrations (0.1-0.5 μg/L) of perchlorate occur under natural conditions in groundwater across a wide range of climates, beyond the arid to semiarid climates in which they mostly have been previously reported. The probability of detecting perchlorate at concentrations greater than 0.1 μg/L under natural conditions ranges from 50-70% in semiarid to arid regions of California and the Southwestern United States to 5-15% in the wettest regions sampled (the Northern California coast). The probability of concentrations above 1 μg/L under natural conditions is low (generally <3%).
Gravity and count probabilities in an expanding universe
Bouchet, Francois R.; Hernquist, Lars
1992-01-01
The time evolution of nonlinear clustering on large scales in cold dark matter, hot dark matter, and white noise models of the universe is investigated using N-body simulations performed with a tree code. Count probabilities in cubic cells are determined as functions of the cell size and the clustering state (redshift), and comparisons are made with various theoretical models. We isolate the features that appear to be the result of gravitational instability, those that depend on the initial conditions, and those that are likely a consequence of numerical limitations. More specifically, we study the development of skewness, kurtosis, and the fifth moment in relation to variance, the dependence of the void probability on time as well as on sparseness of sampling, and the overall shape of the count probability distribution. Implications of our results for theoretical and observational studies are discussed.
International Nuclear Information System (INIS)
Tierney, M.S.
1991-11-01
The Waste Isolation Pilot Plant (WIPP), in southeastern New Mexico, is a research and development facility to demonstrate safe disposal of defense-generated transuranic waste. The US Department of Energy will designate WIPP as a disposal facility if it meets the US Environmental Protection Agency's standard for disposal of such waste; the standard includes a requirement that estimates of cumulative releases of radioactivity to the accessible environment be incorporated in an overall probability distribution. The WIPP Project has chosen an approach to calculation of an overall probability distribution that employs the concept of scenarios for release and transport of radioactivity to the accessible environment. This report reviews the use of Monte Carlo methods in the calculation of an overall probability distribution and presents a logical and mathematical foundation for use of the scenario concept in such calculations. The report also draws preliminary conclusions regarding the shape of the probability distribution for the WIPP system; preliminary conclusions are based on the possible occurrence of three events and the presence of one feature: namely, the events ''attempted boreholes over rooms and drifts,'' ''mining alters ground-water regime,'' ''water-withdrawal wells provide alternate pathways,'' and the feature ''brine pocket below room or drift.'' Calculation of the WIPP systems's overall probability distributions for only five of sixteen possible scenario classes that can be obtained by combining the four postulated events or features
Nuclear data uncertainties: I, Basic concepts of probability
Energy Technology Data Exchange (ETDEWEB)
Smith, D.L.
1988-12-01
Some basic concepts of probability theory are presented from a nuclear-data perspective, in order to provide a foundation for thorough understanding of the role of uncertainties in nuclear data research. Topics included in this report are: events, event spaces, calculus of events, randomness, random variables, random-variable distributions, intuitive and axiomatic probability, calculus of probability, conditional probability and independence, probability distributions, binomial and multinomial probability, Poisson and interval probability, normal probability, the relationships existing between these probability laws, and Bayes' theorem. This treatment emphasizes the practical application of basic mathematical concepts to nuclear data research, and it includes numerous simple examples. 34 refs.
Nuclear data uncertainties: I, Basic concepts of probability
International Nuclear Information System (INIS)
Smith, D.L.
1988-12-01
Some basic concepts of probability theory are presented from a nuclear-data perspective, in order to provide a foundation for thorough understanding of the role of uncertainties in nuclear data research. Topics included in this report are: events, event spaces, calculus of events, randomness, random variables, random-variable distributions, intuitive and axiomatic probability, calculus of probability, conditional probability and independence, probability distributions, binomial and multinomial probability, Poisson and interval probability, normal probability, the relationships existing between these probability laws, and Bayes' theorem. This treatment emphasizes the practical application of basic mathematical concepts to nuclear data research, and it includes numerous simple examples. 34 refs
Choice Probability Generating Functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel L; Bierlaire, Michel
This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications....
Haberlandt, U.; Radtke, I.
2014-01-01
Derived flood frequency analysis allows the estimation of design floods with hydrological modeling for poorly observed basins considering change and taking into account flood protection measures. There are several possible choices regarding precipitation input, discharge output and consequently the calibration of the model. The objective of this study is to compare different calibration strategies for a hydrological model considering various types of rainfall input and runoff output data sets and to propose the most suitable approach. Event based and continuous, observed hourly rainfall data as well as disaggregated daily rainfall and stochastically generated hourly rainfall data are used as input for the model. As output, short hourly and longer daily continuous flow time series as well as probability distributions of annual maximum peak flow series are employed. The performance of the strategies is evaluated using the obtained different model parameter sets for continuous simulation of discharge in an independent validation period and by comparing the model derived flood frequency distributions with the observed one. The investigations are carried out for three mesoscale catchments in northern Germany with the hydrological model HEC-HMS (Hydrologic Engineering Center's Hydrologic Modeling System). The results show that (I) the same type of precipitation input data should be used for calibration and application of the hydrological model, (II) a model calibrated using a small sample of extreme values works quite well for the simulation of continuous time series with moderate length but not vice versa, and (III) the best performance with small uncertainty is obtained when stochastic precipitation data and the observed probability distribution of peak flows are used for model calibration. This outcome suggests to calibrate a hydrological model directly on probability distributions of observed peak flows using stochastic rainfall as input if its purpose is the
A hydroclimatological approach to predicting regional landslide probability using Landlab
Directory of Open Access Journals (Sweden)
R. Strauch
2018-02-01
Full Text Available We develop a hydroclimatological approach to the modeling of regional shallow landslide initiation that integrates spatial and temporal dimensions of parameter uncertainty to estimate an annual probability of landslide initiation based on Monte Carlo simulations. The physically based model couples the infinite-slope stability model with a steady-state subsurface flow representation and operates in a digital elevation model. Spatially distributed gridded data for soil properties and vegetation classification are used for parameter estimation of probability distributions that characterize model input uncertainty. Hydrologic forcing to the model is through annual maximum daily recharge to subsurface flow obtained from a macroscale hydrologic model. We demonstrate the model in a steep mountainous region in northern Washington, USA, over 2700 km2. The influence of soil depth on the probability of landslide initiation is investigated through comparisons among model output produced using three different soil depth scenarios reflecting the uncertainty of soil depth and its potential long-term variability. We found elevation-dependent patterns in probability of landslide initiation that showed the stabilizing effects of forests at low elevations, an increased landslide probability with forest decline at mid-elevations (1400 to 2400 m, and soil limitation and steep topographic controls at high alpine elevations and in post-glacial landscapes. These dominant controls manifest themselves in a bimodal distribution of spatial annual landslide probability. Model testing with limited observations revealed similarly moderate model confidence for the three hazard maps, suggesting suitable use as relative hazard products. The model is available as a component in Landlab, an open-source, Python-based landscape earth systems modeling environment, and is designed to be easily reproduced utilizing HydroShare cyberinfrastructure.
A hydroclimatological approach to predicting regional landslide probability using Landlab
Strauch, Ronda; Istanbulluoglu, Erkan; Nudurupati, Sai Siddhartha; Bandaragoda, Christina; Gasparini, Nicole M.; Tucker, Gregory E.
2018-02-01
We develop a hydroclimatological approach to the modeling of regional shallow landslide initiation that integrates spatial and temporal dimensions of parameter uncertainty to estimate an annual probability of landslide initiation based on Monte Carlo simulations. The physically based model couples the infinite-slope stability model with a steady-state subsurface flow representation and operates in a digital elevation model. Spatially distributed gridded data for soil properties and vegetation classification are used for parameter estimation of probability distributions that characterize model input uncertainty. Hydrologic forcing to the model is through annual maximum daily recharge to subsurface flow obtained from a macroscale hydrologic model. We demonstrate the model in a steep mountainous region in northern Washington, USA, over 2700 km2. The influence of soil depth on the probability of landslide initiation is investigated through comparisons among model output produced using three different soil depth scenarios reflecting the uncertainty of soil depth and its potential long-term variability. We found elevation-dependent patterns in probability of landslide initiation that showed the stabilizing effects of forests at low elevations, an increased landslide probability with forest decline at mid-elevations (1400 to 2400 m), and soil limitation and steep topographic controls at high alpine elevations and in post-glacial landscapes. These dominant controls manifest themselves in a bimodal distribution of spatial annual landslide probability. Model testing with limited observations revealed similarly moderate model confidence for the three hazard maps, suggesting suitable use as relative hazard products. The model is available as a component in Landlab, an open-source, Python-based landscape earth systems modeling environment, and is designed to be easily reproduced utilizing HydroShare cyberinfrastructure.
Probability distribution of wave packet delay time for strong overlapping of resonance levels
International Nuclear Information System (INIS)
Lyuboshits, V.L.
1983-01-01
Time behaviour of nuclear reactions in the case of high level densities is investigated basing on the theory of overlapping resonances. In the framework of a model of n equivalent channels an analytical expression is obtained for the probability distribution function for wave packet delay time at the compound nucleus production. It is shown that at strong overlapping of the resonance levels the relative fluctuation of the delay time is small at the stage of compound nucleus production. A possible increase in the duration of nuclear reactions with the excitation energy rise is discussed
Probability distribution of machining center failures
International Nuclear Information System (INIS)
Jia Yazhou; Wang Molin; Jia Zhixin
1995-01-01
Through field tracing research for 24 Chinese cutter-changeable CNC machine tools (machining centers) over a period of one year, a database of operation and maintenance for machining centers was built, the failure data was fitted to the Weibull distribution and the exponential distribution, the effectiveness was tested, and the failure distribution pattern of machining centers was found. Finally, the reliability characterizations for machining centers are proposed
Statistical physics of pairwise probability models
DEFF Research Database (Denmark)
Roudi, Yasser; Aurell, Erik; Hertz, John
2009-01-01
(dansk abstrakt findes ikke) Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data......: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying...
Probable Inference and Quantum Mechanics
International Nuclear Information System (INIS)
Grandy, W. T. Jr.
2009-01-01
In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.
Choice probability generating functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel
2013-01-01
This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications. The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended...
Wu, Yunna; Chen, Kaifeng; Xu, Hu; Xu, Chuanbo; Zhang, Haobo; Yang, Meng
2017-12-01
There is insufficient research relating to offshore wind farm site selection in China. The current methods for site selection have some defects. First, information loss is caused by two aspects: the implicit assumption that the probability distribution on the interval number is uniform; and ignoring the value of decision makers' (DMs') common opinion on the criteria information evaluation. Secondly, the difference in DMs' utility function has failed to receive attention. An innovative method is proposed in this article to solve these drawbacks. First, a new form of interval number and its weighted operator are proposed to reflect the uncertainty and reduce information loss. Secondly, a new stochastic dominance degree is proposed to quantify the interval number with a probability distribution. Thirdly, a two-stage method integrating the weighted operator with stochastic dominance degree is proposed to evaluate the alternatives. Finally, a case from China proves the effectiveness of this method.
Mark A. Finney; Charles W. McHugh; Isaac Grenfell; Karin L. Riley
2010-01-01
Components of a quantitative risk assessment were produced by simulation of burn probabilities and fire behavior variation for 134 fire planning units (FPUs) across the continental U.S. The system uses fire growth simulation of ignitions modeled from relationships between large fire occurrence and the fire danger index Energy Release Component (ERC). Simulations of 10,...
The quantum probability calculus
International Nuclear Information System (INIS)
Jauch, J.M.
1976-01-01
The Wigner anomaly (1932) for the joint distribution of noncompatible observables is an indication that the classical probability calculus is not applicable for quantum probabilities. It should, therefore, be replaced by another, more general calculus, which is specifically adapted to quantal systems. In this article this calculus is exhibited and its mathematical axioms and the definitions of the basic concepts such as probability field, random variable, and expectation values are given. (B.R.H)
Joint probabilities and quantum cognition
International Nuclear Information System (INIS)
Acacio de Barros, J.
2012-01-01
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.
Joint probabilities and quantum cognition
Energy Technology Data Exchange (ETDEWEB)
Acacio de Barros, J. [Liberal Studies, 1600 Holloway Ave., San Francisco State University, San Francisco, CA 94132 (United States)
2012-12-18
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.
Directory of Open Access Journals (Sweden)
X. Shen
2018-01-01
Full Text Available In this work, the spatial extent of new particle formation (NPF events and the relative probability of observing particles originating from different spatial origins around three rural sites in eastern China were investigated using the NanoMap method, using particle number size distribution (PNSD data and air mass back trajectories. The length of the datasets used were 7, 1.5, and 3 years at rural sites Shangdianzi (SDZ in the North China Plain (NCP, Mt. Tai (TS in central eastern China, and Lin'an (LAN in the Yangtze River Delta region in eastern China, respectively. Regional NPF events were observed to occur with the horizontal extent larger than 500 km at SDZ and TS, favoured by the fast transport of northwesterly air masses. At LAN, however, the spatial footprint of NPF events was mostly observed around the site within 100–200 km. Difference in the horizontal spatial distribution of new particle source areas at different sites was connected to typical meteorological conditions at the sites. Consecutive large-scale regional NPF events were observed at SDZ and TS simultaneously and were associated with a high surface pressure system dominating over this area. Simultaneous NPF events at SDZ and LAN were seldom observed. At SDZ the polluted air masses arriving over the NCP were associated with higher particle growth rate (GR and new particle formation rate (J than air masses from Inner Mongolia (IM. At TS the same phenomenon was observed for J, but GR was somewhat lower in air masses arriving over the NCP compared to those arriving from IM. The capability of NanoMap to capture the NPF occurrence probability depends on the length of the dataset of PNSD measurement but also on topography around the measurement site and typical air mass advection speed during NPF events. Thus the long-term measurements of PNSD in the planetary boundary layer are necessary in the further study of spatial extent and the probability of NPF events. The spatial
Modeling of spatial distribution for scorpions of medical importance in the São Paulo State, Brazil
Directory of Open Access Journals (Sweden)
José Brites-Neto
2015-07-01
Full Text Available Aim: In this work, we aimed to develop maps of modeling geographic distribution correlating to environmental suitability for the two species of scorpions of medical importance at São Paulo State and to develop spatial configuration parameters for epidemiological surveillance of these species of venomous animals. Materials and Methods: In this study, 54 georeferenced points for Tityus serrulatus and 86 points for Tityus bahiensis and eight environmental indicators, were used to generate species distribution models in Maxent (maximum entropy modeling of species geographic distributions version 3.3.3k using 70% of data for training (n=38 to T. serrulatus and n=60 to T. bahiensis and 30% to test the models (n=16 for T. serrulatus and n=26 for T. bahiensis. The logistic threshold used to cut models in converting the continuous probability model into a binary model was the “maximum test sensitivity plus specificity,” provided by Maxent, with results of 0.4143 to T. serrulatus and of 0.3401 to T. bahiensis. The models were evaluated by the area under the curve (AUC, using the omission error and the binomial probability. With the data generated by Maxent, distribution maps were produced using the “ESRI® ArcGIS 10.2.2 for Desktop” software. Results: The models had high predictive success (AUC=0.7698±0.0533, omission error=0.2467 and p<0.001 for T. serrulatus and AUC=0.8205±0.0390, omission error=0.1917 and p<0.001 for T. bahiensis and the resultant maps showed a high environmental suitability in the north, central, and southeast of the state, confirming the increasing spread of these species. The environmental variables that mostly contributed to the scorpions species distribution model were rain precipitation (28.9% and tree cover (28.2% for the T. serrulatus and temperature (45.8% and thermal amplitude (12.6% for the T. bahiensis. Conclusion: The distribution model of these species of medical importance scorpions in São Paulo State
Probability elements of the mathematical theory
Heathcote, C R
2000-01-01
Designed for students studying mathematical statistics and probability after completing a course in calculus and real variables, this text deals with basic notions of probability spaces, random variables, distribution functions and generating functions, as well as joint distributions and the convergence properties of sequences of random variables. Includes worked examples and over 250 exercises with solutions.
DEFF Research Database (Denmark)
Rojas-Nandayapa, Leonardo
Tail probabilities of sums of heavy-tailed random variables are of a major importance in various branches of Applied Probability, such as Risk Theory, Queueing Theory, Financial Management, and are subject to intense research nowadays. To understand their relevance one just needs to think...... analytic expression for the distribution function of a sum of random variables. The presence of heavy-tailed random variables complicates the problem even more. The objective of this dissertation is to provide better approximations by means of sharp asymptotic expressions and Monte Carlo estimators...
Multiple model cardinalized probability hypothesis density filter
Georgescu, Ramona; Willett, Peter
2011-09-01
The Probability Hypothesis Density (PHD) filter propagates the first-moment approximation to the multi-target Bayesian posterior distribution while the Cardinalized PHD (CPHD) filter propagates both the posterior likelihood of (an unlabeled) target state and the posterior probability mass function of the number of targets. Extensions of the PHD filter to the multiple model (MM) framework have been published and were implemented either with a Sequential Monte Carlo or a Gaussian Mixture approach. In this work, we introduce the multiple model version of the more elaborate CPHD filter. We present the derivation of the prediction and update steps of the MMCPHD particularized for the case of two target motion models and proceed to show that in the case of a single model, the new MMCPHD equations reduce to the original CPHD equations.
A statistical model for deriving probability distributions of contamination for accidental releases
International Nuclear Information System (INIS)
ApSimon, H.M.; Davison, A.C.
1986-01-01
Results generated from a detailed long-range transport model, MESOS, simulating dispersal of a large number of hypothetical releases of radionuclides in a variety of meteorological situations over Western Europe have been used to derive a simpler statistical model, MESOSTAT. This model may be used to generate probability distributions of different levels of contamination at a receptor point 100-1000 km or so from the source (for example, across a frontier in another country) without considering individual release and dispersal scenarios. The model is embodied in a series of equations involving parameters which are determined from such factors as distance between source and receptor, nuclide decay and deposition characteristics, release duration, and geostrophic windrose at the source. Suitable geostrophic windrose data have been derived for source locations covering Western Europe. Special attention has been paid to the relatively improbable extreme values of contamination at the top end of the distribution. The MESOSTAT model and its development are described, with illustrations of its use and comparison with the original more detailed modelling techniques. (author)
Yampolsky, M; Salafia, C M; Shlakhter, O
2013-06-01
While the mean shape of human placenta is round with centrally inserted umbilical cord, significant deviations from this ideal are fairly common, and may be clinically meaningful. Traditionally, they are explained by trophotropism. We have proposed a hypothesis explaining typical variations in placental shape by randomly determined fluctuations in the growth process of the vascular tree. It has been recently reported that umbilical cord displacement in a birth cohort has a log-normal probability distribution, which indicates that the displacement between an initial point of origin and the centroid of the mature shape is a result of accumulation of random fluctuations of the dynamic growth of the placenta. To confirm this, we investigate statistical distributions of other features of placental morphology. In a cohort of 1023 births at term digital photographs of placentas were recorded at delivery. Excluding cases with velamentous cord insertion, or missing clinical data left 1001 (97.8%) for which placental surface morphology features were measured. Best-fit statistical distributions for them were obtained using EasyFit. The best-fit distributions of umbilical cord displacement, placental disk diameter, area, perimeter, and maximal radius calculated from the cord insertion point are of heavy-tailed type, similar in shape to log-normal distributions. This is consistent with a stochastic origin of deviations of placental shape from normal. Deviations of placental shape descriptors from average have heavy-tailed distributions similar in shape to log-normal. This evidence points away from trophotropism, and towards a spontaneous stochastic evolution of the variants of placental surface shape features. Copyright © 2013 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Cai, H.; Wang, M.; Elgowainy, A.; Han, J.
2012-01-01
Greenhouse gas (CO 2 , CH 4 and N 2 O, hereinafter GHG) and criteria air pollutant (CO, NO x , VOC, PM 10 , PM 2.5 and SO x , hereinafter CAP) emission factors for various types of power plants burning various fuels with different technologies are important upstream parameters for estimating life-cycle emissions associated with alternative vehicle/fuel systems in the transportation sector, especially electric vehicles. The emission factors are typically expressed in grams of GHG or CAP per kWh of electricity generated by a specific power generation technology. This document describes our approach for updating and expanding GHG and CAP emission factors in the GREET (Greenhouse Gases, Regulated Emissions, and Energy Use in Transportation) model developed at Argonne National Laboratory (see Wang 1999 and the GREET website at http://greet.es.anl.gov/main) for various power generation technologies. These GHG and CAP emissions are used to estimate the impact of electricity use by stationary and transportation applications on their fuel-cycle emissions. The electricity generation mixes and the fuel shares attributable to various combustion technologies at the national, regional and state levels are also updated in this document. The energy conversion efficiencies of electric generating units (EGUs) by fuel type and combustion technology are calculated on the basis of the lower heating values of each fuel, to be consistent with the basis used in GREET for transportation fuels. On the basis of the updated GHG and CAP emission factors and energy efficiencies of EGUs, the probability distribution functions (PDFs), which are functions that describe the relative likelihood for the emission factors and energy efficiencies as random variables to take on a given value by the integral of their own probability distributions, are updated using best-fit statistical curves to characterize the uncertainties associated with GHG and CAP emissions in life-cycle modeling with GREET.
Ortega, R.; Gutierrez, E.; Carciumaru, D. D.; Huesca-Perez, E.
2017-12-01
We present a method to compute the conditional and no-conditional probability density function (PDF) of the finite fault distance distribution (FFDD). Two cases are described: lines and areas. The case of lines has a simple analytical solution while, in the case of areas, the geometrical probability of a fault based on the strike, dip, and fault segment vertices is obtained using the projection of spheres in a piecewise rectangular surface. The cumulative distribution is computed by measuring the projection of a sphere of radius r in an effective area using an algorithm that estimates the area of a circle within a rectangle. In addition, we introduce the finite fault distance metrics. This distance is the distance where the maximum stress release occurs within the fault plane and generates a peak ground motion. Later, we can apply the appropriate ground motion prediction equations (GMPE) for PSHA. The conditional probability of distance given magnitude is also presented using different scaling laws. A simple model of constant distribution of the centroid at the geometrical mean is discussed, in this model hazard is reduced at the edges because the effective size is reduced. Nowadays there is a trend of using extended source distances in PSHA, however it is not possible to separate the fault geometry from the GMPE. With this new approach, it is possible to add fault rupture models separating geometrical and propagation effects.
Introduction to probability with R
Baclawski, Kenneth
2008-01-01
FOREWORD PREFACE Sets, Events, and Probability The Algebra of Sets The Bernoulli Sample Space The Algebra of Multisets The Concept of Probability Properties of Probability Measures Independent Events The Bernoulli Process The R Language Finite Processes The Basic Models Counting Rules Computing Factorials The Second Rule of Counting Computing Probabilities Discrete Random Variables The Bernoulli Process: Tossing a Coin The Bernoulli Process: Random Walk Independence and Joint Distributions Expectations The Inclusion-Exclusion Principle General Random Variable
Mestres-Missé, Anna; Trampel, Robert; Turner, Robert; Kotz, Sonja A
2016-04-01
A key aspect of optimal behavior is the ability to predict what will come next. To achieve this, we must have a fairly good idea of the probability of occurrence of possible outcomes. This is based both on prior knowledge about a particular or similar situation and on immediately relevant new information. One question that arises is: when considering converging prior probability and external evidence, is the most probable outcome selected or does the brain represent degrees of uncertainty, even highly improbable ones? Using functional magnetic resonance imaging, the current study explored these possibilities by contrasting words that differ in their probability of occurrence, namely, unbalanced ambiguous words and unambiguous words. Unbalanced ambiguous words have a strong frequency-based bias towards one meaning, while unambiguous words have only one meaning. The current results reveal larger activation in lateral prefrontal and insular cortices in response to dominant ambiguous compared to unambiguous words even when prior and contextual information biases one interpretation only. These results suggest a probability distribution, whereby all outcomes and their associated probabilities of occurrence--even if very low--are represented and maintained.
Sheng, Li; Wang, Zidong; Tian, Engang; Alsaadi, Fuad E
2016-12-01
This paper deals with the H ∞ state estimation problem for a class of discrete-time neural networks with stochastic delays subject to state- and disturbance-dependent noises (also called (x,v)-dependent noises) and fading channels. The time-varying stochastic delay takes values on certain intervals with known probability distributions. The system measurement is transmitted through fading channels described by the Rice fading model. The aim of the addressed problem is to design a state estimator such that the estimation performance is guaranteed in the mean-square sense against admissible stochastic time-delays, stochastic noises as well as stochastic fading signals. By employing the stochastic analysis approach combined with the Kronecker product, several delay-distribution-dependent conditions are derived to ensure that the error dynamics of the neuron states is stochastically stable with prescribed H ∞ performance. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.
State distribution and reliability of some multi- state systems with ...
African Journals Online (AJOL)
mn : G series systems and second, the multi-state consecutive kn-out-of-mn : G parallel systems (see denitions 1 and 2).We begin by giving a non recursive formula which calculates the state distribution and the reliability of multi-state ...
Wenger, Seth J; Freeman, Mary C
2008-10-01
Researchers have developed methods to account for imperfect detection of species with either occupancy (presence absence) or count data using replicated sampling. We show how these approaches can be combined to simultaneously estimate occurrence, abundance, and detection probability by specifying a zero-inflated distribution for abundance. This approach may be particularly appropriate when patterns of occurrence and abundance arise from distinct processes operating at differing spatial or temporal scales. We apply the model to two data sets: (1) previously published data for a species of duck, Anas platyrhynchos, and (2) data for a stream fish species, Etheostoma scotti. We show that in these cases, an incomplete-detection zero-inflated modeling approach yields a superior fit to the data than other models. We propose that zero-inflated abundance models accounting for incomplete detection be considered when replicate count data are available.
Probability distribution of distance in a uniform ellipsoid: Theory and applications to physics
International Nuclear Information System (INIS)
Parry, Michelle; Fischbach, Ephraim
2000-01-01
A number of authors have previously found the probability P n (r) that two points uniformly distributed in an n-dimensional sphere are separated by a distance r. This result greatly facilitates the calculation of self-energies of spherically symmetric matter distributions interacting by means of an arbitrary radially symmetric two-body potential. We present here the analogous results for P 2 (r;ε) and P 3 (r;ε) which respectively describe an ellipse and an ellipsoid whose major and minor axes are 2a and 2b. It is shown that for ε=(1-b 2 /a 2 ) 1/2 ≤1, P 2 (r;ε) and P 3 (r;ε) can be obtained as an expansion in powers of ε, and our results are valid through order ε 4 . As an application of these results we calculate the Coulomb energy of an ellipsoidal nucleus, and compare our result to an earlier result quoted in the literature. (c) 2000 American Institute of Physics
On probability-possibility transformations
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.
Modeling the probability distribution of positional errors incurred by residential address geocoding
Directory of Open Access Journals (Sweden)
Mazumdar Soumya
2007-01-01
Full Text Available Abstract Background The assignment of a point-level geocode to subjects' residences is an important data assimilation component of many geographic public health studies. Often, these assignments are made by a method known as automated geocoding, which attempts to match each subject's address to an address-ranged street segment georeferenced within a streetline database and then interpolate the position of the address along that segment. Unfortunately, this process results in positional errors. Our study sought to model the probability distribution of positional errors associated with automated geocoding and E911 geocoding. Results Positional errors were determined for 1423 rural addresses in Carroll County, Iowa as the vector difference between each 100%-matched automated geocode and its true location as determined by orthophoto and parcel information. Errors were also determined for 1449 60%-matched geocodes and 2354 E911 geocodes. Huge (> 15 km outliers occurred among the 60%-matched geocoding errors; outliers occurred for the other two types of geocoding errors also but were much smaller. E911 geocoding was more accurate (median error length = 44 m than 100%-matched automated geocoding (median error length = 168 m. The empirical distributions of positional errors associated with 100%-matched automated geocoding and E911 geocoding exhibited a distinctive Greek-cross shape and had many other interesting features that were not capable of being fitted adequately by a single bivariate normal or t distribution. However, mixtures of t distributions with two or three components fit the errors very well. Conclusion Mixtures of bivariate t distributions with few components appear to be flexible enough to fit many positional error datasets associated with geocoding, yet parsimonious enough to be feasible for nascent applications of measurement-error methodology to spatial epidemiology.
Hansen, John P
2003-01-01
Healthcare quality improvement professionals need to understand and use inferential statistics to interpret sample data from their organizations. In quality improvement and healthcare research studies all the data from a population often are not available, so investigators take samples and make inferences about the population by using inferential statistics. This three-part series will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals for samples of data. This article, Part 2, describes probability, populations, and samples. The uses of descriptive and inferential statistics are outlined. The article also discusses the properties and probability of normal distributions, including the standard normal distribution.
Local correlations of mixed two-qubit states
International Nuclear Information System (INIS)
Zhang Fulin; Chen Jingling; Ren Changliang; Shi Mingjun
2010-01-01
The quantum probability distribution arising from single-copy von Neumann measurements on an arbitrary two-qubit state is decomposed into the local and nonlocal parts, in the approach of Elitzur, Popescu and Rohrlich [A. Elitzur, S. Popescu, D. Rohrlich, Phys. Lett. A 162 (1992) 25]. A lower bound of the local weight is proved being connected with the concurrence of the state p L max =1-C(ρ). The local probability distributions for two families of mixed states are constructed independently, which accord with the lower bound.
Tools for Bramwell-Holdsworth-Pinton Probability Distribution
Directory of Open Access Journals (Sweden)
Mirela Danubianu
2009-01-01
Full Text Available This paper is a synthesis of a range of papers presentedat various conferences related to distribution Bramwell-Holdsworth-Pinton. S. T. Bramwell, P. C. W. Holdsworth, J. F.Pinton introduced a new non-parametric distribution (calledBHP after studying some magnetization problems in 2D. Probabilitydensity function of distribution can be aproximated as amodified GFT (Gumbel-Fisher-Tippitt distribution.
Directory of Open Access Journals (Sweden)
Elmer P. Dadios
2009-01-01
Full Text Available This paper presents a new algorithm for real time event detection using Finite State Machines with multiple Fuzzy Logic Probability Evaluators (FLPEs. A machine referee for a robot soccer game is developed and is used as the platform to test the proposed algorithm. A novel technique to detect collisions and other events in microrobot soccer game under inaccurate and insufficient information is presented. The robots' collision is used to determine goalkeeper charging and goal score events which are crucial for the machine referee's decisions. The Main State Machine (MSM handles the schedule of event activation. The FLPE calculates the probabilities of the true occurrence of the events. Final decisions about the occurrences of events are evaluated and compared through threshold crisp probability values. The outputs of FLPEs can be combined to calculate the probability of an event composed of subevents. Using multiple fuzzy logic system, the FLPE utilizes minimal number of rules and can be tuned individually. Experimental results show the accuracy and robustness of the proposed algorithm.
Wigner distribution function for an oscillator
International Nuclear Information System (INIS)
Davies, R.W.; Davies, K.T.R.
1975-01-01
We present two new derivations of the Wigner distribution function for a simple harmonic oscillator Hamiltonian. Both methods are facilitated using a formula which expresses the Wigner function as a simple trace. The first method of derivation utilizes a modification of a theorem due to Messiah. An alternative procedure makes use of the coherent state representation of an oscillator. The Wigner distribution function gives a semiclassical joint probability for finding the system with given coordinates and momenta, and the joint probability is factorable for the special case of an oscillator. An important application of this result occurs in the theory of nuclear fission for calculating the probability distributions for the masses, kinetic energies, and vibrational energies of the fission fragments at infinite separation. (U.S.)
Concise method for evaluating the probability distribution of the marginal cost of power generation
International Nuclear Information System (INIS)
Zhang, S.H.; Li, Y.Z.
2000-01-01
In the developing electricity market, many questions on electricity pricing and the risk modelling of forward contracts require the evaluation of the expected value and probability distribution of the short-run marginal cost of power generation at any given time. A concise forecasting method is provided, which is consistent with the definitions of marginal costs and the techniques of probabilistic production costing. The method embodies clear physical concepts, so that it can be easily understood theoretically and computationally realised. A numerical example has been used to test the proposed method. (author)
Alimi, Jean-Michel; de Fromont, Paul
2018-04-01
The statistical properties of cosmic structures are well known to be strong probes for cosmology. In particular, several studies tried to use the cosmic void counting number to obtain tight constrains on dark energy. In this paper, we model the statistical properties of these regions using the CoSphere formalism (de Fromont & Alimi) in both primordial and non-linearly evolved Universe in the standard Λ cold dark matter model. This formalism applies similarly for minima (voids) and maxima (such as DM haloes), which are here considered symmetrically. We first derive the full joint Gaussian distribution of CoSphere's parameters in the Gaussian random field. We recover the results of Bardeen et al. only in the limit where the compensation radius becomes very large, i.e. when the central extremum decouples from its cosmic environment. We compute the probability distribution of the compensation size in this primordial field. We show that this distribution is redshift independent and can be used to model cosmic voids size distribution. We also derive the statistical distribution of the peak parameters introduced by Bardeen et al. and discuss their correlation with the cosmic environment. We show that small central extrema with low density are associated with narrow compensation regions with deep compensation density, while higher central extrema are preferentially located in larger but smoother over/under massive regions.
Huang, N. E.; Long, S. R.
1980-01-01
Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.
International Nuclear Information System (INIS)
Morishita, K.; Ishino, S.; Sekimura, N.
1995-01-01
The spatial distributions of atomic displacement at the end of the collisional phase of cascade damage processes were calculated using the computer simulation code MARLOWE, which is based on the binary collision approximation (BCA). The densities of the atomic displacement were evaluated in high dense regions (HDRs) of cascades in several pure metals (Fe, Ni, Cu, Ag, Au, Mo and W). They were compared with the measured cascade collapse probabilities reported in the literature where TEM observations were carried out using thin metal foils irradiated by low-dose ions at room temperature. We found that there exists the minimum or ''critical'' values of the atomic displacement densities for the HDR to collapse into TEM-visible vacancy clusters. The critical densities are generally independent of the cascade energy in the same metal. Furthermore, the material dependence of the critical densities can be explained by the difference in the vacancy mobility at the melting temperature of target materials. This critical density calibration, which is extracted from the ion-irradiation experiments and the BCA simulations, is applied to estimation of cascade collapse probabilities in the metals irradiated by fusion neutrons. (orig.)
Plutonium valence state distributions
International Nuclear Information System (INIS)
Silver, G.L.
1974-01-01
A calculational method for ascertaining equilibrium valence state distributions of plutonium in acid solutions as a function of the plutonium oxidation number and the solution acidity is illustrated with an example. The method may be more practical for manual use than methods based upon polynomial equations. (T.G.)
Entropy Concept for Paramacrosystems with Complex States
Directory of Open Access Journals (Sweden)
Yuri S. Popkov
2012-05-01
Full Text Available Consideration is given to macrosystems called paramacrosystems with states of finite capacity and distinguishable and undistinguishable elements with stochastic behavior. The paramacrosystems fill a gap between Fermi and Einstein macrosystems. Using the method of the generating functions, we have obtained expressions for probabilistic characteristics (distribution of the macrostate probabilities, physical and information entropies of the paramacrosystems. The cases with equal and unequal prior probabilities for elements to occupy the states with finite capacities are considered. The unequal prior probabilities influence the morphological properties of the entropy functions and the functions of the macrostate probabilities, transforming them in the multimodal functions. The examples of the paramacrosystems with two-modal functions of the entropy and distribution of the macrostate probabilities are presented. The variation principle does not work for such cases.
Introduction to probability with statistical applications
Schay, Géza
2016-01-01
Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises
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
Poisson Processes in Free Probability
An, Guimei; Gao, Mingchu
2015-01-01
We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of (compound) Poisson processes in classical probability. We proved that the sum of finitely many freely independent compound free Poisson processes is a compound free Poisson processes. We give a step by step procedure for constructing a (compound) free Poisso...
von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo
2014-06-01
Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.
Normal probability plots with confidence.
Chantarangsi, Wanpen; Liu, Wei; Bretz, Frank; Kiatsupaibul, Seksan; Hayter, Anthony J; Wan, Fang
2015-01-01
Normal probability plots are widely used as a statistical tool for assessing whether an observed simple random sample is drawn from a normally distributed population. The users, however, have to judge subjectively, if no objective rule is provided, whether the plotted points fall close to a straight line. In this paper, we focus on how a normal probability plot can be augmented by intervals for all the points so that, if the population distribution is normal, then all the points should fall into the corresponding intervals simultaneously with probability 1-α. These simultaneous 1-α probability intervals provide therefore an objective mean to judge whether the plotted points fall close to the straight line: the plotted points fall close to the straight line if and only if all the points fall into the corresponding intervals. The powers of several normal probability plot based (graphical) tests and the most popular nongraphical Anderson-Darling and Shapiro-Wilk tests are compared by simulation. Based on this comparison, recommendations are given in Section 3 on which graphical tests should be used in what circumstances. An example is provided to illustrate the methods. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
The reduced transition probabilities for excited states of rare-earths and actinide even-even nuclei
Energy Technology Data Exchange (ETDEWEB)
Ghumman, S. S. [Department of Physics, Sant Longowal Institute of Engineering and Technology (Deemed University), Longowal, Sangrur-148106, Punjab, India s-ghumman@yahoo.com (India)
2015-08-28
The theoretical B(E2) ratios have been calculated on DF, DR and Krutov models. A simple method based on the work of Arima and Iachello is used to calculate the reduced transition probabilities within SU(3) limit of IBA-I framework. The reduced E2 transition probabilities from second excited states of rare-earths and actinide even–even nuclei calculated from experimental energies and intensities from recent data, have been found to compare better with those calculated on the Krutov model and the SU(3) limit of IBA than the DR and DF models.
Directory of Open Access Journals (Sweden)
Khvedelidze Arsen
2018-01-01
Full Text Available The generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. In particular, we consider the generation of random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.
Effect of Smart Meter Measurements Data On Distribution State Estimation
DEFF Research Database (Denmark)
Pokhrel, Basanta Raj; Nainar, Karthikeyan; Bak-Jensen, Birgitte
2018-01-01
Smart distribution grids with renewable energy based generators and demand response resources (DRR) requires accurate state estimators for real time control. Distribution grid state estimators are normally based on accumulated smart meter measurements. However, increase of measurements in the phy......Smart distribution grids with renewable energy based generators and demand response resources (DRR) requires accurate state estimators for real time control. Distribution grid state estimators are normally based on accumulated smart meter measurements. However, increase of measurements...... in the physical grid can enforce significant stress not only on the communication infrastructure but also in the control algorithms. This paper aims to propose a methodology to analyze needed real time smart meter data from low voltage distribution grids and their applicability in distribution state estimation...
The Multivariate Gaussian Probability Distribution
DEFF Research Database (Denmark)
Ahrendt, Peter
2005-01-01
This technical report intends to gather information about the multivariate gaussian distribution, that was previously not (at least to my knowledge) to be found in one place and written as a reference manual. Additionally, some useful tips and tricks are collected that may be useful in practical ...
International Nuclear Information System (INIS)
Bunder, J.E.J.E.; McKenzie, R.H.Ross H.
2001-01-01
We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states. Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled 'spins' which are elements of u(1,1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams
Directory of Open Access Journals (Sweden)
Luis Vicente Chamorro Marcillllo
2013-06-01
Full Text Available Engineering, within its academic and application forms, as well as any formal research work requires the use of statistics and every inferential statistical analysis requires the use of values of probability distribution functions that are generally available in tables. Generally, management of those tables have physical problems (wasteful transport and wasteful consultation and operational (incomplete lists and limited accuracy. The study, “Probability distribution function values in mobile phones”, permitted determining – through a needs survey applied to students involved in statistics studies at Universidad de Nariño – that the best known and most used values correspond to Chi-Square, Binomial, Student’s t, and Standard Normal distributions. Similarly, it showed user’s interest in having the values in question within an alternative means to correct, at least in part, the problems presented by “the famous tables”. To try to contribute to the solution, we built software that allows immediately and dynamically obtaining the values of the probability distribution functions most commonly used by mobile phones.
Shorack, Galen R
2017-01-01
This 2nd edition textbook offers a rigorous introduction to measure theoretic probability with particular attention to topics of interest to mathematical statisticians—a textbook for courses in probability for students in mathematical statistics. It is recommended to anyone interested in the probability underlying modern statistics, providing a solid grounding in the probabilistic tools and techniques necessary to do theoretical research in statistics. For the teaching of probability theory to post graduate statistics students, this is one of the most attractive books available. Of particular interest is a presentation of the major central limit theorems via Stein's method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. Martingale coverage includes coverage of censored data martingales. The text includes measure theoretic...
High throughput nonparametric probability density estimation.
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.
Earth Data Analysis Center, University of New Mexico — USFS, State Forestry, BLM, and DOI fire occurrence point locations from 1987 to 2008 were combined and converted into a fire occurrence probability or density grid...
Statistics and Probability at Secondary Schools in the Federal State of Salzburg: An Empirical Study
Directory of Open Access Journals (Sweden)
Wolfgang Voit
2014-12-01
Full Text Available Knowledge about the practical use of statistics and probability in today's mathematics instruction at secondary schools is vital in order to improve the academic education for future teachers. We have conducted an empirical study among school teachers to inform towards improved mathematics instruction and teacher preparation. The study provides a snapshot into the daily practice of instruction at school. Centered around the four following questions, the status of statistics and probability was examined. Where did the current mathematics teachers study? What relevance do statistics and probability have in school? Which contents are actually taught in class? What kind of continuing education would be desirable for teachers? The study population consisted of all teachers of mathematics at secondary schools in the federal state of Salzburg.
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Liu, W. F.
2013-01-01
Estimation of extreme response and failure probability of structures subjected to ultimate design loads is essential for structural design of wind turbines according to the new standard IEC61400-1. This task is focused on in the present paper in virtue of probability density evolution method (PDEM......), which underlies the schemes of random vibration analysis and structural reliability assessment. The short-term rare failure probability of 5-mega-watt wind turbines, for illustrative purposes, in case of given mean wind speeds and turbulence levels is investigated through the scheme of extreme value...... distribution instead of any other approximate schemes of fitted distribution currently used in statistical extrapolation techniques. Besides, the comparative studies against the classical fitted distributions and the standard Monte Carlo techniques are carried out. Numerical results indicate that PDEM exhibits...
Probability of Failure in Random Vibration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Sørensen, John Dalsgaard
1988-01-01
Close approximations to the first-passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first-passage probability density function and the distribution function for the time interval spent below a barrier before out......-crossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval and thus for the first-passage probability...
Approximation of ruin probabilities via Erlangized scale mixtures
DEFF Research Database (Denmark)
Peralta, Oscar; Rojas-Nandayapa, Leonardo; Xie, Wangyue
2018-01-01
In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér–Lundbergreserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale...... a simple methodology for constructing a sequence of distributions having the form Π⋆G with the purpose of approximating the integrated tail distribution of the claim sizes. Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size...... distribution is modeled as an Erlangized scale mixture. We provide simplified expressions for the approximation of the probability of ruin and construct explicit bounds for the error of approximation. We complement our results with a classical example where the claim sizes are heavy-tailed....
Fortran code for generating random probability vectors, unitaries, and quantum states
Directory of Open Access Journals (Sweden)
Jonas eMaziero
2016-03-01
Full Text Available The usefulness of generating random configurations is recognized in many areas of knowledge. Fortran was born for scientific computing and has been one of the main programming languages in this area since then. And several ongoing projects targeting towards its betterment indicate that it will keep this status in the decades to come. In this article, we describe Fortran codes produced, or organized, for the generation of the following random objects: numbers, probability vectors, unitary matrices, and quantum state vectors and density matrices. Some matrix functions are also included and may be of independent interest.
Optical field-strength polarization of two-mode single-photon states
Energy Technology Data Exchange (ETDEWEB)
Linares, J; Nistal, M C; Barral, D; Moreno, V, E-mail: suso.linares.beiras@usc.e [Optics Area, Department of Applied Physics, Faculty of Physics and School of Optics and Optometry, University of Santiago de Compostela, Campus Universitario Sur s/n, 15782-Santiago de Compostela, Galicia (Spain)
2010-09-15
We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of the two-mode optical field-strength plane. We will show that the mentioned probability distributions along with the values of quantum Stokes parameters allow us to characterize the polarization of a two-mode single-photon state, in an analogous way to the classical case, and to distinguish conceptually between mixture and partially polarized quantum states; in this way, we propose a simple definition of the quantum polarization degree based on the recent concept of distance measure to an unpolarized distribution, which gives rise to a depolarization degree equivalent to an overlapping between the probability distribution of the quantum state and a non-polarized two-mode Gaussian distribution. The work is particularly intended to university physics teachers and graduate students as well as to physicists and specialists concerned with the issue of optical polarization.
Optical field-strength polarization of two-mode single-photon states
International Nuclear Information System (INIS)
Linares, J; Nistal, M C; Barral, D; Moreno, V
2010-01-01
We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of the two-mode optical field-strength plane. We will show that the mentioned probability distributions along with the values of quantum Stokes parameters allow us to characterize the polarization of a two-mode single-photon state, in an analogous way to the classical case, and to distinguish conceptually between mixture and partially polarized quantum states; in this way, we propose a simple definition of the quantum polarization degree based on the recent concept of distance measure to an unpolarized distribution, which gives rise to a depolarization degree equivalent to an overlapping between the probability distribution of the quantum state and a non-polarized two-mode Gaussian distribution. The work is particularly intended to university physics teachers and graduate students as well as to physicists and specialists concerned with the issue of optical polarization.
Quantum processes: probability fluxes, transition probabilities in unit time and vacuum vibrations
International Nuclear Information System (INIS)
Oleinik, V.P.; Arepjev, Ju D.
1989-01-01
Transition probabilities in unit time and probability fluxes are compared in studying the elementary quantum processes -the decay of a bound state under the action of time-varying and constant electric fields. It is shown that the difference between these quantities may be considerable, and so the use of transition probabilities W instead of probability fluxes Π, in calculating the particle fluxes, may lead to serious errors. The quantity W represents the rate of change with time of the population of the energy levels relating partly to the real states and partly to the virtual ones, and it cannot be directly measured in experiment. The vacuum background is shown to be continuously distorted when a perturbation acts on a system. Because of this the viewpoint of an observer on the physical properties of real particles continuously varies with time. This fact is not taken into consideration in the conventional theory of quantum transitions based on using the notion of probability amplitude. As a result, the probability amplitudes lose their physical meaning. All the physical information on quantum dynamics of a system is contained in the mean values of physical quantities. The existence of considerable differences between the quantities W and Π permits one in principle to make a choice of the correct theory of quantum transitions on the basis of experimental data. (author)
DEFF Research Database (Denmark)
Nielsen, Bjørn Gilbert; Jensen, Morten Østergaard; Bohr, Henrik
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....
Scoring Rules for Subjective Probability Distributions
DEFF Research Database (Denmark)
Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd
2017-01-01
significantly due to risk aversion. We characterize an approach for eliciting the entire subjective belief distribution that is minimally biased due to risk aversion. We offer simulated examples to demonstrate the intuition of our approach. We also provide theory to formally characterize our framework. And we...... provide experimental evidence which corroborates our theoretical results. We conclude that for empirically plausible levels of risk aversion, one can reliably elicit most important features of the latent subjective belief distribution without undertaking calibration for risk attitudes providing one...
Energy Technology Data Exchange (ETDEWEB)
Cai, H.; Wang, M.; Elgowainy, A.; Han, J. (Energy Systems)
2012-07-06
Greenhouse gas (CO{sub 2}, CH{sub 4} and N{sub 2}O, hereinafter GHG) and criteria air pollutant (CO, NO{sub x}, VOC, PM{sub 10}, PM{sub 2.5} and SO{sub x}, hereinafter CAP) emission factors for various types of power plants burning various fuels with different technologies are important upstream parameters for estimating life-cycle emissions associated with alternative vehicle/fuel systems in the transportation sector, especially electric vehicles. The emission factors are typically expressed in grams of GHG or CAP per kWh of electricity generated by a specific power generation technology. This document describes our approach for updating and expanding GHG and CAP emission factors in the GREET (Greenhouse Gases, Regulated Emissions, and Energy Use in Transportation) model developed at Argonne National Laboratory (see Wang 1999 and the GREET website at http://greet.es.anl.gov/main) for various power generation technologies. These GHG and CAP emissions are used to estimate the impact of electricity use by stationary and transportation applications on their fuel-cycle emissions. The electricity generation mixes and the fuel shares attributable to various combustion technologies at the national, regional and state levels are also updated in this document. The energy conversion efficiencies of electric generating units (EGUs) by fuel type and combustion technology are calculated on the basis of the lower heating values of each fuel, to be consistent with the basis used in GREET for transportation fuels. On the basis of the updated GHG and CAP emission factors and energy efficiencies of EGUs, the probability distribution functions (PDFs), which are functions that describe the relative likelihood for the emission factors and energy efficiencies as random variables to take on a given value by the integral of their own probability distributions, are updated using best-fit statistical curves to characterize the uncertainties associated with GHG and CAP emissions in life
Probability densities and Lévy densities
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler
For positive Lévy processes (i.e. subordinators) formulae are derived that express the probability density or the distribution function in terms of power series in time t. The applicability of the results to finance and to turbulence is briefly indicated.......For positive Lévy processes (i.e. subordinators) formulae are derived that express the probability density or the distribution function in terms of power series in time t. The applicability of the results to finance and to turbulence is briefly indicated....
Grimmett, Geoffrey
2014-01-01
Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit th...
Probability theory and mathematical statistics for engineers
Pugachev, V S
1984-01-01
Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector
Distributed Graph-Based State Space Generation
Blom, Stefan; Kant, Gijs; Rensink, Arend; De Lara, J.; Varro, D.
LTSMIN provides a framework in which state space generation can be distributed easily over many cores on a single compute node, as well as over multiple compute nodes. The tool works on the basis of a vector representation of the states; the individual cores are assigned the task of computing all
Propensity, Probability, and Quantum Theory
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
VIBRATION ISOLATION SYSTEM PROBABILITY ANALYSIS
Directory of Open Access Journals (Sweden)
Smirnov Vladimir Alexandrovich
2012-10-01
Full Text Available The article deals with the probability analysis for a vibration isolation system of high-precision equipment, which is extremely sensitive to low-frequency oscillations even of submicron amplitude. The external sources of low-frequency vibrations may include the natural city background or internal low-frequency sources inside buildings (pedestrian activity, HVAC. Taking Gauss distribution into account, the author estimates the probability of the relative displacement of the isolated mass being still lower than the vibration criteria. This problem is being solved in the three dimensional space, evolved by the system parameters, including damping and natural frequency. According to this probability distribution, the chance of exceeding the vibration criteria for a vibration isolation system is evaluated. Optimal system parameters - damping and natural frequency - are being developed, thus the possibility of exceeding vibration criteria VC-E and VC-D is assumed to be less than 0.04.
Mielke, Steven L.; Truhlar, Donald G.; Schwenke, David W.
1991-01-01
Improved techniques and well-optimized basis sets are presented for application of the outgoing wave variational principle to calculate converged quantum mechanical reaction probabilities. They are illustrated with calculations for the reactions D + H2 yields HD + H with total angular momentum J = 3 and F + H2 yields HF + H with J = 0 and 3. The optimization involves the choice of distortion potential, the grid for calculating half-integrated Green's functions, the placement, width, and number of primitive distributed Gaussians, and the computationally most efficient partition between dynamically adapted and primitive basis functions. Benchmark calculations with 224-1064 channels are presented.
Directory of Open Access Journals (Sweden)
Pradeep K. Goyal
2011-09-01
Full Text Available This paper presents a study conducted on the probabilistic distribution of key cyclone parameters and the cyclonic wind speed by analyzing the cyclone track records obtained from India meteorological department for east coast region of India. The dataset of historical landfalling storm tracks in India from 1975–2007 with latitude /longitude and landfall locations are used to map the cyclone tracks in a region of study. The statistical tests were performed to find a best fit distribution to the track data for each cyclone parameter. These parameters include central pressure difference, the radius of maximum wind speed, the translation velocity, track angle with site and are used to generate digital simulated cyclones using wind field simulation techniques. For this, different sets of values for all the cyclone key parameters are generated randomly from their probability distributions. Using these simulated values of the cyclone key parameters, the distribution of wind velocity at a particular site is obtained. The same distribution of wind velocity at the site is also obtained from actual track records and using the distributions of the cyclone key parameters as published in the literature. The simulated distribution is compared with the wind speed distributions obtained from actual track records. The findings are useful in cyclone disaster mitigation.
Spatial probability aids visual stimulus discrimination
Directory of Open Access Journals (Sweden)
Michael Druker
2010-08-01
Full Text Available We investigated whether the statistical predictability of a target's location would influence how quickly and accurately it was classified. Recent results have suggested that spatial probability can be a cue for the allocation of attention in visual search. One explanation for probability cuing is spatial repetition priming. In our two experiments we used probability distributions that were continuous across the display rather than relying on a few arbitrary screen locations. This produced fewer spatial repeats and allowed us to dissociate the effect of a high probability location from that of short-term spatial repetition. The task required participants to quickly judge the color of a single dot presented on a computer screen. In Experiment 1, targets were more probable in an off-center hotspot of high probability that gradually declined to a background rate. Targets garnered faster responses if they were near earlier target locations (priming and if they were near the high probability hotspot (probability cuing. In Experiment 2, target locations were chosen on three concentric circles around fixation. One circle contained 80% of targets. The value of this ring distribution is that it allowed for a spatially restricted high probability zone in which sequentially repeated trials were not likely to be physically close. Participant performance was sensitive to the high-probability circle in addition to the expected effects of eccentricity and the distance to recent targets. These two experiments suggest that inhomogeneities in spatial probability can be learned and used by participants on-line and without prompting as an aid for visual stimulus discrimination and that spatial repetition priming is not a sufficient explanation for this effect. Future models of attention should consider explicitly incorporating the probabilities of targets locations and features.
Energy Technology Data Exchange (ETDEWEB)
O' Rourke, Patrick Francis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-10-27
The purpose of this report is to provide the reader with an understanding of how a Monte Carlo neutron transport code was written, developed, and evolved to calculate the probability distribution functions (PDFs) and their moments for the neutron number at a final time as well as the cumulative fission number, along with introducing several basic Monte Carlo concepts.
Lei, Yaguo; Liu, Zongyao; Wang, Delong; Yang, Xiao; Liu, Huan; Lin, Jing
2018-06-01
Tooth damage often causes a reduction in gear mesh stiffness. Thus time-varying mesh stiffness (TVMS) can be treated as an indication of gear health conditions. This study is devoted to investigating the mesh stiffness variations of a pair of external spur gears with tooth pitting, and proposes a new model for describing tooth pitting based on probability distribution. In the model, considering the appearance and development process of tooth pitting, we model the pitting on the surface of spur gear teeth as a series of pits with a uniform distribution in the direction of tooth width and a normal distribution in the direction of tooth height, respectively. In addition, four pitting degrees, from no pitting to severe pitting, are modeled. Finally, influences of tooth pitting on TVMS are analyzed in details and the proposed model is validated by comparing with a finite element model. The comparison results show that the proposed model is effective for the TVMS evaluations of pitting gears.
Probability distribution functions for ELM bursts in a series of JET tokamak discharges
International Nuclear Information System (INIS)
Greenhough, J; Chapman, S C; Dendy, R O; Ward, D J
2003-01-01
A novel statistical treatment of the full raw edge localized mode (ELM) signal from a series of previously studied JET plasmas is tested. The approach involves constructing probability distribution functions (PDFs) for ELM amplitudes and time separations, and quantifying the fit between the measured PDFs and model distributions (Gaussian, inverse exponential) and Poisson processes. Uncertainties inherent in the discreteness of the raw signal require the application of statistically rigorous techniques to distinguish ELM data points from background, and to extrapolate peak amplitudes. The accuracy of PDF construction is further constrained by the relatively small number of ELM bursts (several hundred) in each sample. In consequence the statistical technique is found to be difficult to apply to low frequency (typically Type I) ELMs, so the focus is narrowed to four JET plasmas with high frequency (typically Type III) ELMs. The results suggest that there may be several fundamentally different kinds of Type III ELMing process at work. It is concluded that this novel statistical treatment can be made to work, may have wider applications to ELM data, and has immediate practical value as an additional quantitative discriminant between classes of ELMing behaviour
Directory of Open Access Journals (Sweden)
Michael J. Markham
2011-07-01
Full Text Available Some problems occurring in Expert Systems can be resolved by employing a causal (Bayesian network and methodologies exist for this purpose. These require data in a specific form and make assumptions about the independence relationships involved. Methodologies using Maximum Entropy (ME are free from these conditions and have the potential to be used in a wider context including systems consisting of given sets of linear and independence constraints, subject to consistency and convergence. ME can also be used to validate results from the causal network methodologies. Three ME methods for determining the prior probability distribution of causal network systems are considered. The first method is Sequential Maximum Entropy in which the computation of a progression of local distributions leads to the over-all distribution. This is followed by development of the Method of Tribus. The development takes the form of an algorithm that includes the handling of explicit independence constraints. These fall into two groups those relating parents of vertices, and those deduced from triangulation of the remaining graph. The third method involves a variation in the part of that algorithm which handles independence constraints. Evidence is presented that this adaptation only requires the linear constraints and the parental independence constraints to emulate the second method in a substantial class of examples.
Collision Probability Analysis
DEFF Research Database (Denmark)
Hansen, Peter Friis; Pedersen, Preben Terndrup
1998-01-01
It is the purpose of this report to apply a rational model for prediction of ship-ship collision probabilities as function of the ship and the crew characteristics and the navigational environment for MS Dextra sailing on a route between Cadiz and the Canary Islands.The most important ship and crew...... characteristics are: ship speed, ship manoeuvrability, the layout of the navigational bridge, the radar system, the number and the training of navigators, the presence of a look out etc. The main parameters affecting the navigational environment are ship traffic density, probability distributions of wind speeds...... probability, i.e. a study of the navigator's role in resolving critical situations, a causation factor is derived as a second step.The report documents the first step in a probabilistic collision damage analysis. Future work will inlcude calculation of energy released for crushing of structures giving...
Energy Technology Data Exchange (ETDEWEB)
Wampler, William R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Myers, Samuel M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Modine, Normand A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-09-01
The energy-dependent probability density of tunneled carrier states for arbitrarily specified longitudinal potential-energy profiles in planar bipolar devices is numerically computed using the scattering method. Results agree accurately with a previous treatment based on solution of the localized eigenvalue problem, where computation times are much greater. These developments enable quantitative treatment of tunneling-assisted recombination in irradiated heterojunction bipolar transistors, where band offsets may enhance the tunneling effect by orders of magnitude. The calculations also reveal the density of non-tunneled carrier states in spatially varying potentials, and thereby test the common approximation of uniform- bulk values for such densities.
International Nuclear Information System (INIS)
Rechard, Rob P.; Tierney, Martin S.
2005-01-01
A managed process was used to consistently and traceably develop probability distributions for parameters representing epistemic uncertainty in four preliminary and the final 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP). The key to the success of the process was the use of a three-member team consisting of a Parameter Task Leader, PA Analyst, and Subject Matter Expert. This team, in turn, relied upon a series of guidelines for selecting distribution types. The primary function of the guidelines was not to constrain the actual process of developing a parameter distribution but rather to establish a series of well-defined steps where recognized methods would be consistently applied to all parameters. An important guideline was to use a small set of distributions satisfying the maximum entropy formalism. Another important guideline was the consistent use of the log transform for parameters with large ranges (i.e. maximum/minimum>10 3 ). A parameter development team assigned 67 probability density functions (PDFs) in the 1989 PA and 236 PDFs in the 1996 PA using these and other guidelines described
Concepts of probability theory
Pfeiffer, Paul E
1979-01-01
Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.
Choice probability generating functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel
2010-01-01
This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice...... probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications....... The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended to competing risk survival models....
Generation of distributed W-states over long distances
Li, Yi
2017-08-01
Ultra-secure quantum communication between distant locations requires distributed entangled states between nodes. Various methodologies have been proposed to tackle this technological challenge, of which the so-called DLCZ protocol is the most promising and widely adopted scheme. This paper aims to extend this well-known protocol to a multi-node setting where the entangled W-state is generated between nodes over long distances. The generation of multipartite W-states is the foundation of quantum networks, paving the way for quantum communication and distributed quantum computation.
Energy Technology Data Exchange (ETDEWEB)
Ramos, Alessandro Candido Lopes [CELG - Companhia Energetica de Goias, Goiania, GO (Brazil). Generation and Transmission. System' s Operation Center], E-mail: alessandro.clr@celg.com.br; Batista, Adalberto Jose [Universidade Federal de Goias (UFG), Goiania, GO (Brazil)], E-mail: batista@eee.ufg.br; Leborgne, Roberto Chouhy [Universidade Federal do Rio Grande do Sul (UFRS), Porto Alegre, RS (Brazil)], E-mail: rcl@ece.ufrgs.br; Emiliano, Pedro Henrique Mota, E-mail: ph@phph.com.br
2009-07-01
This article presents the impact of distributed generation in studies of voltage sags caused by faults in the electrical system. We simulated short-circuit-to-ground in 62 lines of 230, 138, 69 and 13.8 kV that are part of the electrical system of the city of Goiania, of Goias state . For each fault position was monitored the bus voltage of 380 V in an industrial consumer sensitive to such sags. Were inserted different levels of GD near the consumer. The simulations of a short circuit, with the monitoring bar 380 V, were performed again. A study using stochastic simulation Monte Carlo (SMC) was performed to obtain, at each level of GD, the probability curves and sags of the probability density and its voltage class. With these curves were obtained the average number of sags according to each class, that the consumer bar may be submitted annually. The simulations were performed using the Program Analysis of Simultaneous Faults - ANAFAS. In order to overcome the intrinsic limitations of the methods of simulation of this program and allow data entry via windows, a computational tool was developed in Java language. Data processing was done using the MATLAB software.
Energy Technology Data Exchange (ETDEWEB)
Shabbir, Aqsa
2016-07-07
In this doctoral work, pattern recognition techniques are developed and applied to data from tokamak plasmas, in order to contribute to a systematic analysis of edge-localized modes (ELMs). We employ probabilistic models for a quantitative data description geared towards an enhanced systematization of ELM phenomenology. Hence, we start from the point of view that the fundamental object resulting from the observation of a system is a probability distribution, with every single measurement providing a sample from this distribution. In exploring the patterns emerging from the various ELM regimes and relations, we need methods that can handle the intrinsic probabilistic nature of the data. The original contributions of this work are twofold. First, several novel pattern recognition methods in non-Euclidean spaces of probability distribution functions (PDFs) are developed and validated. The second main contribution lies in the application of these and other techniques to a systematic analysis of ELMs in tokamak plasmas. In regard to the methodological aims of the work, we employ the framework of information geometry to develop pattern visualization and classification methods in spaces of probability distributions. In information geometry, a family of probability distributions is considered as a Riemannian manifold. Every point on the manifold represents a single PDF and the distribution parameters provide local coordinates on the manifold. The Fisher information plays the role of a Riemannian metric tensor, enabling calculation of geodesic curves on the surface. The length of such curves yields the geodesic distance (GD) on probabilistic manifolds, which is a natural similarity (distance) measure between PDFs. Equipped with a suitable distance measure, we extrapolate several distance-based pattern recognition methods to the manifold setting. This includes k-nearest neighbor (kNN) and conformal predictor (CP) methods for classification, as well as multidimensional
International Nuclear Information System (INIS)
Shabbir, Aqsa
2016-01-01
In this doctoral work, pattern recognition techniques are developed and applied to data from tokamak plasmas, in order to contribute to a systematic analysis of edge-localized modes (ELMs). We employ probabilistic models for a quantitative data description geared towards an enhanced systematization of ELM phenomenology. Hence, we start from the point of view that the fundamental object resulting from the observation of a system is a probability distribution, with every single measurement providing a sample from this distribution. In exploring the patterns emerging from the various ELM regimes and relations, we need methods that can handle the intrinsic probabilistic nature of the data. The original contributions of this work are twofold. First, several novel pattern recognition methods in non-Euclidean spaces of probability distribution functions (PDFs) are developed and validated. The second main contribution lies in the application of these and other techniques to a systematic analysis of ELMs in tokamak plasmas. In regard to the methodological aims of the work, we employ the framework of information geometry to develop pattern visualization and classification methods in spaces of probability distributions. In information geometry, a family of probability distributions is considered as a Riemannian manifold. Every point on the manifold represents a single PDF and the distribution parameters provide local coordinates on the manifold. The Fisher information plays the role of a Riemannian metric tensor, enabling calculation of geodesic curves on the surface. The length of such curves yields the geodesic distance (GD) on probabilistic manifolds, which is a natural similarity (distance) measure between PDFs. Equipped with a suitable distance measure, we extrapolate several distance-based pattern recognition methods to the manifold setting. This includes k-nearest neighbor (kNN) and conformal predictor (CP) methods for classification, as well as multidimensional
Burst suppression probability algorithms: state-space methods for tracking EEG burst suppression
Chemali, Jessica; Ching, ShiNung; Purdon, Patrick L.; Solt, Ken; Brown, Emery N.
2013-10-01
Objective. Burst suppression is an electroencephalogram pattern in which bursts of electrical activity alternate with an isoelectric state. This pattern is commonly seen in states of severely reduced brain activity such as profound general anesthesia, anoxic brain injuries, hypothermia and certain developmental disorders. Devising accurate, reliable ways to quantify burst suppression is an important clinical and research problem. Although thresholding and segmentation algorithms readily identify burst suppression periods, analysis algorithms require long intervals of data to characterize burst suppression at a given time and provide no framework for statistical inference. Approach. We introduce the concept of the burst suppression probability (BSP) to define the brain's instantaneous propensity of being in the suppressed state. To conduct dynamic analyses of burst suppression we propose a state-space model in which the observation process is a binomial model and the state equation is a Gaussian random walk. We estimate the model using an approximate expectation maximization algorithm and illustrate its application in the analysis of rodent burst suppression recordings under general anesthesia and a patient during induction of controlled hypothermia. Main result. The BSP algorithms track burst suppression on a second-to-second time scale, and make possible formal statistical comparisons of burst suppression at different times. Significance. The state-space approach suggests a principled and informative way to analyze burst suppression that can be used to monitor, and eventually to control, the brain states of patients in the operating room and in the intensive care unit.
States of Cybersecurity: Electricity Distribution System Discussions
Energy Technology Data Exchange (ETDEWEB)
Pena, Ivonne [National Renewable Energy Lab. (NREL), Golden, CO (United States); Ingram, Michael [National Renewable Energy Lab. (NREL), Golden, CO (United States); Martin, Maurice [National Renewable Energy Lab. (NREL), Golden, CO (United States)
2017-03-16
State and local entities that oversee the reliable, affordable provision of electricity are faced with growing and evolving threats from cybersecurity risks to our nation's electricity distribution system. All-hazards system resilience is a shared responsibility among electric utilities and their regulators or policy-setting boards of directors. Cybersecurity presents new challenges and should be a focus for states, local governments, and Native American tribes that are developing energy-assurance plans to protect critical infrastructure. This research sought to investigate the implementation of governance and policy at the distribution utility level that facilitates cybersecurity preparedness to inform the U.S. Department of Energy (DOE), Office of Energy Policy and Systems Analysis; states; local governments; and other stakeholders on the challenges, gaps, and opportunities that may exist for future analysis. The need is urgent to identify the challenges and inconsistencies in how cybersecurity practices are being applied across the United States to inform the development of best practices, mitigations, and future research and development investments in securing the electricity infrastructure. By examining the current practices and applications of cybersecurity preparedness, this report seeks to identify the challenges and persistent gaps between policy and execution and reflect the underlying motivations of distinct utility structures as they play out at the local level. This study aims to create an initial baseline of cybersecurity preparedness within the distribution electricity sector. The focus of this study is on distribution utilities not bound by the cybersecurity guidelines of the North American Electric Reliability Corporation (NERC) to examine the range of mechanisms taken by state regulators, city councils that own municipal utilities, and boards of directors of rural cooperatives.
Investigation of Probability Distributions Using Dice Rolling Simulation
Lukac, Stanislav; Engel, Radovan
2010-01-01
Dice are considered one of the oldest gambling devices and thus many mathematicians have been interested in various dice gambling games in the past. Dice have been used to teach probability, and dice rolls can be effectively simulated using technology. The National Council of Teachers of Mathematics (NCTM) recommends that teachers use simulations…
Strength distributions of electromagnetic transitions in light nuclei
International Nuclear Information System (INIS)
Kostin, V.Ya.; Koval', A.A.; Kopanets, E.G.; Tsytko, S.P.
1980-01-01
Distributions of probabilities of electromagnetic transitions from resonance levels of light nuclei with masses A=Z-40 for eight types of transition (epsilon1, epsilon2, M1, M8, isoscalar and isovector) are obtained. Recommended upper limits (RUL) of transition probabilities are determined for each type of transitions. A comparison with analogous characteristics for transitions between bound states is carried out. It has been causes found that RUL for resonance states substantially differ from RUL for transitions between bound states. Possible causes of such difference are discussed
Distributed Dynamic State Estimation with Extended Kalman Filter
Energy Technology Data Exchange (ETDEWEB)
Du, Pengwei; Huang, Zhenyu; Sun, Yannan; Diao, Ruisheng; Kalsi, Karanjit; Anderson, Kevin K.; Li, Yulan; Lee, Barry
2011-08-04
Increasing complexity associated with large-scale renewable resources and novel smart-grid technologies necessitates real-time monitoring and control. Our previous work applied the extended Kalman filter (EKF) with the use of phasor measurement data (PMU) for dynamic state estimation. However, high computation complexity creates significant challenges for real-time applications. In this paper, the problem of distributed dynamic state estimation is investigated. One domain decomposition method is proposed to utilize decentralized computing resources. The performance of distributed dynamic state estimation is tested on a 16-machine, 68-bus test system.
International Nuclear Information System (INIS)
Misdaq, M.A.; Bakhchi, A.; Ktata, A.; Koutit, A.; Lamine, J.; Ait nouh, F.; Oufni, L.
2000-01-01
A method based on using solid state nuclear track detectors (SSNTD) CR- 39 and LR-115 type II and calculating the probabilities for the alpha particles emitted by the uranium and thorium series to reach and be registered on these films was utilized for uranium and thorium contents determination in various geological samples. The distribution of uranium and thorium in different volcanic rocks has been investigated using the track fission method. In this work, the uranium and thorium contents have been determined in different volcanic rock samples by using CR-39 and LR-115 type II solid state nuclear track detectors (SSNTD). The mean critical angles of etching of the solid state nuclear track detectors utilized have been calculated. A petrographical study of the volcanic rock thin layers studied has been conducted. The uranium and thorium distribution inside different rock thin layers has been studied. The mechanism of inclusion of the uranium and thorium nuclei inside the volcanic rock samples studied has been investigated. (author)
Directory of Open Access Journals (Sweden)
Paul B. Slater
2015-01-01
Full Text Available Previously, a formula, incorporating a 5F4 hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments ρPTnρk/ρk of 4×4 density-matrices (ρ and their partial transposes (|ρPT|, was applied with k=0 to the generalized two-qubit separability probability question. The formula can, furthermore, be viewed, as we note here, as an averaging over “induced measures in the space of mixed quantum states.” The associated induced-measure separability probabilities (k=1,2,… are found—via a high-precision density approximation procedure—to assume interesting, relatively simple rational values in the two-re[al]bit (α=1/2, (standard two-qubit (α=1, and two-quater[nionic]bit (α=2 cases. We deduce rather simple companion (rebit, qubit, quaterbit, … formulas that successfully reproduce the rational values assumed for general k. These formulas are observed to share certain features, possibly allowing them to be incorporated into a single master formula.
Drakos, Nicole E; Wahl, Lindi M
2015-12-01
Theoretical approaches are essential to our understanding of the complex dynamics of mobile genetic elements (MGEs) within genomes. Recently, the birth-death-diversification model was developed to describe the dynamics of mobile promoters (MPs), a particular class of MGEs in prokaryotes. A unique feature of this model is that genetic diversification of elements was included. To explore the implications of diversification on the longterm fate of MGE lineages, in this contribution we analyze the extinction probabilities, extinction times and equilibrium solutions of the birth-death-diversification model. We find that diversification increases both the survival and growth rate of MGE families, but the strength of this effect depends on the rate of horizontal gene transfer (HGT). We also find that the distribution of MGE families per genome is not necessarily monotonically decreasing, as observed for MPs, but may have a peak in the distribution that is related to the HGT rate. For MPs specifically, we find that new families have a high extinction probability, and predict that the number of MPs is increasing, albeit at a very slow rate. Additionally, we develop an extension of the birth-death-diversification model which allows MGEs in different regions of the genome, for example coding and non-coding, to be described by different rates. This extension may offer a potential explanation as to why the majority of MPs are located in non-promoter regions of the genome. Copyright © 2015 Elsevier Inc. All rights reserved.
Distribution Pattern of Healthcare Facilities in Osun State, Nigeria ...
African Journals Online (AJOL)
`123456789jkl''''#
existing spatial pattern of distribution of healthcare facilities play very prominent role in gauging the level of efficiency or ... distribution pattern of healthcare facilities in the thirty local government areas in Osun State, Nigeria. Twelve indices ... (Federal, State and Local) always budget huge .... This, we believe, will help policy.
Optimal design of unit hydrographs using probability distribution and ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
optimization formulation is solved using binary-coded genetic algorithms. The number of variables to ... Unit hydrograph; rainfall-runoff; hydrology; genetic algorithms; optimization; probability ..... Application of the model. Data derived from the ...
Continuous variable quantum key distribution with modulated entangled states
DEFF Research Database (Denmark)
Madsen, Lars S; Usenko, Vladyslav C.; Lassen, Mikael
2012-01-01
Quantum key distribution enables two remote parties to grow a shared key, which they can use for unconditionally secure communication over a certain distance. The maximal distance depends on the loss and the excess noise of the connecting quantum channel. Several quantum key distribution schemes...... based on coherent states and continuous variable measurements are resilient to high loss in the channel, but are strongly affected by small amounts of channel excess noise. Here we propose and experimentally address a continuous variable quantum key distribution protocol that uses modulated fragile...... entangled states of light to greatly enhance the robustness to channel noise. We experimentally demonstrate that the resulting quantum key distribution protocol can tolerate more noise than the benchmark set by the ideal continuous variable coherent state protocol. Our scheme represents a very promising...
Energy Technology Data Exchange (ETDEWEB)
Weise, K.
2004-06-01
Recent metrological developments concerning measurement uncertainty, founded on Bayesian statistics, give rise to a revision of several parts of the DIN 25482 and ISO 11929 standard series. These series stipulate detection limits and decision thresholds for ionizing-radiation measurements. Part 3 and, respectively, part 4 of them deal with measurements by use of linear-scale analogue ratemeters. A normal frequency distribution of the momentary ratemeter indication for a fixed count rate value is assumed. The actual distribution, which is first calculated numerically by solving an integral equation, differs, however, considerably from the normal distribution although this one represents an approximation of it for sufficiently large values of the count rate to be measured. As is shown, this similarly holds true for the Bayesian probability distribution of the count rate for sufficiently large given measured values indicated by the ratemeter. This distribution follows from the first one mentioned by means of the Bayes theorem. Its expectation value and variance are needed for the standards to be revised on the basis of Bayesian statistics. Simple expressions are given by the present standards for estimating these parameters and for calculating the detection limit and the decision threshold. As is also shown, the same expressions can similarly be used as sufficient approximations by the revised standards if, roughly, the present indicated value exceeds the reciprocal ratemeter relaxation time constant. (orig.)
Path probabilities of continuous time random walks
International Nuclear Information System (INIS)
Eule, Stephan; Friedrich, Rudolf
2014-01-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)
International Nuclear Information System (INIS)
Bhattacharyya, Pratip; Chakrabarti, Bikas K
2008-01-01
We study different ways of determining the mean distance (r n ) between a reference point and its nth neighbour among random points distributed with uniform density in a D-dimensional Euclidean space. First, we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating (r n ). Next, we describe two alternative means of deriving the exact expression of (r n ): we review the method using absolute probability and develop an alternative method using conditional probability. Finally, we obtain an approximation to (r n ) from the mean volume between the reference point and its nth neighbour and compare it with the heuristic and exact results
An Empirical Method to Fuse Partially Overlapping State Vectors for Distributed State Estimation
Sijs, J.; Hanebeck, U.; Noack, B.
2013-01-01
State fusion is a method for merging multiple estimates of the same state into a single fused estimate. Dealing with multiple estimates is one of the main concerns in distributed state estimation, where an estimated value of the desired state vector is computed in each node of a networked system.
Furbish, David; Schmeeckle, Mark; Schumer, Rina; Fathel, Siobhan
2016-01-01
We describe the most likely forms of the probability distributions of bed load particle velocities, accelerations, hop distances, and travel times, in a manner that formally appeals to inferential statistics while honoring mechanical and kinematic constraints imposed by equilibrium transport conditions. The analysis is based on E. Jaynes's elaboration of the implications of the similarity between the Gibbs entropy in statistical mechanics and the Shannon entropy in information theory. By maximizing the information entropy of a distribution subject to known constraints on its moments, our choice of the form of the distribution is unbiased. The analysis suggests that particle velocities and travel times are exponentially distributed and that particle accelerations follow a Laplace distribution with zero mean. Particle hop distances, viewed alone, ought to be distributed exponentially. However, the covariance between hop distances and travel times precludes this result. Instead, the covariance structure suggests that hop distances follow a Weibull distribution. These distributions are consistent with high-resolution measurements obtained from high-speed imaging of bed load particle motions. The analysis brings us closer to choosing distributions based on our mechanical insight.
Directory of Open Access Journals (Sweden)
Han Liwei
2014-07-01
Full Text Available Monitoring data on an earth-rockfill dam constitutes a form of spatial data. Such data include much uncertainty owing to the limitation of measurement information, material parameters, load, geometry size, initial conditions, boundary conditions and the calculation model. So the cloud probability density of the monitoring data must be addressed. In this paper, the cloud theory model was used to address the uncertainty transition between the qualitative concept and the quantitative description. Then an improved algorithm of cloud probability distribution density based on a backward cloud generator was proposed. This was used to effectively convert certain parcels of accurate data into concepts which can be described by proper qualitative linguistic values. Such qualitative description was addressed as cloud numerical characteristics-- {Ex, En, He}, which could represent the characteristics of all cloud drops. The algorithm was then applied to analyze the observation data of a piezometric tube in an earth-rockfill dam. And experiment results proved that the proposed algorithm was feasible, through which, we could reveal the changing regularity of piezometric tube’s water level. And the damage of the seepage in the body was able to be found out.
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
Geometry of Gaussian quantum states
International Nuclear Information System (INIS)
Link, Valentin; Strunz, Walter T
2015-01-01
We study the Hilbert–Schmidt measure on the manifold of mixed Gaussian states in multi-mode continuous variable quantum systems. An analytical expression for the Hilbert–Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert–Schmidt measure. (paper)
A Database Approach to Distributed State Space Generation
Blom, Stefan; Lisser, Bert; van de Pol, Jan Cornelis; Weber, M.
2007-01-01
We study distributed state space generation on a cluster of workstations. It is explained why state space partitioning by a global hash function is problematic when states contain variables from unbounded domains, such as lists or other recursive datatypes. Our solution is to introduce a database
A Database Approach to Distributed State Space Generation
Blom, Stefan; Lisser, Bert; van de Pol, Jan Cornelis; Weber, M.; Cerna, I.; Haverkort, Boudewijn R.H.M.
2008-01-01
We study distributed state space generation on a cluster of workstations. It is explained why state space partitioning by a global hash function is problematic when states contain variables from unbounded domains, such as lists or other recursive datatypes. Our solution is to introduce a database
Li, Ning; Liu, Xueqin; Xie, Wei; Wu, Jidong; Zhang, Peng
2013-01-01
New features of natural disasters have been observed over the last several years. The factors that influence the disasters' formation mechanisms, regularity of occurrence and main characteristics have been revealed to be more complicated and diverse in nature than previously thought. As the uncertainty involved increases, the variables need to be examined further. This article discusses the importance and the shortage of multivariate analysis of natural disasters and presents a method to estimate the joint probability of the return periods and perform a risk analysis. Severe dust storms from 1990 to 2008 in Inner Mongolia were used as a case study to test this new methodology, as they are normal and recurring climatic phenomena on Earth. Based on the 79 investigated events and according to the dust storm definition with bivariate, the joint probability distribution of severe dust storms was established using the observed data of maximum wind speed and duration. The joint return periods of severe dust storms were calculated, and the relevant risk was analyzed according to the joint probability. The copula function is able to simulate severe dust storm disasters accurately. The joint return periods generated are closer to those observed in reality than the univariate return periods and thus have more value in severe dust storm disaster mitigation, strategy making, program design, and improvement of risk management. This research may prove useful in risk-based decision making. The exploration of multivariate analysis methods can also lay the foundation for further applications in natural disaster risk analysis. © 2012 Society for Risk Analysis.
Constructing inverse probability weights for continuous exposures: a comparison of methods.
Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S
2014-03-01
Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.
International Nuclear Information System (INIS)
Strigini, Lorenzo; Wright, David
2014-01-01
When deciding whether to accept into service a new safety-critical system, or choosing between alternative systems, uncertainty about the parameters that affect future failure probability may be a major problem. This uncertainty can be extreme if there is the possibility of unknown design errors (e.g. in software), or wide variation between nominally equivalent components. We study the effect of parameter uncertainty on future reliability (survival probability), for systems required to have low risk of even only one failure or accident over the long term (e.g. their whole operational lifetime) and characterised by a single reliability parameter (e.g. probability of failure per demand – pfd). A complete mathematical treatment requires stating a probability distribution for any parameter with uncertain value. This is hard, so calculations are often performed using point estimates, like the expected value. We investigate conditions under which such simplified descriptions yield reliability values that are sure to be pessimistic (or optimistic) bounds for a prediction based on the true distribution. Two important observations are (i) using the expected value of the reliability parameter as its true value guarantees a pessimistic estimate of reliability, a useful property in most safety-related decisions; (ii) with a given expected pfd, broader distributions (in a formally defined meaning of “broader”), that is, systems that are a priori “less predictable”, lower the risk of failures or accidents. Result (i) justifies the simplification of using a mean in reliability modelling; we discuss within which scope this justification applies, and explore related scenarios, e.g. how things improve if we can test the system before operation. Result (ii) not only offers more flexible ways of bounding reliability predictions, but also has important, often counter-intuitive implications for decision making in various areas, like selection of components, project management
Energy Technology Data Exchange (ETDEWEB)
Cowart, R.; Harrington, C.; Moskovitz, D.; Shirley, W.; Weston, F.; Sedano, R.
2002-10-01
Designing and implementing credit-based pilot programs for distributed resources distribution is a low-cost, low-risk opportunity to find out how these resources can help defer or avoid costly electric power system (utility grid) distribution upgrades. This report describes implementation options for deaveraged distribution credits and distributed resource development zones. Developing workable programs implementing these policies can dramatically increase the deployment of distributed resources in ways that benefit distributed resource vendors, users, and distribution utilities. This report is one in the State Electricity Regulatory Policy and Distributed Resources series developed under contract to NREL (see Annual Technical Status Report of the Regulatory Assistance Project: September 2000-September 2001, NREL/SR-560-32733). Other titles in this series are: (1) Accommodating Distributed Resources in Wholesale Markets, NREL/SR-560-32497; (2) Distributed Resources and Electric System Re liability, NREL/SR-560-32498; (3) Distribution System Cost Methodologies for Distributed Generation, NREL/SR-560-32500; (4) Distribution System Cost Methodologies for Distributed Generation Appendices, NREL/SR-560-32501.
Finding upper bounds for software failure probabilities - experiments and results
International Nuclear Information System (INIS)
Kristiansen, Monica; Winther, Rune
2005-09-01
This report looks into some aspects of using Bayesian hypothesis testing to find upper bounds for software failure probabilities. In the first part, the report evaluates the Bayesian hypothesis testing approach for finding upper bounds for failure probabilities of single software components. The report shows how different choices of prior probability distributions for a software component's failure probability influence the number of tests required to obtain adequate confidence in a software component. In the evaluation, both the effect of the shape of the prior distribution as well as one's prior confidence in the software component were investigated. In addition, different choices of prior probability distributions are discussed based on their relevance in a software context. In the second part, ideas on how the Bayesian hypothesis testing approach can be extended to assess systems consisting of multiple software components are given. One of the main challenges when assessing systems consisting of multiple software components is to include dependency aspects in the software reliability models. However, different types of failure dependencies between software components must be modelled differently. Identifying different types of failure dependencies are therefore an important condition for choosing a prior probability distribution, which correctly reflects one's prior belief in the probability for software components failing dependently. In this report, software components include both general in-house software components, as well as pre-developed software components (e.g. COTS, SOUP, etc). (Author)
International Nuclear Information System (INIS)
Booth, J.T.; Zavgorodni, S.F.; Royal Adelaide Hospital, SA
2001-01-01
Uncertainty in the precise quantity of radiation dose delivered to tumours in external beam radiotherapy is present due to many factors, and can result in either spatially uniform (Gaussian) or spatially non-uniform dose errors. These dose errors are incorporated into the calculation of tumour control probability (TCP) and produce a distribution of possible TCP values over a population. We also study the effect of inter-patient cell sensitivity heterogeneity on the population distribution of patient TCPs. This study aims to investigate the relative importance of these three uncertainties (spatially uniform dose uncertainty, spatially non-uniform dose uncertainty, and inter-patient cell sensitivity heterogeneity) on the delivered dose and TCP distribution following a typical course of fractionated external beam radiotherapy. The dose distributions used for patient treatments are modelled in one dimension. Geometric positioning uncertainties during and before treatment are considered as shifts of a pre-calculated dose distribution. Following the simulation of a population of patients, distributions of dose across the patient population are used to calculate mean treatment dose, standard deviation in mean treatment dose, mean TCP, standard deviation in TCP, and TCP mode. These parameters are calculated with each of the three uncertainties included separately. The calculations show that the dose errors in the tumour volume are dominated by the spatially uniform component of dose uncertainty. This could be related to machine specific parameters, such as linear accelerator calibration. TCP calculation is affected dramatically by inter-patient variation in the cell sensitivity and to a lesser extent by the spatially uniform dose errors. The positioning errors with the 1.5 cm margins used cause dose uncertainty outside the tumour volume and have a small effect on mean treatment dose (in the tumour volume) and tumour control. Copyright (2001) Australasian College of
Irreversibility and conditional probability
International Nuclear Information System (INIS)
Stuart, C.I.J.M.
1989-01-01
The mathematical entropy - unlike physical entropy - is simply a measure of uniformity for probability distributions in general. So understood, conditional entropies have the same logical structure as conditional probabilities. If, as is sometimes supposed, conditional probabilities are time-reversible, then so are conditional entropies and, paradoxically, both then share this symmetry with physical equations of motion. The paradox is, of course that probabilities yield a direction to time both in statistical mechanics and quantum mechanics, while the equations of motion do not. The supposed time-reversibility of both conditionals seems also to involve a form of retrocausality that is related to, but possibly not the same as, that described by Costa de Beaurgard. The retrocausality is paradoxically at odds with the generally presumed irreversibility of the quantum mechanical measurement process. Further paradox emerges if the supposed time-reversibility of the conditionals is linked with the idea that the thermodynamic entropy is the same thing as 'missing information' since this confounds the thermodynamic and mathematical entropies. However, it is shown that irreversibility is a formal consequence of conditional entropies and, hence, of conditional probabilities also. 8 refs. (Author)
Introduction to probability and statistics for science, engineering, and finance
Rosenkrantz, Walter A
2008-01-01
Data Analysis Orientation The Role and Scope of Statistics in Science and Engineering Types of Data: Examples from Engineering, Public Health, and Finance The Frequency Distribution of a Variable Defined on a Population Quantiles of a Distribution Measures of Location (Central Value) and Variability Covariance, Correlation, and Regression: Computing a Stock's Beta Mathematical Details and Derivations Large Data Sets Probability Theory Orientation Sample Space, Events, Axioms of Probability Theory Mathematical Models of Random Sampling Conditional Probability and Baye
International Nuclear Information System (INIS)
Keall, P J; Webb, S
2007-01-01
The heterogeneity of human tumour radiation response is well known. Researchers have used the normal distribution to describe interpatient tumour radiosensitivity. However, many natural phenomena show a log-normal distribution. Log-normal distributions are common when mean values are low, variances are large and values cannot be negative. These conditions apply to radiosensitivity. The aim of this work was to evaluate the log-normal distribution to predict clinical tumour control probability (TCP) data and to compare the results with the homogeneous (δ-function with single α-value) and normal distributions. The clinically derived TCP data for four tumour types-melanoma, breast, squamous cell carcinoma and nodes-were used to fit the TCP models. Three forms of interpatient tumour radiosensitivity were considered: the log-normal, normal and δ-function. The free parameters in the models were the radiosensitivity mean, standard deviation and clonogenic cell density. The evaluation metric was the deviance of the maximum likelihood estimation of the fit of the TCP calculated using the predicted parameters to the clinical data. We conclude that (1) the log-normal and normal distributions of interpatient tumour radiosensitivity heterogeneity more closely describe clinical TCP data than a single radiosensitivity value and (2) the log-normal distribution has some theoretical and practical advantages over the normal distribution. Further work is needed to test these models on higher quality clinical outcome datasets
International Nuclear Information System (INIS)
Li Hai-Xia; Cheng Chuan-Fu
2011-01-01
We study the light scattering of an orthogonal anisotropic rough surface with secondary most probable slope distribution. It is found that the scattered intensity profiles have obvious secondary maxima, and in the direction perpendicular to the plane of incidence, the secondary maxima are oriented in a curve on the observation plane, which is called the orientation curve. By numerical calculation of the scattering wave fields with the height data of the sample, it is validated that the secondary maxima are induced by the side face element, which constitutes the prismoid structure of the anisotropic surface. We derive the equation of the quadratic orientation curve. Experimentally, we construct the system for light scattering measurement using a CCD. The scattered intensity profiles are extracted from the images at different angles of incidence along the orientation curves. The experimental results conform to the theory. (fundamental areas of phenomenology(including applications))
Characterizing the Lyα forest flux probability distribution function using Legendre polynomials
Energy Technology Data Exchange (ETDEWEB)
Cieplak, Agnieszka M.; Slosar, Anže, E-mail: acieplak@bnl.gov, E-mail: anze@bnl.gov [Brookhaven National Laboratory, Bldg 510, Upton, NY, 11973 (United States)
2017-10-01
The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n -th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. We find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.
Characterizing the Lyα forest flux probability distribution function using Legendre polynomials
Cieplak, Agnieszka M.; Slosar, Anže
2017-10-01
The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n-th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. We find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.
International Nuclear Information System (INIS)
Lyuboshitz, V.L.
1982-01-01
The time development of nuclear reactions at a large density of levels is investigated using the theory of overlapping resonances. The analytical expression for the function describing the time delay probability distribution of a wave packet is obtained in the framework of the model of n equi - valent channels. It is shown that a relative fluctuation of the time delay at the stage of the compound nucleus is snall. The possibility is discussed of increasing the duration of nuclear raactions with rising excitation energy
Secure quantum key distribution using squeezed states
International Nuclear Information System (INIS)
Gottesman, Daniel; Preskill, John
2001-01-01
We prove the security of a quantum key distribution scheme based on transmission of squeezed quantum states of a harmonic oscillator. Our proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q. If the noise in the quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor e r =1.34) is sufficient in principle to ensure the security of a protocol that is suitably enhanced by classical error correction and privacy amplification. Secure key distribution can be achieved over distances comparable to the attenuation length of the quantum channel
First hitting probabilities for semi markov chains and estimation
DEFF Research Database (Denmark)
Georgiadis, Stylianos
2017-01-01
We first consider a stochastic system described by an absorbing semi-Markov chain with finite state space and we introduce the absorption probability to a class of recurrent states. Afterwards, we study the first hitting probability to a subset of states for an irreducible semi-Markov chain...
Recent trends in the probability of high out-of-pocket medical expenses in the United States
Directory of Open Access Journals (Sweden)
Katherine E Baird
2016-09-01
Full Text Available Objective: This article measures the probability that out-of-pocket expenses in the United States exceed a threshold share of income. It calculates this probability separately by individuals’ health condition, income, and elderly status and estimates changes occurring in these probabilities between 2010 and 2013. Data and Method: This article uses nationally representative household survey data on 344,000 individuals. Logistic regressions estimate the probabilities that out-of-pocket expenses exceed 5% and alternatively 10% of income in the two study years. These probabilities are calculated for individuals based on their income, health status, and elderly status. Results: Despite favorable changes in both health policy and the economy, large numbers of Americans continue to be exposed to high out-of-pocket expenditures. For instance, the results indicate that in 2013 over a quarter of nonelderly low-income citizens in poor health spent 10% or more of their income on out-of-pocket expenses, and over 40% of this group spent more than 5%. Moreover, for Americans as a whole, the probability of spending in excess of 5% of income on out-of-pocket costs increased by 1.4 percentage points between 2010 and 2013, with the largest increases occurring among low-income Americans; the probability of Americans spending more than 10% of income grew from 9.3% to 9.6%, with the largest increases also occurring among the poor. Conclusion: The magnitude of out-of-pocket’s financial burden and the most recent upward trends in it underscore a need to develop good measures of the degree to which health care policy exposes individuals to financial risk, and to closely monitor the Affordable Care Act’s success in reducing Americans’ exposure to large medical bills.
Charge state distributions for heavy ions in carbon stripper foils
International Nuclear Information System (INIS)
McMahan, M.A.; Lebed, R.F.; Feinberg, B.
1989-03-01
We have extended the database of measured charge state distributions available in the literature through measurements at the SuperHILAC using carbon stripper foils in the energy range 1.2--8.5 MeV/u. Modifying a semi-empirical model to include the effect of electronic shells, we are able to correctly predict the mean charge state to within 1/2 a charge state for 6≤Z≤92 and energies from 30 keV/u to 16 MeV/u. We have determined parameters for the widths of the distributions for each electronic shell. For distributions lying across a shell boundary, we join the two Gaussians of different widths to get an asymmetric distribution. 18 refs., 4 figs., 2 tabs
Probabilistic Q-function distributions in fermionic phase-space
International Nuclear Information System (INIS)
Rosales-Zárate, Laura E C; Drummond, P D
2015-01-01
We obtain a positive probability distribution or Q-function for an arbitrary fermionic many-body system. This is different to previous Q-function proposals, which were either restricted to a subspace of the overall Hilbert space, or used Grassmann methods that do not give probabilities. The fermionic Q-function obtained here is constructed using normally ordered Gaussian operators, which include both non-interacting thermal density matrices and BCS states. We prove that the Q-function exists for any density matrix, is real and positive, and has moments that correspond to Fermi operator moments. It is defined on a finite symmetric phase-space equivalent to the space of real, antisymmetric matrices. This has the natural SO(2M) symmetry expected for Majorana fermion operators. We show that there is a physical interpretation of the Q-function: it is the relative probability for observing a given Gaussian density matrix. The distribution has a uniform probability across the space at infinite temperature, while for pure states it has a maximum value on the phase-space boundary. The advantage of probabilistic representations is that they can be used for computational sampling without a sign problem. (fast track communication)
The distribution choice for the threshold of solid state relay
International Nuclear Information System (INIS)
Sun Beiyun; Zhou Hui; Cheng Xiangyue; Mao Congguang
2009-01-01
Either normal distribution or Weibull distribution can be accepted as sample distribution of the threshold of solid state relay. By goodness-of-fit method, bootstrap method and Bayesian method, the Weibull distribution is chosen later. (authors)
Spectral analysis of growing graphs a quantum probability point of view
Obata, Nobuaki
2017-01-01
This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs. This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectr...
Holbrook, Christopher M.; Johnson, Nicholas S.; Steibel, Juan P.; Twohey, Michael B.; Binder, Thomas R.; Krueger, Charles C.; Jones, Michael L.
2014-01-01
Improved methods are needed to evaluate barriers and traps for control and assessment of invasive sea lamprey (Petromyzon marinus) in the Great Lakes. A Bayesian state-space model provided reach-specific probabilities of movement, including trap capture and dam passage, for 148 acoustic tagged invasive sea lamprey in the lower Cheboygan River, Michigan, a tributary to Lake Huron. Reach-specific movement probabilities were combined to obtain estimates of spatial distribution and abundance needed to evaluate a barrier and trap complex for sea lamprey control and assessment. Of an estimated 21 828 – 29 300 adult sea lampreys in the river, 0%–2%, or 0–514 untagged lampreys, could have passed upstream of the dam, and 46%–61% were caught in the trap. Although no tagged lampreys passed above the dam (0/148), our sample size was not sufficient to consider the lock and dam a complete barrier to sea lamprey. Results also showed that existing traps are in good locations because 83%–96% of the population was vulnerable to existing traps. However, only 52%–69% of lampreys vulnerable to traps were caught, suggesting that traps can be improved. The approach used in this study was a novel use of Bayesian state-space models that may have broader applications, including evaluation of barriers for other invasive species (e.g., Asian carp (Hypophthalmichthys spp.)) and fish passage structures for other diadromous fishes.
Random graph states, maximal flow and Fuss-Catalan distributions
International Nuclear Information System (INIS)
Collins, BenoIt; Nechita, Ion; Zyczkowski, Karol
2010-01-01
For any graph consisting of k vertices and m edges we construct an ensemble of random pure quantum states which describe a system composed of 2m subsystems. Each edge of the graph represents a bipartite, maximally entangled state. Each vertex represents a random unitary matrix generated according to the Haar measure, which describes the coupling between subsystems. Dividing all subsystems into two parts, one may study entanglement with respect to this partition. A general technique to derive an expression for the average entanglement entropy of random pure states associated with a given graph is presented. Our technique relies on Weingarten calculus and flow problems. We analyze the statistical properties of spectra of such random density matrices and show for which cases they are described by the free Poissonian (Marchenko-Pastur) distribution. We derive a discrete family of generalized, Fuss-Catalan distributions and explicitly construct graphs which lead to ensembles of random states characterized by these novel distributions of eigenvalues.
International Nuclear Information System (INIS)
Zheng Xiaojing; Xie Li; Zhou Youhe
2005-01-01
The wind-blown sand saltating movement is mainly categorized into two mechanical processes, that is, the interaction between the moving sand particles and the wind in the saltation layer, and the collisions of incident particles with sand bed, and the latter produces a lift-off velocity of a sand particle moving into saltation. In this Letter a methodology of phenomenological analysis is presented to get probability density (distribution) function (pdf) of the lift-off velocity of sand particles from sand bed based on the stochastic particle-bed collision. After the sand particles are dealt with by uniform circular disks and a 2D collision between an incident particle and the granular bed is employed, we get the analytical formulas of lift-off velocity of ejected and rebound particles in saltation, which are functions of some random parameters such as angle and magnitude of incident velocity of the impacting particles, impact and contact angles between the collision particles, and creeping velocity of sand particles, etc. By introducing the probability density functions (pdf's) of these parameters in communion with all possible patterns of sand bed and all possible particle-bed collisions, and using the essential arithmetic of multi-dimension random variables' pdf, the pdf's of lift-off velocities are deduced out and expressed by the pdf's of the random parameters in the collisions. The numerical results of the distributions of lift-off velocities display that they agree well with experimental ones
Excluding joint probabilities from quantum theory
Allahverdyan, Armen E.; Danageozian, Arshag
2018-03-01
Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.
On the Hitting Probability of Max-Stable Processes
Hofmann, Martin
2012-01-01
The probability that a max-stable process {\\eta} in C[0, 1] with identical marginal distribution function F hits x \\in R with 0 < F (x) < 1 is the hitting probability of x. We show that the hitting probability is always positive, unless the components of {\\eta} are completely dependent. Moreover, we consider the event that the paths of standard MSP hit some x \\in R twice and we give a sufficient condition for a positive probability of this event.
30 CFR 285.540 - How will MMS equitably distribute revenues to States?
2010-07-01
... 30 Mineral Resources 2 2010-07-01 2010-07-01 false How will MMS equitably distribute revenues to... Financial Assurance Requirements Revenue Sharing with States § 285.540 How will MMS equitably distribute revenues to States? (a) The MMS will distribute among the eligible coastal States 27 percent of the...
Applied probability and stochastic processes
Sumita, Ushio
1999-01-01
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...
Moments of generalized Husimi distributions and complexity of many-body quantum states
International Nuclear Information System (INIS)
Sugita, Ayumu
2003-01-01
We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the single-particle transformation group. Then the coherent states are independent-particle states, and, at the same time, the most localized states in the Husimi representation. Therefore delocalization of the Husimi distribution, which can be measured by the moments, is a sign of many-body correlation (entanglement). Since the delocalization of the Husimi distribution is also related to chaoticity of the dynamics, it suggests a relation between entanglement and chaos. Our definition of the Husimi distribution can be applied not only to systems of distinguishable particles, but also to those of identical particles, i.e., fermions and bosons. We derive an algebraic formula to evaluate the moments of the Husimi distribution
Energy Technology Data Exchange (ETDEWEB)
Diwold, Konrad; Yan, Wei [Fraunhofer IWES, Kassel (Germany); Braun, Martin [Fraunhofer IWES, Kassel (Germany); Stuttgart Univ. (Germany). Inst. fuer Energieuebertragung und Hochspannungstechnik (IEH)
2012-07-01
The increased integration of distributed energy units creates challenges for the operators of distribution systems. This is due to the fact that distribution systems that were initially designed for distributed consumption and central generation now face decentralized feed-in. One imminent problem associated with decentralised fee-in are local voltage violations in the distribution system, which are hard to handle via conventional voltage control strategies. This article proposes a new voltage control framework for distribution system operation. The framework utilizes reactive power of distributed energy units as well on-load tap changers to mitigate voltage problems in the network. Using an optimization-band the control strategy can be used in situations where network information is derived from distribution state estimators and thus holds some error. The control capabilities in combination with a distribution state estimator are tested using data from a real rural distribution network. The results are very promising, as voltage control is achieved fast and accurate, preventing a majority of the voltage violations during system operation under realistic system conditions. (orig.)
Distribution of standard deviation of an observable among superposed states
International Nuclear Information System (INIS)
Yu, Chang-shui; Shao, Ting-ting; Li, Dong-mo
2016-01-01
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a superposition state is distributed.
Distribution of standard deviation of an observable among superposed states
Yu, Chang-shui; Shao, Ting-ting; Li, Dong-mo
2016-10-01
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a superposition state is distributed.
Observation of moving wave packets reveals their quantum state
International Nuclear Information System (INIS)
Leonhardt, U.; Raymer, M.G.
1996-01-01
We show how to infer the quantum state of a wave packet from position probability distributions measured during the packet close-quote s motion in an arbitrary potential. We assume a nonrelativistic one-dimensional or radial wave packet. Temporal Fourier transformation and spatial sampling with respect to a newly found set of functions project the density-matrix elements out of the probability distributions. The sampling functions are derivatives of products of regular and irregular wave functions. We note that the ability to infer quantum states in this way depends on the structure of the Schroedinger equation. copyright 1996 The American Physical Society
Estimation of monthly solar radiation distribution for solar energy system analysis
International Nuclear Information System (INIS)
Coskun, C.; Oktay, Z.; Dincer, I.
2011-01-01
The concept of probability density frequency, which is successfully used for analyses of wind speed and outdoor temperature distributions, is now modified and proposed for estimating solar radiation distributions for design and analysis of solar energy systems. In this study, global solar radiation distribution is comprehensively analyzed for photovoltaic (PV) panel and thermal collector systems. In this regard, a case study is conducted with actual global solar irradiation data of the last 15 years recorded by the Turkish State Meteorological Service. It is found that intensity of global solar irradiance greatly affects energy and exergy efficiencies and hence the performance of collectors. -- Research highlights: → The first study to apply global solar radiation distribution in solar system analyzes. → The first study showing global solar radiation distribution as a parameter of the solar irradiance intensity. → Time probability intensity frequency and probability power distribution do not have similar distribution patterns for each month. → There is no relation between the distribution of annual time lapse and solar energy with the intensity of solar irradiance.
Probability based load factors for design of concrete containment structures
International Nuclear Information System (INIS)
Hwang, H.; Kagami, S.; Reich, M.; Ellingwood, B.; Shinozuka, M.
1985-01-01
This paper describes a procedure for developing probability-based load combinations for the design of concrete containments. The proposed criteria are in a load and resistance factor design (LRFD) format. The load factors and resistance factors are derived for use in limit states design and are based on a target limit state probability. In this paper, the load factors for accident pressure and safe shutdown earthquake are derived for three target limit state probabilities. Other load factors are recommended on the basis of prior experience with probability-based design criteria for ordinary building construction. 6 refs
Quantum Key Distribution Using Four-Qubit W State
International Nuclear Information System (INIS)
Cai Haijing; Song Heshan
2006-01-01
A new theoretical quantum key distribution scheme based on entanglement swapping is proposed, where four-qubit symmetric W state functions as quantum channel. It is shown that two legitimate users can secretly share a series of key bits by using Bell-state measurements and classical communication.
Supervised learning of probability distributions by neural networks
Baum, Eric B.; Wilczek, Frank
1988-01-01
Supervised learning algorithms for feedforward neural networks are investigated analytically. The back-propagation algorithm described by Werbos (1974), Parker (1985), and Rumelhart et al. (1986) is generalized by redefining the values of the input and output neurons as probabilities. The synaptic weights are then varied to follow gradients in the logarithm of likelihood rather than in the error. This modification is shown to provide a more rigorous theoretical basis for the algorithm and to permit more accurate predictions. A typical application involving a medical-diagnosis expert system is discussed.
Encounter Probability of Individual Wave Height
DEFF Research Database (Denmark)
Liu, Z.; Burcharth, H. F.
1998-01-01
wave height corresponding to a certain exceedence probability within a structure lifetime (encounter probability), based on the statistical analysis of long-term extreme significant wave height. Then the design individual wave height is calculated as the expected maximum individual wave height...... associated with the design significant wave height, with the assumption that the individual wave heights follow the Rayleigh distribution. However, the exceedence probability of such a design individual wave height within the structure lifetime is unknown. The paper presents a method for the determination...... of the design individual wave height corresponding to an exceedence probability within the structure lifetime, given the long-term extreme significant wave height. The method can also be applied for estimation of the number of relatively large waves for fatigue analysis of constructions....
Conditional probability of the tornado missile impact given a tornado occurrence
International Nuclear Information System (INIS)
Goodman, J.; Koch, J.E.
1982-01-01
Using an approach based on statistical mechanics, an expression for the probability of the first missile strike is developed. The expression depends on two generic parameters (injection probability eta(F) and height distribution psi(Z,F)), which are developed in this study, and one plant specific parameter (number of potential missiles N/sub p/). The expression for the joint probability of simultaneous impact of muitiple targets is also developed. This espression is applicable to calculation of the probability of common cause failure due to tornado missiles. It is shown that the probability of the first missile strike can be determined using a uniform missile distribution model. It is also shown that the conditional probability of the second strike, given the first, is underestimated by the uniform model. The probability of the second strike is greatly increased if the missiles are in clusters large enough to cover both targets
Cieplak, Agnieszka; Slosar, Anze
2018-01-01
The Lyman-alpha forest has become a powerful cosmological probe at intermediate redshift. It is a highly non-linear field with much information present beyond the power spectrum. The flux probability flux distribution (PDF) in particular has been a successful probe of small scale physics. However, it is also sensitive to pixel noise, spectrum resolution, and continuum fitting, all of which lead to possible biased estimators. Here we argue that measuring the coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. Since the n-th Legendre coefficient can be expressed as a linear combination of the first n moments of the field, this allows for the coefficients to be measured in the presence of noise and allows for a clear route towards marginalization over the mean flux. Additionally, in the presence of noise, a finite number of these coefficients are well measured with a very sharp transition into noise dominance. This compresses the information into a small amount of well-measured quantities. Finally, we find that measuring fewer quasars with high signal-to-noise produces a higher amount of recoverable information.
Models for probability and statistical inference theory and applications
Stapleton, James H
2007-01-01
This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readersModels for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping.Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses mo...
Imprecise Probability Methods for Weapons UQ
Energy Technology Data Exchange (ETDEWEB)
Picard, Richard Roy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vander Wiel, Scott Alan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-05-13
Building on recent work in uncertainty quanti cation, we examine the use of imprecise probability methods to better characterize expert knowledge and to improve on misleading aspects of Bayesian analysis with informative prior distributions. Quantitative approaches to incorporate uncertainties in weapons certi cation are subject to rigorous external peer review, and in this regard, certain imprecise probability methods are well established in the literature and attractive. These methods are illustrated using experimental data from LANL detonator impact testing.
Eliciting Subjective Probability Distributions with Binary Lotteries
DEFF Research Database (Denmark)
Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd
2015-01-01
We test in a laboratory experiment the theoretical prediction that risk attitudes have a surprisingly small role in distorting reports from true belief distributions. We find evidence consistent with theory in our experiment....
Spiking Activity of a LIF Neuron in Distributed Delay Framework
Directory of Open Access Journals (Sweden)
Saket Kumar Choudhary
2016-06-01
Full Text Available Evolution of membrane potential and spiking activity for a single leaky integrate-and-fire (LIF neuron in distributed delay framework (DDF is investigated. DDF provides a mechanism to incorporate memory element in terms of delay (kernel function into a single neuron models. This investigation includes LIF neuron model with two different kinds of delay kernel functions, namely, gamma distributed delay kernel function and hypo-exponential distributed delay kernel function. Evolution of membrane potential for considered models is studied in terms of stationary state probability distribution (SPD. Stationary state probability distribution of membrane potential (SPDV for considered neuron models are found asymptotically similar which is Gaussian distributed. In order to investigate the effect of membrane potential delay, rate code scheme for neuronal information processing is applied. Firing rate and Fano-factor for considered neuron models are calculated and standard LIF model is used for comparative study. It is noticed that distributed delay increases the spiking activity of a neuron. Increase in spiking activity of neuron in DDF is larger for hypo-exponential distributed delay function than gamma distributed delay function. Moreover, in case of hypo-exponential delay function, a LIF neuron generates spikes with Fano-factor less than 1.
Collective probabilities algorithm for surface hopping calculations
International Nuclear Information System (INIS)
Bastida, Adolfo; Cruz, Carlos; Zuniga, Jose; Requena, Alberto
2003-01-01
General equations that transition probabilities of the hopping algorithms in surface hopping calculations must obey to assure the equality between the average quantum and classical populations are derived. These equations are solved for two particular cases. In the first it is assumed that probabilities are the same for all trajectories and that the number of hops is kept to a minimum. These assumptions specify the collective probabilities (CP) algorithm, for which the transition probabilities depend on the average populations for all trajectories. In the second case, the probabilities for each trajectory are supposed to be completely independent of the results from the other trajectories. There is, then, a unique solution of the general equations assuring that the transition probabilities are equal to the quantum population of the target state, which is referred to as the independent probabilities (IP) algorithm. The fewest switches (FS) algorithm developed by Tully is accordingly understood as an approximate hopping algorithm which takes elements from the accurate CP and IP solutions. A numerical test of all these hopping algorithms is carried out for a one-dimensional two-state problem with two avoiding crossings which shows the accuracy and computational efficiency of the collective probabilities algorithm proposed, the limitations of the FS algorithm and the similarity between the results offered by the IP algorithm and those obtained with the Ehrenfest method
Directory of Open Access Journals (Sweden)
Yuan You
2018-01-01
Full Text Available The analytical solutions to a double ring-shaped Coulomb potential (RSCP are presented. The visualizations of the space probability distribution (SPD are illustrated for the two- (contour and three-dimensional (isosurface cases. The quantum numbers (n,l,m are mainly relevant for those quasi-quantum numbers (n′,l′,m′ via the double RSCP parameter c. The SPDs are of circular ring shape in spherical coordinates. The properties for the relative probability values (RPVs P are also discussed. For example, when we consider the special case (n,l,m=(6,5,0, the SPD moves towards two poles of z-axis when P increases. Finally, we discuss the different cases for the potential parameter b, which is taken as negative and positive values for c>0. Compared with the particular case b=0, the SPDs are shrunk for b=-0.5, while they are spread out for b=0.5.
The perception of probability.
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).
Branch current state estimation of three phase distribution networks suitable for paralellization
Blaauwbroek, N.; Nguyen, H.P.; Gibescu, M.; Slootweg, J.G.
2017-01-01
The evolution of distribution networks from passive to active distribution systems puts new requirements on the monitoring and control capabilities of these systems. The development of state estimation algorithms to gain insight in the actual system state of a distribution network has resulted in a
Directory of Open Access Journals (Sweden)
L. M. Nuriyeva
2013-01-01
Full Text Available The paper looks at implementing the probability theory and mathematical statistics while analyzing the outcomes of the unified state examination (USE. The research is aimed at investigating the impact of closed questions that make the greater part of USE, on test results. The methodology is based on so called Bernoulli’s trial. The research findings demonstrate the higher probability of incidental right answers to the closed questions compared with the open ones. The author makes a conclusion that the considerable number of closed questions in the test can misrepresent the final result which tends to improve. The proposed method of statistic analysis can provide the explanation for the USE results anomalies, evaluate the quality of examination materials and scoring system, and give the quantified assessment of social implications.
Eilers, Anna-Christina; Hennawi, Joseph F.; Lee, Khee-Gan
2017-08-01
We present a new Bayesian algorithm making use of Markov Chain Monte Carlo sampling that allows us to simultaneously estimate the unknown continuum level of each quasar in an ensemble of high-resolution spectra, as well as their common probability distribution function (PDF) for the transmitted Lyα forest flux. This fully automated PDF regulated continuum fitting method models the unknown quasar continuum with a linear principal component analysis (PCA) basis, with the PCA coefficients treated as nuisance parameters. The method allows one to estimate parameters governing the thermal state of the intergalactic medium (IGM), such as the slope of the temperature-density relation γ -1, while marginalizing out continuum uncertainties in a fully Bayesian way. Using realistic mock quasar spectra created from a simplified semi-numerical model of the IGM, we show that this method recovers the underlying quasar continua to a precision of ≃ 7 % and ≃ 10 % at z = 3 and z = 5, respectively. Given the number of principal component spectra, this is comparable to the underlying accuracy of the PCA model itself. Most importantly, we show that we can achieve a nearly unbiased estimate of the slope γ -1 of the IGM temperature-density relation with a precision of +/- 8.6 % at z = 3 and +/- 6.1 % at z = 5, for an ensemble of ten mock high-resolution quasar spectra. Applying this method to real quasar spectra and comparing to a more realistic IGM model from hydrodynamical simulations would enable precise measurements of the thermal and cosmological parameters governing the IGM, albeit with somewhat larger uncertainties, given the increased flexibility of the model.
Towards a Categorical Account of Conditional Probability
Directory of Open Access Journals (Sweden)
Robert Furber
2015-11-01
Full Text Available This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and joint probabilities, in the Kleisli category of the distribution monad. The conditional probabilities are induced by a map together with a predicate (the condition. The latter is a predicate in the logic of effect modules on this Kleisli category. This same approach can be transferred to the category of C*-algebras (with positive unital maps, whose predicate logic is also expressed in terms of effect modules. Conditional probabilities can again be expressed via a triangle-fill-in property. In the literature, there are several proposals for what quantum conditional probability should be, and also there are extra difficulties not present in the classical case. At this stage, we only describe quantum systems with classical parametrization.
Vacuum arc ion charge state distributions
International Nuclear Information System (INIS)
Brown, I.G.; Godechot, X.
1990-06-01
We have measured vacuum arc ion charge state spectra for a wide range of metallic cathode materials. The charge state distributions were measured using a time-of-flight diagnostic to monitor the energetic ion beam produced by a metal vapor vacuum arc ion source. We have obtained data for 48 metallic cathode elements: Li, C, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ge, Sr, Y, Zr, Nb, Mo, Pd, Ag, Cd, In, Sn, Ba, La, Ce, Pr, Nd, Sm, Gd, Dy, Ho, Er, Yb, Hf, Ta, W, Ir, Pt, Au, Pb, Bi, Th and U. The arc was operated in a pulsed mode with pulse length 0.25 msec; arc current was 100 A throughout. This array of elements extends and completes previous work by us. In this paper the measured distributions are cataloged and compared with our earlier results and with those of other workers. We also make some observations about the performance of the various elements as suitable vacuum arc cathode materials
Vacuum arc ion charge-state distributions
International Nuclear Information System (INIS)
Brown, I.G.; Godechot, X.
1991-01-01
The authors have measured vacuum arc ion charge-state spectra for a wide range of metallic cathode materials. The charge-state distributions were measured using a time-of-flight diagnostic to monitor the energetic ion beam produced by a metal vapor vacuum arc ion source. They have obtained data for 48 metallic cathode elements: Li, C, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ge, Sr, Y, Zr, Nb, Mo, Pd, Ag, Cd, In, Sn, Ba, La, Ce, Pr, Nd, Sm, Gd, Dy, Ho, Er, Yb, Hf, Ta, W, Ir, Pt, Au, Pb, Bi, Th, and U. The arc was operated in a pulsed mode with pulse length 0.25 ms; arc current was 100 A throughout. This array of elements extends and completes previous work by the authors. In this paper the measured distributions are cataloged and compared with their earlier results and those of other workers. They also make some observations about the performance of the various elements as suitable vacuum arc cathode materials
Kroese, A.H.; van der Meulen, E.A.; Poortema, Klaas; Schaafsma, W.
1995-01-01
The making of statistical inferences in distributional form is conceptionally complicated because the epistemic 'probabilities' assigned are mixtures of fact and fiction. In this respect they are essentially different from 'physical' or 'frequency-theoretic' probabilities. The distributional form is
Path probability of stochastic motion: A functional approach
Hattori, Masayuki; Abe, Sumiyoshi
2016-06-01
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically evaluated in a way analogous to continuous measurements in quantum mechanics. Then, the formalism developed here is applied to the stochastic dynamics of stock price in finance.
International Nuclear Information System (INIS)
Niestegge, Gerd
2010-01-01
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases. (general)
Francisco, E.; Pendás, A. Martín; Blanco, M. A.
2008-04-01
Given an N-electron molecule and an exhaustive partition of the real space ( R) into m arbitrary regions Ω,Ω,…,Ω ( ⋃i=1mΩ=R), the edf program computes all the probabilities P(n,n,…,n) of having exactly n electrons in Ω, n electrons in Ω,…, and n electrons ( n+n+⋯+n=N) in Ω. Each Ω may correspond to a single basin (atomic domain) or several such basins (functional group). In the later case, each atomic domain must belong to a single Ω. The program can manage both single- and multi-determinant wave functions which are read in from an aimpac-like wave function description ( .wfn) file (T.A. Keith et al., The AIMPAC95 programs, http://www.chemistry.mcmaster.ca/aimpac, 1995). For multi-determinantal wave functions a generalization of the original .wfn file has been introduced. The new format is completely backwards compatible, adding to the previous structure a description of the configuration interaction (CI) coefficients and the determinants of correlated wave functions. Besides the .wfn file, edf only needs the overlap integrals over all the atomic domains between the molecular orbitals (MO). After the P(n,n,…,n) probabilities are computed, edf obtains from them several magnitudes relevant to chemical bonding theory, such as average electronic populations and localization/delocalization indices. Regarding spin, edf may be used in two ways: with or without a splitting of the P(n,n,…,n) probabilities into α and β spin components. Program summaryProgram title: edf Catalogue identifier: AEAJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5387 No. of bytes in distributed program, including test data, etc.: 52 381 Distribution format: tar.gz Programming language: Fortran 77 Computer
Modelling the Probability of Landslides Impacting Road Networks
Taylor, F. E.; Malamud, B. D.
2012-04-01
During a landslide triggering event, the threat of landslides blocking roads poses a risk to logistics, rescue efforts and communities dependant on those road networks. Here we present preliminary results of a stochastic model we have developed to evaluate the probability of landslides intersecting a simple road network during a landslide triggering event and apply simple network indices to measure the state of the road network in the affected region. A 4000 x 4000 cell array with a 5 m x 5 m resolution was used, with a pre-defined simple road network laid onto it, and landslides 'randomly' dropped onto it. Landslide areas (AL) were randomly selected from a three-parameter inverse gamma probability density function, consisting of a power-law decay of about -2.4 for medium and large values of AL and an exponential rollover for small values of AL; the rollover (maximum probability) occurs at about AL = 400 m2 This statistical distribution was chosen based on three substantially complete triggered landslide inventories recorded in existing literature. The number of landslide areas (NL) selected for each triggered event iteration was chosen to have an average density of 1 landslide km-2, i.e. NL = 400 landslide areas chosen randomly for each iteration, and was based on several existing triggered landslide event inventories. A simple road network was chosen, in a 'T' shape configuration, with one road 1 x 4000 cells (5 m x 20 km) in a 'T' formation with another road 1 x 2000 cells (5 m x 10 km). The landslide areas were then randomly 'dropped' over the road array and indices such as the location, size (ABL) and number of road blockages (NBL) recorded. This process was performed 500 times (iterations) in a Monte-Carlo type simulation. Initial results show that for a landslide triggering event with 400 landslides over a 400 km2 region, the number of road blocks per iteration, NBL,ranges from 0 to 7. The average blockage area for the 500 iterations (A¯ BL) is about 3000 m
International Nuclear Information System (INIS)
Pfeifle, T.W.; Mellegard, K.D.; Munson, D.E.
1992-10-01
The modified Munson-Dawson (M-D) constitutive model that describes the creep behavior of salt will be used in performance assessment calculations to assess compliance of the Waste Isolation Pilot Plant (WIPP) facility with requirements governing the disposal of nuclear waste. One of these standards requires that the uncertainty of future states of the system, material model parameters, and data be addressed in the performance assessment models. This paper presents a method in which measurement uncertainty and the inherent variability of the material are characterized by treating the M-D model parameters as random variables. The random variables can be described by appropriate probability distribution functions which then can be used in Monte Carlo or structural reliability analyses. Estimates of three random variables in the M-D model were obtained by fitting a scalar form of the model to triaxial compression creep data generated from tests of WIPP salt. Candidate probability distribution functions for each of the variables were then fitted to the estimates and their relative goodness-of-fit tested using the Kolmogorov-Smirnov statistic. A sophisticated statistical software package obtained from BMDP Statistical Software, Inc. was used in the M-D model fitting. A separate software package, STATGRAPHICS, was used in fitting the candidate probability distribution functions to estimates of the variables. Skewed distributions, i.e., lognormal and Weibull, were found to be appropriate for the random variables analyzed
Probable Rotation States of Rocket Bodies in Low Earth Orbit
Ojakangas, Gregory W.; Anz-Meador, P.; Cowardin, H.
2012-01-01
In order for Active Debris Removal to be accomplished, it is critically important to understand the probable rotation states of orbiting, spent rocket bodies. As compared to the question of characterizing small unresolved debris, in this problem there are several advantages: (1) objects are of known size, mass, shape and color, (2) they have typically been in orbit for a known period of time, (3) they are large enough that resolved images may be obtainable for verification of predicted orientation, and (4) the dynamical problem is simplified to first order by largely cylindrical symmetry. It is also nearly certain for realistic rocket bodies that internal friction is appreciable in the case where residual liquid or, to a lesser degree, unconsolidated solid fuels exist. Equations of motion have been developed for this problem in which internal friction as well as torques due to solar radiation, magnetic induction, and gravitational gradient are included. In the case of pure cylindrical symmetry, the results are compared to analytical predictions patterned after the standard approach for analysis of symmetrical tops. This is possible because solar radiation and gravitational torques may be treated as conservative. Agreement between results of both methods ensures their mutual validity. For monotone symmetric cylinders, solar radiation torque vanishes if the center of mass resides at the geometric center of the object. Results indicate that in the absence of solar radiation effects, rotation states tend toward an equilibrium configuration in which rotation is about the axis of maximum inertia, with the axis of minimum inertia directed toward the center of the earth. Solar radiation torque introduces a modification to this orientation. The equilibrium state is asymptotically approached within a characteristic timescale given by a simple ratio of relevant characterizing parameters for the body in question. Light curves are simulated for the expected asymptotic final
Sexual differentiation in the distribution potential of northern jaguars (Panthera onca)
Erin E. Boydston; Carlos A. Lopez Gonzalez
2005-01-01
We estimated the potential geographic distribution of jaguars in the southwestern United States and northwestern Mexico by modeling the jaguar ecological niche from occurrence records. We modeled separately the distributions of males and females, assuming records of females probably represented established home ranges while male records likely included dispersal...
A stochastic-bayesian model for the fracture probability of PWR pressure vessels
Energy Technology Data Exchange (ETDEWEB)
Francisco, Alexandre S.; Duran, Jorge Alberto R., E-mail: afrancisco@metal.eeimvr.uff.br, E-mail: duran@metal.eeimvr.uff.br [Universidade Federal Fluminense (UFF), Volta Redonda, RJ (Brazil). Dept. de Engenharia Mecanica
2013-07-01
Fracture probability of pressure vessels containing cracks can be obtained by methodologies of easy understanding, which require a deterministic treatment, complemented by statistical methods. However, more accurate results are required, methodologies need to be better formulated. This paper presents a new methodology to address this problem. First, a more rigorous methodology is obtained by means of the relationship of probability distributions that model crack incidence and nondestructive inspection efficiency using the Bayes' theorem. The result is an updated crack incidence distribution. Further, the accuracy of the methodology is improved by using a stochastic model for the crack growth. The stochastic model incorporates the statistical variability of the crack growth process, combining the stochastic theory with experimental data. Stochastic differential equations are derived by the randomization of empirical equations. From the solution of this equation, a distribution function related to the crack growth is derived. The fracture probability using both probability distribution functions is in agreement with theory, and presents realistic value for pressure vessels. (author)
A stochastic-bayesian model for the fracture probability of PWR pressure vessels
International Nuclear Information System (INIS)
Francisco, Alexandre S.; Duran, Jorge Alberto R.
2013-01-01
Fracture probability of pressure vessels containing cracks can be obtained by methodologies of easy understanding, which require a deterministic treatment, complemented by statistical methods. However, more accurate results are required, methodologies need to be better formulated. This paper presents a new methodology to address this problem. First, a more rigorous methodology is obtained by means of the relationship of probability distributions that model crack incidence and nondestructive inspection efficiency using the Bayes' theorem. The result is an updated crack incidence distribution. Further, the accuracy of the methodology is improved by using a stochastic model for the crack growth. The stochastic model incorporates the statistical variability of the crack growth process, combining the stochastic theory with experimental data. Stochastic differential equations are derived by the randomization of empirical equations. From the solution of this equation, a distribution function related to the crack growth is derived. The fracture probability using both probability distribution functions is in agreement with theory, and presents realistic value for pressure vessels. (author)
Dynamic shared state maintenance in distributed virtual environments
Hamza-Lup, Felix George
Advances in computer networks and rendering systems facilitate the creation of distributed collaborative environments in which the distribution of information at remote locations allows efficient communication. Particularly challenging are distributed interactive Virtual Environments (VE) that allow knowledge sharing through 3D information. The purpose of this work is to address the problem of latency in distributed interactive VE and to develop a conceptual model for consistency maintenance in these environments based on the participant interaction model. An area that needs to be explored is the relationship between the dynamic shared state and the interaction with the virtual entities present in the shared scene. Mixed Reality (MR) and VR environments must bring the human participant interaction into the loop through a wide range of electronic motion sensors, and haptic devices. Part of the work presented here defines a novel criterion for categorization of distributed interactive VE and introduces, as well as analyzes, an adaptive synchronization algorithm for consistency maintenance in such environments. As part of the work, a distributed interactive Augmented Reality (AR) testbed and the algorithm implementation details are presented. Currently the testbed is part of several research efforts at the Optical Diagnostics and Applications Laboratory including 3D visualization applications using custom built head-mounted displays (HMDs) with optical motion tracking and a medical training prototype for endotracheal intubation and medical prognostics. An objective method using quaternion calculus is applied for the algorithm assessment. In spite of significant network latency, results show that the dynamic shared state can be maintained consistent at multiple remotely located sites. In further consideration of the latency problems and in the light of the current trends in interactive distributed VE applications, we propose a hybrid distributed system architecture for
Distribution of specialized care centers in the United States.
Wang, Henry E; Yealy, Donald M
2012-11-01
As a recommended strategy for optimally managing critical illness, regionalization of care involves matching the needs of the target population with available hospital resources. The national supply and characteristics of hospitals providing specialized critical care services is currently unknown. We seek to characterize the current distribution of specialized care centers in the United States. Using public data linked with the American Hospital Association directory and US Census, we identified US general acute hospitals providing specialized care for ST-segment elevation myocardial infarction (STEMI) (≥40 annual primary percutaneous coronary interventions reported in Medicare Hospital Compare), stroke (The Joint Commission certified stroke centers), trauma (American College of Surgeons or state-designated, adult or pediatric, level I or II), and pediatric critical care (presence of a pediatric ICU) services. We determined the characteristics and state-level distribution and density of specialized care centers (centers per state and centers per state population). Among 4,931 acute care hospitals in the United States, 1,325 (26.9%) provided one of the 4 defined specialized care services, including 574 STEMI, 763 stroke, 508 trauma, and 457 pediatric critical care centers. Approximately half of the 1,325 hospitals provided 2 or more specialized services, and one fifth provided 3 or 4 specialized services. There was variation in the number of each type of specialized care center in each state: STEMI median 7 interquartile range (IQR 2 to 14), stroke 8 (IQR 3 to 17), trauma 6 (IQR 3 to 11), pediatric specialized care 6 (IQR 3 to 11). Similarly, there was variation in the number of each type of specialized care center per population: STEMI median 1 center per 585,135 persons (IQR 418,729 to 696,143), stroke 1 center per 412,188 persons (IQR 321,604 to 572,387), trauma 1 center per 610,589 persons (IQR 406,192 to 917,588), and pediatric critical care 1 center per 665
Energy Technology Data Exchange (ETDEWEB)
Weston, F.; Harrington, C.; Moskovitz, D.; Shirley, W.; Cowart, R.; Sedano, R.
2002-10-01
Distributed resources can provide cost-effective reliability and energy services - in many cases, obviating the need for more expensive investments in wires and central station electricity generating facilities. Given the unique features of distributed resources, the challenge facing policymakers today is how to restructure wholesale markets for electricity and related services so as to reveal the full value that distributed resources can provide to the electric power system (utility grid). This report looks at the functions that distributed resources can perform and examines the barriers to them. It then identifies a series of policy and operational approaches to promoting DR in wholesale markets. This report is one in the State Electricity Regulatory Policy and Distributed Resources series developed under contract to NREL (see Annual Technical Status Report of the Regulatory Assistance Project: September 2000-September 2001, NREL/SR-560-32733). Other titles in this series are: (1) Distributed Resource Distribution Credit Pilot Programs - Revealing the Value to Consumers and Vendors, NREL/SR-560-32499; (2) Distributed Resources and Electric System Reliability, NREL/SR-560-32498; (3) Distribution System Cost Methodologies for Distributed Generation, NREL/SR-560-32500; (4) Distribution System Cost Methodologies for Distributed Generation Appendices, NREL/SR-560-32501
Probability functions in the context of signed involutive meadows
Bergstra, J.A.; Ponse, A.
2016-01-01
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability theory are restated in this framework.
Probability of crack-initiation and application to NDE
Energy Technology Data Exchange (ETDEWEB)
Prantl, G [Nuclear Safety Inspectorate HSK, (Switzerland)
1988-12-31
Fracture toughness is a property with a certain variability. When a statistical distribution is assumed, the probability of crack initiation may be calculated for a given problem defined by its geometry and the applied stress. Experiments have shown, that cracks which experience a certain small amount of ductile growth can reliably be detected by acoustic emission measurements. The probability of crack detection by AE-techniques may be estimated using this experimental finding and the calculated probability of crack initiation. (author).
Comparing linear probability model coefficients across groups
DEFF Research Database (Denmark)
Holm, Anders; Ejrnæs, Mette; Karlson, Kristian Bernt
2015-01-01
of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate......This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more...... these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons....
On misclassication probabilities of linear and quadratic classiers ...
African Journals Online (AJOL)
We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...
Akibue, Seiseki; Kato, Go
2018-04-01
For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a composite system consisting of N subsystems, where each subsystem is shared between two parties and the state of each subsystem is randomly sampled from a particular ensemble comprising the Bell states. We show that the success probability of perfectly identifying the state converges to 1 as N →∞ if the entropy of the probability distribution associated with the ensemble is less than 1, even if the success probability is less than 1 for any finite N . In other words, the nonlocality of the N -fold ensemble asymptotically disappears if the probability distribution associated with each ensemble is concentrated. Furthermore, we show that the disappearance of the nonlocality can be regarded as a remarkable counterexample of a fundamental open question in theoretical computer science, called a parallel repetition conjecture of interactive games with two classically communicating players. Measurements for the discrimination task include a projective measurement of one party represented by stabilizer states, which enable the other party to perfectly distinguish states that are sampled with high probability.
Knitting distributed cluster-state ladders with spin chains
Energy Technology Data Exchange (ETDEWEB)
Ronke, R.; D' Amico, I. [Department of Physics, University of York, York YO10 5DD, United Kingdom. (United Kingdom); Spiller, T. P. [School of Physics and Astronomy, E C Stoner Building, University of Leeds, Leeds, LS2 9JT (United Kingdom)
2011-09-15
Recently there has been much study on the application of spin chains to quantum state transfer and communication. Here we discuss the utilization of spin chains (set up for perfect quantum state transfer) for the knitting of distributed cluster-state structures, between spin qubits repeatedly injected and extracted at the ends of the chain. The cluster states emerge from the natural evolution of the system across different excitation number sectors. We discuss the decohering effects of errors in the injection and extraction process as well as the effects of fabrication and random errors.
Knitting distributed cluster-state ladders with spin chains
International Nuclear Information System (INIS)
Ronke, R.; D'Amico, I.; Spiller, T. P.
2011-01-01
Recently there has been much study on the application of spin chains to quantum state transfer and communication. Here we discuss the utilization of spin chains (set up for perfect quantum state transfer) for the knitting of distributed cluster-state structures, between spin qubits repeatedly injected and extracted at the ends of the chain. The cluster states emerge from the natural evolution of the system across different excitation number sectors. We discuss the decohering effects of errors in the injection and extraction process as well as the effects of fabrication and random errors.
Extreme value distribution of earthquake magnitude
Zi, Jun Gan; Tung, C. C.
1983-07-01
Probability distribution of maximum earthquake magnitude is first derived for an unspecified probability distribution of earthquake magnitude. A model for energy release of large earthquakes, similar to that of Adler-Lomnitz and Lomnitz, is introduced from which the probability distribution of earthquake magnitude is obtained. An extensive set of world data for shallow earthquakes, covering the period from 1904 to 1980, is used to determine the parameters of the probability distribution of maximum earthquake magnitude. Because of the special form of probability distribution of earthquake magnitude, a simple iterative scheme is devised to facilitate the estimation of these parameters by the method of least-squares. The agreement between the empirical and derived probability distributions of maximum earthquake magnitude is excellent.
Probability intervals for the top event unavailability of fault trees
International Nuclear Information System (INIS)
Lee, Y.T.; Apostolakis, G.E.
1976-06-01
The evaluation of probabilities of rare events is of major importance in the quantitative assessment of the risk from large technological systems. In particular, for nuclear power plants the complexity of the systems, their high reliability and the lack of significant statistical records have led to the extensive use of logic diagrams in the estimation of low probabilities. The estimation of probability intervals for the probability of existence of the top event of a fault tree is examined. Given the uncertainties of the primary input data, a method is described for the evaluation of the first four moments of the top event occurrence probability. These moments are then used to estimate confidence bounds by several approaches which are based on standard inequalities (e.g., Tchebycheff, Cantelli, etc.) or on empirical distributions (the Johnson family). Several examples indicate that the Johnson family of distributions yields results which are in good agreement with those produced by Monte Carlo simulation
Linear and nonlinear optical signals in probability and phase-space representations
International Nuclear Information System (INIS)
Man'ko, Margarita A
2006-01-01
Review of different representations of signals including the phase-space representations and tomographic representations is presented. The signals under consideration are either linear or nonlinear ones. The linear signals satisfy linear quantumlike Schroedinger and von Neumann equations. Nonlinear signals satisfy nonlinear Schroedinger equations as well as Gross-Pitaevskii equation describing solitons in Bose-Einstein condensate. The Ville-Wigner distributions for solitons are considered in comparison with tomographic-probability densities describing solitons completely. different kinds of tomographies - symplectic tomography, optical tomography and Fresnel tomography are reviewed. New kind of map of the signals onto probability distributions of discrete photon number-like variable is discussed. Mutual relations between different transformations of signal functions are established in explicit form. Such characteristics of the signal-probability distribution as entropy is discussed
Distributed and decentralized state estimation in gas networks as distributed parameter systems.
Ahmadian Behrooz, Hesam; Boozarjomehry, R Bozorgmehry
2015-09-01
In this paper, a framework for distributed and decentralized state estimation in high-pressure and long-distance gas transmission networks (GTNs) is proposed. The non-isothermal model of the plant including mass, momentum and energy balance equations are used to simulate the dynamic behavior. Due to several disadvantages of implementing a centralized Kalman filter for large-scale systems, the continuous/discrete form of extended Kalman filter for distributed and decentralized estimation (DDE) has been extended for these systems. Accordingly, the global model is decomposed into several subsystems, called local models. Some heuristic rules are suggested for system decomposition in gas pipeline networks. In the construction of local models, due to the existence of common states and interconnections among the subsystems, the assimilation and prediction steps of the Kalman filter are modified to take the overlapping and external states into account. However, dynamic Riccati equation for each subsystem is constructed based on the local model, which introduces a maximum error of 5% in the estimated standard deviation of the states in the benchmarks studied in this paper. The performance of the proposed methodology has been shown based on the comparison of its accuracy and computational demands against their counterparts in centralized Kalman filter for two viable benchmarks. In a real life network, it is shown that while the accuracy is not significantly decreased, the real-time factor of the state estimation is increased by a factor of 10. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Farkas, A.; Balashazy, I.; Szoeke, I.
2003-01-01
The general objective of our research is modelling the biophysical processes of the effects of inhaled radon progenies. This effort is related to the rejection or support of the linear no threshold (LNT) dose-effect hypothesis, which seems to be one of the most challenging tasks of current radiation protection. Our approximation and results may also serve as a useful tool for lung cancer models. In this study, deposition patterns, activity distributions and alpha-hit probabilities of inhaled radon progenies in the large airways of the human tracheobronchial tree are computed. The airflow fields and related particle deposition patterns strongly depend on the shape of airway geometry and breathing pattern. Computed deposition patterns of attached an unattached radon progenies are strongly inhomogeneous creating hot spots at the carinal regions and downstream of the inner sides of the daughter airways. The results suggest that in the vicinity of the carinal regions the multiple hit probabilities are quite high even at low average doses and increase exponentially in the low-dose range. Thus, even the so-called low doses may present high doses for large clusters of cells. The cell transformation probabilities are much higher in these regions and this phenomenon cannot be modeled with average burdens. (authors)
Lunsford, M. Leigh; Rowell, Ginger Holmes; Goodson-Espy, Tracy
2006-01-01
We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…
Whittle, Peter
1992-01-01
This book is a complete revision of the earlier work Probability which ap peared in 1970. While revised so radically and incorporating so much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability, de manding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level'. In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character. The particular novelty of the approach was that expectation was taken as the prime concept, and the concept of expectation axiomatized rather than that of a probability measure. In the preface to the original text of 1970 (reproduced below, together with that to the Russian edition of 1982) I listed what I saw as the advantages of the approach in as unlaboured a fashion as I could. I also took the view that the text...
Energy Technology Data Exchange (ETDEWEB)
Moskovitz, D.; Harrington, C.; Shirley, W.; Cowart, R.; Sedano, R.; Weston, F.
2002-10-01
Designing and implementing credit-based pilot programs for distributed resources distribution is a low-cost, low-risk opportunity to find out how these resources can help defer or avoid costly electric power system (utility grid) distribution upgrades. This report describes implementation options for deaveraged distribution credits and distributed resource development zones. Developing workable programs implementing these policies can dramatically increase the deployment of distributed resources in ways that benefit distributed resource vendors, users, and distribution utilities. This report is one in the State Electricity Regulatory Policy and Distributed Resources series developed under contract to NREL (see Annual Technical Status Report of the Regulatory Assistance Project: September 2000-September 2001, NREL/SR-560-32733). Other titles in this series are: (1) Accommodating Distributed Resources in Wholesale Markets, NREL/SR-560-32497; (2) Distributed Resources and Electric System Re liability, NREL/SR-560-32498; (3) Distribution System Cost Methodologies for Distributed Generation, NREL/SR-560-32500; (4) Distribution System Cost Methodologies for Distributed Generation Appendices, NREL/SR-560-32501.
Bayesian Nonparametric Model for Estimating Multistate Travel Time Distribution
Directory of Open Access Journals (Sweden)
Emmanuel Kidando
2017-01-01
Full Text Available Multistate models, that is, models with more than two distributions, are preferred over single-state probability models in modeling the distribution of travel time. Literature review indicated that the finite multistate modeling of travel time using lognormal distribution is superior to other probability functions. In this study, we extend the finite multistate lognormal model of estimating the travel time distribution to unbounded lognormal distribution. In particular, a nonparametric Dirichlet Process Mixture Model (DPMM with stick-breaking process representation was used. The strength of the DPMM is that it can choose the number of components dynamically as part of the algorithm during parameter estimation. To reduce computational complexity, the modeling process was limited to a maximum of six components. Then, the Markov Chain Monte Carlo (MCMC sampling technique was employed to estimate the parameters’ posterior distribution. Speed data from nine links of a freeway corridor, aggregated on a 5-minute basis, were used to calculate the corridor travel time. The results demonstrated that this model offers significant flexibility in modeling to account for complex mixture distributions of the travel time without specifying the number of components. The DPMM modeling further revealed that freeway travel time is characterized by multistate or single-state models depending on the inclusion of onset and offset of congestion periods.
Theory of overdispersion in counting statistics caused by fluctuating probabilities
International Nuclear Information System (INIS)
Semkow, Thomas M.
1999-01-01
It is shown that the random Lexis fluctuations of probabilities such as probability of decay or detection cause the counting statistics to be overdispersed with respect to the classical binomial, Poisson, or Gaussian distributions. The generating and the distribution functions for the overdispersed counting statistics are derived. Applications to radioactive decay with detection and more complex experiments are given, as well as distinguishing between the source and background, in the presence of overdispersion. Monte-Carlo verifications are provided
Finite-size scaling of survival probability in branching processes
Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Alvaro
2014-01-01
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival probability for a given branching process ruled by a probability distribution of the number of offspring per element whose standard deviation is finite, obtaining the exact scaling function as well as the critical exponents. Our findings prove the universal behavi...
Wigner functions for nonclassical states of a collection of two-level atoms
Agarwal, G. S.; Dowling, Jonathan P.; Schleich, Wolfgang P.
1993-01-01
The general theory of atomic angular momentum states is used to derive the Wigner distribution function for atomic angular momentum number states, coherent states, and squeezed states. These Wigner functions W(theta,phi) are represented as a pseudo-probability distribution in spherical coordinates theta and phi on the surface of a sphere of radius the square root of j(j +1) where j is the total angular momentum.
Miller, Brian W.; Frid, Leonardo; Chang, Tony; Piekielek, N. B.; Hansen, Andrew J.; Morisette, Jeffrey T.
2015-01-01
State-and-transition simulation models (STSMs) are known for their ability to explore the combined effects of multiple disturbances, ecological dynamics, and management actions on vegetation. However, integrating the additional impacts of climate change into STSMs remains a challenge. We address this challenge by combining an STSM with species distribution modeling (SDM). SDMs estimate the probability of occurrence of a given species based on observed presence and absence locations as well as environmental and climatic covariates. Thus, in order to account for changes in habitat suitability due to climate change, we used SDM to generate continuous surfaces of species occurrence probabilities. These data were imported into ST-Sim, an STSM platform, where they dictated the probability of each cell transitioning between alternate potential vegetation types at each time step. The STSM was parameterized to capture additional processes of vegetation growth and disturbance that are relevant to a keystone species in the Greater Yellowstone Ecosystem—whitebark pine (Pinus albicaulis). We compared historical model runs against historical observations of whitebark pine and a key disturbance agent (mountain pine beetle, Dendroctonus ponderosae), and then projected the simulation into the future. Using this combination of correlative and stochastic simulation models, we were able to reproduce historical observations and identify key data gaps. Results indicated that SDMs and STSMs are complementary tools, and combining them is an effective way to account for the anticipated impacts of climate change, biotic interactions, and disturbances, while also allowing for the exploration of management options.
An analytic initial-state parton shower
International Nuclear Information System (INIS)
Kilian, W.
2011-12-01
We present a new algorithm for an analytic parton shower. While the algorithm for the final-state shower has been known in the literature, the construction of an initial-state shower along these lines is new. The aim is to have a parton shower algorithm for which the full analytic form of the probability distribution for all branchings is known. For these parton shower algorithms it is therefore possible to calculate the probability for a given event to be generated, providing the potential to reweight the event after the simulation. We develop the algorithm for this shower including scale choices and angular ordering. Merging to matrix elements is used to describe high-energy tails of distributions correctly. Finally, we compare our results with those of other parton showers and with experimental data from LEP, Tevatron and LHC. (orig.)
An analytic initial-state parton shower
Energy Technology Data Exchange (ETDEWEB)
Kilian, W. [Siegen Univ. (Germany). Dept. Physik; Reuter, J.; Schmidt, S.; Wiesler, D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2011-12-15
We present a new algorithm for an analytic parton shower. While the algorithm for the final-state shower has been known in the literature, the construction of an initial-state shower along these lines is new. The aim is to have a parton shower algorithm for which the full analytic form of the probability distribution for all branchings is known. For these parton shower algorithms it is therefore possible to calculate the probability for a given event to be generated, providing the potential to reweight the event after the simulation. We develop the algorithm for this shower including scale choices and angular ordering. Merging to matrix elements is used to describe high-energy tails of distributions correctly. Finally, we compare our results with those of other parton showers and with experimental data from LEP, Tevatron and LHC. (orig.)
Non-equilibrium random matrix theory. Transition probabilities
International Nuclear Information System (INIS)
Pedro, Francisco Gil; Westphal, Alexander
2016-06-01
In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
Non-equilibrium random matrix theory. Transition probabilities
Energy Technology Data Exchange (ETDEWEB)
Pedro, Francisco Gil [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie
2016-06-15
In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
Burst wait time simulation of CALIBAN reactor at delayed super-critical state
International Nuclear Information System (INIS)
Humbert, P.; Authier, N.; Richard, B.; Grivot, P.; Casoli, P.
2012-01-01
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 the 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)
Burst wait time simulation of CALIBAN reactor at delayed super-critical state
Energy Technology Data Exchange (ETDEWEB)
Humbert, P. [Commissariat a l' Energie Atomique CEA, Centre de Bruyeres-le-Chatel, 91297 Arpajon (France); Authier, N.; Richard, B.; Grivot, P.; Casoli, P. [Commissariat a l' Energie Atomique CEA, Centre de Valduc, 21120 Is-sur-Tille (France)
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 the 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)
Zhang, Yuanhui; Wu, Haipeng; Denton, Brian T; Wilson, James R; Lobo, Jennifer M
2017-10-27
Markov models are commonly used for decision-making studies in many application domains; however, there are no widely adopted methods for performing sensitivity analysis on such models with uncertain transition probability matrices (TPMs). This article describes two simulation-based approaches for conducting probabilistic sensitivity analysis on a given discrete-time, finite-horizon, finite-state Markov model using TPMs that are sampled over a specified uncertainty set according to a relevant probability distribution. The first approach assumes no prior knowledge of the probability distribution, and each row of a TPM is independently sampled from the uniform distribution on the row's uncertainty set. The second approach involves random sampling from the (truncated) multivariate normal distribution of the TPM's maximum likelihood estimators for its rows subject to the condition that each row has nonnegative elements and sums to one. The two sampling methods are easily implemented and have reasonable computation times. A case study illustrates the application of these methods to a medical decision-making problem involving the evaluation of treatment guidelines for glycemic control of patients with type 2 diabetes, where natural variation in a patient's glycated hemoglobin (HbA1c) is modeled as a Markov chain, and the associated TPMs are subject to uncertainty.
Fusion barrier distributions - What have we learned?
International Nuclear Information System (INIS)
Hinde, D. J.; Dasgupta, M.
1998-01-01
The study of nuclear fusion received a strong impetus from the realisation that an experimental fusion barrier distribution could be determined from precisely measured fusion cross-sections. Experimental data for different reactions have shown in the fusion barrier distributions clear signatures of a range of nuclear excitations, for example the effects of static quadrupole and hexadecapole deformations, single- and double-phonon states, transfer of nucleons, and high-lying excited states. The improved understanding of fusion barrier distributions allows more reliable prediction of fusion angular momentum distributions, which aids interpretation of fission probabilities and fission anisotropies, and understanding of the population of super-deformed bands for nuclear structure studies. Studies of the relationship between the fusion barrier distribution and the extra-push energy should improve our understanding of the mechanism of the extra-push effect, and may help to predict new ways of forming very heavy or super-heavy nuclei
International Nuclear Information System (INIS)
Khayat, Omid; Afarideh, Hossein; Mohammadnia, Meisam
2015-01-01
In the solid state nuclear track detectors of chemically etched type, nuclear tracks with center-to-center neighborhood of distance shorter than two times the radius of tracks will emerge as overlapping tracks. Track overlapping in this type of detectors causes tracks count losses and it becomes rather severe in high track densities. Therefore, tracks counting in this condition should include a correction factor for count losses of different tracks overlapping orders since a number of overlapping tracks may be counted as one track. Another aspect of the problem is the cases where imaging the whole area of the detector and counting all tracks are not possible. In these conditions a statistical generalization method is desired to be applicable in counting a segmented area of the detector and the results can be generalized to the whole surface of the detector. Also there is a challenge in counting the tracks in densely overlapped tracks because not sufficient geometrical or contextual information are available. It this paper we present a statistical counting method which gives the user a relation between the tracks overlapping probabilities on a segmented area of the detector surface and the total number of tracks. To apply the proposed method one can estimate the total number of tracks on a solid state detector of arbitrary shape and dimensions by approximating the tracks averaged area, whole detector surface area and some orders of tracks overlapping probabilities. It will be shown that this method is applicable in high and ultra high density tracks images and the count loss error can be enervated using a statistical generalization approach. - Highlights: • A correction factor for count losses of different tracks overlapping orders. • For the cases imaging the whole area of the detector is not possible. • Presenting a statistical generalization method for segmented areas. • Giving a relation between the tracks overlapping probabilities and the total tracks
Probability theory for 3-layer remote sensing radiative transfer model: univariate case.
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
Comment on ''Semiquantum-key distribution using less than four quantum states''
International Nuclear Information System (INIS)
Boyer, Michel; Mor, Tal
2011-01-01
For several decades it was believed that information-secure key distribution requires both the sender and receiver to have the ability to generate and/or manipulate quantum states. Earlier, we showed that quantum key distribution in which one party is classical is possible [Boyer, Kenigsberg, and Mor, Phys. Rev. Lett. 99, 140501 (2007)]. A surprising and very nice extension of that result was suggested by Zou, Qiu, Li, Wu, and Li [Phys. Rev. A 79, 052312 (2009)]. Their paper suggests that it is sufficient for the originator of the states (the person holding the quantum technology) to generate just one state. The resulting semiquantum key distribution, which we call here 'quantum key distribution with classical Alice' is indeed completely robust against eavesdropping. However, their proof (that no eavesdropper can get information without being possibly detected) is faulty. We provide here a fully detailed and direct proof of their very important result.
Failure probability analysis of optical grid
Zhong, Yaoquan; Guo, Wei; Sun, Weiqiang; Jin, Yaohui; Hu, Weisheng
2008-11-01
Optical grid, the integrated computing environment based on optical network, is expected to be an efficient infrastructure to support advanced data-intensive grid applications. In optical grid, the faults of both computational and network resources are inevitable due to the large scale and high complexity of the system. With the optical network based distributed computing systems extensive applied in the processing of data, the requirement of the application failure probability have been an important indicator of the quality of application and an important aspect the operators consider. This paper will present a task-based analysis method of the application failure probability in optical grid. Then the failure probability of the entire application can be quantified, and the performance of reducing application failure probability in different backup strategies can be compared, so that the different requirements of different clients can be satisfied according to the application failure probability respectively. In optical grid, when the application based DAG (directed acyclic graph) is executed in different backup strategies, the application failure probability and the application complete time is different. This paper will propose new multi-objective differentiated services algorithm (MDSA). New application scheduling algorithm can guarantee the requirement of the failure probability and improve the network resource utilization, realize a compromise between the network operator and the application submission. Then differentiated services can be achieved in optical grid.
Carpenter, J. R.; Markley, F. L.; Alfriend, K. T.; Wright, C.; Arcido, J.
2011-01-01
Sequential probability ratio tests explicitly allow decision makers to incorporate false alarm and missed detection risks, and are potentially less sensitive to modeling errors than a procedure that relies solely on a probability of collision threshold. Recent work on constrained Kalman filtering has suggested an approach to formulating such a test for collision avoidance maneuver decisions: a filter bank with two norm-inequality-constrained epoch-state extended Kalman filters. One filter models 1he null hypothesis 1ha1 the miss distance is inside the combined hard body radius at the predicted time of closest approach, and one filter models the alternative hypothesis. The epoch-state filter developed for this method explicitly accounts for any process noise present in the system. The method appears to work well using a realistic example based on an upcoming highly-elliptical orbit formation flying mission.
The extinction probability in systems randomly varying in time
Directory of Open Access Journals (Sweden)
Imre Pázsit
2017-09-01
Full Text Available The extinction probability of a branching process (a neutron chain in a multiplying medium is calculated for a system randomly varying in time. The evolution of the first two moments of such a process was calculated previously by the authors in a system randomly shifting between two states of different multiplication properties. The same model is used here for the investigation of the extinction probability. It is seen that the determination of the extinction probability is significantly more complicated than that of the moments, and it can only be achieved by pure numerical methods. The numerical results indicate that for systems fluctuating between two subcritical or two supercritical states, the extinction probability behaves as expected, but for systems fluctuating between a supercritical and a subcritical state, there is a crucial and unexpected deviation from the predicted behaviour. The results bear some significance not only for neutron chains in a multiplying medium, but also for the evolution of biological populations in a time-varying environment.
Yin, Yuan; Shi, Deheng; Sun, Jinfeng; Zhu, Zunlue
2018-03-01
This work calculates the potential energy curves of 9 Λ-S and 28 Ω states of the NCl+ cation. The technique employed is the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson correction. The Λ-S states are X2Π, 12Σ+, 14Π, 14Σ+, 14Σ-, 24Π, 14Δ, 16Σ+, and 16Π, which are yielded from the first two dissociation channels of NCl+ cation. The Ω states are generated from these Λ-S states. The 14Π, 14Δ, 16Σ+, and 16Π states are inverted with the spin-orbit coupling effect included. The 14Σ+, 16Σ+, and 16Π states are very weakly bound, whose well depths are only several-hundred cm- 1. One avoided crossing of PECs occurs between the 12Σ+ and 22Σ+ states. To improve the quality of potential energy curves, core-valence correlation and scalar relativistic corrections are included. The potential energies are extrapolated to the complete basis set limit. The spectroscopic parameters and vibrational levels are calculated. The transition dipole moments are computed. The Franck-Condon factors, Einstein coefficients, and radiative lifetimes of many transitions are determined. The spectroscopic approaches are proposed for observing these states according to the transition probabilities. The spin-orbit coupling effect on the spectroscopic and vibrational properties is evaluated. The spectroscopic parameters, vibrational levels, transition dipole moments, as well as transition probabilities reported in this paper could be considered to be very reliable.
Estimating the Probability of Wind Ramping Events: A Data-driven Approach
Wang, Cheng; Wei, Wei; Wang, Jianhui; Qiu, Feng
2016-01-01
This letter proposes a data-driven method for estimating the probability of wind ramping events without exploiting the exact probability distribution function (PDF) of wind power. Actual wind data validates the proposed method.
Probability of success for phase III after exploratory biomarker analysis in phase II.
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.
The influence of initial beliefs on judgments of probability.
Yu, Erica C; Lagnado, David A
2012-01-01
This study aims to investigate whether experimentally induced prior beliefs affect processing of evidence including the updating of beliefs under uncertainty about the unknown probabilities of outcomes and the structural, outcome-generating nature of the environment. Participants played a gambling task in the form of computer-simulated slot machines and were given information about the slot machines' possible outcomes without their associated probabilities. One group was induced with a prior belief about the outcome space that matched the space of actual outcomes to be sampled; the other group was induced with a skewed prior belief that included the actual outcomes and also fictional higher outcomes. In reality, however, all participants sampled evidence from the same underlying outcome distribution, regardless of priors given. Before and during sampling, participants expressed their beliefs about the outcome distribution (values and probabilities). Evaluation of those subjective probability distributions suggests that all participants' judgments converged toward the observed outcome distribution. However, despite observing no supporting evidence for fictional outcomes, a significant proportion of participants in the skewed priors condition expected them in the future. A probe of the participants' understanding of the underlying outcome-generating processes indicated that participants' judgments were based on the information given in the induced priors and consequently, a significant proportion of participants in the skewed condition believed the slot machines were not games of chance while participants in the control condition believed the machines generated outcomes at random. Beyond Bayesian or heuristic belief updating, priors not only contribute to belief revision but also affect one's deeper understanding of the environment.
Optimizing Probability of Detection Point Estimate Demonstration
Koshti, Ajay M.
2017-01-01
Probability of detection (POD) analysis is used in assessing reliably detectable flaw size in nondestructive evaluation (NDE). MIL-HDBK-18231and associated mh18232POD software gives most common methods of POD analysis. Real flaws such as cracks and crack-like flaws are desired to be detected using these NDE methods. A reliably detectable crack size is required for safe life analysis of fracture critical parts. The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using Point Estimate Method. POD Point estimate method is used by NASA for qualifying special NDE procedures. The point estimate method uses binomial distribution for probability density. Normally, a set of 29 flaws of same size within some tolerance are used in the demonstration. The optimization is performed to provide acceptable value for probability of passing demonstration (PPD) and achieving acceptable value for probability of false (POF) calls while keeping the flaw sizes in the set as small as possible.
The maximum entropy method of moments and Bayesian probability theory
Bretthorst, G. Larry
2013-08-01
The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.
Xiao, Chuan-Le; Chen, Xiao-Zhou; Du, Yang-Li; Sun, Xuesong; Zhang, Gong; He, Qing-Yu
2013-01-04
Mass spectrometry has become one of the most important technologies in proteomic analysis. Tandem mass spectrometry (LC-MS/MS) is a major tool for the analysis of peptide mixtures from protein samples. The key step of MS data processing is the identification of peptides from experimental spectra by searching public sequence databases. Although a number of algorithms to identify peptides from MS/MS data have been already proposed, e.g. Sequest, OMSSA, X!Tandem, Mascot, etc., they are mainly based on statistical models considering only peak-matches between experimental and theoretical spectra, but not peak intensity information. Moreover, different algorithms gave different results from the same MS data, implying their probable incompleteness and questionable reproducibility. We developed a novel peptide identification algorithm, ProVerB, based on a binomial probability distribution model of protein tandem mass spectrometry combined with a new scoring function, making full use of peak intensity information and, thus, enhancing the ability of identification. Compared with Mascot, Sequest, and SQID, ProVerB identified significantly more peptides from LC-MS/MS data sets than the current algorithms at 1% False Discovery Rate (FDR) and provided more confident peptide identifications. ProVerB is also compatible with various platforms and experimental data sets, showing its robustness and versatility. The open-source program ProVerB is available at http://bioinformatics.jnu.edu.cn/software/proverb/ .
Roosma, F.; van Oorschot, W.J.H.; Gelissen, J.P.T.M.
2016-01-01
Whether people believe that tax burdens are fairly distributed is an important condition for welfare state legitimacy. This article examines how people evaluate this distribution of tax burdens in their country by using latent cluster analysis. We use 2006 International Social Survey Program data
Power distribution, the environment, and public health. A state-level analysis
International Nuclear Information System (INIS)
Boyce, James K.; Klemer, Andrew R.; Templet, Paul H.; Willis, Cleve E.
1999-01-01
This paper examines relationships among power distribution, the environment, and public health by means of a cross-sectional analysis of the 50 US states. A measure of inter-state variations in power distribution is derived from data on voter participation, tax fairness, Medicaid access, and educational attainment. We develop and estimate a recursive model linking the distribution of power to environmental policy, environmental stress, and public health. The results support the hypothesis that greater power inequality leads to weaker environmental policies, which in turn lead to greater environmental degradation and to adverse public health outcomes
Power distribution, the environment, and public health. A state-level analysis
Energy Technology Data Exchange (ETDEWEB)
Boyce, James K. [Department of Economics, University of Massachusetts, Amherst, MA 01003 (United States); Klemer, Andrew R. [Department of Biology, University of Minnesota, Duluth, MN (United States); Templet, Paul H. [Institute of Environmental Studies, Louisiana State University, Baton Rouge, LA (United States); Willis, Cleve E. [Department of Resource Economics, University of Massachusetts, Amherst, MA 01003 (United States)
1999-04-15
This paper examines relationships among power distribution, the environment, and public health by means of a cross-sectional analysis of the 50 US states. A measure of inter-state variations in power distribution is derived from data on voter participation, tax fairness, Medicaid access, and educational attainment. We develop and estimate a recursive model linking the distribution of power to environmental policy, environmental stress, and public health. The results support the hypothesis that greater power inequality leads to weaker environmental policies, which in turn lead to greater environmental degradation and to adverse public health outcomes.
Power distribution, the environment, and public health. A state-level analysis
Energy Technology Data Exchange (ETDEWEB)
Boyce, James K. [Department of Economics, University of Massachusetts, Amherst, MA 01003 (United States); Klemer, Andrew R. [Department of Biology, University of Minnesota, Duluth, MN (United States); Templet, Paul H. [Institute of Environmental Studies, Louisiana State University, Baton Rouge, LA (United States); Willis, Cleve E. [Department of Resource Economics, University of Massachusetts, Amherst, MA 01003 (United States)
1999-04-15
This paper examines relationships among power distribution, the environment, and public health by means of a cross-sectional analysis of the 50 US states. A measure of inter-state variations in power distribution is derived from data on voter participation, tax fairness, Medicaid access, and educational attainment. We develop and estimate a recursive model linking the distribution of power to environmental policy, environmental stress, and public health. The results support the hypothesis that greater power inequality leads to weaker environmental policies, which in turn lead to greater environmental degradation and to adverse public health outcomes
Probability theory a foundational course
Pakshirajan, R P
2013-01-01
This book shares the dictum of J. L. Doob in treating Probability Theory as a branch of Measure Theory and establishes this relation early. Probability measures in product spaces are introduced right at the start by way of laying the ground work to later claim the existence of stochastic processes with prescribed finite dimensional distributions. Other topics analysed in the book include supports of probability measures, zero-one laws in product measure spaces, Erdos-Kac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains. This book is offered as a text book for students pursuing graduate programs in Mathematics and or Statistics. The book aims to help the teacher present the theory with ease, and to help the student sustain his interest and joy in learning the subject.
Modified Stieltjes Transform and Generalized Convolutions of Probability Distributions
Directory of Open Access Journals (Sweden)
Lev B. Klebanov
2018-01-01
Full Text Available The classical Stieltjes transform is modified in such a way as to generalize both Stieltjes and Fourier transforms. This transform allows the introduction of new classes of commutative and non-commutative generalized convolutions. A particular case of such a convolution for degenerate distributions appears to be the Wigner semicircle distribution.
Aylward, C.M.; Murdoch, J.D.; Donovan, Therese M.; Kilpatrick, C.W.; Bernier, C.; Katz, J.
2018-01-01
The American marten Martes americana is a species of conservation concern in the northeastern United States due to widespread declines from over‐harvesting and habitat loss. Little information exists on current marten distribution and how landscape characteristics shape patterns of occupancy across the region, which could help develop effective recovery strategies. The rarity of marten and lack of historical distribution records are also problematic for region‐wide conservation planning. Expert opinion can provide a source of information for estimating species–landscape relationships and is especially useful when empirical data are sparse. We created a survey to elicit expert opinion and build a model that describes marten occupancy in the northeastern United States as a function of landscape conditions. We elicited opinions from 18 marten experts that included wildlife managers, trappers and researchers. Each expert estimated occupancy probability at 30 sites in their geographic region of expertise. We, then, fit the response data with a set of 58 models that incorporated the effects of covariates related to forest characteristics, climate, anthropogenic impacts and competition at two spatial scales (1.5 and 5 km radii), and used model selection techniques to determine the best model in the set. Three top models had strong empirical support, which we model averaged based on AIC weights. The final model included effects of five covariates at the 5‐km scale: percent canopy cover (positive), percent spruce‐fir land cover (positive), winter temperature (negative), elevation (positive) and road density (negative). A receiver operating characteristic curve indicated that the model performed well based on recent occurrence records. We mapped distribution across the region and used circuit theory to estimate movement corridors between isolated core populations. The results demonstrate the effectiveness of expert‐opinion data at modeling occupancy for rare
Automatic diagnosis and control of distributed solid state lighting systems
Dong, J.; van Driel, W.D.; Zhang, G.Q.
2011-01-01
This paper describes a new design concept of automatically diagnosing and compensating LED degradations in distributed solid state lighting (SSL) systems. A failed LED may significantly reduce the overall illumination level, and destroy the uniform illumination distribution achieved by a nominal