Statistics of intensity in adaptive-optics images and their usefulness for detection and photometry of exoplanets.

PubMed

Gladysz, Szymon; Yaitskova, Natalia; Christou, Julian C

2010-11-01

This paper is an introduction to the problem of modeling the probability density function of adaptive-optics speckle. We show that with the modified Rician distribution one cannot describe the statistics of light on axis. A dual solution is proposed: the modified Rician distribution for off-axis speckle and gamma-based distribution for the core of the point spread function. From these two distributions we derive optimal statistical discriminators between real sources and quasi-static speckles. In the second part of the paper the morphological difference between the two probability density functions is used to constrain a one-dimensional, "blind," iterative deconvolution at the position of an exoplanet. Separation of the probability density functions of signal and speckle yields accurate differential photometry in our simulations of the SPHERE planet finder instrument.

Exact probability distribution function for the volatility of cumulative production

NASA Astrophysics Data System (ADS)

Zadourian, Rubina; Klümper, Andreas

2018-04-01

In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in Lafond et al. (2017), which addressed the effects of normally distributed noise in the production process. Due to its wide applicability in industrial and technological activities we present here the mathematical foundation for an arbitrary distribution function of the process, which we expect will pave the future research on forecasting of the production process.

Bivariate normal, conditional and rectangular probabilities: A computer program with applications

NASA Technical Reports Server (NTRS)

Swaroop, R.; Brownlow, J. D.; Ashwworth, G. R.; Winter, W. R.

1980-01-01

Some results for the bivariate normal distribution analysis are presented. Computer programs for conditional normal probabilities, marginal probabilities, as well as joint probabilities for rectangular regions are given: routines for computing fractile points and distribution functions are also presented. Some examples from a closed circuit television experiment are included.

Exact probability distribution functions for Parrondo's games

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Exact probability distribution functions for Parrondo's games.

PubMed

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

2016-12-01

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

Properties of the probability density function of the non-central chi-squared distribution

NASA Astrophysics Data System (ADS)

András, Szilárd; Baricz, Árpád

2008-10-01

In this paper we consider the probability density function (pdf) of a non-central [chi]2 distribution with arbitrary number of degrees of freedom. For this function we prove that can be represented as a finite sum and we deduce a partial derivative formula. Moreover, we show that the pdf is log-concave when the degrees of freedom is greater or equal than 2. At the end of this paper we present some Turán-type inequalities for this function and an elegant application of the monotone form of l'Hospital's rule in probability theory is given.

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

NASA Astrophysics Data System (ADS)

Iskandar, I.

2018-03-01

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

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

NASA Technical Reports Server (NTRS)

Lanzi, R. James; Vincent, Brett T.

1993-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Stochastic analysis of particle movement over a dune bed

USGS Publications Warehouse

Lee, Baum K.; Jobson, Harvey E.

1977-01-01

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

High throughput nonparametric probability density estimation.

PubMed

Farmer, Jenny; Jacobs, Donald

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.

High throughput nonparametric probability density estimation

PubMed Central

Farmer, Jenny

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference. PMID:29750803

Sampling probability distributions of lesions in mammograms

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

A brief introduction to probability.

PubMed

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

2018-02-01

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

Probability distribution functions in turbulent convection

NASA Technical Reports Server (NTRS)

Balachandar, S.; Sirovich, L.

1991-01-01

Results of an extensive investigation of probability distribution functions (pdfs) for Rayleigh-Benard convection, in hard turbulence regime, are presented. It is shown that the pdfs exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to the universality is presented.

The force distribution probability function for simple fluids by density functional theory.

PubMed

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.

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

NASA Astrophysics Data System (ADS)

Gernez, Pierre; Stramski, Dariusz; Darecki, Miroslaw

2011-07-01

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

Quantile Functions, Convergence in Quantile, and Extreme Value Distribution Theory.

DTIC Science & Technology

1980-11-01

Gnanadesikan (1968). Quantile functions are advocated by Parzen (1979) as providing an approach to probability-based data analysis. Quantile functions are... Gnanadesikan , R. (1968). Probability Plotting Methods for the Analysis of Data, Biomtrika, 55, 1-17.

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

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

1991-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2009-05-01

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

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

Code of Federal Regulations, 2014 CFR

2014-07-01

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

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

Code of Federal Regulations, 2011 CFR

2011-07-01

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

Nonadditive entropies yield probability distributions with biases not warranted by the data.

PubMed

Pressé, Steve; Ghosh, Kingshuk; Lee, Julian; Dill, Ken A

2013-11-01

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann-Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types of entropies that violate the Shore and Johnson axioms, including nonadditive entropies such as the Tsallis entropy, violate this basic consistency requirement. Here we use the axiomatic framework of Shore and Johnson to show how such nonadditive entropy functions generate biases in probability distributions that are not warranted by the underlying data.

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

NASA Astrophysics Data System (ADS)

Sallah, M.

2014-03-01

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

On Orbital Elements of Extrasolar Planetary Candidates and Spectroscopic Binaries

NASA Technical Reports Server (NTRS)

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

2001-01-01

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

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

NASA Astrophysics Data System (ADS)

Liland, Kristian Hovde; Snipen, Lars

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

Path probability of stochastic motion: A functional approach

NASA Astrophysics Data System (ADS)

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.

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

Gravitational lensing, time delay, and gamma-ray bursts

NASA Technical Reports Server (NTRS)

Mao, Shude

1992-01-01

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

Opacity probability distribution functions for electronic systems of CN and C2 molecules including their stellar isotopic forms.

NASA Technical Reports Server (NTRS)

Querci, F.; Kunde, V. G.; Querci, M.

1971-01-01

The basis and techniques are presented for generating opacity probability distribution functions for the CN molecule (red and violet systems) and the C2 molecule (Swan, Phillips, Ballik-Ramsay systems), two of the more important diatomic molecules in the spectra of carbon stars, with a view to including these distribution functions in equilibrium model atmosphere calculations. Comparisons to the CO molecule are also shown. T he computation of the monochromatic absorption coefficient uses the most recent molecular data with revision of the oscillator strengths for some of the band systems. The total molecular stellar mass absorption coefficient is established through fifteen equations of molecular dissociation equilibrium to relate the distribution functions to each other on a per gram of stellar material basis.

The maximum entropy method of moments and Bayesian probability theory

NASA Astrophysics Data System (ADS)

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.

On Interpreting and Extracting Information from the Cumulative Distribution Function Curve: A New Perspective with Applications

ERIC Educational Resources Information Center

Balasooriya, Uditha; Li, Jackie; Low, Chan Kee

2012-01-01

For any density function (or probability function), there always corresponds a "cumulative distribution function" (cdf). It is a well-known mathematical fact that the cdf is more general than the density function, in the sense that for a given distribution the former may exist without the existence of the latter. Nevertheless, while the…

Fitness Probability Distribution of Bit-Flip Mutation.

PubMed

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

2015-01-01

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

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

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

Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati

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

Teaching Uncertainties

ERIC Educational Resources Information Center

Duerdoth, Ian

2009-01-01

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

Interpolating Non-Parametric Distributions of Hourly Rainfall Intensities Using Random Mixing

NASA Astrophysics Data System (ADS)

Mosthaf, Tobias; Bárdossy, András; Hörning, Sebastian

2015-04-01

The correct spatial interpolation of hourly rainfall intensity distributions is of great importance for stochastical rainfall models. Poorly interpolated distributions may lead to over- or underestimation of rainfall and consequently to wrong estimates of following applications, like hydrological or hydraulic models. By analyzing the spatial relation of empirical rainfall distribution functions, a persistent order of the quantile values over a wide range of non-exceedance probabilities is observed. As the order remains similar, the interpolation weights of quantile values for one certain non-exceedance probability can be applied to the other probabilities. This assumption enables the use of kernel smoothed distribution functions for interpolation purposes. Comparing the order of hourly quantile values over different gauges with the order of their daily quantile values for equal probabilities, results in high correlations. The hourly quantile values also show high correlations with elevation. The incorporation of these two covariates into the interpolation is therefore tested. As only positive interpolation weights for the quantile values assure a monotonically increasing distribution function, the use of geostatistical methods like kriging is problematic. Employing kriging with external drift to incorporate secondary information is not applicable. Nonetheless, it would be fruitful to make use of covariates. To overcome this shortcoming, a new random mixing approach of spatial random fields is applied. Within the mixing process hourly quantile values are considered as equality constraints and correlations with elevation values are included as relationship constraints. To profit from the dependence of daily quantile values, distribution functions of daily gauges are used to set up lower equal and greater equal constraints at their locations. In this way the denser daily gauge network can be included in the interpolation of the hourly distribution functions. The applicability of this new interpolation procedure will be shown for around 250 hourly rainfall gauges in the German federal state of Baden-Württemberg. The performance of the random mixing technique within the interpolation is compared to applicable kriging methods. Additionally, the interpolation of kernel smoothed distribution functions is compared with the interpolation of fitted parametric distributions.

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

NASA Technical Reports Server (NTRS)

Smith, O. E.

1976-01-01

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

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

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Krishnapur, Manjunath

2009-09-01

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

Method and device for landing aircraft dependent on runway occupancy time

NASA Technical Reports Server (NTRS)

Ghalebsaz Jeddi, Babak (Inventor)

2012-01-01

A technique for landing aircraft using an aircraft landing accident avoidance device is disclosed. The technique includes determining at least two probability distribution functions; determining a safe lower limit on a separation between a lead aircraft and a trail aircraft on a glide slope to the runway; determining a maximum sustainable safe attempt-to-land rate on the runway based on the safe lower limit and the probability distribution functions; directing the trail aircraft to enter the glide slope with a target separation from the lead aircraft corresponding to the maximum sustainable safe attempt-to-land rate; while the trail aircraft is in the glide slope, determining an actual separation between the lead aircraft and the trail aircraft; and directing the trail aircraft to execute a go-around maneuver if the actual separation approaches the safe lower limit. Probability distribution functions include runway occupancy time, and landing time interval and/or inter-arrival distance.

An evaluation of procedures to estimate monthly precipitation probabilities

NASA Astrophysics Data System (ADS)

Legates, David R.

1991-01-01

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

Performance of mixed RF/FSO systems in exponentiated Weibull distributed channels

NASA Astrophysics Data System (ADS)

Zhao, Jing; Zhao, Shang-Hong; Zhao, Wei-Hu; Liu, Yun; Li, Xuan

2017-12-01

This paper presented the performances of asymmetric mixed radio frequency (RF)/free-space optical (FSO) system with the amplify-and-forward relaying scheme. The RF channel undergoes Nakagami- m channel, and the Exponentiated Weibull distribution is adopted for the FSO component. The mathematical formulas for cumulative distribution function (CDF), probability density function (PDF) and moment generating function (MGF) of equivalent signal-to-noise ratio (SNR) are achieved. According to the end-to-end statistical characteristics, the new analytical expressions of outage probability are obtained. Under various modulation techniques, we derive the average bit-error-rate (BER) based on the Meijer's G function. The evaluation and simulation are provided for the system performance, and the aperture average effect is discussed as well.

Time-dependent landslide probability mapping

USGS Publications Warehouse

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

1993-01-01

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

Generalized Wishart Mixtures for Unsupervised Classification of PolSAR Data

NASA Astrophysics Data System (ADS)

Li, Lan; Chen, Erxue; Li, Zengyuan

2013-01-01

This paper presents an unsupervised clustering algorithm based upon the expectation maximization (EM) algorithm for finite mixture modelling, using the complex wishart probability density function (PDF) for the probabilities. The mixture model enables to consider heterogeneous thematic classes which could not be better fitted by the unimodal wishart distribution. In order to make it fast and robust to calculate, we use the recently proposed generalized gamma distribution (GΓD) for the single polarization intensity data to make the initial partition. Then we use the wishart probability density function for the corresponding sample covariance matrix to calculate the posterior class probabilities for each pixel. The posterior class probabilities are used for the prior probability estimates of each class and weights for all class parameter updates. The proposed method is evaluated and compared with the wishart H-Alpha-A classification. Preliminary results show that the proposed method has better performance.

Unifying distribution functions: some lesser known distributions.

PubMed

Moya-Cessa, J R; Moya-Cessa, H; Berriel-Valdos, L R; Aguilar-Loreto, O; Barberis-Blostein, P

2008-08-01

We show that there is a way to unify distribution functions that describe simultaneously a classical signal in space and (spatial) frequency and position and momentum for a quantum system. Probably the most well known of them is the Wigner distribution function. We show how to unify functions of the Cohen class, Rihaczek's complex energy function, and Husimi and Glauber-Sudarshan distribution functions. We do this by showing how they may be obtained from ordered forms of creation and annihilation operators and by obtaining them in terms of expectation values in different eigenbases.

Ensemble Kalman filtering in presence of inequality constraints

NASA Astrophysics Data System (ADS)

van Leeuwen, P. J.

2009-04-01

Kalman filtering is presence of constraints is an active area of research. Based on the Gaussian assumption for the probability-density functions, it looks hard to bring in extra constraints in the formalism. On the other hand, in geophysical systems we often encounter constraints related to e.g. the underlying physics or chemistry, which are violated by the Gaussian assumption. For instance, concentrations are always non-negative, model layers have non-negative thickness, and sea-ice concentration is between 0 and 1. Several methods to bring inequality constraints into the Kalman-filter formalism have been proposed. One of them is probability density function (pdf) truncation, in which the Gaussian mass from the non-allowed part of the variables is just equally distributed over the pdf where the variables are alolwed, as proposed by Shimada et al. 1998. However, a problem with this method is that the probability that e.g. the sea-ice concentration is zero, is zero! The new method proposed here does not have this drawback. It assumes that the probability-density function is a truncated Gaussian, but the truncated mass is not distributed equally over all allowed values of the variables, but put into a delta distribution at the truncation point. This delta distribution can easily be handled with in Bayes theorem, leading to posterior probability density functions that are also truncated Gaussians with delta distributions at the truncation location. In this way a much better representation of the system is obtained, while still keeping most of the benefits of the Kalman-filter formalism. In the full Kalman filter the formalism is prohibitively expensive in large-scale systems, but efficient implementation is possible in ensemble variants of the kalman filter. Applications to low-dimensional systems and large-scale systems will be discussed.

Probability and the changing shape of response distributions for orientation.

PubMed

Anderson, Britt

2014-11-18

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

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

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

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

Qualitative fusion technique based on information poor system and its application to factor analysis for vibration of rolling bearings

NASA Astrophysics Data System (ADS)

Xia, Xintao; Wang, Zhongyu

2008-10-01

For some methods of stability analysis of a system using statistics, it is difficult to resolve the problems of unknown probability distribution and small sample. Therefore, a novel method is proposed in this paper to resolve these problems. This method is independent of probability distribution, and is useful for small sample systems. After rearrangement of the original data series, the order difference and two polynomial membership functions are introduced to estimate the true value, the lower bound and the supper bound of the system using fuzzy-set theory. Then empirical distribution function is investigated to ensure confidence level above 95%, and the degree of similarity is presented to evaluate stability of the system. Cases of computer simulation investigate stable systems with various probability distribution, unstable systems with linear systematic errors and periodic systematic errors and some mixed systems. The method of analysis for systematic stability is approved.

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1972-01-01

The error variance of the process prior multivariate normal distributions of the parameters of the models are assumed to be specified, prior probabilities of the models being correct. A rule for termination of sampling is proposed. Upon termination, the model with the largest posterior probability is chosen as correct. If sampling is not terminated, posterior probabilities of the models and posterior distributions of the parameters are computed. An experiment was chosen to maximize the expected Kullback-Leibler information function. Monte Carlo simulation experiments were performed to investigate large and small sample behavior of the sequential adaptive procedure.

Surveillance system and method having an adaptive sequential probability fault detection test

NASA Technical Reports Server (NTRS)

Herzog, James P. (Inventor); Bickford, Randall L. (Inventor)

2005-01-01

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Surveillance system and method having an adaptive sequential probability fault detection test

NASA Technical Reports Server (NTRS)

Bickford, Randall L. (Inventor); Herzog, James P. (Inventor)

2006-01-01

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Surveillance System and Method having an Adaptive Sequential Probability Fault Detection Test

NASA Technical Reports Server (NTRS)

Bickford, Randall L. (Inventor); Herzog, James P. (Inventor)

2008-01-01

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Computer simulation of random variables and vectors with arbitrary probability distribution laws

NASA Technical Reports Server (NTRS)

Bogdan, V. M.

1981-01-01

Assume that there is given an arbitrary n-dimensional probability distribution F. A recursive construction is found for a sequence of functions x sub 1 = f sub 1 (U sub 1, ..., U sub n), ..., x sub n = f sub n (U sub 1, ..., U sub n) such that if U sub 1, ..., U sub n are independent random variables having uniform distribution over the open interval (0,1), then the joint distribution of the variables x sub 1, ..., x sub n coincides with the distribution F. Since uniform independent random variables can be well simulated by means of a computer, this result allows one to simulate arbitrary n-random variables if their joint probability distribution is known.

Confidence as Bayesian Probability: From Neural Origins to Behavior.

PubMed

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

2015-10-07

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

A least squares approach to estimating the probability distribution of unobserved data in multiphoton microscopy

NASA Astrophysics Data System (ADS)

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.

Multivariate η-μ fading distribution with arbitrary correlation model

NASA Astrophysics Data System (ADS)

Ghareeb, Ibrahim; Atiani, Amani

2018-03-01

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

Continuous-Time Finance and the Waiting Time Distribution: Multiple Characteristic Times

NASA Astrophysics Data System (ADS)

Fa, Kwok Sau

2012-09-01

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

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

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

Probability density cloud as a geometrical tool to describe statistics of scattered light.

PubMed

Yaitskova, Natalia

2017-04-01

First-order statistics of scattered light is described using the representation of the probability density cloud, which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail and are connected to the statistical properties of phase. The moment-generating function for intensity is obtained in a closed form through these parameters. An example of exponentially modified normal distribution is provided to illustrate the functioning of this geometrical approach.

A probabilistic approach to photovoltaic generator performance prediction

NASA Astrophysics Data System (ADS)

Khallat, M. A.; Rahman, S.

1986-09-01

A method for predicting the performance of a photovoltaic (PV) generator based on long term climatological data and expected cell performance is described. The equations for cell model formulation are provided. Use of the statistical model for characterizing the insolation level is discussed. The insolation data is fitted to appropriate probability distribution functions (Weibull, beta, normal). The probability distribution functions are utilized to evaluate the capacity factors of PV panels or arrays. An example is presented revealing the applicability of the procedure.

Aging ballistic Lévy walks

NASA Astrophysics Data System (ADS)

Magdziarz, Marcin; Zorawik, Tomasz

2017-02-01

Aging can be observed for numerous physical systems. In such systems statistical properties [like probability distribution, mean square displacement (MSD), first-passage time] depend on a time span ta between the initialization and the beginning of observations. In this paper we study aging properties of ballistic Lévy walks and two closely related jump models: wait-first and jump-first. We calculate explicitly their probability distributions and MSDs. It turns out that despite similarities these models react very differently to the delay ta. Aging weakly affects the shape of probability density function and MSD of standard Lévy walks. For the jump models the shape of the probability density function is changed drastically. Moreover for the wait-first jump model we observe a different behavior of MSD when ta≪t and ta≫t .

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Probability distribution functions for unit hydrographs with optimization using genetic algorithm

NASA Astrophysics Data System (ADS)

Ghorbani, Mohammad Ali; Singh, Vijay P.; Sivakumar, Bellie; H. Kashani, Mahsa; Atre, Atul Arvind; Asadi, Hakimeh

2017-05-01

A unit hydrograph (UH) of a watershed may be viewed as the unit pulse response function of a linear system. In recent years, the use of probability distribution functions (pdfs) for determining a UH has received much attention. In this study, a nonlinear optimization model is developed to transmute a UH into a pdf. The potential of six popular pdfs, namely two-parameter gamma, two-parameter Gumbel, two-parameter log-normal, two-parameter normal, three-parameter Pearson distribution, and two-parameter Weibull is tested on data from the Lighvan catchment in Iran. The probability distribution parameters are determined using the nonlinear least squares optimization method in two ways: (1) optimization by programming in Mathematica; and (2) optimization by applying genetic algorithm. The results are compared with those obtained by the traditional linear least squares method. The results show comparable capability and performance of two nonlinear methods. The gamma and Pearson distributions are the most successful models in preserving the rising and recession limbs of the unit hydographs. The log-normal distribution has a high ability in predicting both the peak flow and time to peak of the unit hydrograph. The nonlinear optimization method does not outperform the linear least squares method in determining the UH (especially for excess rainfall of one pulse), but is comparable.

Probability distributions for multimeric systems.

PubMed

Albert, Jaroslav; Rooman, Marianne

2016-01-01

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

A Pearson VII distribution function for fast calculation of dechanneling and angular dispersion of beams

NASA Astrophysics Data System (ADS)

Shao, Lin; Peng, Luohan

2009-12-01

Although multiple scattering theories have been well developed, numerical calculation is complicated and only tabulated values have been available, which has caused inconvenience in practical use. We have found that a Pearson VII distribution function can be used to fit Lugujjo and Mayer's probability curves in describing the dechanneling phenomenon in backscattering analysis, over a wide range of disorder levels. Differentiation of the obtained function gives another function to calculate angular dispersion of the beam in the frameworks by Sigmund and Winterbon. The present work provides an easy calculation of both dechanneling probability and angular dispersion for any arbitrary combination of beam and target having a reduced thickness ⩾0.6, which can be implemented in modeling of channeling spectra. Furthermore, we used a Monte Carlo simulation program to calculate the deflection probability and compared them with previously tabulated data. A good agreement was reached.

Probability and Statistics in Sensor Performance Modeling

DTIC Science & Technology

2010-12-01

language software program is called Environmental Awareness for Sensor and Emitter Employment. Some important numerical issues in the implementation...3 Statistical analysis for measuring sensor performance...complementary cumulative distribution function cdf cumulative distribution function DST decision-support tool EASEE Environmental Awareness of

Product of Ginibre matrices: Fuss-Catalan and Raney distributions

NASA Astrophysics Data System (ADS)

Penson, Karol A.; Życzkowski, Karol

2011-06-01

Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions Ps(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions Ps(x) in terms of a combination of s hypergeometric functions of the type sFs-1. The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

Product of Ginibre matrices: Fuss-Catalan and Raney distributions.

PubMed

Penson, Karol A; Zyczkowski, Karol

2011-06-01

Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions P(s)(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions P(s)(x) in terms of a combination of s hypergeometric functions of the type (s)F(s-1). The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

Computing exact bundle compliance control charts via probability generating functions.

PubMed

Chen, Binchao; Matis, Timothy; Benneyan, James

2016-06-01

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

Statistical description of non-Gaussian samples in the F2 layer of the ionosphere during heliogeophysical disturbances

NASA Astrophysics Data System (ADS)

Sergeenko, N. P.

2017-11-01

An adequate statistical method should be developed in order to predict probabilistically the range of ionospheric parameters. This problem is solved in this paper. The time series of the critical frequency of the layer F2- foF2( t) were subjected to statistical processing. For the obtained samples {δ foF2}, statistical distributions and invariants up to the fourth order are calculated. The analysis shows that the distributions differ from the Gaussian law during the disturbances. At levels of sufficiently small probability distributions, there are arbitrarily large deviations from the model of the normal process. Therefore, it is attempted to describe statistical samples {δ foF2} based on the Poisson model. For the studied samples, the exponential characteristic function is selected under the assumption that time series are a superposition of some deterministic and random processes. Using the Fourier transform, the characteristic function is transformed into a nonholomorphic excessive-asymmetric probability-density function. The statistical distributions of the samples {δ foF2} calculated for the disturbed periods are compared with the obtained model distribution function. According to the Kolmogorov's criterion, the probabilities of the coincidence of a posteriori distributions with the theoretical ones are P 0.7-0.9. The conducted analysis makes it possible to draw a conclusion about the applicability of a model based on the Poisson random process for the statistical description and probabilistic variation estimates during heliogeophysical disturbances of the variations {δ foF2}.

A general formula for computing maximum proportion correct scores in various psychophysical paradigms with arbitrary probability distributions of stimulus observations.

PubMed

Dai, Huanping; Micheyl, Christophe

2015-05-01

Proportion correct (Pc) is a fundamental measure of task performance in psychophysics. The maximum Pc score that can be achieved by an optimal (maximum-likelihood) observer in a given task is of both theoretical and practical importance, because it sets an upper limit on human performance. Within the framework of signal detection theory, analytical solutions for computing the maximum Pc score have been established for several common experimental paradigms under the assumption of Gaussian additive internal noise. However, as the scope of applications of psychophysical signal detection theory expands, the need is growing for psychophysicists to compute maximum Pc scores for situations involving non-Gaussian (internal or stimulus-induced) noise. In this article, we provide a general formula for computing the maximum Pc in various psychophysical experimental paradigms for arbitrary probability distributions of sensory activity. Moreover, easy-to-use MATLAB code implementing the formula is provided. Practical applications of the formula are illustrated, and its accuracy is evaluated, for two paradigms and two types of probability distributions (uniform and Gaussian). The results demonstrate that Pc scores computed using the formula remain accurate even for continuous probability distributions, as long as the conversion from continuous probability density functions to discrete probability mass functions is supported by a sufficiently high sampling resolution. We hope that the exposition in this article, and the freely available MATLAB code, facilitates calculations of maximum performance for a wider range of experimental situations, as well as explorations of the impact of different assumptions concerning internal-noise distributions on maximum performance in psychophysical experiments.

A Comparative Study of Probability Collectives Based Multi-agent Systems and Genetic Algorithms

NASA Technical Reports Server (NTRS)

Huang, Chien-Feng; Wolpert, David H.; Bieniawski, Stefan; Strauss, Charles E. M.

2005-01-01

We compare Genetic Algorithms (GA's) with Probability Collectives (PC), a new framework for distributed optimization and control. In contrast to GA's, PC-based methods do not update populations of solutions. Instead they update an explicitly parameterized probability distribution p over the space of solutions. That updating of p arises as the optimization of a functional of p. The functional is chosen so that any p that optimizes it should be p peaked about good solutions. The PC approach works in both continuous and discrete problems. It does not suffer from the resolution limitation of the finite bit length encoding of parameters into GA alleles. It also has deep connections with both game theory and statistical physics. We review the PC approach using its motivation as the information theoretic formulation of bounded rationality for multi-agent systems. It is then compared with GA's on a diverse set of problems. To handle high dimensional surfaces, in the PC method investigated here p is restricted to a product distribution. Each distribution in that product is controlled by a separate agent. The test functions were selected for their difficulty using either traditional gradient descent or genetic algorithms. On those functions the PC-based approach significantly outperforms traditional GA's in both rate of descent, trapping in false minima, and long term optimization.

Construction and identification of a D-Vine model applied to the probability distribution of modal parameters in structural dynamics

NASA Astrophysics Data System (ADS)

Dubreuil, S.; Salaün, M.; Rodriguez, E.; Petitjean, F.

2018-01-01

This study investigates the construction and identification of the probability distribution of random modal parameters (natural frequencies and effective parameters) in structural dynamics. As these parameters present various types of dependence structures, the retained approach is based on pair copula construction (PCC). A literature review leads us to choose a D-Vine model for the construction of modal parameters probability distributions. Identification of this model is based on likelihood maximization which makes it sensitive to the dimension of the distribution, namely the number of considered modes in our context. To this respect, a mode selection preprocessing step is proposed. It allows the selection of the relevant random modes for a given transfer function. The second point, addressed in this study, concerns the choice of the D-Vine model. Indeed, D-Vine model is not uniquely defined. Two strategies are proposed and compared. The first one is based on the context of the study whereas the second one is purely based on statistical considerations. Finally, the proposed approaches are numerically studied and compared with respect to their capabilities, first in the identification of the probability distribution of random modal parameters and second in the estimation of the 99 % quantiles of some transfer functions.

The Homotopic Probability Distribution and the Partition Function for the Entangled System Around a Ribbon Segment Chain

NASA Astrophysics Data System (ADS)

Qian, Shang-Wu; Gu, Zhi-Yu

2001-12-01

Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution P_L^n for the winding number n and the partition function P_L of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.

Bragg-cell receiver study

NASA Technical Reports Server (NTRS)

Wilson, Lonnie A.

1987-01-01

Bragg-cell receivers are employed in specialized Electronic Warfare (EW) applications for the measurement of frequency. Bragg-cell receiver characteristics are fully characterized for simple RF emitter signals. This receiver is early in its development cycle when compared to the IFM receiver. Functional mathematical models are derived and presented in this report for the Bragg-cell receiver. Theoretical analysis is presented and digital computer signal processing results are presented for the Bragg-cell receiver. Probability density function analysis are performed for output frequency. Probability density function distributions are observed to depart from assumed distributions for wideband and complex RF signals. This analysis is significant for high resolution and fine grain EW Bragg-cell receiver systems.

Use of the Weibull function to predict future diameter distributions from current plot data

Treesearch

Quang V. Cao

2012-01-01

The Weibull function has been widely used to characterize diameter distributions in forest stands. The future diameter distribution of a forest stand can be predicted by use of a Weibull probability density function from current inventory data for that stand. The parameter recovery approach has been used to “recover” the Weibull parameters from diameter moments or...

Probability distribution functions for intermittent scrape-off layer plasma fluctuations

NASA Astrophysics Data System (ADS)

Theodorsen, A.; Garcia, O. E.

2018-03-01

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

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

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

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

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

2012-07-01

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

Applying the log-normal distribution to target detection

NASA Astrophysics Data System (ADS)

Holst, Gerald C.

1992-09-01

Holst and Pickard experimentally determined that MRT responses tend to follow a log-normal distribution. The log normal distribution appeared reasonable because nearly all visual psychological data is plotted on a logarithmic scale. It has the additional advantage that it is bounded to positive values; an important consideration since probability of detection is often plotted in linear coordinates. Review of published data suggests that the log-normal distribution may have universal applicability. Specifically, the log-normal distribution obtained from MRT tests appears to fit the target transfer function and the probability of detection of rectangular targets.

General formulation of long-range degree correlations in complex networks

NASA Astrophysics Data System (ADS)

Fujiki, Yuka; Takaguchi, Taro; Yakubo, Kousuke

2018-06-01

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

The beta distribution: A statistical model for world cloud cover

NASA Technical Reports Server (NTRS)

Falls, L. W.

1973-01-01

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

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

PubMed

Agresti, Alan; Kateri, Maria

2017-03-01

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

Probability density function of non-reactive solute concentration in heterogeneous porous formations

Treesearch

Alberto Bellin; Daniele Tonina

2007-01-01

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for...

Reinforcement Learning for Constrained Energy Trading Games With Incomplete Information.

PubMed

Wang, Huiwei; Huang, Tingwen; Liao, Xiaofeng; Abu-Rub, Haitham; Chen, Guo

2017-10-01

This paper considers the problem of designing adaptive learning algorithms to seek the Nash equilibrium (NE) of the constrained energy trading game among individually strategic players with incomplete information. In this game, each player uses the learning automaton scheme to generate the action probability distribution based on his/her private information for maximizing his own averaged utility. It is shown that if one of admissible mixed-strategies converges to the NE with probability one, then the averaged utility and trading quantity almost surely converge to their expected ones, respectively. For the given discontinuous pricing function, the utility function has already been proved to be upper semicontinuous and payoff secure which guarantee the existence of the mixed-strategy NE. By the strict diagonal concavity of the regularized Lagrange function, the uniqueness of NE is also guaranteed. Finally, an adaptive learning algorithm is provided to generate the strategy probability distribution for seeking the mixed-strategy NE.

Modeling pore corrosion in normally open gold- plated copper connectors.

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

Battaile, Corbett Chandler; Moffat, Harry K.; Sun, Amy Cha-Tien

2008-09-01

The goal of this study is to model the electrical response of gold plated copper electrical contacts exposed to a mixed flowing gas stream consisting of air containing 10 ppb H{sub 2}S at 30 C and a relative humidity of 70%. This environment accelerates the attack normally observed in a light industrial environment (essentially a simplified version of the Battelle Class 2 environment). Corrosion rates were quantified by measuring the corrosion site density, size distribution, and the macroscopic electrical resistance of the aged surface as a function of exposure time. A pore corrosion numerical model was used to predict bothmore » the growth of copper sulfide corrosion product which blooms through defects in the gold layer and the resulting electrical contact resistance of the aged surface. Assumptions about the distribution of defects in the noble metal plating and the mechanism for how corrosion blooms affect electrical contact resistance were needed to complete the numerical model. Comparisons are made to the experimentally observed number density of corrosion sites, the size distribution of corrosion product blooms, and the cumulative probability distribution of the electrical contact resistance. Experimentally, the bloom site density increases as a function of time, whereas the bloom size distribution remains relatively independent of time. These two effects are included in the numerical model by adding a corrosion initiation probability proportional to the surface area along with a probability for bloom-growth extinction proportional to the corrosion product bloom volume. The cumulative probability distribution of electrical resistance becomes skewed as exposure time increases. While the electrical contact resistance increases as a function of time for a fraction of the bloom population, the median value remains relatively unchanged. In order to model this behavior, the resistance calculated for large blooms has been weighted more heavily.« less

Nematode Damage Functions: The Problems of Experimental and Sampling Error

PubMed Central

Ferris, H.

1984-01-01

The development and use of pest damage functions involves measurement and experimental errors associated with cultural, environmental, and distributional factors. Damage predictions are more valuable if considered with associated probability. Collapsing population densities into a geometric series of population classes allows a pseudo-replication removal of experimental and sampling error in damage function development. Recognition of the nature of sampling error for aggregated populations allows assessment of probability associated with the population estimate. The product of the probabilities incorporated in the damage function and in the population estimate provides a basis for risk analysis of the yield loss prediction and the ensuing management decision. PMID:19295865

Electron number probability distributions for correlated wave functions.

PubMed

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

2007-03-07

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

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

The tensor distribution function.

PubMed

Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M

2009-01-01

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties

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

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

1996-06-01

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

Benchmarking PARTISN with Analog Monte Carlo: Moments of the Neutron Number and the Cumulative Fission Number Probability Distributions

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

O'Rourke, Patrick Francis

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.

Stochastic optimal operation of reservoirs based on copula functions

NASA Astrophysics Data System (ADS)

Lei, Xiao-hui; Tan, Qiao-feng; Wang, Xu; Wang, Hao; Wen, Xin; Wang, Chao; Zhang, Jing-wen

2018-02-01

Stochastic dynamic programming (SDP) has been widely used to derive operating policies for reservoirs considering streamflow uncertainties. In SDP, there is a need to calculate the transition probability matrix more accurately and efficiently in order to improve the economic benefit of reservoir operation. In this study, we proposed a stochastic optimization model for hydropower generation reservoirs, in which 1) the transition probability matrix was calculated based on copula functions; and 2) the value function of the last period was calculated by stepwise iteration. Firstly, the marginal distribution of stochastic inflow in each period was built and the joint distributions of adjacent periods were obtained using the three members of the Archimedean copulas, based on which the conditional probability formula was derived. Then, the value in the last period was calculated by a simple recursive equation with the proposed stepwise iteration method and the value function was fitted with a linear regression model. These improvements were incorporated into the classic SDP and applied to the case study in Ertan reservoir, China. The results show that the transition probability matrix can be more easily and accurately obtained by the proposed copula function based method than conventional methods based on the observed or synthetic streamflow series, and the reservoir operation benefit can also be increased.

Computation of marginal distributions of peak-heights in electropherograms for analysing single source and mixture STR DNA samples.

PubMed

Cowell, Robert G

2018-05-04

Current models for single source and mixture samples, and probabilistic genotyping software based on them used for analysing STR electropherogram data, assume simple probability distributions, such as the gamma distribution, to model the allelic peak height variability given the initial amount of DNA prior to PCR amplification. Here we illustrate how amplicon number distributions, for a model of the process of sample DNA collection and PCR amplification, may be efficiently computed by evaluating probability generating functions using discrete Fourier transforms. Copyright © 2018 Elsevier B.V. All rights reserved.

Conditional probability distribution function of "energy transfer rate" (PDF(ɛ|PVI)) as compared with its counterpart of temperature (PDF(T|PVI)) at the same condition of fluctuation

NASA Astrophysics Data System (ADS)

He, Jiansen; Wang, Yin; Pei, Zhongtian; Zhang, Lei; Tu, Chuanyi

2017-04-01

Energy transfer rate of turbulence is not uniform everywhere but suggested to follow a certain distribution, e.g., lognormal distribution (Kolmogorov 1962). The inhomogeneous transfer rate leads to emergence of intermittency, which may be identified with some parameter, e.g., normalized partial variance increments (PVI) (Greco et al., 2009). Large PVI of magnetic field fluctuations are found to have a temperature distribution with the median and mean values higher than that for small PVI level (Osman et al., 2012). However, there is a large proportion of overlap between temperature distributions associated with the smaller and larger PVIs. So it is recognized that only PVI cannot fully determine the temperature, since the one-to-one mapping relationship does not exist. One may be curious about the reason responsible for the considerable overlap of conditional temperature distribution for different levels of PVI. Usually the hotter plasma with higher temperature is speculated to be heated more with more dissipation of turbulence energy corresponding to more energy cascading rate, if the temperature fluctuation of the eigen wave mode is not taken into account. To explore the statistical relationship between turbulence cascading and plasma thermal state, we aim to study and reveal, for the first time, the conditional probability function of "energy transfer rate" under different levels of PVI condition (PDF(ɛ|PVI)), and compare it with the conditional probability function of temperature. The conditional probability distribution function, PDF(ɛ|PVI), is derived from PDF(PVI|ɛ)·PDF(ɛ)/PDF(PVI) according to the Bayesian theorem. PDF(PVI) can be obtained directly from the data. PDF(ɛ) is derived from the conjugate-gradient inversion of PDF(PVI) by assuming reasonably that PDF(δB|σ) is a Gaussian distribution, where PVI=|δB|/ σ and σ ( ɛι)1/3. PDF(ɛ) can also be acquired from fitting PDF(δB) with an integral function ∫PDF(δB|σ)PDF(σ)d σ. As a result, PDF(ɛ|PVI) is found to shift to higher median value of ɛ with increasing PVI but with a significant overlap of PDFs for different PVIs. Therefore, PDF(ɛ|PVI) is similar to PDF(T|PVI) in the sense of slow migration along with increasing PVI. The detailed comparison between these two conditional PDFs are also performed.

Calculation of the number of Monte Carlo histories for a planetary protection probability of impact estimation

NASA Astrophysics Data System (ADS)

Barengoltz, Jack

2016-07-01

Monte Carlo (MC) is a common method to estimate probability, effectively by a simulation. For planetary protection, it may be used to estimate the probability of impact P{}_{I} by a launch vehicle (upper stage) of a protected planet. The object of the analysis is to provide a value for P{}_{I} with a given level of confidence (LOC) that the true value does not exceed the maximum allowed value of P{}_{I}. In order to determine the number of MC histories required, one must also guess the maximum number of hits that will occur in the analysis. This extra parameter is needed because a LOC is desired. If more hits occur, the MC analysis would indicate that the true value may exceed the specification value with a higher probability than the LOC. (In the worst case, even the mean value of the estimated P{}_{I} might exceed the specification value.) After the analysis is conducted, the actual number of hits is, of course, the mean. The number of hits arises from a small probability per history and a large number of histories; these are the classic requirements for a Poisson distribution. For a known Poisson distribution (the mean is the only parameter), the probability for some interval in the number of hits is calculable. Before the analysis, this is not possible. Fortunately, there are methods that can bound the unknown mean for a Poisson distribution. F. Garwoodfootnote{ F. Garwood (1936), ``Fiduciary limits for the Poisson distribution.'' Biometrika 28, 437-442.} published an appropriate method that uses the Chi-squared function, actually its inversefootnote{ The integral chi-squared function would yield probability α as a function of the mean µ and an actual value n.} (despite the notation used): This formula for the upper and lower limits of the mean μ with the two-tailed probability 1-α depends on the LOC α and an estimated value of the number of "successes" n. In a MC analysis for planetary protection, only the upper limit is of interest, i.e., the single-tailed distribution. (Smaller actual P{}_{I }is no problem.) {}_{ } One advantage of this method is that this function is available in EXCEL. Note that care must be taken with the definition of the CHIINV function (the inverse of the integral chi-squared distribution). The equivalent inequality in EXCEL is μ < CHIINV[1-α, 2(n+1)] In practice, one calculates this upper limit for a specified LOC, α , and a guess of how many hits n will be found after the MC analysis. Then the estimate of the number of histories required is this upper limit divided by the specification for the allowed P{}_{I} (rounded up). However, if the number of hits actually exceeds the guess, the P{}_{I} requirement will be met only with a smaller LOC. A disadvantage is that the intervals about the mean are "in general too wide, yielding coverage probabilities much greater than 1- α ." footnote{ G. Casella and C. Robert (1988), Purdue University-Technical Report #88-7 or Cornell University-Technical Report BU-903-M.} For planetary protection, this technical issue means that the upper limit of the interval and the probability associated with the interval (i.e., the LOC) are conservative.

Introduction and Application of non-stationary Standardized Precipitation Index Considering Probability Distribution Function and Return Period

NASA Astrophysics Data System (ADS)

Park, J.; Lim, Y. J.; Sung, J. H.; Kang, H. S.

2017-12-01

The widely used meteorological drought index, the Standardized Precipitation Index (SPI) basically assumes stationarity, but recent change 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 has been proposed. The results are evaluated for two severe drought cases during the last 10 years in South Korea. As a result, SPIs considered the non-stationary hypothesis underestimated the drought severity than the stationary SPI despite 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 shape of probability distribution function wider than before. This understanding 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.

Comparing the ISO-recommended and the cumulative data-reduction algorithms in S-on-1 laser damage test by a reverse approach method

NASA Astrophysics Data System (ADS)

Zorila, Alexandru; Stratan, Aurel; Nemes, George

2018-01-01

We compare the ISO-recommended (the standard) data-reduction algorithm used to determine the surface laser-induced damage threshold of optical materials by the S-on-1 test with two newly suggested algorithms, both named "cumulative" algorithms/methods, a regular one and a limit-case one, intended to perform in some respects better than the standard one. To avoid additional errors due to real experiments, a simulated test is performed, named the reverse approach. This approach simulates the real damage experiments, by generating artificial test-data of damaged and non-damaged sites, based on an assumed, known damage threshold fluence of the target and on a given probability distribution function to induce the damage. In this work, a database of 12 sets of test-data containing both damaged and non-damaged sites was generated by using four different reverse techniques and by assuming three specific damage probability distribution functions. The same value for the threshold fluence was assumed, and a Gaussian fluence distribution on each irradiated site was considered, as usual for the S-on-1 test. Each of the test-data was independently processed by the standard and by the two cumulative data-reduction algorithms, the resulting fitted probability distributions were compared with the initially assumed probability distribution functions, and the quantities used to compare these algorithms were determined. These quantities characterize the accuracy and the precision in determining the damage threshold and the goodness of fit of the damage probability curves. The results indicate that the accuracy in determining the absolute damage threshold is best for the ISO-recommended method, the precision is best for the limit-case of the cumulative method, and the goodness of fit estimator (adjusted R-squared) is almost the same for all three algorithms.

Stability Criteria Analysis for Landing Craft Utility

DTIC Science & Technology

2017-12-01

Square meter m/s Meters per Second m/s2 Meters per Second Squared n Vertical Displacement of Sea Water Free Surface n3 Ship’s Heave... Displacement n5 Ship’s Pitch Angle p(ξ) Rayleigh Distribution Probability Function POSSE Program of Ship Salvage Engineering pk...Spectrum Constant γ JONSWAP Wave Spectrum Peak Factor Γ(λ) Gamma Probability Function Δ Ship’s Displacement Δω Small Frequency

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

NASA Astrophysics Data System (ADS)

Perline, Richard; Perline, Ron

2016-03-01

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

CUMPOIS- CUMULATIVE POISSON DISTRIBUTION PROGRAM

NASA Technical Reports Server (NTRS)

Bowerman, P. N.

1994-01-01

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

Optimal estimation for discrete time jump processes

NASA Technical Reports Server (NTRS)

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

1978-01-01

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

MaxEnt, second variation, and generalized statistics

NASA Astrophysics Data System (ADS)

Plastino, A.; Rocca, M. C.

2015-10-01

There are two kinds of Tsallis-probability distributions: heavy tail ones and compact support distributions. We show here, by appeal to functional analysis' tools, that for lower bound Hamiltonians, the second variation's analysis of the entropic functional guarantees that the heavy tail q-distribution constitutes a maximum of Tsallis' entropy. On the other hand, in the compact support instance, a case by case analysis is necessary in order to tackle the issue.

Probability Density Functions of Observed Rainfall in Montana

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

The H-Function and Probability Density Functions of Certain Algebraic Combinations of Independent Random Variables with H-Function Probability Distribution

DTIC Science & Technology

1981-05-01

functions and the H- function," Boletin do la Academia de Ciencias Fisicas Matematicas v Naturales (Caracas), 31, 95- 102 (1971). 120. Jain, U. C...Society, 37, 329- 334 (1973). 32. Oliver, M. L., and S. L. Kalla, "On the derivative of Fox’s H- function," (Spanish) Acta 14,dlcana de Ciencia -v...34 Universidade de Lisboa Revista de Faculdade de Ciencias FMatematicas, II, Series A, 13, 109-114 (1969-70). 92. Bajpai, S. D., "On some results involving Fox’s H

A Gaussian Model-Based Probabilistic Approach for Pulse Transit Time Estimation.

PubMed

Jang, Dae-Geun; Park, Seung-Hun; Hahn, Minsoo

2016-01-01

In this paper, we propose a new probabilistic approach to pulse transit time (PTT) estimation using a Gaussian distribution model. It is motivated basically by the hypothesis that PTTs normalized by RR intervals follow the Gaussian distribution. To verify the hypothesis, we demonstrate the effects of arterial compliance on the normalized PTTs using the Moens-Korteweg equation. Furthermore, we observe a Gaussian distribution of the normalized PTTs on real data. In order to estimate the PTT using the hypothesis, we first assumed that R-waves in the electrocardiogram (ECG) can be correctly identified. The R-waves limit searching ranges to detect pulse peaks in the photoplethysmogram (PPG) and to synchronize the results with cardiac beats--i.e., the peaks of the PPG are extracted within the corresponding RR interval of the ECG as pulse peak candidates. Their probabilities of being the actual pulse peak are then calculated using a Gaussian probability function. The parameters of the Gaussian function are automatically updated when a new pulse peak is identified. This update makes the probability function adaptive to variations of cardiac cycles. Finally, the pulse peak is identified as the candidate with the highest probability. The proposed approach is tested on a database where ECG and PPG waveforms are collected simultaneously during the submaximal bicycle ergometer exercise test. The results are promising, suggesting that the method provides a simple but more accurate PTT estimation in real applications.

Inverse Gaussian gamma distribution model for turbulence-induced fading in free-space optical communication.

PubMed

Cheng, Mingjian; Guo, Ya; Li, Jiangting; Zheng, Xiaotong; Guo, Lixin

2018-04-20

We introduce an alternative distribution to the gamma-gamma (GG) distribution, called inverse Gaussian gamma (IGG) distribution, which can efficiently describe moderate-to-strong irradiance fluctuations. The proposed stochastic model is based on a modulation process between small- and large-scale irradiance fluctuations, which are modeled by gamma and inverse Gaussian distributions, respectively. The model parameters of the IGG distribution are directly related to atmospheric parameters. The accuracy of the fit among the IGG, log-normal, and GG distributions with the experimental probability density functions in moderate-to-strong turbulence are compared, and results indicate that the newly proposed IGG model provides an excellent fit to the experimental data. As the receiving diameter is comparable with the atmospheric coherence radius, the proposed IGG model can reproduce the shape of the experimental data, whereas the GG and LN models fail to match the experimental data. The fundamental channel statistics of a free-space optical communication system are also investigated in an IGG-distributed turbulent atmosphere, and a closed-form expression for the outage probability of the system is derived with Meijer's G-function.

Chord-length and free-path distribution functions for many-body systems

NASA Astrophysics Data System (ADS)

Lu, Binglin; Torquato, S.

1993-04-01

We study fundamental morphological descriptors of disordered media (e.g., heterogeneous materials, liquids, and amorphous solids): the chord-length distribution function p(z) and the free-path distribution function p(z,a). For concreteness, we will speak in the language of heterogeneous materials composed of two different materials or ``phases.'' The probability density function p(z) describes the distribution of chord lengths in the sample and is of great interest in stereology. For example, the first moment of p(z) is the ``mean intercept length'' or ``mean chord length.'' The chord-length distribution function is of importance in transport phenomena and problems involving ``discrete free paths'' of point particles (e.g., Knudsen diffusion and radiative transport). The free-path distribution function p(z,a) takes into account the finite size of a simple particle of radius a undergoing discrete free-path motion in the heterogeneous material and we show that it is actually the chord-length distribution function for the system in which the ``pore space'' is the space available to a finite-sized particle of radius a. Thus it is shown that p(z)=p(z,0). We demonstrate that the functions p(z) and p(z,a) are related to another fundamentally important morphological descriptor of disordered media, namely, the so-called lineal-path function L(z) studied by us in previous work [Phys. Rev. A 45, 922 (1992)]. The lineal path function gives the probability of finding a line segment of length z wholly in one of the ``phases'' when randomly thrown into the sample. We derive exact series representations of the chord-length and free-path distribution functions for systems of spheres with a polydispersivity in size in arbitrary dimension D. For the special case of spatially uncorrelated spheres (i.e., fully penetrable spheres) we evaluate exactly the aforementioned functions, the mean chord length, and the mean free path. We also obtain corresponding analytical formulas for the case of mutually impenetrable (i.e., spatially correlated) polydispersed spheres.

ATTITUDE FILTERING ON SO(3)

NASA Technical Reports Server (NTRS)

Markley, F. Landis

2005-01-01

A new method is presented for the simultaneous estimation of the attitude of a spacecraft and an N-vector of bias parameters. This method uses a probability distribution function defined on the Cartesian product of SO(3), the group of rotation matrices, and the Euclidean space W N .The Fokker-Planck equation propagates the probability distribution function between measurements, and Bayes s formula incorporates measurement update information. This approach avoids all the issues of singular attitude representations or singular covariance matrices encountered in extended Kalman filters. In addition, the filter has a consistent initialization for a completely unknown initial attitude, owing to the fact that SO(3) is a compact space.

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

NASA Astrophysics Data System (ADS)

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

2011-07-01

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

Probability density function of non-reactive solute concentration in heterogeneous porous formations.

PubMed

Bellin, Alberto; Tonina, Daniele

2007-10-30

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution, mechanical mixing within the sampling volume and spreading due to formation heterogeneity. It is developed by modeling local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta probability distribution function (pdf) for the solute concentration. This model shows large flexibility in capturing the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Furthermore, it is fully characterized by the first two moments of the solute concentration, and these are the same pieces of information required for standard geostatistical techniques employing Normal or Log-Normal distributions. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of [Dagan, G., 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resour. Res. 18 (4), 835-848.], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, we demonstrate that the same model with the spatial moments replacing the statistical moments can be applied to estimate the proportion of the plume volume where solute concentrations are above or below critical thresholds. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time it shows the superiority of the Beta model to both Normal and Log-Normal models in interpreting field data. Furthermore, we show that assuming a-priori that local concentrations are normally or log-normally distributed may result in a severe underestimate of the probability of exceeding large concentrations.

Characterising RNA secondary structure space using information entropy

PubMed Central

2013-01-01

Comparative methods for RNA secondary structure prediction use evolutionary information from RNA alignments to increase prediction accuracy. The model is often described in terms of stochastic context-free grammars (SCFGs), which generate a probability distribution over secondary structures. It is, however, unclear how this probability distribution changes as a function of the input alignment. As prediction programs typically only return a single secondary structure, better characterisation of the underlying probability space of RNA secondary structures is of great interest. In this work, we show how to efficiently compute the information entropy of the probability distribution over RNA secondary structures produced for RNA alignments by a phylo-SCFG, and implement it for the PPfold model. We also discuss interpretations and applications of this quantity, including how it can clarify reasons for low prediction reliability scores. PPfold and its source code are available from http://birc.au.dk/software/ppfold/. PMID:23368905

Superstatistics analysis of the ion current distribution function: Met3PbCl influence study.

PubMed

Miśkiewicz, Janusz; Trela, Zenon; Przestalski, Stanisław; Karcz, Waldemar

2010-09-01

A novel analysis of ion current time series is proposed. It is shown that higher (second, third and fourth) statistical moments of the ion current probability distribution function (PDF) can yield new information about ion channel properties. The method is illustrated on a two-state model where the PDF of the compound states are given by normal distributions. The proposed method was applied to the analysis of the SV cation channels of vacuolar membrane of Beta vulgaris and the influence of trimethyllead chloride (Met(3)PbCl) on the ion current probability distribution. Ion currents were measured by patch-clamp technique. It was shown that Met(3)PbCl influences the variance of the open-state ion current but does not alter the PDF of the closed-state ion current. Incorporation of higher statistical moments into the standard investigation of ion channel properties is proposed.

On the emergence of a generalised Gamma distribution. Application to traded volume in financial markets

NASA Astrophysics Data System (ADS)

Duarte Queirós, S. M.

2005-08-01

This letter reports on a stochastic dynamical scenario whose associated stationary probability density function is exactly a generalised form, with a power law instead of exponencial decay, of the ubiquitous Gamma distribution. This generalisation, also known as F-distribution, was empirically proposed for the first time to adjust for high-frequency stock traded volume distributions in financial markets and verified in experiments with granular material. The dynamical assumption presented herein is based on local temporal fluctuations of the average value of the observable under study. This proposal is related to superstatistics and thus to the current nonextensive statistical mechanics framework. For the specific case of stock traded volume, we connect the local fluctuations in the mean stock traded volume with the typical herding behaviour presented by financial traders. Last of all, NASDAQ 1 and 2 minute stock traded volume sequences and probability density functions are numerically reproduced.

Universality classes of fluctuation dynamics in hierarchical complex systems

NASA Astrophysics Data System (ADS)

Macêdo, A. M. S.; González, Iván R. Roa; Salazar, D. S. P.; Vasconcelos, G. L.

2017-03-01

A unified approach is proposed to describe the statistics of the short-time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a large time-scale distribution weighted by the distribution of certain internal variables that characterize the slowly changing background. The dynamics of the background is formulated as a hierarchical stochastic model whose form is derived from simple physical constraints, which in turn restrict the dynamics to only two possible classes. The probability distributions of both the signal and the background have simple representations in terms of Meijer G functions. The two universality classes for the background dynamics manifest themselves in the signal distribution as two types of tails: power law and stretched exponential, respectively. A detailed analysis of empirical data from classical turbulence and financial markets shows excellent agreement with the theory.

Reconstructing the equilibrium Boltzmann distribution from well-tempered metadynamics.

PubMed

Bonomi, M; Barducci, A; Parrinello, M

2009-08-01

Metadynamics is a widely used and successful method for reconstructing the free-energy surface of complex systems as a function of a small number of suitably chosen collective variables. This is achieved by biasing the dynamics of the system. The bias acting on the collective variables distorts the probability distribution of the other variables. Here we present a simple reweighting algorithm for recovering the unbiased probability distribution of any variable from a well-tempered metadynamics simulation. We show the efficiency of the reweighting procedure by reconstructing the distribution of the four backbone dihedral angles of alanine dipeptide from two and even one dimensional metadynamics simulation. 2009 Wiley Periodicals, Inc.

Functional Bregman Divergence and Bayesian Estimation of Distributions (Preprint)

DTIC Science & Technology

2008-01-01

shows that if the set of possible minimizers A includes EPF [F ], then g∗ = EPF [F ] minimizes the expectation of any Bregman divergence. Note the theorem...probability distribution PF defined over the set M. Let A be a set of functions that includes EPF [F ] if it exists. Suppose the function g∗ minimizes...the expected Bregman divergence between the random function F and any function g ∈ A such that g∗ = arg inf g∈A EPF [dφ(F, g)]. Then, if g∗ exists

Assignment of functional activations to probabilistic cytoarchitectonic areas revisited.

PubMed

Eickhoff, Simon B; Paus, Tomas; Caspers, Svenja; Grosbras, Marie-Helene; Evans, Alan C; Zilles, Karl; Amunts, Katrin

2007-07-01

Probabilistic cytoarchitectonic maps in standard reference space provide a powerful tool for the analysis of structure-function relationships in the human brain. While these microstructurally defined maps have already been successfully used in the analysis of somatosensory, motor or language functions, several conceptual issues in the analysis of structure-function relationships still demand further clarification. In this paper, we demonstrate the principle approaches for anatomical localisation of functional activations based on probabilistic cytoarchitectonic maps by exemplary analysis of an anterior parietal activation evoked by visual presentation of hand gestures. After consideration of the conceptual basis and implementation of volume or local maxima labelling, we comment on some potential interpretational difficulties, limitations and caveats that could be encountered. Extending and supplementing these methods, we then propose a supplementary approach for quantification of structure-function correspondences based on distribution analysis. This approach relates the cytoarchitectonic probabilities observed at a particular functionally defined location to the areal specific null distribution of probabilities across the whole brain (i.e., the full probability map). Importantly, this method avoids the need for a unique classification of voxels to a single cortical area and may increase the comparability between results obtained for different areas. Moreover, as distribution-based labelling quantifies the "central tendency" of an activation with respect to anatomical areas, it will, in combination with the established methods, allow an advanced characterisation of the anatomical substrates of functional activations. Finally, the advantages and disadvantages of the various methods are discussed, focussing on the question of which approach is most appropriate for a particular situation.

A Seakeeping Performance and Affordability Tradeoff Study for the Coast Guard Offshore Patrol Cutter

DTIC Science & Technology

2016-06-01

Index Polar Plot for Sea State 4, All Headings Are Relative to the Wave Motion and Velocity is Given in Meters per Second...40 Figure 15. Probability and Cumulative Density Functions of Annual Sea State Occurrences in the Open Ocean, North Pacific...criteria at a given sea state. Probability distribution functions are available that describe the likelihood that an operational area will experience

A testable model of earthquake probability based on changes in mean event size

NASA Astrophysics Data System (ADS)

Imoto, Masajiro

2003-02-01

We studied changes in mean event size using data on microearthquakes obtained from a local network in Kanto, central Japan, from a viewpoint that a mean event size tends to increase as the critical point is approached. A parameter describing changes was defined using a simple weighting average procedure. In order to obtain the distribution of the parameter in the background, we surveyed values of the parameter from 1982 to 1999 in a 160 × 160 × 80 km volume. The 16 events of M5.5 or larger in this volume were selected as target events. The conditional distribution of the parameter was estimated from the 16 values, each of which referred to the value immediately prior to each target event. The distribution of the background becomes a function of symmetry, the center of which corresponds to no change in b value. In contrast, the conditional distribution exhibits an asymmetric feature, which tends to decrease the b value. The difference in the distributions between the two groups was significant and provided us a hazard function for estimating earthquake probabilities. Comparing the hazard function with a Poisson process, we obtained an Akaike Information Criterion (AIC) reduction of 24. This reduction agreed closely with the probability gains of a retrospective study in a range of 2-4. A successful example of the proposed model can be seen in the earthquake of 3 June 2000, which is the only event during the period of prospective testing.

14 CFR 23.1309 - Equipment, systems, and installations.

Code of Federal Regulations, 2010 CFR

2010-01-01

... compliance with this section with regard to the electrical power system and to equipment design and... the system must be able to supply the following power loads in probable operating combinations and for probable durations: (1) Loads connected to the power distribution system with the system functioning...

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

PubMed

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

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

On defense strategies for system of systems using aggregated correlations

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

Rao, Nageswara S.; Imam, Neena; Ma, Chris Y. T.

2017-04-01

We consider a System of Systems (SoS) wherein each system Si, i = 1; 2; ... ;N, is composed of discrete cyber and physical components which can be attacked and reinforced. We characterize the disruptions using aggregate failure correlation functions given by the conditional failure probability of SoS given the failure of an individual system. We formulate the problem of ensuring the survival of SoS as a game between an attacker and a provider, each with a utility function composed of asurvival probability term and a cost term, both expressed in terms of the number of components attacked and reinforced.more » The survival probabilities of systems satisfy simple product-form, first-order differential conditions, which simplify the Nash Equilibrium (NE) conditions. We derive the sensitivity functions that highlight the dependence of SoS survival probability at NE on cost terms, correlation functions, and individual system survival probabilities.We apply these results to a simplified model of distributed cloud computing infrastructure.« less

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

Chang, Shih-Jung

Dynamic strength of the High Flux Isotope Reactor (HFIR) vessel to resist hypothetical accidents is analyzed by using the method of fracture mechanics. Vessel critical stresses are estimated by applying dynamic pressure pulses of a range of magnitudes and pulse-durations. The pulses versus time functions are assumed to be step functions. The probability of vessel fracture is then calculated by assuming a distribution of possible surface cracks of different crack depths. The probability distribution function for the crack depths is based on the form that is recommended by the Marshall report. The toughness of the vessel steel used in themore » analysis is based on the projected and embrittled value after 10 effective full power years from 1986. From the study made by Cheverton, Merkle and Nanstad, the weakest point on the vessel for fracture evaluation is known to be located within the region surrounding the tangential beam tube HB3. The increase in the probability of fracture is obtained as an extension of the result from that report for the regular operating condition to include conditions of higher dynamic pressures due to accident loadings. The increase in the probability of vessel fracture is plotted for a range of hoop stresses to indicate the vessel strength against hypothetical accident conditions.« less

Unstable density distribution associated with equatorial plasma bubble

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

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

2016-04-15

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

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

PubMed

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

2010-03-01

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

14 CFR 23.1309 - Equipment, systems, and installations.

Code of Federal Regulations, 2011 CFR

2011-01-01

... chapter and that requires a power supply is an “essential load” on the power supply. The power sources and the system must be able to supply the following power loads in probable operating combinations and for probable durations: (1) Loads connected to the power distribution system with the system functioning...

Probability Distributions of Minkowski Distances between Discrete Random Variables.

ERIC Educational Resources Information Center

Schroger, Erich; And Others

1993-01-01

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

Large Deviations: Advanced Probability for Undergrads

ERIC Educational Resources Information Center

Rolls, David A.

2007-01-01

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

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise.

PubMed

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Game-Theoretic strategies for systems of components using product-form utilities

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

Rao, Nageswara S; Ma, Cheng-Yu; Hausken, K.

Many critical infrastructures are composed of multiple systems of components which are correlated so that disruptions to one may propagate to others. We consider such infrastructures with correlations characterized in two ways: (i) an aggregate failure correlation function specifies the conditional failure probability of the infrastructure given the failure of an individual system, and (ii) a pairwise correlation function between two systems specifies the failure probability of one system given the failure of the other. We formulate a game for ensuring the resilience of the infrastructure, wherein the utility functions of the provider and attacker are products of an infrastructuremore » survival probability term and a cost term, both expressed in terms of the numbers of system components attacked and reinforced. The survival probabilities of individual systems satisfy first-order differential conditions that lead to simple Nash Equilibrium conditions. We then derive sensitivity functions that highlight the dependence of infrastructure resilience on the cost terms, correlation functions, and individual system survival probabilities. We apply these results to simplified models of distributed cloud computing and energy grid infrastructures.« less

Wigner functions for nonclassical states of a collection of two-level atoms

NASA Technical Reports Server (NTRS)

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.

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

NASA Astrophysics Data System (ADS)

Donkov, Sava; Stefanov, Ivan Z.

2018-03-01

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

A non-stationary cost-benefit based bivariate extreme flood estimation approach

NASA Astrophysics Data System (ADS)

Qi, Wei; Liu, Junguo

2018-02-01

Cost-benefit analysis and flood frequency analysis have been integrated into a comprehensive framework to estimate cost effective design values. However, previous cost-benefit based extreme flood estimation is based on stationary assumptions and analyze dependent flood variables separately. A Non-Stationary Cost-Benefit based bivariate design flood estimation (NSCOBE) approach is developed in this study to investigate influence of non-stationarities in both the dependence of flood variables and the marginal distributions on extreme flood estimation. The dependence is modeled utilizing copula functions. Previous design flood selection criteria are not suitable for NSCOBE since they ignore time changing dependence of flood variables. Therefore, a risk calculation approach is proposed based on non-stationarities in both marginal probability distributions and copula functions. A case study with 54-year observed data is utilized to illustrate the application of NSCOBE. Results show NSCOBE can effectively integrate non-stationarities in both copula functions and marginal distributions into cost-benefit based design flood estimation. It is also found that there is a trade-off between maximum probability of exceedance calculated from copula functions and marginal distributions. This study for the first time provides a new approach towards a better understanding of influence of non-stationarities in both copula functions and marginal distributions on extreme flood estimation, and could be beneficial to cost-benefit based non-stationary bivariate design flood estimation across the world.

A Method for Evaluating Tuning Functions of Single Neurons based on Mutual Information Maximization

NASA Astrophysics Data System (ADS)

Brostek, Lukas; Eggert, Thomas; Ono, Seiji; Mustari, Michael J.; Büttner, Ulrich; Glasauer, Stefan

2011-03-01

We introduce a novel approach for evaluation of neuronal tuning functions, which can be expressed by the conditional probability of observing a spike given any combination of independent variables. This probability can be estimated out of experimentally available data. By maximizing the mutual information between the probability distribution of the spike occurrence and that of the variables, the dependence of the spike on the input variables is maximized as well. We used this method to analyze the dependence of neuronal activity in cortical area MSTd on signals related to movement of the eye and retinal image movement.

Polynomial probability distribution estimation using the method of moments

PubMed Central

Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram–Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation. PMID:28394949

Polynomial probability distribution estimation using the method of moments.

PubMed

Munkhammar, Joakim; Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram-Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

Void probability as a function of the void's shape and scale-invariant models. [in studies of spacial galactic distribution

NASA Technical Reports Server (NTRS)

Elizalde, E.; Gaztanaga, E.

1992-01-01

The dependence of counts in cells on the shape of the cell for the large scale galaxy distribution is studied. A very concrete prediction can be done concerning the void distribution for scale invariant models. The prediction is tested on a sample of the CfA catalog, and good agreement is found. It is observed that the probability of a cell to be occupied is bigger for some elongated cells. A phenomenological scale invariant model for the observed distribution of the counts in cells, an extension of the negative binomial distribution, is presented in order to illustrate how this dependence can be quantitatively determined. An original, intuitive derivation of this model is presented.

Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles.

PubMed

Bhatnagar, Akshay; Gustavsson, K; Mitra, Dhrubaditya

2018-02-01

We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component V_{R} for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D_{2}. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011)PLEEE81539-375510.1103/PhysRevE.84.045304; J. Turbul. 15, 34 (2014)1468-524810.1080/14685248.2013.875188] that the scale invariant part of the distribution has two asymptotic regimes: (1) |V_{R}|≪R, where the distribution depends solely on R, and (2) |V_{R}|≫R, where the distribution is a function of |V_{R}| alone. The probability distributions in these two regimes are matched along a straight line: |V_{R}|=z^{*}R. Our simulations confirm that this is indeed correct. We further obtain D_{2} and z^{*} as a function of the Stokes number, St. The former depends nonmonotonically on St with a minimum at about St≈0.7 and the latter has only a weak dependence on St.

Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles

NASA Astrophysics Data System (ADS)

Bhatnagar, Akshay; Gustavsson, K.; Mitra, Dhrubaditya

2018-02-01

We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component VR for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D2. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011), 10.1103/PhysRevE.84.045304; J. Turbul. 15, 34 (2014), 10.1080/14685248.2013.875188] that the scale invariant part of the distribution has two asymptotic regimes: (1) | VR|≪R , where the distribution depends solely on R , and (2) | VR|≫R , where the distribution is a function of | VR| alone. The probability distributions in these two regimes are matched along a straight line: | VR|= z*R . Our simulations confirm that this is indeed correct. We further obtain D2 and z* as a function of the Stokes number, St. The former depends nonmonotonically on St with a minimum at about St≈0.7 and the latter has only a weak dependence on St.

Detection of anomalous events

DOEpatents

Ferragut, Erik M.; Laska, Jason A.; Bridges, Robert A.

2016-06-07

A system is described for receiving a stream of events and scoring the events based on anomalousness and maliciousness (or other classification). The system can include a plurality of anomaly detectors that together implement an algorithm to identify low-probability events and detect atypical traffic patterns. The anomaly detector provides for comparability of disparate sources of data (e.g., network flow data and firewall logs.) Additionally, the anomaly detector allows for regulatability, meaning that the algorithm can be user configurable to adjust a number of false alerts. The anomaly detector can be used for a variety of probability density functions, including normal Gaussian distributions, irregular distributions, as well as functions associated with continuous or discrete variables.

We'll Meet Again: Revealing Distributional and Temporal Patterns of Social Contact

PubMed Central

Pachur, Thorsten; Schooler, Lael J.; Stevens, Jeffrey R.

2014-01-01

What are the dynamics and regularities underlying social contact, and how can contact with the people in one's social network be predicted? In order to characterize distributional and temporal patterns underlying contact probability, we asked 40 participants to keep a diary of their social contacts for 100 consecutive days. Using a memory framework previously used to study environmental regularities, we predicted that the probability of future contact would follow in systematic ways from the frequency, recency, and spacing of previous contact. The distribution of contact probability across the members of a person's social network was highly skewed, following an exponential function. As predicted, it emerged that future contact scaled linearly with frequency of past contact, proportionally to a power function with recency of past contact, and differentially according to the spacing of past contact. These relations emerged across different contact media and irrespective of whether the participant initiated or received contact. We discuss how the identification of these regularities might inspire more realistic analyses of behavior in social networks (e.g., attitude formation, cooperation). PMID:24475073

Influence of the random walk finite step on the first-passage probability

NASA Astrophysics Data System (ADS)

Klimenkova, Olga; Menshutin, Anton; Shchur, Lev

2018-01-01

A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with fixed step length. We measure first-passage probability to touch the absorbing sphere of radius R in 2D. We found a regular deviation of the first-passage probability from the exact function, which we attribute to the finiteness of the random walk step.

Bounding the Failure Probability Range of Polynomial Systems Subject to P-box Uncertainties

NASA Technical Reports Server (NTRS)

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

2012-01-01

This paper proposes a reliability analysis framework for systems subject to multiple design requirements that depend polynomially on the uncertainty. Uncertainty is prescribed by probability boxes, also known as p-boxes, whose distribution functions have free or fixed functional forms. An approach based on the Bernstein expansion of polynomials and optimization is proposed. In particular, we search for the elements of a multi-dimensional p-box that minimize (i.e., the best-case) and maximize (i.e., the worst-case) the probability of inner and outer bounding sets of the failure domain. This technique yields intervals that bound the range of failure probabilities. The offset between this bounding interval and the actual failure probability range can be made arbitrarily tight with additional computational effort.

Wireless cellular networks with Pareto-distributed call holding times

NASA Astrophysics Data System (ADS)

Rodriguez-Dagnino, Ramon M.; Takagi, Hideaki

2001-07-01

Nowadays, there is a growing interest in providing internet to mobile users. For instance, NTT DoCoMo in Japan deploys an important mobile phone network with that offers the Internet service, named 'i-mode', to more than 17 million subscribers. Internet traffic measurements show that the session duration of Call Holding Time (CHT) has probability distributions with heavy-tails, which tells us that they depart significantly from the traffic statistics of traditional voice services. In this environment, it is particularly important to know the number of handovers during a call for a network designer to make an appropriate dimensioning of virtual circuits for a wireless cell. The handover traffic has a direct impact on the Quality of Service (QoS); e.g. the service disruption due to the handover failure may significantly degrade the specified QoS of time-constrained services. In this paper, we first study the random behavior of the number of handovers during a call, where we assume that the CHT are Pareto distributed (heavy-tail distribution), and the Cell Residence Times (CRT) are exponentially distributed. Our approach is based on renewal theory arguments. We present closed-form formulae for the probability mass function (pmf) of the number of handovers during a Pareto distributed CHT, and obtain the probability of call completion as well as handover rates. Most of the formulae are expressed in terms of the Whittaker's function. We compare the Pareto case with cases of $k(subscript Erlang and hyperexponential distributions for the CHT.

Bayes classification of terrain cover using normalized polarimetric data

NASA Technical Reports Server (NTRS)

Yueh, H. A.; Swartz, A. A.; Kong, J. A.; Shin, R. T.; Novak, L. M.

1988-01-01

The normalized polarimetric classifier (NPC) which uses only the relative magnitudes and phases of the polarimetric data is proposed for discrimination of terrain elements. The probability density functions (PDFs) of polarimetric data are assumed to have a complex Gaussian distribution, and the marginal PDF of the normalized polarimetric data is derived by adopting the Euclidean norm as the normalization function. The general form of the distance measure for the NPC is also obtained. It is demonstrated that for polarimetric data with an arbitrary PDF, the distance measure of NPC will be independent of the normalization function selected even when the classifier is mistrained. A complex Gaussian distribution is assumed for the polarimetric data consisting of grass and tree regions. The probability of error for the NPC is compared with those of several other single-feature classifiers. The classification error of NPCs is shown to be independent of the normalization function.

Void probability as a function of the void's shape and scale-invariant models

NASA Technical Reports Server (NTRS)

Elizalde, E.; Gaztanaga, E.

1991-01-01

The dependence of counts in cells on the shape of the cell for the large scale galaxy distribution is studied. A very concrete prediction can be done concerning the void distribution for scale invariant models. The prediction is tested on a sample of the CfA catalog, and good agreement is found. It is observed that the probability of a cell to be occupied is bigger for some elongated cells. A phenomenological scale invariant model for the observed distribution of the counts in cells, an extension of the negative binomial distribution, is presented in order to illustrate how this dependence can be quantitatively determined. An original, intuitive derivation of this model is presented.

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

DTIC Science & Technology

2009-03-01

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

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

DTIC Science & Technology

2009-03-01

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

Non-linear relationship of cell hit and transformation probabilities in a low dose of inhaled radon progenies.

PubMed

Balásházy, Imre; Farkas, Arpád; Madas, Balázs Gergely; Hofmann, Werner

2009-06-01

Cellular hit probabilities of alpha particles emitted by inhaled radon progenies in sensitive bronchial epithelial cell nuclei were simulated at low exposure levels to obtain useful data for the rejection or support of the linear-non-threshold (LNT) hypothesis. In this study, local distributions of deposited inhaled radon progenies in airway bifurcation models were computed at exposure conditions characteristic of homes and uranium mines. Then, maximum local deposition enhancement factors at bronchial airway bifurcations, expressed as the ratio of local to average deposition densities, were determined to characterise the inhomogeneity of deposition and to elucidate their effect on resulting hit probabilities. The results obtained suggest that in the vicinity of the carinal regions of the central airways the probability of multiple hits can be quite high, even at low average doses. Assuming a uniform distribution of activity there are practically no multiple hits and the hit probability as a function of dose exhibits a linear shape in the low dose range. The results are quite the opposite in the case of hot spots revealed by realistic deposition calculations, where practically all cells receive multiple hits and the hit probability as a function of dose is non-linear in the average dose range of 10-100 mGy.

Quantum Jeffreys prior for displaced squeezed thermal states

NASA Astrophysics Data System (ADS)

Kwek, L. C.; Oh, C. H.; Wang, Xiang-Bin

1999-09-01

It is known that, by extending the equivalence of the Fisher information matrix to its quantum version, the Bures metric, the quantum Jeffreys prior can be determined from the volume element of the Bures metric. We compute the Bures metric for the displaced squeezed thermal state and analyse the quantum Jeffreys prior and its marginal probability distributions. To normalize the marginal probability density function, it is necessary to provide a range of values of the squeezing parameter or the inverse temperature. We find that if the range of the squeezing parameter is kept narrow, there are significant differences in the marginal probability density functions in terms of the squeezing parameters for the displaced and undisplaced situations. However, these differences disappear as the range increases. Furthermore, marginal probability density functions against temperature are very different in the two cases.

Principle of maximum entropy for reliability analysis in the design of machine components

NASA Astrophysics Data System (ADS)

Zhang, Yimin

2018-03-01

We studied the reliability of machine components with parameters that follow an arbitrary statistical distribution using the principle of maximum entropy (PME). We used PME to select the statistical distribution that best fits the available information. We also established a probability density function (PDF) and a failure probability model for the parameters of mechanical components using the concept of entropy and the PME. We obtained the first four moments of the state function for reliability analysis and design. Furthermore, we attained an estimate of the PDF with the fewest human bias factors using the PME. This function was used to calculate the reliability of the machine components, including a connecting rod, a vehicle half-shaft, a front axle, a rear axle housing, and a leaf spring, which have parameters that typically follow a non-normal distribution. Simulations were conducted for comparison. This study provides a design methodology for the reliability of mechanical components for practical engineering projects.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

NASA Astrophysics Data System (ADS)

Batac, Rene C.; Paguirigan, Antonino A., Jr.; Tarun, Anjali B.; Longjas, Anthony G.

2017-04-01

We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of self-organized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy distributions closely follow power-law probability density functions (PDFs) with a scaling exponent of around -1. 6, consistent with the expectations of the Gutenberg-Richter (GR) law, for a wide range of the targeted triggering probability values. Additionally, for targeted triggering probabilities within the range 0.004-0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, the foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, while introducing minimal parameters in the simple rules of the sandpile. We believe that the critical targeting probability parameterizes the memory that is inherently present in earthquake-generating regions.

A computational framework to empower probabilistic protein design

PubMed Central

Fromer, Menachem; Yanover, Chen

2008-01-01

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

Universal noise and Efimov physics

NASA Astrophysics Data System (ADS)

Nicholson, Amy N.

2016-03-01

Probability distributions for correlation functions of particles interacting via random-valued fields are discussed as a novel tool for determining the spectrum of a theory. In particular, this method is used to determine the energies of universal N-body clusters tied to Efimov trimers, for even N, by investigating the distribution of a correlation function of two particles at unitarity. Using numerical evidence that this distribution is log-normal, an analytical prediction for the N-dependence of the N-body binding energies is made.

Wave theory of turbulence in compressible media (acoustic theory of turbulence)

NASA Technical Reports Server (NTRS)

Kentzer, C. P.

1975-01-01

The generation and the transmission of sound in turbulent flows are treated as one of the several aspects of wave propagation in turbulence. Fluid fluctuations are decomposed into orthogonal Fourier components, with five interacting modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. Wave interactions, governed by the inhomogeneous and nonlinear terms of the perturbed Navier-Stokes equations, are modeled by random functions which give the rates of change of wave amplitudes equal to the averaged interaction terms. The statistical framework adopted is a quantum-like formulation in terms of complex distribution functions. The spatial probability distributions are given by the squares of the absolute values of the complex characteristic functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation.

Search for function coefficient distribution in traditional Chinese medicine network

NASA Astrophysics Data System (ADS)

He, Yue; Zhang, Peipei; Sun, Anzheng; Su, Beibei; He, Da-Ren

2004-03-01

We suggest a model for a simulation on development of traditional Chinese medicine system. Suppose there are a certain number of Chinese medicines. Each of them is given randomly a "function coefficient", which has a value between 0 and 1. The larger it is the stronger is its function for solving one healthy problem and serving as an "emperor" in a prescription formulation. The smaller it is the stronger is its function for harmonizing and/or accessorizing a prescription formulation. In every step of time a new medicine is discovered. With a probability, P(m), which is determined according to our statistical investigation results, it can produce a new prescription formulation with other m-1 medicines. We assume that the probability for choosing the function coefficients of these m medicines follow a distribution function, which is everywhere smooth. A program has been set up to perform a search for this function form so that the simulation results show a best agreement to our statistical data. We believe the result function form will be helpful for an understanding on real development of traditional Chinese medicine system.

On the optimal identification of tag sets in time-constrained RFID configurations.

PubMed

Vales-Alonso, Javier; Bueno-Delgado, María Victoria; Egea-López, Esteban; Alcaraz, Juan José; Pérez-Mañogil, Juan Manuel

2011-01-01

In Radio Frequency Identification facilities the identification delay of a set of tags is mainly caused by the random access nature of the reading protocol, yielding a random identification time of the set of tags. In this paper, the cumulative distribution function of the identification time is evaluated using a discrete time Markov chain for single-set time-constrained passive RFID systems, namely those ones where a single group of tags is assumed to be in the reading area and only for a bounded time (sojourn time) before leaving. In these scenarios some tags in a set may leave the reader coverage area unidentified. The probability of this event is obtained from the cumulative distribution function of the identification time as a function of the sojourn time. This result provides a suitable criterion to minimize the probability of losing tags. Besides, an identification strategy based on splitting the set of tags in smaller subsets is also considered. Results demonstrate that there are optimal splitting configurations that reduce the overall identification time while keeping the same probability of losing tags.

Probability of lensing magnification by cosmologically distributed galaxies

NASA Technical Reports Server (NTRS)

Pei, Yichuan C.

1993-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

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

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

Do key dimensions of seed and seedling functional trait variation capture variation in recruitment probability?

USDA-ARS?s Scientific Manuscript database

1. Plant functional traits provide a mechanistic basis for understanding ecological variation among plant species and the implications of this variation for species distribution, community assembly and restoration. 2. The bulk of our functional trait understanding, however, is centered on traits rel...

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

PubMed

Kendal, W S

2000-04-01

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

A Non-Parametric Probability Density Estimator and Some Applications.

DTIC Science & Technology

1984-05-01

distributions, which are assumed to be representa- tive of platykurtic , mesokurtic, and leptokurtic distribu- tions in general. The dissertation is... platykurtic distributions. Consider, for example, the uniform distribution shown in Figure 4. 34 o . 1., Figure 4 -Sensitivity to Support Estimation The...results of the density function comparisons indicate that the new estimator is clearly -Z superior for platykurtic distributions, equal to the best 59

A quantum anharmonic oscillator model for the stock market

NASA Astrophysics Data System (ADS)

Gao, Tingting; Chen, Yu

2017-02-01

A financially interpretable quantum model is proposed to study the probability distributions of the stock price return. The dynamics of a quantum particle is considered an analog of the motion of stock price. Then the probability distributions of price return can be computed from the wave functions that evolve according to Schrodinger equation. Instead of a harmonic oscillator in previous studies, a quantum anharmonic oscillator is applied to the stock in liquid market. The leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed-state and multi-potential. The trend following dominant market, in which the price return follows a bimodal distribution, is discussed as a specific case of the illiquid market.

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

NASA Astrophysics Data System (ADS)

Denuit, Michel; Dhaene, Jan

2007-06-01

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

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

PubMed

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

2018-10-01

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

ON CONTINUOUS-REVIEW (S-1,S) INVENTORY POLICIES WITH STATE-DEPENDENT LEADTIMES,

DTIC Science & Technology

INVENTORY CONTROL, *REPLACEMENT THEORY), MATHEMATICAL MODELS, LEAD TIME , MANAGEMENT ENGINEERING, DISTRIBUTION FUNCTIONS, PROBABILITY, QUEUEING THEORY, COSTS, OPTIMIZATION, STATISTICAL PROCESSES, DIFFERENCE EQUATIONS

Quantum Probability Cancellation Due to a Single-Photon State

NASA Technical Reports Server (NTRS)

Ou, Z. Y.

1996-01-01

When an N-photon state enters a lossless symmetric beamsplitter from one input port, the photon distribution for the two output ports has the form of Bernouli Binormial, with highest probability at equal partition (N/2 at one outport and N/2 at the other). However, injection of a single photon state at the other input port can dramatically change the photon distribution at the outputs, resulting in zero probability at equal partition. Such a strong deviation from classical particle theory stems from quantum probability amplitude cancellation. The effect persists even if the N-photon state is replaced by an arbitrary state of light. A special case is the coherent state which corresponds to homodyne detection of a single photon state and can lead to the measurement of the wave function of a single photon state.

Statistical Characterization of the Mechanical Parameters of Intact Rock Under Triaxial Compression: An Experimental Proof of the Jinping Marble

NASA Astrophysics Data System (ADS)

Jiang, Quan; Zhong, Shan; Cui, Jie; Feng, Xia-Ting; Song, Leibo

2016-12-01

We investigated the statistical characteristics and probability distribution of the mechanical parameters of natural rock using triaxial compression tests. Twenty cores of Jinping marble were tested under each different levels of confining stress (i.e., 5, 10, 20, 30, and 40 MPa). From these full stress-strain data, we summarized the numerical characteristics and determined the probability distribution form of several important mechanical parameters, including deformational parameters, characteristic strength, characteristic strains, and failure angle. The statistical proofs relating to the mechanical parameters of rock presented new information about the marble's probabilistic distribution characteristics. The normal and log-normal distributions were appropriate for describing random strengths of rock; the coefficients of variation of the peak strengths had no relationship to the confining stress; the only acceptable random distribution for both Young's elastic modulus and Poisson's ratio was the log-normal function; and the cohesive strength had a different probability distribution pattern than the frictional angle. The triaxial tests and statistical analysis also provided experimental evidence for deciding the minimum reliable number of experimental sample and for picking appropriate parameter distributions to use in reliability calculations for rock engineering.

Bivariate sub-Gaussian model for stock index returns

NASA Astrophysics Data System (ADS)

Jabłońska-Sabuka, Matylda; Teuerle, Marek; Wyłomańska, Agnieszka

2017-11-01

Financial time series are commonly modeled with methods assuming data normality. However, the real distribution can be nontrivial, also not having an explicitly formulated probability density function. In this work we introduce novel parameter estimation and high-powered distribution testing methods which do not rely on closed form densities, but use the characteristic functions for comparison. The approach applied to a pair of stock index returns demonstrates that such a bivariate vector can be a sample coming from a bivariate sub-Gaussian distribution. The methods presented here can be applied to any nontrivially distributed financial data, among others.

Cumulative Poisson Distribution Program

NASA Technical Reports Server (NTRS)

Bowerman, Paul N.; Scheuer, Ernest M.; Nolty, Robert

1990-01-01

Overflow and underflow in sums prevented. Cumulative Poisson Distribution Program, CUMPOIS, one of two computer programs that make calculations involving cumulative Poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), used independently of one another. CUMPOIS determines cumulative Poisson distribution, used to evaluate cumulative distribution function (cdf) for gamma distributions with integer shape parameters and cdf for X (sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Written in C.

Distribution of Base Pair Alternations in a Periodic DNA Chain: Application of Pólya Counting to a Physical System

NASA Astrophysics Data System (ADS)

Hillebrand, Malcolm; Paterson-Jones, Guy; Kalosakas, George; Skokos, Charalampos

2018-03-01

In modeling DNA chains, the number of alternations between Adenine-Thymine (AT) and Guanine-Cytosine (GC) base pairs can be considered as a measure of the heterogeneity of the chain, which in turn could affect its dynamics. A probability distribution function of the number of these alternations is derived for circular or periodic DNA. Since there are several symmetries to account for in the periodic chain, necklace counting methods are used. In particular, Polya's Enumeration Theorem is extended for the case of a group action that preserves partitioned necklaces. This, along with the treatment of generating functions as formal power series, allows for the direct calculation of the number of possible necklaces with a given number of AT base pairs, GC base pairs and alternations. The theoretically obtained probability distribution functions of the number of alternations are accurately reproduced by Monte Carlo simulations and fitted by Gaussians. The effect of the number of base pairs on the characteristics of these distributions is also discussed, as well as the effect of the ratios of the numbers of AT and GC base pairs.

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

NASA Astrophysics Data System (ADS)

Dragulescu, Adrian Antoniu

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

New approach in bivariate drought duration and severity analysis

NASA Astrophysics Data System (ADS)

Montaseri, Majid; Amirataee, Babak; Rezaie, Hossein

2018-04-01

The copula functions have been widely applied as an advance technique to create joint probability distribution of drought duration and severity. The approach of data collection as well as the amount of data and dispersion of data series can last a significant impact on creating such joint probability distribution using copulas. Usually, such traditional analyses have shed an Unconnected Drought Runs (UDR) approach towards droughts. In other word, droughts with different durations would be independent of each other. Emphasis on such data collection method causes the omission of actual potentials of short-term extreme droughts located within a long-term UDR. Meanwhile, traditional method is often faced with significant gap in drought data series. However, a long-term UDR can be approached as a combination of short-term Connected Drought Runs (CDR). Therefore this study aims to evaluate systematically two UDR and CDR procedures in joint probability of drought duration and severity investigations. For this purpose, rainfall data (1971-2013) from 24 rain gauges in Lake Urmia basin, Iran were applied. Also, seven common univariate marginal distributions and seven types of bivariate copulas were examined. Compared to traditional approach, the results demonstrated a significant comparative advantage of the new approach. Such comparative advantages led to determine the correct copula function, more accurate estimation of copula parameter, more realistic estimation of joint/conditional probabilities of drought duration and severity and significant reduction in uncertainty for modeling.

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

NASA Astrophysics Data System (ADS)

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

2014-10-01

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

Scaling the Poisson Distribution

ERIC Educational Resources Information Center

Farnsworth, David L.

2014-01-01

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

Augmenting Phase Space Quantization to Introduce Additional Physical Effects

NASA Astrophysics Data System (ADS)

Robbins, Matthew P. G.

Quantum mechanics can be done using classical phase space functions and a star product. The state of the system is described by a quasi-probability distribution. A classical system can be quantized in phase space in different ways with different quasi-probability distributions and star products. A transition differential operator relates different phase space quantizations. The objective of this thesis is to introduce additional physical effects into the process of quantization by using the transition operator. As prototypical examples, we first look at the coarse-graining of the Wigner function and the damped simple harmonic oscillator. By generalizing the transition operator and star product to also be functions of the position and momentum, we show that additional physical features beyond damping and coarse-graining can be introduced into a quantum system, including the generalized uncertainty principle of quantum gravity phenomenology, driving forces, and decoherence.

Study of sea-surface slope distribution and its effect on radar backscatter based on Global Precipitation Measurement Ku-band precipitation radar measurements

NASA Astrophysics Data System (ADS)

Yan, Qiushuang; Zhang, Jie; Fan, Chenqing; Wang, Jing; Meng, Junmin

2018-01-01

The collocated normalized radar backscattering cross-section measurements from the Global Precipitation Measurement (GPM) Ku-band precipitation radar (KuPR) and the winds from the moored buoys are used to study the effect of different sea-surface slope probability density functions (PDFs), including the Gaussian PDF, the Gram-Charlier PDF, and the Liu PDF, on the geometrical optics (GO) model predictions of the radar backscatter at low incidence angles (0 deg to 18 deg) at different sea states. First, the peakedness coefficient in the Liu distribution is determined using the collocations at the normal incidence angle, and the results indicate that the peakedness coefficient is a nonlinear function of the wind speed. Then, the performance of the modified Liu distribution, i.e., Liu distribution using the obtained peakedness coefficient estimate; the Gaussian distribution; and the Gram-Charlier distribution is analyzed. The results show that the GO model predictions with the modified Liu distribution agree best with the KuPR measurements, followed by the predictions with the Gaussian distribution, while the predictions with the Gram-Charlier distribution have larger differences as the total or the slick filtered, not the radar filtered, probability density is included in the distribution. The best-performing distribution changes with incidence angle and changes with wind speed.

Derivation of low flow frequency distributions under human activities and its implications

NASA Astrophysics Data System (ADS)

Gao, Shida; Liu, Pan; Pan, Zhengke; Ming, Bo; Guo, Shenglian; Xiong, Lihua

2017-06-01

Low flow, refers to a minimum streamflow in dry seasons, is crucial to water supply, agricultural irrigation and navigation. Human activities, such as groundwater pumping, influence low flow severely. In order to derive the low flow frequency distribution functions under human activities, this study incorporates groundwater pumping and return flow as variables in the recession process. Steps are as follows: (1) the original low flow without human activities is assumed to follow a Pearson type three distribution, (2) the probability distribution of climatic dry spell periods is derived based on a base flow recession model, (3) the base flow recession model is updated under human activities, and (4) the low flow distribution under human activities is obtained based on the derived probability distribution of dry spell periods and the updated base flow recession model. Linear and nonlinear reservoir models are used to describe the base flow recession, respectively. The Wudinghe basin is chosen for the case study, with daily streamflow observations during 1958-2000. Results show that human activities change the location parameter of the low flow frequency curve for the linear reservoir model, while alter the frequency distribution function for the nonlinear one. It is indicated that alter the parameters of the low flow frequency distribution is not always feasible to tackle the changing environment.

An innovative method for offshore wind farm site selection based on the interval number with probability distribution

NASA Astrophysics Data System (ADS)

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.

A Test of the Exponential Distribution for Stand Structure Definition in Uneven-aged Loblolly-Shortleaf Pine Stands

Treesearch

Paul A. Murphy; Robert M. Farrar

1981-01-01

In this study, 588 before-cut and 381 after-cut diameter distributions of uneven-aged loblolly-shortleaf pinestands were fitted to two different forms of the exponential probability density function. The left truncated and doubly truncated forms of the exponential were used.

Estimating sales and sales market share from sales rank data for consumer appliances

NASA Astrophysics Data System (ADS)

Touzani, Samir; Van Buskirk, Robert

2016-06-01

Our motivation in this work is to find an adequate probability distribution to fit sales volumes of different appliances. This distribution allows for the translation of sales rank into sales volume. This paper shows that the log-normal distribution and specifically the truncated version are well suited for this purpose. We demonstrate that using sales proxies derived from a calibrated truncated log-normal distribution function can be used to produce realistic estimates of market average product prices, and product attributes. We show that the market averages calculated with the sales proxies derived from the calibrated, truncated log-normal distribution provide better market average estimates than sales proxies estimated with simpler distribution functions.

Diffusion of active chiral particles

NASA Astrophysics Data System (ADS)

Sevilla, Francisco J.

2016-12-01

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v ̂ at time t , and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

A Search Model for Imperfectly Detected Targets

NASA Technical Reports Server (NTRS)

Ahumada, Albert

2012-01-01

Under the assumptions that 1) the search region can be divided up into N non-overlapping sub-regions that are searched sequentially, 2) the probability of detection is unity if a sub-region is selected, and 3) no information is available to guide the search, there are two extreme case models. The search can be done perfectly, leading to a uniform distribution over the number of searches required, or the search can be done with no memory, leading to a geometric distribution for the number of searches required with a success probability of 1/N. If the probability of detection P is less than unity, but the search is done otherwise perfectly, the searcher will have to search the N regions repeatedly until detection occurs. The number of searches is thus the sum two random variables. One is N times the number of full searches (a geometric distribution with success probability P) and the other is the uniform distribution over the integers 1 to N. The first three moments of this distribution were computed, giving the mean, standard deviation, and the kurtosis of the distribution as a function of the two parameters. The model was fit to the data presented last year (Ahumada, Billington, & Kaiwi, 2 required to find a single pixel target on a simulated horizon. The model gave a good fit to the three moments for all three observers.

Application of Probabilistic Methods for the Determination of an Economically Robust HSCT Configuration

NASA Technical Reports Server (NTRS)

Mavris, Dimitri N.; Bandte, Oliver; Schrage, Daniel P.

1996-01-01

This paper outlines an approach for the determination of economically viable robust design solutions using the High Speed Civil Transport (HSCT) as a case study. Furthermore, the paper states the advantages of a probability based aircraft design over the traditional point design approach. It also proposes a new methodology called Robust Design Simulation (RDS) which treats customer satisfaction as the ultimate design objective. RDS is based on a probabilistic approach to aerospace systems design, which views the chosen objective as a distribution function introduced by so called noise or uncertainty variables. Since the designer has no control over these variables, a variability distribution is defined for each one of them. The cumulative effect of all these distributions causes the overall variability of the objective function. For cases where the selected objective function depends heavily on these noise variables, it may be desirable to obtain a design solution that minimizes this dependence. The paper outlines a step by step approach on how to achieve such a solution for the HSCT case study and introduces an evaluation criterion which guarantees the highest customer satisfaction. This customer satisfaction is expressed by the probability of achieving objective function values less than a desired target value.

On the Structure of a Best Possible Crossover Selection Strategy in Genetic Algorithms

NASA Astrophysics Data System (ADS)

Lässig, Jörg; Hoffmann, Karl Heinz

The paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover to find a solution with high fitness for a given optimization problem. Many different schemes have been described in the literature as possible strategies for this task but so far comparisons have been predominantly empirical. It is shown that if one wishes to maximize any linear function of the final state probabilities, e.g. the fitness of the best individual in the final population of the algorithm, then a best probability distribution for selecting an individual in each generation is a rectangular distribution over the individuals sorted in descending sequence by their fitness values. This means uniform probabilities have to be assigned to a group of the best individuals of the population but probabilities equal to zero to individuals with lower fitness, assuming that the probability distribution to choose individuals from the current population can be chosen independently for each iteration and each individual. This result is then generalized also to typical practically applied performance measures, such as maximizing the expected fitness value of the best individual seen in any generation.

Estimating probable flaw distributions in PWR steam generator tubes

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

Gorman, J.A.; Turner, A.P.L.

1997-02-01

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 regardingmore » uncertainties and assumptions in the data and analyses.« less

On the issues of probability distribution of GPS carrier phase observations

NASA Astrophysics Data System (ADS)

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

Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas.

PubMed

Chevallier, Maguelonne; Krauth, Werner

2007-11-01

We discuss the relationship between the cycle probabilities in the path-integral representation of the ideal Bose gas, off-diagonal long-range order, and Bose-Einstein condensation. Starting from the Landsberg recursion relation for the canonic partition function, we use elementary considerations to show that in a box of size L3 the sum of the cycle probabilities of length k>L2 equals the off-diagonal long-range order parameter in the thermodynamic limit. For arbitrary systems of ideal bosons, the integer derivative of the cycle probabilities is related to the probability of condensing k bosons. We use this relation to derive the precise form of the pik in the thermodynamic limit. We also determine the function pik for arbitrary systems. Furthermore, we use the cycle probabilities to compute the probability distribution of the maximum-length cycles both at T=0, where the ideal Bose gas reduces to the study of random permutations, and at finite temperature. We close with comments on the cycle probabilities in interacting Bose gases.

Variation in the standard deviation of the lure rating distribution: Implications for estimates of recollection probability.

PubMed

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.

A Performance Comparison on the Probability Plot Correlation Coefficient Test using Several Plotting Positions for GEV Distribution.

NASA Astrophysics Data System (ADS)

Ahn, Hyunjun; Jung, Younghun; Om, Ju-Seong; Heo, Jun-Haeng

2014-05-01

It is very important to select the probability distribution in Statistical hydrology. Goodness of fit test is a statistical method that selects an appropriate probability model for a given data. The probability plot correlation coefficient (PPCC) test as one of the goodness of fit tests was originally developed for normal distribution. Since then, this test has been widely applied to other probability models. The PPCC test is known as one of the best goodness of fit test because it shows higher rejection powers among them. In this study, we focus on the PPCC tests for the GEV distribution which is widely used in the world. For the GEV model, several plotting position formulas are suggested. However, the PPCC statistics are derived only for the plotting position formulas (Goel and De, In-na and Nguyen, and Kim et al.) in which the skewness coefficient (or shape parameter) are included. And then the regression equations are derived as a function of the shape parameter and sample size for a given significance level. In addition, the rejection powers of these formulas are compared using Monte-Carlo simulation. Keywords: Goodness-of-fit test, Probability plot correlation coefficient test, Plotting position, Monte-Carlo Simulation ACKNOWLEDGEMENTS This research was supported by a grant 'Establishing Active Disaster Management System of Flood Control Structures by using 3D BIM Technique' [NEMA-12-NH-57] from the Natural Hazard Mitigation Research Group, National Emergency Management Agency of Korea.

Tensor distribution function

NASA Astrophysics Data System (ADS)

Leow, Alex D.; Zhu, Siwei

2008-03-01

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

Probability density function formalism for optical coherence tomography signal analysis: a controlled phantom study.

PubMed

Weatherbee, Andrew; Sugita, Mitsuro; Bizheva, Kostadinka; Popov, Ivan; Vitkin, Alex

2016-06-15

The distribution of backscattered intensities as described by the probability density function (PDF) of tissue-scattered light contains information that may be useful for tissue assessment and diagnosis, including characterization of its pathology. In this Letter, we examine the PDF description of the light scattering statistics in a well characterized tissue-like particulate medium using optical coherence tomography (OCT). It is shown that for low scatterer density, the governing statistics depart considerably from a Gaussian description and follow the K distribution for both OCT amplitude and intensity. The PDF formalism is shown to be independent of the scatterer flow conditions; this is expected from theory, and suggests robustness and motion independence of the OCT amplitude (and OCT intensity) PDF metrics in the context of potential biomedical applications.

Gravity dual for a model of perception

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

Nakayama, Yu, E-mail: nakayama@berkeley.edu

2011-01-15

One of the salient features of human perception is its invariance under dilatation in addition to the Euclidean group, but its non-invariance under special conformal transformation. We investigate a holographic approach to the information processing in image discrimination with this feature. We claim that a strongly coupled analogue of the statistical model proposed by Bialek and Zee can be holographically realized in scale invariant but non-conformal Euclidean geometries. We identify the Bayesian probability distribution of our generalized Bialek-Zee model with the GKPW partition function of the dual gravitational system. We provide a concrete example of the geometric configuration based onmore » a vector condensation model coupled with the Euclidean Einstein-Hilbert action. From the proposed geometry, we study sample correlation functions to compute the Bayesian probability distribution.« less

Connection between two statistical approaches for the modelling of particle velocity and concentration distributions in turbulent flow: The mesoscopic Eulerian formalism and the two-point probability density function method

NASA Astrophysics Data System (ADS)

Simonin, Olivier; Zaichik, Leonid I.; Alipchenkov, Vladimir M.; Février, Pierre

2006-12-01

The objective of the paper is to elucidate a connection between two approaches that have been separately proposed for modelling the statistical spatial properties of inertial particles in turbulent fluid flows. One of the approaches proposed recently by Février, Simonin, and Squires [J. Fluid Mech. 533, 1 (2005)] is based on the partitioning of particle turbulent velocity field into spatially correlated (mesoscopic Eulerian) and random-uncorrelated (quasi-Brownian) components. The other approach stems from a kinetic equation for the two-point probability density function of the velocity distributions of two particles [Zaichik and Alipchenkov, Phys. Fluids 15, 1776 (2003)]. Comparisons between these approaches are performed for isotropic homogeneous turbulence and demonstrate encouraging agreement.

Statistics of cosmic density profiles from perturbation theory

NASA Astrophysics Data System (ADS)

Bernardeau, Francis; Pichon, Christophe; Codis, Sandrine

2014-11-01

The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with Λ -cold dark matter simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope—the density difference between adjacent cells—and its fluctuations is also computed from the two-cell joint PDF; it also compares very well to simulations. It is emphasized that this could prove useful when studying the statistical properties of voids as it can serve as a statistical indicator to test gravity models and/or probe key cosmological parameters.

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

USGS Publications Warehouse

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

2016-01-01

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

Covering Numbers for Semicontinuous Functions

DTIC Science & Technology

2016-04-29

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

On the use of the noncentral chi-square density function for the distribution of helicopter spectral estimates

NASA Technical Reports Server (NTRS)

Garber, Donald P.

1993-01-01

A probability density function for the variability of ensemble averaged spectral estimates from helicopter acoustic signals in Gaussian background noise was evaluated. Numerical methods for calculating the density function and for determining confidence limits were explored. Density functions were predicted for both synthesized and experimental data and compared with observed spectral estimate variability.

Maximum-entropy probability distributions under Lp-norm constraints

NASA Technical Reports Server (NTRS)

Dolinar, S.

1991-01-01

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

Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws

NASA Technical Reports Server (NTRS)

Nemeth, Noel

2013-01-01

Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software

Multidimensional stochastic approximation using locally contractive functions

NASA Technical Reports Server (NTRS)

Lawton, W. M.

1975-01-01

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

The impacts of precipitation amount simulation on hydrological modeling in Nordic watersheds

NASA Astrophysics Data System (ADS)

Li, Zhi; Brissette, Fancois; Chen, Jie

2013-04-01

Stochastic modeling of daily precipitation is very important for hydrological modeling, especially when no observed data are available. Precipitation is usually modeled by two component model: occurrence generation and amount simulation. For occurrence simulation, the most common method is the first-order two-state Markov chain due to its simplification and good performance. However, various probability distributions have been reported to simulate precipitation amount, and spatiotemporal differences exist in the applicability of different distribution models. Therefore, assessing the applicability of different distribution models is necessary in order to provide more accurate precipitation information. Six precipitation probability distributions (exponential, Gamma, Weibull, skewed normal, mixed exponential, and hybrid exponential/Pareto distributions) are directly and indirectly evaluated on their ability to reproduce the original observed time series of precipitation amount. Data from 24 weather stations and two watersheds (Chute-du-Diable and Yamaska watersheds) in the province of Quebec (Canada) are used for this assessment. Various indices or statistics, such as the mean, variance, frequency distribution and extreme values are used to quantify the performance in simulating the precipitation and discharge. Performance in reproducing key statistics of the precipitation time series is well correlated to the number of parameters of the distribution function, and the three-parameter precipitation models outperform the other models, with the mixed exponential distribution being the best at simulating daily precipitation. The advantage of using more complex precipitation distributions is not as clear-cut when the simulated time series are used to drive a hydrological model. While the advantage of using functions with more parameters is not nearly as obvious, the mixed exponential distribution appears nonetheless as the best candidate for hydrological modeling. The implications of choosing a distribution function with respect to hydrological modeling and climate change impact studies are also discussed.

Generalized skew-symmetric interfacial probability distribution in reflectivity and small-angle scattering analysis

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

Jiang, Zhang; Chen, Wei

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the `effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivities via Parratt's recursive formula, or small-angle scattering via the concentric onion model that is also developed in this work.

Statistics of velocity gradients in two-dimensional Navier-Stokes and ocean turbulence.

PubMed

Schorghofer, Norbert; Gille, Sarah T

2002-02-01

Probability density functions and conditional averages of velocity gradients derived from upper ocean observations are compared with results from forced simulations of the two-dimensional Navier-Stokes equations. Ocean data are derived from TOPEX satellite altimeter measurements. The simulations use rapid forcing on large scales, characteristic of surface winds. The probability distributions of transverse velocity derivatives from the ocean observations agree with the forced simulations, although they differ from unforced simulations reported elsewhere. The distribution and cross correlation of velocity derivatives provide clear evidence that large coherent eddies play only a minor role in generating the observed statistics.

Generalized skew-symmetric interfacial probability distribution in reflectivity and small-angle scattering analysis

DOE PAGES

Jiang, Zhang; Chen, Wei

2017-11-03

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the `effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivities via Parratt's recursive formula, or small-angle scattering via the concentric onion model that is also developed in this work.

Dynamical complexity changes during two forms of meditation

NASA Astrophysics Data System (ADS)

Li, Jin; Hu, Jing; Zhang, Yinhong; Zhang, Xiaofeng

2011-06-01

Detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meaning. We use the base-scale entropy method to analyze dynamical complexity changes for heart rate variability (HRV) series during specific traditional forms of Chinese Chi and Kundalini Yoga meditation techniques in healthy young adults. The results show that dynamical complexity decreases in meditation states for two forms of meditation. Meanwhile, we detected changes in probability distribution of m-words during meditation and explained this changes using probability distribution of sine function. The base-scale entropy method may be used on a wider range of physiologic signals.

Application of Financial Risk-reward Theory to Link and Network Optimization

DTIC Science & Technology

2011-10-01

OFDM systems the matrices V k and U k are Fourier matrices which diagonalize a circulant or block-circulant matrix Hk [18]. In multi-antenna systems...probability α=Pr(η r <=t) Figure 13: Mean link spectral efficiency as a function of target link spectral efficiency ηt and outage probability ζ in a MIMO ...in a MIMO channel. Distribution A: Approved for public release; distribution is unlimited. 41 (75) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 2 4 6 8

Estimating the population size and colony boundary of subterranean termites by using the density functions of directionally averaged capture probability.

PubMed

Su, Nan-Yao; Lee, Sang-Hee

2008-04-01

Marked termites were released in a linear-connected foraging arena, and the spatial heterogeneity of their capture probabilities was averaged for both directions at distance r from release point to obtain a symmetrical distribution, from which the density function of directionally averaged capture probability P(x) was derived. We hypothesized that as marked termites move into the population and given sufficient time, the directionally averaged capture probability may reach an equilibrium P(e) over the distance r and thus satisfy the equal mixing assumption of the mark-recapture protocol. The equilibrium capture probability P(e) was used to estimate the population size N. The hypothesis was tested in a 50-m extended foraging arena to simulate the distance factor of field colonies of subterranean termites. Over the 42-d test period, the density functions of directionally averaged capture probability P(x) exhibited four phases: exponential decline phase, linear decline phase, equilibrium phase, and postequilibrium phase. The equilibrium capture probability P(e), derived as the intercept of the linear regression during the equilibrium phase, correctly projected N estimates that were not significantly different from the known number of workers in the arena. Because the area beneath the probability density function is a constant (50% in this study), preequilibrium regression parameters and P(e) were used to estimate the population boundary distance 1, which is the distance between the release point and the boundary beyond which the population is absent.

Derived distribution of floods based on the concept of partial area coverage with a climatic appeal

NASA Astrophysics Data System (ADS)

Iacobellis, Vito; Fiorentino, Mauro

2000-02-01

A new rationale for deriving the probability distribution of floods and help in understanding the physical processes underlying the distribution itself is presented. On the basis of this a model that presents a number of new assumptions is developed. The basic ideas are as follows: (1) The peak direct streamflow Q can always be expressed as the product of two random variates, namely, the average runoff per unit area ua and the peak contributing area a; (2) the distribution of ua conditional on a can be related to that of the rainfall depth occurring in a duration equal to a characteristic response time тa of the contributing part of the basin; and (3) тa is assumed to vary with a according to a power law. Consequently, the probability density function of Q can be found as the integral, over the total basin area A of that of a times the density function of ua given a. It is suggested that ua can be expressed as a fraction of the excess rainfall and that the annual flood distribution can be related to that of Q by the hypothesis that the flood occurrence process is Poissonian. In the proposed model it is assumed, as an exploratory attempt, that a and ua are gamma and Weibull distributed, respectively. The model was applied to the annual flood series of eight gauged basins in Basilicata (southern Italy) with catchment areas ranging from 40 to 1600 km2. The results showed strong physical consistence as the parameters tended to assume values in good agreement with well-consolidated geomorphologic knowledge and suggested a new key to understanding the climatic control of the probability distribution of floods.

Probabilistic analysis of preload in the abutment screw of a dental implant complex.

PubMed

Guda, Teja; Ross, Thomas A; Lang, Lisa A; Millwater, Harry R

2008-09-01

Screw loosening is a problem for a percentage of implants. A probabilistic analysis to determine the cumulative probability distribution of the preload, the probability of obtaining an optimal preload, and the probabilistic sensitivities identifying important variables is lacking. The purpose of this study was to examine the inherent variability of material properties, surface interactions, and applied torque in an implant system to determine the probability of obtaining desired preload values and to identify the significant variables that affect the preload. Using software programs, an abutment screw was subjected to a tightening torque and the preload was determined from finite element (FE) analysis. The FE model was integrated with probabilistic analysis software. Two probabilistic analysis methods (advanced mean value and Monte Carlo sampling) were applied to determine the cumulative distribution function (CDF) of preload. The coefficient of friction, elastic moduli, Poisson's ratios, and applied torque were modeled as random variables and defined by probability distributions. Separate probability distributions were determined for the coefficient of friction in well-lubricated and dry environments. The probabilistic analyses were performed and the cumulative distribution of preload was determined for each environment. A distinct difference was seen between the preload probability distributions generated in a dry environment (normal distribution, mean (SD): 347 (61.9) N) compared to a well-lubricated environment (normal distribution, mean (SD): 616 (92.2) N). The probability of obtaining a preload value within the target range was approximately 54% for the well-lubricated environment and only 0.02% for the dry environment. The preload is predominately affected by the applied torque and coefficient of friction between the screw threads and implant bore at lower and middle values of the preload CDF, and by the applied torque and the elastic modulus of the abutment screw at high values of the preload CDF. Lubrication at the threaded surfaces between the abutment screw and implant bore affects the preload developed in the implant complex. For the well-lubricated surfaces, only approximately 50% of implants will have preload values within the generally accepted range. This probability can be improved by applying a higher torque than normally recommended or a more closely controlled torque than typically achieved. It is also suggested that materials with higher elastic moduli be used in the manufacture of the abutment screw to achieve a higher preload.

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

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Cocco, Simona; Monasson, Rémi

2015-11-01

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

FUNSTAT and statistical image representations

NASA Technical Reports Server (NTRS)

Parzen, E.

1983-01-01

General ideas of functional statistical inference analysis of one sample and two samples, univariate and bivariate are outlined. ONESAM program is applied to analyze the univariate probability distributions of multi-spectral image data.

Probabilistic #D data fusion for multiresolution surface generation

NASA Technical Reports Server (NTRS)

Manduchi, R.; Johnson, A. E.

2002-01-01

In this paper we present an algorithm for adaptive resolution integration of 3D data collected from multiple distributed sensors. The input to the algorithm is a set of 3D surface points and associated sensor models. Using a probabilistic rule, a surface probability function is generated that represents the probability that a particular volume of space contains the surface. The surface probability function is represented using an octree data structure; regions of space with samples of large conariance are stored at a coarser level than regions of space containing samples with smaller covariance. The algorithm outputs an adaptive resolution surface generated by connecting points that lie on the ridge of surface probability with triangles scaled to match the local discretization of space given by the algorithm, we present results from 3D data generated by scanning lidar and structure from motion.

Probabilistic treatment of the uncertainty from the finite size of weighted Monte Carlo data

NASA Astrophysics Data System (ADS)

Glüsenkamp, Thorsten

2018-06-01

Parameter estimation in HEP experiments often involves Monte Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization schemes with a new simulation set for each parameter value. Problematically, the finite size of such Monte Carlo samples carries intrinsic uncertainty that can lead to a substantial bias in parameter estimation if it is neglected and the sample size is small. We introduce a probabilistic treatment of this problem by replacing the usual likelihood functions with novel generalized probability distributions that incorporate the finite statistics via suitable marginalization. These new PDFs are analytic, and can be used to replace the Poisson, multinomial, and sample-based unbinned likelihoods, which covers many use cases in high-energy physics. In the limit of infinite statistics, they reduce to the respective standard probability distributions. In the general case of arbitrary Monte Carlo weights, the expressions involve the fourth Lauricella function FD, for which we find a new finite-sum representation in a certain parameter setting. The result also represents an exact form for Carlson's Dirichlet average Rn with n > 0, and thereby an efficient way to calculate the probability generating function of the Dirichlet-multinomial distribution, the extended divided difference of a monomial, or arbitrary moments of univariate B-splines. We demonstrate the bias reduction of our approach with a typical toy Monte Carlo problem, estimating the normalization of a peak in a falling energy spectrum, and compare the results with previously published methods from the literature.

Derivation of Hunt equation for suspension distribution using Shannon entropy theory

NASA Astrophysics Data System (ADS)

Kundu, Snehasis

2017-12-01

In this study, the Hunt equation for computing suspension concentration in sediment-laden flows is derived using Shannon entropy theory. Considering the inverse of the void ratio as a random variable and using principle of maximum entropy, probability density function and cumulative distribution function of suspension concentration is derived. A new and more general cumulative distribution function for the flow domain is proposed which includes several specific other models of CDF reported in literature. This general form of cumulative distribution function also helps to derive the Rouse equation. The entropy based approach helps to estimate model parameters using suspension data of sediment concentration which shows the advantage of using entropy theory. Finally model parameters in the entropy based model are also expressed as functions of the Rouse number to establish a link between the parameters of the deterministic and probabilistic approaches.

An understanding of human dynamics in urban subway traffic from the Maximum Entropy Principle

NASA Astrophysics Data System (ADS)

Yong, Nuo; Ni, Shunjiang; Shen, Shifei; Ji, Xuewei

2016-08-01

We studied the distribution of entry time interval in Beijing subway traffic by analyzing the smart card transaction data, and then deduced the probability distribution function of entry time interval based on the Maximum Entropy Principle. Both theoretical derivation and data statistics indicated that the entry time interval obeys power-law distribution with an exponential cutoff. In addition, we pointed out the constraint conditions for the distribution form and discussed how the constraints affect the distribution function. It is speculated that for bursts and heavy tails in human dynamics, when the fitted power exponent is less than 1.0, it cannot be a pure power-law distribution, but with an exponential cutoff, which may be ignored in the previous studies.

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

NASA Astrophysics Data System (ADS)

Nerantzaki, Sofia; Papalexiou, Simon Michael

2017-04-01

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

Superthermal photon bunching in terms of simple probability distributions

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

PubMed Central

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

2016-01-01

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

Neural response to reward anticipation under risk is nonlinear in probabilities.

PubMed

Hsu, Ming; Krajbich, Ian; Zhao, Chen; Camerer, Colin F

2009-02-18

A widely observed phenomenon in decision making under risk is the apparent overweighting of unlikely events and the underweighting of nearly certain events. This violates standard assumptions in expected utility theory, which requires that expected utility be linear (objective) in probabilities. Models such as prospect theory have relaxed this assumption and introduced the notion of a "probability weighting function," which captures the key properties found in experimental data. This study reports functional magnetic resonance imaging (fMRI) data that neural response to expected reward is nonlinear in probabilities. Specifically, we found that activity in the striatum during valuation of monetary gambles are nonlinear in probabilities in the pattern predicted by prospect theory, suggesting that probability distortion is reflected at the level of the reward encoding process. The degree of nonlinearity reflected in individual subjects' decisions is also correlated with striatal activity across subjects. Our results shed light on the neural mechanisms of reward processing, and have implications for future neuroscientific studies of decision making involving extreme tails of the distribution, where probability weighting provides an explanation for commonly observed behavioral anomalies.

Defense strategies for asymmetric networked systems under composite utilities

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

Rao, Nageswara S.; Ma, Chris Y. T.; Hausken, Kjell

We consider an infrastructure of networked systems with discrete components that can be reinforced at certain costs to guard against attacks. The communications network plays a critical, asymmetric role of providing the vital connectivity between the systems. We characterize the correlations within this infrastructure at two levels using (a) aggregate failure correlation function that specifies the infrastructure failure probability giventhe failure of an individual system or network, and (b) first order differential conditions on system survival probabilities that characterize component-level correlations. We formulate an infrastructure survival game between an attacker and a provider, who attacks and reinforces individual components, respectively.more » They use the composite utility functions composed of a survival probability term and a cost term, and the previously studiedsum-form and product-form utility functions are their special cases. At Nash Equilibrium, we derive expressions for individual system survival probabilities and the expected total number of operational components. We apply and discuss these estimates for a simplified model of distributed cloud computing infrastructure« less

Kinetic energy as functional of the correlation hole

NASA Astrophysics Data System (ADS)

Nalewajski, Roman F.

2003-01-01

Using the marginal decomposition of the many-body probability distribution the electronic kinetic energy is expressed as the functional of the electron density and correlation hole. The analysis covers both the molecule as a whole and its constituent subsystems. The importance of the Fisher information for locality is emphasized.

Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Majumdar, Satya N.; Huse, David A.

2017-03-01

We calculate the probability distribution of entanglement entropy S across a cut of a finite one-dimensional spin chain of length L at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form p (S |L ) ˜L-ψ (k ) , where k ≡S /ln[L /L0] , the large deviation function ψ (k ) is found explicitly, and L0 is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

Delineating Hydrofacies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics

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

Song, Xuehang; Chen, Xingyuan; Ye, Ming

2015-07-01

This study develops a new framework of facies-based data assimilation for characterizing spatial distribution of hydrofacies and estimating their associated hydraulic properties. This framework couples ensemble data assimilation with transition probability-based geostatistical model via a parameterization based on a level set function. The nature of ensemble data assimilation makes the framework efficient and flexible to be integrated with various types of observation data. The transition probability-based geostatistical model keeps the updated hydrofacies distributions under geological constrains. The framework is illustrated by using a two-dimensional synthetic study that estimates hydrofacies spatial distribution and permeability in each hydrofacies from transient head data.more » Our results show that the proposed framework can characterize hydrofacies distribution and associated permeability with adequate accuracy even with limited direct measurements of hydrofacies. Our study provides a promising starting point for hydrofacies delineation in complex real problems.« less

Density probability distribution functions of diffuse gas in the Milky Way

NASA Astrophysics Data System (ADS)

Berkhuijsen, E. M.; Fletcher, A.

2008-10-01

In a search for the signature of turbulence in the diffuse interstellar medium (ISM) in gas density distributions, we determined the probability distribution functions (PDFs) of the average volume densities of the diffuse gas. The densities were derived from dispersion measures and HI column densities towards pulsars and stars at known distances. The PDFs of the average densities of the diffuse ionized gas (DIG) and the diffuse atomic gas are close to lognormal, especially when lines of sight at |b| < 5° and |b| >= 5° are considered separately. The PDF of at high |b| is twice as wide as that at low |b|. The width of the PDF of the DIG is about 30 per cent smaller than that of the warm HI at the same latitudes. The results reported here provide strong support for the existence of a lognormal density PDF in the diffuse ISM, consistent with a turbulent origin of density structure in the diffuse gas.

In favor of general probability distributions: lateral prefrontal and insular cortices respond to stimulus inherent, but irrelevant differences.

PubMed

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.

Neuroactive substances in the human vestibular end organs.

PubMed

Usami, S; Matsubara, A; Shinkawa, H; Matsunaga, T; Kanzaki, J

1995-01-01

In order to evaluate the involvement of neuroactive substances in the human vestibular periphery, the immunocytochemical distribution of substance P (SP), calcitonin gene-related peptide (CGRP), and choline acetyltransferase (ChAT) was examined. SP-like immunoreactivity (LI) was present around and beneath sensory hair cells, probably corresponding to their afferent nerve endings. SP-LI was found predominantly in subpopulations of the primary afferents distributed in the peripheral region of the end organs. ChAT-LI and CGRP-LI were found throughout as small puncta below the hair cell layer, probably corresponding to efferent endings. The present results indicate that these neuroactive substances, previously described in animals, are also distributed in the human vestibular periphery, and almost certainly contribute to human vestibular function.

The Pearson walk with shrinking steps in two dimensions

NASA Astrophysics Data System (ADS)

Serino, C. A.; Redner, S.

2010-01-01

We study the shrinking Pearson random walk in two dimensions and greater, in which the direction of the Nth step is random and its length equals λN-1, with λ<1. As λ increases past a critical value λc, the endpoint distribution in two dimensions, P(r), changes from having a global maximum away from the origin to being peaked at the origin. The probability distribution for a single coordinate, P(x), undergoes a similar transition, but exhibits multiple maxima on a fine length scale for λ close to λc. We numerically determine P(r) and P(x) by applying a known algorithm that accurately inverts the exact Bessel function product form of the Fourier transform for the probability distributions.

MaxEnt alternatives to pearson family distributions

NASA Astrophysics Data System (ADS)

Stokes, Barrie J.

2012-05-01

In a previous MaxEnt conference [11] a method of obtaining MaxEnt univariate distributions under a variety of constraints was presented. The Mathematica function Interpolation[], normally used with numerical data, can also process "semi-symbolic" data, and Lagrange Multiplier equations were solved for a set of symbolic ordinates describing the required MaxEnt probability density function. We apply a more developed version of this approach to finding MaxEnt distributions having prescribed β1 and β2 values, and compare the entropy of the MaxEnt distribution to that of the Pearson family distribution having the same β1 and β2. These MaxEnt distributions do have, in general, greater entropy than the related Pearson distribution. In accordance with Jaynes' Maximum Entropy Principle, these MaxEnt distributions are thus to be preferred to the corresponding Pearson distributions as priors in Bayes' Theorem.

Unraveling hadron structure with generalized parton distributions

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

Andrei Belitsky; Anatoly Radyushkin

2004-10-01

The recently introduced generalized parton distributions have emerged as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom. They combine the features of form factors, parton densities and distribution amplitudes - the functions used for a long time in studies of hadronic structure. Generalized parton distributions are analogous to the phase-space Wigner quasi-probability function of non-relativistic quantum mechanics which encodes full information on a quantum-mechanical system. We give an extensive review of main achievements in the development of this formalism. We discuss physical interpretation and basic properties of generalized parton distributions, their modeling andmore » QCD evolution in the leading and next-to-leading orders. We describe how these functions enter a wide class of exclusive reactions, such as electro- and photo-production of photons, lepton pairs, or mesons.« less

Axon and dendrite geography predict the specificity of synaptic connections in a functioning spinal cord network.

PubMed

Li, Wen-Chang; Cooke, Tom; Sautois, Bart; Soffe, Stephen R; Borisyuk, Roman; Roberts, Alan

2007-09-10

How specific are the synaptic connections formed as neuronal networks develop and can simple rules account for the formation of functioning circuits? These questions are assessed in the spinal circuits controlling swimming in hatchling frog tadpoles. This is possible because detailed information is now available on the identity and synaptic connections of the main types of neuron. The probabilities of synapses between 7 types of identified spinal neuron were measured directly by making electrical recordings from 500 pairs of neurons. For the same neuron types, the dorso-ventral distributions of axons and dendrites were measured and then used to calculate the probabilities that axons would encounter particular dendrites and so potentially form synaptic connections. Surprisingly, synapses were found between all types of neuron but contact probabilities could be predicted simply by the anatomical overlap of their axons and dendrites. These results suggested that synapse formation may not require axons to recognise specific, correct dendrites. To test the plausibility of simpler hypotheses, we first made computational models that were able to generate longitudinal axon growth paths and reproduce the axon distribution patterns and synaptic contact probabilities found in the spinal cord. To test if probabilistic rules could produce functioning spinal networks, we then made realistic computational models of spinal cord neurons, giving them established cell-specific properties and connecting them into networks using the contact probabilities we had determined. A majority of these networks produced robust swimming activity. Simple factors such as morphogen gradients controlling dorso-ventral soma, dendrite and axon positions may sufficiently constrain the synaptic connections made between different types of neuron as the spinal cord first develops and allow functional networks to form. Our analysis implies that detailed cellular recognition between spinal neuron types may not be necessary for the reliable formation of functional networks to generate early behaviour like swimming.

On the development of a semi-nonparametric generalized multinomial logit model for travel-related choices

PubMed Central

Ye, Xin; Pendyala, Ram M.; Zou, Yajie

2017-01-01

A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimation. The proposed method is applied to model commute mode choice among four alternatives (auto, transit, bicycle and walk) using travel behavior data from Argau, Switzerland. Comparisons between the multinomial logit model and the proposed semi-nonparametric model show that violations of the standard Gumbel distribution assumption lead to considerable inconsistency in parameter estimates and model inferences. PMID:29073152

On the development of a semi-nonparametric generalized multinomial logit model for travel-related choices.

PubMed

Wang, Ke; Ye, Xin; Pendyala, Ram M; Zou, Yajie

2017-01-01

A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimation. The proposed method is applied to model commute mode choice among four alternatives (auto, transit, bicycle and walk) using travel behavior data from Argau, Switzerland. Comparisons between the multinomial logit model and the proposed semi-nonparametric model show that violations of the standard Gumbel distribution assumption lead to considerable inconsistency in parameter estimates and model inferences.

A Dual Power Law Distribution for the Stellar Initial Mass Function

NASA Astrophysics Data System (ADS)

Hoffmann, Karl Heinz; Essex, Christopher; Basu, Shantanu; Prehl, Janett

2018-05-01

We introduce a new dual power law (DPL) probability distribution function for the mass distribution of stellar and substellar objects at birth, otherwise known as the initial mass function (IMF). The model contains both deterministic and stochastic elements, and provides a unified framework within which to view the formation of brown dwarfs and stars resulting from an accretion process that starts from extremely low mass seeds. It does not depend upon a top down scenario of collapsing (Jeans) masses or an initial lognormal or otherwise IMF-like distribution of seed masses. Like the modified lognormal power law (MLP) distribution, the DPL distribution has a power law at the high mass end, as a result of exponential growth of mass coupled with equally likely stopping of accretion at any time interval. Unlike the MLP, a power law decay also appears at the low mass end of the IMF. This feature is closely connected to the accretion stopping probability rising from an initially low value up to a high value. This might be associated with physical effects of ejections sometimes (i.e., rarely) stopping accretion at early times followed by outflow driven accretion stopping at later times, with the transition happening at a critical time (therefore mass). Comparing the DPL to empirical data, the critical mass is close to the substellar mass limit, suggesting that the onset of nuclear fusion plays an important role in the subsequent accretion history of a young stellar object.

Comparison of probability statistics for automated ship detection in SAR imagery

NASA Astrophysics Data System (ADS)

Henschel, Michael D.; Rey, Maria T.; Campbell, J. W. M.; Petrovic, D.

1998-12-01

This paper discuses the initial results of a recent operational trial of the Ocean Monitoring Workstation's (OMW) ship detection algorithm which is essentially a Constant False Alarm Rate filter applied to Synthetic Aperture Radar data. The choice of probability distribution and methodologies for calculating scene specific statistics are discussed in some detail. An empirical basis for the choice of probability distribution used is discussed. We compare the results using a l-look, k-distribution function with various parameter choices and methods of estimation. As a special case of sea clutter statistics the application of a (chi) 2-distribution is also discussed. Comparisons are made with reference to RADARSAT data collected during the Maritime Command Operation Training exercise conducted in Atlantic Canadian Waters in June 1998. Reference is also made to previously collected statistics. The OMW is a commercial software suite that provides modules for automated vessel detection, oil spill monitoring, and environmental monitoring. This work has been undertaken to fine tune the OMW algorithm's, with special emphasis on the false alarm rate of each algorithm.

Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data

NASA Technical Reports Server (NTRS)

Pierson, Willard J., Jr.

1989-01-01

The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.

Echo Statistics of Aggregations of Scatterers in a Random Waveguide: Application to Biologic Sonar Clutter

DTIC Science & Technology

2012-09-01

used in this paper to compare probability density functions, the Lilliefors test and the Kullback - Leibler distance. The Lilliefors test is a goodness ... of interest in this study are the Rayleigh distribution and the exponential distribution. The Lilliefors test is used to test goodness - of - fit for...Lilliefors test for goodness of fit with an exponential distribution. These results suggests that,

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

PubMed

Yura, Harold T; Hanson, Steen G

2011-04-01

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

Statistical analysis and modeling of intermittent transport events in the tokamak scrape-off layer

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

Anderson, Johan, E-mail: anderson.johan@gmail.com; Halpern, Federico D.; Ricci, Paolo

The turbulence observed in the scrape-off-layer of a tokamak is often characterized by intermittent events of bursty nature, a feature which raises concerns about the prediction of heat loads on the physical boundaries of the device. It appears thus necessary to delve into the statistical properties of turbulent physical fields such as density, electrostatic potential, and temperature, focusing on the mathematical expression of tails of the probability distribution functions. The method followed here is to generate statistical information from time-traces of the plasma density stemming from Braginskii-type fluid simulations and check this against a first-principles theoretical model. The analysis ofmore » the numerical simulations indicates that the probability distribution function of the intermittent process contains strong exponential tails, as predicted by the analytical theory.« less

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

NASA Astrophysics Data System (ADS)

Gonzalez, Diego; Einstein, Theodore; Pimpinelli, Alberto

2011-03-01

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

Computer Simulation Results for the Two-Point Probability Function of Composite Media

NASA Astrophysics Data System (ADS)

Smith, P.; Torquato, S.

1988-05-01

Computer simulation results are reported for the two-point matrix probability function S2 of two-phase random media composed of disks distributed with an arbitrary degree of impenetrability λ. The novel technique employed to sample S2( r) (which gives the probability of finding the endpoints of a line segment of length r in the matrix) is very accurate and has a fast execution time. Results for the limiting cases λ = 0 (fully penetrable disks) and λ = 1 (hard disks), respectively, compare very favorably with theoretical predictions made by Torquato and Beasley and by Torquato and Lado. Results are also reported for several values of λ. that lie between these two extremes: cases which heretofore have not been examined.

The Two-Dimensional Gabor Function Adapted to Natural Image Statistics: A Model of Simple-Cell Receptive Fields and Sparse Structure in Images.

PubMed

Loxley, P N

2017-10-01

The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles, or generate basis functions for sparse coding applications. Learning is found to be most pronounced in three Gabor function parameters representing the size and spatial frequency of the two-dimensional Gabor function and characterized by a nonuniform probability distribution with heavy tails. All three parameters are found to be strongly correlated, resulting in a basis of multiscale Gabor functions with similar aspect ratios and size-dependent spatial frequencies. A key finding is that the distribution of receptive-field sizes is scale invariant over a wide range of values, so there is no characteristic receptive field size selected by natural image statistics. The Gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics. This allows for three distinct solutions: a basis of Gabor functions with sharp orientation resolution at the expense of spatial-frequency resolution, a basis of Gabor functions with sharp spatial-frequency resolution at the expense of orientation resolution, or a basis with unit aspect ratio. Arbitrary mixtures of all three cases are also possible. Two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions. The best-performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with Pareto marginal probability density functions.

Proton Straggling in Thick Silicon Detectors

NASA Technical Reports Server (NTRS)

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

2017-01-01

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

Relay-aided free-space optical communications using α - μ distribution over atmospheric turbulence channels with misalignment errors

NASA Astrophysics Data System (ADS)

Upadhya, Abhijeet; Dwivedi, Vivek K.; Singh, G.

2018-06-01

In this paper, we have analyzed the performance of dual hop radio frequency (RF)/free-space optical (FSO) fixed gain relay environment confined by atmospheric turbulence induced fading channel over FSO link and modeled using α - μ distribution. The RF hop of the amplify-and-forward scheme undergoes the Rayleigh fading and the proposed system model also considers the pointing error effect on the FSO link. A novel and accurate mathematical expression of the probability density function for a FSO link experiencing α - μ distributed atmospheric turbulence in the presence of pointing error is derived. Further, we have presented analytical expressions of outage probability and bit error rate in terms of Meijer-G function. In addition to this, a useful and mathematically tractable closed-form expression for the end-to-end ergodic capacity of the dual hop scheme in terms of bivariate Fox's H function is derived. The atmospheric turbulence, misalignment errors and various binary modulation schemes for intensity modulation on optical wireless link are considered to yield the results. Finally, we have analyzed each of the three performance metrics for high SNR in order to represent them in terms of elementary functions and the achieved analytical results are supported by computer-based simulations.

Microscopic modeling of gas-surface scattering: II. Application to argon atom adsorption on a platinum (111) surface

NASA Astrophysics Data System (ADS)

Filinov, A.; Bonitz, M.; Loffhagen, D.

2018-06-01

A new combination of first principle molecular dynamics (MD) simulations with a rate equation model presented in the preceding paper (paper I) is applied to analyze in detail the scattering of argon atoms from a platinum (111) surface. The combined model is based on a classification of all atom trajectories according to their energies into trapped, quasi-trapped and scattering states. The number of particles in each of the three classes obeys coupled rate equations. The coefficients in the rate equations are the transition probabilities between these states which are obtained from MD simulations. While these rates are generally time-dependent, after a characteristic time scale t E of several tens of picoseconds they become stationary allowing for a rather simple analysis. Here, we investigate this time scale by analyzing in detail the temporal evolution of the energy distribution functions of the adsorbate atoms. We separately study the energy loss distribution function of the atoms and the distribution function of in-plane and perpendicular energy components. Further, we compute the sticking probability of argon atoms as a function of incident energy, angle and lattice temperature. Our model is important for plasma-surface modeling as it allows to extend accurate simulations to longer time scales.

VizieR Online Data Catalog: Proper motions of PM2000 open clusters (Krone-Martins+, 2010)

NASA Astrophysics Data System (ADS)

Krone-Martins, A.; Soubiran, C.; Ducourant, C.; Teixeira, R.; Le Campion, J. F.

2010-04-01

We present lists of proper-motions and kinematic membership probabilities in the region of 49 open clusters or possible open clusters. The stellar proper motions were taken from the Bordeaux PM2000 catalogue. The segregation between cluster and field stars and the assignment of membership probabilities was accomplished by applying a fully automated method based on parametrisations for the probability distribution functions and genetic algorithm optimisation heuristics associated with a derivative-based hill climbing algorithm for the likelihood optimization. (3 data files).

Probabilistic Evaluation of Blade Impact Damage

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Abumeri, G. H.

2003-01-01

The response to high velocity impact of a composite blade is probabilistically evaluated. The evaluation is focused on quantifying probabilistically the effects of uncertainties (scatter) in the variables that describe the impact, the blade make-up (geometry and material), the blade response (displacements, strains, stresses, frequencies), the blade residual strength after impact, and the blade damage tolerance. The results of probabilistic evaluations results are in terms of probability cumulative distribution functions and probabilistic sensitivities. Results show that the blade has relatively low damage tolerance at 0.999 probability of structural failure and substantial at 0.01 probability.

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

PubMed

Gan, Xinjun; Waxman, David

2015-01-01

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

Singular solution of the Feller diffusion equation via a spectral decomposition

NASA Astrophysics Data System (ADS)

Gan, Xinjun; Waxman, David

2015-01-01

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

Bayesian statistics and Monte Carlo methods

NASA Astrophysics Data System (ADS)

Koch, K. R.

2018-03-01

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

Statistical Characteristics of the Gaussian-Noise Spikes Exceeding the Specified Threshold as Applied to Discharges in a Thundercloud

NASA Astrophysics Data System (ADS)

Klimenko, V. V.

2017-12-01

We obtain expressions for the probabilities of the normal-noise spikes with the Gaussian correlation function and for the probability density of the inter-spike intervals. As distinct from the delta-correlated noise, in which the intervals are distributed by the exponential law, the probability of the subsequent spike depends on the previous spike and the interval-distribution law deviates from the exponential one for a finite noise-correlation time (frequency-bandwidth restriction). This deviation is the most pronounced for a low detection threshold. Similarity of the behaviors of the distributions of the inter-discharge intervals in a thundercloud and the noise spikes for the varying repetition rate of the discharges/spikes, which is determined by the ratio of the detection threshold to the root-mean-square value of noise, is observed. The results of this work can be useful for the quantitative description of the statistical characteristics of the noise spikes and studying the role of fluctuations for the discharge emergence in a thundercloud.

Introduction and application of non-stationary standardized precipitation index considering probability distribution function and return period

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

Li, Xue; Hjorth, Jens; Richard, Johan

2012-11-01

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

Probability density function learning by unsupervised neurons.

PubMed

Fiori, S

2001-10-01

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

The emergence of different tail exponents in the distributions of firm size variables

NASA Astrophysics Data System (ADS)

Ishikawa, Atushi; Fujimoto, Shouji; Watanabe, Tsutomu; Mizuno, Takayuki

2013-05-01

We discuss a mechanism through which inversion symmetry (i.e., invariance of a joint probability density function under the exchange of variables) and Gibrat’s law generate power-law distributions with different tail exponents. Using a dataset of firm size variables, that is, tangible fixed assets K, the number of workers L, and sales Y, we confirm that these variables have power-law tails with different exponents, and that inversion symmetry and Gibrat’s law hold. Based on these findings, we argue that there exists a plane in the three dimensional space (logK,logL,logY), with respect to which the joint probability density function for the three variables is invariant under the exchange of variables. We provide empirical evidence suggesting that this plane fits the data well, and argue that the plane can be interpreted as the Cobb-Douglas production function, which has been extensively used in various areas of economics since it was first introduced almost a century ago.

ANNz2: Photometric Redshift and Probability Distribution Function Estimation using Machine Learning

NASA Astrophysics Data System (ADS)

Sadeh, I.; Abdalla, F. B.; Lahav, O.

2016-10-01

We present ANNz2, a new implementation of the public software for photometric redshift (photo-z) estimation of Collister & Lahav, which now includes generation of full probability distribution functions (PDFs). ANNz2 utilizes multiple machine learning methods, such as artificial neural networks and boosted decision/regression trees. The objective of the algorithm is to optimize the performance of the photo-z estimation, to properly derive the associated uncertainties, and to produce both single-value solutions and PDFs. In addition, estimators are made available, which mitigate possible problems of non-representative or incomplete spectroscopic training samples. ANNz2 has already been used as part of the first weak lensing analysis of the Dark Energy Survey, and is included in the experiment's first public data release. Here we illustrate the functionality of the code using data from the tenth data release of the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey. The code is available for download at http://github.com/IftachSadeh/ANNZ.

An efficient distribution method for nonlinear transport problems in stochastic porous media

NASA Astrophysics Data System (ADS)

Ibrahima, F.; Tchelepi, H.; Meyer, D. W.

2015-12-01

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are convenient to explore possible scenarios and assess risks in subsurface problems. In particular, understanding how uncertainties propagate in porous media with nonlinear two-phase flow is essential, yet challenging, in reservoir simulation and hydrology. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the water saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. The method draws inspiration from the streamline approach and expresses the distributions of interest essentially in terms of an analytically derived mapping and the distribution of the time of flight. In a large class of applications the latter can be estimated at low computational costs (even via conventional Monte Carlo). Once the water saturation distribution is determined, any one-point statistics thereof can be obtained, especially its average and standard deviation. Moreover, rarely available in other approaches, yet crucial information such as the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be derived from the method. We provide various examples and comparisons with Monte Carlo simulations to illustrate the performance of the method.

Flow of foams in two-dimensional disordered porous media

NASA Astrophysics Data System (ADS)

Dollet, Benjamin; Geraud, Baudouin; Jones, Sian A.; Meheust, Yves; Cantat, Isabelle; Institut de Physique de Rennes Team; Geosciences Rennes Team

2015-11-01

Liquid foams are a yield stress fluid with elastic properties. When a foam flow is confined by solid walls, viscous dissipation arises from the contact zones between soap films and walls, giving very peculiar friction laws. In particular, foams potentially invade narrow pores much more efficiently than Newtonian fluids, which is of great importance for enhanced oil recovery. To quantify this effect, we study experimentally flows of foam in a model two-dimensional porous medium, consisting of an assembly of circular obstacles placed randomly in a Hele-Shaw cell, and use image analysis to quantify foam flow at the local scale. We show that bubbles split as they flow through the porous medium, by a mechanism of film pinching during contact with an obstacle, yielding two daughter bubbles per split bubble. We quantify the evolution of the bubble size distribution as a function of the distance along the porous medium, the splitting probability as a function of bubble size, and the probability distribution function of the daughter bubbles. We propose an evolution equation to model this splitting phenomenon and compare it successfully to the experiments, showing how at long distance, the porous medium itself dictates the size distribution of the foam.

Probabilistic Models For Earthquakes With Large Return Periods In Himalaya Region

NASA Astrophysics Data System (ADS)

Chaudhary, Chhavi; Sharma, Mukat Lal

2017-12-01

Determination of the frequency of large earthquakes is of paramount importance for seismic risk assessment as large events contribute to significant fraction of the total deformation and these long return period events with low probability of occurrence are not easily captured by classical distributions. Generally, with a small catalogue these larger events follow different distribution function from the smaller and intermediate events. It is thus of special importance to use statistical methods that analyse as closely as possible the range of its extreme values or the tail of the distributions in addition to the main distributions. The generalised Pareto distribution family is widely used for modelling the events which are crossing a specified threshold value. The Pareto, Truncated Pareto, and Tapered Pareto are the special cases of the generalised Pareto family. In this work, the probability of earthquake occurrence has been estimated using the Pareto, Truncated Pareto, and Tapered Pareto distributions. As a case study, the Himalayas whose orogeny lies in generation of large earthquakes and which is one of the most active zones of the world, has been considered. The whole Himalayan region has been divided into five seismic source zones according to seismotectonic and clustering of events. Estimated probabilities of occurrence of earthquakes have also been compared with the modified Gutenberg-Richter distribution and the characteristics recurrence distribution. The statistical analysis reveals that the Tapered Pareto distribution better describes seismicity for the seismic source zones in comparison to other distributions considered in the present study.

Reward and uncertainty in exploration programs

NASA Technical Reports Server (NTRS)

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

1971-01-01

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

Noise deconvolution based on the L1-metric and decomposition of discrete distributions of postsynaptic responses.

PubMed

Astrelin, A V; Sokolov, M V; Behnisch, T; Reymann, K G; Voronin, L L

1997-04-25

A statistical approach to analysis of amplitude fluctuations of postsynaptic responses is described. This includes (1) using a L1-metric in the space of distribution functions for minimisation with application of linear programming methods to decompose amplitude distributions into a convolution of Gaussian and discrete distributions; (2) deconvolution of the resulting discrete distribution with determination of the release probabilities and the quantal amplitude for cases with a small number (< 5) of discrete components. The methods were tested against simulated data over a range of sample sizes and signal-to-noise ratios which mimicked those observed in physiological experiments. In computer simulation experiments, comparisons were made with other methods of 'unconstrained' (generalized) and constrained reconstruction of discrete components from convolutions. The simulation results provided additional criteria for improving the solutions to overcome 'over-fitting phenomena' and to constrain the number of components with small probabilities. Application of the programme to recordings from hippocampal neurones demonstrated its usefulness for the analysis of amplitude distributions of postsynaptic responses.

Use of the Digamma Function in Statistical Astrophysics Distributions

NASA Astrophysics Data System (ADS)

Cahill, Michael

2017-06-01

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

The Havriliak-Negami relaxation and its relatives: the response, relaxation and probability density functions

NASA Astrophysics Data System (ADS)

Górska, K.; Horzela, A.; Bratek, Ł.; Dattoli, G.; Penson, K. A.

2018-04-01

We study functions related to the experimentally observed Havriliak-Negami dielectric relaxation pattern proportional in the frequency domain to [1+(iωτ0){\\hspace{0pt}}α]-β with τ0 > 0 being some characteristic time. For α = l/k< 1 (l and k being positive and relatively prime integers) and β > 0 we furnish exact and explicit expressions for response and relaxation functions in the time domain and suitable probability densities in their domain dual in the sense of the inverse Laplace transform. All these functions are expressed as finite sums of generalized hypergeometric functions, convenient to handle analytically and numerically. Introducing a reparameterization β = (2-q)/(q-1) and τ0 = (q-1){\\hspace{0pt}}1/α (1 < q < 2) we show that for 0 < α < 1 the response functions fα, β(t/τ0) go to the one-sided Lévy stable distributions when q tends to one. Moreover, applying the self-similarity property of the probability densities gα, β(u) , we introduce two-variable densities and show that they satisfy the integral form of the evolution equation.

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

DOE PAGES

Smallwood, David O.

1997-01-01

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

Uncertainty Analysis via Failure Domain Characterization: Polynomial Requirement Functions

NASA Technical Reports Server (NTRS)

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

2011-01-01

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

Uncertainty Analysis via Failure Domain Characterization: Unrestricted Requirement Functions

NASA Technical Reports Server (NTRS)

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

2011-01-01

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

On the distribution of a product of N Gaussian random variables

NASA Astrophysics Data System (ADS)

Stojanac, Željka; Suess, Daniel; Kliesch, Martin

2017-08-01

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

Characterization of Cloud Water-Content Distribution

NASA Technical Reports Server (NTRS)

Lee, Seungwon

2010-01-01

The development of realistic cloud parameterizations for climate models requires accurate characterizations of subgrid distributions of thermodynamic variables. To this end, a software tool was developed to characterize cloud water-content distributions in climate-model sub-grid scales. This software characterizes distributions of cloud water content with respect to cloud phase, cloud type, precipitation occurrence, and geo-location using CloudSat radar measurements. It uses a statistical method called maximum likelihood estimation to estimate the probability density function of the cloud water content.

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Entropy and wigner functions

PubMed

Manfredi; Feix

2000-10-01

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

Probability, geometry, and dynamics in the toss of a thick coin

NASA Astrophysics Data System (ADS)

Yong, Ee Hou; Mahadevan, L.

2011-12-01

When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and precession and calculate the probability distribution of heads, tails, and sides for a thick coin as a function of its dimensions and the distribution of its initial conditions. Our theory yields a simple expression for the aspect ratio of homogeneous coins with a prescribed frequency of heads or tails compared to sides, which we validate using data from the results of tossing coins of different aspect ratios.

Exact joint density-current probability function for the asymmetric exclusion process.

PubMed

Depken, Martin; Stinchcombe, Robin

2004-07-23

We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra. Copyright 2004 The American Physical Society

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

AUTOCLASS III - AUTOMATIC CLASS DISCOVERY FROM DATA

NASA Technical Reports Server (NTRS)

Cheeseman, P. C.

1994-01-01

The program AUTOCLASS III, Automatic Class Discovery from Data, uses Bayesian probability theory to provide a simple and extensible approach to problems such as classification and general mixture separation. Its theoretical basis is free from ad hoc quantities, and in particular free of any measures which alter the data to suit the needs of the program. As a result, the elementary classification model used lends itself easily to extensions. The standard approach to classification in much of artificial intelligence and statistical pattern recognition research involves partitioning of the data into separate subsets, known as classes. AUTOCLASS III uses the Bayesian approach in which classes are described by probability distributions over the attributes of the objects, specified by a model function and its parameters. The calculation of the probability of each object's membership in each class provides a more intuitive classification than absolute partitioning techniques. AUTOCLASS III is applicable to most data sets consisting of independent instances, each described by a fixed length vector of attribute values. An attribute value may be a number, one of a set of attribute specific symbols, or omitted. The user specifies a class probability distribution function by associating attribute sets with supplied likelihood function terms. AUTOCLASS then searches in the space of class numbers and parameters for the maximally probable combination. It returns the set of class probability function parameters, and the class membership probabilities for each data instance. AUTOCLASS III is written in Common Lisp, and is designed to be platform independent. This program has been successfully run on Symbolics and Explorer Lisp machines. It has been successfully used with the following implementations of Common LISP on the Sun: Franz Allegro CL, Lucid Common Lisp, and Austin Kyoto Common Lisp and similar UNIX platforms; under the Lucid Common Lisp implementations on VAX/VMS v5.4, VAX/Ultrix v4.1, and MIPS/Ultrix v4, rev. 179; and on the Macintosh personal computer. The minimum Macintosh required is the IIci. This program will not run under CMU Common Lisp or VAX/VMS DEC Common Lisp. A minimum of 8Mb of RAM is required for Macintosh platforms and 16Mb for workstations. The standard distribution medium for this program is a .25 inch streaming magnetic tape cartridge in UNIX tar format. It is also available on a 3.5 inch diskette in UNIX tar format and a 3.5 inch diskette in Macintosh format. An electronic copy of the documentation is included on the distribution medium. AUTOCLASS was developed between March 1988 and March 1992. It was initially released in May 1991. Sun is a trademark of Sun Microsystems, Inc. UNIX is a registered trademark of AT&T Bell Laboratories. DEC, VAX, VMS, and ULTRIX are trademarks of Digital Equipment Corporation. Macintosh is a trademark of Apple Computer, Inc. Allegro CL is a registered trademark of Franz, Inc.

A functional model of sensemaking in a neurocognitive architecture.

PubMed

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

2013-01-01

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

A Functional Model of Sensemaking in a Neurocognitive Architecture

PubMed Central

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

2013-01-01

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

Bayesian image reconstruction - The pixon and optimal image modeling

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

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.

Naima: a Python package for inference of particle distribution properties from nonthermal spectra

NASA Astrophysics Data System (ADS)

Zabalza, V.

2015-07-01

The ultimate goal of the observation of nonthermal emission from astrophysical sources is to understand the underlying particle acceleration and evolution processes, and few tools are publicly available to infer the particle distribution properties from the observed photon spectra from X-ray to VHE gamma rays. Here I present naima, an open source Python package that provides models for nonthermal radiative emission from homogeneous distribution of relativistic electrons and protons. Contributions from synchrotron, inverse Compton, nonthermal bremsstrahlung, and neutral-pion decay can be computed for a series of functional shapes of the particle energy distributions, with the possibility of using user-defined particle distribution functions. In addition, naima provides a set of functions that allow to use these models to fit observed nonthermal spectra through an MCMC procedure, obtaining probability distribution functions for the particle distribution parameters. Here I present the models and methods available in naima and an example of their application to the understanding of a galactic nonthermal source. naima's documentation, including how to install the package, is available at http://naima.readthedocs.org.

The Difference Calculus and The NEgative Binomial Distribution

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

Bowman, Kimiko o; Shenton, LR

2007-01-01

In a previous paper we state the dominant term in the third central moment of the maximum likelihood estimator k of the parameter k in the negative binomial probability function where the probability generating function is (p + 1 - pt){sup -k}. A partial sum of the series {Sigma}1/(k + x){sup 3} is involved, where x is a negative binomial random variate. In expectation this sum can only be found numerically using the computer. Here we give a simple definite integral in (0,1) for the generalized case. This means that now we do have a valid expression for {radical}{beta}{sub 11}(k)more » and {radical}{beta}{sub 11}(p). In addition we use the finite difference operator {Delta}, and E = 1 + {Delta} to set up formulas for low order moments. Other examples of the operators are quoted relating to the orthogonal set of polynomials associated with the negative binomial probability function used as a weight function.« less

Building a generalized distributed system model

NASA Technical Reports Server (NTRS)

Mukkamala, Ravi; Foudriat, E. C.

1991-01-01

A modeling tool for both analysis and design of distributed systems is discussed. Since many research institutions have access to networks of workstations, the researchers decided to build a tool running on top of the workstations to function as a prototype as well as a distributed simulator for a computing system. The effects of system modeling on performance prediction in distributed systems and the effect of static locking and deadlocks on the performance predictions of distributed transactions are also discussed. While the probability of deadlock is considerably small, its effects on performance could be significant.

Predictive modelling of habitat selection by marine predators with respect to the abundance and depth distribution of pelagic prey.

PubMed

Boyd, Charlotte; Castillo, Ramiro; Hunt, George L; Punt, André E; VanBlaricom, Glenn R; Weimerskirch, Henri; Bertrand, Sophie

2015-11-01

Understanding the ecological processes that underpin species distribution patterns is a fundamental goal in spatial ecology. However, developing predictive models of habitat use is challenging for species that forage in marine environments, as both predators and prey are often highly mobile and difficult to monitor. Consequently, few studies have developed resource selection functions for marine predators based directly on the abundance and distribution of their prey. We analysed contemporaneous data on the diving locations of two seabird species, the shallow-diving Peruvian Booby (Sula variegata) and deeper diving Guanay Cormorant (Phalacrocorax bougainvilliorum), and the abundance and depth distribution of their main prey, Peruvian anchoveta (Engraulis ringens). Based on this unique data set, we developed resource selection functions to test the hypothesis that the probability of seabird diving behaviour at a given location is a function of the relative abundance of prey in the upper water column. For both species, we show that the probability of diving behaviour is mostly explained by the distribution of prey at shallow depths. While the probability of diving behaviour increases sharply with prey abundance at relatively low levels of abundance, support for including abundance in addition to the depth distribution of prey is weak, suggesting that prey abundance was not a major factor determining the location of diving behaviour during the study period. The study thus highlights the importance of the depth distribution of prey for two species of seabird with different diving capabilities. The results complement previous research that points towards the importance of oceanographic processes that enhance the accessibility of prey to seabirds. The implications are that locations where prey is predictably found at accessible depths may be more important for surface foragers, such as seabirds, than locations where prey is predictably abundant. Analysis of the relative importance of abundance and accessibility is essential for the design and evaluation of effective management responses to reduced prey availability for seabirds and other top predators in marine systems. © 2015 The Authors. Journal of Animal Ecology © 2015 British Ecological Society.

Probability shapes perceptual precision: A study in orientation estimation.

PubMed

Jabar, Syaheed B; Anderson, Britt

2015-12-01

Probability is known to affect perceptual estimations, but an understanding of mechanisms is lacking. Moving beyond binary classification tasks, we had naive participants report the orientation of briefly viewed gratings where we systematically manipulated contingent probability. Participants rapidly developed faster and more precise estimations for high-probability tilts. The shapes of their error distributions, as indexed by a kurtosis measure, also showed a distortion from Gaussian. This kurtosis metric was robust, capturing probability effects that were graded, contextual, and varying as a function of stimulus orientation. Our data can be understood as a probability-induced reduction in the variability or "shape" of estimation errors, as would be expected if probability affects the perceptual representations. As probability manipulations are an implicit component of many endogenous cuing paradigms, changes at the perceptual level could account for changes in performance that might have traditionally been ascribed to "attention." (c) 2015 APA, all rights reserved).

Applicability of AgMERRA Forcing Dataset to Fill Gaps in Historical in-situ Meteorological Data

NASA Astrophysics Data System (ADS)

Bannayan, M.; Lashkari, A.; Zare, H.; Asadi, S.; Salehnia, N.

2015-12-01

Integrated assessment studies of food production systems use crop models to simulate the effects of climate and socio-economic changes on food security. Climate forcing data is one of those key inputs of crop models. This study evaluated the performance of AgMERRA climate forcing dataset to fill gaps in historical in-situ meteorological data for different climatic regions of Iran. AgMERRA dataset intercompared with in- situ observational dataset for daily maximum and minimum temperature and precipitation during 1980-2010 periods via Root Mean Square error (RMSE), Mean Absolute Error (MAE) and Mean Bias Error (MBE) for 17 stations in four climatic regions included humid and moderate, cold, dry and arid, hot and humid. Moreover, probability distribution function and cumulative distribution function compared between model and observed data. The results of measures of agreement between AgMERRA data and observed data demonstrated that there are small errors in model data for all stations. Except for stations which are located in cold regions, model data in the other stations illustrated under-prediction for daily maximum temperature and precipitation. However, it was not significant. In addition, probability distribution function and cumulative distribution function showed the same trend for all stations between model and observed data. Therefore, the reliability of AgMERRA dataset is high to fill gaps in historical observations in different climatic regions of Iran as well as it could be applied as a basis for future climate scenarios.

Distribution functions of probabilistic automata

NASA Technical Reports Server (NTRS)

Vatan, F.

2001-01-01

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

Generalized ensemble theory with non-extensive statistics

NASA Astrophysics Data System (ADS)

Shen, Ke-Ming; Zhang, Ben-Wei; Wang, En-Ke

2017-12-01

The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' q -average of physical quantities, the sum ∑ pjq, is independent of the probability pi for Tsallis parameter q. The self-referential problem in the deduced probability and thermal quantities in non-extensive statistics is thus avoided, and thermodynamical relationships are obtained in a consistent and natural way. We also extend the study to the non-extensive grand canonical ensemble theory and obtain the q-deformed Bose-Einstein distribution as well as the q-deformed Fermi-Dirac distribution. The theory is further applied to the generalized Planck law to demonstrate the distinct behaviors of the various generalized q-distribution functions discussed in literature.

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

PubMed

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

2012-06-01

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

Encounter risk analysis of rainfall and reference crop evapotranspiration in the irrigation district

NASA Astrophysics Data System (ADS)

Zhang, Jinping; Lin, Xiaomin; Zhao, Yong; Hong, Yang

2017-09-01

Rainfall and reference crop evapotranspiration are random but mutually affected variables in the irrigation district, and their encounter situation can determine water shortage risks under the contexts of natural water supply and demand. However, in reality, the rainfall and reference crop evapotranspiration may have different marginal distributions and their relations are nonlinear. In this study, based on the annual rainfall and reference crop evapotranspiration data series from 1970 to 2013 in the Luhun irrigation district of China, the joint probability distribution of rainfall and reference crop evapotranspiration are developed with the Frank copula function. Using the joint probability distribution, the synchronous-asynchronous encounter risk, conditional joint probability, and conditional return period of different combinations of rainfall and reference crop evapotranspiration are analyzed. The results show that the copula-based joint probability distributions of rainfall and reference crop evapotranspiration are reasonable. The asynchronous encounter probability of rainfall and reference crop evapotranspiration is greater than their synchronous encounter probability, and the water shortage risk associated with meteorological drought (i.e. rainfall variability) is more prone to appear. Compared with other states, there are higher conditional joint probability and lower conditional return period in either low rainfall or high reference crop evapotranspiration. For a specifically high reference crop evapotranspiration with a certain frequency, the encounter risk of low rainfall and high reference crop evapotranspiration is increased with the decrease in frequency. For a specifically low rainfall with a certain frequency, the encounter risk of low rainfall and high reference crop evapotranspiration is decreased with the decrease in frequency. When either the high reference crop evapotranspiration exceeds a certain frequency or low rainfall does not exceed a certain frequency, the higher conditional joint probability and lower conditional return period of various combinations likely cause a water shortage, but the water shortage is not severe.

A Further Note on Generalized Hyperexponential Distributions

DTIC Science & Technology

1989-11-15

functions. The inverse transform of each of m factors is of the form The requirement that 0, < r7 thus yields a mixture of an atom at the origin and a...real and (0, + 0,+,)/2 < Re(r/,) when (7h, 77t4) are a complex conjugate pair. Then the inverse transform of f*(s) is a probability distribution. To

Rotated sigmoid structures in managed uneven-aged northern hardwood stands: a look at the Burr Type III distribution

Treesearch

Jeffrey H. Gove; Mark J. Ducey; William B. Leak; Lianjun Zhang

2008-01-01

Stand structures from a combined density manipulation and even- to uneven-aged conversion experiment on the Bartlett Experimental Forest (New Hampshire, USA) were examined 25 years after initial treatment for rotated sigmoidal diameter distributions. A comparison was made on these stands between two probability density functions for fitting these residual structures:...

Metabolic networks evolve towards states of maximum entropy production.

PubMed

Unrean, Pornkamol; Srienc, Friedrich

2011-11-01

A metabolic network can be described by a set of elementary modes or pathways representing discrete metabolic states that support cell function. We have recently shown that in the most likely metabolic state the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law while complying with the principle of maximum entropy production. To demonstrate that a metabolic network evolves towards such state we have carried out adaptive evolution experiments with Thermoanaerobacterium saccharolyticum operating with a reduced metabolic functionality based on a reduced set of elementary modes. In such reduced metabolic network metabolic fluxes can be conveniently computed from the measured metabolite secretion pattern. Over a time span of 300 generations the specific growth rate of the strain continuously increased together with a continuous increase in the rate of entropy production. We show that the rate of entropy production asymptotically approaches the maximum entropy production rate predicted from the state when the usage probability of individual elementary modes is distributed according to the Boltzmann distribution. Therefore, the outcome of evolution of a complex biological system can be predicted in highly quantitative terms using basic statistical mechanical principles. Copyright © 2011 Elsevier Inc. All rights reserved.

The decline and fall of Type II error rates

Treesearch

Steve Verrill; Mark Durst

2005-01-01

For general linear models with normally distributed random errors, the probability of a Type II error decreases exponentially as a function of sample size. This potentially rapid decline reemphasizes the importance of performing power calculations.

Audio feature extraction using probability distribution function

NASA Astrophysics Data System (ADS)

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.

Peelle's pertinent puzzle using the Monte Carlo technique

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

Kawano, Toshihiko; Talou, Patrick; Burr, Thomas

2009-01-01

We try to understand the long-standing problem of the Peelle's Pertinent Puzzle (PPP) using the Monte Carlo technique. We allow the probability density functions to be any kind of form to assume the impact of distribution, and obtain the least-squares solution directly from numerical simulations. We found that the standard least squares method gives the correct answer if a weighting function is properly provided. Results from numerical simulations show that the correct answer of PPP is 1.1 {+-} 0.25 if the common error is multiplicative. The thought-provoking answer of 0.88 is also correct, if the common error is additive, andmore » if the error is proportional to the measured values. The least squares method correctly gives us the most probable case, where the additive component has a negative value. Finally, the standard method fails for PPP due to a distorted (non Gaussian) joint distribution.« less

Evolution of the microstructure during the process of consolidation and bonding in soft granular solids.

PubMed

Yohannes, B; Gonzalez, M; Abebe, A; Sprockel, O; Nikfar, F; Kiang, S; Cuitiño, A M

2016-04-30

The evolution of microstructure during powder compaction process was investigated using a discrete particle modeling, which accounts for particle size distribution and material properties, such as plasticity, elasticity, and inter-particle bonding. The material properties were calibrated based on powder compaction experiments and validated based on tensile strength test experiments for lactose monohydrate and microcrystalline cellulose, which are commonly used excipient in pharmaceutical industry. The probability distribution function and the orientation of contact forces were used to study the evolution of the microstructure during the application of compaction pressure, unloading, and ejection of the compact from the die. The probability distribution function reveals that the compression contact forces increase as the compaction force increases (or the relative density increases), while the maximum value of the tensile contact forces remains the same. During unloading of the compaction pressure, the distribution approaches a normal distribution with a mean value of zero. As the contact forces evolve, the anisotropy of the powder bed also changes. Particularly, during loading, the compression contact forces are aligned along the direction of the compaction pressure, whereas the tensile contact forces are oriented perpendicular to direction of the compaction pressure. After ejection, the contact forces become isotropic. Copyright © 2016 Elsevier B.V. All rights reserved.

A probabilistic multi-criteria decision making technique for conceptual and preliminary aerospace systems design

NASA Astrophysics Data System (ADS)

Bandte, Oliver

It has always been the intention of systems engineering to invent or produce the best product possible. Many design techniques have been introduced over the course of decades that try to fulfill this intention. Unfortunately, no technique has succeeded in combining multi-criteria decision making with probabilistic design. The design technique developed in this thesis, the Joint Probabilistic Decision Making (JPDM) technique, successfully overcomes this deficiency by generating a multivariate probability distribution that serves in conjunction with a criterion value range of interest as a universally applicable objective function for multi-criteria optimization and product selection. This new objective function constitutes a meaningful Xnetric, called Probability of Success (POS), that allows the customer or designer to make a decision based on the chance of satisfying the customer's goals. In order to incorporate a joint probabilistic formulation into the systems design process, two algorithms are created that allow for an easy implementation into a numerical design framework: the (multivariate) Empirical Distribution Function and the Joint Probability Model. The Empirical Distribution Function estimates the probability that an event occurred by counting how many times it occurred in a given sample. The Joint Probability Model on the other hand is an analytical parametric model for the multivariate joint probability. It is comprised of the product of the univariate criterion distributions, generated by the traditional probabilistic design process, multiplied with a correlation function that is based on available correlation information between pairs of random variables. JPDM is an excellent tool for multi-objective optimization and product selection, because of its ability to transform disparate objectives into a single figure of merit, the likelihood of successfully meeting all goals or POS. The advantage of JPDM over other multi-criteria decision making techniques is that POS constitutes a single optimizable function or metric that enables a comparison of all alternative solutions on an equal basis. Hence, POS allows for the use of any standard single-objective optimization technique available and simplifies a complex multi-criteria selection problem into a simple ordering problem, where the solution with the highest POS is best. By distinguishing between controllable and uncontrollable variables in the design process, JPDM can account for the uncertain values of the uncontrollable variables that are inherent to the design problem, while facilitating an easy adjustment of the controllable ones to achieve the highest possible POS. Finally, JPDM's superiority over current multi-criteria decision making techniques is demonstrated with an optimization of a supersonic transport concept and ten contrived equations as well as a product selection example, determining an airline's best choice among Boeing's B-747, B-777, Airbus' A340, and a Supersonic Transport. The optimization examples demonstrate JPDM's ability to produce a better solution with a higher POS than an Overall Evaluation Criterion or Goal Programming approach. Similarly, the product selection example demonstrates JPDM's ability to produce a better solution with a higher POS and different ranking than the Overall Evaluation Criterion or Technique for Order Preferences by Similarity to the Ideal Solution (TOPSIS) approach.

Analysis of scattering statistics and governing distribution functions in optical coherence tomography.

PubMed

Sugita, Mitsuro; Weatherbee, Andrew; Bizheva, Kostadinka; Popov, Ivan; Vitkin, Alex

2016-07-01

The probability density function (PDF) of light scattering intensity can be used to characterize the scattering medium. We have recently shown that in optical coherence tomography (OCT), a PDF formalism can be sensitive to the number of scatterers in the probed scattering volume and can be represented by the K-distribution, a functional descriptor for non-Gaussian scattering statistics. Expanding on this initial finding, here we examine polystyrene microsphere phantoms with different sphere sizes and concentrations, and also human skin and fingernail in vivo. It is demonstrated that the K-distribution offers an accurate representation for the measured OCT PDFs. The behavior of the shape parameter of K-distribution that best fits the OCT scattering results is investigated in detail, and the applicability of this methodology for biological tissue characterization is demonstrated and discussed.

Three statistical models for estimating length of stay.

PubMed Central

Selvin, S

1977-01-01

The probability density functions implied by three methods of collecting data on the length of stay in an institution are derived. The expected values associated with these density functions are used to calculate unbiased estimates of the expected length of stay. Two of the methods require an assumption about the form of the underlying distribution of length of stay; the third method does not. The three methods are illustrated with hypothetical data exhibiting the Poisson distribution, and the third (distribution-independent) method is used to estimate the length of stay in a skilled nursing facility and in an intermediate care facility for patients enrolled in California's MediCal program. PMID:914532

Three statistical models for estimating length of stay.

PubMed

Selvin, S

1977-01-01

The probability density functions implied by three methods of collecting data on the length of stay in an institution are derived. The expected values associated with these density functions are used to calculate unbiased estimates of the expected length of stay. Two of the methods require an assumption about the form of the underlying distribution of length of stay; the third method does not. The three methods are illustrated with hypothetical data exhibiting the Poisson distribution, and the third (distribution-independent) method is used to estimate the length of stay in a skilled nursing facility and in an intermediate care facility for patients enrolled in California's MediCal program.

Geotechnical parameter spatial distribution stochastic analysis based on multi-precision information assimilation

NASA Astrophysics Data System (ADS)

Wang, C.; Rubin, Y.

2014-12-01

Spatial distribution of important geotechnical parameter named compression modulus Es contributes considerably to the understanding of the underlying geological processes and the adequate assessment of the Es mechanics effects for differential settlement of large continuous structure foundation. These analyses should be derived using an assimilating approach that combines in-situ static cone penetration test (CPT) with borehole experiments. To achieve such a task, the Es distribution of stratum of silty clay in region A of China Expo Center (Shanghai) is studied using the Bayesian-maximum entropy method. This method integrates rigorously and efficiently multi-precision of different geotechnical investigations and sources of uncertainty. Single CPT samplings were modeled as a rational probability density curve by maximum entropy theory. Spatial prior multivariate probability density function (PDF) and likelihood PDF of the CPT positions were built by borehole experiments and the potential value of the prediction point, then, preceding numerical integration on the CPT probability density curves, the posterior probability density curve of the prediction point would be calculated by the Bayesian reverse interpolation framework. The results were compared between Gaussian Sequential Stochastic Simulation and Bayesian methods. The differences were also discussed between single CPT samplings of normal distribution and simulated probability density curve based on maximum entropy theory. It is shown that the study of Es spatial distributions can be improved by properly incorporating CPT sampling variation into interpolation process, whereas more informative estimations are generated by considering CPT Uncertainty for the estimation points. Calculation illustrates the significance of stochastic Es characterization in a stratum, and identifies limitations associated with inadequate geostatistical interpolation techniques. This characterization results will provide a multi-precision information assimilation method of other geotechnical parameters.

A review of contemporary methods for the presentation of scientific uncertainty.

PubMed

Makinson, K A; Hamby, D M; Edwards, J A

2012-12-01

Graphic methods for displaying uncertainty are often the most concise and informative way to communicate abstract concepts. Presentation methods currently in use for the display and interpretation of scientific uncertainty are reviewed. Numerous subjective and objective uncertainty display methods are presented, including qualitative assessments, node and arrow diagrams, standard statistical methods, box-and-whisker plots,robustness and opportunity functions, contribution indexes, probability density functions, cumulative distribution functions, and graphical likelihood functions.

Count distribution for mixture of two exponentials as renewal process duration with applications

NASA Astrophysics Data System (ADS)

Low, Yeh Ching; Ong, Seng Huat

2016-06-01

A count distribution is presented by considering a renewal process where the distribution of the duration is a finite mixture of exponential distributions. This distribution is able to model over dispersion, a feature often found in observed count data. The computation of the probabilities and renewal function (expected number of renewals) are examined. Parameter estimation by the method of maximum likelihood is considered with applications of the count distribution to real frequency count data exhibiting over dispersion. It is shown that the mixture of exponentials count distribution fits over dispersed data better than the Poisson process and serves as an alternative to the gamma count distribution.

Axion excursions of the landscape during inflation

NASA Astrophysics Data System (ADS)

Palma, Gonzalo A.; Riquelme, Walter

2017-07-01

Because of their quantum fluctuations, axion fields had a chance to experience field excursions traversing many minima of their potentials during inflation. We study this situation by analyzing the dynamics of an axion field ψ , present during inflation, with a periodic potential given by v (ψ )=Λ4[1 -cos (ψ /f )]. By assuming that the vacuum expectation value of the field is stabilized at one of its minima, say, ψ =0 , we compute every n -point correlation function of ψ up to first order in Λ4 using the in-in formalism. This computation allows us to identify the distribution function describing the probability of measuring ψ at a particular amplitude during inflation. Because ψ is able to tunnel between the barriers of the potential, we find that the probability distribution function consists of a non-Gaussian multimodal distribution such that the probability of measuring ψ at a minimum of v (ψ ) different from ψ =0 increases with time. As a result, at the end of inflation, different patches of the Universe are characterized by different values of the axion field amplitude, leading to important cosmological phenomenology: (a) Isocurvature fluctuations induced by the axion at the end of inflation could be highly non-Gaussian. (b) If the axion defines the strength of standard model couplings, then one is led to a concrete realization of the multiverse. (c) If the axion corresponds to dark matter, one is led to the possibility that, within our observable Universe, dark matter started with a nontrivial initial condition, implying novel signatures for future surveys.

Simulation of flight maneuver-load distributions by utilizing stationary, non-Gaussian random load histories

NASA Technical Reports Server (NTRS)

Leybold, H. A.

1971-01-01

Random numbers were generated with the aid of a digital computer and transformed such that the probability density function of a discrete random load history composed of these random numbers had one of the following non-Gaussian distributions: Poisson, binomial, log-normal, Weibull, and exponential. The resulting random load histories were analyzed to determine their peak statistics and were compared with cumulative peak maneuver-load distributions for fighter and transport aircraft in flight.

Probabilistic performance estimators for computational chemistry methods: The empirical cumulative distribution function of absolute errors

NASA Astrophysics Data System (ADS)

Pernot, Pascal; Savin, Andreas

2018-06-01

Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform end-users on the expected amplitude of prediction errors attached to these methods. We show that, the distributions of model errors being neither normal nor zero-centered, these error statistics cannot be used to infer prediction error probabilities. To overcome this limitation, we advocate for the use of more informative statistics, based on the empirical cumulative distribution function of unsigned errors, namely, (1) the probability for a new calculation to have an absolute error below a chosen threshold and (2) the maximal amplitude of errors one can expect with a chosen high confidence level. Those statistics are also shown to be well suited for benchmarking and ranking studies. Moreover, the standard error on all benchmarking statistics depends on the size of the reference dataset. Systematic publication of these standard errors would be very helpful to assess the statistical reliability of benchmarking conclusions.

Universal characteristics of fractal fluctuations in prime number distribution

NASA Astrophysics Data System (ADS)

Selvam, A. M.

2014-11-01

The frequency of occurrence of prime numbers at unit number spacing intervals exhibits self-similar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations and population dynamics. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed general systems theory visualizes the eddy continuum underlying fractals to result from the growth of large eddies as the integrated mean of enclosed small scale eddies, thereby generating a hierarchy of eddy circulations or an inter-connected network with associated long-range correlations. The model predictions are as follows: (1) The probability distribution and power spectrum of fractals follow the same inverse power law which is a function of the golden mean. The predicted inverse power law distribution is very close to the statistical normal distribution for fluctuations within two standard deviations from the mean of the distribution. (2) Fractals signify quantum-like chaos since variance spectrum represents probability density distribution, a characteristic of quantum systems such as electron or photon. (3) Fractal fluctuations of frequency distribution of prime numbers signify spontaneous organization of underlying continuum number field into the ordered pattern of the quasiperiodic Penrose tiling pattern. The model predictions are in agreement with the probability distributions and power spectra for different sets of frequency of occurrence of prime numbers at unit number interval for successive 1000 numbers. Prime numbers in the first 10 million numbers were used for the study.

Performance evaluation and bias correction of DBS measurements for a 1290-MHz boundary layer profiler.

PubMed

Liu, Zhao; Zheng, Chaorong; Wu, Yue

2018-02-01

Recently, the government installed a boundary layer profiler (BLP), which is operated under the Doppler beam swinging mode, in a coastal area of China, to acquire useful wind field information in the atmospheric boundary layer for several purposes. And under strong wind conditions, the performance of the BLP is evaluated. It is found that, even though the quality controlled BLP data show good agreement with the balloon observations, a systematic bias can always be found for the BLP data. For the low wind velocities, the BLP data tend to overestimate the atmospheric wind. However, with the increment of wind velocity, the BLP data show a tendency of underestimation. In order to remove the effect of poor quality data on bias correction, the probability distribution function of the differences between the two instruments is discussed, and it is found that the t location scale distribution is the most suitable probability model when compared to other probability models. After the outliers with a large discrepancy, which are outside of 95% confidence interval of the t location scale distribution, are discarded, the systematic bias can be successfully corrected using a first-order polynomial correction function. The methodology of bias correction used in the study not only can be referred for the correction of other wind profiling radars, but also can lay a solid basis for further analysis of the wind profiles.

Performance evaluation and bias correction of DBS measurements for a 1290-MHz boundary layer profiler

NASA Astrophysics Data System (ADS)

Liu, Zhao; Zheng, Chaorong; Wu, Yue

2018-02-01

Recently, the government installed a boundary layer profiler (BLP), which is operated under the Doppler beam swinging mode, in a coastal area of China, to acquire useful wind field information in the atmospheric boundary layer for several purposes. And under strong wind conditions, the performance of the BLP is evaluated. It is found that, even though the quality controlled BLP data show good agreement with the balloon observations, a systematic bias can always be found for the BLP data. For the low wind velocities, the BLP data tend to overestimate the atmospheric wind. However, with the increment of wind velocity, the BLP data show a tendency of underestimation. In order to remove the effect of poor quality data on bias correction, the probability distribution function of the differences between the two instruments is discussed, and it is found that the t location scale distribution is the most suitable probability model when compared to other probability models. After the outliers with a large discrepancy, which are outside of 95% confidence interval of the t location scale distribution, are discarded, the systematic bias can be successfully corrected using a first-order polynomial correction function. The methodology of bias correction used in the study not only can be referred for the correction of other wind profiling radars, but also can lay a solid basis for further analysis of the wind profiles.

An efficient distribution method for nonlinear transport problems in highly heterogeneous stochastic porous media

NASA Astrophysics Data System (ADS)

Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi

2016-04-01

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are crucial to explore possible scenarios and assess risks in subsurface problems. In particular, nonlinear two-phase flows in porous media are essential, yet challenging, in reservoir simulation and hydrology. Adding highly heterogeneous and uncertain input, such as the permeability and porosity fields, transforms the estimation of the flow response into a tough stochastic problem for which computationally expensive Monte Carlo (MC) simulations remain the preferred option.We propose an alternative approach to evaluate the probability distribution of the (water) saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the (water) saturation. The distribution method draws inspiration from a Lagrangian approach of the stochastic transport problem and expresses the saturation PDF and CDF essentially in terms of a deterministic mapping and the distribution and statistics of scalar random fields. In a large class of applications these random fields can be estimated at low computational costs (few MC runs), thus making the distribution method attractive. Even though the method relies on a key assumption of fixed streamlines, we show that it performs well for high input variances, which is the case of interest. Once the saturation distribution is determined, any one-point statistics thereof can be obtained, especially the saturation average and standard deviation. Moreover, the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be efficiently derived from the distribution method. These statistics can then be used for risk assessment, as well as data assimilation and uncertainty reduction in the prior knowledge of input distributions. We provide various examples and comparisons with MC simulations to illustrate the performance of the method.

A bivariate gamma probability distribution with application to gust modeling. [for the ascent flight of the space shuttle

NASA Technical Reports Server (NTRS)

Smith, O. E.; Adelfang, S. I.; Tubbs, J. D.

1982-01-01

A five-parameter gamma distribution (BGD) having two shape parameters, two location parameters, and a correlation parameter is investigated. This general BGD is expressed as a double series and as a single series of the modified Bessel function. It reduces to the known special case for equal shape parameters. Practical functions for computer evaluations for the general BGD and for special cases are presented. Applications to wind gust modeling for the ascent flight of the space shuttle are illustrated.

Computer Vision Tracking Using Particle Filters for 3D Position Estimation

DTIC Science & Technology

2014-03-27

the United States Air Force, the Department of Defense, or the United States Government. This material is declared a work of the U.S. Government and is...probability distribution (unless otherwise noted) π proposal distribution ω importance weight i index of normalized weights δ Dirac -delta function x...p(x) and the importance weights, where δ is the Dirac delta function [2, p. 178]. p(x) = N∑ n=1 ωnδ (x − xn) (2.14) ωn ∝ p(x) π(x) (2.15) Applying

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Spatial distribution of nuclei in progressive nucleation: Modeling and application

NASA Astrophysics Data System (ADS)

Tomellini, Massimo

2018-04-01

Phase transformations ruled by non-simultaneous nucleation and growth do not lead to random distribution of nuclei. Since nucleation is only allowed in the untransformed portion of space, positions of nuclei are correlated. In this article an analytical approach is presented for computing pair-correlation function of nuclei in progressive nucleation. This quantity is further employed for characterizing the spatial distribution of nuclei through the nearest neighbor distribution function. The modeling is developed for nucleation in 2D space with power growth law and it is applied to describe electrochemical nucleation where correlation effects are significant. Comparison with both computer simulations and experimental data lends support to the model which gives insights into the transition from Poissonian to correlated nearest neighbor probability density.

Imaging basal ganglia function

PubMed Central

BROOKS, DAVID J.

2000-01-01

In this review, the value of functional imaging for providing insight into the role of the basal ganglia in motor control is reviewed. Brain activation findings in normal subjects and Parkinson's disease patients are examined and evidence supporting the existence for functionally independent distributed basal ganglia-frontal loops is presented. It is argued that the basal ganglia probably act to focus and filter cortical output, optimising the running of motor programs. PMID:10923986

Maximum entropy analysis of NMR data of flexible multirotor molecules partially oriented in nematic solution: 2,2':5',2″-terthiophene, 2,2'- and 3,3'-dithiophene

NASA Astrophysics Data System (ADS)

Caldarelli, Stefano; Catalano, Donata; Di Bari, Lorenzo; Lumetti, Marco; Ciofalo, Maurizio; Alberto Veracini, Carlo

1994-07-01

The dipolar couplings observed by NMR spectroscopy of solutes in nematic solvents (LX-NMR) are used to build up the maximum entropy (ME) probability distribution function of the variables describing the orientational and internal motion of the molecule. The ME conformational distributions of 2,2'- and 3,3'-dithiophene and 2,2':5',2″-terthiophene (α-terthienyl)thus obtained are compared with the results of previous studies. The 2,2'- and 3,3'-dithiophene molecules exhibit equilibria among cisoid and transoid forms; the probability maxima correspond to planar and twisted conformers for 2,2'- or 3,3'-dithiophene, respectively, 2,2':5',2″-Terthiophene has two internal degrees of freedom; the ME approach indicates that the trans, trans and cis, trans planar conformations are the most probable. The correlation between the two intramolecular rotations is also discussed.

Statistics of work performed on a forced quantum oscillator.

PubMed

Talkner, Peter; Burada, P Sekhar; Hänggi, Peter

2008-07-01

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to completely characterize the force protocol. Explicit results for the characteristic function of work and the corresponding probability distribution are provided and discussed for three different types of initial states of the oscillator: microcanonical, canonical, and coherent states. Depending on the choice of the initial state the probability distributions of the performed work may greatly differ. This result in particular also holds true for identical force protocols. General fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed.

Zero-truncated negative binomial - Erlang distribution

NASA Astrophysics Data System (ADS)

Bodhisuwan, Winai; Pudprommarat, Chookait; Bodhisuwan, Rujira; Saothayanun, Luckhana

2017-11-01

The zero-truncated negative binomial-Erlang distribution is introduced. It is developed from negative binomial-Erlang distribution. In this work, the probability mass function is derived and some properties are included. The parameters of the zero-truncated negative binomial-Erlang distribution are estimated by using the maximum likelihood estimation. Finally, the proposed distribution is applied to real data, the number of methamphetamine in the Bangkok, Thailand. Based on the results, it shows that the zero-truncated negative binomial-Erlang distribution provided a better fit than the zero-truncated Poisson, zero-truncated negative binomial, zero-truncated generalized negative-binomial and zero-truncated Poisson-Lindley distributions for this data.

Electron-phonon relaxation and excited electron distribution in gallium nitride

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

Zhukov, V. P.; Donostia International Physics Center; Tyuterev, V. G., E-mail: valtyut00@mail.ru

2016-08-28

We develop a theory of energy relaxation in semiconductors and insulators highly excited by the long-acting external irradiation. We derive the equation for the non-equilibrium distribution function of excited electrons. The solution for this function breaks up into the sum of two contributions. The low-energy contribution is concentrated in a narrow range near the bottom of the conduction band. It has the typical form of a Fermi distribution with an effective temperature and chemical potential. The effective temperature and chemical potential in this low-energy term are determined by the intensity of carriers' generation, the speed of electron-phonon relaxation, rates ofmore » inter-band recombination, and electron capture on the defects. In addition, there is a substantial high-energy correction. This high-energy “tail” largely covers the conduction band. The shape of the high-energy “tail” strongly depends on the rate of electron-phonon relaxation but does not depend on the rates of recombination and trapping. We apply the theory to the calculation of a non-equilibrium distribution of electrons in an irradiated GaN. Probabilities of optical excitations from the valence to conduction band and electron-phonon coupling probabilities in GaN were calculated by the density functional perturbation theory. Our calculation of both parts of distribution function in gallium nitride shows that when the speed of the electron-phonon scattering is comparable with the rate of recombination and trapping then the contribution of the non-Fermi “tail” is comparable with that of the low-energy Fermi-like component. So the high-energy contribution can essentially affect the charge transport in the irradiated and highly doped semiconductors.« less

Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure.

PubMed

Özarslan, Evren; Koay, Cheng Guan; Shepherd, Timothy M; Komlosh, Michal E; İrfanoğlu, M Okan; Pierpaoli, Carlo; Basser, Peter J

2013-09-01

Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in "q-space," and the corresponding "mean apparent propagator (MAP)" describing molecular displacements in "r-space." We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit "displacement" sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions-the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue. Copyright © 2013 Elsevier Inc. All rights reserved.

r.randomwalk v1.0, a multi-functional conceptual tool for mass movement routing

NASA Astrophysics Data System (ADS)

Mergili, M.; Krenn, J.; Chu, H.-J.

2015-09-01

We introduce r.randomwalk, a flexible and multi-functional open source tool for backward- and forward-analyses of mass movement propagation. r.randomwalk builds on GRASS GIS, the R software for statistical computing and the programming languages Python and C. Using constrained random walks, mass points are routed from defined release pixels of one to many mass movements through a digital elevation model until a defined break criterion is reached. Compared to existing tools, the major innovative features of r.randomwalk are: (i) multiple break criteria can be combined to compute an impact indicator score, (ii) the uncertainties of break criteria can be included by performing multiple parallel computations with randomized parameter settings, resulting in an impact indicator index in the range 0-1, (iii) built-in functions for validation and visualization of the results are provided, (iv) observed landslides can be back-analyzed to derive the density distribution of the observed angles of reach. This distribution can be employed to compute impact probabilities for each pixel. Further, impact indicator scores and probabilities can be combined with release indicator scores or probabilities, and with exposure indicator scores. We demonstrate the key functionalities of r.randomwalk (i) for a single event, the Acheron Rock Avalanche in New Zealand, (ii) for landslides in a 61.5 km2 study area in the Kao Ping Watershed, Taiwan; and (iii) for lake outburst floods in a 2106 km2 area in the Gunt Valley, Tajikistan.

r.randomwalk v1, a multi-functional conceptual tool for mass movement routing

NASA Astrophysics Data System (ADS)

Mergili, M.; Krenn, J.; Chu, H.-J.

2015-12-01

We introduce r.randomwalk, a flexible and multi-functional open-source tool for backward and forward analyses of mass movement propagation. r.randomwalk builds on GRASS GIS (Geographic Resources Analysis Support System - Geographic Information System), the R software for statistical computing and the programming languages Python and C. Using constrained random walks, mass points are routed from defined release pixels of one to many mass movements through a digital elevation model until a defined break criterion is reached. Compared to existing tools, the major innovative features of r.randomwalk are (i) multiple break criteria can be combined to compute an impact indicator score; (ii) the uncertainties of break criteria can be included by performing multiple parallel computations with randomized parameter sets, resulting in an impact indicator index in the range 0-1; (iii) built-in functions for validation and visualization of the results are provided; (iv) observed landslides can be back analysed to derive the density distribution of the observed angles of reach. This distribution can be employed to compute impact probabilities for each pixel. Further, impact indicator scores and probabilities can be combined with release indicator scores or probabilities, and with exposure indicator scores. We demonstrate the key functionalities of r.randomwalk for (i) a single event, the Acheron rock avalanche in New Zealand; (ii) landslides in a 61.5 km2 study area in the Kao Ping Watershed, Taiwan; and (iii) lake outburst floods in a 2106 km2 area in the Gunt Valley, Tajikistan.

Assessing the Risk of Primary Amoebic Meningoencephalitis from Swimming in the Presence of Environmental Naegleria fowleri

PubMed Central

Cabanes, Pierre-André; Wallet, France; Pringuez, Emmanuelle; Pernin, Pierre

2001-01-01

Free-living Naegleria fowleri amoebae cause primary amoebic meningoencephalitis (PAM). Because of the apparent conflict between their ubiquity and the rarity of cases observed, we sought to develop a model characterizing the risk of PAM after swimming as a function of the concentration of N. fowleri. The probability of death from PAM as a function of the number of amoebae inhaled is modeled according to results obtained from animals infected with amoeba strains. The calculation of the probability of inhaling one or more amoebae while swimming is based on a double hypothesis: that the distribution of amoebae in the water follows a Poisson distribution and that the mean quantity of water inhaled while swimming is 10 ml. The risk of PAM for a given concentration of amoebae is then obtained by summing the following products: the probability of inhaling n amoebae × the probability of PAM associated with inhaling these n amoebae. We chose the lognormal model to assess the risk of PAM because it yielded the best analysis of the studentized residuals. Nonetheless, the levels of risk thereby obtained cannot be applied to humans without correction, because they are substantially greater than those indicated by available epidemiologic data. The curve was thus adjusted by a factor calculated with the least-squares method. This provides the PAM risk in humans as a function of the N. fowleri concentration in the river. For example, the risk is 8.5 × 10−8 at a concentration of 10 N. fowleri amoebae per liter. PMID:11425704

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

NASA Astrophysics Data System (ADS)

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

2013-06-01

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

Partial knowledge, entropy, and estimation

PubMed Central

MacQueen, James; Marschak, Jacob

1975-01-01

In a growing body of literature, available partial knowledge is used to estimate the prior probability distribution p≡(p1,...,pn) by maximizing entropy H(p)≡-Σpi log pi, subject to constraints on p which express that partial knowledge. The method has been applied to distributions of income, of traffic, of stock-price changes, and of types of brand-article purchases. We shall respond to two justifications given for the method: (α) It is “conservative,” and therefore good, to maximize “uncertainty,” as (uniquely) represented by the entropy parameter. (β) One should apply the mathematics of statistical thermodynamics, which implies that the most probable distribution has highest entropy. Reason (α) is rejected. Reason (β) is valid when “complete ignorance” is defined in a particular way and both the constraint and the estimator's loss function are of certain kinds. PMID:16578733

Optimal Information Processing in Biochemical Networks

NASA Astrophysics Data System (ADS)

Wiggins, Chris

2012-02-01

A variety of experimental results over the past decades provide examples of near-optimal information processing in biological networks, including in biochemical and transcriptional regulatory networks. Computing information-theoretic quantities requires first choosing or computing the joint probability distribution describing multiple nodes in such a network --- for example, representing the probability distribution of finding an integer copy number of each of two interacting reactants or gene products while respecting the `intrinsic' small copy number noise constraining information transmission at the scale of the cell. I'll given an overview of some recent analytic and numerical work facilitating calculation of such joint distributions and the associated information, which in turn makes possible numerical optimization of information flow in models of noisy regulatory and biochemical networks. Illustrating cases include quantification of form-function relations, ideal design of regulatory cascades, and response to oscillatory driving.

On the robustness of the q-Gaussian family

NASA Astrophysics Data System (ADS)

Sicuro, Gabriele; Tempesta, Piergiulio; Rodríguez, Antonio; Tsallis, Constantino

2015-12-01

We introduce three deformations, called α-, β- and γ-deformation respectively, of a N-body probabilistic model, first proposed by Rodríguez et al. (2008), having q-Gaussians as N → ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas the γ-deformation is not. We prove that, for both α- and β-deformations, the resulting deformed triangles still have q-Gaussians as limiting distributions, with a value of q independent (dependent) on the deformation parameter in the α-case (β-case). In contrast, the γ-case, where we have used the celebrated Q-numbers and the Gauss binomial coefficients, yields other limiting probability distribution functions, outside the q-Gaussian family. These results suggest that scale-invariance might play an important role regarding the robustness of the q-Gaussian family.

Probability density function characterization for aggregated large-scale wind power based on Weibull mixtures

DOE PAGES

Gomez-Lazaro, Emilio; Bueso, Maria C.; Kessler, Mathieu; ...

2016-02-02

Here, the Weibull probability distribution has been widely applied to characterize wind speeds for wind energy resources. Wind power generation modeling is different, however, due in particular to power curve limitations, wind turbine control methods, and transmission system operation requirements. These differences are even greater for aggregated wind power generation in power systems with high wind penetration. Consequently, models based on one-Weibull component can provide poor characterizations for aggregated wind power generation. With this aim, the present paper focuses on discussing Weibull mixtures to characterize the probability density function (PDF) for aggregated wind power generation. PDFs of wind power datamore » are firstly classified attending to hourly and seasonal patterns. The selection of the number of components in the mixture is analyzed through two well-known different criteria: the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Finally, the optimal number of Weibull components for maximum likelihood is explored for the defined patterns, including the estimated weight, scale, and shape parameters. Results show that multi-Weibull models are more suitable to characterize aggregated wind power data due to the impact of distributed generation, variety of wind speed values and wind power curtailment.« less

A critical analysis of high-redshift, massive, galaxy clusters. Part I

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

Hoyle, Ben; Jimenez, Raul; Verde, Licia

2012-02-01

We critically investigate current statistical tests applied to high redshift clusters of galaxies in order to test the standard cosmological model and describe their range of validity. We carefully compare a sample of high-redshift, massive, galaxy clusters with realistic Poisson sample simulations of the theoretical mass function, which include the effect of Eddington bias. We compare the observations and simulations using the following statistical tests: the distributions of ensemble and individual existence probabilities (in the > M, > z sense), the redshift distributions, and the 2d Kolmogorov-Smirnov test. Using seemingly rare clusters from Hoyle et al. (2011), and Jee etmore » al. (2011) and assuming the same survey geometry as in Jee et al. (2011, which is less conservative than Hoyle et al. 2011), we find that the ( > M, > z) existence probabilities of all clusters are fully consistent with ΛCDM. However assuming the same survey geometry, we use the 2d K-S test probability to show that the observed clusters are not consistent with being the least probable clusters from simulations at > 95% confidence, and are also not consistent with being a random selection of clusters, which may be caused by the non-trivial selection function and survey geometry. Tension can be removed if we examine only a X-ray selected sub sample, with simulations performed assuming a modified survey geometry.« less

Intermittent particle distribution in synthetic free-surface turbulent flows.

PubMed

Ducasse, Lauris; Pumir, Alain

2008-06-01

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

Multiscale Characterization of the Probability Density Functions of Velocity and Temperature Increment Fields

NASA Astrophysics Data System (ADS)

DeMarco, Adam Ward

The turbulent motions with the atmospheric boundary layer exist over a wide range of spatial and temporal scales and are very difficult to characterize. Thus, to explore the behavior of such complex flow enviroments, it is customary to examine their properties from a statistical perspective. Utilizing the probability density functions of velocity and temperature increments, deltau and deltaT, respectively, this work investigates their multiscale behavior to uncover the unique traits that have yet to be thoroughly studied. Utilizing diverse datasets, including idealized, wind tunnel experiments, atmospheric turbulence field measurements, multi-year ABL tower observations, and mesoscale models simulations, this study reveals remarkable similiarities (and some differences) between the small and larger scale components of the probability density functions increments fields. This comprehensive analysis also utilizes a set of statistical distributions to showcase their ability to capture features of the velocity and temperature increments' probability density functions (pdfs) across multiscale atmospheric motions. An approach is proposed for estimating their pdfs utilizing the maximum likelihood estimation (MLE) technique, which has never been conducted utilizing atmospheric data. Using this technique, we reveal the ability to estimate higher-order moments accurately with a limited sample size, which has been a persistent concern for atmospheric turbulence research. With the use robust Goodness of Fit (GoF) metrics, we quantitatively reveal the accuracy of the distributions to the diverse dataset. Through this analysis, it is shown that the normal inverse Gaussian (NIG) distribution is a prime candidate to be used as an estimate of the increment pdfs fields. Therefore, using the NIG model and its parameters, we display the variations in the increments over a range of scales revealing some unique scale-dependent qualities under various stability and ow conditions. This novel approach can provide a method of characterizing increment fields with the sole use of only four pdf parameters. Also, we investigate the capability of the current state-of-the-art mesoscale atmospheric models to predict the features and highlight the potential for use for future model development. With the knowledge gained in this study, a number of applications can benefit by using our methodology, including the wind energy and optical wave propagation fields.

Finite-size scaling of survival probability in branching processes

NASA Astrophysics Data System (ADS)

Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Álvaro

2015-04-01

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 derive analytically the existence of finite-size scaling for the survival probability as a function of the control parameter and the maximum number of generations, obtaining the critical exponents as well as the exact scaling function, which is G (y ) =2 y ey /(ey-1 ) , with y the rescaled distance to the critical point. Our findings are valid for any branching process of the Galton-Watson type, independently of the distribution of the number of offspring, provided its variance is finite. This proves the universal behavior of the finite-size effects in branching processes, including the universality of the metric factors. The direct relation to mean-field percolation is also discussed.

Normal and abnormal tissue identification system and method for medical images such as digital mammograms

NASA Technical Reports Server (NTRS)

Heine, John J. (Inventor); Clarke, Laurence P. (Inventor); Deans, Stanley R. (Inventor); Stauduhar, Richard Paul (Inventor); Cullers, David Kent (Inventor)

2001-01-01

A system and method for analyzing a medical image to determine whether an abnormality is present, for example, in digital mammograms, includes the application of a wavelet expansion to a raw image to obtain subspace images of varying resolution. At least one subspace image is selected that has a resolution commensurate with a desired predetermined detection resolution range. A functional form of a probability distribution function is determined for each selected subspace image, and an optimal statistical normal image region test is determined for each selected subspace image. A threshold level for the probability distribution function is established from the optimal statistical normal image region test for each selected subspace image. A region size comprising at least one sector is defined, and an output image is created that includes a combination of all regions for each selected subspace image. Each region has a first value when the region intensity level is above the threshold and a second value when the region intensity level is below the threshold. This permits the localization of a potential abnormality within the image.

Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

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

Cieplak, Agnieszka M.; Slosar, Anze

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 overmore » 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. In conclusion, 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.« less

Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

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

Cieplak, Agnieszka M.; Slosar, Anže, E-mail: acieplak@bnl.gov, E-mail: anze@bnl.gov

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 marginalisationmore » 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.« less

Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

DOE PAGES

Cieplak, Agnieszka M.; Slosar, Anze

2017-10-12

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 overmore » 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. In conclusion, 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.« less

Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

NASA Astrophysics Data System (ADS)

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.

Neural Mechanisms for Integrating Prior Knowledge and Likelihood in Value-Based Probabilistic Inference

PubMed Central

Ting, Chih-Chung; Yu, Chia-Chen; Maloney, Laurence T.

2015-01-01

In Bayesian decision theory, knowledge about the probabilities of possible outcomes is captured by a prior distribution and a likelihood function. The prior reflects past knowledge and the likelihood summarizes current sensory information. The two combined (integrated) form a posterior distribution that allows estimation of the probability of different possible outcomes. In this study, we investigated the neural mechanisms underlying Bayesian integration using a novel lottery decision task in which both prior knowledge and likelihood information about reward probability were systematically manipulated on a trial-by-trial basis. Consistent with Bayesian integration, as sample size increased, subjects tended to weigh likelihood information more compared with prior information. Using fMRI in humans, we found that the medial prefrontal cortex (mPFC) correlated with the mean of the posterior distribution, a statistic that reflects the integration of prior knowledge and likelihood of reward probability. Subsequent analysis revealed that both prior and likelihood information were represented in mPFC and that the neural representations of prior and likelihood in mPFC reflected changes in the behaviorally estimated weights assigned to these different sources of information in response to changes in the environment. Together, these results establish the role of mPFC in prior-likelihood integration and highlight its involvement in representing and integrating these distinct sources of information. PMID:25632152

Statistical analysis of dislocations and dislocation boundaries from EBSD data.

PubMed

Moussa, C; Bernacki, M; Besnard, R; Bozzolo, N

2017-08-01

Electron BackScatter Diffraction (EBSD) is often used for semi-quantitative analysis of dislocations in metals. In general, disorientation is used to assess Geometrically Necessary Dislocations (GNDs) densities. In the present paper, we demonstrate that the use of disorientation can lead to inaccurate results. For example, using the disorientation leads to different GND density in recrystallized grains which cannot be physically justified. The use of disorientation gradients allows accounting for measurement noise and leads to more accurate results. Misorientation gradient is then used to analyze dislocations boundaries following the same principle applied on TEM data before. In previous papers, dislocations boundaries were defined as Geometrically Necessary Boundaries (GNBs) and Incidental Dislocation Boundaries (IDBs). It has been demonstrated in the past, through transmission electron microscopy data, that the probability density distribution of the disorientation of IDBs and GNBs can be described with a linear combination of two Rayleigh functions. Such function can also describe the probability density of disorientation gradient obtained through EBSD data as reported in this paper. This opens the route for determining IDBs and GNBs probability density distribution functions separately from EBSD data, with an increased statistical relevance as compared to TEM data. The method is applied on deformed Tantalum where grains exhibit dislocation boundaries, as observed using electron channeling contrast imaging. Copyright © 2017 Elsevier B.V. All rights reserved.

Exact Extremal Statistics in the Classical 1D Coulomb Gas

NASA Astrophysics Data System (ADS)

Dhar, Abhishek; Kundu, Anupam; Majumdar, Satya N.; Sabhapandit, Sanjib; Schehr, Grégory

2017-08-01

We consider a one-dimensional classical Coulomb gas of N -like charges in a harmonic potential—also known as the one-dimensional one-component plasma. We compute, analytically, the probability distribution of the position xmax of the rightmost charge in the limit of large N . We show that the typical fluctuations of xmax around its mean are described by a nontrivial scaling function, with asymmetric tails. This distribution is different from the Tracy-Widom distribution of xmax for Dyson's log gas. We also compute the large deviation functions of xmax explicitly and show that the system exhibits a third-order phase transition, as in the log gas. Our theoretical predictions are verified numerically.

Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface.

PubMed

Shen, Jian; Deng, Degang; Kong, Weijin; Liu, Shijie; Shen, Zicai; Wei, Chaoyang; He, Hongbo; Shao, Jianda; Fan, Zhengxiu

2006-11-01

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions.

Analysis of mean seismic ground motion and its uncertainty based on the UCERF3 geologic slip rate model with uncertainty for California

USGS Publications Warehouse

Zeng, Yuehua

2018-01-01

The Uniform California Earthquake Rupture Forecast v.3 (UCERF3) model (Field et al., 2014) considers epistemic uncertainty in fault‐slip rate via the inclusion of multiple rate models based on geologic and/or geodetic data. However, these slip rates are commonly clustered about their mean value and do not reflect the broader distribution of possible rates and associated probabilities. Here, we consider both a double‐truncated 2σ Gaussian and a boxcar distribution of slip rates and use a Monte Carlo simulation to sample the entire range of the distribution for California fault‐slip rates. We compute the seismic hazard following the methodology and logic‐tree branch weights applied to the 2014 national seismic hazard model (NSHM) for the western U.S. region (Petersen et al., 2014, 2015). By applying a new approach developed in this study to the probabilistic seismic hazard analysis (PSHA) using precomputed rates of exceedance from each fault as a Green’s function, we reduce the computer time by about 10^5‐fold and apply it to the mean PSHA estimates with 1000 Monte Carlo samples of fault‐slip rates to compare with results calculated using only the mean or preferred slip rates. The difference in the mean probabilistic peak ground motion corresponding to a 2% in 50‐yr probability of exceedance is less than 1% on average over all of California for both the Gaussian and boxcar probability distributions for slip‐rate uncertainty but reaches about 18% in areas near faults compared with that calculated using the mean or preferred slip rates. The average uncertainties in 1σ peak ground‐motion level are 5.5% and 7.3% of the mean with the relative maximum uncertainties of 53% and 63% for the Gaussian and boxcar probability density function (PDF), respectively.

Exploring image data assimilation in the prospect of high-resolution satellite oceanic observations

NASA Astrophysics Data System (ADS)

Durán Moro, Marina; Brankart, Jean-Michel; Brasseur, Pierre; Verron, Jacques

2017-07-01

Satellite sensors increasingly provide high-resolution (HR) observations of the ocean. They supply observations of sea surface height (SSH) and of tracers of the dynamics such as sea surface salinity (SSS) and sea surface temperature (SST). In particular, the Surface Water Ocean Topography (SWOT) mission will provide measurements of the surface ocean topography at very high-resolution (HR) delivering unprecedented information on the meso-scale and submeso-scale dynamics. This study investigates the feasibility to use these measurements to reconstruct meso-scale features simulated by numerical models, in particular on the vertical dimension. A methodology to reconstruct three-dimensional (3D) multivariate meso-scale scenes is developed by using a HR numerical model of the Solomon Sea region. An inverse problem is defined in the framework of a twin experiment where synthetic observations are used. A true state is chosen among the 3D multivariate states which is considered as a reference state. In order to correct a first guess of this true state, a two-step analysis is carried out. A probability distribution of the first guess is defined and updated at each step of the analysis: (i) the first step applies the analysis scheme of a reduced-order Kalman filter to update the first guess probability distribution using SSH observation; (ii) the second step minimizes a cost function using observations of HR image structure and a new probability distribution is estimated. The analysis is extended to the vertical dimension using 3D multivariate empirical orthogonal functions (EOFs) and the probabilistic approach allows the update of the probability distribution through the two-step analysis. Experiments show that the proposed technique succeeds in correcting a multivariate state using meso-scale and submeso-scale information contained in HR SSH and image structure observations. It also demonstrates how the surface information can be used to reconstruct the ocean state below the surface.

Investigation of the relation between the return periods of major drought characteristics using copula functions

NASA Astrophysics Data System (ADS)

Hüsami Afşar, Mehdi; Unal Şorman, Ali; Tugrul Yilmaz, Mustafa

2016-04-01

Different drought characteristics (e.g. duration, average severity, and average areal extent) often have monotonic relation that increased magnitude of one often follows a similar increase in the magnitude of the other drought characteristic. Hence it is viable to establish a relationship between different drought characteristics with the goal of predicting one using other ones. Copula functions that relate different variables using their joint and conditional cumulative probability distributions are often used to statistically model the drought characteristics. In this study bivariate and trivariate joint probabilities of these characteristics are obtained over Ankara (Turkey) between 1960 and 2013. Copula-based return period estimation of drought characteristics of duration, average severity, and average areal extent show joint probabilities of these characteristics can be satisfactorily achieved. Among different copula families investigated in this study, elliptical family (i.e. including normal and t-student copula functions) resulted in the lowest root mean square error. "This study was supported by TUBITAK fund #114Y676)."

Are there common mathematical structures in economics and physics?

NASA Astrophysics Data System (ADS)

Mimkes, Jürgen

2016-12-01

Economics is a field that looks into the future. We may know a few things ahead (ex ante), but most things we only know, afterwards (ex post). How can we work in a field, where much of the important information is missing? Mathematics gives two answers: 1. Probability theory leads to microeconomics: the Lagrange function optimizes utility under constraints of economic terms (like costs). The utility function is the entropy, the logarithm of probability. The optimal result is given by a probability distribution and an integrating factor. 2. Calculus leads to macroeconomics: In economics we have two production factors, capital and labour. This requires two dimensional calculus with exact and not-exact differentials, which represent the "ex ante" and "ex post" terms of economics. An integrating factor turns a not-exact term (like income) into an exact term (entropy, the natural production function). The integrating factor is the same as in microeconomics and turns the not-exact field of economics into an exact physical science.

Idealized models of the joint probability distribution of wind speeds

NASA Astrophysics Data System (ADS)

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.

End-to-end distance and contour length distribution functions of DNA helices

NASA Astrophysics Data System (ADS)

Zoli, Marco

2018-06-01

I present a computational method to evaluate the end-to-end and the contour length distribution functions of short DNA molecules described by a mesoscopic Hamiltonian. The method generates a large statistical ensemble of possible configurations for each dimer in the sequence, selects the global equilibrium twist conformation for the molecule, and determines the average base pair distances along the molecule backbone. Integrating over the base pair radial and angular fluctuations, I derive the room temperature distribution functions as a function of the sequence length. The obtained values for the most probable end-to-end distance and contour length distance, providing a measure of the global molecule size, are used to examine the DNA flexibility at short length scales. It is found that, also in molecules with less than ˜60 base pairs, coiled configurations maintain a large statistical weight and, consistently, the persistence lengths may be much smaller than in kilo-base DNA.

M-dwarf exoplanet surface density distribution. A log-normal fit from 0.07 to 400 AU

NASA Astrophysics Data System (ADS)

Meyer, Michael R.; Amara, Adam; Reggiani, Maddalena; Quanz, Sascha P.

2018-04-01

Aims: We fit a log-normal function to the M-dwarf orbital surface density distribution of gas giant planets, over the mass range 1-10 times that of Jupiter, from 0.07 to 400 AU. Methods: We used a Markov chain Monte Carlo approach to explore the likelihoods of various parameter values consistent with point estimates of the data given our assumed functional form. Results: This fit is consistent with radial velocity, microlensing, and direct-imaging observations, is well-motivated from theoretical and phenomenological points of view, and predicts results of future surveys. We present probability distributions for each parameter and a maximum likelihood estimate solution. Conclusions: We suggest that this function makes more physical sense than other widely used functions, and we explore the implications of our results on the design of future exoplanet surveys.

Timing in a Variable Interval Procedure: Evidence for a Memory Singularity

PubMed Central

Matell, Matthew S.; Kim, Jung S.; Hartshorne, Loryn

2013-01-01

Rats were trained in either a 30s peak-interval procedure, or a 15–45s variable interval peak procedure with a uniform distribution (Exp 1) or a ramping probability distribution (Exp 2). Rats in all groups showed peak shaped response functions centered around 30s, with the uniform group having an earlier and broader peak response function and rats in the ramping group having a later peak function as compared to the single duration group. The changes in these mean functions, as well as the statistics from single trial analyses, can be better captured by a model of timing in which memory is represented by a single, average, delay to reinforcement compared to one in which all durations are stored as a distribution, such as the complete memory model of Scalar Expectancy Theory or a simple associative model. PMID:24012783

78 FR 27365 - Gulf of Mexico Fishery Management Council; Public Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2013-05-10

..., Special Mackerel and Ecosystem Scientific and Statistical Committees (SSC). DATES: The meeting will... certain parameters necessary to produce the probability distribution functions (PDFs) needed to determine... Scientific and Statistical Committees for discussion, in accordance with the Magnuson-Stevens Fishery...

A Model Based on Environmental Factors for Diameter Distribution in Black Wattle in Brazil

PubMed Central

Sanquetta, Carlos Roberto; Behling, Alexandre; Dalla Corte, Ana Paula; Péllico Netto, Sylvio; Rodrigues, Aurelio Lourenço; Simon, Augusto Arlindo

2014-01-01

This article discusses the dynamics of a diameter distribution in stands of black wattle throughout its growth cycle using the Weibull probability density function. Moreover, the parameters of this distribution were related to environmental variables from meteorological data and surface soil horizon with the aim of finding a model for diameter distribution which their coefficients were related to the environmental variables. We found that the diameter distribution of the stand changes only slightly over time and that the estimators of the Weibull function are correlated with various environmental variables, with accumulated rainfall foremost among them. Thus, a model was obtained in which the estimators of the Weibull function are dependent on rainfall. Such a function can have important applications, such as in simulating growth potential in regions where historical growth data is lacking, as well as the behavior of the stand under different environmental conditions. The model can also be used to project growth in diameter, based on the rainfall affecting the forest over a certain time period. PMID:24932909

Improved work zone design guidelines and enhanced model of travel delays in work zones : Phase I, portability and scalability of interarrival and service time probability distribution functions for different locations in Ohio and the establishment of impr

DOT National Transportation Integrated Search

2006-01-01

The project focuses on two major issues - the improvement of current work zone design practices and an analysis of : vehicle interarrival time (IAT) and speed distributions for the development of a digital computer simulation model for : queues and t...

A Statistical Treatment of Bioassay Pour Fractions

NASA Technical Reports Server (NTRS)

Barengoltz, Jack; Hughes, David W.

2014-01-01

The binomial probability distribution is used to treat the statistics of a microbiological sample that is split into two parts, with only one part evaluated for spore count. One wishes to estimate the total number of spores in the sample based on the counts obtained from the part that is evaluated (pour fraction). Formally, the binomial distribution is recharacterized as a function of the observed counts (successes), with the total number (trials) an unknown. The pour fraction is the probability of success per spore (trial). This distribution must be renormalized in terms of the total number. Finally, the new renormalized distribution is integrated and mathematically inverted to yield the maximum estimate of the total number as a function of a desired level of confidence ( P(

On the continuity of the stationary state distribution of DPCM

NASA Astrophysics Data System (ADS)

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.

On the Use of a Cumulative Distribution as a Utility Function in Educational or Employment Selection.

DTIC Science & Technology

1981-02-01

monotonic increasing function of true ability or performance score. A cumulative probability function is * then very convenient for describiny; one’s...possible outcomes such as test scores, grade-point averages or other common outcome variables. Utility is usually a monotonic increasing function of true ...r(0) is negative for 8 <i and positive for 0 > M, U(o) is risk-prone for low 0 values and risk-averse for high 0 values. This property is true for

Site-to-Source Finite Fault Distance Probability Distribution in Probabilistic Seismic Hazard and the Relationship Between Minimum Distances

NASA Astrophysics Data System (ADS)

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.

Space shuttle solid rocket booster recovery system definition, volume 1

NASA Technical Reports Server (NTRS)

1973-01-01

The performance requirements, preliminary designs, and development program plans for an airborne recovery system for the space shuttle solid rocket booster are discussed. The analyses performed during the study phase of the program are presented. The basic considerations which established the system configuration are defined. A Monte Carlo statistical technique using random sampling of the probability distribution for the critical water impact parameters was used to determine the failure probability of each solid rocket booster component as functions of impact velocity and component strength capability.

Bivariate Rainfall and Runoff Analysis Using Shannon Entropy Theory

NASA Astrophysics Data System (ADS)

Rahimi, A.; Zhang, L.

2012-12-01

Rainfall-Runoff analysis is the key component for many hydrological and hydraulic designs in which the dependence of rainfall and runoff needs to be studied. It is known that the convenient bivariate distribution are often unable to model the rainfall-runoff variables due to that they either have constraints on the range of the dependence or fixed form for the marginal distributions. Thus, this paper presents an approach to derive the entropy-based joint rainfall-runoff distribution using Shannon entropy theory. The distribution derived can model the full range of dependence and allow different specified marginals. The modeling and estimation can be proceeded as: (i) univariate analysis of marginal distributions which includes two steps, (a) using the nonparametric statistics approach to detect modes and underlying probability density, and (b) fitting the appropriate parametric probability density functions; (ii) define the constraints based on the univariate analysis and the dependence structure; (iii) derive and validate the entropy-based joint distribution. As to validate the method, the rainfall-runoff data are collected from the small agricultural experimental watersheds located in semi-arid region near Riesel (Waco), Texas, maintained by the USDA. The results of unviariate analysis show that the rainfall variables follow the gamma distribution, whereas the runoff variables have mixed structure and follow the mixed-gamma distribution. With this information, the entropy-based joint distribution is derived using the first moments, the first moments of logarithm transformed rainfall and runoff, and the covariance between rainfall and runoff. The results of entropy-based joint distribution indicate: (1) the joint distribution derived successfully preserves the dependence between rainfall and runoff, and (2) the K-S goodness of fit statistical tests confirm the marginal distributions re-derived reveal the underlying univariate probability densities which further assure that the entropy-based joint rainfall-runoff distribution are satisfactorily derived. Overall, the study shows the Shannon entropy theory can be satisfactorily applied to model the dependence between rainfall and runoff. The study also shows that the entropy-based joint distribution is an appropriate approach to capture the dependence structure that cannot be captured by the convenient bivariate joint distributions. Joint Rainfall-Runoff Entropy Based PDF, and Corresponding Marginal PDF and Histogram for W12 Watershed The K-S Test Result and RMSE on Univariate Distributions Derived from the Maximum Entropy Based Joint Probability Distribution;

Weak values of a quantum observable and the cross-Wigner distribution.

PubMed

de Gosson, Maurice A; de Gosson, Serge M

2012-01-09

We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor here is the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar theory and time-frequency analysis. It allows us to express weak values using a complex probability distribution. We suggest that our approach seems to confirm that the weak value of an observable is, as conjectured by several authors, due to the interference of two wavefunctions, one coming from the past, and the other from the future.

An empirical analysis of the distribution of the duration of overshoots in a stationary gaussian stochastic process

NASA Technical Reports Server (NTRS)

Parrish, R. S.; Carter, M. C.

1974-01-01

This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.

Testing anthropic reasoning for the cosmological constant with a realistic galaxy formation model

NASA Astrophysics Data System (ADS)

Sudoh, Takahiro; Totani, Tomonori; Makiya, Ryu; Nagashima, Masahiro

2017-01-01

The anthropic principle is one of the possible explanations for the cosmological constant (Λ) problem. In previous studies, a dark halo mass threshold comparable with our Galaxy must be assumed in galaxy formation to get a reasonably large probability of finding the observed small value, P(<Λobs), though stars are found in much smaller galaxies as well. Here we examine the anthropic argument by using a semi-analytic model of cosmological galaxy formation, which can reproduce many observations such as galaxy luminosity functions. We calculate the probability distribution of Λ by running the model code for a wide range of Λ, while other cosmological parameters and model parameters for baryonic processes of galaxy formation are kept constant. Assuming that the prior probability distribution is flat per unit Λ, and that the number of observers is proportional to stellar mass, we find P(<Λobs) = 6.7 per cent without introducing any galaxy mass threshold. We also investigate the effect of metallicity; we find P(<Λobs) = 9.0 per cent if observers exist only in galaxies whose metallicity is higher than the solar abundance. If the number of observers is proportional to metallicity, we find P(<Λobs) = 9.7 per cent. Since these probabilities are not extremely small, we conclude that the anthropic argument is a viable explanation, if the value of Λ observed in our Universe is determined by a probability distribution.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Velocity statistics of the Nagel-Schreckenberg model

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

Velocity statistics of the Nagel-Schreckenberg model.

PubMed

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

2016-02-01

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

On the use of the energy probability distribution zeros in the study of phase transitions

NASA Astrophysics Data System (ADS)

Mól, L. A. S.; Rodrigues, R. G. M.; Stancioli, R. A.; Rocha, J. C. S.; Costa, B. V.

2018-04-01

This contribution is devoted to cover some technical aspects related to the use of the recently proposed energy probability distribution zeros in the study of phase transitions. This method is based on the partial knowledge of the partition function zeros and has been shown to be extremely efficient to precisely locate phase transition temperatures. It is based on an iterative method in such a way that the transition temperature can be approached at will. The iterative method will be detailed and some convergence issues that has been observed in its application to the 2D Ising model and to an artificial spin ice model will be shown, together with ways to circumvent them.

Craig's XY distribution and the statistics of Lagrangian power in two-dimensional turbulence

NASA Astrophysics Data System (ADS)

Bandi, Mahesh M.; Connaughton, Colm

2008-03-01

We examine the probability distribution function (PDF) of the energy injection rate (power) in numerical simulations of stationary two-dimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an electromagnetically driven fluid layer, a well-documented system for generating 2D turbulence in the laboratory. In our simulations, the forcing and velocity fields are close to Gaussian. On the other hand, the measured PDF of injected power is very sharply peaked at zero, suggestive of a singularity there, with tails which are exponential but asymmetric. Large positive fluctuations are more probable than large negative fluctuations. It is this asymmetry of the tails which leads to a net positive mean value for the energy input despite the most probable value being zero. The main features of the power distribution are well described by Craig’s XY distribution for the PDF of the product of two correlated normal variables. We show that the power distribution should exhibit a logarithmic singularity at zero and decay exponentially for large absolute values of the power. We calculate the asymptotic behavior and express the asymmetry of the tails in terms of the correlation coefficient of the force and velocity. We compare the measured PDFs with the theoretical calculations and briefly discuss how the power PDF might change with other forcing mechanisms.

Craig's XY distribution and the statistics of Lagrangian power in two-dimensional turbulence.

PubMed

Bandi, Mahesh M; Connaughton, Colm

2008-03-01

We examine the probability distribution function (PDF) of the energy injection rate (power) in numerical simulations of stationary two-dimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an electromagnetically driven fluid layer, a well-documented system for generating 2D turbulence in the laboratory. In our simulations, the forcing and velocity fields are close to Gaussian. On the other hand, the measured PDF of injected power is very sharply peaked at zero, suggestive of a singularity there, with tails which are exponential but asymmetric. Large positive fluctuations are more probable than large negative fluctuations. It is this asymmetry of the tails which leads to a net positive mean value for the energy input despite the most probable value being zero. The main features of the power distribution are well described by Craig's XY distribution for the PDF of the product of two correlated normal variables. We show that the power distribution should exhibit a logarithmic singularity at zero and decay exponentially for large absolute values of the power. We calculate the asymptotic behavior and express the asymmetry of the tails in terms of the correlation coefficient of the force and velocity. We compare the measured PDFs with the theoretical calculations and briefly discuss how the power PDF might change with other forcing mechanisms.

Joint analysis of air pollution in street canyons in St. Petersburg and Copenhagen

NASA Astrophysics Data System (ADS)

Genikhovich, E. L.; Ziv, A. D.; Iakovleva, E. A.; Palmgren, F.; Berkowicz, R.

The bi-annual data set of concentrations of several traffic-related air pollutants, measured continuously in street canyons in St. Petersburg and Copenhagen, is analysed jointly using different statistical techniques. Annual mean concentrations of NO 2, NO x and, especially, benzene are found systematically higher in St. Petersburg than in Copenhagen but for ozone the situation is opposite. In both cities probability distribution functions (PDFs) of concentrations and their daily or weekly extrema are fitted with the Weibull and double exponential distributions, respectively. Sample estimates of bi-variate distributions of concentrations, concentration roses, and probabilities of concentration of one pollutant being extreme given that another one reaches its extremum are presented in this paper as well as auto- and co-spectra. It is demonstrated that there is a reasonably high correlation between seasonally averaged concentrations of pollutants in St. Petersburg and Copenhagen.

Wormholes and the cosmological constant problem.

NASA Astrophysics Data System (ADS)

Klebanov, I.

The author reviews the cosmological constant problem and the recently proposed wormhole mechanism for its solution. Summation over wormholes in the Euclidean path integral for gravity turns all the coupling parameters into dynamical variables, sampled from a probability distribution. A formal saddle point analysis results in a distribution with a sharp peak at the cosmological constant equal to zero, which appears to solve the cosmological constant problem. He discusses the instabilities of the gravitational Euclidean path integral and the difficulties with its interpretation. He presents an alternate formalism for baby universes, based on the "third quantization" of the Wheeler-De Witt equation. This approach is analyzed in a minisuperspace model for quantum gravity, where it reduces to simple quantum mechanics. Once again, the coupling parameters become dynamical. Unfortunately, the a priori probability distribution for the cosmological constant and other parameters is typically a smooth function, with no sharp peaks.

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

NASA Astrophysics Data System (ADS)

Zhang, Hong; Li, Guo-Hua

2016-11-01

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).

Size Effect on Specific Energy Distribution in Particle Comminution

NASA Astrophysics Data System (ADS)

Xu, Yongfu; Wang, Yidong

A theoretical study is made to derive an energy distribution equation for the size reduction process from the fractal model for the particle comminution. Fractal model is employed as a valid measure of the self-similar size distribution of comminution daughter products. The tensile strength of particles varies with particle size in the manner of a power function law. The energy consumption for comminuting single particle is found to be proportional to the 5(D-3)/3rd order of the particle size, D being the fractal dimension of particle comminution daughter. The Weibull statistics is applied to describe the relationship between the breakage probability and specific energy of particle comminution. A simple equation is derived for the breakage probability of particles in view of the dependence of fracture energy on particle size. The calculated exponents and Weibull coefficients are generally in conformity with published data for fracture of particles.

Comparing hard and soft prior bounds in geophysical inverse problems

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describes the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.

Comparing hard and soft prior bounds in geophysical inverse problems

NASA Technical Reports Server (NTRS)

Backus, George E.

1987-01-01

In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describeds the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.

Maximum Entropy Principle for Transportation

NASA Astrophysics Data System (ADS)

Bilich, F.; DaSilva, R.

2008-11-01

In this work we deal with modeling of the transportation phenomenon for use in the transportation planning process and policy-impact studies. The model developed is based on the dependence concept, i.e., the notion that the probability of a trip starting at origin i is dependent on the probability of a trip ending at destination j given that the factors (such as travel time, cost, etc.) which affect travel between origin i and destination j assume some specific values. The derivation of the solution of the model employs the maximum entropy principle combining a priori multinomial distribution with a trip utility concept. This model is utilized to forecast trip distributions under a variety of policy changes and scenarios. The dependence coefficients are obtained from a regression equation where the functional form is derived based on conditional probability and perception of factors from experimental psychology. The dependence coefficients encode all the information that was previously encoded in the form of constraints. In addition, the dependence coefficients encode information that cannot be expressed in the form of constraints for practical reasons, namely, computational tractability. The equivalence between the standard formulation (i.e., objective function with constraints) and the dependence formulation (i.e., without constraints) is demonstrated. The parameters of the dependence-based trip-distribution model are estimated, and the model is also validated using commercial air travel data in the U.S. In addition, policy impact analyses (such as allowance of supersonic flights inside the U.S. and user surcharge at noise-impacted airports) on air travel are performed.

Use of Fermi-Dirac statistics for defects in solids

NASA Astrophysics Data System (ADS)

Johnson, R. A.

1981-12-01

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

Generalized spherical and simplicial coordinates

NASA Astrophysics Data System (ADS)

Richter, Wolf-Dieter

2007-12-01

Elementary trigonometric quantities are defined in l2,p analogously to that in l2,2, the sine and cosine functions are generalized for each p>0 as functions sinp and cosp such that they satisfy the basic equation cosp([phi])p+sinp([phi])p=1. The p-generalized radius coordinate of a point [xi][set membership, variant]Rn is defined for each p>0 as . On combining these quantities, ln,p-spherical coordinates are defined. It is shown that these coordinates are nearly related to ln,p-simplicial coordinates. The Jacobians of these generalized coordinate transformations are derived. Applications and interpretations from analysis deal especially with the definition of a generalized surface content on ln,p-spheres which is nearly related to a modified co-area formula and an extension of Cavalieri's and Torricelli's indivisibeln method, and with differential equations. Applications from probability theory deal especially with a geometric interpretation of the uniform probability distribution on the ln,p-sphere and with the derivation of certain generalized statistical distributions.

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

NASA Technical Reports Server (NTRS)

Chadwick, C.

1984-01-01

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

Bayesian predictive power: choice of prior and some recommendations for its use as probability of success in drug development.

PubMed

Rufibach, Kaspar; Burger, Hans Ulrich; Abt, Markus

2016-09-01

Bayesian predictive power, the expectation of the power function with respect to a prior distribution for the true underlying effect size, is routinely used in drug development to quantify the probability of success of a clinical trial. Choosing the prior is crucial for the properties and interpretability of Bayesian predictive power. We review recommendations on the choice of prior for Bayesian predictive power and explore its features as a function of the prior. The density of power values induced by a given prior is derived analytically and its shape characterized. We find that for a typical clinical trial scenario, this density has a u-shape very similar, but not equal, to a β-distribution. Alternative priors are discussed, and practical recommendations to assess the sensitivity of Bayesian predictive power to its input parameters are provided. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II - Quantitative analysis

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Noz, Marilyn E.

1989-01-01

It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.

Statistics of voids in hierarchical universes

NASA Technical Reports Server (NTRS)

Fry, J. N.

1986-01-01

As one alternative to the N-point galaxy correlation function statistics, the distribution of holes or the probability that a volume of given size and shape be empty of galaxies can be considered. The probability of voids resulting from a variety of hierarchical patterns of clustering is considered, and these are compared with the results of numerical simulations and with observations. A scaling relation required by the hierarchical pattern of higher order correlation functions is seen to be obeyed in the simulations, and the numerical results show a clear difference between neutrino models and cold-particle models; voids are more likely in neutrino universes. Observational data do not yet distinguish but are close to being able to distinguish between models.

Improved techniques for outgoing wave variational principle calculations of converged state-to-state transition probabilities for chemical reactions

NASA Technical Reports Server (NTRS)

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.

Mode switching in volcanic seismicity: El Hierro 2011-2013

NASA Astrophysics Data System (ADS)

Roberts, Nick S.; Bell, Andrew F.; Main, Ian G.

2016-05-01

The Gutenberg-Richter b value is commonly used in volcanic eruption forecasting to infer material or mechanical properties from earthquake distributions. Such studies typically analyze discrete time windows or phases, but the choice of such windows is subjective and can introduce significant bias. Here we minimize this sample bias by iteratively sampling catalogs with randomly chosen windows and then stack the resulting probability density functions for the estimated b>˜ value to determine a net probability density function. We examine data from the El Hierro seismic catalog during a period of unrest in 2011-2013 and demonstrate clear multimodal behavior. Individual modes are relatively stable in time, but the most probable b>˜ value intermittently switches between modes, one of which is similar to that of tectonic seismicity. Multimodality is primarily associated with intermittent activation and cessation of activity in different parts of the volcanic system rather than with respect to any systematic inferred underlying process.

A Bayesian Approach to Magnetic Moment Determination Using μSR

NASA Astrophysics Data System (ADS)

Blundell, S. J.; Steele, A. J.; Lancaster, T.; Wright, J. D.; Pratt, F. L.

A significant challenge in zero-field μSR experiments arises from the uncertainty in the muon site. It is possible to calculate the dipole field (and hence precession frequency v) at any particular site given the magnetic moment μ and magnetic structure. One can also evaluate f(v), the probability distribution function of v assuming that the muon site can be anywhere within the unit cell with equal probability, excluding physically forbidden sites. Since v is obtained from experiment, what we would like to know is g(μjv), the probability density function of μ given the observed v. This can be obtained from our calculated f(v/μ) using Bayes' theorem. We describe an approach to this problem which we have used to extract information about real systems including a low-moment osmate compound, a family of molecular magnets, and an iron-arsenide compound.

Wealth distribution on complex networks

NASA Astrophysics Data System (ADS)

Ichinomiya, Takashi

2012-12-01

We study the wealth distribution of the Bouchaud-Mézard model on complex networks. It is known from numerical simulations that this distribution depends on the topology of the network; however, no one has succeeded in explaining it. Using “adiabatic” and “independent” assumptions along with the central-limit theorem, we derive equations that determine the probability distribution function. The results are compared to those of simulations for various networks. We find good agreement between our theory and the simulations, except for the case of Watts-Strogatz networks with a low rewiring rate due to the breakdown of independent assumption.

Suboptimal Decision Criteria Are Predicted by Subjectively Weighted Probabilities and Rewards

PubMed Central

Ackermann, John F.; Landy, Michael S.

2014-01-01

Subjects performed a visual detection task in which the probability of target occurrence at each of the two possible locations, and the rewards for correct responses for each, were varied across conditions. To maximize monetary gain, observers should bias their responses, choosing one location more often than the other in line with the varied probabilities and rewards. Typically, and in our task, observers do not bias their responses to the extent they should, and instead distribute their responses more evenly across locations, a phenomenon referred to as ‘conservatism.’ We investigated several hypotheses regarding the source of the conservatism. We measured utility and probability weighting functions under Prospect Theory for each subject in an independent economic choice task and used the weighting-function parameters to calculate each subject’s subjective utility (SU(c)) as a function of the criterion c, and the corresponding weighted optimal criteria (wcopt). Subjects’ criteria were not close to optimal relative to wcopt. The slope of SU (c) and of expected gain EG(c) at the neutral criterion corresponding to β = 1 were both predictive of subjects’ criteria. The slope of SU(c) was a better predictor of observers’ decision criteria overall. Thus, rather than behaving optimally, subjects move their criterion away from the neutral criterion by estimating how much they stand to gain by such a change based on the slope of subjective gain as a function of criterion, using inherently distorted probabilities and values. PMID:25366822

Suboptimal decision criteria are predicted by subjectively weighted probabilities and rewards.

PubMed

Ackermann, John F; Landy, Michael S

2015-02-01

Subjects performed a visual detection task in which the probability of target occurrence at each of the two possible locations, and the rewards for correct responses for each, were varied across conditions. To maximize monetary gain, observers should bias their responses, choosing one location more often than the other in line with the varied probabilities and rewards. Typically, and in our task, observers do not bias their responses to the extent they should, and instead distribute their responses more evenly across locations, a phenomenon referred to as 'conservatism.' We investigated several hypotheses regarding the source of the conservatism. We measured utility and probability weighting functions under Prospect Theory for each subject in an independent economic choice task and used the weighting-function parameters to calculate each subject's subjective utility (SU(c)) as a function of the criterion c, and the corresponding weighted optimal criteria (wc opt ). Subjects' criteria were not close to optimal relative to wc opt . The slope of SU(c) and of expected gain EG(c) at the neutral criterion corresponding to β = 1 were both predictive of the subjects' criteria. The slope of SU(c) was a better predictor of observers' decision criteria overall. Thus, rather than behaving optimally, subjects move their criterion away from the neutral criterion by estimating how much they stand to gain by such a change based on the slope of subjective gain as a function of criterion, using inherently distorted probabilities and values.

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

PubMed

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

2013-02-01

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

Spatial distribution of traffic in a cellular mobile data network

NASA Astrophysics Data System (ADS)

Linnartz, J. P. M. G.

1987-02-01

The use of integral transforms of the probability density function for the received power to analyze the relation between the spatial distributions of offered and throughout packet traffic in a mobile radio network with Rayleigh fading channels and ALOHA multiple access was assessed. A method to obtain the spatial distribution of throughput traffic from a prescribed spatial distribution of offered traffic is presented. Incoherent and coherent addition of interference signals is considered. The channel behavior for heavy traffic loads is studied. In both the incoherent and coherent case, the spatial distribution of offered traffic required to ensure a prescribed spatially uniform throughput is synthesized numerically.

Dissociating error-based and reinforcement-based loss functions during sensorimotor learning

PubMed Central

McGregor, Heather R.; Mohatarem, Ayman

2017-01-01

It has been proposed that the sensorimotor system uses a loss (cost) function to evaluate potential movements in the presence of random noise. Here we test this idea in the context of both error-based and reinforcement-based learning. In a reaching task, we laterally shifted a cursor relative to true hand position using a skewed probability distribution. This skewed probability distribution had its mean and mode separated, allowing us to dissociate the optimal predictions of an error-based loss function (corresponding to the mean of the lateral shifts) and a reinforcement-based loss function (corresponding to the mode). We then examined how the sensorimotor system uses error feedback and reinforcement feedback, in isolation and combination, when deciding where to aim the hand during a reach. We found that participants compensated differently to the same skewed lateral shift distribution depending on the form of feedback they received. When provided with error feedback, participants compensated based on the mean of the skewed noise. When provided with reinforcement feedback, participants compensated based on the mode. Participants receiving both error and reinforcement feedback continued to compensate based on the mean while repeatedly missing the target, despite receiving auditory, visual and monetary reinforcement feedback that rewarded hitting the target. Our work shows that reinforcement-based and error-based learning are separable and can occur independently. Further, when error and reinforcement feedback are in conflict, the sensorimotor system heavily weights error feedback over reinforcement feedback. PMID:28753634

Characterization of the Ionospheric Scintillations at High Latitude using GPS Signal

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Dissociating error-based and reinforcement-based loss functions during sensorimotor learning.

PubMed

Cashaback, Joshua G A; McGregor, Heather R; Mohatarem, Ayman; Gribble, Paul L

2017-07-01

It has been proposed that the sensorimotor system uses a loss (cost) function to evaluate potential movements in the presence of random noise. Here we test this idea in the context of both error-based and reinforcement-based learning. In a reaching task, we laterally shifted a cursor relative to true hand position using a skewed probability distribution. This skewed probability distribution had its mean and mode separated, allowing us to dissociate the optimal predictions of an error-based loss function (corresponding to the mean of the lateral shifts) and a reinforcement-based loss function (corresponding to the mode). We then examined how the sensorimotor system uses error feedback and reinforcement feedback, in isolation and combination, when deciding where to aim the hand during a reach. We found that participants compensated differently to the same skewed lateral shift distribution depending on the form of feedback they received. When provided with error feedback, participants compensated based on the mean of the skewed noise. When provided with reinforcement feedback, participants compensated based on the mode. Participants receiving both error and reinforcement feedback continued to compensate based on the mean while repeatedly missing the target, despite receiving auditory, visual and monetary reinforcement feedback that rewarded hitting the target. Our work shows that reinforcement-based and error-based learning are separable and can occur independently. Further, when error and reinforcement feedback are in conflict, the sensorimotor system heavily weights error feedback over reinforcement feedback.

Characterizing the Lyman-alpha forest flux probability distribution function using Legendre polynomials

NASA Astrophysics Data System (ADS)

Cieplak, Agnieszka; Slosar, Anze

2017-01-01

The Lyman-alpha forest has become a powerful cosmological probe of the underlying matter distribution at high redshift. It is a highly non-linear field with much information present beyond the two-point statistics of the power spectrum. The flux probability distribution function (PDF) in particular has been used as a successful probe of small-scale physics. In addition to the cosmological evolution 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 coefficients of the Legendre polynomial expansion of the PDF offers several advantages over the binned PDF as is commonly done. Since the n-th 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. In addition, we use hydrodynamic cosmological simulations to demonstrate that 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 finite small number of well-measured quantities.

An exactly solvable coarse-grained model for species diversity

NASA Astrophysics Data System (ADS)

Suweis, Samir; Rinaldo, Andrea; Maritan, Amos

2012-07-01

We present novel analytical results concerning ecosystem species diversity that stem from a proposed coarse-grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results from ecological neutral theory and empirical evidence on species diversity preservation. The neutral model of biodiversity deals with ecosystems at the same trophic level, where per capita vital rates are assumed to be species independent. Closed-form analytical solutions for the neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain to: the probability distribution function of the number of species in the ecosystem, both in transient and in stationary states; the n-point connected time correlation function; and the survival probability, defined as the distribution of time spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from an estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications for biodiversity and conservation biology.

Electrostatic field and charge distribution in small charged dielectric droplets

NASA Astrophysics Data System (ADS)

Storozhev, V. B.

2004-08-01

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

qPR: An adaptive partial-report procedure based on Bayesian inference.

PubMed

Baek, Jongsoo; Lesmes, Luis Andres; Lu, Zhong-Lin

2016-08-01

Iconic memory is best assessed with the partial report procedure in which an array of letters appears briefly on the screen and a poststimulus cue directs the observer to report the identity of the cued letter(s). Typically, 6-8 cue delays or 600-800 trials are tested to measure the iconic memory decay function. Here we develop a quick partial report, or qPR, procedure based on a Bayesian adaptive framework to estimate the iconic memory decay function with much reduced testing time. The iconic memory decay function is characterized by an exponential function and a joint probability distribution of its three parameters. Starting with a prior of the parameters, the method selects the stimulus to maximize the expected information gain in the next test trial. It then updates the posterior probability distribution of the parameters based on the observer's response using Bayesian inference. The procedure is reiterated until either the total number of trials or the precision of the parameter estimates reaches a certain criterion. Simulation studies showed that only 100 trials were necessary to reach an average absolute bias of 0.026 and a precision of 0.070 (both in terms of probability correct). A psychophysical validation experiment showed that estimates of the iconic memory decay function obtained with 100 qPR trials exhibited good precision (the half width of the 68.2% credible interval = 0.055) and excellent agreement with those obtained with 1,600 trials of the conventional method of constant stimuli procedure (RMSE = 0.063). Quick partial-report relieves the data collection burden in characterizing iconic memory and makes it possible to assess iconic memory in clinical populations.

qPR: An adaptive partial-report procedure based on Bayesian inference

PubMed Central

Baek, Jongsoo; Lesmes, Luis Andres; Lu, Zhong-Lin

2016-01-01

Iconic memory is best assessed with the partial report procedure in which an array of letters appears briefly on the screen and a poststimulus cue directs the observer to report the identity of the cued letter(s). Typically, 6–8 cue delays or 600–800 trials are tested to measure the iconic memory decay function. Here we develop a quick partial report, or qPR, procedure based on a Bayesian adaptive framework to estimate the iconic memory decay function with much reduced testing time. The iconic memory decay function is characterized by an exponential function and a joint probability distribution of its three parameters. Starting with a prior of the parameters, the method selects the stimulus to maximize the expected information gain in the next test trial. It then updates the posterior probability distribution of the parameters based on the observer's response using Bayesian inference. The procedure is reiterated until either the total number of trials or the precision of the parameter estimates reaches a certain criterion. Simulation studies showed that only 100 trials were necessary to reach an average absolute bias of 0.026 and a precision of 0.070 (both in terms of probability correct). A psychophysical validation experiment showed that estimates of the iconic memory decay function obtained with 100 qPR trials exhibited good precision (the half width of the 68.2% credible interval = 0.055) and excellent agreement with those obtained with 1,600 trials of the conventional method of constant stimuli procedure (RMSE = 0.063). Quick partial-report relieves the data collection burden in characterizing iconic memory and makes it possible to assess iconic memory in clinical populations. PMID:27580045

Quantifying Similarity and Distance Measures for Vector-Based Datasets: Histograms, Signals, and Probability Distribution Functions

DTIC Science & Technology

2017-02-01

note, a number of different measures implemented in both MATLAB and Python as functions are used to quantify similarity/distance between 2 vector-based...this technical note are widely used and may have an important role when computing the distance and similarity of large datasets and when considering high...throughput processes. In this technical note, a number of different measures implemented in both MAT- LAB and Python as functions are used to

Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Malik, Pradeep; Swaminathan, A.

2010-11-01

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

The heliolongitudinal distribution of solar flares associated with solar proton events.

PubMed

Smart, D F; Shea, M A

1996-01-01

We find that the heliolongitudinal distribution of solar flares associated with earth-observed solar proton events is a function of the particle measurement energy. For solar proton events containing fluxes with energies exceeding 1 GeV, we find a Gaussian distribution about the probable root of the Archimedean spiral favorable propagation path leading from the earth to the sun. This distribution is modified as the detection threshold is lowered. For > 100 MeV solar proton events with fluxes > or = 10 protons (cm2-sec-ster)-1 we find the distribution becomes wider with a secondary peak near the solar central meridian. When the threshold is lowered to 10 MeV the distribution further evolves. For > 10 MeV solar proton events having a flux threshold at 10 protons (cm2-sec-ster)-1 the distribution can be considered to be a composite of two Gaussians. One distribution is centered about the probable root of the Archimedean spiral favorable propagation path leading from the earth to the sun, and the other is centered about the solar central meridian. For large flux solar proton events, those with flux threshold of 1000 (cm2-sec-ster)-1 at energies > 10 MeV, we find the distribution is rather flat for about 40 degrees either side of central meridian.

Identification of cloud fields by the nonparametric algorithm of pattern recognition from normalized video data recorded with the AVHRR instrument

NASA Astrophysics Data System (ADS)

Protasov, Konstantin T.; Pushkareva, Tatyana Y.; Artamonov, Evgeny S.

2002-02-01

The problem of cloud field recognition from the NOAA satellite data is urgent for solving not only meteorological problems but also for resource-ecological monitoring of the Earth's underlying surface associated with the detection of thunderstorm clouds, estimation of the liquid water content of clouds and the moisture of the soil, the degree of fire hazard, etc. To solve these problems, we used the AVHRR/NOAA video data that regularly displayed the situation in the territory. The complexity and extremely nonstationary character of problems to be solved call for the use of information of all spectral channels, mathematical apparatus of testing statistical hypotheses, and methods of pattern recognition and identification of the informative parameters. For a class of detection and pattern recognition problems, the average risk functional is a natural criterion for the quality and the information content of the synthesized decision rules. In this case, to solve efficiently the problem of identifying cloud field types, the informative parameters must be determined by minimization of this functional. Since the conditional probability density functions, representing mathematical models of stochastic patterns, are unknown, the problem of nonparametric reconstruction of distributions from the leaning samples arises. To this end, we used nonparametric estimates of distributions with the modified Epanechnikov kernel. The unknown parameters of these distributions were determined by minimization of the risk functional, which for the learning sample was substituted by the empirical risk. After the conditional probability density functions had been reconstructed for the examined hypotheses, a cloudiness type was identified using the Bayes decision rule.

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

PubMed Central

König, Sandra; Schauer, Stefan

2016-01-01

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

NEWTPOIS- NEWTON POISSON DISTRIBUTION PROGRAM

NASA Technical Reports Server (NTRS)

Bowerman, P. N.

1994-01-01

The cumulative poisson distribution program, NEWTPOIS, is one of two programs which make calculations involving cumulative poisson distributions. Both programs, NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714), can be used independently of one another. NEWTPOIS determines percentiles for gamma distributions with integer shape parameters and calculates percentiles for chi-square distributions with even degrees of freedom. It can be used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. NEWTPOIS determines the Poisson parameter (lambda), that is; the mean (or expected) number of events occurring in a given unit of time, area, or space. Given that the user already knows the cumulative probability for a specific number of occurrences (n) it is usually a simple matter of substitution into the Poisson distribution summation to arrive at lambda. However, direct calculation of the Poisson parameter becomes difficult for small positive values of n and unmanageable for large values. NEWTPOIS uses Newton's iteration method to extract lambda from the initial value condition of the Poisson distribution where n=0, taking successive estimations until some user specified error term (epsilon) is reached. The NEWTPOIS program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly on most C compilers. The program format is interactive, accepting epsilon, n, and the cumulative probability of the occurrence of n as inputs. It has been implemented under DOS 3.2 and has a memory requirement of 30K. NEWTPOIS was developed in 1988.

Radar sea reflection for low-e targets

NASA Astrophysics Data System (ADS)

Chow, Winston C.; Groves, Gordon W.

1998-09-01

Modeling radar signal reflection from a wavy sea surface uses a realistic characteristic of the large surface features and parameterizes the effect of the small roughness elements. Representation of the reflection coefficient at each point of the sea surface as a function of the Specular Deviation Angle is, to our knowledge, a novel approach. The objective is to achieve enough simplification and retain enough fidelity to obtain a practical multipath model. The 'specular deviation angle' as used in this investigation is defined and explained. Being a function of the sea elevations, which are stochastic in nature, this quantity is also random and has a probability density function. This density function depends on the relative geometry of the antenna and target positions, and together with the beam- broadening effect of the small surface ripples determined the reflectivity of the sea surface at each point. The probability density function of the specular deviation angle is derived. The distribution of the specular deviation angel as function of position on the mean sea surface is described.

Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model.

PubMed

Semenov, Yuri S; Novozhilov, Artem S

2015-08-01

We reformulate the eigenvalue problem for the selection-mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations. Copyright © 2015. Published by Elsevier Inc.

Gain statistics of a fiber optical parametric amplifier with a temporally incoherent pump.

PubMed

Xu, Y Q; Murdoch, S G

2010-03-15

We present an investigation of the statistics of the gain fluctuations of a fiber optical parametric amplifier pumped with a temporally incoherent pump. We derive a simple expression for the probability distribution of the gain of the amplified optical signal. The gain statistics are shown to be a strong function of the signal detuning and allow the possibility of generating optical gain distributions with controllable long-tails. Very good agreement is found between this theory and the experimentally measured gain distributions of an incoherently pumped amplifier.

On the probability distribution function of the mass surface density of molecular clouds. I

NASA Astrophysics Data System (ADS)

Fischera, Jörg

2014-05-01

The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a composition of a broad distribution around the maximum and a decreasing tail at high mass surface densities. The first component is attributed to the random distribution of gas which is modeled using a log-normal function while the second component is attributed to condensed structures modeled using a simple power-law. The aim of this paper is to provide an analytical model of the PDF of condensed structures which can be used by observers to extract information about the condensations. The condensed structures are considered to be either spheres or cylinders with a truncated radial density profile at cloud radius rcl. The assumed profile is of the form ρ(r) = ρc/ (1 + (r/r0)2)n/ 2 for arbitrary power n where ρc and r0 are the central density and the inner radius, respectively. An implicit function is obtained which either truncates (sphere) or has a pole (cylinder) at maximal mass surface density. The PDF of spherical condensations and the asymptotic PDF of cylinders in the limit of infinite overdensity ρc/ρ(rcl) flattens for steeper density profiles and has a power law asymptote at low and high mass surface densities and a well defined maximum. The power index of the asymptote Σ- γ of the logarithmic PDF (ΣP(Σ)) in the limit of high mass surface densities is given by γ = (n + 1)/(n - 1) - 1 (spheres) or by γ = n/ (n - 1) - 1 (cylinders in the limit of infinite overdensity). Appendices are available in electronic form at http://www.aanda.org

Functional aging in pilots : an examination of a mathematical model based on medical data on general aviation pilots.

DOT National Transportation Integrated Search

1982-06-01

The purpose of this study was to apply mathematical procedures to the Federal Aviation Administration (FAA) pilot medical data to examine the feasibility of devising a linear numbering system such that (1) the cumulative probability distribution func...

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

NASA Astrophysics Data System (ADS)

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

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

Representation of analysis results involving aleatory and epistemic uncertainty.

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

Johnson, Jay Dean; Helton, Jon Craig; Oberkampf, William Louis

2008-08-01

Procedures are described for the representation of results in analyses that involve both aleatory uncertainty and epistemic uncertainty, with aleatory uncertainty deriving from an inherent randomness in the behavior of the system under study and epistemic uncertainty deriving from a lack of knowledge about the appropriate values to use for quantities that are assumed to have fixed but poorly known values in the context of a specific study. Aleatory uncertainty is usually represented with probability and leads to cumulative distribution functions (CDFs) or complementary cumulative distribution functions (CCDFs) for analysis results of interest. Several mathematical structures are available for themore » representation of epistemic uncertainty, including interval analysis, possibility theory, evidence theory and probability theory. In the presence of epistemic uncertainty, there is not a single CDF or CCDF for a given analysis result. Rather, there is a family of CDFs and a corresponding family of CCDFs that derive from epistemic uncertainty and have an uncertainty structure that derives from the particular uncertainty structure (i.e., interval analysis, possibility theory, evidence theory, probability theory) used to represent epistemic uncertainty. Graphical formats for the representation of epistemic uncertainty in families of CDFs and CCDFs are investigated and presented for the indicated characterizations of epistemic uncertainty.« less

Fundamental Bounds for Sequence Reconstruction from Nanopore Sequencers.

PubMed

Magner, Abram; Duda, Jarosław; Szpankowski, Wojciech; Grama, Ananth

2016-06-01

Nanopore sequencers are emerging as promising new platforms for high-throughput sequencing. As with other technologies, sequencer errors pose a major challenge for their effective use. In this paper, we present a novel information theoretic analysis of the impact of insertion-deletion (indel) errors in nanopore sequencers. In particular, we consider the following problems: (i) for given indel error characteristics and rate, what is the probability of accurate reconstruction as a function of sequence length; (ii) using replicated extrusion (the process of passing a DNA strand through the nanopore), what is the number of replicas needed to accurately reconstruct the true sequence with high probability? Our results provide a number of important insights: (i) the probability of accurate reconstruction of a sequence from a single sample in the presence of indel errors tends quickly (i.e., exponentially) to zero as the length of the sequence increases; and (ii) replicated extrusion is an effective technique for accurate reconstruction. We show that for typical distributions of indel errors, the required number of replicas is a slow function (polylogarithmic) of sequence length - implying that through replicated extrusion, we can sequence large reads using nanopore sequencers. Moreover, we show that in certain cases, the required number of replicas can be related to information-theoretic parameters of the indel error distributions.

Deep Learning Role in Early Diagnosis of Prostate Cancer

PubMed Central

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

2018-01-01

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

flexsurv: A Platform for Parametric Survival Modeling in R

PubMed Central

Jackson, Christopher H.

2018-01-01

flexsurv is an R package for fully-parametric modeling of survival data. Any parametric time-to-event distribution may be fitted if the user supplies a probability density or hazard function, and ideally also their cumulative versions. Standard survival distributions are built in, including the three and four-parameter generalized gamma and F distributions. Any parameter of any distribution can be modeled as a linear or log-linear function of covariates. The package also includes the spline model of Royston and Parmar (2002), in which both baseline survival and covariate effects can be arbitrarily flexible parametric functions of time. The main model-fitting function, flexsurvreg, uses the familiar syntax of survreg from the standard survival package (Therneau 2016). Censoring or left-truncation are specified in ‘Surv’ objects. The models are fitted by maximizing the full log-likelihood, and estimates and confidence intervals for any function of the model parameters can be printed or plotted. flexsurv also provides functions for fitting and predicting from fully-parametric multi-state models, and connects with the mstate package (de Wreede, Fiocco, and Putter 2011). This article explains the methods and design principles of the package, giving several worked examples of its use. PMID:29593450

Bayesian functional integral method for inferring continuous data from discrete measurements.

PubMed

Heuett, William J; Miller, Bernard V; Racette, Susan B; Holloszy, John O; Chow, Carson C; Periwal, Vipul

2012-02-08

Inference of the insulin secretion rate (ISR) from C-peptide measurements as a quantification of pancreatic β-cell function is clinically important in diseases related to reduced insulin sensitivity and insulin action. ISR derived from C-peptide concentration is an example of nonparametric Bayesian model selection where a proposed ISR time-course is considered to be a "model". An inferred value of inaccessible continuous variables from discrete observable data is often problematic in biology and medicine, because it is a priori unclear how robust the inference is to the deletion of data points, and a closely related question, how much smoothness or continuity the data actually support. Predictions weighted by the posterior distribution can be cast as functional integrals as used in statistical field theory. Functional integrals are generally difficult to evaluate, especially for nonanalytic constraints such as positivity of the estimated parameters. We propose a computationally tractable method that uses the exact solution of an associated likelihood function as a prior probability distribution for a Markov-chain Monte Carlo evaluation of the posterior for the full model. As a concrete application of our method, we calculate the ISR from actual clinical C-peptide measurements in human subjects with varying degrees of insulin sensitivity. Our method demonstrates the feasibility of functional integral Bayesian model selection as a practical method for such data-driven inference, allowing the data to determine the smoothing timescale and the width of the prior probability distribution on the space of models. In particular, our model comparison method determines the discrete time-step for interpolation of the unobservable continuous variable that is supported by the data. Attempts to go to finer discrete time-steps lead to less likely models. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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

PubMed

Garriguet, Didier

2016-04-01

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

Integrated measurements and modeling of CO2, CH4, and N2O fluxes using soil microsite frequency distributions

NASA Astrophysics Data System (ADS)

Davidson, Eric; Sihi, Debjani; Savage, Kathleen

2017-04-01

Soil fluxes of greenhouse gases (GHGs) play a significant role as biotic feedbacks to climate change. Production and consumption of carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O) are affected by complex interactions of temperature, moisture, and substrate supply, which are further complicated by spatial heterogeneity of the soil matrix. Models of belowground processes of these GHGs should be internally consistent with respect to the biophysical processes of gaseous production, consumption, and transport within the soil, including the contrasting effects of oxygen (O2) as either substrate or inhibitor. We installed automated chambers to simultaneously measure soil fluxes of CO2 (using LiCor-IRGA), CH4, and N2O (using Aerodyne quantum cascade laser) along soil moisture gradients at the Howland Forest in Maine, USA. Measured fluxes of these GHGs were used to develop and validate a merged model. While originally intended for aerobic respiration, the core structure of the Dual Arrhenius and Michaelis-Menten (DAMM) model was modified by adding M-M and Arrhenius functions for each GHG production and consumption process, and then using the same diffusion functions for each GHG and for O2. The area under a soil chamber was partitioned according to a log-normal probability distribution function, where only a small fraction of microsites had high available-C. The probability distribution of soil C leads to a simulated distribution of heterotrophic respiration, which translates to a distribution of O2 consumption among microsites. Linking microsite consumption of O2 with a diffusion model generates microsite concentrations of O2, which then determine the distribution of microsite production and consumption of CH4 and N2O, and subsequently their microsite concentrations using the same diffusion function. At many moisture values, there are some microsites of production and some of consumption for each gas, and the resulting simulated microsite concentrations of CH4 and N2O range from below ambient to above ambient atmospheric values. As soil moisture or temperature increase, the skewness of the microsite distributions of heterotrophic respiration and CH4 concentrations shifts toward a larger fraction of high values, while the skewness of microsite distributions of O2 and N2O concentrations shifts toward a larger fraction of low values. This approach of probability distribution functions for each gas simulates the importance of microsite hotspots of methanogenesis and N2O reduction at high moisture (and temperature). In addition, the model demonstrates that net consumption of atmospheric CH4 and N2O can occur simultaneously within a chamber due to the distribution of soil microsite conditions, which is consistent with some episodes of measured fluxes. Because soil CO2, N2O and CH4 fluxes are linked through substrate supply and O2 effects, the multiple constraints of simultaneous measurements of all three GHGs proved to be effective when applied to our combined model. Simulating all three GHGs simultaneously in a parsimonious modeling framework provides confidence that the most important mechanisms are skillfully simulated using appropriate parameterization and good process representation.

Probability techniques for reliability analysis of composite materials

NASA Technical Reports Server (NTRS)

Wetherhold, Robert C.; Ucci, Anthony M.

1994-01-01

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

Multi-Agent Cooperative Target Search

PubMed Central

Hu, Jinwen; Xie, Lihua; Xu, Jun; Xu, Zhao

2014-01-01

This paper addresses a vision-based cooperative search for multiple mobile ground targets by a group of unmanned aerial vehicles (UAVs) with limited sensing and communication capabilities. The airborne camera on each UAV has a limited field of view and its target discriminability varies as a function of altitude. First, by dividing the whole surveillance region into cells, a probability map can be formed for each UAV indicating the probability of target existence within each cell. Then, we propose a distributed probability map updating model which includes the fusion of measurement information, information sharing among neighboring agents, information decay and transmission due to environmental changes such as the target movement. Furthermore, we formulate the target search problem as a multi-agent cooperative coverage control problem by optimizing the collective coverage area and the detection performance. The proposed map updating model and the cooperative control scheme are distributed, i.e., assuming that each agent only communicates with its neighbors within its communication range. Finally, the effectiveness of the proposed algorithms is illustrated by simulation. PMID:24865884

Prediction of fatty acid-binding residues on protein surfaces with three-dimensional probability distributions of interacting atoms.

PubMed

Mahalingam, Rajasekaran; Peng, Hung-Pin; Yang, An-Suei

2014-08-01

Protein-fatty acid interaction is vital for many cellular processes and understanding this interaction is important for functional annotation as well as drug discovery. In this work, we present a method for predicting the fatty acid (FA)-binding residues by using three-dimensional probability density distributions of interacting atoms of FAs on protein surfaces which are derived from the known protein-FA complex structures. A machine learning algorithm was established to learn the characteristic patterns of the probability density maps specific to the FA-binding sites. The predictor was trained with five-fold cross validation on a non-redundant training set and then evaluated with an independent test set as well as on holo-apo pair's dataset. The results showed good accuracy in predicting the FA-binding residues. Further, the predictor developed in this study is implemented as an online server which is freely accessible at the following website, http://ismblab.genomics.sinica.edu.tw/. Copyright © 2014 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Smisc - A collection of miscellaneous functions

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

Landon Sego, PNNL

2015-08-31

A collection of functions for statistical computing and data manipulation. These include routines for rapidly aggregating heterogeneous matrices, manipulating file names, loading R objects, sourcing multiple R files, formatting datetimes, multi-core parallel computing, stream editing, specialized plotting, etc. Smisc-package A collection of miscellaneous functions allMissing Identifies missing rows or columns in a data frame or matrix as.numericSilent Silent wrapper for coercing a vector to numeric comboList Produces all possible combinations of a set of linear model predictors cumMax Computes the maximum of the vector up to the current index cumsumNA Computes the cummulative sum of a vector without propogating NAsmore » d2binom Probability functions for the sum of two independent binomials dataIn A flexible way to import data into R. dbb The Beta-Binomial Distribution df2list Row-wise conversion of a data frame to a list dfplapply Parallelized single row processing of a data frame dframeEquiv Examines the equivalence of two dataframes or matrices dkbinom Probability functions for the sum of k independent binomials factor2character Converts all factor variables in a dataframe to character variables findDepMat Identify linearly dependent rows or columns in a matrix formatDT Converts date or datetime strings into alternate formats getExtension Filename manipulations: remove the extension or path, extract the extension or path getPath Filename manipulations: remove the extension or path, extract the extension or path grabLast Filename manipulations: remove the extension or path, extract the extension or path ifelse1 Non-vectorized version of ifelse integ Simple numerical integration routine interactionPlot Two-way Interaction Plot with Error Bar linearMap Linear mapping of a numerical vector or scalar list2df Convert a list to a data frame loadObject Loads and returns the object(s) in an ".Rdata" file more Display the contents of a file to the R terminal movAvg2 Calculate the moving average using a 2-sided window openDevice Opens a graphics device based on the filename extension p2binom Probability functions for the sum of two independent binomials padZero Pad a vector of numbers with zeros parseJob Parses a collection of elements into (almost) equal sized groups pbb The Beta-Binomial Distribution pcbinom A continuous version of the binomial cdf pkbinom Probability functions for the sum of k independent binomials plapply Simple parallelization of lapply plotFun Plot one or more functions on a single plot PowerData An example of power data pvar Prints the name and value of one or more objects qbb The Beta-Binomial Distribution rbb And numerous others (space limits reporting).« less

[Establishment of the mathematic model of total quantum statistical moment standard similarity for application to medical theoretical research].

PubMed

He, Fu-yuan; Deng, Kai-wen; Huang, Sheng; Liu, Wen-long; Shi, Ji-lian

2013-09-01

The paper aims to elucidate and establish a new mathematic model: the total quantum statistical moment standard similarity (TQSMSS) on the base of the original total quantum statistical moment model and to illustrate the application of the model to medical theoretical research. The model was established combined with the statistical moment principle and the normal distribution probability density function properties, then validated and illustrated by the pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical method for them, and by analysis of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving the Buyanghanwu-decoction extract. The established model consists of four mainly parameters: (1) total quantum statistical moment similarity as ST, an overlapped area by two normal distribution probability density curves in conversion of the two TQSM parameters; (2) total variability as DT, a confidence limit of standard normal accumulation probability which is equal to the absolute difference value between the two normal accumulation probabilities within integration of their curve nodical; (3) total variable probability as 1-Ss, standard normal distribution probability within interval of D(T); (4) total variable probability (1-beta)alpha and (5) stable confident probability beta(1-alpha): the correct probability to make positive and negative conclusions under confident coefficient alpha. With the model, we had analyzed the TQSMS similarities of pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical methods for them were at range of 0.3852-0.9875 that illuminated different pharmacokinetic behaviors of each other; and the TQSMS similarities (ST) of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving Buyanghuanwu-decoction-extract were at range of 0.6842-0.999 2 that showed different constituents with various solvent extracts. The TQSMSS can characterize the sample similarity, by which we can quantitate the correct probability with the test of power under to make positive and negative conclusions no matter the samples come from same population under confident coefficient a or not, by which we can realize an analysis at both macroscopic and microcosmic levels, as an important similar analytical method for medical theoretical research.

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

DOE PAGES

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

2013-01-01

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

A Riemannian framework for orientation distribution function computing.

PubMed

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

2009-01-01

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

Decision theory for computing variable and value ordering decisions for scheduling problems

NASA Technical Reports Server (NTRS)

Linden, Theodore A.

1993-01-01

Heuristics that guide search are critical when solving large planning and scheduling problems, but most variable and value ordering heuristics are sensitive to only one feature of the search state. One wants to combine evidence from all features of the search state into a subjective probability that a value choice is best, but there has been no solid semantics for merging evidence when it is conceived in these terms. Instead, variable and value ordering decisions should be viewed as problems in decision theory. This led to two key insights: (1) The fundamental concept that allows heuristic evidence to be merged is the net incremental utility that will be achieved by assigning a value to a variable. Probability distributions about net incremental utility can merge evidence from the utility function, binary constraints, resource constraints, and other problem features. The subjective probability that a value is the best choice is then derived from probability distributions about net incremental utility. (2) The methods used for rumor control in Bayesian Networks are the primary way to prevent cycling in the computation of probable net incremental utility. These insights lead to semantically justifiable ways to compute heuristic variable and value ordering decisions that merge evidence from all available features of the search state.

Dynamic Response of an Optomechanical System to a Stationary Random Excitation in the Time Domain

DOE PAGES

Palmer, Jeremy A.; Paez, Thomas L.

2011-01-01

Modern electro-optical instruments are typically designed with assemblies of optomechanical members that support optics such that alignment is maintained in service environments that include random vibration loads. This paper presents a nonlinear numerical analysis that calculates statistics for the peak lateral response of optics in an optomechanical sub-assembly subject to random excitation of the housing. The work is unique in that the prior art does not address peak response probability distribution for stationary random vibration in the time domain for a common lens-retainer-housing system with Coulomb damping. Analytical results are validated by using displacement response data from random vibration testingmore » of representative prototype sub-assemblies. A comparison of predictions to experimental results yields reasonable agreement. The Type I Asymptotic form provides the cumulative distribution function for peak response probabilities. Probabilities are calculated for actual lens centration tolerances. The probability that peak response will not exceed the centration tolerance is greater than 80% for prototype configurations where the tolerance is high (on the order of 30 micrometers). Conversely, the probability is low for those where the tolerance is less than 20 micrometers. The analysis suggests a design paradigm based on the influence of lateral stiffness on the magnitude of the response.« less

Modelling road accident blackspots data with the discrete generalized Pareto distribution.

PubMed

Prieto, Faustino; Gómez-Déniz, Emilio; Sarabia, José María

2014-10-01

This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of crashes and the number of fatalities on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the μ and (μ+1) frequency method and the maximum likelihood method; used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrap resampling; and compared them with the classical negative binomial distribution in terms of absolute probabilities and in models including covariates. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed. Copyright © 2014 Elsevier Ltd. All rights reserved.

Functionally Graded Designer Viscoelastic Materials Tailored to Perform Prescribed Tasks with Probabilistic Failures and Lifetimes

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

Hilton, Harry H.

Protocols are developed for formulating optimal viscoelastic designer functionally graded materials tailored to best respond to prescribed loading and boundary conditions. In essence, an inverse approach is adopted where material properties instead of structures per se are designed and then distributed throughout structural elements. The final measure of viscoelastic material efficacy is expressed in terms of failure probabilities vs. survival time000.

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

The probability density function (PDF) of Lagrangian Turbulence

NASA Astrophysics Data System (ADS)

Birnir, B.

2012-12-01

The statistical theory of Lagrangian turbulence is derived from the stochastic Navier-Stokes equation. Assuming that the noise in fully-developed turbulence is a generic noise determined by the general theorems in probability, the central limit theorem and the large deviation principle, we are able to formulate and solve the Kolmogorov-Hopf equation for the invariant measure of the stochastic Navier-Stokes equations. The intermittency corrections to the scaling exponents of the structure functions require a multiplicative (multipling the fluid velocity) noise in the stochastic Navier-Stokes equation. We let this multiplicative noise, in the equation, consists of a simple (Poisson) jump process and then show how the Feynmann-Kac formula produces the log-Poissonian processes, found by She and Leveque, Waymire and Dubrulle. These log-Poissonian processes give the intermittency corrections that agree with modern direct Navier-Stokes simulations (DNS) and experiments. The probability density function (PDF) plays a key role when direct Navier-Stokes simulations or experimental results are compared to theory. The statistical theory of turbulence is determined, including the scaling of the structure functions of turbulence, by the invariant measure of the Navier-Stokes equation and the PDFs for the various statistics (one-point, two-point, N-point) can be obtained by taking the trace of the corresponding invariant measures. Hopf derived in 1952 a functional equation for the characteristic function (Fourier transform) of the invariant measure. In distinction to the nonlinear Navier-Stokes equation, this is a linear functional differential equation. The PDFs obtained from the invariant measures for the velocity differences (two-point statistics) are shown to be the four parameter generalized hyperbolic distributions, found by Barndorff-Nilsen. These PDF have heavy tails and a convex peak at the origin. A suitable projection of the Kolmogorov-Hopf equations is the differential equation determining the generalized hyperbolic distributions. Then we compare these PDFs with DNS results and experimental data.

Self-imposed length limits in recreational fisheries

USGS Publications Warehouse

Chizinski, Christopher J.; Martin, Dustin R.; Hurley, Keith L.; Pope, Kevin L.

2014-01-01

A primary motivating factor on the decision to harvest a fish among consumptive-orientated anglers is the size of the fish. There is likely a cost-benefit trade-off for harvest of individual fish that is size and species dependent, which should produce a logistic-type response of fish fate (release or harvest) as a function of fish size and species. We define the self-imposed length limit as the length at which a captured fish had a 50% probability of being harvested, which was selected because it marks the length of the fish where the probability of harvest becomes greater than the probability of release. We assessed the influences of fish size, catch per unit effort, size distribution of caught fish, and creel limit on the self-imposed length limits for bluegill Lepomis macrochirus, channel catfish Ictalurus punctatus, black crappie Pomoxis nigromaculatus and white crappie Pomoxis annularis combined, white bass Morone chrysops, and yellow perch Perca flavescens at six lakes in Nebraska, USA. As we predicted, the probability of harvest increased with increasing size for all species harvested, which supported the concept of a size-dependent trade-off in costs and benefits of harvesting individual fish. It was also clear that probability of harvest was not simply defined by fish length, but rather was likely influenced to various degrees by interactions between species, catch rate, size distribution, creel-limit regulation and fish size. A greater understanding of harvest decisions within the context of perceived likelihood that a creel limit will be realized by a given angler party, which is a function of fish availability, harvest regulation and angler skill and orientation, is needed to predict the influence that anglers have on fish communities and to allow managers to sustainable manage exploited fish populations in recreational fisheries.

Emission Depth Distribution Function of Al 2s Photoelectrons in Al2O3

NASA Astrophysics Data System (ADS)

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

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

Statistical properties and correlation functions for drift waves

NASA Technical Reports Server (NTRS)

Horton, W.

1986-01-01

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

Modeling evaporation of Jet A, JP-7 and RP-1 drops at 1 to 15 bars

NASA Technical Reports Server (NTRS)

Harstad, K.; Bellan, J.

2003-01-01

A model describing the evaportion of an isolated drop of a multicomponent fuel containing hundreds of species has been developed. The model is based on Continuous Thermodynamics concepts wherein the composition of a fuel is statistically described using a Probability Distribution Function (PDF).

Release the Prisoners Game

ERIC Educational Resources Information Center

Van Hecke, Tanja

2011-01-01

This article presents the mathematical approach of the optimal strategy to win the "Release the prisoners" game and the integration of this analysis in a math class. Outline lesson plans at three different levels are given, where simulations are suggested as well as theoretical findings about the probability distribution function and its mean…

The Dutch Identity: A New Tool for the Study of Item Response Models.

ERIC Educational Resources Information Center

Holland, Paul W.

1990-01-01

The Dutch Identity is presented as a useful tool for expressing the basic equations of item response models that relate the manifest probabilities to the item response functions and the latent trait distribution. Ways in which the identity may be exploited are suggested and illustrated. (SLD)

Study on length distribution of ramie fibers

USDA-ARS?s Scientific Manuscript database

The extra-long length of ramie fibers and the high variation in fiber length has a negative impact on the spinning processes. In order to better study the feature of ramie fiber length, in this research, the probability density function of the mixture model applied in the characterization of cotton...

Numerical Estimation of Information Theoretic Measures for Large Data Sets

DTIC Science & Technology

2013-01-30

probability including a new indifference rule,” J. Inst. of Actuaries Students’ Soc. 73, 285–334 (1947). 7. M. Hutter and M. Zaffalon, “Distribution...Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York (1972). 13. K.B. Oldham et al., An Atlas

Game-theoretic strategies for asymmetric networked systems

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

Rao, Nageswara S.; Ma, Chris Y. T.; Hausken, Kjell

Abstract—We consider an infrastructure consisting of a network of systems each composed of discrete components that can be reinforced at a certain cost to guard against attacks. The network provides the vital connectivity between systems, and hence plays a critical, asymmetric role in the infrastructure operations. We characterize the system-level correlations using the aggregate failure correlation function that specifies the infrastructure failure probability given the failure of an individual system or network. The survival probabilities of systems and network satisfy first-order differential conditions that capture the component-level correlations. We formulate the problem of ensuring the infrastructure survival as a gamemore » between anattacker and a provider, using the sum-form and product-form utility functions, each composed of a survival probability term and a cost term. We derive Nash Equilibrium conditions which provide expressions for individual system survival probabilities, and also the expected capacity specified by the total number of operational components. These expressions differ only in a single term for the sum-form and product-form utilities, despite their significant differences.We apply these results to simplified models of distributed cloud computing infrastructures.« less

Queues with Dropping Functions and General Arrival Processes

PubMed Central

Chydzinski, Andrzej; Mrozowski, Pawel

2016-01-01

In a queueing system with the dropping function the arriving customer can be denied service (dropped) with the probability that is a function of the queue length at the time of arrival of this customer. The potential applicability of such mechanism is very wide due to the fact that by choosing the shape of this function one can easily manipulate several performance characteristics of the queueing system. In this paper we carry out analysis of the queueing system with the dropping function and a very general model of arrival process—the model which includes batch arrivals and the interarrival time autocorrelation, and allows for fitting the actual shape of the interarrival time distribution and its moments. For such a system we obtain formulas for the distribution of the queue length and the overall customer loss ratio. The analytical results are accompanied with numerical examples computed for several dropping functions. PMID:26943171

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

NASA Astrophysics Data System (ADS)

Rosenberg, Phil

2017-04-01

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

Advances in modeling trait-based plant community assembly.

PubMed

Laughlin, Daniel C; Laughlin, David E

2013-10-01

In this review, we examine two new trait-based models of community assembly that predict the relative abundance of species from a regional species pool. The models use fundamentally different mathematical approaches and the predictions can differ considerably. Maxent obtains the most even probability distribution subject to community-weighted mean trait constraints. Traitspace predicts low probabilities for any species whose trait distribution does not pass through the environmental filter. Neither model maximizes functional diversity because of the emphasis on environmental filtering over limiting similarity. Traitspace can test for the effects of limiting similarity by explicitly incorporating intraspecific trait variation. The range of solutions in both models could be used to define the range of natural variability of community composition in restoration projects. Copyright © 2013 Elsevier Ltd. All rights reserved.

Computational analysis of kidney scintigrams

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

Vrincianu, D.; Puscasu, E.; Creanga, D.

The scintigraphic investigation of normal and pathological kidneys was carried out using specialized gamma-camera device from nuclear medicine hospital department. Technetium 90m isotope with gamma radiation emission, coupled with vector molecules for kidney tissues was introduced into the subject body, its dynamics being recorded as data source for kidney clearance capacity. Two representative data series were investigated, corresponding to healthy and pathological organs respectively. The semi-quantitative tests applied for the comparison of the two distinct medical situations were: the shape of probability distribution histogram, the power spectrum, the auto-correlation function and the Lyapunov exponent. While power spectrum led to similarmore » results in both cases, significant differences were revealed by means of distribution probability, Lyapunov exponent and correlation time, recommending these numerical tests as possible complementary tools in clinical diagnosis.« less

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

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

The structure of water around the compressibility minimum

DOE PAGES

L. B. Skinner; Benmore, C. J.; Parise, J.; ...

2014-12-03

Here we present diffraction data that yield the oxygen-oxygen pair distribution function, gOO(r) over the range 254.2–365.9 K. The running O-O coordination number, which represents the integral of the pair distribution function as a function of radial distance, is found to exhibit an isosbestic point at 3.30(5) Å. The probability of finding an oxygen atom surrounding another oxygen at this distance is therefore shown to be independent of temperature and corresponds to an O-O coordination number of 4.3(2). Moreover, the experimental data also show a continuous transition associated with the second peak position in gOO(r) concomitant with the compressibility minimummore » at 319 K.« less

Distributed Constrained Optimization with Semicoordinate Transformations

NASA Technical Reports Server (NTRS)

Macready, William; Wolpert, David

2006-01-01

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Diameter distribution in a Brazilian tropical dry forest domain: predictions for the stand and species.

PubMed

Lima, Robson B DE; Bufalino, Lina; Alves, Francisco T; Silva, José A A DA; Ferreira, Rinaldo L C

2017-01-01

Currently, there is a lack of studies on the correct utilization of continuous distributions for dry tropical forests. Therefore, this work aims to investigate the diameter structure of a brazilian tropical dry forest and to select suitable continuous distributions by means of statistic tools for the stand and the main species. Two subsets were randomly selected from 40 plots. Diameter at base height was obtained. The following functions were tested: log-normal; gamma; Weibull 2P and Burr. The best fits were selected by Akaike's information validation criterion. Overall, the diameter distribution of the dry tropical forest was better described by negative exponential curves and positive skewness. The forest studied showed diameter distributions with decreasing probability for larger trees. This behavior was observed for both the main species and the stand. The generalization of the function fitted for the main species show that the development of individual models is needed. The Burr function showed good flexibility to describe the diameter structure of the stand and the behavior of Mimosa ophthalmocentra and Bauhinia cheilantha species. For Poincianella bracteosa, Aspidosperma pyrifolium and Myracrodum urundeuva better fitting was obtained with the log-normal function.

A New Self-Constrained Inversion Method of Potential Fields Based on Probability Tomography

NASA Astrophysics Data System (ADS)

Sun, S.; Chen, C.; WANG, H.; Wang, Q.

2014-12-01

The self-constrained inversion method of potential fields uses a priori information self-extracted from potential field data. Differing from external a priori information, the self-extracted information are generally parameters derived exclusively from the analysis of the gravity and magnetic data (Paoletti et al., 2013). Here we develop a new self-constrained inversion method based on probability tomography. Probability tomography doesn't need any priori information, as well as large inversion matrix operations. Moreover, its result can describe the sources, especially the distribution of which is complex and irregular, entirely and clearly. Therefore, we attempt to use the a priori information extracted from the probability tomography results to constrain the inversion for physical properties. The magnetic anomaly data was taken as an example in this work. The probability tomography result of magnetic total field anomaly(ΔΤ) shows a smoother distribution than the anomalous source and cannot display the source edges exactly. However, the gradients of ΔΤ are with higher resolution than ΔΤ in their own direction, and this characteristic is also presented in their probability tomography results. So we use some rules to combine the probability tomography results of ∂ΔΤ⁄∂x, ∂ΔΤ⁄∂y and ∂ΔΤ⁄∂z into a new result which is used for extracting a priori information, and then incorporate the information into the model objective function as spatial weighting functions to invert the final magnetic susceptibility. Some magnetic synthetic examples incorporated with and without a priori information extracted from the probability tomography results were made to do comparison, results of which show that the former are more concentrated and with higher resolution of the source body edges. This method is finally applied in an iron mine in China with field measured ΔΤ data and performs well. ReferencesPaoletti, V., Ialongo, S., Florio, G., Fedi, M. & Cella, F., 2013. Self-constrained inversion of potential fields, Geophys J Int.This research is supported by the Fundamental Research Funds for Institute for Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences (Grant Nos. WHS201210 and WHS201211).

The 2-10 keV unabsorbed luminosity function of AGN from the LSS, CDFS, and COSMOS surveys

NASA Astrophysics Data System (ADS)

Ranalli, P.; Koulouridis, E.; Georgantopoulos, I.; Fotopoulou, S.; Hsu, L.-T.; Salvato, M.; Comastri, A.; Pierre, M.; Cappelluti, N.; Carrera, F. J.; Chiappetti, L.; Clerc, N.; Gilli, R.; Iwasawa, K.; Pacaud, F.; Paltani, S.; Plionis, E.; Vignali, C.

2016-05-01

The XMM-Large scale structure (XMM-LSS), XMM-Cosmological evolution survey (XMM-COSMOS), and XMM-Chandra deep field south (XMM-CDFS) surveys are complementary in terms of sky coverage and depth. Together, they form a clean sample with the least possible variance in instrument effective areas and point spread function. Therefore this is one of the best samples available to determine the 2-10 keV luminosity function of active galactic nuclei (AGN) and their evolution. The samples and the relevant corrections for incompleteness are described. A total of 2887 AGN is used to build the LF in the luminosity interval 1042-1046 erg s-1 and in the redshift interval 0.001-4. A new method to correct for absorption by considering the probability distribution for the column density conditioned on the hardness ratio is presented. The binned luminosity function and its evolution is determined with a variant of the Page-Carrera method, which is improved to include corrections for absorption and to account for the full probability distribution of photometric redshifts. Parametric models, namely a double power law with luminosity and density evolution (LADE) or luminosity-dependent density evolution (LDDE), are explored using Bayesian inference. We introduce the Watanabe-Akaike information criterion (WAIC) to compare the models and estimate their predictive power. Our data are best described by the LADE model, as hinted by the WAIC indicator. We also explore the recently proposed 15-parameter extended LDDE model and find that this extension is not supported by our data. The strength of our method is that it provides unabsorbed, non-parametric estimates, credible intervals for luminosity function parameters, and a model choice based on predictive power for future data. Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA member states and NASA.Tables with the samples of the posterior probability distributions are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/590/A80

Neutrino mass priors for cosmology from random matrices

NASA Astrophysics Data System (ADS)

Long, Andrew J.; Raveri, Marco; Hu, Wayne; Dodelson, Scott

2018-02-01

Cosmological measurements of structure are placing increasingly strong constraints on the sum of the neutrino masses, Σ mν, through Bayesian inference. Because these constraints depend on the choice for the prior probability π (Σ mν), we argue that this prior should be motivated by fundamental physical principles rather than the ad hoc choices that are common in the literature. The first step in this direction is to specify the prior directly at the level of the neutrino mass matrix Mν, since this is the parameter appearing in the Lagrangian of the particle physics theory. Thus by specifying a probability distribution over Mν, and by including the known squared mass splittings, we predict a theoretical probability distribution over Σ mν that we interpret as a Bayesian prior probability π (Σ mν). Assuming a basis-invariant probability distribution on Mν, also known as the anarchy hypothesis, we find that π (Σ mν) peaks close to the smallest Σ mν allowed by the measured mass splittings, roughly 0.06 eV (0.1 eV) for normal (inverted) ordering, due to the phenomenon of eigenvalue repulsion in random matrices. We consider three models for neutrino mass generation: Dirac, Majorana, and Majorana via the seesaw mechanism; differences in the predicted priors π (Σ mν) allow for the possibility of having indications about the physical origin of neutrino masses once sufficient experimental sensitivity is achieved. We present fitting functions for π (Σ mν), which provide a simple means for applying these priors to cosmological constraints on the neutrino masses or marginalizing over their impact on other cosmological parameters.

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

A bioinformatic survey of distribution, conservation, and probable functions of LuxR solo regulators in bacteria.

PubMed

Subramoni, Sujatha; Florez Salcedo, Diana Vanessa; Suarez-Moreno, Zulma R

2015-01-01

LuxR solo transcriptional regulators contain both an autoinducer binding domain (ABD; N-terminal) and a DNA binding Helix-Turn-Helix domain (HTH; C-terminal), but are not associated with a cognate N-acyl homoserine lactone (AHL) synthase coding gene in the same genome. Although a few LuxR solos have been characterized, their distributions as well as their role in bacterial signal perception and other processes are poorly understood. In this study we have carried out a systematic survey of distribution of all ABD containing LuxR transcriptional regulators (QS domain LuxRs) available in the InterPro database (IPR005143), and identified those lacking a cognate AHL synthase. These LuxR solos were then analyzed regarding their taxonomical distribution, predicted functions of neighboring genes and the presence of complete AHL-QS systems in the genomes that carry them. Our analyses reveal the presence of one or multiple predicted LuxR solos in many proteobacterial genomes carrying QS domain LuxRs, some of them harboring genes for one or more AHL-QS circuits. The presence of LuxR solos in bacteria occupying diverse environments suggests potential ecological functions for these proteins beyond AHL and interkingdom signaling. Based on gene context and the conservation levels of invariant amino acids of ABD, we have classified LuxR solos into functionally meaningful groups or putative orthologs. Surprisingly, putative LuxR solos were also found in a few non-proteobacterial genomes which are not known to carry AHL-QS systems. Multiple predicted LuxR solos in the same genome appeared to have different levels of conservation of invariant amino acid residues of ABD questioning their binding to AHLs. In summary, this study provides a detailed overview of distribution of LuxR solos and their probable roles in bacteria with genome sequence information.

A bioinformatic survey of distribution, conservation, and probable functions of LuxR solo regulators in bacteria

PubMed Central

Subramoni, Sujatha; Florez Salcedo, Diana Vanessa; Suarez-Moreno, Zulma R.

2015-01-01

LuxR solo transcriptional regulators contain both an autoinducer binding domain (ABD; N-terminal) and a DNA binding Helix-Turn-Helix domain (HTH; C-terminal), but are not associated with a cognate N-acyl homoserine lactone (AHL) synthase coding gene in the same genome. Although a few LuxR solos have been characterized, their distributions as well as their role in bacterial signal perception and other processes are poorly understood. In this study we have carried out a systematic survey of distribution of all ABD containing LuxR transcriptional regulators (QS domain LuxRs) available in the InterPro database (IPR005143), and identified those lacking a cognate AHL synthase. These LuxR solos were then analyzed regarding their taxonomical distribution, predicted functions of neighboring genes and the presence of complete AHL-QS systems in the genomes that carry them. Our analyses reveal the presence of one or multiple predicted LuxR solos in many proteobacterial genomes carrying QS domain LuxRs, some of them harboring genes for one or more AHL-QS circuits. The presence of LuxR solos in bacteria occupying diverse environments suggests potential ecological functions for these proteins beyond AHL and interkingdom signaling. Based on gene context and the conservation levels of invariant amino acids of ABD, we have classified LuxR solos into functionally meaningful groups or putative orthologs. Surprisingly, putative LuxR solos were also found in a few non-proteobacterial genomes which are not known to carry AHL-QS systems. Multiple predicted LuxR solos in the same genome appeared to have different levels of conservation of invariant amino acid residues of ABD questioning their binding to AHLs. In summary, this study provides a detailed overview of distribution of LuxR solos and their probable roles in bacteria with genome sequence information. PMID:25759807

Computer models of social processes: the case of migration.

PubMed

Beshers, J M

1967-06-01

The demographic model is a program for representing births, deaths, migration, and social mobility as social processes in a non-stationary stochastic process (Markovian). Transition probabilities for each age group are stored and then retrieved at the next appearance of that age cohort. In this way new transition probabilities can be calculated as a function of the old transition probabilities and of two successive distribution vectors.Transition probabilities can be calculated to represent effects of the whole age-by-state distribution at any given time period, too. Such effects as saturation or queuing may be represented by a market mechanism; for example, migration between metropolitan areas can be represented as depending upon job supplies and labor markets. Within metropolitan areas, migration can be represented as invasion and succession processes with tipping points (acceleration curves), and the market device has been extended to represent this phenomenon.Thus, the demographic model makes possible the representation of alternative classes of models of demographic processes. With each class of model one can deduce implied time series (varying parame-terswithin the class) and the output of the several classes can be compared to each other and to outside criteria, such as empirical time series.

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

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

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

PubMed

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

2016-06-01

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

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

PubMed Central

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

2015-01-01

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

Extreme Mean and Its Applications

NASA Technical Reports Server (NTRS)

Swaroop, R.; Brownlow, J. D.

1979-01-01

Extreme value statistics obtained from normally distributed data are considered. An extreme mean is defined as the mean of p-th probability truncated normal distribution. An unbiased estimate of this extreme mean and its large sample distribution are derived. The distribution of this estimate even for very large samples is found to be nonnormal. Further, as the sample size increases, the variance of the unbiased estimate converges to the Cramer-Rao lower bound. The computer program used to obtain the density and distribution functions of the standardized unbiased estimate, and the confidence intervals of the extreme mean for any data are included for ready application. An example is included to demonstrate the usefulness of extreme mean application.

The Self-Organization of a Spoken Word

PubMed Central

Holden, John G.; Rajaraman, Srinivasan

2012-01-01

Pronunciation time probability density and hazard functions from large speeded word naming data sets were assessed for empirical patterns consistent with multiplicative and reciprocal feedback dynamics – interaction dominant dynamics. Lognormal and inverse power law distributions are associated with multiplicative and interdependent dynamics in many natural systems. Mixtures of lognormal and inverse power law distributions offered better descriptions of the participant’s distributions than the ex-Gaussian or ex-Wald – alternatives corresponding to additive, superposed, component processes. The evidence for interaction dominant dynamics suggests fundamental links between the observed coordinative synergies that support speech production and the shapes of pronunciation time distributions. PMID:22783213

Maximum entropy principal for transportation

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

Bilich, F.; Da Silva, R.

In this work we deal with modeling of the transportation phenomenon for use in the transportation planning process and policy-impact studies. The model developed is based on the dependence concept, i.e., the notion that the probability of a trip starting at origin i is dependent on the probability of a trip ending at destination j given that the factors (such as travel time, cost, etc.) which affect travel between origin i and destination j assume some specific values. The derivation of the solution of the model employs the maximum entropy principle combining a priori multinomial distribution with a trip utilitymore » concept. This model is utilized to forecast trip distributions under a variety of policy changes and scenarios. The dependence coefficients are obtained from a regression equation where the functional form is derived based on conditional probability and perception of factors from experimental psychology. The dependence coefficients encode all the information that was previously encoded in the form of constraints. In addition, the dependence coefficients encode information that cannot be expressed in the form of constraints for practical reasons, namely, computational tractability. The equivalence between the standard formulation (i.e., objective function with constraints) and the dependence formulation (i.e., without constraints) is demonstrated. The parameters of the dependence-based trip-distribution model are estimated, and the model is also validated using commercial air travel data in the U.S. In addition, policy impact analyses (such as allowance of supersonic flights inside the U.S. and user surcharge at noise-impacted airports) on air travel are performed.« less

A rapid local singularity analysis algorithm with applications

NASA Astrophysics Data System (ADS)

Chen, Zhijun; Cheng, Qiuming; Agterberg, Frits

2015-04-01

The local singularity model developed by Cheng is fast gaining popularity in characterizing mineralization and detecting anomalies of geochemical, geophysical and remote sensing data. However in one of the conventional algorithms involving the moving average values with different scales is time-consuming especially while analyzing a large dataset. Summed area table (SAT), also called as integral image, is a fast algorithm used within the Viola-Jones object detection framework in computer vision area. Historically, the principle of SAT is well-known in the study of multi-dimensional probability distribution functions, namely in computing 2D (or ND) probabilities (area under the probability distribution) from the respective cumulative distribution functions. We introduce SAT and it's variation Rotated Summed Area Table in the isotropic, anisotropic or directional local singularity mapping in this study. Once computed using SAT, any one of the rectangular sum can be computed at any scale or location in constant time. The area for any rectangular region in the image can be computed by using only 4 array accesses in constant time independently of the size of the region; effectively reducing the time complexity from O(n) to O(1). New programs using Python, Julia, matlab and C++ are implemented respectively to satisfy different applications, especially to the big data analysis. Several large geochemical and remote sensing datasets are tested. A wide variety of scale changes (linear spacing or log spacing) for non-iterative or iterative approach are adopted to calculate the singularity index values and compare the results. The results indicate that the local singularity analysis with SAT is more robust and superior to traditional approach in identifying anomalies.

Nanomechanical characterization of heterogeneous and hierarchical biomaterials and tissues using nanoindentation: the role of finite mixture models.

PubMed

Zadpoor, Amir A

2015-03-01

Mechanical characterization of biological tissues and biomaterials at the nano-scale is often performed using nanoindentation experiments. The different constituents of the characterized materials will then appear in the histogram that shows the probability of measuring a certain range of mechanical properties. An objective technique is needed to separate the probability distributions that are mixed together in such a histogram. In this paper, finite mixture models (FMMs) are proposed as a tool capable of performing such types of analysis. Finite Gaussian mixture models assume that the measured probability distribution is a weighted combination of a finite number of Gaussian distributions with separate mean and standard deviation values. Dedicated optimization algorithms are available for fitting such a weighted mixture model to experimental data. Moreover, certain objective criteria are available to determine the optimum number of Gaussian distributions. In this paper, FMMs are used for interpreting the probability distribution functions representing the distributions of the elastic moduli of osteoarthritic human cartilage and co-polymeric microspheres. As for cartilage experiments, FMMs indicate that at least three mixture components are needed for describing the measured histogram. While the mechanical properties of the softer mixture components, often assumed to be associated with Glycosaminoglycans, were found to be more or less constant regardless of whether two or three mixture components were used, those of the second mixture component (i.e. collagen network) considerably changed depending on the number of mixture components. Regarding the co-polymeric microspheres, the optimum number of mixture components estimated by the FMM theory, i.e. 3, nicely matches the number of co-polymeric components used in the structure of the polymer. The computer programs used for the presented analyses are made freely available online for other researchers to use. Copyright © 2014 Elsevier B.V. All rights reserved.

Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps

NASA Astrophysics Data System (ADS)

Goto, Shin-itiro; Umeno, Ken

2018-03-01

Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps, where it is defined on a subset of the real line and its probability distribution function is the Cauchy distribution with some parameters. With this reduction, some relations between the statistical picture and the orbital one are shown. From the viewpoint of information geometry, the parameter space can be identified with a statistical manifold, and then it is shown that the derived maps can be characterized. Also, with an induced symplectic structure from a statistical structure, symplectic and information geometric aspects of the derived maps are discussed.

A modified weighted function method for parameter estimation of Pearson type three distribution

NASA Astrophysics Data System (ADS)

Liang, Zhongmin; Hu, Yiming; Li, Binquan; Yu, Zhongbo

2014-04-01

In this paper, an unconventional method called Modified Weighted Function (MWF) is presented for the conventional moment estimation of a probability distribution function. The aim of MWF is to estimate the coefficient of variation (CV) and coefficient of skewness (CS) from the original higher moment computations to the first-order moment calculations. The estimators for CV and CS of Pearson type three distribution function (PE3) were derived by weighting the moments of the distribution with two weight functions, which were constructed by combining two negative exponential-type functions. The selection of these weight functions was based on two considerations: (1) to relate weight functions to sample size in order to reflect the relationship between the quantity of sample information and the role of weight function and (2) to allocate more weights to data close to medium-tail positions in a sample series ranked in an ascending order. A Monte-Carlo experiment was conducted to simulate a large number of samples upon which statistical properties of MWF were investigated. For the PE3 parent distribution, results of MWF were compared to those of the original Weighted Function (WF) and Linear Moments (L-M). The results indicate that MWF was superior to WF and slightly better than L-M, in terms of statistical unbiasness and effectiveness. In addition, the robustness of MWF, WF, and L-M were compared by designing the Monte-Carlo experiment that samples are obtained from Log-Pearson type three distribution (LPE3), three parameter Log-Normal distribution (LN3), and Generalized Extreme Value distribution (GEV), respectively, but all used as samples from the PE3 distribution. The results show that in terms of statistical unbiasness, no one method possesses the absolutely overwhelming advantage among MWF, WF, and L-M, while in terms of statistical effectiveness, the MWF is superior to WF and L-M.

Gravity and count probabilities in an expanding universe

NASA Technical Reports Server (NTRS)

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.

Fusion of Imaging and Inertial Sensors for Navigation

DTIC Science & Technology

2006-09-01

combat operations. The Global Positioning System (GPS) was fielded in the 1980’s and first used for precision navigation and targeting in combat...equations [37]. Consider the homogeneous nonlinear differential equation ẋ(t) = f [x(t),u(t), t] ; x(t0) = x0 (2.4) For a given input function , u0(t...differential equation is a time-varying probability density function . The Kalman filter derivation assumes Gaussian distributions for all random

The global impact distribution of Near-Earth objects

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

Optimized lower leg injury probability curves from postmortem human subject tests under axial impacts.

PubMed

Yoganandan, Narayan; Arun, Mike W J; Pintar, Frank A; Szabo, Aniko

2014-01-01

Derive optimum injury probability curves to describe human tolerance of the lower leg using parametric survival analysis. The study reexamined lower leg postmortem human subjects (PMHS) data from a large group of specimens. Briefly, axial loading experiments were conducted by impacting the plantar surface of the foot. Both injury and noninjury tests were included in the testing process. They were identified by pre- and posttest radiographic images and detailed dissection following the impact test. Fractures included injuries to the calcaneus and distal tibia-fibula complex (including pylon), representing severities at the Abbreviated Injury Score (AIS) level 2+. For the statistical analysis, peak force was chosen as the main explanatory variable and the age was chosen as the covariable. Censoring statuses depended on experimental outcomes. Parameters from the parametric survival analysis were estimated using the maximum likelihood approach and the dfbetas statistic was used to identify overly influential samples. The best fit from the Weibull, log-normal, and log-logistic distributions was based on the Akaike information criterion. Plus and minus 95% confidence intervals were obtained for the optimum injury probability distribution. The relative sizes of the interval were determined at predetermined risk levels. Quality indices were described at each of the selected probability levels. The mean age, stature, and weight were 58.2±15.1 years, 1.74±0.08 m, and 74.9±13.8 kg, respectively. Excluding all overly influential tests resulted in the tightest confidence intervals. The Weibull distribution was the most optimum function compared to the other 2 distributions. A majority of quality indices were in the good category for this optimum distribution when results were extracted for 25-, 45- and 65-year-olds at 5, 25, and 50% risk levels age groups for lower leg fracture. For 25, 45, and 65 years, peak forces were 8.1, 6.5, and 5.1 kN at 5% risk; 9.6, 7.7, and 6.1 kN at 25% risk; and 10.4, 8.3, and 6.6 kN at 50% risk, respectively. This study derived axial loading-induced injury risk curves based on survival analysis using peak force and specimen age; adopting different censoring schemes; considering overly influential samples in the analysis; and assessing the quality of the distribution at discrete probability levels. Because procedures used in the present survival analysis are accepted by international automotive communities, current optimum human injury probability distributions can be used at all risk levels with more confidence in future crashworthiness applications for automotive and other disciplines.

Functional response and population dynamics for fighting predator, based on activity distribution.

PubMed

Garay, József; Varga, Zoltán; Gámez, Manuel; Cabello, Tomás

2015-03-07

The classical Holling type II functional response, describing the per capita predation as a function of prey density, was modified by Beddington and de Angelis to include interference of predators that increases with predator density and decreases the number of killed prey. In the present paper we further generalize the Beddington-de Angelis functional response, considering that all predator activities (searching and handling prey, fight and recovery) have time duration, the probabilities of predator activities depend on the encounter probabilities, and hence on the prey and predator abundance, too. Under these conditions, the aim of the study is to introduce a functional response for fighting the predator and to analyse the corresponding dynamics, when predator-predator-prey encounters also occur. From this general approach, the Holling type functional responses can also be obtained as particular cases. In terms of the activity distribution, we give biologically interpretable sufficient conditions for stable coexistence. We consider two-individual (predator-prey) and three-individual (predator-predator-prey) encounters. In the three-individual encounter model there is a relatively higher fighting rate and a lower killing rate. Using numerical simulation, we surprisingly found that when the intrinsic prey growth rate and the conversion rate are small enough, the equilibrium predator abundance is higher in the three-individual encounter case. The above means that, when the equilibrium abundance of the predator is small, coexistence appears first in the three-individual encounter model. Copyright © 2014 Elsevier Ltd. All rights reserved.

Time-Series INSAR: An Integer Least-Squares Approach For Distributed Scatterers

NASA Astrophysics Data System (ADS)

Samiei-Esfahany, Sami; Hanssen, Ramon F.

2012-01-01

The objective of this research is to extend the geode- tic mathematical model which was developed for persistent scatterers to a model which can exploit distributed scatterers (DS). The main focus is on the integer least- squares framework, and the main challenge is to include the decorrelation effect in the mathematical model. In order to adapt the integer least-squares mathematical model for DS we altered the model from a single master to a multi-master configuration and introduced the decorrelation effect stochastically. This effect is described in our model by a full covariance matrix. We propose to de- rive this covariance matrix by numerical integration of the (joint) probability distribution function (PDF) of interferometric phases. This PDF is a function of coherence values and can be directly computed from radar data. We show that the use of this model can improve the performance of temporal phase unwrapping of distributed scatterers.

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

PubMed

Wu, Wei; Wang, Jin

2013-09-28

We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is found to be a Lyapunov functional of the deterministic spatially dependent system. Therefore, the intrinsic potential landscape can characterize the global stability of the deterministic system. The relative entropy functional of the stochastic spatially dependent non-equilibrium system is found to be the Lyapunov functional of the stochastic dynamics of the system. Therefore, the relative entropy functional quantifies the global stability of the stochastic system with finite fluctuations. Our theory offers an alternative general approach to other field-theoretic techniques, to study the global stability and dynamics of spatially dependent non-equilibrium field systems. It can be applied to many physical, chemical, and biological spatially dependent non-equilibrium systems.