Stretched exponential distributions in nature and economy: ``fat tails'' with characteristic scales

NASA Astrophysics Data System (ADS)

Laherrère, J.; Sornette, D.

1998-04-01

To account quantitatively for many reported "natural" fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power law distributions. It has many advantages, among which to be economical with only two adjustable parameters with clear physical interpretation. Furthermore, it derives from a simple and generic mechanism in terms of multiplicative processes. We show that stretched exponentials describe very well the distributions of radio and light emissions from galaxies, of US GOM OCS oilfield reserve sizes, of World, US and French agglomeration sizes, of country population sizes, of daily Forex US-Mark and Franc-Mark price variations, of Vostok (near the south pole) temperature variations over the last 400 000 years, of the Raup-Sepkoski's kill curve and of citations of the most cited physicists in the world. We also discuss its potential for the distribution of earthquake sizes and fault displacements. We suggest physical interpretations of the parameters and provide a short toolkit of the statistical properties of the stretched exponentials. We also provide a comparison with other distributions, such as the shifted linear fractal, the log-normal and the recently introduced parabolic fractal distributions.

A demographic study of the exponential distribution applied to uneven-aged forests

Treesearch

Jeffrey H. Gove

2016-01-01

A demographic approach based on a size-structured version of the McKendrick-Von Foerster equation is used to demonstrate a theoretical link between the population size distribution and the underlying vital rates (recruitment, mortality and diameter growth) for the population of individuals whose diameter distribution is negative exponential. This model supports the...

Exponentiated power Lindley distribution.

PubMed

Ashour, Samir K; Eltehiwy, Mahmoud A

2015-11-01

A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data.

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.

High-Performance Clock Synchronization Algorithms for Distributed Wireless Airborne Computer Networks with Applications to Localization and Tracking of Targets

DTIC Science & Technology

2010-06-01

GMKPF represents a better and more flexible alternative to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ...accurate results relative to GML and EML when the network delays are modeled in terms of a single non-Gaussian/non-exponential distribution or as a...to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ) estimators for clock offset estimation in non-Gaussian or non

New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays.

PubMed

Zhang, Guodong; Zeng, Zhigang; Hu, Junhao

2018-01-01

This paper is concerned with the global exponential dissipativity of memristive inertial neural networks with discrete and distributed time-varying delays. By constructing appropriate Lyapunov-Krasovskii functionals, some new sufficient conditions ensuring global exponential dissipativity of memristive inertial neural networks are derived. Moreover, the globally exponential attractive sets and positive invariant sets are also presented here. In addition, the new proposed results here complement and extend the earlier publications on conventional or memristive neural network dynamical systems. Finally, numerical simulations are given to illustrate the effectiveness of obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Dynamic heterogeneity and conditional statistics of non-Gaussian temperature fluctuations in turbulent thermal convection

NASA Astrophysics Data System (ADS)

He, Xiaozhou; Wang, Yin; Tong, Penger

2018-05-01

Non-Gaussian fluctuations with an exponential tail in their probability density function (PDF) are often observed in nonequilibrium steady states (NESSs) and one does not understand why they appear so often. Turbulent Rayleigh-Bénard convection (RBC) is an example of such a NESS, in which the measured PDF P (δ T ) of temperature fluctuations δ T in the central region of the flow has a long exponential tail. Here we show that because of the dynamic heterogeneity in RBC, the exponential PDF is generated by a convolution of a set of dynamics modes conditioned on a constant local thermal dissipation rate ɛ . The conditional PDF G (δ T |ɛ ) of δ T under a constant ɛ is found to be of Gaussian form and its variance σT2 for different values of ɛ follows an exponential distribution. The convolution of the two distribution functions gives rise to the exponential PDF P (δ T ) . This work thus provides a physical mechanism of the observed exponential distribution of δ T in RBC and also sheds light on the origin of non-Gaussian fluctuations in other NESSs.

A model of canopy photosynthesis incorporating protein distribution through the canopy and its acclimation to light, temperature and CO2

PubMed Central

Johnson, Ian R.; Thornley, John H. M.; Frantz, Jonathan M.; Bugbee, Bruce

2010-01-01

Background and Aims The distribution of photosynthetic enzymes, or nitrogen, through the canopy affects canopy photosynthesis, as well as plant quality and nitrogen demand. Most canopy photosynthesis models assume an exponential distribution of nitrogen, or protein, through the canopy, although this is rarely consistent with experimental observation. Previous optimization schemes to derive the nitrogen distribution through the canopy generally focus on the distribution of a fixed amount of total nitrogen, which fails to account for the variation in both the actual quantity of nitrogen in response to environmental conditions and the interaction of photosynthesis and respiration at similar levels of complexity. Model A model of canopy photosynthesis is presented for C3 and C4 canopies that considers a balanced approach between photosynthesis and respiration as well as plant carbon partitioning. Protein distribution is related to irradiance in the canopy by a flexible equation for which the exponential distribution is a special case. The model is designed to be simple to parameterize for crop, pasture and ecosystem studies. The amount and distribution of protein that maximizes canopy net photosynthesis is calculated. Key Results The optimum protein distribution is not exponential, but is quite linear near the top of the canopy, which is consistent with experimental observations. The overall concentration within the canopy is dependent on environmental conditions, including the distribution of direct and diffuse components of irradiance. Conclusions The widely used exponential distribution of nitrogen or protein through the canopy is generally inappropriate. The model derives the optimum distribution with characteristics that are consistent with observation, so overcoming limitations of using the exponential distribution. Although canopies may not always operate at an optimum, optimization analysis provides valuable insight into plant acclimation to environmental conditions. Protein distribution has implications for the prediction of carbon assimilation, plant quality and nitrogen demand. PMID:20861273

Relationship between Item Responses of Negative Affect Items and the Distribution of the Sum of the Item Scores in the General Population

PubMed Central

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

2016-01-01

Background Several studies have shown that total depressive symptom scores in the general population approximate an exponential pattern, except for the lower end of the distribution. The Center for Epidemiologic Studies Depression Scale (CES-D) consists of 20 items, each of which may take on four scores: “rarely,” “some,” “occasionally,” and “most of the time.” Recently, we reported that the item responses for 16 negative affect items commonly exhibit exponential patterns, except for the level of “rarely,” leading us to hypothesize that the item responses at the level of “rarely” may be related to the non-exponential pattern typical of the lower end of the distribution. To verify this hypothesis, we investigated how the item responses contribute to the distribution of the sum of the item scores. Methods Data collected from 21,040 subjects who had completed the CES-D questionnaire as part of a Japanese national survey were analyzed. To assess the item responses of negative affect items, we used a parameter r, which denotes the ratio of “rarely” to “some” in each item response. The distributions of the sum of negative affect items in various combinations were analyzed using log-normal scales and curve fitting. Results The sum of the item scores approximated an exponential pattern regardless of the combination of items, whereas, at the lower end of the distributions, there was a clear divergence between the actual data and the predicted exponential pattern. At the lower end of the distributions, the sum of the item scores with high values of r exhibited higher scores compared to those predicted from the exponential pattern, whereas the sum of the item scores with low values of r exhibited lower scores compared to those predicted. Conclusions The distributional pattern of the sum of the item scores could be predicted from the item responses of such items. PMID:27806132

Anomalous yet Brownian.

PubMed

Wang, Bo; Anthony, Stephen M; Bae, Sung Chul; Granick, Steve

2009-09-08

We describe experiments using single-particle tracking in which mean-square displacement is simply proportional to time (Fickian), yet the distribution of displacement probability is not Gaussian as should be expected of a classical random walk but, instead, is decidedly exponential for large displacements, the decay length of the exponential being proportional to the square root of time. The first example is when colloidal beads diffuse along linear phospholipid bilayer tubes whose radius is the same as that of the beads. The second is when beads diffuse through entangled F-actin networks, bead radius being less than one-fifth of the actin network mesh size. We explore the relevance to dynamic heterogeneity in trajectory space, which has been extensively discussed regarding glassy systems. Data for the second system might suggest activated diffusion between pores in the entangled F-actin networks, in the same spirit as activated diffusion and exponential tails observed in glassy systems. But the first system shows exceptionally rapid diffusion, nearly as rapid as for identical colloids in free suspension, yet still displaying an exponential probability distribution as in the second system. Thus, although the exponential tail is reminiscent of glassy systems, in fact, these dynamics are exceptionally rapid. We also compare with particle trajectories that are at first subdiffusive but Fickian at the longest measurement times, finding that displacement probability distributions fall onto the same master curve in both regimes. The need is emphasized for experiments, theory, and computer simulation to allow definitive interpretation of this simple and clean exponential probability distribution.

Pattern analysis of total item score and item response of the Kessler Screening Scale for Psychological Distress (K6) in a nationally representative sample of US adults

PubMed Central

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

2017-01-01

Background Several recent studies have shown that total scores on depressive symptom measures in a general population approximate an exponential pattern except for the lower end of the distribution. Furthermore, we confirmed that the exponential pattern is present for the individual item responses on the Center for Epidemiologic Studies Depression Scale (CES-D). To confirm the reproducibility of such findings, we investigated the total score distribution and item responses of the Kessler Screening Scale for Psychological Distress (K6) in a nationally representative study. Methods Data were drawn from the National Survey of Midlife Development in the United States (MIDUS), which comprises four subsamples: (1) a national random digit dialing (RDD) sample, (2) oversamples from five metropolitan areas, (3) siblings of individuals from the RDD sample, and (4) a national RDD sample of twin pairs. K6 items are scored using a 5-point scale: “none of the time,” “a little of the time,” “some of the time,” “most of the time,” and “all of the time.” The pattern of total score distribution and item responses were analyzed using graphical analysis and exponential regression model. Results The total score distributions of the four subsamples exhibited an exponential pattern with similar rate parameters. The item responses of the K6 approximated a linear pattern from “a little of the time” to “all of the time” on log-normal scales, while “none of the time” response was not related to this exponential pattern. Discussion The total score distribution and item responses of the K6 showed exponential patterns, consistent with other depressive symptom scales. PMID:28289560

Investigation of non-Gaussian effects in the Brazilian option market

NASA Astrophysics Data System (ADS)

Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.

2018-04-01

An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.

Calculating Formulae of Proportion Factor and Mean Neutron Exposure in the Exponential Expression of Neutron Exposure Distribution

NASA Astrophysics Data System (ADS)

Feng-Hua, Zhang; Gui-De, Zhou; Kun, Ma; Wen-Juan, Ma; Wen-Yuan, Cui; Bo, Zhang

2016-07-01

Previous studies have shown that, for the three main stages of the development and evolution of asymptotic giant branch (AGB) star s-process models, the neutron exposure distribution (DNE) in the nucleosynthesis region can always be considered as an exponential function, i.e., ρAGB(τ) = C/τ0 exp(-τ/τ0) in an effective range of the neutron exposure values. However, the specific expressions of the proportion factor C and the mean neutron exposure τ0 in the exponential distribution function for different models are not completely determined in the related literature. Through dissecting the basic method to obtain the exponential DNE, and systematically analyzing the solution procedures of neutron exposure distribution functions in different stellar models, the general formulae, as well as their auxiliary equations, for calculating C and τ0 are derived. Given the discrete neutron exposure distribution Pk, the relationships of C and τ0 with the model parameters can be determined. The result of this study has effectively solved the problem to analytically calculate the DNE in the current low-mass AGB star s-process nucleosynthesis model of 13C-pocket radiative burning.

Scaling in the distribution of intertrade durations of Chinese stocks

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Chen, Wei; Zhou, Wei-Xing

2008-10-01

The distribution of intertrade durations, defined as the waiting times between two consecutive transactions, is investigated based upon the limit order book data of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. A scaling pattern is observed in the distributions of intertrade durations, where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve. The scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions. The ensemble distributions for all stocks are modeled by the Weibull and the Tsallis q-exponential distributions. Maximum likelihood estimation shows that the Weibull distribution outperforms the q-exponential for not-too-large intertrade durations which account for more than 98.5% of the data. Alternatively, nonlinear least-squares estimation selects the q-exponential as a better model, in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities. The distribution of intertrade durations is Weibull followed by a power-law tail with an asymptotic tail exponent close to 3.

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,

The size distribution of Pacific Seamounts

NASA Astrophysics Data System (ADS)

Smith, Deborah K.; Jordan, Thomas H.

1987-11-01

An analysis of wide-beam, Sea Beam and map-count data in the eastern and southern Pacific confirms the hypothesis that the average number of "ordinary" seamounts with summit heights h ≥ H can be approximated by the exponential frequency-size distribution: v(H) = vo e-βH. The exponential model, characterized by the single scale parameter β-1, is found to be superior to a power-law (self-similar) model. The exponential model provides a good first-order description of the summit-height distribution over a very broad spectrum of seamount sizes, from small cones (h < 300 m) to tall composite volcanoes (h > 3500 m). The distribution parameters obtained from 157,000 km of wide-beam profiles in the eastern and southern Pacific Ocean are vo = (5.4 ± 0.65) × 10-9m-2 and β = (3.5 ± 0.21) × 10-3 m-1, yielding an average of 5400 ± 650 seamounts per million square kilometers, of which 170 ± 17 are greater than one kilometer in height. The exponential distribution provides a reference for investigating the populations of not-so-ordinary seamounts, such as those on hotspot swells and near fracture zones, and seamounts in other ocean basins. If we assume that volcano height is determined by a hydraulic head proportional to the source depth of the magma column, then our observations imply an approximately exponential distribution of source depths. For reasonable values of magma and crustal densities, a volcano with the characteristic height β-1 = 285 m has an apparent source depth on the order of the crustal thickness.

A mechanism producing power law etc. distributions

NASA Astrophysics Data System (ADS)

Li, Heling; Shen, Hongjun; Yang, Bin

2017-07-01

Power law distribution is playing an increasingly important role in the complex system study. Based on the insolvability of complex systems, the idea of incomplete statistics is utilized and expanded, three different exponential factors are introduced in equations about the normalization condition, statistical average and Shannon entropy, with probability distribution function deduced about exponential function, power function and the product form between power function and exponential function derived from Shannon entropy and maximal entropy principle. So it is shown that maximum entropy principle can totally replace equal probability hypothesis. Owing to the fact that power and probability distribution in the product form between power function and exponential function, which cannot be derived via equal probability hypothesis, can be derived by the aid of maximal entropy principle, it also can be concluded that maximal entropy principle is a basic principle which embodies concepts more extensively and reveals basic principles on motion laws of objects more fundamentally. At the same time, this principle also reveals the intrinsic link between Nature and different objects in human society and principles complied by all.

Extended q -Gaussian and q -exponential distributions from gamma random variables

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2015-05-01

The family of q -Gaussian and q -exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q -Gaussian and q -exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q -Gaussian and modified q -exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.

Not all nonnormal distributions are created equal: Improved theoretical and measurement precision.

PubMed

Joo, Harry; Aguinis, Herman; Bradley, Kyle J

2017-07-01

We offer a four-category taxonomy of individual output distributions (i.e., distributions of cumulative results): (1) pure power law; (2) lognormal; (3) exponential tail (including exponential and power law with an exponential cutoff); and (4) symmetric or potentially symmetric (including normal, Poisson, and Weibull). The four categories are uniquely associated with mutually exclusive generative mechanisms: self-organized criticality, proportionate differentiation, incremental differentiation, and homogenization. We then introduce distribution pitting, a falsification-based method for comparing distributions to assess how well each one fits a given data set. In doing so, we also introduce decision rules to determine the likely dominant shape and generative mechanism among many that may operate concurrently. Next, we implement distribution pitting using 229 samples of individual output for several occupations (e.g., movie directors, writers, musicians, athletes, bank tellers, call center employees, grocery checkers, electrical fixture assemblers, and wirers). Results suggest that for 75% of our samples, exponential tail distributions and their generative mechanism (i.e., incremental differentiation) likely constitute the dominant distribution shape and explanation of nonnormally distributed individual output. This finding challenges past conclusions indicating the pervasiveness of other types of distributions and their generative mechanisms. Our results further contribute to theory by offering premises about the link between past and future individual output. For future research, our taxonomy and methodology can be used to pit distributions of other variables (e.g., organizational citizenship behaviors). Finally, we offer practical insights on how to increase overall individual output and produce more top performers. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Square Root Graphical Models: Multivariate Generalizations of Univariate Exponential Families that Permit Positive Dependencies

PubMed Central

Inouye, David I.; Ravikumar, Pradeep; Dhillon, Inderjit S.

2016-01-01

We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models (Yang et al., 2015) did not allow positive dependencies for the exponential and Poisson generalizations. However, in many real-world datasets, variables clearly have positive dependencies. For example, the airport delay time in New York—modeled as an exponential distribution—is positively related to the delay time in Boston. With this motivation, we give an example of our model class derived from the univariate exponential distribution that allows for almost arbitrary positive and negative dependencies with only a mild condition on the parameter matrix—a condition akin to the positive definiteness of the Gaussian covariance matrix. Our Poisson generalization allows for both positive and negative dependencies without any constraints on the parameter values. We also develop parameter estimation methods using node-wise regressions with ℓ1 regularization and likelihood approximation methods using sampling. Finally, we demonstrate our exponential generalization on a synthetic dataset and a real-world dataset of airport delay times. PMID:27563373

Universality in stochastic exponential growth.

PubMed

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Universality in Stochastic Exponential Growth

NASA Astrophysics Data System (ADS)

Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.

2014-07-01

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Conditional optimal spacing in exponential distribution.

PubMed

Park, Sangun

2006-12-01

In this paper, we propose the conditional optimal spacing defined as the optimal spacing after specifying a predetermined order statistic. If we specify a censoring time, then the optimal inspection times for grouped inspection can be determined from this conditional optimal spacing. We take an example of exponential distribution, and provide a simple method of finding the conditional optimal spacing.

Reliability and sensitivity analysis of a system with multiple unreliable service stations and standby switching failures

NASA Astrophysics Data System (ADS)

Ke, Jyh-Bin; Lee, Wen-Chiung; Wang, Kuo-Hsiung

2007-07-01

This paper presents the reliability and sensitivity analysis of a system with M primary units, W warm standby units, and R unreliable service stations where warm standby units switching to the primary state might fail. Failure times of primary and warm standby units are assumed to have exponential distributions, and service times of the failed units are exponentially distributed. In addition, breakdown times and repair times of the service stations also follow exponential distributions. Expressions for system reliability, RY(t), and mean time to system failure, MTTF are derived. Sensitivity analysis, relative sensitivity analysis of the system reliability and the mean time to failure, with respect to system parameters are also investigated.

Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution.

PubMed

Rigby, Robert A; Stasinopoulos, D Mikis

2004-10-15

The Box-Cox power exponential (BCPE) distribution, developed in this paper, provides a model for a dependent variable Y exhibiting both skewness and kurtosis (leptokurtosis or platykurtosis). The distribution is defined by a power transformation Y(nu) having a shifted and scaled (truncated) standard power exponential distribution with parameter tau. The distribution has four parameters and is denoted BCPE (mu,sigma,nu,tau). The parameters, mu, sigma, nu and tau, may be interpreted as relating to location (median), scale (approximate coefficient of variation), skewness (transformation to symmetry) and kurtosis (power exponential parameter), respectively. Smooth centile curves are obtained by modelling each of the four parameters of the distribution as a smooth non-parametric function of an explanatory variable. A Fisher scoring algorithm is used to fit the non-parametric model by maximizing a penalized likelihood. The first and expected second and cross derivatives of the likelihood, with respect to mu, sigma, nu and tau, required for the algorithm, are provided. The centiles of the BCPE distribution are easy to calculate, so it is highly suited to centile estimation. This application of the BCPE distribution to smooth centile estimation provides a generalization of the LMS method of the centile estimation to data exhibiting kurtosis (as well as skewness) different from that of a normal distribution and is named here the LMSP method of centile estimation. The LMSP method of centile estimation is applied to modelling the body mass index of Dutch males against age. 2004 John Wiley & Sons, Ltd.

Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping.

PubMed

Salje, Ekhard K H; Planes, Antoni; Vives, Eduard

2017-10-01

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.

The shock waves in decaying supersonic turbulence

NASA Astrophysics Data System (ADS)

Smith, M. D.; Mac Low, M.-M.; Zuev, J. M.

2000-04-01

We here analyse numerical simulations of supersonic, hypersonic and magnetohydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock waves produced. This will be useful for interpretation of observations of both motions in molecular clouds and sources of non-thermal radiation. We find that decaying hypersonic turbulence possesses an exponential tail of fast shocks and an exponential decay in time, i.e. the number of shocks is proportional to t exp (-ktv) for shock velocity jump v and mean initial wavenumber k. In contrast to the velocity gradients, the velocity Probability Distribution Function remains Gaussian with a more complex decay law. The energy is dissipated not by fast shocks but by a large number of low Mach number shocks. The power loss peaks near a low-speed turn-over in an exponential distribution. An analytical extension of the mapping closure technique is able to predict the basic decay features. Our analytic description of the distribution of shock strengths should prove useful for direct modeling of observable emission. We note that an exponential distribution of shocks such as we find will, in general, generate very low excitation shock signatures.

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

USGS Publications Warehouse

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

2012-01-01

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

Universal patterns of inequality

NASA Astrophysics Data System (ADS)

Banerjee, Anand; Yakovenko, Victor M.

2010-07-01

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

Study on probability distributions for evolution in modified extremal optimization

NASA Astrophysics Data System (ADS)

Zeng, Guo-Qiang; Lu, Yong-Zai; Mao, Wei-Jie; Chu, Jian

2010-05-01

It is widely believed that the power-law is a proper probability distribution being effectively applied for evolution in τ-EO (extremal optimization), a general-purpose stochastic local-search approach inspired by self-organized criticality, and its applications in some NP-hard problems, e.g., graph partitioning, graph coloring, spin glass, etc. In this study, we discover that the exponential distributions or hybrid ones (e.g., power-laws with exponential cutoff) being popularly used in the research of network sciences may replace the original power-laws in a modified τ-EO method called self-organized algorithm (SOA), and provide better performances than other statistical physics oriented methods, such as simulated annealing, τ-EO and SOA etc., from the experimental results on random Euclidean traveling salesman problems (TSP) and non-uniform instances. From the perspective of optimization, our results appear to demonstrate that the power-law is not the only proper probability distribution for evolution in EO-similar methods at least for TSP, the exponential and hybrid distributions may be other choices.

A fractal process of hydrogen diffusion in a-Si:H with exponential energy distribution

NASA Astrophysics Data System (ADS)

Hikita, Harumi; Ishikawa, Hirohisa; Morigaki, Kazuo

2017-04-01

Hydrogen diffusion in a-Si:H with exponential distribution of the states in energy exhibits the fractal structure. It is shown that a probability P(t) of the pausing time t has a form of tα (α: fractal dimension). It is shown that the fractal dimension α = Tr/T0 (Tr: hydrogen temperature, T0: a temperature corresponding to the width of exponential distribution of the states in energy) is in agreement with the Hausdorff dimension. A fractal graph for the case of α ≤ 1 is like the Cantor set. A fractal graph for the case of α > 1 is like the Koch curves. At α = ∞, hydrogen migration exhibits Brownian motion. Hydrogen diffusion in a-Si:H should be the fractal process.

Photocounting distributions for exponentially decaying sources.

PubMed

Teich, M C; Card, H C

1979-05-01

Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model.

Weblog patterns and human dynamics with decreasing interest

NASA Astrophysics Data System (ADS)

Guo, J.-L.; Fan, C.; Guo, Z.-H.

2011-06-01

In order to describe the phenomenon that people's interest in doing something always keep high in the beginning while gradually decreases until reaching the balance, a model which describes the attenuation of interest is proposed to reflect the fact that people's interest becomes more stable after a long time. We give a rigorous analysis on this model by non-homogeneous Poisson processes. Our analysis indicates that the interval distribution of arrival-time is a mixed distribution with exponential and power-law feature, which is a power law with an exponential cutoff. After that, we collect blogs in ScienceNet.cn and carry on empirical study on the interarrival time distribution. The empirical results agree well with the theoretical analysis, obeying a special power law with the exponential cutoff, that is, a special kind of Gamma distribution. These empirical results verify the model by providing an evidence for a new class of phenomena in human dynamics. It can be concluded that besides power-law distributions, there are other distributions in human dynamics. These findings demonstrate the variety of human behavior dynamics.

Three-Dimensional Flow of Nanofluid Induced by an Exponentially Stretching Sheet: An Application to Solar Energy

PubMed Central

Khan, Junaid Ahmad; Mustafa, M.; Hayat, T.; Sheikholeslami, M.; Alsaedi, A.

2015-01-01

This work deals with the three-dimensional flow of nanofluid over a bi-directional exponentially stretching sheet. The effects of Brownian motion and thermophoretic diffusion of nanoparticles are considered in the mathematical model. The temperature and nanoparticle volume fraction at the sheet are also distributed exponentially. Local similarity solutions are obtained by an implicit finite difference scheme known as Keller-box method. The results are compared with the existing studies in some limiting cases and found in good agreement. The results reveal the existence of interesting Sparrow-Gregg-type hills for temperature distribution corresponding to some range of parametric values. PMID:25785857

Velocity distributions of granular gases with drag and with long-range interactions.

PubMed

Kohlstedt, K; Snezhko, A; Sapozhnikov, M V; Aranson, I S; Olafsen, J S; Ben-Naim, E

2005-08-05

We study velocity statistics of electrostatically driven granular gases. For two different experiments, (i) nonmagnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(upsilon) approximately exp(-/upsilon/). This behavior is consistent with the kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.

Exponential order statistic models of software reliability growth

NASA Technical Reports Server (NTRS)

Miller, D. R.

1985-01-01

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

A spatial scan statistic for survival data based on Weibull distribution.

PubMed

Bhatt, Vijaya; Tiwari, Neeraj

2014-05-20

The spatial scan statistic has been developed as a geographical cluster detection analysis tool for different types of data sets such as Bernoulli, Poisson, ordinal, normal and exponential. We propose a scan statistic for survival data based on Weibull distribution. It may also be used for other survival distributions, such as exponential, gamma, and log normal. The proposed method is applied on the survival data of tuberculosis patients for the years 2004-2005 in Nainital district of Uttarakhand, India. Simulation studies reveal that the proposed method performs well for different survival distribution functions. Copyright © 2013 John Wiley & Sons, Ltd.

Discrete Time Rescaling Theorem: Determining Goodness of Fit for Discrete Time Statistical Models of Neural Spiking

PubMed Central

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-01-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time rescaling theorem provides a goodness of fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model’s spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies upon assumptions of continuously defined time and instantaneous events. However spikes have finite width and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time rescaling theorem which analytically corrects for the effects of finite resolution. This allows us to define a rescaled time which is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting Generalized Linear Models (GLMs) to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false positive rate of the KS test and greatly increasing the reliability of model evaluation based upon the time rescaling theorem. PMID:20608868

Discrete time rescaling theorem: determining goodness of fit for discrete time statistical models of neural spiking.

PubMed

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-10-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model's spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies on assumptions of continuously defined time and instantaneous events. However, spikes have finite width, and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time-rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time-rescaling theorem that analytically corrects for the effects of finite resolution. This allows us to define a rescaled time that is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting generalized linear models to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false-positive rate of the KS test and greatly increasing the reliability of model evaluation based on the time-rescaling theorem.

Discrete Deterministic and Stochastic Petri Nets

NASA Technical Reports Server (NTRS)

Zijal, Robert; Ciardo, Gianfranco

1996-01-01

Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.

Exponential blocking-temperature distribution in ferritin extracted from magnetization measurements

NASA Astrophysics Data System (ADS)

Lee, T. H.; Choi, K.-Y.; Kim, G.-H.; Suh, B. J.; Jang, Z. H.

2014-11-01

We developed a direct method to extract the zero-field zero-temperature anisotropy energy barrier distribution of magnetic particles in the form of a blocking-temperature distribution. The key idea is to modify measurement procedures slightly to make nonequilibrium magnetization calculations (including the time evolution of magnetization) easier. We applied this method to the biomagnetic molecule ferritin and successfully reproduced field-cool magnetization by using the extracted distribution. We find that the resulting distribution is more like an exponential type and that the distribution cannot be correlated simply to the widely known log-normal particle-size distribution. The method also allows us to determine the values of the zero-temperature coercivity and Bloch coefficient, which are in good agreement with those determined from other techniques.

AN EMPIRICAL FORMULA FOR THE DISTRIBUTION FUNCTION OF A THIN EXPONENTIAL DISC

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

Sharma, Sanjib; Bland-Hawthorn, Joss

2013-08-20

An empirical formula for a Shu distribution function that reproduces a thin disc with exponential surface density to good accuracy is presented. The formula has two free parameters that specify the functional form of the velocity dispersion. Conventionally, this requires the use of an iterative algorithm to produce the correct solution, which is computationally taxing for applications like Markov Chain Monte Carlo model fitting. The formula has been shown to work for flat, rising, and falling rotation curves. Application of this methodology to one of the Dehnen distribution functions is also shown. Finally, an extension of this formula to reproducemore » velocity dispersion profiles that are an exponential function of radius is also presented. Our empirical formula should greatly aid the efficient comparison of disc models with large stellar surveys or N-body simulations.« less

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

Parameter estimation for the exponential-normal convolution model for background correction of affymetrix GeneChip data.

PubMed

McGee, Monnie; Chen, Zhongxue

2006-01-01

There are many methods of correcting microarray data for non-biological sources of error. Authors routinely supply software or code so that interested analysts can implement their methods. Even with a thorough reading of associated references, it is not always clear how requisite parts of the method are calculated in the software packages. However, it is important to have an understanding of such details, as this understanding is necessary for proper use of the output, or for implementing extensions to the model. In this paper, the calculation of parameter estimates used in Robust Multichip Average (RMA), a popular preprocessing algorithm for Affymetrix GeneChip brand microarrays, is elucidated. The background correction method for RMA assumes that the perfect match (PM) intensities observed result from a convolution of the true signal, assumed to be exponentially distributed, and a background noise component, assumed to have a normal distribution. A conditional expectation is calculated to estimate signal. Estimates of the mean and variance of the normal distribution and the rate parameter of the exponential distribution are needed to calculate this expectation. Simulation studies show that the current estimates are flawed; therefore, new ones are suggested. We examine the performance of preprocessing under the exponential-normal convolution model using several different methods to estimate the parameters.

Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

1/f oscillations in a model of moth populations oriented by diffusive pheromones

NASA Astrophysics Data System (ADS)

Barbosa, L. A.; Martins, M. L.; Lima, E. R.

2005-01-01

An individual-based model for the population dynamics of Spodoptera frugiperda in a homogeneous environment is proposed. The model involves moths feeding plants, mating through an anemotaxis search (i.e., oriented by odor dispersed in a current of air), and dying due to resource competition or at a maximum age. As observed in the laboratory, the females release pheromones at exponentially distributed time intervals, and it is assumed that the ranges of the male flights follow a power-law distribution. Computer simulations of the model reveal the central role of anemotaxis search for the persistence of moth population. Such stationary populations are exponentially distributed in age, exhibit random temporal fluctuations with 1/f spectrum, and self-organize in disordered spatial patterns with long-range correlations. In addition, the model results demonstrate that pest control through pheromone mass trapping is effective only if the amounts of pheromone released by the traps decay much slower than the exponential distribution for calling female.

A study on some urban bus transport networks

NASA Astrophysics Data System (ADS)

Chen, Yong-Zhou; Li, Nan; He, Da-Ren

2007-03-01

In this paper, we present the empirical investigation results on the urban bus transport networks (BTNs) of four major cities in China. In BTN, nodes are bus stops. Two nodes are connected by an edge when the stops are serviced by a common bus route. The empirical results show that the degree distributions of BTNs take exponential function forms. Other two statistical properties of BTNs are also considered, and they are suggested as the distributions of so-called “the number of stops in a bus route” (represented by S) and “the number of bus routes a stop joins” (by R). The distributions of R also show exponential function forms, while the distributions of S follow asymmetric, unimodal functions. To explain these empirical results and attempt to simulate a possible evolution process of BTN, we introduce a model by which the analytic and numerical result obtained agrees well with the empirical facts. Finally, we also discuss some other possible evolution cases, where the degree distribution shows a power law or an interpolation between the power law and the exponential decay.

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.

A Decreasing Failure Rate, Mixed Exponential Model Applied to Reliability.

DTIC Science & Technology

1981-06-01

Trident missile systems have been observed. The mixed exponential distribu- tion has been shown to fit the life data for the electronic equipment on...these systems . This paper discusses some of the estimation problems which occur with the decreasing failure rate mixed exponential distribution when...assumption of constant or increasing failure rate seemed to be incorrect. 2. However, the design of this electronic equipment indicated that

Analysis of the Chinese air route network as a complex network

NASA Astrophysics Data System (ADS)

Cai, Kai-Quan; Zhang, Jun; Du, Wen-Bo; Cao, Xian-Bin

2012-02-01

The air route network, which supports all the flight activities of the civil aviation, is the most fundamental infrastructure of air traffic management system. In this paper, we study the Chinese air route network (CARN) within the framework of complex networks. We find that CARN is a geographical network possessing exponential degree distribution, low clustering coefficient, large shortest path length and exponential spatial distance distribution that is obviously different from that of the Chinese airport network (CAN). Besides, via investigating the flight data from 2002 to 2010, we demonstrate that the topology structure of CARN is homogeneous, howbeit the distribution of flight flow on CARN is rather heterogeneous. In addition, the traffic on CARN keeps growing in an exponential form and the increasing speed of west China is remarkably larger than that of east China. Our work will be helpful to better understand Chinese air traffic systems.

Colloquium: Statistical mechanics of money, wealth, and income

NASA Astrophysics Data System (ADS)

Yakovenko, Victor M.; Rosser, J. Barkley, Jr.

2009-10-01

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.

Evidence for a scale-limited low-frequency earthquake source process

NASA Astrophysics Data System (ADS)

Chestler, S. R.; Creager, K. C.

2017-04-01

We calculate the seismic moments for 34,264 low-frequency earthquakes (LFEs) beneath the Olympic Peninsula, Washington. LFE moments range from 1.4 × 1010 to 1.9 × 1012 N m (Mw = 0.7-2.1). While regular earthquakes follow a power law moment-frequency distribution with a b value near 1 (the number of events increases by a factor of 10 for each unit increase in Mw), we find that while for large LFEs the b value is 6, for small LFEs it is <1. The magnitude-frequency distribution for all LFEs is best fit by an exponential distribution with a mean seismic moment (characteristic moment) of 2.0 × 1011 N m. The moment-frequency distributions for each of the 43 LFE families, or spots on the plate interface where LFEs repeat, can also be fit by exponential distributions. An exponential moment-frequency distribution implies a scale-limited source process. We consider two end-member models where LFE moment is limited by (1) the amount of slip or (2) slip area. We favor the area-limited model. Based on the observed exponential distribution of LFE moment and geodetically observed total slip, we estimate that the total area that slips within an LFE family has a diameter of 300 m. Assuming an area-limited model, we estimate the slips, subpatch diameters, stress drops, and slip rates for LFEs during episodic tremor and slip events. We allow for LFEs to rupture smaller subpatches within the LFE family patch. Models with 1-10 subpatches produce slips of 0.1-1 mm, subpatch diameters of 80-275 m, and stress drops of 30-1000 kPa. While one subpatch is often assumed, we believe 3-10 subpatches are more likely.

Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model.

PubMed

Bennett, Kevin M; Schmainda, Kathleen M; Bennett, Raoqiong Tong; Rowe, Daniel B; Lu, Hanbing; Hyde, James S

2003-10-01

Experience with diffusion-weighted imaging (DWI) shows that signal attenuation is consistent with a multicompartmental theory of water diffusion in the brain. The source of this so-called nonexponential behavior is a topic of debate, because the cerebral cortex contains considerable microscopic heterogeneity and is therefore difficult to model. To account for this heterogeneity and understand its implications for current models of diffusion, a stretched-exponential function was developed to describe diffusion-related signal decay as a continuous distribution of sources decaying at different rates, with no assumptions made about the number of participating sources. DWI experiments were performed using a spin-echo diffusion-weighted pulse sequence with b-values of 500-6500 s/mm(2) in six rats. Signal attenuation curves were fit to a stretched-exponential function, and 20% of the voxels were better fit to the stretched-exponential model than to a biexponential model, even though the latter model had one more adjustable parameter. Based on the calculated intravoxel heterogeneity measure, the cerebral cortex contains considerable heterogeneity in diffusion. The use of a distributed diffusion coefficient (DDC) is suggested to measure mean intravoxel diffusion rates in the presence of such heterogeneity. Copyright 2003 Wiley-Liss, Inc.

The dynamics of photoinduced defect creation in amorphous chalcogenides: The origin of the stretched exponential function

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

Freitas, R. J.; Shimakawa, K.; Department of Electrical and Electronic Engineering, Gifu University, Gifu 501-1193

The article discusses the dynamics of photoinduced defect creations (PDC) in amorphous chalcogenides, which is described by the stretched exponential function (SEF), while the well known photodarkening (PD) and photoinduced volume expansion (PVE) are governed only by the exponential function. It is shown that the exponential distribution of the thermal activation barrier produces the SEF in PDC, suggesting that thermal energy, as well as photon energy, is incorporated in PDC mechanisms. The differences in dynamics among three major photoinduced effects (PD, PVE, and PDC) in amorphous chalcogenides are now well understood.

Global exponential stability of bidirectional associative memory neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Song, Qiankun; Cao, Jinde

2007-05-01

A bidirectional associative memory neural network model with distributed delays is considered. By constructing a new Lyapunov functional, employing the homeomorphism theory, M-matrix theory and the inequality (a[greater-or-equal, slanted]0,bk[greater-or-equal, slanted]0,qk>0 with , and r>1), a sufficient condition is obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the model. Moreover, the exponential converging velocity index is estimated, which depends on the delay kernel functions and the system parameters. The results generalize and improve the earlier publications, and remove the usual assumption that the activation functions are bounded . Two numerical examples are given to show the effectiveness of the obtained results.

Income inequality in Romania: The exponential-Pareto distribution

NASA Astrophysics Data System (ADS)

Oancea, Bogdan; Andrei, Tudorel; Pirjol, Dan

2017-03-01

We present a study of the distribution of the gross personal income and income inequality in Romania, using individual tax income data, and both non-parametric and parametric methods. Comparing with official results based on household budget surveys (the Family Budgets Survey and the EU-SILC data), we find that the latter underestimate the income share of the high income region, and the overall income inequality. A parametric study shows that the income distribution is well described by an exponential distribution in the low and middle incomes region, and by a Pareto distribution in the high income region with Pareto coefficient α = 2.53. We note an anomaly in the distribution in the low incomes region (∼9,250 RON), and present a model which explains it in terms of partial income reporting.

On the q-type distributions

NASA Astrophysics Data System (ADS)

Nadarajah, Saralees; Kotz, Samuel

2007-04-01

Various q-type distributions have appeared in the physics literature in the recent years, see e.g. L.C. Malacarne, R.S. Mendes, E. K. Lenzi, q-exponential distribution in urban agglomeration, Phys. Rev. E 65, (2002) 017106. S.M.D. Queiros, On a possible dynamical scenario leading to a generalised Gamma distribution, in xxx.lanl.gov-physics/0411111. U.M.S. Costa, V.N. Freire, L.C. Malacarne, R.S. Mendes, S. Picoli Jr., E.A. de Vasconcelos, E.F. da Silva Jr., An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution, Physica A 361, (2006) 215. S. Picoli, Jr., R.S. Mendes, L.C. Malacarne, q-exponential, Weibull, and q-Weibull distributions: an empirical analysis, Physica A 324 (2003) 678-688. A.M.C. de Souza, C. Tsallis, Student's t- and r- distributions: unified derivation from an entropic variational principle, Physica A 236 (1997) 52-57. It is pointed out in the paper that many of these are the same as or particular cases of what has been known in the statistics literature. Several of these statistical distributions are discussed and references provided. We feel that this paper could be of assistance for modeling problems of the type considered by L.C. Malacarne, R.S. Mendes, E. K. Lenzi, q-exponential distribution in urban agglomeration, Phys. Rev. E 65, (2002) 017106. S.M.D. Queiros, On a possible dynamical scenario leading to a generalised Gamma distribution, in xxx.lanl.gov-physics/0411111. U.M.S. Costa, V.N. Freire, L.C. Malacarne, R.S. Mendes, S. Picoli Jr., E.A. de Vasconcelos, E.F. da Silva Jr., An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution, Physica A 361, (2006) 215. S. Picoli, Jr., R.S. Mendes, L.C. Malacarne, q-exponential, Weibull, and q-Weibull distributions: an empirical analysis, Physica A 324 (2003) 678-688. A.M.C. de Souza, C. Tsallis, Student's t- and r- distributions: unified derivation from an entropic variational principle, Physica A 236 (1997) 52-57 and others.

Role of the locus coeruleus in the emergence of power law wake bouts in a model of the brainstem sleep-wake system through early infancy.

PubMed

Patel, Mainak; Rangan, Aaditya

2017-08-07

Infant rats randomly cycle between the sleeping and waking states, which are tightly correlated with the activity of mutually inhibitory brainstem sleep and wake populations. Bouts of sleep and wakefulness are random; from P2-P10, sleep and wake bout lengths are exponentially distributed with increasing means, while during P10-P21, the sleep bout distribution remains exponential while the distribution of wake bouts gradually transforms to power law. The locus coeruleus (LC), via an undeciphered interaction with sleep and wake populations, has been shown experimentally to be responsible for the exponential to power law transition. Concurrently during P10-P21, the LC undergoes striking physiological changes - the LC exhibits strong global 0.3 Hz oscillations up to P10, but the oscillation frequency gradually rises and synchrony diminishes from P10-P21, with oscillations and synchrony vanishing at P21 and beyond. In this work, we construct a biologically plausible Wilson Cowan-style model consisting of the LC along with sleep and wake populations. We show that external noise and strong reciprocal inhibition can lead to switching between sleep and wake populations and exponentially distributed sleep and wake bout durations as during P2-P10, with the parameters of inhibition between the sleep and wake populations controlling mean bout lengths. Furthermore, we show that the changing physiology of the LC from P10-P21, coupled with reciprocal excitation between the LC and wake population, can explain the shift from exponential to power law of the wake bout distribution. To our knowledge, this is the first study that proposes a plausible biological mechanism, which incorporates the known changing physiology of the LC, for tying the developing sleep-wake circuit and its interaction with the LC to the transformation of sleep and wake bout dynamics from P2-P21. Copyright © 2017 Elsevier Ltd. All rights reserved.

Statistical mechanics of money and income

NASA Astrophysics Data System (ADS)

Dragulescu, Adrian; Yakovenko, Victor

2001-03-01

Money: In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money will assume the exponential Boltzmann-Gibbs form characterized by an effective temperature. We demonstrate how the Boltzmann-Gibbs distribution emerges in computer simulations of economic models. We discuss thermal machines, the role of debt, and models with broken time-reversal symmetry for which the Boltzmann-Gibbs law does not hold. Reference: A. Dragulescu and V. M. Yakovenko, "Statistical mechanics of money", Eur. Phys. J. B 17, 723-729 (2000), [cond-mat/0001432]. Income: Using tax and census data, we demonstrate that the distribution of individual income in the United States is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data. We derive the distribution function of income for families with two earners and show that it also agrees well with the data. The family data for the period 1947-1994 fit the Lorenz curve and Gini coefficient 3/8=0.375 calculated for two-earners families. Reference: A. Dragulescu and V. M. Yakovenko, "Evidence for the exponential distribution of income in the USA", cond-mat/0008305.

Heavy tailed bacterial motor switching statistics define macroscopic transport properties during upstream contamination by E. coli

NASA Astrophysics Data System (ADS)

Figueroa-Morales, N.; Rivera, A.; Altshuler, E.; Darnige, T.; Douarche, C.; Soto, R.; Lindner, A.; Clément, E.

The motility of E. Coli bacteria is described as a run and tumble process. Changes of direction correspond to a switch in the flagellar motor rotation. The run time distribution is described as an exponential decay of characteristic time close to 1s. Remarkably, it has been demonstrated that the generic response for the distribution of run times is not exponential, but a heavy tailed power law decay, which is at odds with the motility findings. We investigate the consequences of the motor statistics in the macroscopic bacterial transport. During upstream contamination processes in very confined channels, we have identified very long contamination tongues. Using a stochastic model considering bacterial dwelling times on the surfaces related to the run times, we are able to reproduce qualitatively and quantitatively the evolution of the contamination profiles when considering the power law run time distribution. However, the model fails to reproduce the qualitative dynamics when the classical exponential run and tumble distribution is considered. Moreover, we have corroborated the existence of a power law run time distribution by means of 3D Lagrangian tracking. We then argue that the macroscopic transport of bacteria is essentially determined by the motor rotation statistics.

Redshift data and statistical inference

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Human mobility in space from three modes of public transportation

NASA Astrophysics Data System (ADS)

Jiang, Shixiong; Guan, Wei; Zhang, Wenyi; Chen, Xu; Yang, Liu

2017-10-01

The human mobility patterns have drew much attention from researchers for decades, considering about its importance for urban planning and traffic management. In this study, the taxi GPS trajectories, smart card transaction data of subway and bus from Beijing are utilized to model human mobility in space. The original datasets are cleaned and processed to attain the displacement of each trip according to the origin and destination locations. Then, the Akaike information criterion is adopted to screen out the best fitting distribution for each mode from candidate ones. The results indicate that displacements of taxi trips follow the exponential distribution. Besides, the exponential distribution also fits displacements of bus trips well. However, their exponents are significantly different. Displacements of subway trips show great specialties and can be well fitted by the gamma distribution. It is obvious that human mobility of each mode is different. To explore the overall human mobility, the three datasets are mixed up to form a fusion dataset according to the annual ridership proportions. Finally, the fusion displacements follow the power-law distribution with an exponential cutoff. It is innovative to combine different transportation modes to model human mobility in the city.

Voter model with non-Poissonian interevent intervals

NASA Astrophysics Data System (ADS)

Takaguchi, Taro; Masuda, Naoki

2011-09-01

Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a non-Poissonian nature of human behavior on dynamics of opinion formation. We use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks. Compared with the exponential distribution of interevent intervals (i.e., the standard voter model), the power-law distribution of interevent intervals slows down consensus on the ring. This is because of the memory effect; in the power-law case, the expected time until the next update event on a link is large if the link has not had an update event for a long time. On the complete graph, the consensus time in the power-law case is close to that in the exponential case. Regular graphs bridge these two results such that the slowing down of the consensus in the power-law case as compared to the exponential case is less pronounced as the degree increases.

Non-Poissonian Distribution of Tsunami Waiting Times

NASA Astrophysics Data System (ADS)

Geist, E. L.; Parsons, T.

2007-12-01

Analysis of the global tsunami catalog indicates that tsunami waiting times deviate from an exponential distribution one would expect from a Poisson process. Empirical density distributions of tsunami waiting times were determined using both global tsunami origin times and tsunami arrival times at a particular site with a sufficient catalog: Hilo, Hawai'i. Most sources for the tsunamis in the catalog are earthquakes; other sources include landslides and volcanogenic processes. Both datasets indicate an over-abundance of short waiting times in comparison to an exponential distribution. Two types of probability models are investigated to explain this observation. Model (1) is a universal scaling law that describes long-term clustering of sources with a gamma distribution. The shape parameter (γ) for the global tsunami distribution is similar to that of the global earthquake catalog γ=0.63-0.67 [Corral, 2004]. For the Hilo catalog, γ is slightly greater (0.75-0.82) and closer to an exponential distribution. This is explained by the fact that tsunamis from smaller triggered earthquakes or landslides are less likely to be recorded at a far-field station such as Hilo in comparison to the global catalog, which includes a greater proportion of local tsunamis. Model (2) is based on two distributions derived from Omori's law for the temporal decay of triggered sources (aftershocks). The first is the ETAS distribution derived by Saichev and Sornette [2007], which is shown to fit the distribution of observed tsunami waiting times. The second is a simpler two-parameter distribution that is the exponential distribution augmented by a linear decay in aftershocks multiplied by a time constant Ta. Examination of the sources associated with short tsunami waiting times indicate that triggered events include both earthquake and landslide tsunamis that begin in the vicinity of the primary source. Triggered seismogenic tsunamis do not necessarily originate from the same fault zone, however. For example, subduction-thrust and outer-rise earthquake pairs are evident, such as the November 2006 and January 2007 Kuril Islands tsunamigenic pair. Because of variations in tsunami source parameters, such as water depth above the source, triggered tsunami events with short waiting times are not systematically smaller than the primary tsunami.

Periodic bidirectional associative memory neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Chen, Anping; Huang, Lihong; Liu, Zhigang; Cao, Jinde

2006-05-01

Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin's coincidence degree theory and the Lyapunov functional method and the Young's inequality technique. These results are helpful for designing a globally exponentially stable and periodic oscillatory BAM neural network, and the conditions can be easily verified and be applied in practice. An example is also given to illustrate our results.

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays.

PubMed

Zhao, Kaihong

2018-12-01

In this paper, we study the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.

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.

A mathematical model for evolution and SETI.

PubMed

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

Modelling Evolution and SETI Mathematically

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2012-05-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factor increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions constrained between the time axis and the exponential growth curve. Finally, since each lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

A Mathematical Model for Evolution and SETI

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

Accounting for inherent variability of growth in microbial risk assessment.

PubMed

Marks, H M; Coleman, M E

2005-04-15

Risk assessments of pathogens need to account for the growth of small number of cells under varying conditions. In order to determine the possible risks that occur when there are small numbers of cells, stochastic models of growth are needed that would capture the distribution of the number of cells over replicate trials of the same scenario or environmental conditions. This paper provides a simple stochastic growth model, accounting only for inherent cell-growth variability, assuming constant growth kinetic parameters, for an initial, small, numbers of cells assumed to be transforming from a stationary to an exponential phase. Two, basic, microbial sets of assumptions are considered: serial, where it is assume that cells transform through a lag phase before entering the exponential phase of growth; and parallel, where it is assumed that lag and exponential phases develop in parallel. The model is based on, first determining the distribution of the time when growth commences, and then modelling the conditional distribution of the number of cells. For the latter distribution, it is found that a Weibull distribution provides a simple approximation to the conditional distribution of the relative growth, so that the model developed in this paper can be easily implemented in risk assessments using commercial software packages.

Graphical analysis for gel morphology II. New mathematical approach for stretched exponential function with β>1

NASA Astrophysics Data System (ADS)

Hashimoto, Chihiro; Panizza, Pascal; Rouch, Jacques; Ushiki, Hideharu

2005-10-01

A new analytical concept is applied to the kinetics of the shrinking process of poly(N-isopropylacrylamide) (PNIPA) gels. When PNIPA gels are put into hot water above the critical temperature, two-step shrinking is observed and the secondary shrinking of gels is fitted well by a stretched exponential function. The exponent β characterizing the stretched exponential is always higher than one, although there are few analytical concepts for the stretched exponential function with β>1. As a new interpretation for this function, we propose a superposition of step (Heaviside) function and a new distribution function of characteristic time is deduced.

Chronology of Postglacial Eruptive Activity and Calculation of Eruption Probabilities for Medicine Lake Volcano, Northern California

USGS Publications Warehouse

Nathenson, Manuel; Donnelly-Nolan, Julie M.; Champion, Duane E.; Lowenstern, Jacob B.

2007-01-01

Medicine Lake volcano has had 4 eruptive episodes in its postglacial history (since 13,000 years ago) comprising 16 eruptions. Time intervals between events within the episodes are relatively short, whereas time intervals between the episodes are much longer. An updated radiocarbon chronology for these eruptions is presented that uses paleomagnetic data to constrain the choice of calibrated ages. This chronology is used with exponential, Weibull, and mixed-exponential probability distributions to model the data for time intervals between eruptions. The mixed exponential distribution is the best match to the data and provides estimates for the conditional probability of a future eruption given the time since the last eruption. The probability of an eruption at Medicine Lake volcano in the next year from today is 0.00028.

Min and Max Exponential Extreme Interval Values and Statistics

ERIC Educational Resources Information Center

Jance, Marsha; Thomopoulos, Nick

2009-01-01

The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

Heterogeneous characters modeling of instant message services users’ online behavior

PubMed Central

Fang, Yajun; Horn, Berthold

2018-01-01

Research on temporal characteristics of human dynamics has attracted much attentions for its contribution to various areas such as communication, medical treatment, finance, etc. Existing studies show that the time intervals between two consecutive events present different non-Poisson characteristics, such as power-law, Pareto, bimodal distribution of power-law, exponential distribution, piecewise power-law, et al. With the occurrences of new services, new types of distributions may arise. In this paper, we study the distributions of the time intervals between two consecutive visits to QQ and WeChat service, the top two popular instant messaging services in China, and present a new finding that when the value of statistical unit T is set to 0.001s, the inter-event time distribution follows a piecewise distribution of exponential and power-law, indicating the heterogeneous character of IM services users’ online behavior in different time scales. We infer that the heterogeneous character is related to the communication mechanism of IM and the habits of users. Then we develop a combination model of exponential model and interest model to characterize the heterogeneity. Furthermore, we find that the exponent of the inter-event time distribution of the same service is different in two cities, which is correlated with the popularity of the services. Our research is useful for the application of information diffusion, prediction of economic development of cities, and so on. PMID:29734327

Heterogeneous characters modeling of instant message services users' online behavior.

PubMed

Cui, Hongyan; Li, Ruibing; Fang, Yajun; Horn, Berthold; Welsch, Roy E

2018-01-01

Research on temporal characteristics of human dynamics has attracted much attentions for its contribution to various areas such as communication, medical treatment, finance, etc. Existing studies show that the time intervals between two consecutive events present different non-Poisson characteristics, such as power-law, Pareto, bimodal distribution of power-law, exponential distribution, piecewise power-law, et al. With the occurrences of new services, new types of distributions may arise. In this paper, we study the distributions of the time intervals between two consecutive visits to QQ and WeChat service, the top two popular instant messaging services in China, and present a new finding that when the value of statistical unit T is set to 0.001s, the inter-event time distribution follows a piecewise distribution of exponential and power-law, indicating the heterogeneous character of IM services users' online behavior in different time scales. We infer that the heterogeneous character is related to the communication mechanism of IM and the habits of users. Then we develop a combination model of exponential model and interest model to characterize the heterogeneity. Furthermore, we find that the exponent of the inter-event time distribution of the same service is different in two cities, which is correlated with the popularity of the services. Our research is useful for the application of information diffusion, prediction of economic development of cities, and so on.

Impact of oxide thickness on the density distribution of near-interface traps in 4H-SiC MOS capacitors

NASA Astrophysics Data System (ADS)

Zhang, Xufang; Okamoto, Dai; Hatakeyama, Tetsuo; Sometani, Mitsuru; Harada, Shinsuke; Iwamuro, Noriyuki; Yano, Hiroshi

2018-06-01

The impact of oxide thickness on the density distribution of near-interface traps (NITs) in SiO2/4H-SiC structure was investigated. We used the distributed circuit model that had successfully explained the frequency-dependent characteristics of both capacitance and conductance under strong accumulation conditions for SiO2/4H-SiC MOS capacitors with thick oxides by assuming an exponentially decaying distribution of NITs. In this work, it was found that the exponentially decaying distribution is the most plausible approximation of the true NIT distribution because it successfully explained the frequency dependences of capacitance and conductance under strong accumulation conditions for various oxide thicknesses. The thickness dependence of the NIT density distribution was also characterized. It was found that the NIT density increases with increasing oxide thickness, and a possible physical reason was discussed.

Scaling behavior of sleep-wake transitions across species

NASA Astrophysics Data System (ADS)

Lo, Chung-Chuan; Chou, Thomas; Ivanov, Plamen Ch.; Penzel, Thomas; Mochizuki, Takatoshi; Scammell, Thomas; Saper, Clifford B.; Stanley, H. Eugene

2003-03-01

Uncovering the mechanisms controlling sleep is a fascinating scientific challenge. It can be viewed as transitions of states of a very complex system, the brain. We study the time dynamics of short awakenings during sleep for three species: humans, rats and mice. We find, for all three species, that wake durations follow a power-law distribution, and sleep durations follow exponential distributions. Surprisingly, all three species have the same power-law exponent for the distribution of wake durations, but the exponential time scale of the distributions of sleep durations varies across species. We suggest that the dynamics of short awakenings are related to species-independent fluctuations of the system, while the dynamics of sleep is related to system-dependent mechanisms which change with species.

Linear prediction and single-channel recording.

PubMed

Carter, A A; Oswald, R E

1995-08-01

The measurement of individual single-channel events arising from the gating of ion channels provides a detailed data set from which the kinetic mechanism of a channel can be deduced. In many cases, the pattern of dwells in the open and closed states is very complex, and the kinetic mechanism and parameters are not easily determined. Assuming a Markov model for channel kinetics, the probability density function for open and closed time dwells should consist of a sum of decaying exponentials. One method of approaching the kinetic analysis of such a system is to determine the number of exponentials and the corresponding parameters which comprise the open and closed dwell time distributions. These can then be compared to the relaxations predicted from the kinetic model to determine, where possible, the kinetic constants. We report here the use of a linear technique, linear prediction/singular value decomposition, to determine the number of exponentials and the exponential parameters. Using simulated distributions and comparing with standard maximum-likelihood analysis, the singular value decomposition techniques provide advantages in some situations and are a useful adjunct to other single-channel analysis techniques.

Global synchronization of memristive neural networks subject to random disturbances via distributed pinning control.

PubMed

Guo, Zhenyuan; Yang, Shaofu; Wang, Jun

2016-12-01

This paper presents theoretical results on global exponential synchronization of multiple memristive neural networks in the presence of external noise by means of two types of distributed pinning control. The multiple memristive neural networks are coupled in a general structure via a nonlinear function, which consists of a linear diffusive term and a discontinuous sign term. A pinning impulsive control law is introduced in the coupled system to synchronize all neural networks. Sufficient conditions are derived for ascertaining global exponential synchronization in mean square. In addition, a pinning adaptive control law is developed to achieve global exponential synchronization in mean square. Both pinning control laws utilize only partial state information received from the neighborhood of the controlled neural network. Simulation results are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Design and implementation of the NaI(Tl)/CsI(Na) detectors output signal generator

NASA Astrophysics Data System (ADS)

Zhou, Xu; Liu, Cong-Zhan; Zhao, Jian-Ling; Zhang, Fei; Zhang, Yi-Fei; Li, Zheng-Wei; Zhang, Shuo; Li, Xu-Fang; Lu, Xue-Feng; Xu, Zhen-Ling; Lu, Fang-Jun

2014-02-01

We designed and implemented a signal generator that can simulate the output of the NaI(Tl)/CsI(Na) detectors' pre-amplifier onboard the Hard X-ray Modulation Telescope (HXMT). Using the development of the FPGA (Field Programmable Gate Array) with VHDL language and adding a random constituent, we have finally produced the double exponential random pulse signal generator. The statistical distribution of the signal amplitude is programmable. The occurrence time intervals of the adjacent signals contain negative exponential distribution statistically.

Bonus-Malus System with the Claim Frequency Distribution is Geometric and the Severity Distribution is Truncated Weibull

NASA Astrophysics Data System (ADS)

Santi, D. N.; Purnaba, I. G. P.; Mangku, I. W.

2016-01-01

Bonus-Malus system is said to be optimal if it is financially balanced for insurance companies and fair for policyholders. Previous research about Bonus-Malus system concern with the determination of the risk premium which applied to all of the severity that guaranteed by the insurance company. In fact, not all of the severity that proposed by policyholder may be covered by insurance company. When the insurance company sets a maximum bound of the severity incurred, so it is necessary to modify the model of the severity distribution into the severity bound distribution. In this paper, optimal Bonus-Malus system is compound of claim frequency component has geometric distribution and severity component has truncated Weibull distribution is discussed. The number of claims considered to follow a Poisson distribution, and the expected number λ is exponentially distributed, so the number of claims has a geometric distribution. The severity with a given parameter θ is considered to have a truncated exponential distribution is modelled using the Levy distribution, so the severity have a truncated Weibull distribution.

Exponential model for option prices: Application to the Brazilian market

NASA Astrophysics Data System (ADS)

Ramos, Antônio M. T.; Carvalho, J. A.; Vasconcelos, G. L.

2016-03-01

In this paper we report an empirical analysis of the Ibovespa index of the São Paulo Stock Exchange and its respective option contracts. We compare the empirical data on the Ibovespa options with two option pricing models, namely the standard Black-Scholes model and an empirical model that assumes that the returns are exponentially distributed. It is found that at times near the option expiration date the exponential model performs better than the Black-Scholes model, in the sense that it fits the empirical data better than does the latter model.

Generalization of the normal-exponential model: exploration of a more accurate parametrisation for the signal distribution on Illumina BeadArrays.

PubMed

Plancade, Sandra; Rozenholc, Yves; Lund, Eiliv

2012-12-11

Illumina BeadArray technology includes non specific negative control features that allow a precise estimation of the background noise. As an alternative to the background subtraction proposed in BeadStudio which leads to an important loss of information by generating negative values, a background correction method modeling the observed intensities as the sum of the exponentially distributed signal and normally distributed noise has been developed. Nevertheless, Wang and Ye (2012) display a kernel-based estimator of the signal distribution on Illumina BeadArrays and suggest that a gamma distribution would represent a better modeling of the signal density. Hence, the normal-exponential modeling may not be appropriate for Illumina data and background corrections derived from this model may lead to wrong estimation. We propose a more flexible modeling based on a gamma distributed signal and a normal distributed background noise and develop the associated background correction, implemented in the R-package NormalGamma. Our model proves to be markedly more accurate to model Illumina BeadArrays: on the one hand, it is shown on two types of Illumina BeadChips that this model offers a more correct fit of the observed intensities. On the other hand, the comparison of the operating characteristics of several background correction procedures on spike-in and on normal-gamma simulated data shows high similarities, reinforcing the validation of the normal-gamma modeling. The performance of the background corrections based on the normal-gamma and normal-exponential models are compared on two dilution data sets, through testing procedures which represent various experimental designs. Surprisingly, we observe that the implementation of a more accurate parametrisation in the model-based background correction does not increase the sensitivity. These results may be explained by the operating characteristics of the estimators: the normal-gamma background correction offers an improvement in terms of bias, but at the cost of a loss in precision. This paper addresses the lack of fit of the usual normal-exponential model by proposing a more flexible parametrisation of the signal distribution as well as the associated background correction. This new model proves to be considerably more accurate for Illumina microarrays, but the improvement in terms of modeling does not lead to a higher sensitivity in differential analysis. Nevertheless, this realistic modeling makes way for future investigations, in particular to examine the characteristics of pre-processing strategies.

Analysis of two production inventory systems with buffer, retrials and different production rates

NASA Astrophysics Data System (ADS)

Jose, K. P.; Nair, Salini S.

2017-09-01

This paper considers the comparison of two ( {s,S} ) production inventory systems with retrials of unsatisfied customers. The time for producing and adding each item to the inventory is exponentially distributed with rate β. However, a production rate α β higher than β is used at the beginning of the production. The higher production rate will reduce customers' loss when inventory level approaches zero. The demand from customers is according to a Poisson process. Service times are exponentially distributed. Upon arrival, the customers enter into a buffer of finite capacity. An arriving customer, who finds the buffer full, moves to an orbit. They can retry from there and inter-retrial times are exponentially distributed. The two models differ in the capacity of the buffer. The aim is to find the minimum value of total cost by varying different parameters and compare the efficiency of the models. The optimum value of α corresponding to minimum total cost is an important evaluation. Matrix analytic method is used to find an algorithmic solution to the problem. We also provide several numerical or graphical illustrations.

A non-Boltzmannian behavior of the energy distribution for quasi-stationary regimes of the Fermi–Pasta–Ulam β system

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

Leo, Mario, E-mail: mario.leo@le.infn.it; Leo, Rosario Antonio, E-mail: leora@le.infn.it; Tempesta, Piergiulio, E-mail: p.tempesta@fis.ucm.es

2013-06-15

In a recent paper [M. Leo, R.A. Leo, P. Tempesta, C. Tsallis, Phys. Rev. E 85 (2012) 031149], the existence of quasi-stationary states for the Fermi–Pasta–Ulam β system has been shown numerically, by analyzing the stability properties of the N/4-mode exact nonlinear solution. Here we study the energy distribution of the modes N/4, N/3 and N/2, when they are unstable, as a function of N and of the initial excitation energy. We observe that the classical Boltzmann weight is replaced by a different weight, expressed by a q-exponential function. -- Highlights: ► New statistical properties of the Fermi–Pasta–Ulam beta systemmore » are found. ► The energy distribution of specific observables are studied: a deviation from the standard Boltzmann behavior is found. ► A q-exponential weight should be used instead. ► The classical exponential weight is restored in the large particle limit (mesoscopic nature of the phenomenon)« less

Statistical analyses support power law distributions found in neuronal avalanches.

PubMed

Klaus, Andreas; Yu, Shan; Plenz, Dietmar

2011-01-01

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.

Spatial analysis of soil organic carbon in Zhifanggou catchment of the Loess Plateau.

PubMed

Li, Mingming; Zhang, Xingchang; Zhen, Qing; Han, Fengpeng

2013-01-01

Soil organic carbon (SOC) reflects soil quality and plays a critical role in soil protection, food safety, and global climate changes. This study involved grid sampling at different depths (6 layers) between 0 and 100 cm in a catchment. A total of 1282 soil samples were collected from 215 plots over 8.27 km(2). A combination of conventional analytical methods and geostatistical methods were used to analyze the data for spatial variability and soil carbon content patterns. The mean SOC content in the 1282 samples from the study field was 3.08 g · kg(-1). The SOC content of each layer decreased with increasing soil depth by a power function relationship. The SOC content of each layer was moderately variable and followed a lognormal distribution. The semi-variograms of the SOC contents of the six different layers were fit with the following models: exponential, spherical, exponential, Gaussian, exponential, and exponential, respectively. A moderate spatial dependence was observed in the 0-10 and 10-20 cm layers, which resulted from stochastic and structural factors. The spatial distribution of SOC content in the four layers between 20 and 100 cm exhibit were mainly restricted by structural factors. Correlations within each layer were observed between 234 and 562 m. A classical Kriging interpolation was used to directly visualize the spatial distribution of SOC in the catchment. The variability in spatial distribution was related to topography, land use type, and human activity. Finally, the vertical distribution of SOC decreased. Our results suggest that the ordinary Kriging interpolation can directly reveal the spatial distribution of SOC and the sample distance about this study is sufficient for interpolation or plotting. More research is needed, however, to clarify the spatial variability on the bigger scale and better understand the factors controlling spatial variability of soil carbon in the Loess Plateau region.

Non-extensive quantum statistics with particle-hole symmetry

NASA Astrophysics Data System (ADS)

Biró, T. S.; Shen, K. M.; Zhang, B. W.

2015-06-01

Based on Tsallis entropy (1988) and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while Teweldeberhan et al. (2003) and Silva et al. (2010). However, aiming at a non-extensive quantum statistics further requirements arise from the symmetric handling of particles and holes (excitations above and below the Fermi level). Naive replacements of the exponential function or "cut and paste" solutions fail to satisfy this symmetry and to be smooth at the Fermi level at the same time. We solve this problem by a general ansatz dividing the deformed exponential to odd and even terms and demonstrate that how earlier suggestions, like the κ- and q-exponential behave in this respect.

Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models

NASA Astrophysics Data System (ADS)

Aydiner, Ekrem; Cherstvy, Andrey G.; Metzler, Ralf

2018-01-01

We study by Monte Carlo simulations a kinetic exchange trading model for both fixed and distributed saving propensities of the agents and rationalize the person and wealth distributions. We show that the newly introduced wealth distribution - that may be more amenable in certain situations - features a different power-law exponent, particularly for distributed saving propensities of the agents. For open agent-based systems, we analyze the person and wealth distributions and find that the presence of trap agents alters their amplitude, leaving however the scaling exponents nearly unaffected. For an open system, we show that the total wealth - for different trap agent densities and saving propensities of the agents - decreases in time according to the classical Kohlrausch-Williams-Watts stretched exponential law. Interestingly, this decay does not depend on the trap agent density, but rather on saving propensities. The system relaxation for fixed and distributed saving schemes are found to be different.

Crack problem in superconducting cylinder with exponential distribution of critical-current density

NASA Astrophysics Data System (ADS)

Zhao, Yufeng; Xu, Chi; Shi, Liang

2018-04-01

The general problem of a center crack in a long cylindrical superconductor with inhomogeneous critical-current distribution is studied based on the extended Bean model for zero-field cooling (ZFC) and field cooling (FC) magnetization processes, in which the inhomogeneous parameter η is introduced for characterizing the critical-current density distribution in inhomogeneous superconductor. The effect of the inhomogeneous parameter η on both the magnetic field distribution and the variations of the normalized stress intensity factors is also obtained based on the plane strain approach and J-integral theory. The numerical results indicate that the exponential distribution of critical-current density will lead a larger trapped field inside the inhomogeneous superconductor and cause the center of the cylinder to fracture more easily. In addition, it is worth pointing out that the nonlinear field distribution is unique to the Bean model by comparing the curve shapes of the magnetization loop with homogeneous and inhomogeneous critical-current distribution.

How extreme are extremes?

NASA Astrophysics Data System (ADS)

Cucchi, Marco; Petitta, Marcello; Calmanti, Sandro

2016-04-01

High temperatures have an impact on the energy balance of any living organism and on the operational capabilities of critical infrastructures. Heat-wave indicators have been mainly developed with the aim of capturing the potential impacts on specific sectors (agriculture, health, wildfires, transport, power generation and distribution). However, the ability to capture the occurrence of extreme temperature events is an essential property of a multi-hazard extreme climate indicator. Aim of this study is to develop a standardized heat-wave indicator, that can be combined with other indices in order to describe multiple hazards in a single indicator. The proposed approach can be used in order to have a quantified indicator of the strenght of a certain extreme. As a matter of fact, extremes are usually distributed in exponential or exponential-exponential functions and it is difficult to quickly asses how strong was an extreme events considering only its magnitude. The proposed approach simplify the quantitative and qualitative communication of extreme magnitude

Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

NASA Astrophysics Data System (ADS)

Rizki, S. W.; Mara, M. N.; Sulistianingsih, E.

2017-06-01

This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior {\\hat{λ }}BL by using Linex approximation. After getting {\\hat{λ }}BL, the estimators of hazard function {\\hat{h}}BL and survival function {\\hat{S}}BL can be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.

Effect of the state of internal boundaries on granite fracture nature under quasi-static compression

NASA Astrophysics Data System (ADS)

Damaskinskaya, E. E.; Panteleev, I. A.; Kadomtsev, A. G.; Naimark, O. B.

2017-05-01

Based on an analysis of the spatial distribution of hypocenters of acoustic emission signal sources and an analysis of the energy distributions of acoustic emission signals, the effect of the liquid phase and a weak electric field on the spatiotemporal nature of granite sample fracture is studied. Experiments on uniaxial compression of granite samples of natural moisture showed that the damage accumulation process is twostage: disperse accumulation of damages is followed by localized accumulation of damages in the formed macrofracture nucleus region. In energy distributions of acoustic emission signals, this transition is accompanied by a change in the distribution shape from exponential to power-law. Granite water saturation qualitatively changes the damage accumulation nature: the process is delocalized until macrofracture with the exponential energy distribution of acoustic emission signals. An exposure to a weak electric field results in a selective change in the damage accumulation nature in the sample volume.

Turbulence hierarchy in a random fibre laser

PubMed Central

González, Iván R. Roa; Lima, Bismarck C.; Pincheira, Pablo I. R.; Brum, Arthur A.; Macêdo, Antônio M. S.; Vasconcelos, Giovani L.; de S. Menezes, Leonardo; Raposo, Ernesto P.; Gomes, Anderson S. L.; Kashyap, Raman

2017-01-01

Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a continuous-wave-pumped erbium-based random fibre laser, with random Bragg grating scatterers. The distribution of intensity fluctuations in an extensive data set exhibits three qualitatively distinct behaviours: a Gaussian regime below threshold, a mixture of two distributions with exponentially decaying tails near the threshold and a mixture of distributions with stretched-exponential tails above threshold. All distributions are well described by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence, which includes energy cascade and the intermittence phenomenon. Our findings have implications for explaining the remarkably challenging turbulent behaviour in photonics, using a random fibre laser as the experimental platform. PMID:28561064

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

Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation betweenmore » ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.« less

Global exponential stability analysis on impulsive BAM neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Li, Yao-Tang; Yang, Chang-Bo

2006-12-01

Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.

Existence and global exponential stability of periodic solution to BAM neural networks with periodic coefficients and continuously distributed delays

NASA Astrophysics Data System (ADS)

Zhou, distributed delays [rapid communication] T.; Chen, A.; Zhou, Y.

2005-08-01

By using the continuation theorem of coincidence degree theory and Liapunov function, we obtain some sufficient criteria to ensure the existence and global exponential stability of periodic solution to the bidirectional associative memory (BAM) neural networks with periodic coefficients and continuously distributed delays. These results improve and generalize the works of papers [J. Cao, L. Wang, Phys. Rev. E 61 (2000) 1825] and [Z. Liu, A. Chen, J. Cao, L. Huang, IEEE Trans. Circuits Systems I 50 (2003) 1162]. An example is given to illustrate that the criteria are feasible.

On the minimum of independent geometrically distributed random variables

NASA Technical Reports Server (NTRS)

Ciardo, Gianfranco; Leemis, Lawrence M.; Nicol, David

1994-01-01

The expectations E(X(sub 1)), E(Z(sub 1)), and E(Y(sub 1)) of the minimum of n independent geometric, modifies geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E(X(sub 1))/E(Y(sub 1)) equals the expected number of ties at the minimum for the geometric random variables. We then introduce the 'shifted geometric distribution' and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in the minimums.

Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme

NASA Astrophysics Data System (ADS)

Bakoban, Rana A.

2017-08-01

The coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.

Deuteron spin-lattice relaxation in the presence of an activation energy distribution: application to methanols in zeolite NaX.

PubMed

Stoch, G; Ylinen, E E; Birczynski, A; Lalowicz, Z T; Góra-Marek, K; Punkkinen, M

2013-02-01

A new method is introduced for analyzing deuteron spin-lattice relaxation in molecular systems with a broad distribution of activation energies and correlation times. In such samples the magnetization recovery is strongly non-exponential but can be fitted quite accurately by three exponentials. The considered system may consist of molecular groups with different mobility. For each group a Gaussian distribution of the activation energy is introduced. By assuming for every subsystem three parameters: the mean activation energy E(0), the distribution width σ and the pre-exponential factor τ(0) for the Arrhenius equation defining the correlation time, the relaxation rate is calculated for every part of the distribution. Experiment-based limiting values allow the grouping of the rates into three classes. For each class the relaxation rate and weight is calculated and compared with experiment. The parameters E(0), σ and τ(0) are determined iteratively by repeating the whole cycle many times. The temperature dependence of the deuteron relaxation was observed in three samples containing CD(3)OH (200% and 100% loading) and CD(3)OD (200%) in NaX zeolite and analyzed by the described method between 20K and 170K. The obtained parameters, equal for all the three samples, characterize the methyl and hydroxyl mobilities of the methanol molecules at two different locations. Copyright © 2012 Elsevier Inc. All rights reserved.

Apparent power-law distributions in animal movements can arise from intraspecific interactions

PubMed Central

Breed, Greg A.; Severns, Paul M.; Edwards, Andrew M.

2015-01-01

Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight. PMID:25519992

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.

Race, gender and the econophysics of income distribution in the USA

NASA Astrophysics Data System (ADS)

Shaikh, Anwar; Papanikolaou, Nikolaos; Wiener, Noe

2014-12-01

The econophysics “two-class” theory of Yakovenko and his co-authors shows that the distribution of labor incomes is roughly exponential. This paper extends this result to US subgroups categorized by gender and race. It is well known that Males have higher average incomes than Females, and Whites have higher average incomes than African-Americans. It is also evident that social policies can affect these income gaps. Our surprising finding is that nonetheless intra-group distributions of pre-tax labor incomes are remarkably similar and remain close to exponential. This suggests that income inequality can be usefully addressed by taxation policies, and overall income inequality can be modified by also shifting the balance between labor and property incomes.

Diversity of individual mobility patterns and emergence of aggregated scaling laws

PubMed Central

Yan, Xiao-Yong; Han, Xiao-Pu; Wang, Bing-Hong; Zhou, Tao

2013-01-01

Uncovering human mobility patterns is of fundamental importance to the understanding of epidemic spreading, urban transportation and other socioeconomic dynamics embodying spatiality and human travel. According to the direct travel diaries of volunteers, we show the absence of scaling properties in the displacement distribution at the individual level,while the aggregated displacement distribution follows a power law with an exponential cutoff. Given the constraint on total travelling cost, this aggregated scaling law can be analytically predicted by the mixture nature of human travel under the principle of maximum entropy. A direct corollary of such theory is that the displacement distribution of a single mode of transportation should follow an exponential law, which also gets supportive evidences in known data. We thus conclude that the travelling cost shapes the displacement distribution at the aggregated level. PMID:24045416

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

PubMed

Porto, Markus; Roman, H Eduardo

2002-04-01

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

Statistical modeling of storm-level Kp occurrences

USGS Publications Warehouse

Remick, K.J.; Love, J.J.

2006-01-01

We consider the statistical modeling of the occurrence in time of large Kp magnetic storms as a Poisson process, testing whether or not relatively rare, large Kp events can be considered to arise from a stochastic, sequential, and memoryless process. For a Poisson process, the wait times between successive events occur statistically with an exponential density function. Fitting an exponential function to the durations between successive large Kp events forms the basis of our analysis. Defining these wait times by calculating the differences between times when Kp exceeds a certain value, such as Kp ??? 5, we find the wait-time distribution is not exponential. Because large storms often have several periods with large Kp values, their occurrence in time is not memoryless; short duration wait times are not independent of each other and are often clumped together in time. If we remove same-storm large Kp occurrences, the resulting wait times are very nearly exponentially distributed and the storm arrival process can be characterized as Poisson. Fittings are performed on wait time data for Kp ??? 5, 6, 7, and 8. The mean wait times between storms exceeding such Kp thresholds are 7.12, 16.55, 42.22, and 121.40 days respectively.

An efficient and accurate technique to compute the absorption, emission, and transmission of radiation by the Martian atmosphere

NASA Technical Reports Server (NTRS)

Lindner, Bernhard Lee; Ackerman, Thomas P.; Pollack, James B.

1990-01-01

CO2 comprises 95 pct. of the composition of the Martian atmosphere. However, the Martian atmosphere also has a high aerosol content. Dust particles vary from less than 0.2 to greater than 3.0. CO2 is an active absorber and emitter in near IR and IR wavelengths; the near IR absorption bands of CO2 provide significant heating of the atmosphere, and the 15 micron band provides rapid cooling. Including both CO2 and aerosol radiative transfer simultaneously in a model is difficult. Aerosol radiative transfer requires a multiple scattering code, while CO2 radiative transfer must deal with complex wavelength structure. As an alternative to the pure atmosphere treatment in most models which causes inaccuracies, a treatment was developed called the exponential sum or k distribution approximation. The chief advantage of the exponential sum approach is that the integration over k space of f(k) can be computed more quickly than the integration of k sub upsilon over frequency. The exponential sum approach is superior to the photon path distribution and emissivity techniques for dusty conditions. This study was the first application of the exponential sum approach to Martian conditions.

Wealth of the world's richest publicly traded companies per industry and per employee: Gamma, Log-normal and Pareto power-law as universal distributions?

NASA Astrophysics Data System (ADS)

Soriano-Hernández, P.; del Castillo-Mussot, M.; Campirán-Chávez, I.; Montemayor-Aldrete, J. A.

2017-04-01

Forbes Magazine published its list of leading or strongest publicly-traded two thousand companies in the world (G-2000) based on four independent metrics: sales or revenues, profits, assets and market value. Every one of these wealth metrics yields particular information on the corporate size or wealth size of each firm. The G-2000 cumulative probability wealth distribution per employee (per capita) for all four metrics exhibits a two-class structure: quasi-exponential in the lower part, and a Pareto power-law in the higher part. These two-class structure per capita distributions are qualitatively similar to income and wealth distributions in many countries of the world, but the fraction of firms per employee within the high-class Pareto is about 49% in sales per employee, and 33% after averaging on the four metrics, whereas in countries the fraction of rich agents in the Pareto zone is less than 10%. The quasi-exponential zone can be adjusted by Gamma or Log-normal distributions. On the other hand, Forbes classifies the G-2000 firms in 82 different industries or economic activities. Within each industry, the wealth distribution per employee also follows a two-class structure, but when the aggregate wealth of firms in each industry for the four metrics is divided by the total number of employees in that industry, then the 82 points of the aggregate wealth distribution by industry per employee can be well adjusted by quasi-exponential curves for the four metrics.

Multi-exponential analysis of magnitude MR images using a quantitative multispectral edge-preserving filter.

PubMed

Bonny, Jean Marie; Boespflug-Tanguly, Odile; Zanca, Michel; Renou, Jean Pierre

2003-03-01

A solution for discrete multi-exponential analysis of T(2) relaxation decay curves obtained in current multi-echo imaging protocol conditions is described. We propose a preprocessing step to improve the signal-to-noise ratio and thus lower the signal-to-noise ratio threshold from which a high percentage of true multi-exponential detection is detected. It consists of a multispectral nonlinear edge-preserving filter that takes into account the signal-dependent Rician distribution of noise affecting magnitude MR images. Discrete multi-exponential decomposition, which requires no a priori knowledge, is performed by a non-linear least-squares procedure initialized with estimates obtained from a total least-squares linear prediction algorithm. This approach was validated and optimized experimentally on simulated data sets of normal human brains.

Choice of time-scale in Cox's model analysis of epidemiologic cohort data: a simulation study.

PubMed

Thiébaut, Anne C M; Bénichou, Jacques

2004-12-30

Cox's regression model is widely used for assessing associations between potential risk factors and disease occurrence in epidemiologic cohort studies. Although age is often a strong determinant of disease risk, authors have frequently used time-on-study instead of age as the time-scale, as for clinical trials. Unless the baseline hazard is an exponential function of age, this approach can yield different estimates of relative hazards than using age as the time-scale, even when age is adjusted for. We performed a simulation study in order to investigate the existence and magnitude of bias for different degrees of association between age and the covariate of interest. Age to disease onset was generated from exponential, Weibull or piecewise Weibull distributions, and both fixed and time-dependent dichotomous covariates were considered. We observed no bias upon using age as the time-scale. Upon using time-on-study, we verified the absence of bias for exponentially distributed age to disease onset. For non-exponential distributions, we found that bias could occur even when the covariate of interest was independent from age. It could be severe in case of substantial association with age, especially with time-dependent covariates. These findings were illustrated on data from a cohort of 84,329 French women followed prospectively for breast cancer occurrence. In view of our results, we strongly recommend not using time-on-study as the time-scale for analysing epidemiologic cohort data. 2004 John Wiley & Sons, Ltd.

Evaluation of Mean and Variance Integrals without Integration

ERIC Educational Resources Information Center

Joarder, A. H.; Omar, M. H.

2007-01-01

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential…

Intra-Individual Response Variability Assessed by Ex-Gaussian Analysis may be a New Endophenotype for Attention-Deficit/Hyperactivity Disorder.

PubMed

Henríquez-Henríquez, Marcela Patricia; Billeke, Pablo; Henríquez, Hugo; Zamorano, Francisco Javier; Rothhammer, Francisco; Aboitiz, Francisco

2014-01-01

Intra-individual variability of response times (RTisv) is considered as potential endophenotype for attentional deficit/hyperactivity disorder (ADHD). Traditional methods for estimating RTisv lose information regarding response times (RTs) distribution along the task, with eventual effects on statistical power. Ex-Gaussian analysis captures the dynamic nature of RTisv, estimating normal and exponential components for RT distribution, with specific phenomenological correlates. Here, we applied ex-Gaussian analysis to explore whether intra-individual variability of RTs agrees with criteria proposed by Gottesman and Gould for endophenotypes. Specifically, we evaluated if normal and/or exponential components of RTs may (a) present the stair-like distribution expected for endophenotypes (ADHD > siblings > typically developing children (TD) without familiar history of ADHD) and (b) represent a phenotypic correlate for previously described genetic risk variants. This is a pilot study including 55 subjects (20 ADHD-discordant sibling-pairs and 15 TD children), all aged between 8 and 13 years. Participants resolved a visual Go/Nogo with 10% Nogo probability. Ex-Gaussian distributions were fitted to individual RT data and compared among the three samples. In order to test whether intra-individual variability may represent a correlate for previously described genetic risk variants, VNTRs at DRD4 and SLC6A3 were identified in all sibling-pairs following standard protocols. Groups were compared adjusting independent general linear models for the exponential and normal components from the ex-Gaussian analysis. Identified trends were confirmed by the non-parametric Jonckheere-Terpstra test. Stair-like distributions were observed for μ (p = 0.036) and σ (p = 0.009). An additional "DRD4-genotype" × "clinical status" interaction was present for τ (p = 0.014) reflecting a possible severity factor. Thus, normal and exponential RTisv components are suitable as ADHD endophenotypes.

Weighted Scaling in Non-growth Random Networks

NASA Astrophysics Data System (ADS)

Chen, Guang; Yang, Xu-Hua; Xu, Xin-Li

2012-09-01

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth random networks. In this model, we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it. The network evolves according to a vertex strength preferential selection mechanism. During the evolution process, the network always holds its total number of vertices and its total number of single-edges constantly. We show analytically and numerically that a network will form steady scale-free distributions with our model. The results show that a weighted non-growth random network can evolve into scale-free state. It is interesting that the network also obtains the character of an exponential edge weight distribution. Namely, coexistence of scale-free distribution and exponential distribution emerges.

Contact Time in Random Walk and Random Waypoint: Dichotomy in Tail Distribution

NASA Astrophysics Data System (ADS)

Zhao, Chen; Sichitiu, Mihail L.

Contact time (or link duration) is a fundamental factor that affects performance in Mobile Ad Hoc Networks. Previous research on theoretical analysis of contact time distribution for random walk models (RW) assume that the contact events can be modeled as either consecutive random walks or direct traversals, which are two extreme cases of random walk, thus with two different conclusions. In this paper we conduct a comprehensive research on this topic in the hope of bridging the gap between the two extremes. The conclusions from the two extreme cases will result in a power-law or exponential tail in the contact time distribution, respectively. However, we show that the actual distribution will vary between the two extremes: a power-law-sub-exponential dichotomy, whose transition point depends on the average flight duration. Through simulation results we show that such conclusion also applies to random waypoint.

Turbulent particle transport in streams: can exponential settling be reconciled with fluid mechanics?

PubMed

McNair, James N; Newbold, J Denis

2012-05-07

Most ecological studies of particle transport in streams that focus on fine particulate organic matter or benthic invertebrates use the Exponential Settling Model (ESM) to characterize the longitudinal pattern of particle settling on the bed. The ESM predicts that if particles are released into a stream, the proportion that have not yet settled will decline exponentially with transport time or distance and will be independent of the release elevation above the bed. To date, no credible basis in fluid mechanics has been established for this model, nor has it been rigorously tested against more-mechanistic alternative models. One alternative is the Local Exchange Model (LEM), which is a stochastic advection-diffusion model that includes both longitudinal and vertical spatial dimensions and is based on classical fluid mechanics. The LEM predicts that particle settling will be non-exponential in the near field but will become exponential in the far field, providing a new theoretical justification for far-field exponential settling that is based on plausible fluid mechanics. We review properties of the ESM and LEM and compare these with available empirical evidence. Most evidence supports the prediction of both models that settling will be exponential in the far field but contradicts the ESM's prediction that a single exponential distribution will hold for all transport times and distances. Copyright © 2012 Elsevier Ltd. All rights reserved.

Probability distributions of bed load particle velocities, accelerations, hop distances, and travel times informed by Jaynes's principle of maximum entropy

USGS Publications Warehouse

Furbish, David; Schmeeckle, Mark; Schumer, Rina; Fathel, Siobhan

2016-01-01

We describe the most likely forms of the probability distributions of bed load particle velocities, accelerations, hop distances, and travel times, in a manner that formally appeals to inferential statistics while honoring mechanical and kinematic constraints imposed by equilibrium transport conditions. The analysis is based on E. Jaynes's elaboration of the implications of the similarity between the Gibbs entropy in statistical mechanics and the Shannon entropy in information theory. By maximizing the information entropy of a distribution subject to known constraints on its moments, our choice of the form of the distribution is unbiased. The analysis suggests that particle velocities and travel times are exponentially distributed and that particle accelerations follow a Laplace distribution with zero mean. Particle hop distances, viewed alone, ought to be distributed exponentially. However, the covariance between hop distances and travel times precludes this result. Instead, the covariance structure suggests that hop distances follow a Weibull distribution. These distributions are consistent with high-resolution measurements obtained from high-speed imaging of bed load particle motions. The analysis brings us closer to choosing distributions based on our mechanical insight.

Time Correlations in Mode Hopping of Coupled Oscillators

NASA Astrophysics Data System (ADS)

Heltberg, Mathias L.; Krishna, Sandeep; Jensen, Mogens H.

2017-05-01

We study the dynamics in a system of coupled oscillators when Arnold Tongues overlap. By varying the initial conditions, the deterministic system can be attracted to different limit cycles. Adding noise, the mode hopping between different states become a dominating part of the dynamics. We simplify the system through a Poincare section, and derive a 1D model to describe the dynamics. We explain that for some parameter values of the external oscillator, the time distribution of occupancy in a state is exponential and thus memoryless. In the general case, on the other hand, it is a sum of exponential distributions characteristic of a system with time correlations.

Exponential Stability of Almost Periodic Solutions for Memristor-Based Neural Networks with Distributed Leakage Delays.

PubMed

Xu, Changjin; Li, Peiluan; Pang, Yicheng

2016-12-01

In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).

Characterization of x-ray framing cameras for the National Ignition Facility using single photon pulse height analysis.

PubMed

Holder, J P; Benedetti, L R; Bradley, D K

2016-11-01

Single hit pulse height analysis is applied to National Ignition Facility x-ray framing cameras to quantify gain and gain variation in a single micro-channel plate-based instrument. This method allows the separation of gain from detectability in these photon-detecting devices. While pulse heights measured by standard-DC calibration methods follow the expected exponential distribution at the limit of a compound-Poisson process, gain-gated pulse heights follow a more complex distribution that may be approximated as a weighted sum of a few exponentials. We can reproduce this behavior with a simple statistical-sampling model.

The diffusion of a Ga atom on GaAs(001)β2(2 × 4): Local superbasin kinetic Monte Carlo

NASA Astrophysics Data System (ADS)

Lin, Yangzheng; Fichthorn, Kristen A.

2017-10-01

We use first-principles density-functional theory to characterize the binding sites and diffusion mechanisms for a Ga adatom on the GaAs(001)β 2(2 × 4) surface. Diffusion in this system is a complex process involving eleven unique binding sites and sixteen different hops between neighboring binding sites. Among the binding sites, we can identify four different superbasins such that the motion between binding sites within a superbasin is much faster than hops exiting the superbasin. To describe diffusion, we use a recently developed local superbasin kinetic Monte Carlo (LSKMC) method, which accelerates a conventional kinetic Monte Carlo (KMC) simulation by describing the superbasins as absorbing Markov chains. We find that LSKMC is up to 4300 times faster than KMC for the conditions probed in this study. We characterize the distribution of exit times from the superbasins and find that these are sometimes, but not always, exponential and we characterize the conditions under which the superbasin exit-time distribution should be exponential. We demonstrate that LSKMC simulations assuming an exponential superbasin exit-time distribution yield the same diffusion coefficients as conventional KMC.

Average BER of subcarrier intensity modulated free space optical systems over the exponentiated Weibull fading channels.

PubMed

Wang, Ping; Zhang, Lu; Guo, Lixin; Huang, Feng; Shang, Tao; Wang, Ranran; Yang, Yintang

2014-08-25

The average bit error rate (BER) for binary phase-shift keying (BPSK) modulation in free-space optical (FSO) links over turbulence atmosphere modeled by the exponentiated Weibull (EW) distribution is investigated in detail. The effects of aperture averaging on the average BERs for BPSK modulation under weak-to-strong turbulence conditions are studied. The average BERs of EW distribution are compared with Lognormal (LN) and Gamma-Gamma (GG) distributions in weak and strong turbulence atmosphere, respectively. The outage probability is also obtained for different turbulence strengths and receiver aperture sizes. The analytical results deduced by the generalized Gauss-Laguerre quadrature rule are verified by the Monte Carlo simulation. This work is helpful for the design of receivers for FSO communication systems.

Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions.

ERIC Educational Resources Information Center

Holland, Paul W.; Thayer, Dorothy T.

2000-01-01

Applied the theory of exponential families of distributions to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. Considers efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and computationally efficient…

Analysis of domestic refrigerator temperatures and home storage time distributions for shelf-life studies and food safety risk assessment.

PubMed

Roccato, Anna; Uyttendaele, Mieke; Membré, Jeanne-Marie

2017-06-01

In the framework of food safety, when mimicking the consumer phase, the storage time and temperature used are mainly considered as single point estimates instead of probability distributions. This singlepoint approach does not take into account the variability within a population and could lead to an overestimation of the parameters. Therefore, the aim of this study was to analyse data on domestic refrigerator temperatures and storage times of chilled food in European countries in order to draw general rules which could be used either in shelf-life testing or risk assessment. In relation to domestic refrigerator temperatures, 15 studies provided pertinent data. Twelve studies presented normal distributions, according to the authors or from the data fitted into distributions. Analysis of temperature distributions revealed that the countries were separated into two groups: northern European countries and southern European countries. The overall variability of European domestic refrigerators is described by a normal distribution: N (7.0, 2.7)°C for southern countries, and, N (6.1, 2.8)°C for the northern countries. Concerning storage times, seven papers were pertinent. Analysis indicated that the storage time was likely to end in the first days or weeks (depending on the product use-by-date) after purchase. Data fitting showed the exponential distribution was the most appropriate distribution to describe the time that food spent at consumer's place. The storage time was described by an exponential distribution corresponding to the use-by date period divided by 4. In conclusion, knowing that collecting data is time and money consuming, in the absence of data, and at least for the European market and for refrigerated products, building a domestic refrigerator temperature distribution using a Normal law and a time-to-consumption distribution using an Exponential law would be appropriate. Copyright © 2017 Elsevier Ltd. All rights reserved.

Determination of the functioning parameters in asymmetrical flow field-flow fractionation with an exponential channel.

PubMed

Déjardin, P

2013-08-30

The flow conditions in normal mode asymmetric flow field-flow fractionation are determined to approach the high retention limit with the requirement d≪l≪w, where d is the particle diameter, l the characteristic length of the sample exponential distribution and w the channel height. The optimal entrance velocity is determined from the solute characteristics, the channel geometry (exponential to rectangular) and the membrane properties, according to a model providing the velocity fields all over the cell length. In addition, a method is proposed for in situ determination of the channel height. Copyright © 2013 Elsevier B.V. All rights reserved.

Resource acquisition, distribution and end-use efficiencies and the growth of industrial society

NASA Astrophysics Data System (ADS)

Jarvis, A.; Jarvis, S.; Hewitt, N.

2015-01-01

A key feature of the growth of industrial society is the acquisition of increasing quantities of resources from the environment and their distribution for end use. With respect to energy, growth has been near exponential for the last 160 years. We attempt to show that the global distribution of resources that underpins this growth may be facilitated by the continual development and expansion of near optimal directed networks. If so, the distribution efficiencies of these networks must decline as they expand due to path lengths becoming longer and more tortuous. To maintain long-term exponential growth the physical limits placed on the distribution networks appear to be counteracted by innovations deployed elsewhere in the system: namely at the points of acquisition and end use. We postulate that the maintenance of growth at the specific rate of ~2.4% yr-1 stems from an implicit desire to optimise patterns of energy use over human working lifetimes.

Plume characteristics of MPD thrusters: A preliminary examination

NASA Technical Reports Server (NTRS)

Myers, Roger M.

1989-01-01

A diagnostics facility for MPD thruster plume measurements was built and is currently undergoing testing. The facility includes electrostatic probes for electron temperature and density measurements, Hall probes for magnetic field and current distribution mapping, and an imaging system to establish the global distribution of plasma species. Preliminary results for MPD thrusters operated at power levels between 30 and 60 kW with solenoidal applied magnetic fields show that the electron density decreases exponentially from 1x10(2) to 2x10(18)/cu m over the first 30 cm of the expansion, while the electron temperature distribution is relatively uniform, decreasing from approximately 2.5 eV to 1.5 eV over the same distance. The radiant intensity of the ArII 4879 A line emission also decays exponentially. Current distribution measurements indicate that a significant fraction of the discharge current is blown into the plume region, and that its distribution depends on the magnitudes of both the discharge current and the applied magnetic field.

Magnetic pattern at supergranulation scale: the void size distribution

NASA Astrophysics Data System (ADS)

Berrilli, F.; Scardigli, S.; Del Moro, D.

2014-08-01

The large-scale magnetic pattern observed in the photosphere of the quiet Sun is dominated by the magnetic network. This network, created by photospheric magnetic fields swept into convective downflows, delineates the boundaries of large-scale cells of overturning plasma and exhibits "voids" in magnetic organization. These voids include internetwork fields, which are mixed-polarity sparse magnetic fields that populate the inner part of network cells. To single out voids and to quantify their intrinsic pattern we applied a fast circle-packing-based algorithm to 511 SOHO/MDI high-resolution magnetograms acquired during the unusually long solar activity minimum between cycles 23 and 24. The computed void distribution function shows a quasi-exponential decay behavior in the range 10-60 Mm. The lack of distinct flow scales in this range corroborates the hypothesis of multi-scale motion flows at the solar surface. In addition to the quasi-exponential decay, we have found that the voids depart from a simple exponential decay at about 35 Mm.

Optical absorption, TL and IRSL of basic plagioclase megacrysts from the pinacate (Sonora, Mexico) quaternary alkalic volcanics.

PubMed

Chernov, V; Paz-Moreno, F; Piters, T M; Barboza-Flores, M

2006-01-01

The paper presents the first results of an investigation on optical absorption (OA), thermally and infrared stimulated luminescence (TL and IRSL) of the Pinacate plagioclase (labradorite). The OA spectra reveal two bands with maxima at 1.0 and 3.2 eV connected with absorption of the Fe3+ and Fe2+ and IR absorption at wavelengths longer than 2700 nm. The ultraviolet absorption varies exponentially with the photon energy following the 'vitreous' empirical Urbach rule indicating exponential distribution of localised states in the forbidden band. The natural TL is peaked at 700 K. Laboratory beta irradiation creates a very broad TL peak with maximum at 430 K. The change of the 430 K TL peak shape under the thermal cleaning procedure and dark storage after irradiation reveals a monotonous increasing of the activation energy that can be explained by the exponential distribution of traps. The IRSL response is weak and exhibits a typical decay behaviour.

A stochastic evolutionary model generating a mixture of exponential distributions

NASA Astrophysics Data System (ADS)

Fenner, Trevor; Levene, Mark; Loizou, George

2016-02-01

Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in [T. Fenner, M. Levene, G. Loizou, J. Stat. Mech. 2015, P08015 (2015)] so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.

Determination of bulk and interface density of states in metal oxide semiconductor thin-film transistors by using capacitance-voltage characteristics

NASA Astrophysics Data System (ADS)

Wei, Xixiong; Deng, Wanling; Fang, Jielin; Ma, Xiaoyu; Huang, Junkai

2017-10-01

A physical-based straightforward extraction technique for interface and bulk density of states in metal oxide semiconductor thin film transistors (TFTs) is proposed by using the capacitance-voltage (C-V) characteristics. The interface trap density distribution with energy has been extracted from the analysis of capacitance-voltage characteristics. Using the obtained interface state distribution, the bulk trap density has been determined. With this method, for the interface trap density, it is found that deep state density nearing the mid-gap is approximately constant and tail states density increases exponentially with energy; for the bulk trap density, it is a superposition of exponential deep states and exponential tail states. The validity of the extraction is verified by comparisons with the measured current-voltage (I-V) characteristics and the simulation results by the technology computer-aided design (TCAD) model. This extraction method uses non-numerical iteration which is simple, fast and accurate. Therefore, it is very useful for TFT device characterization.

Distinguishing response conflict and task conflict in the Stroop task: evidence from ex-Gaussian distribution analysis.

PubMed

Steinhauser, Marco; Hübner, Ronald

2009-10-01

It has been suggested that performance in the Stroop task is influenced by response conflict as well as task conflict. The present study investigated the idea that both conflict types can be isolated by applying ex-Gaussian distribution analysis which decomposes response time into a Gaussian and an exponential component. Two experiments were conducted in which manual versions of a standard Stroop task (Experiment 1) and a separated Stroop task (Experiment 2) were performed under task-switching conditions. Effects of response congruency and stimulus bivalency were used to measure response conflict and task conflict, respectively. Ex-Gaussian analysis revealed that response conflict was mainly observed in the Gaussian component, whereas task conflict was stronger in the exponential component. Moreover, task conflict in the exponential component was selectively enhanced under task-switching conditions. The results suggest that ex-Gaussian analysis can be used as a tool to isolate different conflict types in the Stroop task. PsycINFO Database Record (c) 2009 APA, all rights reserved.

Estimating Age Distributions of Base Flow in Watersheds Underlain by Single and Dual Porosity Formations Using Groundwater Transport Simulation and Weighted Weibull Functions

NASA Astrophysics Data System (ADS)

Sanford, W. E.

2015-12-01

Age distributions of base flow to streams are important to estimate for predicting the timing of water-quality responses to changes in distributed inputs of nutrients or pollutants at the land surface. Simple models of shallow aquifers will predict exponential age distributions, but more realistic 3-D stream-aquifer geometries will cause deviations from an exponential curve. In addition, in fractured rock terrains the dual nature of the effective and total porosity of the system complicates the age distribution further. In this study shallow groundwater flow and advective transport were simulated in two regions in the Eastern United States—the Delmarva Peninsula and the upper Potomac River basin. The former is underlain by layers of unconsolidated sediment, while the latter consists of folded and fractured sedimentary rocks. Transport of groundwater to streams was simulated using the USGS code MODPATH within 175 and 275 watersheds, respectively. For the fractured rock terrain, calculations were also performed along flow pathlines to account for exchange between mobile and immobile flow zones. Porosities at both sites were calibrated using environmental tracer data (3H, 3He, CFCs and SF6) in wells and springs, and with a 30-year tritium record from the Potomac River. Carbonate and siliciclastic rocks were calibrated to have mobile porosity values of one and six percent, and immobile porosity values of 18 and 12 percent, respectively. The age distributions were fitted to Weibull functions. Whereas an exponential function has one parameter that controls the median age of the distribution, a Weibull function has an extra parameter that controls the slope of the curve. A weighted Weibull function was also developed that potentially allows for four parameters, two that control the median age and two that control the slope, one of each weighted toward early or late arrival times. For both systems the two-parameter Weibull function nearly always produced a substantially better fit to the data than the one-parameter exponential function. For the single porosity system it was found that the use of three parameters was often optimal for accurately describing the base-flow age distribution, whereas for the dual porosity system the fourth parameter was often required to fit the more complicated response curves.

Exploiting the Adaptation Dynamics to Predict the Distribution of Beneficial Fitness Effects

PubMed Central

2016-01-01

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depends on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remains nearly a constant for exponentially decaying distributions and increases when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold good for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments. PMID:26990188

A non-Gaussian option pricing model based on Kaniadakis exponential deformation

NASA Astrophysics Data System (ADS)

Moretto, Enrico; Pasquali, Sara; Trivellato, Barbara

2017-09-01

A way to make financial models effective is by letting them to represent the so called "fat tails", i.e., extreme changes in stock prices that are regarded as almost impossible by the standard Gaussian distribution. In this article, the Kaniadakis deformation of the usual exponential function is used to define a random noise source in the dynamics of price processes capable of capturing such real market phenomena.

Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.

PubMed

Potdar, Alka A; Jeon, Junhwan; Weaver, Alissa M; Quaranta, Vito; Cummings, Peter T

2010-03-10

Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW). Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases) each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation). Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.

Fast radiative transfer models for retrieval of cloud properties in the back-scattering region: application to DSCOVR-EPIC sensor

NASA Astrophysics Data System (ADS)

Molina Garcia, Victor; Sasi, Sruthy; Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego

2017-04-01

In this work, the requirements for the retrieval of cloud properties in the back-scattering region are described, and their application to the measurements taken by the Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR) is shown. Various radiative transfer models and their linearizations are implemented, and their advantages and issues are analyzed. As radiative transfer calculations in the back-scattering region are computationally time-consuming, several acceleration techniques are also studied. The radiative transfer models analyzed include the exact Discrete Ordinate method with Matrix Exponential (DOME), the Matrix Operator method with Matrix Exponential (MOME), and the approximate asymptotic and equivalent Lambertian cloud models. To reduce the computational cost of the line-by-line (LBL) calculations, the k-distribution method, the Principal Component Analysis (PCA) and a combination of the k-distribution method plus PCA are used. The linearized radiative transfer models for retrieval of cloud properties include the Linearized Discrete Ordinate method with Matrix Exponential (LDOME), the Linearized Matrix Operator method with Matrix Exponential (LMOME) and the Forward-Adjoint Discrete Ordinate method with Matrix Exponential (FADOME). These models were applied to the EPIC oxygen-A band absorption channel at 764 nm. It is shown that the approximate asymptotic and equivalent Lambertian cloud models give inaccurate results, so an offline processor for the retrieval of cloud properties in the back-scattering region requires the use of exact models such as DOME and MOME, which behave similarly. The combination of the k-distribution method plus PCA presents similar accuracy to the LBL calculations, but it is up to 360 times faster, and the relative errors for the computed radiances are less than 1.5% compared to the results when the exact phase function is used. Finally, the linearized models studied show similar behavior, with relative errors less than 1% for the radiance derivatives, but FADOME is 2 times faster than LDOME and 2.5 times faster than LMOME.

Computerized glow curve deconvolution of thermoluminescent emission from polyminerals of Jamaica Mexican flower

NASA Astrophysics Data System (ADS)

Favalli, A.; Furetta, C.; Zaragoza, E. Cruz; Reyes, A.

The aim of this work is to study the main thermoluminescence (TL) characteristics of the inorganic polyminerals extracted from dehydrated Jamaica flower or roselle (Hibiscus sabdariffa L.) belonging to Malvaceae family of Mexican origin. TL emission properties of the polymineral fraction in powder were studied using the initial rise (IR) method. The complex structure and kinetic parameters of the glow curves have been analysed accurately using the computerized glow curve deconvolution (CGCD) assuming an exponential distribution of trapping levels. The extension of the IR method to the case of a continuous and exponential distribution of traps is reported, such as the derivation of the TL glow curve deconvolution functions for continuous trap distribution. CGCD is performed both in the case of frequency factor, s, temperature independent, and in the case with the s function of temperature.

Empirical analysis of individual popularity and activity on an online music service system

NASA Astrophysics Data System (ADS)

Hu, Hai-Bo; Han, Ding-Yi

2008-10-01

Quantitative understanding of human behaviors supplies basic comprehension of the dynamics of many socio-economic systems. Based on the log data of an online music service system, we investigate the statistical characteristics of individual activity and popularity, and find that the distributions of both of them follow a stretched exponential form which interpolates between exponential and power law distribution. We also study the human dynamics on the online system and find that the distribution of interevent time between two consecutive listenings of music shows the fat tail feature. Besides, with the reduction of user activity the fat tail becomes more and more irregular, indicating different behavior patterns for users with diverse activities. The research results may shed some light on the in-depth understanding of collective behaviors in socio-economic systems.

A partial exponential lumped parameter model to evaluate groundwater age distributions and nitrate trends in long-screened wells

USGS Publications Warehouse

Jurgens, Bryant; Böhlke, John Karl; Kauffman, Leon J.; Belitz, Kenneth; Esser, Bradley K.

2016-01-01

A partial exponential lumped parameter model (PEM) was derived to determine age distributions and nitrate trends in long-screened production wells. The PEM can simulate age distributions for wells screened over any finite interval of an aquifer that has an exponential distribution of age with depth. The PEM has 3 parameters – the ratio of saturated thickness to the top and bottom of the screen and mean age, but these can be reduced to 1 parameter (mean age) by using well construction information and estimates of the saturated thickness. The PEM was tested with data from 30 production wells in a heterogeneous alluvial fan aquifer in California, USA. Well construction data were used to guide parameterization of a PEM for each well and mean age was calibrated to measured environmental tracer data (3H, 3He, CFC-113, and 14C). Results were compared to age distributions generated for individual wells using advective particle tracking models (PTMs). Age distributions from PTMs were more complex than PEM distributions, but PEMs provided better fits to tracer data, partly because the PTMs did not simulate 14C accurately in wells that captured varying amounts of old groundwater recharged at lower rates prior to groundwater development and irrigation. Nitrate trends were simulated independently of the calibration process and the PEM provided good fits for at least 11 of 24 wells. This work shows that the PEM, and lumped parameter models (LPMs) in general, can often identify critical features of the age distributions in wells that are needed to explain observed tracer data and nonpoint source contaminant trends, even in systems where aquifer heterogeneity and water-use complicate distributions of age. While accurate PTMs are preferable for understanding and predicting aquifer-scale responses to water use and contaminant transport, LPMs can be sensitive to local conditions near individual wells that may be inaccurately represented or missing in an aquifer-scale flow model.

Improving Bed Management at Wright-Patterson Medical Center

DTIC Science & Technology

1989-09-01

arrival distributions are Poisson, as in Sim2, then interarrival times are distributed exponentially (Budnick, Mcleavey , and Mojena, 1988:770). While... McLeavey , D. and Mojena R., Principles of Operations Research for Management (second edition). Homewood IL: Irwin, 1988. Cannoodt, L. J. and

Compact continuous-variable entanglement distillation.

PubMed

Datta, Animesh; Zhang, Lijian; Nunn, Joshua; Langford, Nathan K; Feito, Alvaro; Plenio, Martin B; Walmsley, Ian A

2012-02-10

We introduce a new scheme for continuous-variable entanglement distillation that requires only linear temporal and constant physical or spatial resources. Distillation is the process by which high-quality entanglement may be distributed between distant nodes of a network in the unavoidable presence of decoherence. The known versions of this protocol scale exponentially in space and doubly exponentially in time. Our optimal scheme therefore provides exponential improvements over existing protocols. It uses a fixed-resource module-an entanglement distillery-comprising only four quantum memories of at most 50% storage efficiency and allowing a feasible experimental implementation. Tangible quantum advantages are obtainable by using existing off-resonant Raman quantum memories outside their conventional role of storage.

Liver fibrosis: stretched exponential model outperforms mono-exponential and bi-exponential models of diffusion-weighted MRI.

PubMed

Seo, Nieun; Chung, Yong Eun; Park, Yung Nyun; Kim, Eunju; Hwang, Jinwoo; Kim, Myeong-Jin

2018-07-01

To compare the ability of diffusion-weighted imaging (DWI) parameters acquired from three different models for the diagnosis of hepatic fibrosis (HF). Ninety-five patients underwent DWI using nine b values at 3 T magnetic resonance. The hepatic apparent diffusion coefficient (ADC) from a mono-exponential model, the true diffusion coefficient (D t ), pseudo-diffusion coefficient (D p ) and perfusion fraction (f) from a biexponential model, and the distributed diffusion coefficient (DDC) and intravoxel heterogeneity index (α) from a stretched exponential model were compared with the pathological HF stage. For the stretched exponential model, parameters were also obtained using a dataset of six b values (DDC # , α # ). The diagnostic performances of the parameters for HF staging were evaluated with Obuchowski measures and receiver operating characteristics (ROC) analysis. The measurement variability of DWI parameters was evaluated using the coefficient of variation (CoV). Diagnostic accuracy for HF staging was highest for DDC # (Obuchowski measures, 0.770 ± 0.03), and it was significantly higher than that of ADC (0.597 ± 0.05, p < 0.001), D t (0.575 ± 0.05, p < 0.001) and f (0.669 ± 0.04, p = 0.035). The parameters from stretched exponential DWI and D p showed higher areas under the ROC curve (AUCs) for determining significant fibrosis (≥F2) and cirrhosis (F = 4) than other parameters. However, D p showed significantly higher measurement variability (CoV, 74.6%) than DDC # (16.1%, p < 0.001) and α # (15.1%, p < 0.001). Stretched exponential DWI is a promising method for HF staging with good diagnostic performance and fewer b-value acquisitions, allowing shorter acquisition time. • Stretched exponential DWI provides a precise and accurate model for HF staging. • Stretched exponential DWI parameters are more reliable than D p from bi-exponential DWI model • Acquisition of six b values is sufficient to obtain accurate DDC and α.

The Comparison Study of Quadratic Infinite Beam Program on Optimization Instensity Modulated Radiation Therapy Treatment Planning (IMRTP) between Threshold and Exponential Scatter Method with CERR® In The Case of Lung Cancer

NASA Astrophysics Data System (ADS)

Hardiyanti, Y.; Haekal, M.; Waris, A.; Haryanto, F.

2016-08-01

This research compares the quadratic optimization program on Intensity Modulated Radiation Therapy Treatment Planning (IMRTP) with the Computational Environment for Radiotherapy Research (CERR) software. We assumed that the number of beams used for the treatment planner was about 9 and 13 beams. The case used the energy of 6 MV with Source Skin Distance (SSD) of 100 cm from target volume. Dose calculation used Quadratic Infinite beam (QIB) from CERR. CERR was used in the comparison study between Gauss Primary threshold method and Gauss Primary exponential method. In the case of lung cancer, the threshold variation of 0.01, and 0.004 was used. The output of the dose was distributed using an analysis in the form of DVH from CERR. The maximum dose distributions obtained were on the target volume (PTV) Planning Target Volume, (CTV) Clinical Target Volume, (GTV) Gross Tumor Volume, liver, and skin. It was obtained that if the dose calculation method used exponential and the number of beam 9. When the dose calculation method used the threshold and the number of beam 13, the maximum dose distributions obtained were on the target volume PTV, GTV, heart, and skin.

A Hierarchical Bayesian Model for Calibrating Estimates of Species Divergence Times

PubMed Central

Heath, Tracy A.

2012-01-01

In Bayesian divergence time estimation methods, incorporating calibrating information from the fossil record is commonly done by assigning prior densities to ancestral nodes in the tree. Calibration prior densities are typically parametric distributions offset by minimum age estimates provided by the fossil record. Specification of the parameters of calibration densities requires the user to quantify his or her prior knowledge of the age of the ancestral node relative to the age of its calibrating fossil. The values of these parameters can, potentially, result in biased estimates of node ages if they lead to overly informative prior distributions. Accordingly, determining parameter values that lead to adequate prior densities is not straightforward. In this study, I present a hierarchical Bayesian model for calibrating divergence time analyses with multiple fossil age constraints. This approach applies a Dirichlet process prior as a hyperprior on the parameters of calibration prior densities. Specifically, this model assumes that the rate parameters of exponential prior distributions on calibrated nodes are distributed according to a Dirichlet process, whereby the rate parameters are clustered into distinct parameter categories. Both simulated and biological data are analyzed to evaluate the performance of the Dirichlet process hyperprior. Compared with fixed exponential prior densities, the hierarchical Bayesian approach results in more accurate and precise estimates of internal node ages. When this hyperprior is applied using Markov chain Monte Carlo methods, the ages of calibrated nodes are sampled from mixtures of exponential distributions and uncertainty in the values of calibration density parameters is taken into account. PMID:22334343

A comparative study of mixed exponential and Weibull distributions in a stochastic model replicating a tropical rainfall process

NASA Astrophysics Data System (ADS)

Abas, Norzaida; Daud, Zalina M.; Yusof, Fadhilah

2014-11-01

A stochastic rainfall model is presented for the generation of hourly rainfall data in an urban area in Malaysia. In view of the high temporal and spatial variability of rainfall within the tropical rain belt, the Spatial-Temporal Neyman-Scott Rectangular Pulse model was used. The model, which is governed by the Neyman-Scott process, employs a reasonable number of parameters to represent the physical attributes of rainfall. A common approach is to attach each attribute to a mathematical distribution. With respect to rain cell intensity, this study proposes the use of a mixed exponential distribution. The performance of the proposed model was compared to a model that employs the Weibull distribution. Hourly and daily rainfall data from four stations in the Damansara River basin in Malaysia were used as input to the models, and simulations of hourly series were performed for an independent site within the basin. The performance of the models was assessed based on how closely the statistical characteristics of the simulated series resembled the statistics of the observed series. The findings obtained based on graphical representation revealed that the statistical characteristics of the simulated series for both models compared reasonably well with the observed series. However, a further assessment using the AIC, BIC and RMSE showed that the proposed model yields better results. The results of this study indicate that for tropical climates, the proposed model, using a mixed exponential distribution, is the best choice for generation of synthetic data for ungauged sites or for sites with insufficient data within the limit of the fitted region.

The social architecture of capitalism

NASA Astrophysics Data System (ADS)

Wright, Ian

2005-02-01

A dynamic model of the social relations between workers and capitalists is introduced. The model self-organises into a dynamic equilibrium with statistical properties that are in close qualitative and in many cases quantitative agreement with a broad range of known empirical distributions of developed capitalism, including the power-law firm size distribution, the Laplace firm and GDP growth distribution, the lognormal firm demises distribution, the exponential recession duration distribution, the lognormal-Pareto income distribution, and the gamma-like firm rate-of-profit distribution. Normally these distributions are studied in isolation, but this model unifies and connects them within a single causal framework. The model also generates business cycle phenomena, including fluctuating wage and profit shares in national income about values consistent with empirical studies. The generation of an approximately lognormal-Pareto income distribution and an exponential-Pareto wealth distribution demonstrates that the power-law regime of the income distribution can be explained by an additive process on a power-law network that models the social relation between employers and employees organised in firms, rather than a multiplicative process that models returns to investment in financial markets. A testable consequence of the model is the conjecture that the rate-of-profit distribution is consistent with a parameter-mix of a ratio of normal variates with means and variances that depend on a firm size parameter that is distributed according to a power-law.

Network structures sustained by internal links and distributed lifetime of old nodes in stationary state of number of nodes

NASA Astrophysics Data System (ADS)

Ikeda, Nobutoshi

2017-12-01

In network models that take into account growth properties, deletion of old nodes has a serious impact on degree distributions, because old nodes tend to become hub nodes. In this study, we aim to provide a simple explanation for why hubs can exist even in conditions where the number of nodes is stationary due to the deletion of old nodes. We show that an exponential increase in the degree of nodes is a natural consequence of the balance between the deletion and addition of nodes as long as a preferential attachment mechanism holds. As a result, the largest degree is determined by the magnitude relationship between the time scale of the exponential growth of degrees and lifetime of old nodes. The degree distribution exhibits a power-law form ˜ k -γ with exponent γ = 1 when the lifetime of nodes is constant. However, various values of γ can be realized by introducing distributed lifetime of nodes.

The Modelled Raindrop Size Distribution of Skudai, Peninsular Malaysia, Using Exponential and Lognormal Distributions

PubMed Central

Yakubu, Mahadi Lawan; Yusop, Zulkifli; Yusof, Fadhilah

2014-01-01

This paper presents the modelled raindrop size parameters in Skudai region of the Johor Bahru, western Malaysia. Presently, there is no model to forecast the characteristics of DSD in Malaysia, and this has an underpinning implication on wet weather pollution predictions. The climate of Skudai exhibits local variability in regional scale. This study established five different parametric expressions describing the rain rate of Skudai; these models are idiosyncratic to the climate of the region. Sophisticated equipment that converts sound to a relevant raindrop diameter is often too expensive and its cost sometimes overrides its attractiveness. In this study, a physical low-cost method was used to record the DSD of the study area. The Kaplan-Meier method was used to test the aptness of the data to exponential and lognormal distributions, which were subsequently used to formulate the parameterisation of the distributions. This research abrogates the concept of exclusive occurrence of convective storm in tropical regions and presented a new insight into their concurrence appearance. PMID:25126597

Level crossings and excess times due to a superposition of uncorrelated exponential pulses

NASA Astrophysics Data System (ADS)

Theodorsen, A.; Garcia, O. E.

2018-01-01

A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a superposition of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency parameter. Expressions for excess time statistics, that is, the rate of level crossings above a given threshold and the average time spent above the threshold, are derived from the joint distribution of the process and its derivative. Limits of both high and low intermittency are investigated and compared to previously known results. In the case of a strongly intermittent process, the distribution of times spent above threshold is obtained analytically. This expression is verified numerically, and the distribution of times above threshold is explored for other intermittency regimes. The numerical simulations compare favorably to known results for the distribution of times above the mean threshold for an Ornstein-Uhlenbeck process. This contribution generalizes the excess time statistics for the stochastic model, which find applications in a wide diversity of natural and technological systems.

Improved Results for Route Planning in Stochastic Transportation Networks

NASA Technical Reports Server (NTRS)

Boyan, Justin; Mitzenmacher, Michael

2000-01-01

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

Research on the exponential growth effect on network topology: Theoretical and empirical analysis

NASA Astrophysics Data System (ADS)

Li, Shouwei; You, Zongjun

Integrated circuit (IC) industry network has been built in Yangtze River Delta with the constant expansion of IC industry. The IC industry network grows exponentially with the establishment of new companies and the establishment of contacts with old firms. Based on preferential attachment and exponential growth, the paper presents the analytical results in which the vertices degree of scale-free network follows power-law distribution p(k)˜k‑γ (γ=2β+1) and parameter β satisfies 0.5≤β≤1. At the same time, we find that the preferential attachment takes place in a dynamic local world and the size of the dynamic local world is in direct proportion to the size of whole networks. The paper also gives the analytical results of no-preferential attachment and exponential growth on random networks. The computer simulated results of the model illustrate these analytical results. Through some investigations on the enterprises, this paper at first presents the distribution of IC industry, composition of industrial chain and service chain firstly. Then, the correlative network and its analysis of industrial chain and service chain are presented. The correlative analysis of the whole IC industry is also presented at the same time. Based on the theory of complex network, the analysis and comparison of industrial chain network and service chain network in Yangtze River Delta are provided in the paper.

Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R

USGS Publications Warehouse

Asquith, William H.

2014-01-01

The implementation characteristics of two method of L-moments (MLM) algorithms for parameter estimation of the 4-parameter Asymmetric Exponential Power (AEP4) distribution are studied using the R environment for statistical computing. The objective is to validate the algorithms for general application of the AEP4 using R. An algorithm was introduced in the original study of the L-moments for the AEP4. A second or alternative algorithm is shown to have a larger L-moment-parameter domain than the original. The alternative algorithm is shown to provide reliable parameter production and recovery of L-moments from fitted parameters. A proposal is made for AEP4 implementation in conjunction with the 4-parameter Kappa distribution to create a mixed-distribution framework encompassing the joint L-skew and L-kurtosis domains. The example application provides a demonstration of pertinent algorithms with L-moment statistics and two 4-parameter distributions (AEP4 and the Generalized Lambda) for MLM fitting to a modestly asymmetric and heavy-tailed dataset using R.

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

NASA Astrophysics Data System (ADS)

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

2009-12-01

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

Analysis and modeling of optical crosstalk in InP-based Geiger-mode avalanche photodiode FPAs

NASA Astrophysics Data System (ADS)

Chau, Quan; Jiang, Xudong; Itzler, Mark A.; Entwistle, Mark; Piccione, Brian; Owens, Mark; Slomkowski, Krystyna

2015-05-01

Optical crosstalk is a major factor limiting the performance of Geiger-mode avalanche photodiode (GmAPD) focal plane arrays (FPAs). This is especially true for arrays with increased pixel density and broader spectral operation. We have performed extensive experimental and theoretical investigations on the crosstalk effects in InP-based GmAPD FPAs for both 1.06-μm and 1.55-μm applications. Mechanisms responsible for intrinsic dark counts are Poisson processes, and their inter-arrival time distribution is an exponential function. In FPAs, intrinsic dark counts and cross talk events coexist, and the inter-arrival time distribution deviates from purely exponential behavior. From both experimental data and computer simulations, we show the dependence of this deviation on the crosstalk probability. The spatial characteristics of crosstalk are also demonstrated. From the temporal and spatial distribution of crosstalk, an efficient algorithm to identify and quantify crosstalk is introduced.

Preferential attachment and growth dynamics in complex systems

NASA Astrophysics Data System (ADS)

Yamasaki, Kazuko; Matia, Kaushik; Buldyrev, Sergey V.; Fu, Dongfeng; Pammolli, Fabio; Riccaboni, Massimo; Stanley, H. Eugene

2006-09-01

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. According to the model, the distribution changes from a pure exponential form for zero influx of new classes to a power law with an exponential cut-off form when the influx of new classes is substantial. Predictions of the model are tested through the analysis of a unique industrial database, which covers both elementary units (products) and classes (markets, firms) in a given industry (pharmaceuticals), covering the entire size distribution. The model’s predictions are in good agreement with the data. The paper sheds light on the emergence of the exponent τ≈2 observed as a universal feature of many biological, social and economic problems.

Science and Facebook: The same popularity law!

PubMed

Néda, Zoltán; Varga, Levente; Biró, Tamás S

2017-01-01

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of "shares" for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4.

Distributed Consensus of Stochastic Delayed Multi-agent Systems Under Asynchronous Switching.

PubMed

Wu, Xiaotai; Tang, Yang; Cao, Jinde; Zhang, Wenbing

2016-08-01

In this paper, the distributed exponential consensus of stochastic delayed multi-agent systems with nonlinear dynamics is investigated under asynchronous switching. The asynchronous switching considered here is to account for the time of identifying the active modes of multi-agent systems. After receipt of confirmation of mode's switching, the matched controller can be applied, which means that the switching time of the matched controller in each node usually lags behind that of system switching. In order to handle the coexistence of switched signals and stochastic disturbances, a comparison principle of stochastic switched delayed systems is first proved. By means of this extended comparison principle, several easy to verified conditions for the existence of an asynchronously switched distributed controller are derived such that stochastic delayed multi-agent systems with asynchronous switching and nonlinear dynamics can achieve global exponential consensus. Two examples are given to illustrate the effectiveness of the proposed method.

Science and Facebook: The same popularity law!

PubMed Central

Varga, Levente; Biró, Tamás S.

2017-01-01

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of “shares” for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4. PMID:28678796

Software reliability: Additional investigations into modeling with replicated experiments

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

Multi-step rhodopsin inactivation schemes can account for the size variability of single photon responses in Limulus ventral photoreceptors

PubMed Central

1994-01-01

Limulus ventral photoreceptors generate highly variable responses to the absorption of single photons. We have obtained data on the size distribution of these responses, derived the distribution predicted from simple transduction cascade models and compared the theory and data. In the simplest of models, the active state of the visual pigment (defined by its ability to activate G protein) is turned off in a single reaction. The output of such a cascade is predicted to be highly variable, largely because of stochastic variation in the number of G proteins activated. The exact distribution predicted is exponential, but we find that an exponential does not adequately account for the data. The data agree much better with the predictions of a cascade model in which the active state of the visual pigment is turned off by a multi-step process. PMID:8057085

Exponential Family Functional data analysis via a low-rank model.

PubMed

Li, Gen; Huang, Jianhua Z; Shen, Haipeng

2018-05-08

In many applications, non-Gaussian data such as binary or count are observed over a continuous domain and there exists a smooth underlying structure for describing such data. We develop a new functional data method to deal with this kind of data when the data are regularly spaced on the continuous domain. Our method, referred to as Exponential Family Functional Principal Component Analysis (EFPCA), assumes the data are generated from an exponential family distribution, and the matrix of the canonical parameters has a low-rank structure. The proposed method flexibly accommodates not only the standard one-way functional data, but also two-way (or bivariate) functional data. In addition, we introduce a new cross validation method for estimating the latent rank of a generalized data matrix. We demonstrate the efficacy of the proposed methods using a comprehensive simulation study. The proposed method is also applied to a real application of the UK mortality study, where data are binomially distributed and two-way functional across age groups and calendar years. The results offer novel insights into the underlying mortality pattern. © 2018, The International Biometric Society.

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our method to others in the literature as well as the aforementioned TRW estimator.

Pore‐Scale Hydrodynamics in a Progressively Bioclogged Three‐Dimensional Porous Medium: 3‐D Particle Tracking Experiments and Stochastic Transport Modeling

PubMed Central

Carrel, M.; Dentz, M.; Derlon, N.; Morgenroth, E.

2018-01-01

Abstract Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play a central role in services ranging from degradation of pollutants to water purification. Biofilms dynamically change the pore structure of the medium through selective clogging of pores, a process known as bioclogging. This affects how solutes are transported and spread through the porous matrix, but the temporal changes to transport behavior during bioclogging are not well understood. To address this uncertainty, we experimentally study the hydrodynamic changes of a transparent 3‐D porous medium as it experiences progressive bioclogging. Statistical analyses of the system's hydrodynamics at four time points of bioclogging (0, 24, 36, and 48 h in the exponential growth phase) reveal exponential increases in both average and variance of the flow velocity, as well as its correlation length. Measurements for spreading, as mean‐squared displacements, are found to be non‐Fickian and more intensely superdiffusive with progressive bioclogging, indicating the formation of preferential flow pathways and stagnation zones. A gamma distribution describes well the Lagrangian velocity distributions and provides parameters that quantify changes to the flow, which evolves from a parallel pore arrangement under unclogged conditions, toward a more serial arrangement with increasing clogging. Exponentially evolving hydrodynamic metrics agree with an exponential bacterial growth phase and are used to parameterize a correlated continuous time random walk model with a stochastic velocity relaxation. The model accurately reproduces transport observations and can be used to resolve transport behavior at intermediate time points within the exponential growth phase considered. PMID:29780184

Pore-Scale Hydrodynamics in a Progressively Bioclogged Three-Dimensional Porous Medium: 3-D Particle Tracking Experiments and Stochastic Transport Modeling

NASA Astrophysics Data System (ADS)

Carrel, M.; Morales, V. L.; Dentz, M.; Derlon, N.; Morgenroth, E.; Holzner, M.

2018-03-01

Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play a central role in services ranging from degradation of pollutants to water purification. Biofilms dynamically change the pore structure of the medium through selective clogging of pores, a process known as bioclogging. This affects how solutes are transported and spread through the porous matrix, but the temporal changes to transport behavior during bioclogging are not well understood. To address this uncertainty, we experimentally study the hydrodynamic changes of a transparent 3-D porous medium as it experiences progressive bioclogging. Statistical analyses of the system's hydrodynamics at four time points of bioclogging (0, 24, 36, and 48 h in the exponential growth phase) reveal exponential increases in both average and variance of the flow velocity, as well as its correlation length. Measurements for spreading, as mean-squared displacements, are found to be non-Fickian and more intensely superdiffusive with progressive bioclogging, indicating the formation of preferential flow pathways and stagnation zones. A gamma distribution describes well the Lagrangian velocity distributions and provides parameters that quantify changes to the flow, which evolves from a parallel pore arrangement under unclogged conditions, toward a more serial arrangement with increasing clogging. Exponentially evolving hydrodynamic metrics agree with an exponential bacterial growth phase and are used to parameterize a correlated continuous time random walk model with a stochastic velocity relaxation. The model accurately reproduces transport observations and can be used to resolve transport behavior at intermediate time points within the exponential growth phase considered.

Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface

NASA Astrophysics Data System (ADS)

Zaigham Zia, Q. M.; Ullah, Ikram; Waqas, M.; Alsaedi, A.; Hayat, T.

2018-03-01

This research intends to elaborate Soret-Dufour characteristics in mixed convective radiated Casson liquid flow by exponentially heated surface. Novel features of exponential space dependent heat source are introduced. Appropriate variables are implemented for conversion of partial differential frameworks into a sets of ordinary differential expressions. Homotopic scheme is employed for construction of analytic solutions. Behavior of various embedding variables on velocity, temperature and concentration distributions are plotted graphically and analyzed in detail. Besides, skin friction coefficients and heat and mass transfer rates are also computed and interpreted. The results signify the pronounced characteristics of temperature corresponding to convective and radiation variables. Concentration bears opposite response for Soret and Dufour variables.

Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen-Grossberg BAM neural networks with impulses.

PubMed

Yang, Wengui; Yu, Wenwu; Cao, Jinde; Alsaadi, Fuad E; Hayat, Tasawar

2018-02-01

This paper investigates the stability and lag synchronization for memristor-based fuzzy Cohen-Grossberg bidirectional associative memory (BAM) neural networks with mixed delays (asynchronous time delays and continuously distributed delays) and impulses. By applying the inequality analysis technique, homeomorphism theory and some suitable Lyapunov-Krasovskii functionals, some new sufficient conditions for the uniqueness and global exponential stability of equilibrium point are established. Furthermore, we obtain several sufficient criteria concerning globally exponential lag synchronization for the proposed system based on the framework of Filippov solution, differential inclusion theory and control theory. In addition, some examples with numerical simulations are given to illustrate the feasibility and validity of obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Strain, curvature, and twist measurements in digital holographic interferometry using pseudo-Wigner-Ville distribution based method

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

Rajshekhar, G.; Gorthi, Sai Siva; Rastogi, Pramod

2009-09-15

Measurement of strain, curvature, and twist of a deformed object play an important role in deformation analysis. Strain depends on the first order displacement derivative, whereas curvature and twist are determined by second order displacement derivatives. This paper proposes a pseudo-Wigner-Ville distribution based method for measurement of strain, curvature, and twist in digital holographic interferometry where the object deformation or displacement is encoded as interference phase. In the proposed method, the phase derivative is estimated by peak detection of pseudo-Wigner-Ville distribution evaluated along each row/column of the reconstructed interference field. A complex exponential signal with unit amplitude and the phasemore » derivative estimate as the argument is then generated and the pseudo-Wigner-Ville distribution along each row/column of this signal is evaluated. The curvature is estimated by using peak tracking strategy for the new distribution. For estimation of twist, the pseudo-Wigner-Ville distribution is evaluated along each column/row (i.e., in alternate direction with respect to the previous one) for the generated complex exponential signal and the corresponding peak detection gives the twist estimate.« less

Two-state Markov-chain Poisson nature of individual cellphone call statistics

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Zhou, Wei-Xing; Sornette, Didier

2016-07-01

Unfolding the burst patterns in human activities and social interactions is a very important issue especially for understanding the spreading of disease and information and the formation of groups and organizations. Here, we conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73 339 anonymous cellphone users, whose inter-call durations are Weibull distributed. We find that the individual call events exhibit a pattern of bursts, that high activity periods are alternated with low activity periods. In both periods, the number of calls are exponentially distributed for individuals, but power-law distributed for the population. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain, giving significant fits for nearly half of the individuals. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we purport the existence of power-law distributions, via the ‘superposition of distributions’ mechanism. Our findings shed light on the origins of bursty patterns in other human activities.

Rigorous Proof of the Boltzmann-Gibbs Distribution of Money on Connected Graphs

NASA Astrophysics Data System (ADS)

Lanchier, Nicolas

2017-04-01

Models in econophysics, i.e., the emerging field of statistical physics that applies the main concepts of traditional physics to economics, typically consist of large systems of economic agents who are characterized by the amount of money they have. In the simplest model, at each time step, one agent gives one dollar to another agent, with both agents being chosen independently and uniformly at random from the system. Numerical simulations of this model suggest that, at least when the number of agents and the average amount of money per agent are large, the distribution of money converges to an exponential distribution reminiscent of the Boltzmann-Gibbs distribution of energy in physics. The main objective of this paper is to give a rigorous proof of this result and show that the convergence to the exponential distribution holds more generally when the economic agents are located on the vertices of a connected graph and interact locally with their neighbors rather than globally with all the other agents. We also study a closely related model where, at each time step, agents buy with a probability proportional to the amount of money they have, and prove that in this case the limiting distribution of money is Poissonian.

Heterogeneous Link Weight Promotes the Cooperation in Spatial Prisoner's Dilemma

NASA Astrophysics Data System (ADS)

Ma, Zhi-Qin; Xia, Cheng-Yi; Sun, Shi-Wen; Wang, Li; Wang, Huai-Bin; Wang, Juan

The spatial structure has often been identified as a prominent mechanism that substantially promotes the cooperation level in prisoner's dilemma game. In this paper we introduce a weighting mechanism into the spatial prisoner's dilemma game to explore the cooperative behaviors on the square lattice. Here, three types of weight distributions: exponential, power-law and uniform distributions are considered, and the weight is assigned to links between players. Through large-scale numerical simulations we find, compared with the traditional spatial game, that this mechanism can largely enhance the frequency of cooperators. For most ranges of b, we find that the power-law distribution enables the highest promotion of cooperation and the uniform one leads to the lowest enhancement, whereas the exponential one lies often between them. The great improvement of cooperation can be caused by the fact that the distributional link weight yields inhomogeneous interaction strength among individuals, which can facilitate the formation of cooperative clusters to resist the defector's invasion. In addition, the impact of amplitude of the undulation of weight distribution and noise strength on cooperation is also investigated for three kinds of weight distribution. Current researches can aid in the further understanding of evolutionary cooperation in biological and social science.

A Random Variable Transformation Process.

ERIC Educational Resources Information Center

Scheuermann, Larry

1989-01-01

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

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

ERIC Educational Resources Information Center

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

2013-01-01

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

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

PubMed

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

2016-01-01

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

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

PubMed Central

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

2016-01-01

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

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.

Calculating Formulas of Coefficient and Mean Neutron Exposure in the Exponential Expression of Neutron Exposure Distribution

NASA Astrophysics Data System (ADS)

Zhang, F. H.; Zhou, G. D.; Ma, K.; Ma, W. J.; Cui, W. Y.; Zhang, B.

2015-11-01

Present studies have shown that, in the main stages of the development and evolution of asymptotic giant branch (AGB) star s-process models, the distributions of neutron exposures in the nucleosynthesis regions can all be expressed by an exponential function ({ρ_{AGB}}(τ) = C/{τ_0}exp ( - τ/{τ_0})) in the effective range of values. However, the specific expressions of the proportional coefficient C and the mean neutron exposure ({τ_0}) in the formula for different models are not completely determined in the related literatures. Through dissecting the basic solving method of the exponential distribution of neutron exposures, and systematically combing the solution procedure of exposure distribution for different stellar models, the general calculating formulas as well as their auxiliary equations for calculating C and ({τ_0}) are reduced. Given the discrete distribution of neutron exposures ({P_k}), i.e. the mass ratio of the materials which have exposed to neutrons for (k) ((k = 0, 1, 2 \\cdots )) times when reaching the final distribution with respect to the materials of the He intershell, (C = - {P_1}/ln R), and ({τ_0} = - Δ τ /ln R) can be obtained. Here, (R) expresses the probability that the materials can successively experience neutron irradiation for two times in the He intershell. For the convective nucleosynthesis model (including the Ulrich model and the ({}^{13}{C})-pocket convective burning model), (R) is just the overlap factor r, namely the mass ratio of the materials which can undergo two successive thermal pulses in the He intershell. And for the (^{13}{C})-pocket radiative burning model, (R = sumlimits_{k = 1}^∞ {{P_k}} ). This set of formulas practically give the corresponding relationship between C or ({τ_0}) and the model parameters. The results of this study effectively solve the problem of analytically calculating the distribution of neutron exposures in the low-mass AGB star s-process nucleosynthesis model of (^{13}{C})-pocket radiative burning.

A fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution

NASA Astrophysics Data System (ADS)

Dalkilic, Turkan Erbay; Apaydin, Aysen

2009-11-01

In a regression analysis, it is assumed that the observations come from a single class in a data cluster and the simple functional relationship between the dependent and independent variables can be expressed using the general model; Y=f(X)+[epsilon]. However; a data cluster may consist of a combination of observations that have different distributions that are derived from different clusters. When faced with issues of estimating a regression model for fuzzy inputs that have been derived from different distributions, this regression model has been termed the [`]switching regression model' and it is expressed with . Here li indicates the class number of each independent variable and p is indicative of the number of independent variables [J.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Transaction on Systems, Man and Cybernetics 23 (3) (1993) 665-685; M. Michel, Fuzzy clustering and switching regression models using ambiguity and distance rejects, Fuzzy Sets and Systems 122 (2001) 363-399; E.Q. Richard, A new approach to estimating switching regressions, Journal of the American Statistical Association 67 (338) (1972) 306-310]. In this study, adaptive networks have been used to construct a model that has been formed by gathering obtained models. There are methods that suggest the class numbers of independent variables heuristically. Alternatively, in defining the optimal class number of independent variables, the use of suggested validity criterion for fuzzy clustering has been aimed. In the case that independent variables have an exponential distribution, an algorithm has been suggested for defining the unknown parameter of the switching regression model and for obtaining the estimated values after obtaining an optimal membership function, which is suitable for exponential distribution.

On the origin of stretched exponential (Kohlrausch) relaxation kinetics in the room temperature luminescence decay of colloidal quantum dots.

PubMed

Bodunov, E N; Antonov, Yu A; Simões Gamboa, A L

2017-03-21

The non-exponential room temperature luminescence decay of colloidal quantum dots is often well described by a stretched exponential function. However, the physical meaning of the parameters of the function is not clear in the majority of cases reported in the literature. In this work, the room temperature stretched exponential luminescence decay of colloidal quantum dots is investigated theoretically in an attempt to identify the underlying physical mechanisms associated with the parameters of the function. Three classes of non-radiative transition processes between the excited and ground states of colloidal quantum dots are discussed: long-range resonance energy transfer, multiphonon relaxation, and contact quenching without diffusion. It is shown that multiphonon relaxation cannot explain a stretched exponential functional form of the luminescence decay while such dynamics of relaxation can be understood in terms of long-range resonance energy transfer to acceptors (molecules, quantum dots, or anharmonic molecular vibrations) in the environment of the quantum dots acting as energy-donors or by contact quenching by acceptors (surface traps or molecules) distributed statistically on the surface of the quantum dots. These non-radiative transition processes are assigned to different ranges of the stretching parameter β.

Application of a Short Intracellular pH Method to Flow Cytometry for Determining Saccharomyces cerevisiae Vitality ▿

PubMed Central

Weigert, Claudia; Steffler, Fabian; Kurz, Tomas; Shellhammer, Thomas H.; Methner, Frank-Jürgen

2009-01-01

The measurement of yeast's intracellular pH (ICP) is a proven method for determining yeast vitality. Vitality describes the condition or health of viable cells as opposed to viability, which defines living versus dead cells. In contrast to fluorescence photometric measurements, which show only average ICP values of a population, flow cytometry allows the presentation of an ICP distribution. By examining six repeated propagations with three separate growth phases (lag, exponential, and stationary), the ICP method previously established for photometry was transferred successfully to flow cytometry by using the pH-dependent fluorescent probe 5,6-carboxyfluorescein. The correlation between the two methods was good (r2 = 0.898, n = 18). With both methods it is possible to track the course of growth phases. Although photometry did not yield significant differences between exponentially and stationary phases (P = 0.433), ICP via flow cytometry did (P = 0.012). Yeast in an exponential phase has a unimodal ICP distribution, reflective of a homogeneous population; however, yeast in a stationary phase displays a broader ICP distribution, and subpopulations could be defined by using the flow cytometry method. In conclusion, flow cytometry yielded specific evidence of the heterogeneity in vitality of a yeast population as measured via ICP. In contrast to photometry, flow cytometry increases information about the yeast population's vitality via a short measurement, which is suitable for routine analysis. PMID:19581482

Theory for Transitions Between Exponential and Stationary Phases: Universal Laws for Lag Time

NASA Astrophysics Data System (ADS)

Himeoka, Yusuke; Kaneko, Kunihiko

2017-04-01

The quantitative characterization of bacterial growth has attracted substantial attention since Monod's pioneering study. Theoretical and experimental works have uncovered several laws for describing the exponential growth phase, in which the number of cells grows exponentially. However, microorganism growth also exhibits lag, stationary, and death phases under starvation conditions, in which cell growth is highly suppressed, for which quantitative laws or theories are markedly underdeveloped. In fact, the models commonly adopted for the exponential phase that consist of autocatalytic chemical components, including ribosomes, can only show exponential growth or decay in a population; thus, phases that halt growth are not realized. Here, we propose a simple, coarse-grained cell model that includes an extra class of macromolecular components in addition to the autocatalytic active components that facilitate cellular growth. These extra components form a complex with the active components to inhibit the catalytic process. Depending on the nutrient condition, the model exhibits typical transitions among the lag, exponential, stationary, and death phases. Furthermore, the lag time needed for growth recovery after starvation follows the square root of the starvation time and is inversely related to the maximal growth rate. This is in agreement with experimental observations, in which the length of time of cell starvation is memorized in the slow accumulation of molecules. Moreover, the lag time distributed among cells is skewed with a long time tail. If the starvation time is longer, an exponential tail appears, which is also consistent with experimental data. Our theory further predicts a strong dependence of lag time on the speed of substrate depletion, which can be tested experimentally. The present model and theoretical analysis provide universal growth laws beyond the exponential phase, offering insight into how cells halt growth without entering the death phase.

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

NASA Astrophysics Data System (ADS)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

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

Accumulated distribution of material gain at dislocation crystal growth

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

Rakin, V. I., E-mail: rakin@geo.komisc.ru

2016-05-15

A model for slowing down the tangential growth rate of an elementary step at dislocation crystal growth is proposed based on the exponential law of impurity particle distribution over adsorption energy. It is established that the statistical distribution of material gain on structurally equivalent faces obeys the Erlang law. The Erlang distribution is proposed to be used to calculate the occurrence rates of morphological combinatorial types of polyhedra, presenting real simple crystallographic forms.

Nocturnal Dynamics of Sleep-Wake Transitions in Patients With Narcolepsy.

PubMed

Zhang, Xiaozhe; Kantelhardt, Jan W; Dong, Xiao Song; Krefting, Dagmar; Li, Jing; Yan, Han; Pillmann, Frank; Fietze, Ingo; Penzel, Thomas; Zhao, Long; Han, Fang

2017-02-01

We investigate how characteristics of sleep-wake dynamics in humans are modified by narcolepsy, a clinical condition that is supposed to destabilize sleep-wake regulation. Subjects with and without cataplexy are considered separately. Differences in sleep scoring habits as a possible confounder have been examined. Four groups of subjects are considered: narcolepsy patients from China with (n = 88) and without (n = 15) cataplexy, healthy controls from China (n = 110) and from Europe (n = 187, 2 nights each). After sleep-stage scoring and calculation of sleep characteristic parameters, the distributions of wake-episode durations and sleep-episode durations are determined for each group and fitted by power laws (exponent α) and by exponentials (decay time τ). We find that wake duration distributions are consistent with power laws for healthy subjects (China: α = 0.88, Europe: α = 1.02). Wake durations in all groups of narcolepsy patients, however, follow the exponential law (τ = 6.2-8.1 min). All sleep duration distributions are best fitted by exponentials on long time scales (τ = 34-82 min). We conclude that narcolepsy mainly alters the control of wake-episode durations but not sleep-episode durations, irrespective of cataplexy. Observed distributions of shortest wake and sleep durations suggest that differences in scoring habits regarding the scoring of short-term sleep stages may notably influence the fitting parameters but do not affect the main conclusion. © Sleep Research Society 2016. Published by Oxford University Press on behalf of the Sleep Research Society. All rights reserved. For permissions, please e-mail journals.permissions@oup.com.

Improved Reweighting of Accelerated Molecular Dynamics Simulations for Free Energy Calculation.

PubMed

Miao, Yinglong; Sinko, William; Pierce, Levi; Bucher, Denis; Walker, Ross C; McCammon, J Andrew

2014-07-08

Accelerated molecular dynamics (aMD) simulations greatly improve the efficiency of conventional molecular dynamics (cMD) for sampling biomolecular conformations, but they require proper reweighting for free energy calculation. In this work, we systematically compare the accuracy of different reweighting algorithms including the exponential average, Maclaurin series, and cumulant expansion on three model systems: alanine dipeptide, chignolin, and Trp-cage. Exponential average reweighting can recover the original free energy profiles easily only when the distribution of the boost potential is narrow (e.g., the range ≤20 k B T) as found in dihedral-boost aMD simulation of alanine dipeptide. In dual-boost aMD simulations of the studied systems, exponential average generally leads to high energetic fluctuations, largely due to the fact that the Boltzmann reweighting factors are dominated by a very few high boost potential frames. In comparison, reweighting based on Maclaurin series expansion (equivalent to cumulant expansion on the first order) greatly suppresses the energetic noise but often gives incorrect energy minimum positions and significant errors at the energy barriers (∼2-3 k B T). Finally, reweighting using cumulant expansion to the second order is able to recover the most accurate free energy profiles within statistical errors of ∼ k B T, particularly when the distribution of the boost potential exhibits low anharmonicity (i.e., near-Gaussian distribution), and should be of wide applicability. A toolkit of Python scripts for aMD reweighting "PyReweighting" is distributed free of charge at http://mccammon.ucsd.edu/computing/amdReweighting/.

Improved Reweighting of Accelerated Molecular Dynamics Simulations for Free Energy Calculation

PubMed Central

2015-01-01

Accelerated molecular dynamics (aMD) simulations greatly improve the efficiency of conventional molecular dynamics (cMD) for sampling biomolecular conformations, but they require proper reweighting for free energy calculation. In this work, we systematically compare the accuracy of different reweighting algorithms including the exponential average, Maclaurin series, and cumulant expansion on three model systems: alanine dipeptide, chignolin, and Trp-cage. Exponential average reweighting can recover the original free energy profiles easily only when the distribution of the boost potential is narrow (e.g., the range ≤20kBT) as found in dihedral-boost aMD simulation of alanine dipeptide. In dual-boost aMD simulations of the studied systems, exponential average generally leads to high energetic fluctuations, largely due to the fact that the Boltzmann reweighting factors are dominated by a very few high boost potential frames. In comparison, reweighting based on Maclaurin series expansion (equivalent to cumulant expansion on the first order) greatly suppresses the energetic noise but often gives incorrect energy minimum positions and significant errors at the energy barriers (∼2–3kBT). Finally, reweighting using cumulant expansion to the second order is able to recover the most accurate free energy profiles within statistical errors of ∼kBT, particularly when the distribution of the boost potential exhibits low anharmonicity (i.e., near-Gaussian distribution), and should be of wide applicability. A toolkit of Python scripts for aMD reweighting “PyReweighting” is distributed free of charge at http://mccammon.ucsd.edu/computing/amdReweighting/. PMID:25061441

Difference in Dwarf Galaxy Surface Brightness Profiles as a Function of Environment

NASA Astrophysics Data System (ADS)

Lee, Youngdae; Park, Hong Soo; Kim, Sang Chul; Moon, Dae-Sik; Lee, Jae-Joon; Kim, Dong-Jin; Cha, Sang-Mok

2018-05-01

We investigate surface brightness profiles (SBPs) of dwarf galaxies in field, group, and cluster environments. With deep BV I images from the Korea Microlensing Telescope Network Supernova Program, SBPs of 38 dwarfs in the NGC 2784 group are fitted by a single-exponential or double-exponential model. We find that 53% of the dwarfs are fitted with single-exponential profiles (“Type I”), while 47% of the dwarfs show double-exponential profiles; 37% of all dwarfs have smaller sizes for the outer part than the inner part (“Type II”), while 10% have a larger outer than inner part (“Type III”). We compare these results with those in the field and in the Virgo cluster, where the SBP types of 102 field dwarfs are compiled from a previous study and the SBP types of 375 cluster dwarfs are measured using SDSS r-band images. As a result, the distributions of SBP types are different in the three environments. Common SBP types for the field, the NGC 2784 group, and the Virgo cluster are Type II, Type I and II, and Type I and III profiles, respectively. After comparing the sizes of dwarfs in different environments, we suggest that since the sizes of some dwarfs are changed due to environmental effects, SBP types are capable of being transformed and the distributions of SBP types in the three environments are different. We discuss possible environmental mechanisms for the transformation of SBP types. Based on data collected at KMTNet Telescopes and SDSS.

Quantifying patterns of research interest evolution

NASA Astrophysics Data System (ADS)

Jia, Tao; Wang, Dashun; Szymanski, Boleslaw

Changing and shifting research interest is an integral part of a scientific career. Despite extensive investigations of various factors that influence a scientist's choice of research topics, quantitative assessments of mechanisms that give rise to macroscopic patterns characterizing research interest evolution of individual scientists remain limited. Here we perform a large-scale analysis of extensive publication records, finding that research interest change follows a reproducible pattern characterized by an exponential distribution. We identify three fundamental features responsible for the observed exponential distribution, which arise from a subtle interplay between exploitation and exploration in research interest evolution. We develop a random walk based model, which adequately reproduces our empirical observations. Our study presents one of the first quantitative analyses of macroscopic patterns governing research interest change, documenting a high degree of regularity underlying scientific research and individual careers.

Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling.

PubMed

Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian

2012-09-01

This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.

Generalized optimal design for two-arm, randomized phase II clinical trials with endpoints from the exponential dispersion family.

PubMed

Jiang, Wei; Mahnken, Jonathan D; He, Jianghua; Mayo, Matthew S

2016-11-01

For two-arm randomized phase II clinical trials, previous literature proposed an optimal design that minimizes the total sample sizes subject to multiple constraints on the standard errors of the estimated event rates and their difference. The original design is limited to trials with dichotomous endpoints. This paper extends the original approach to be applicable to phase II clinical trials with endpoints from the exponential dispersion family distributions. The proposed optimal design minimizes the total sample sizes needed to provide estimates of population means of both arms and their difference with pre-specified precision. Its applications on data from specific distribution families are discussed under multiple design considerations. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Cell Division and Evolution of Biological Tissues

NASA Astrophysics Data System (ADS)

Rivier, Nicolas; Arcenegui-Siemens, Xavier; Schliecker, Gudrun

A tissue is a geometrical, space-filling, random cellular network; it remains in this steady state while individual cells divide. Cell division (fragmentation) is a local, elementary topological transformation which establishes statistical equilibrium of the structure. Statistical equilibrium is characterized by observable relations (Lewis, Aboav) between cell shapes, sizes and those of their neighbours, obtained through maximum entropy and topological correlation extending to nearest neighbours only, i.e. maximal randomness. For a two-dimensional tissue (epithelium), the distribution of cell shapes and that of mother and daughter cells can be obtained from elementary geometrical and physical arguments, except for an exponential factor favouring division of larger cells, and exponential and combinatorial factors encouraging a most symmetric division. The resulting distributions are very narrow, and stationarity severely restricts the range of an adjustable structural parameter

Exponential Thurston maps and limits of quadratic differentials

NASA Astrophysics Data System (ADS)

Hubbard, John; Schleicher, Dierk; Shishikura, Mitsuhiro

2009-01-01

We give a topological characterization of postsingularly finite topological exponential maps, i.e., universal covers g\\colon{C}to{C}setminus\\{0\\} such that 0 has a finite orbit. Such a map either is Thurston equivalent to a unique holomorphic exponential map λ e^z or it has a topological obstruction called a degenerate Levy cycle. This is the first analog of Thurston's topological characterization theorem of rational maps, as published by Douady and Hubbard, for the case of infinite degree. One main tool is a theorem about the distribution of mass of an integrable quadratic differential with a given number of poles, providing an almost compact space of models for the entire mass of quadratic differentials. This theorem is given for arbitrary Riemann surfaces of finite type in a uniform way.

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

Diwaker, E-mail: diwakerphysics@gmail.com; Chakraborty, Aniruddha

The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.

Decision Support System for hydrological extremes

NASA Astrophysics Data System (ADS)

Bobée, Bernard; El Adlouni, Salaheddine

2014-05-01

The study of the tail behaviour of extreme event distributions is important in several applied statistical fields such as hydrology, finance, and telecommunications. For example in hydrology, it is important to estimate adequately extreme quantiles in order to build and manage safe and effective hydraulic structures (dams, for example). Two main classes of distributions are used in hydrological frequency analysis: the class D of sub-exponential (Gamma (G2), Gumbel, Halphen type A (HA), Halphen type B (HB)…) and the class C of regularly varying distributions (Fréchet, Log-Pearson, Halphen type IB …) with a heavier tail. A Decision Support System (DSS) based on the characterization of the right tail, corresponding low probability of excedence p (high return period T=1/p, in hydrology), has been developed. The DSS allows discriminating between the class C and D and in its last version, a new prior step is added in order to test Lognormality. Indeed, the right tail of the Lognormal distribution (LN) is between the tails of distributions of the classes C and D; studies indicated difficulty with the discrimination between LN and distributions of the classes C and D. Other tools are useful to discriminate between distributions of the same class D (HA, HB and G2; see other communication). Some numerical illustrations show that, the DSS allows discriminating between Lognormal, regularly varying and sub-exponential distributions; and lead to coherent conclusions. Key words: Regularly varying distributions, subexponential distributions, Decision Support System, Heavy tailed distribution, Extreme value theory

Transition from Exponential to Power Law Income Distributions in a Chaotic Market

NASA Astrophysics Data System (ADS)

Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo

Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.

Resource acquisition, distribution and end-use efficiencies and the growth of industrial society

NASA Astrophysics Data System (ADS)

Jarvis, A. J.; Jarvis, S. J.; Hewitt, C. N.

2015-10-01

A key feature of the growth of industrial society is the acquisition of increasing quantities of resources from the environment and their distribution for end-use. With respect to energy, the growth of industrial society appears to have been near-exponential for the last 160 years. We provide evidence that indicates that the global distribution of resources that underpins this growth may be facilitated by the continual development and expansion of near-optimal directed networks (roads, railways, flight paths, pipelines, cables etc.). However, despite this continual striving for optimisation, the distribution efficiencies of these networks must decline over time as they expand due to path lengths becoming longer and more tortuous. Therefore, to maintain long-term exponential growth the physical limits placed on the distribution networks appear to be counteracted by innovations deployed elsewhere in the system, namely at the points of acquisition and end-use of resources. We postulate that the maintenance of the growth of industrial society, as measured by global energy use, at the observed rate of ~ 2.4 % yr-1 stems from an implicit desire to optimise patterns of energy use over human working lifetimes.

A mathematical model for the occurrence of historical events

NASA Astrophysics Data System (ADS)

Ohnishi, Teruaki

2017-12-01

A mathematical model was proposed for the frequency distribution of historical inter-event time τ. A basic ingredient was constructed by assuming the significance of a newly occurring historical event depending on the magnitude of a preceding event, the decrease of its significance by oblivion during the successive events, and an independent Poisson process for the occurrence of the event. The frequency distribution of τ was derived by integrating the basic ingredient with respect to all social fields and to all stake holders. The function of such a distribution was revealed as the forms of an exponential type, a power law type or an exponential-with-a-tail type depending on the values of constants appearing in the ingredient. The validity of this model was studied by applying it to the two cases of Modern China and Northern Ireland Troubles, where the τ-distribution varies depending on the different countries interacting with China and on the different stage of history of the Troubles, respectively. This indicates that history is consisted from many components with such different types of τ-distribution, which are the similar situation to the cases of other general human activities.

Determine Neuronal Tuning Curves by Exploring Optimum Firing Rate Distribution for Information Efficiency

PubMed Central

Han, Fang; Wang, Zhijie; Fan, Hong

2017-01-01

This paper proposed a new method to determine the neuronal tuning curves for maximum information efficiency by computing the optimum firing rate distribution. Firstly, we proposed a general definition for the information efficiency, which is relevant to mutual information and neuronal energy consumption. The energy consumption is composed of two parts: neuronal basic energy consumption and neuronal spike emission energy consumption. A parameter to model the relative importance of energy consumption is introduced in the definition of the information efficiency. Then, we designed a combination of exponential functions to describe the optimum firing rate distribution based on the analysis of the dependency of the mutual information and the energy consumption on the shape of the functions of the firing rate distributions. Furthermore, we developed a rapid algorithm to search the parameter values of the optimum firing rate distribution function. Finally, we found with the rapid algorithm that a combination of two different exponential functions with two free parameters can describe the optimum firing rate distribution accurately. We also found that if the energy consumption is relatively unimportant (important) compared to the mutual information or the neuronal basic energy consumption is relatively large (small), the curve of the optimum firing rate distribution will be relatively flat (steep), and the corresponding optimum tuning curve exhibits a form of sigmoid if the stimuli distribution is normal. PMID:28270760

Properties of single NMDA receptor channels in human dentate gyrus granule cells

PubMed Central

Lieberman, David N; Mody, Istvan

1999-01-01

Cell-attached single-channel recordings of NMDA channels were carried out in human dentate gyrus granule cells acutely dissociated from slices prepared from hippocampi surgically removed for the treatment of temporal lobe epilepsy (TLE). The channels were activated by l-aspartate (250–500 nm) in the presence of saturating glycine (8 μm). The main conductance was 51 ± 3 pS. In ten of thirty granule cells, clear subconductance states were observed with a mean conductance of 42 ± 3 pS, representing 8 ± 2% of the total openings. The mean open times varied from cell to cell, possibly owing to differences in the epileptogenicity of the tissue of origin. The mean open time was 2.70 ± 0.95 ms (range, 1.24–4.78 ms). In 87% of the cells, three exponential components were required to fit the apparent open time distributions. In the remaining neurons, as in control rat granule cells, two exponentials were sufficient. Shut time distributions were fitted by five exponential components. The average numbers of openings in bursts (1.74 ± 0.09) and clusters (3.06 ± 0.26) were similar to values obtained in rodents. The mean burst (6.66 ± 0.9 ms), cluster (20.1 ± 3.3 ms) and supercluster lengths (116.7 ± 17.5 ms) were longer than those in control rat granule cells, but approached the values previously reported for TLE (kindled) rats. As in rat NMDA channels, adjacent open and shut intervals appeared to be inversely related to each other, but it was only the relative areas of the three open time constants that changed with adjacent shut time intervals. The long openings of human TLE NMDA channels resembled those produced by calcineurin inhibitors in control rat granule cells. Yet the calcineurin inhibitor FK-506 (500 nm) did not prolong the openings of human channels, consistent with a decreased calcineurin activity in human TLE. Many properties of the human NMDA channels resemble those recorded in rat hippocampal neurons. Both have similar slope conductances, five exponential shut time distributions, complex groupings of openings, and a comparable number of openings per grouping. Other properties of human TLE NMDA channels correspond to those observed in kindling; the openings are considerably long, requiring an additional exponential component to fit their distributions, and inhibition of calcineurin is without effect in prolonging the openings. PMID:10373689

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.

Base stock system for patient vs impatient customers with varying demand distribution

NASA Astrophysics Data System (ADS)

Fathima, Dowlath; Uduman, P. Sheik

2013-09-01

An optimal Base-Stock inventory policy for Patient and Impatient Customers using finite-horizon models is examined. The Base stock system for Patient and Impatient customers is a different type of inventory policy. In case of the model I, Base stock for Patient customer case is evaluated using the Truncated Exponential Distribution. The model II involves the study of Base-stock inventory policies for Impatient customer. A study on these systems reveals that the Customers wait until the arrival of the next order or the customers leaves the system which leads to lost sale. In both the models demand during the period [0, t] is taken to be a random variable. In this paper, Truncated Exponential Distribution satisfies the Base stock policy for the patient customer as a continuous model. So far the Base stock for Impatient Customers leaded to a discrete case but, in this paper we have modeled this condition into a continuous case. We justify this approach mathematically and also numerically.

The topology of large Open Connectome networks for the human brain.

PubMed

Gastner, Michael T; Ódor, Géza

2016-06-07

The structural human connectome (i.e. the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to nodes and edges. A three-parameter generalized Weibull (also known as a stretched exponential) distribution is a good fit to most of the observed degree distributions. For almost all networks, simple power laws cannot fit the data, but in some cases there is statistical support for power laws with an exponential cutoff. We also calculate the topological (graph) dimension D and the small-world coefficient σ of these networks. While σ suggests a small-world topology, we found that D < 4 showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.

The topology of large Open Connectome networks for the human brain

NASA Astrophysics Data System (ADS)

Gastner, Michael T.; Ódor, Géza

2016-06-01

The structural human connectome (i.e. the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to nodes and edges. A three-parameter generalized Weibull (also known as a stretched exponential) distribution is a good fit to most of the observed degree distributions. For almost all networks, simple power laws cannot fit the data, but in some cases there is statistical support for power laws with an exponential cutoff. We also calculate the topological (graph) dimension D and the small-world coefficient σ of these networks. While σ suggests a small-world topology, we found that D < 4 showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.

The Superstatistical Nature and Interoccurrence Time of Atmospheric Mercury Concentration Fluctuations

NASA Astrophysics Data System (ADS)

Carbone, F.; Bruno, A. G.; Naccarato, A.; De Simone, F.; Gencarelli, C. N.; Sprovieri, F.; Hedgecock, I. M.; Landis, M. S.; Skov, H.; Pfaffhuber, K. A.; Read, K. A.; Martin, L.; Angot, H.; Dommergue, A.; Magand, O.; Pirrone, N.

2018-01-01

The probability density function (PDF) of the time intervals between subsequent extreme events in atmospheric Hg0 concentration data series from different latitudes has been investigated. The Hg0 dynamic possesses a long-term memory autocorrelation function. Above a fixed threshold Q in the data, the PDFs of the interoccurrence time of the Hg0 data are well described by a Tsallis q-exponential function. This PDF behavior has been explained in the framework of superstatistics, where the competition between multiple mesoscopic processes affects the macroscopic dynamics. An extensive parameter μ, encompassing all possible fluctuations related to mesoscopic phenomena, has been identified. It follows a χ2 distribution, indicative of the superstatistical nature of the overall process. Shuffling the data series destroys the long-term memory, the distributions become independent of Q, and the PDFs collapse on to the same exponential distribution. The possible central role of atmospheric turbulence on extreme events in the Hg0 data is highlighted.

Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays.

PubMed

Wang, Dongshu; Huang, Lihong

2014-03-01

In this paper, we investigate the periodic dynamical behaviors for a class of general Cohen-Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and the fixed point theorem of multi-valued maps, the existence of periodic solutions for the neural networks is obtained. After that, we derive some sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of nonsmooth analysis theory with generalized Lyapunov approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, our results will also be valid. Moreover, our results extend previous works not only on discrete time-varying and distributed delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete time-varying and distributed delayed neural networks with discontinuous activations. We give some numerical examples to show the applicability and effectiveness of our main results. Copyright © 2013 Elsevier Ltd. All rights reserved.

Probability Distributions for Random Quantum Operations

NASA Astrophysics Data System (ADS)

Schultz, Kevin

Motivated by uncertainty quantification and inference of quantum information systems, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered in the field of orientation statistics. This approach identifies natural sample spaces and probability distributions upon these spaces that can be used in the analysis, simulation, and inference of quantum information systems. The theory of exponential families on Stiefel manifolds provides the appropriate generalization to the classical case. Furthermore, this viewpoint motivates a number of additional questions into the convex geometry of quantum operations relative to both the differential geometry of Stiefel manifolds as well as the information geometry of exponential families defined upon them. In particular, we draw on results from convex geometry to characterize which quantum operations can be represented as the average of a random quantum operation. This project was supported by the Intelligence Advanced Research Projects Activity via Department of Interior National Business Center Contract Number 2012-12050800010.

GISAXS modelling of helium-induced nano-bubble formation in tungsten and comparison with TEM

NASA Astrophysics Data System (ADS)

Thompson, Matt; Sakamoto, Ryuichi; Bernard, Elodie; Kirby, Nigel; Kluth, Patrick; Riley, Daniel; Corr, Cormac

2016-05-01

Grazing-incidence small angle x-ray scattering (GISAXS) is a powerful non-destructive technique for the measurement of nano-bubble formation in tungsten under helium plasma exposure. Here, we present a comparative study between transmission electron microscopy (TEM) and GISAXS measurements of nano-bubble formation in tungsten exposed to helium plasma in the Large Helical Device (LHD) fusion experiment. Both techniques are in excellent agreement, suggesting that nano-bubbles range from spheroidal to ellipsoidal, displaying exponential diameter distributions with mean diameters μ=0.68 ± 0.04 nm and μ=0.6 ± 0.1 nm measured by TEM and GISAXS respectively. Depth distributions were also computed, with calculated exponential depth distributions with mean depths of 8.4 ± 0.5 nm and 9.1 ± 0.4 nm for TEM and GISAXS. In GISAXS modelling, spheroidal particles were fitted with an aspect ratio ε=0.7 ± 0.1. The GISAXS model used is described in detail.

Changes in speed distribution: Applying aggregated safety effect models to individual vehicle speeds.

PubMed

Vadeby, Anna; Forsman, Åsa

2017-06-01

This study investigated the effect of applying two aggregated models (the Power model and the Exponential model) to individual vehicle speeds instead of mean speeds. This is of particular interest when the measure introduced affects different parts of the speed distribution differently. The aim was to examine how the estimated overall risk was affected when assuming the models are valid on an individual vehicle level. Speed data from two applications of speed measurements were used in the study: an evaluation of movable speed cameras and a national evaluation of new speed limits in Sweden. The results showed that when applied on individual vehicle speed level compared with aggregated level, there was essentially no difference between these for the Power model in the case of injury accidents. However, for fatalities the difference was greater, especially for roads with new cameras where those driving fastest reduced their speed the most. For the case with new speed limits, the individual approach estimated a somewhat smaller effect, reflecting that changes in the 15th percentile (P15) were somewhat larger than changes in P85 in this case. For the Exponential model there was also a clear, although small, difference between applying the model to mean speed changes and individual vehicle speed changes when speed cameras were used. This applied both for injury accidents and fatalities. There were also larger effects for the Exponential model than for the Power model, especially for injury accidents. In conclusion, applying the Power or Exponential model to individual vehicle speeds is an alternative that provides reasonable results in relation to the original Power and Exponential models, but more research is needed to clarify the shape of the individual risk curve. It is not surprising that the impact on severe traffic crashes was larger in situations where those driving fastest reduced their speed the most. Further investigations on use of the Power and/or the Exponential model at individual vehicle level would require more data on the individual level from a range of international studies. Copyright © 2017 Elsevier Ltd. All rights reserved.

Momentum distributions for the quantum delta-kicked rotor with decoherence

PubMed

Vant; Ball; Christensen

2000-05-01

We report on the momentum distribution line shapes for the quantum delta-kicked rotor in the presence of environment induced decoherence. Experimental and numerical results are presented. In the experiment ultracold cesium atoms are subjected to a pulsed standing wave of near resonant light. Spontaneous scattering of photons destroys dynamical localization. For the scattering rates used in our experiment the momentum distribution shapes remain essentially exponential.

Reliability Overhaul Model

DTIC Science & Technology

1989-08-01

Random variables for the conditional exponential distribution are generated using the inverse transform method. C1) Generate U - UCO,i) (2) Set s - A ln...e - [(x+s - 7)/ n] 0 + [Cx-T)/n]0 c. Random variables from the conditional weibull distribution are generated using the inverse transform method. C1...using a standard normal transformation and the inverse transform method. B - 3 APPENDIX 3 DISTRIBUTIONS SUPPORTED BY THE MODEL (1) Generate Y - PCX S

Topics in the Sequential Design of Experiments

DTIC Science & Technology

1992-03-01

decision , unless so designated by other documentation. 12a. DISTRIBUTION /AVAILABIIUTY STATEMENT 12b. DISTRIBUTION CODE Approved for public release...3 0 1992 D 14. SUBJECT TERMS 15. NUMBER OF PAGES12 Design of Experiments, Renewal Theory , Sequential Testing 1 2. PRICE CODE Limit Theory , Local...distributions for one parameter exponential families," by Michael Woodroofe. Stntca, 2 (1991), 91-112. [6] "A non linear renewal theory for a functional of

Statistical properties of effective drought index (EDI) for Seoul, Busan, Daegu, Mokpo in South Korea

NASA Astrophysics Data System (ADS)

Park, Jong-Hyeok; Kim, Ki-Beom; Chang, Heon-Young

2014-08-01

Time series of drought indices has been considered mostly in view of temporal and spatial distributions of a drought index so far. Here we investigate the statistical properties of a daily Effective Drought Index (EDI) itself for Seoul, Busan, Daegu, Mokpo for the period of 100 years from 1913 to 2012. We have found that both in dry and wet seasons the distribution of EDI as a function of EDI follows the Gaussian function. In dry season the shape of the Gaussian function is characteristically broader than that in wet seasons. The total number of drought days during the period we have analyzed is related both to the mean value and more importantly to the standard deviation. We have also found that according to the distribution of the number of occasions where the EDI values of several consecutive days are all less than a threshold, the distribution follows the exponential distribution. The slope of the best fit becomes steeper not only as the critical EDI value becomes more negative but also as the number of consecutive days increases. The slope of the exponential distribution becomes steeper as the number of the city in which EDI is simultaneously less than a critical EDI in a row increases. Finally, we conclude by pointing out implications of our findings.

Survival distributions impact the power of randomized placebo-phase design and parallel groups randomized clinical trials.

PubMed

Abrahamyan, Lusine; Li, Chuan Silvia; Beyene, Joseph; Willan, Andrew R; Feldman, Brian M

2011-03-01

The study evaluated the power of the randomized placebo-phase design (RPPD)-a new design of randomized clinical trials (RCTs), compared with the traditional parallel groups design, assuming various response time distributions. In the RPPD, at some point, all subjects receive the experimental therapy, and the exposure to placebo is for only a short fixed period of time. For the study, an object-oriented simulation program was written in R. The power of the simulated trials was evaluated using six scenarios, where the treatment response times followed the exponential, Weibull, or lognormal distributions. The median response time was assumed to be 355 days for the placebo and 42 days for the experimental drug. Based on the simulation results, the sample size requirements to achieve the same level of power were different under different response time to treatment distributions. The scenario where the response times followed the exponential distribution had the highest sample size requirement. In most scenarios, the parallel groups RCT had higher power compared with the RPPD. The sample size requirement varies depending on the underlying hazard distribution. The RPPD requires more subjects to achieve a similar power to the parallel groups design. Copyright © 2011 Elsevier Inc. All rights reserved.

The Mass Distribution of Stellar-mass Black Holes

NASA Astrophysics Data System (ADS)

Farr, Will M.; Sravan, Niharika; Cantrell, Andrew; Kreidberg, Laura; Bailyn, Charles D.; Mandel, Ilya; Kalogera, Vicky

2011-11-01

We perform a Bayesian analysis of the mass distribution of stellar-mass black holes using the observed masses of 15 low-mass X-ray binary systems undergoing Roche lobe overflow and 5 high-mass, wind-fed X-ray binary systems. Using Markov Chain Monte Carlo calculations, we model the mass distribution both parametrically—as a power law, exponential, Gaussian, combination of two Gaussians, or log-normal distribution—and non-parametrically—as histograms with varying numbers of bins. We provide confidence bounds on the shape of the mass distribution in the context of each model and compare the models with each other by calculating their relative Bayesian evidence as supported by the measurements, taking into account the number of degrees of freedom of each model. The mass distribution of the low-mass systems is best fit by a power law, while the distribution of the combined sample is best fit by the exponential model. This difference indicates that the low-mass subsample is not consistent with being drawn from the distribution of the combined population. We examine the existence of a "gap" between the most massive neutron stars and the least massive black holes by considering the value, M 1%, of the 1% quantile from each black hole mass distribution as the lower bound of black hole masses. Our analysis generates posterior distributions for M 1%; the best model (the power law) fitted to the low-mass systems has a distribution of lower bounds with M 1%>4.3 M sun with 90% confidence, while the best model (the exponential) fitted to all 20 systems has M 1%>4.5 M sun with 90% confidence. We conclude that our sample of black hole masses provides strong evidence of a gap between the maximum neutron star mass and the lower bound on black hole masses. Our results on the low-mass sample are in qualitative agreement with those of Ozel et al., although our broad model selection analysis more reliably reveals the best-fit quantitative description of the underlying mass distribution. The results on the combined sample of low- and high-mass systems are in qualitative agreement with Fryer & Kalogera, although the presence of a mass gap remains theoretically unexplained.

The effect of convective boundary condition on MHD mixed convection boundary layer flow over an exponentially stretching vertical sheet

NASA Astrophysics Data System (ADS)

Isa, Siti Suzilliana Putri Mohamed; Arifin, Norihan Md.; Nazar, Roslinda; Bachok, Norfifah; Ali, Fadzilah Md

2017-12-01

A theoretical study that describes the magnetohydrodynamic mixed convection boundary layer flow with heat transfer over an exponentially stretching sheet with an exponential temperature distribution has been presented herein. This study is conducted in the presence of convective heat exchange at the surface and its surroundings. The system is controlled by viscous dissipation and internal heat generation effects. The governing nonlinear partial differential equations are converted into ordinary differential equations by a similarity transformation. The converted equations are then solved numerically using the shooting method. The results related to skin friction coefficient, local Nusselt number, velocity and temperature profiles are presented for several sets of values of the parameters. The effects of the governing parameters on the features of the flow and heat transfer are examined in detail in this study.

Recurrence time statistics for finite size intervals

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; da Silva, Elton C.; Caldas, Iberê L.

2004-12-01

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected by a kind of memory effect. We interpret this effect as being related to the unstable periodic orbits inside the interval. Although it is restricted to a few short times it changes the whole distribution of recurrences. We show that for systems with strong mixing properties the exponential decay converges to the Poissonian statistics when the width of the interval goes to zero. However, we alert that special attention to the size of the interval is required in order to guarantee that the short time memory effect is negligible when one is interested in numerically or experimentally calculated Poincaré recurrence time statistics.

Fast self contained exponential random deviate algorithm

NASA Astrophysics Data System (ADS)

Fernández, Julio F.

1997-03-01

An algorithm that generates random numbers with an exponential distribution and is about ten times faster than other well known algorithms has been reported before (J. F. Fernández and J. Rivero, Comput. Phys. 10), 83 (1996). That algorithm requires input of uniform random deviates. We now report a new version of it that needs no input and is nearly as fast. The only limitation we predict thus far for the quality of the output is the amount of computer memory available. Performance results under various tests will be reported. The algorithm works in close analogy to the set up that is often used in statistical physics in order to obtain the Gibb's distribution. N numbers, that are are stored in N registers, change with time according to the rules of the algorithm, keeping their sum constant. Further details will be given.

Rainbow net analysis of VAXcluster system availability

NASA Technical Reports Server (NTRS)

Johnson, Allen M., Jr.; Schoenfelder, Michael A.

1991-01-01

A system modeling technique, Rainbow Nets, is used to evaluate the availability and mean-time-to-interrupt of the VAXcluster. These results are compared to the exact analytic results showing that reasonable accuracy is achieved through simulation. The complexity of the Rainbow Net does not increase as the number of processors increases, but remains constant, unlike a Markov model which expands exponentially. The constancy is achieved by using tokens with identity attributes (items) that can have additional attributes associated with them (features) which can exist in multiple states. The time to perform the simulation increases, but this is a polynomial increase rather than exponential. There is no restriction on distributions used for transition firing times, allowing real situations to be modeled more accurately by choosing the distribution which best fits the system performance and eliminating the need for simplifying assumptions.

A closer look at the effect of preliminary goodness-of-fit testing for normality for the one-sample t-test.

PubMed

Rochon, Justine; Kieser, Meinhard

2011-11-01

Student's one-sample t-test is a commonly used method when inference about the population mean is made. As advocated in textbooks and articles, the assumption of normality is often checked by a preliminary goodness-of-fit (GOF) test. In a paper recently published by Schucany and Ng it was shown that, for the uniform distribution, screening of samples by a pretest for normality leads to a more conservative conditional Type I error rate than application of the one-sample t-test without preliminary GOF test. In contrast, for the exponential distribution, the conditional level is even more elevated than the Type I error rate of the t-test without pretest. We examine the reasons behind these characteristics. In a simulation study, samples drawn from the exponential, lognormal, uniform, Student's t-distribution with 2 degrees of freedom (t(2) ) and the standard normal distribution that had passed normality screening, as well as the ingredients of the test statistics calculated from these samples, are investigated. For non-normal distributions, we found that preliminary testing for normality may change the distribution of means and standard deviations of the selected samples as well as the correlation between them (if the underlying distribution is non-symmetric), thus leading to altered distributions of the resulting test statistics. It is shown that for skewed distributions the excess in Type I error rate may be even more pronounced when testing one-sided hypotheses. ©2010 The British Psychological Society.

A Semi-Analytical Extraction Method for Interface and Bulk Density of States in Metal Oxide Thin-Film Transistors

PubMed Central

Chen, Weifeng; Wu, Weijing; Zhou, Lei; Xu, Miao; Wang, Lei; Peng, Junbiao

2018-01-01

A semi-analytical extraction method of interface and bulk density of states (DOS) is proposed by using the low-frequency capacitance–voltage characteristics and current–voltage characteristics of indium zinc oxide thin-film transistors (IZO TFTs). In this work, an exponential potential distribution along the depth direction of the active layer is assumed and confirmed by numerical solution of Poisson’s equation followed by device simulation. The interface DOS is obtained as a superposition of constant deep states and exponential tail states. Moreover, it is shown that the bulk DOS may be represented by the superposition of exponential deep states and exponential tail states. The extracted values of bulk DOS and interface DOS are further verified by comparing the measured transfer and output characteristics of IZO TFTs with the simulation results by a 2D device simulator ATLAS (Silvaco). As a result, the proposed extraction method may be useful for diagnosing and characterising metal oxide TFTs since it is fast to extract interface and bulk density of states (DOS) simultaneously. PMID:29534492

A UNIVERSAL NEUTRAL GAS PROFILE FOR NEARBY DISK GALAXIES

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

Bigiel, F.; Blitz, L., E-mail: bigiel@uni-heidelberg.de

2012-09-10

Based on sensitive CO measurements from HERACLES and H I data from THINGS, we show that the azimuthally averaged radial distribution of the neutral gas surface density ({Sigma}{sub HI}+ {Sigma}{sub H2}) in 33 nearby spiral galaxies exhibits a well-constrained universal exponential distribution beyond 0.2 Multiplication-Sign r{sub 25} (inside of which the scatter is large) with less than a factor of two scatter out to two optical radii r{sub 25}. Scaling the radius to r{sub 25} and the total gas surface density to the surface density at the transition radius, i.e., where {Sigma}{sub HI} and {Sigma}{sub H2} are equal, as wellmore » as removing galaxies that are interacting with their environment, yields a tightly constrained exponential fit with average scale length 0.61 {+-} 0.06 r{sub 25}. In this case, the scatter reduces to less than 40% across the optical disks (and remains below a factor of two at larger radii). We show that the tight exponential distribution of neutral gas implies that the total neutral gas mass of nearby disk galaxies depends primarily on the size of the stellar disk (influenced to some degree by the great variability of {Sigma}{sub H2} inside 0.2 Multiplication-Sign r{sub 25}). The derived prescription predicts the total gas mass in our sub-sample of 17 non-interacting disk galaxies to within a factor of two. Given the short timescale over which star formation depletes the H{sub 2} content of these galaxies and the large range of r{sub 25} in our sample, there appears to be some mechanism leading to these largely self-similar radial gas distributions in nearby disk galaxies.« less

Electrostatic screening in classical Coulomb fluids: exponential or power-law decay or both? An investigation into the effect of dispersion interactions

NASA Astrophysics Data System (ADS)

Kjellander, Roland

2006-04-01

It is shown that the nature of the non-electrostatic part of the pair interaction potential in classical Coulomb fluids can have a profound influence on the screening behaviour. Two cases are compared: (i) when the non-electrostatic part equals an arbitrary finite-ranged interaction and (ii) when a dispersion r-6 interaction potential is included. A formal analysis is done in exact statistical mechanics, including an investigation of the bridge function. It is found that the Coulombic r-1 and the dispersion r-6 potentials are coupled in a very intricate manner as regards the screening behaviour. The classical one-component plasma (OCP) is a particularly clear example due to its simplicity and is investigated in detail. When the dispersion r-6 potential is turned on, the screened electrostatic potential from a particle goes from a monotonic exponential decay, exp(-κr)/r, to a power-law decay, r-8, for large r. The pair distribution function acquire, at the same time, an r-10 decay for large r instead of the exponential one. There still remains exponentially decaying contributions to both functions, but these contributions turn oscillatory when the r-6 interaction is switched on. When the Coulomb interaction is turned off but the dispersion r-6 pair potential is kept, the decay of the pair distribution function for large r goes over from the r-10 to an r-6 behaviour, which is the normal one for fluids of electroneutral particles with dispersion interactions. Differences and similarities compared to binary electrolytes are pointed out.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Reactor Statics Module, RS-9: Multigroup Diffusion Program Using an Exponential Acceleration Technique.

ERIC Educational Resources Information Center

Macek, Victor C.

The nine Reactor Statics Modules are designed to introduce students to the use of numerical methods and digital computers for calculation of neutron flux distributions in space and energy which are needed to calculate criticality, power distribution, and fuel burnup for both slow neutron and fast neutron fission reactors. The last module, RS-9,…

Distinguishing Response Conflict and Task Conflict in the Stroop Task: Evidence from Ex-Gaussian Distribution Analysis

ERIC Educational Resources Information Center

Steinhauser, Marco; Hubner, Ronald

2009-01-01

It has been suggested that performance in the Stroop task is influenced by response conflict as well as task conflict. The present study investigated the idea that both conflict types can be isolated by applying ex-Gaussian distribution analysis which decomposes response time into a Gaussian and an exponential component. Two experiments were…

K-S Test for Goodness of Fit and Waiting Times for Fatal Plane Accidents

ERIC Educational Resources Information Center

Gwanyama, Philip Wagala

2005-01-01

The Kolmogorov?Smirnov (K-S) test for goodness of fit was developed by Kolmogorov in 1933 [1] and Smirnov in 1939 [2]. Its procedures are suitable for testing the goodness of fit of a data set for most probability distributions regardless of sample size [3-5]. These procedures, modified for the exponential distribution by Lilliefors [5] and…

Individual and group dynamics in purchasing activity

NASA Astrophysics Data System (ADS)

Gao, Lei; Guo, Jin-Li; Fan, Chao; Liu, Xue-Jiao

2013-01-01

As a major part of the daily operation in an enterprise, purchasing frequency is in constant change. Recent approaches on the human dynamics can provide some new insights into the economic behavior of companies in the supply chain. This paper captures the attributes of creation times of purchase orders to an individual vendor, as well as to all vendors, and further investigates whether they have some kind of dynamics by applying logarithmic binning to the construction of distribution plots. It’s found that the former displays a power-law distribution with approximate exponent 2.0, while the latter is fitted by a mixture distribution with both power-law and exponential characteristics. Obviously, two distinctive characteristics are presented for the interval time distribution from the perspective of individual dynamics and group dynamics. Actually, this mixing feature can be attributed to the fitting deviations as they are negligible for individual dynamics, but those of different vendors are cumulated and then lead to an exponential factor for group dynamics. To better describe the mechanism generating the heterogeneity of the purchase order assignment process from the objective company to all its vendors, a model driven by product life cycle is introduced, and then the analytical distribution and the simulation result are obtained, which are in good agreement with the empirical data.

In situ observations of snow particle size distributions over a cold frontal rainband within an extratropical cyclone

NASA Astrophysics Data System (ADS)

Yang, Jiefan; Lei, Hengchi

2016-02-01

Cloud microphysical properties of a mixed phase cloud generated by a typical extratropical cyclone in the Tongliao area, Inner Mongolia on 3 May 2014, are analyzed primarily using in situ flight observation data. This study is mainly focused on ice crystal concentration, supercooled cloud water content, and vertical distributions of fit parameters of snow particle size distributions (PSDs). The results showed several discrepancies of microphysical properties obtained during two penetrations. During penetration within precipitating cloud, the maximum ice particle concentration, liquid water content, and ice water content were increased by a factor of 2-3 compared with their counterpart obtained during penetration of a nonprecipitating cloud. The heavy rimed and irregular ice crystals obtained by 2D imagery probe as well as vertical distributions of fitting parameters within precipitating cloud show that the ice particles grow during falling via riming and aggregation process, whereas the lightly rimed and pristine ice particles as well as fitting parameters within non-precipitating cloud indicate the domination of sublimation process. During the two cloud penetrations, the PSDs were generally better represented by gamma distributions than the exponential form in terms of the determining coefficient ( R 2). The correlations between parameters of exponential /gamma form within two penetrations showed no obvious differences compared with previous studies.

Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory

NASA Astrophysics Data System (ADS)

Wang, Na; Li, Dong; Wang, Qiwen

2012-12-01

The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government policies in China on the changes of dynamics of GDP and the three industries adjustment. The work in our paper provides a new way to understand the dynamics of economic development.

The Lunar Rock Size Frequency Distribution from Diviner Infrared Measurements

NASA Astrophysics Data System (ADS)

Elder, C. M.; Hayne, P. O.; Piqueux, S.; Bandfield, J.; Williams, J. P.; Ghent, R. R.; Paige, D. A.

2016-12-01

Knowledge of the rock size frequency distribution on a planetary body is important for understanding its geologic history and for selecting landing sites. The rock size frequency distribution can be estimated by counting rocks in high resolution images, but most bodies in the solar system have limited areas with adequate coverage. We propose an alternative method to derive and map rock size frequency distributions using multispectral thermal infrared data acquired at multiple times during the night. We demonstrate this new technique for the Moon using data from the Lunar Reconnaissance Orbiter (LRO) Diviner radiometer in conjunction with three dimensional thermal modeling, leveraging the differential cooling rates of different rock sizes. We assume an exponential rock size frequency distribution, which has been shown to yield a good fit to rock populations in various locations on the Moon, Mars, and Earth [2, 3] and solve for the best radiance fits as a function of local time and wavelength. This method presents several advantages: 1) unlike other thermally derived rock abundance techniques, it is sensitive to rocks smaller than the diurnal skin depth; 2) it does not result in apparent decrease in rock abundance at night; and 3) it can be validated using images taken at the lunar surface. This method yields both the fraction of the surface covered in rocks of all sizes and the exponential factor, which defines the rate of drop-off in the exponential function at large rock sizes. We will present maps of both these parameters for the Moon, and provide a geological interpretation. In particular, this method reveals rocks in the lunar highlands that are smaller than previous thermal methods could detect. [1] Bandfield J. L. et al. (2011) JGR, 116, E00H02. [2] Golombek and Rapp (1997) JGR, 102, E2, 4117-4129. [3] Cintala, M.J. and K.M. McBride (1995) NASA Technical Memorandum 104804.

Hazard function analysis for flood planning under nonstationarity

NASA Astrophysics Data System (ADS)

Read, Laura K.; Vogel, Richard M.

2016-05-01

The field of hazard function analysis (HFA) involves a probabilistic assessment of the "time to failure" or "return period," T, of an event of interest. HFA is used in epidemiology, manufacturing, medicine, actuarial statistics, reliability engineering, economics, and elsewhere. For a stationary process, the probability distribution function (pdf) of the return period always follows an exponential distribution, the same is not true for nonstationary processes. When the process of interest, X, exhibits nonstationary behavior, HFA can provide a complementary approach to risk analysis with analytical tools particularly useful for hydrological applications. After a general introduction to HFA, we describe a new mathematical linkage between the magnitude of the flood event, X, and its return period, T, for nonstationary processes. We derive the probabilistic properties of T for a nonstationary one-parameter exponential model of X, and then use both Monte-Carlo simulation and HFA to generalize the behavior of T when X arises from a nonstationary two-parameter lognormal distribution. For this case, our findings suggest that a two-parameter Weibull distribution provides a reasonable approximation for the pdf of T. We document how HFA can provide an alternative approach to characterize the probabilistic properties of both nonstationary flood series and the resulting pdf of T.

The Universal Statistical Distributions of the Affinity, Equilibrium Constants, Kinetics and Specificity in Biomolecular Recognition

PubMed Central

Zheng, Xiliang; Wang, Jin

2015-01-01

We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics. PMID:25885453

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

PubMed

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

2012-08-01

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

Markov Analysis of Sleep Dynamics

NASA Astrophysics Data System (ADS)

Kim, J. W.; Lee, J.-S.; Robinson, P. A.; Jeong, D.-U.

2009-05-01

A new approach, based on a Markov transition matrix, is proposed to explain frequent sleep and wake transitions during sleep. The matrix is determined by analyzing hypnograms of 113 obstructive sleep apnea patients. Our approach shows that the statistics of sleep can be constructed via a single Markov process and that durations of all states have modified exponential distributions, in contrast to recent reports of a scale-free form for the wake stage and an exponential form for the sleep stage. Hypnograms of the same subjects, but treated with Continuous Positive Airway Pressure, are analyzed and compared quantitatively with the pretreatment ones, suggesting potential clinical applications.

Is a matrix exponential specification suitable for the modeling of spatial correlation structures?

PubMed Central

Strauß, Magdalena E.; Mezzetti, Maura; Leorato, Samantha

2018-01-01

This paper investigates the adequacy of the matrix exponential spatial specifications (MESS) as an alternative to the widely used spatial autoregressive models (SAR). To provide as complete a picture as possible, we extend the analysis to all the main spatial models governed by matrix exponentials comparing them with their spatial autoregressive counterparts. We propose a new implementation of Bayesian parameter estimation for the MESS model with vague prior distributions, which is shown to be precise and computationally efficient. Our implementations also account for spatially lagged regressors. We further allow for location-specific heterogeneity, which we model by including spatial splines. We conclude by comparing the performances of the different model specifications in applications to a real data set and by running simulations. Both the applications and the simulations suggest that the spatial splines are a flexible and efficient way to account for spatial heterogeneities governed by unknown mechanisms. PMID:29492375

Non-Markovian Infection Spread Dramatically Alters the Susceptible-Infected-Susceptible Epidemic Threshold in Networks

NASA Astrophysics Data System (ADS)

Van Mieghem, P.; van de Bovenkamp, R.

2013-03-01

Most studies on susceptible-infected-susceptible epidemics in networks implicitly assume Markovian behavior: the time to infect a direct neighbor is exponentially distributed. Much effort so far has been devoted to characterize and precisely compute the epidemic threshold in susceptible-infected-susceptible Markovian epidemics on networks. Here, we report the rather dramatic effect of a nonexponential infection time (while still assuming an exponential curing time) on the epidemic threshold by considering Weibullean infection times with the same mean, but different power exponent α. For three basic classes of graphs, the Erdős-Rényi random graph, scale-free graphs and lattices, the average steady-state fraction of infected nodes is simulated from which the epidemic threshold is deduced. For all graph classes, the epidemic threshold significantly increases with the power exponents α. Hence, real epidemics that violate the exponential or Markovian assumption can behave seriously differently than anticipated based on Markov theory.

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.

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.

Probability distribution of financial returns in a model of multiplicative Brownian motion with stochastic diffusion coefficient

NASA Astrophysics Data System (ADS)

Silva, Antonio

2005-03-01

It is well-known that the mathematical theory of Brownian motion was first developed in the Ph. D. thesis of Louis Bachelier for the French stock market before Einstein [1]. In Ref. [2] we studied the so-called Heston model, where the stock-price dynamics is governed by multiplicative Brownian motion with stochastic diffusion coefficient. We solved the corresponding Fokker-Planck equation exactly and found an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula interpolates between the exponential (tent-shaped) distribution for short time lags and the Gaussian (parabolic) distribution for long time lags. The theoretical formula agrees very well with the actual stock-market data ranging from the Dow-Jones index [2] to individual companies [3], such as Microsoft, Intel, etc. [] [1] Louis Bachelier, ``Th'eorie de la sp'eculation,'' Annales Scientifiques de l''Ecole Normale Sup'erieure, III-17:21-86 (1900).[] [2] A. A. Dragulescu and V. M. Yakovenko, ``Probability distribution of returns in the Heston model with stochastic volatility,'' Quantitative Finance 2, 443--453 (2002); Erratum 3, C15 (2003). [cond-mat/0203046] [] [3] A. C. Silva, R. E. Prange, and V. M. Yakovenko, ``Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact,'' Physica A 344, 227--235 (2004). [cond-mat/0401225

The competitiveness versus the wealth of a country.

PubMed

Podobnik, Boris; Horvatić, Davor; Kenett, Dror Y; Stanley, H Eugene

2012-01-01

Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its per capita GDP (gdp) rank within a decade follows an exponential distribution with decay constant λ = 0.12. We use the Corruption Perceptions Index (CPI) and the Global Competitiveness Index (GCI) and find that the distribution of change in CPI (GCI) rank follows exponential functions with approximately the same exponent as λ, suggesting that the dynamics of gdp, CPI, and GCI may share the same origin. Using the GCI, we develop a new measure, which we call relative competitiveness, to evaluate an economy's competitiveness relative to its gdp. For all European and EU countries during the 2008-2011 economic downturn we find that the drop in gdp in more competitve countries relative to gdp was substantially smaller than in relatively less competitive countries, which is valuable information for policymakers.

Study of velocity and temperature distributions in boundary layer flow of fourth grade fluid over an exponential stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Najeeb Alam; Saeed, Umair Bin; Sultan, Faqiha; Ullah, Saif; Rehman, Abdul

2018-02-01

This study deals with the investigation of boundary layer flow of a fourth grade fluid and heat transfer over an exponential stretching sheet. For analyzing two heating processes, namely, (i) prescribed surface temperature (PST), and (ii) prescribed heat flux (PHF), the temperature distribution in a fluid has been considered. The suitable transformations associated with the velocity components and temperature, have been employed for reducing the nonlinear model equation to a system of ordinary differential equations. The flow and temperature fields are revealed by solving these reduced nonlinear equations through an effective analytical method. The important findings in this analysis are to observe the effects of viscoelastic, cross-viscous, third grade fluid, and fourth grade fluid parameters on the constructed analytical expression for velocity profile. Likewise, the heat transfer properties are studied for Prandtl and Eckert numbers.

The competitiveness versus the wealth of a country

PubMed Central

Podobnik, Boris; Horvatić, Davor; Kenett, Dror Y.; Stanley, H. Eugene

2012-01-01

Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its per capita GDP (gdp) rank within a decade follows an exponential distribution with decay constant λ = 0.12. We use the Corruption Perceptions Index (CPI) and the Global Competitiveness Index (GCI) and find that the distribution of change in CPI (GCI) rank follows exponential functions with approximately the same exponent as λ, suggesting that the dynamics of gdp, CPI, and GCI may share the same origin. Using the GCI, we develop a new measure, which we call relative competitiveness, to evaluate an economy's competitiveness relative to its gdp. For all European and EU countries during the 2008–2011 economic downturn we find that the drop in gdp in more competitve countries relative to gdp was substantially smaller than in relatively less competitive countries, which is valuable information for policymakers. PMID:22997552

Inter-occurrence times and universal laws in finance, earthquakes and genomes

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2016-07-01

A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy $S_{BG}$ and its associated exponential BG factor. Frequent behaviors in such complex systems have been shown to be closely related to $q$-statistics instead, based on the nonadditive entropy $S_q$ (with $S_1=S_{BG}$), and its associated $q$-exponential factor which generalizes the usual BG one. In fact, a wide range of phenomena of quite different nature exist which can be described and, in the simplest cases, understood through analytic (and explicit) functions and probability distributions which exhibit some universal features. Universality classes are concomitantly observed which can be characterized through indices such as $q$. We will exhibit here some such cases, namely concerning the distribution of inter-occurrence (or inter-event) times in the areas of finance, earthquakes and genomes.

The competitiveness versus the wealth of a country

NASA Astrophysics Data System (ADS)

Podobnik, Boris; Horvatić, Davor; Kenett, Dror Y.; Stanley, H. Eugene

2012-09-01

Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its per capita GDP (gdp) rank within a decade follows an exponential distribution with decay constant λ = 0.12. We use the Corruption Perceptions Index (CPI) and the Global Competitiveness Index (GCI) and find that the distribution of change in CPI (GCI) rank follows exponential functions with approximately the same exponent as λ, suggesting that the dynamics of gdp, CPI, and GCI may share the same origin. Using the GCI, we develop a new measure, which we call relative competitiveness, to evaluate an economy's competitiveness relative to its gdp. For all European and EU countries during the 2008-2011 economic downturn we find that the drop in gdp in more competitve countries relative to gdp was substantially smaller than in relatively less competitive countries, which is valuable information for policymakers.

Time scale defined by the fractal structure of the price fluctuations in foreign exchange markets

NASA Astrophysics Data System (ADS)

Kumagai, Yoshiaki

2010-04-01

In this contribution, a new time scale named C-fluctuation time is defined by price fluctuations observed at a given resolution. The intraday fractal structures and the relations of the three time scales: real time (physical time), tick time and C-fluctuation time, in foreign exchange markets are analyzed. The data set used is trading prices of foreign exchange rates; US dollar (USD)/Japanese yen (JPY), USD/Euro (EUR), and EUR/JPY. The accuracy of the data is one minute and data within a minute are recorded in order of transaction. The series of instantaneous velocity of C-fluctuation time flowing are exponentially distributed for small C when they are measured by real time and for tiny C when they are measured by tick time. When the market is volatile, for larger C, the series of instantaneous velocity are exponentially distributed.

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

NASA Technical Reports Server (NTRS)

Solakiewicz, Richard; Attele, Rohan; Koshak, William

2011-01-01

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Geomorphic effectiveness of long profile shape and role of inherent geological controls, Ganga River Basin, India

NASA Astrophysics Data System (ADS)

Sonam, Sonam; Jain, Vikrant

2017-04-01

River long profile is one of the fundamental geomorphic parameters which provides a platform to study interaction of geological and geomorphic processes at different time scales. Long profile shape is governed by geological processes at 10 ^ 5 - 10 ^ 6 years' time scale and it controls the modern day (10 ^ 0 - 10 ^ 1 years' time scale) fluvial processes by controlling the spatial variability of channel slope. Identification of an appropriate model for river long profile may provide a tool to analyse the quantitative relationship between basin geology, profile shape and its geomorphic effectiveness. A systematic analysis of long profiles has been carried for the Himalayan tributaries of the Ganga River basin. Long profile shape and stream power distribution pattern is derived using SRTM DEM data (90 m spatial resolution). Peak discharge data from 34 stations is used for hydrological analysis. Lithological variability and major thrusts are marked along the river long profile. The best fit of long profile is analysed for power, logarithmic and exponential function. Second order exponential function provides the best representation of long profiles. The second order exponential equation is Z = K1*exp(-β1*L) + K2*exp(-β2*L), where Z is elevation of channel long profile, L is the length, K and β are coefficients of the exponential function. K1 and K2 are the proportion of elevation change of the long profile represented by β1 (fast) and β2 (slow) decay coefficients of the river long profile. Different values of coefficients express the variability in long profile shapes and is related with the litho-tectonic variability of the study area. Channel slope of long profile is estimated taking the derivative of exponential function. Stream power distribution pattern along long profile is estimated by superimposing the discharge and long profile slope. Sensitivity analysis of stream power distribution with decay coefficients of the second order exponential equation is evaluated for a range of coefficient values. Our analysis suggests that the amplitude of stream power peak value is dependent on K1, the proportion of elevation change coming under the fast decay exponent and the location of stream power peak is dependent of the long profile decay coefficient (β1). Different long profile shapes owing to litho-tectonic variability across the Himalayas are responsible for spatial variability of stream power distribution pattern. Most of the stream power peaks lie in the Higher Himalaya. In general, eastern rivers have higher stream power in hinterland area and low stream power in the alluvial plains. This is responsible for, 1) higher erosion rate and sediment supply in hinterland of eastern rivers, 2) the incised and stable nature of channels in the western alluvial plains and 3) aggrading channels with dynamic nature in the eastern alluvial plains. Our study shows that the spatial variability of litho-units defines the coefficients of long profile function which in turn controls the position and magnitude of stream power maxima and hence the geomorphic variability in a fluvial system.

Cell responses to single pheromone molecules may reflect the activation kinetics of olfactory receptor molecules.

PubMed

Minor, A V; Kaissling, K-E

2003-03-01

Olfactory receptor cells of the silkmoth Bombyx mori respond to single pheromone molecules with "elementary" electrical events that appear as discrete "bumps" a few milliseconds in duration, or bursts of bumps. As revealed by simulation, one bump may result from a series of random openings of one or several ion channels, producing an average inward membrane current of 1.5 pA. The distributions of durations of bumps and of gaps between bumps in a burst can be fitted by single exponentials with time constants of 10.2 ms and 40.5 ms, respectively. The distribution of burst durations is a sum of two exponentials; the number of bumps per burst obeyed a geometric distribution (mean 3.2 bumps per burst). Accordingly the elementary events could reflect transitions among three states of the pheromone receptor molecule: the vacant receptor (state 1), the pheromone-receptor complex (state 2), and the activated complex (state 3). The calculated rate constants of the transitions between states are k(21)=7.7 s(-1), k(23)=16.8 s(-1), and k(32)=98 s(-1).

The stationary non-equilibrium plasma of cosmic-ray electrons and positrons

NASA Astrophysics Data System (ADS)

Tomaschitz, Roman

2016-06-01

The statistical properties of the two-component plasma of cosmic-ray electrons and positrons measured by the AMS-02 experiment on the International Space Station and the HESS array of imaging atmospheric Cherenkov telescopes are analyzed. Stationary non-equilibrium distributions defining the relativistic electron-positron plasma are derived semi-empirically by performing spectral fits to the flux data and reconstructing the spectral number densities of the electronic and positronic components in phase space. These distributions are relativistic power-law densities with exponential cutoff, admitting an extensive entropy variable and converging to the Maxwell-Boltzmann or Fermi-Dirac distributions in the non-relativistic limit. Cosmic-ray electrons and positrons constitute a classical (low-density high-temperature) plasma due to the low fugacity in the quantized partition function. The positron fraction is assembled from the flux densities inferred from least-squares fits to the electron and positron spectra and is subjected to test by comparing with the AMS-02 flux ratio measured in the GeV interval. The calculated positron fraction extends to TeV energies, predicting a broad spectral peak at about 1 TeV followed by exponential decay.

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

NASA Astrophysics Data System (ADS)

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

2010-10-01

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

Effects of topologies on signal propagation in feedforward networks

NASA Astrophysics Data System (ADS)

Zhao, Jia; Qin, Ying-Mei; Che, Yan-Qiu

2018-01-01

We systematically investigate the effects of topologies on signal propagation in feedforward networks (FFNs) based on the FitzHugh-Nagumo neuron model. FFNs with different topological structures are constructed with same number of both in-degrees and out-degrees in each layer and given the same input signal. The propagation of firing patterns and firing rates are found to be affected by the distribution of neuron connections in the FFNs. Synchronous firing patterns emerge in the later layers of FFNs with identical, uniform, and exponential degree distributions, but the number of synchronous spike trains in the output layers of the three topologies obviously differs from one another. The firing rates in the output layers of the three FFNs can be ordered from high to low according to their topological structures as exponential, uniform, and identical distributions, respectively. Interestingly, the sequence of spiking regularity in the output layers of the three FFNs is consistent with the firing rates, but their firing synchronization is in the opposite order. In summary, the node degree is an important factor that can dramatically influence the neuronal network activity.

Effects of topologies on signal propagation in feedforward networks.

PubMed

Zhao, Jia; Qin, Ying-Mei; Che, Yan-Qiu

2018-01-01

We systematically investigate the effects of topologies on signal propagation in feedforward networks (FFNs) based on the FitzHugh-Nagumo neuron model. FFNs with different topological structures are constructed with same number of both in-degrees and out-degrees in each layer and given the same input signal. The propagation of firing patterns and firing rates are found to be affected by the distribution of neuron connections in the FFNs. Synchronous firing patterns emerge in the later layers of FFNs with identical, uniform, and exponential degree distributions, but the number of synchronous spike trains in the output layers of the three topologies obviously differs from one another. The firing rates in the output layers of the three FFNs can be ordered from high to low according to their topological structures as exponential, uniform, and identical distributions, respectively. Interestingly, the sequence of spiking regularity in the output layers of the three FFNs is consistent with the firing rates, but their firing synchronization is in the opposite order. In summary, the node degree is an important factor that can dramatically influence the neuronal network activity.

A study of personal income distributions in Australia and Italy

NASA Astrophysics Data System (ADS)

Banerjee, Anand; Yakovenko, Victor

2006-03-01

The study of income distribution has a long history. A century ago, the Italian physicist and economist Pareto proposed that income distribution obeys a universal power law, valid for all time and countries. Subsequent studies proved that only the top 1-3% of the population follow a power law. For USA, the rest 97-99% of the population follow the exponential distribution [1]. We present the results of a similar study for Australia and Italy. [1] A. C. Silva and V. M. Yakovenko, Europhys. Lett.69, 304 (2005).

Learning Search Control Knowledge for Deep Space Network Scheduling

NASA Technical Reports Server (NTRS)

Gratch, Jonathan; Chien, Steve; DeJong, Gerald

1993-01-01

While the general class of most scheduling problems is NP-hard in worst-case complexity, in practice, for specific distributions of problems and constraints, domain-specific solutions have been shown to perform in much better than exponential time.

Inland empire logistics GIS mapping project.

DOT National Transportation Integrated Search

2009-01-01

The Inland Empire has experienced exponential growth in the area of warehousing and distribution facilities within the last decade and it seems that it will continue way into the future. Where are these facilities located? How large are the facilitie...

Anomalous Diffusion in a Trading Model

NASA Astrophysics Data System (ADS)

Khidzir, Sidiq Mohamad; Wan Abdullah, Wan Ahmad Tajuddin

2009-07-01

The result of the trading model by Chakrabarti et al. [1] is the wealth distribution with a mixed exponential and power law distribution. Based on the motivation of studying the dynamics behind the flow of money similar to work done by Brockmann [2, 3] we track the flow of money in this trading model to observe anomalous diffusion in the form of long waiting times and Levy Flights.

Modeling of microporous silicon betaelectric converter with 63Ni plating in GEANT4 toolkit*

NASA Astrophysics Data System (ADS)

Zelenkov, P. V.; Sidorov, V. G.; Lelekov, E. T.; Khoroshko, A. Y.; Bogdanov, S. V.; Lelekov, A. T.

2016-04-01

The model of electron-hole pairs generation rate distribution in semiconductor is needed to optimize the parameters of microporous silicon betaelectric converter, which uses 63Ni isotope radiation. By using Monte-Carlo methods of GEANT4 software with ultra-low energy electron physics models this distribution in silicon was calculated and approximated with exponential function. Optimal pore configuration was estimated.

A Comparison of the Pencil-of-Function Method with Prony’s Method, Wiener Filters and Other Identification Techniques,

DTIC Science & Technology

1977-12-01

exponentials encountered are complex and zhey are approximately at harmonic frequencies. Moreover, the real parts of the complex exponencials are much...functions as a basis for expanding the current distribution on an antenna by the method of moments results in a regularized ill-posed problem with respect...to the current distribution on the antenna structure. However, the problem is not regularized with respect to chaoge because the chaPge distribution

Droplet size and velocity distributions for spray modelling

NASA Astrophysics Data System (ADS)

Jones, D. P.; Watkins, A. P.

2012-01-01

Methods for constructing droplet size distributions and droplet velocity profiles are examined as a basis for the Eulerian spray model proposed in Beck and Watkins (2002,2003) [5,6]. Within the spray model, both distributions must be calculated at every control volume at every time-step where the spray is present and valid distributions must be guaranteed. Results show that the Maximum Entropy formalism combined with the Gamma distribution satisfy these conditions for the droplet size distributions. Approximating the droplet velocity profile is shown to be considerably more difficult due to the fact that it does not have compact support. An exponential model with a constrained exponent offers plausible profiles.

Exponential stabilization of magnetoelastic waves in a Mindlin-Timoshenko plate by localized internal damping

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-08-01

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.

Parabolic replicator dynamics and the principle of minimum Tsallis information gain

PubMed Central

2013-01-01

Background Non-linear, parabolic (sub-exponential) and hyperbolic (super-exponential) models of prebiological evolution of molecular replicators have been proposed and extensively studied. The parabolic models appear to be the most realistic approximations of real-life replicator systems due primarily to product inhibition. Unlike the more traditional exponential models, the distribution of individual frequencies in an evolving parabolic population is not described by the Maximum Entropy (MaxEnt) Principle in its traditional form, whereby the distribution with the maximum Shannon entropy is chosen among all the distributions that are possible under the given constraints. We sought to identify a more general form of the MaxEnt principle that would be applicable to parabolic growth. Results We consider a model of a population that reproduces according to the parabolic growth law and show that the frequencies of individuals in the population minimize the Tsallis relative entropy (non-additive information gain) at each time moment. Next, we consider a model of a parabolically growing population that maintains a constant total size and provide an “implicit” solution for this system. We show that in this case, the frequencies of the individuals in the population also minimize the Tsallis information gain at each moment of the ‘internal time” of the population. Conclusions The results of this analysis show that the general MaxEnt principle is the underlying law for the evolution of a broad class of replicator systems including not only exponential but also parabolic and hyperbolic systems. The choice of the appropriate entropy (information) function depends on the growth dynamics of a particular class of systems. The Tsallis entropy is non-additive for independent subsystems, i.e. the information on the subsystems is insufficient to describe the system as a whole. In the context of prebiotic evolution, this “non-reductionist” nature of parabolic replicator systems might reflect the importance of group selection and competition between ensembles of cooperating replicators. Reviewers This article was reviewed by Viswanadham Sridhara (nominated by Claus Wilke), Puushottam Dixit (nominated by Sergei Maslov), and Nick Grishin. For the complete reviews, see the Reviewers’ Reports section. PMID:23937956

Bimodal spatial distribution of macular pigment: evidence of a gender relationship

NASA Astrophysics Data System (ADS)

Delori, François C.; Goger, Douglas G.; Keilhauer, Claudia; Salvetti, Paola; Staurenghi, Giovanni

2006-03-01

The spatial distribution of the optical density of the human macular pigment measured by two-wavelength autofluorescence imaging exhibits in over half of the subjects an annulus of higher density superimposed on a central exponential-like distribution. This annulus is located at about 0.7° from the fovea. Women have broader distributions than men, and they are more likely to exhibit this bimodal distribution. Maxwell's spot reported by subjects matches the measured distribution of their pigment. Evidence that the shape of the foveal depression may be gender related leads us to hypothesize that differences in macular pigment distribution are related to anatomical differences in the shape of the foveal depression.

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.

Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations

PubMed Central

Good, Benjamin H.; Rouzine, Igor M.; Balick, Daniel J.; Hallatschek, Oskar; Desai, Michael M.

2012-01-01

When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix. This phenomenon of interference arises from competition between mutations of different strengths as well as competition between mutations that arise on different fitness backgrounds. Previous work has explored each of these effects in isolation, but the way they combine to influence the dynamics of adaptation remains largely unknown. Here, we describe a theoretical model to treat both aspects of interference in large populations. We calculate the rate of adaptation and the distribution of fixed mutational effects accumulated by the population. We focus particular attention on the case when the effects of beneficial mutations are exponentially distributed, as well as on a more general class of exponential-like distributions. In both cases, we show that the rate of adaptation and the influence of genetic background on the fixation of new mutants is equivalent to an effective model with a single selection coefficient and rescaled mutation rate, and we explicitly calculate these effective parameters. We find that the effective selection coefficient exactly coincides with the most common fixed mutational effect. This equivalence leads to an intuitive picture of the relative importance of different types of interference effects, which can shift dramatically as a function of the population size, mutation rate, and the underlying distribution of fitness effects. PMID:22371564

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.

Anomalous NMR Relaxation in Cartilage Matrix Components and Native Cartilage: Fractional-Order Models

PubMed Central

Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-01-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Li, Weiguo; Pilar Velasco, M.; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-06-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena ( T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter ( α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues.

Mathematical Aspects of Reliability-Centered Maintenance

DTIC Science & Technology

1977-01-01

exponential distribu~tion, .whose parameter (-hazard rate) can be realistically estimated., La ma SuWiaWItib~ This distribution is als4.. frequently...statistical methods to the study ýf hysicA3 reality was beset with .philosc\\phicsl problems arising from the irrefutable observacion that there isibut one...STATISTICS, 2nd ed. New York: John Wiley & Sons ; 1954. 5. Kolmogorov, A. Interpolation und Extrapolation von stationwren zuf-lligen Folgen. BULL. DE

Context-Sensitive Detection of Local Community Structure

DTIC Science & Technology

2011-04-01

characters in the Victor Hugo novel Les Miserables (lesmis).[77 vertices, 254 edges] [Knu93]. • The neural network of the nematode C. Elegans (c.elegans...adjectives and nouns in the Novel David Cop- perfield by Charles Dickens.[112 vertices, 425 edges] [New06]. • Les Miserables . Co-appearance network of...exponential distribution. The degree distributions of the Network Science, Les Miserables , and Word Adjacencies networks display a similar heavy tail. By

Complexity and Productivity Differentiation Models of Metallogenic Indicator Elements in Rocks and Supergene Media Around Daijiazhuang Pb-Zn Deposit in Dangchang County, Gansu Province

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

He, Jin-zhong, E-mail: viewsino@163.com; Yao, Shu-zhen; Zhang, Zhong-ping

2013-03-15

With the help of complexity indices, we quantitatively studied multifractals, frequency distributions, and linear and nonlinear characteristics of geochemical data for exploration of the Daijiazhuang Pb-Zn deposit. Furthermore, we derived productivity differentiation models of elements from thermodynamics and self-organized criticality of metallogenic systems. With respect to frequency distributions and multifractals, only Zn in rocks and most elements except Sb in secondary media, which had been derived mainly from weathering and alluviation, exhibit nonlinear distributions. The relations of productivity to concentrations of metallogenic elements and paragenic elements in rocks and those of elements strongly leached in secondary media can be seenmore » as linear addition of exponential functions with a characteristic weak chaos. The relations of associated elements such as Mo, Sb, and Hg in rocks and other elements in secondary media can be expressed as an exponential function, and the relations of one-phase self-organized geological or metallogenic processes can be represented by a power function, each representing secondary chaos or strong chaos. For secondary media, exploration data of most elements should be processed using nonlinear mathematical methods or should be transformed to linear distributions before processing using linear mathematical methods.« less

Fluctuations in Wikipedia access-rate and edit-event data

NASA Astrophysics Data System (ADS)

Kämpf, Mirko; Tismer, Sebastian; Kantelhardt, Jan W.; Muchnik, Lev

2012-12-01

Internet-based social networks often reflect extreme events in nature and society by drastic increases in user activity. We study and compare the dynamics of the two major complex processes necessary for information spread via the online encyclopedia ‘Wikipedia’, i.e., article editing (information upload) and article access (information viewing) based on article edit-event time series and (hourly) user access-rate time series for all articles. Daily and weekly activity patterns occur in addition to fluctuations and bursting activity. The bursts (i.e., significant increases in activity for an extended period of time) are characterized by a power-law distribution of durations of increases and decreases. For describing the recurrence and clustering of bursts we investigate the statistics of the return intervals between them. We find stretched exponential distributions of return intervals in access-rate time series, while edit-event time series yield simple exponential distributions. To characterize the fluctuation behavior we apply detrended fluctuation analysis (DFA), finding that most article access-rate time series are characterized by strong long-term correlations with fluctuation exponents α≈0.9. The results indicate significant differences in the dynamics of information upload and access and help in understanding the complex process of collecting, processing, validating, and distributing information in self-organized social networks.

Beyond Word Frequency: Bursts, Lulls, and Scaling in the Temporal Distributions of Words

PubMed Central

Altmann, Eduardo G.; Pierrehumbert, Janet B.; Motter, Adilson E.

2009-01-01

Background Zipf's discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication. More recent research has also identified scaling regularities in the dynamics underlying the successive occurrences of events, suggesting the possibility of similar findings for language as well. Methodology/Principal Findings By considering frequent words in USENET discussion groups and in disparate databases where the language has different levels of formality, here we show that the distributions of distances between successive occurrences of the same word display bursty deviations from a Poisson process and are well characterized by a stretched exponential (Weibull) scaling. The extent of this deviation depends strongly on semantic type – a measure of the logicality of each word – and less strongly on frequency. We develop a generative model of this behavior that fully determines the dynamics of word usage. Conclusions/Significance Recurrence patterns of words are well described by a stretched exponential distribution of recurrence times, an empirical scaling that cannot be anticipated from Zipf's law. Because the use of words provides a uniquely precise and powerful lens on human thought and activity, our findings also have implications for other overt manifestations of collective human dynamics. PMID:19907645

Cluster-cluster aggregation with particle replication and chemotaxy: a simple model for the growth of animal cells in culture

NASA Astrophysics Data System (ADS)

Alves, S. G.; Martins, M. L.

2010-09-01

Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and in vitro drug testing. In the present paper, a cluster-cluster aggregation model with stochastic particle replication and chemotactically driven motility is investigated as a model for the growth of animal cells in culture. The focus is on the scaling laws governing the aggregation kinetics. Our simulations reveal that in the absence of chemotaxy the mean cluster size and the total number of clusters scale in time as stretched exponentials dependent on the particle replication rate. Also, the dynamical cluster size distribution functions are represented by a scaling relation in which the scaling function involves a stretched exponential of the time. The introduction of chemoattraction among the particles leads to distribution functions decaying as power laws with exponents that decrease in time. The fractal dimensions and size distributions of the simulated clusters are qualitatively discussed in terms of those determined experimentally for several normal and tumoral cell lines growing in culture. It is shown that particle replication and chemotaxy account for the simplest cluster size distributions of cellular aggregates observed in culture.

Exponential Arithmetic Based Self-Healing Group Key Distribution Scheme with Backward Secrecy under the Resource-Constrained Wireless Networks

PubMed Central

Guo, Hua; Zheng, Yandong; Zhang, Xiyong; Li, Zhoujun

2016-01-01

In resource-constrained wireless networks, resources such as storage space and communication bandwidth are limited. To guarantee secure communication in resource-constrained wireless networks, group keys should be distributed to users. The self-healing group key distribution (SGKD) scheme is a promising cryptographic tool, which can be used to distribute and update the group key for the secure group communication over unreliable wireless networks. Among all known SGKD schemes, exponential arithmetic based SGKD (E-SGKD) schemes reduce the storage overhead to constant, thus is suitable for the the resource-constrained wireless networks. In this paper, we provide a new mechanism to achieve E-SGKD schemes with backward secrecy. We first propose a basic E-SGKD scheme based on a known polynomial-based SGKD, where it has optimal storage overhead while having no backward secrecy. To obtain the backward secrecy and reduce the communication overhead, we introduce a novel approach for message broadcasting and self-healing. Compared with other E-SGKD schemes, our new E-SGKD scheme has the optimal storage overhead, high communication efficiency and satisfactory security. The simulation results in Zigbee-based networks show that the proposed scheme is suitable for the resource-restrained wireless networks. Finally, we show the application of our proposed scheme. PMID:27136550

Bayesian analysis of the kinetics of quantal transmitter secretion at the neuromuscular junction.

PubMed

Saveliev, Anatoly; Khuzakhmetova, Venera; Samigullin, Dmitry; Skorinkin, Andrey; Kovyazina, Irina; Nikolsky, Eugeny; Bukharaeva, Ellya

2015-10-01

The timing of transmitter release from nerve endings is considered nowadays as one of the factors determining the plasticity and efficacy of synaptic transmission. In the neuromuscular junction, the moments of release of individual acetylcholine quanta are related to the synaptic delays of uniquantal endplate currents recorded under conditions of lowered extracellular calcium. Using Bayesian modelling, we performed a statistical analysis of synaptic delays in mouse neuromuscular junction with different patterns of rhythmic nerve stimulation and when the entry of calcium ions into the nerve terminal was modified. We have obtained a statistical model of the release timing which is represented as the summation of two independent statistical distributions. The first of these is the exponentially modified Gaussian distribution. The mixture of normal and exponential components in this distribution can be interpreted as a two-stage mechanism of early and late periods of phasic synchronous secretion. The parameters of this distribution depend on both the stimulation frequency of the motor nerve and the calcium ions' entry conditions. The second distribution was modelled as quasi-uniform, with parameters independent of nerve stimulation frequency and calcium entry. Two different probability density functions for the distribution of synaptic delays suggest at least two independent processes controlling the time course of secretion, one of them potentially involving two stages. The relative contribution of these processes to the total number of mediator quanta released depends differently on the motor nerve stimulation pattern and on calcium ion entry into nerve endings.

Lévy flight with absorption: A model for diffusing diffusivity with long tails

NASA Astrophysics Data System (ADS)

Jain, Rohit; Sebastian, K. L.

2017-03-01

We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016), 10.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., ∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., πe(D ) ˜e-D /D0 . In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., πe(D ) ˜D-1 -α with 0 <α <1 . We find that in the short time limit, the width of displacement distribution is proportional to √{T }, implying that the diffusion is Fickian. But for long times, the width is proportional to T1 /2 α which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2 α which preserves its shape at all times.

Obstructive sleep apnea alters sleep stage transition dynamics.

PubMed

Bianchi, Matt T; Cash, Sydney S; Mietus, Joseph; Peng, Chung-Kang; Thomas, Robert

2010-06-28

Enhanced characterization of sleep architecture, compared with routine polysomnographic metrics such as stage percentages and sleep efficiency, may improve the predictive phenotyping of fragmented sleep. One approach involves using stage transition analysis to characterize sleep continuity. We analyzed hypnograms from Sleep Heart Health Study (SHHS) participants using the following stage designations: wake after sleep onset (WASO), non-rapid eye movement (NREM) sleep, and REM sleep. We show that individual patient hypnograms contain insufficient number of bouts to adequately describe the transition kinetics, necessitating pooling of data. We compared a control group of individuals free of medications, obstructive sleep apnea (OSA), medical co-morbidities, or sleepiness (n = 374) with mild (n = 496) or severe OSA (n = 338). WASO, REM sleep, and NREM sleep bout durations exhibited multi-exponential temporal dynamics. The presence of OSA accelerated the "decay" rate of NREM and REM sleep bouts, resulting in instability manifesting as shorter bouts and increased number of stage transitions. For WASO bouts, previously attributed to a power law process, a multi-exponential decay described the data well. Simulations demonstrated that a multi-exponential process can mimic a power law distribution. OSA alters sleep architecture dynamics by decreasing the temporal stability of NREM and REM sleep bouts. Multi-exponential fitting is superior to routine mono-exponential fitting, and may thus provide improved predictive metrics of sleep continuity. However, because a single night of sleep contains insufficient transitions to characterize these dynamics, extended monitoring of sleep, probably at home, would be necessary for individualized clinical application.

Stochastic processes in the social sciences: Markets, prices and wealth distributions

NASA Astrophysics Data System (ADS)

Romero, Natalia E.

The present work uses statistical mechanics tools to investigate the dynamics of markets, prices, trades and wealth distribution. We studied the evolution of market dynamics in different stages of historical development by analyzing commodity prices from two distinct periods ancient Babylon, and medieval and early modern England. We find that the first-digit distributions of both Babylon and England commodity prices follow Benfords law, indicating that the data represent empirical observations typically arising from a free market. Further, we find that the normalized prices of both Babylon and England agricultural commodities are characterized by stretched exponential distributions, and exhibit persistent correlations of a power law type over long periods of up to several centuries, in contrast to contemporary markets. Our findings suggest that similar market interactions may underlie the dynamics of ancient agricultural commodity prices, and that these interactions may remain stable across centuries. To further investigate the dynamics of markets we present the analogy between transfers of money between individuals and the transfer of energy through particle collisions by means of the kinetic theory of gases. We introduce a theoretical framework of how the micro rules of trading lead to the emergence of income and wealth distribution. Particularly, we study the effects of different types of distribution of savings/investments among individuals in a society and different welfare/subsidies redistribution policies. Results show that while considering savings propensities the models approach empirical distributions of wealth quite well the effect of redistribution better captures specific features of the distributions which earlier models failed to do; moreover the models still preserve the exponential decay observed in empirical income distributions reported by tax data and surveys.

Frequency Distribution of Seismic Intensity in Japan between 1950 and 2009

NASA Astrophysics Data System (ADS)

Kato, M.; Kohayakawa, Y.

2012-12-01

JMA Seismic Intensity is an index of seismic ground motion which is frequently used and reported in the media. While it is always difficult to represent complex ground motion with one index, the fact that it is widely accepted in the society makes the use of JMA Seismic Intensity preferable when seismologists communicate with the public and discuss hazard assessment and risk management. With the introduction on JMA Instrumental Intensity in 1996, the number of seismic intensity observation sites has substantially increased and the spatial coverage has improved vastly. Together with a long history of non-instrumental intensity records, the intensity data represent some aspects of the seismic ground motion in Japan. We investigate characteristics of seismic ground motion between 1950 and 2009 utilizing JMA Seismic Intensity Database. Specifically we are interested in the frequency distribution of intensity recordings. Observations of large intensity is rare compared to those of small intensity, and previous studies such as Ikegami [1961] demonstrated that frequency distribution of observed intensity obeys an exponential law, which is equivalent to the Ishimoto-Iida law [Ishimoto & Iida, 1939]. Such behavior could be used to empirically construct probabilistic seismic hazard maps [e.g., Kawasumi, 1951]. For the recent instrumental intensity data as well as pre-instrumental data, we are able to confirm that Ishimoto-Iida law explains the observation. Exponents of the Ishimoto-Iida law, or slope of the exponential law in the semi-log plot, is approximately 0.5. At stations with long recordings, there is no apparent difference between pre-instrumental and instrumental intensities when Ishimoto-Iida law is used as a measure. Numbers of average intensity reports per year and exponents of the frequency distribution curve vary regionally and local seismicity is apparently the controlling factor. The observed numbers of large intensity is slightly less than extrapolated and predicted from those of small intensity assuming the exponential relation.

Wigner functions for evanescent waves.

PubMed

Petruccelli, Jonathan C; Tian, Lei; Oh, Se Baek; Barbastathis, George

2012-09-01

We propose phase space distributions, based on an extension of the Wigner distribution function, to describe fields of any state of coherence that contain evanescent components emitted into a half-space. The evanescent components of the field are described in an optical phase space of spatial position and complex-valued angle. Behavior of these distributions upon propagation is also considered, where the rapid decay of the evanescent components is associated with the exponential decay of the associated phase space distributions. To demonstrate the structure and behavior of these distributions, we consider the fields generated from total internal reflection of a Gaussian Schell-model beam at a planar interface.

Avalanche Analysis from Multielectrode Ensemble Recordings in Cat, Monkey, and Human Cerebral Cortex during Wakefulness and Sleep

PubMed Central

Dehghani, Nima; Hatsopoulos, Nicholas G.; Haga, Zach D.; Parker, Rebecca A.; Greger, Bradley; Halgren, Eric; Cash, Sydney S.; Destexhe, Alain

2012-01-01

Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been observed in neural systems, particularly, in neuronal cultures. However, the presence of critical states in the awake brain remains controversial. Here, we compared avalanche analyses performed on different in vivo preparations during wakefulness, slow-wave sleep, and REM sleep, using high density electrode arrays in cat motor cortex (96 electrodes), monkey motor cortex and premotor cortex and human temporal cortex (96 electrodes) in epileptic patients. In neuronal avalanches defined from units (up to 160 single units), the size of avalanches never clearly scaled as power-law, but rather scaled exponentially or displayed intermediate scaling. We also analyzed the dynamics of local field potentials (LFPs) and in particular LFP negative peaks (nLFPs) among the different electrodes (up to 96 sites in temporal cortex or up to 128 sites in adjacent motor and premotor cortices). In this case, the avalanches defined from nLFPs displayed power-law scaling in double logarithmic representations, as reported previously in monkey. However, avalanche defined as positive LFP (pLFP) peaks, which are less directly related to neuronal firing, also displayed apparent power-law scaling. Closer examination of this scaling using the more reliable cumulative distribution function (CDF) and other rigorous statistical measures, did not confirm power-law scaling. The same pattern was seen for cats, monkey, and human, as well as for different brain states of wakefulness and sleep. We also tested other alternative distributions. Multiple exponential fitting yielded optimal fits of the avalanche dynamics with bi-exponential distributions. Collectively, these results show no clear evidence for power-law scaling or self-organized critical states in the awake and sleeping brain of mammals, from cat to man. PMID:22934053

Distributions of Autocorrelated First-Order Kinetic Outcomes: Illness Severity

PubMed Central

Englehardt, James D.

2015-01-01

Many complex systems produce outcomes having recurring, power law-like distributions over wide ranges. However, the form necessarily breaks down at extremes, whereas the Weibull distribution has been demonstrated over the full observed range. Here the Weibull distribution is derived as the asymptotic distribution of generalized first-order kinetic processes, with convergence driven by autocorrelation, and entropy maximization subject to finite positive mean, of the incremental compounding rates. Process increments represent multiplicative causes. In particular, illness severities are modeled as such, occurring in proportion to products of, e.g., chronic toxicant fractions passed by organs along a pathway, or rates of interacting oncogenic mutations. The Weibull form is also argued theoretically and by simulation to be robust to the onset of saturation kinetics. The Weibull exponential parameter is shown to indicate the number and widths of the first-order compounding increments, the extent of rate autocorrelation, and the degree to which process increments are distributed exponential. In contrast with the Gaussian result in linear independent systems, the form is driven not by independence and multiplicity of process increments, but by increment autocorrelation and entropy. In some physical systems the form may be attracting, due to multiplicative evolution of outcome magnitudes towards extreme values potentially much larger and smaller than control mechanisms can contain. The Weibull distribution is demonstrated in preference to the lognormal and Pareto I for illness severities versus (a) toxicokinetic models, (b) biologically-based network models, (c) scholastic and psychological test score data for children with prenatal mercury exposure, and (d) time-to-tumor data of the ED01 study. PMID:26061263

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

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2016-02-01

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

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

PubMed

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

2013-07-21

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

Power laws in citation distributions: evidence from Scopus.

PubMed

Brzezinski, Michal

Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper is concerned with rigorous empirical detection of power-law behaviour in the distribution of citations received by the most highly cited scientific papers. We have used a large, novel data set on citations to scientific papers published between 1998 and 2002 drawn from Scopus. The power-law model is compared with a number of alternative models using a likelihood ratio test. We have found that the power-law hypothesis is rejected for around half of the Scopus fields of science. For these fields of science, the Yule, power-law with exponential cut-off and log-normal distributions seem to fit the data better than the pure power-law model. On the other hand, when the power-law hypothesis is not rejected, it is usually empirically indistinguishable from most of the alternative models. The pure power-law model seems to be the best model only for the most highly cited papers in "Physics and Astronomy". Overall, our results seem to support theories implying that the most highly cited scientific papers follow the Yule, power-law with exponential cut-off or log-normal distribution. Our findings suggest also that power laws in citation distributions, when present, account only for a very small fraction of the published papers (less than 1 % for most of science fields) and that the power-law scaling parameter (exponent) is substantially higher (from around 3.2 to around 4.7) than found in the older literature.

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

PubMed

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2013-04-01

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling , or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.

Numerical study of MHD nanofluid flow and heat transfer past a bidirectional exponentially stretching sheet

NASA Astrophysics Data System (ADS)

Ahmad, Rida; Mustafa, M.; Hayat, T.; Alsaedi, A.

2016-06-01

Recent advancements in nanotechnology have led to the discovery of new generation coolants known as nanofluids. Nanofluids possess novel and unique characteristics which are fruitful in numerous cooling applications. Current work is undertaken to address the heat transfer in MHD three-dimensional flow of magnetic nanofluid (ferrofluid) over a bidirectional exponentially stretching sheet. The base fluid is considered as water which consists of magnetite-Fe3O4 nanoparticles. Exponentially varying surface temperature distribution is accounted. Problem formulation is presented through the Maxwell models for effective electrical conductivity and effective thermal conductivity of nanofluid. Similarity transformations give rise to a coupled non-linear differential system which is solved numerically. Appreciable growth in the convective heat transfer coefficient is observed when nanoparticle volume fraction is augmented. Temperature exponent parameter serves to enhance the heat transfer from the surface. Moreover the skin friction coefficient is directly proportional to both magnetic field strength and nanoparticle volume fraction.

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS

PubMed Central

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2015-01-01

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM’s expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses. PMID:26166910

Single-channel activations and concentration jumps: comparison of recombinant NR1a/NR2A and NR1a/NR2D NMDA receptors

PubMed Central

Wyllie, David J A; Béhé, Philippe; Colquhoun, David

1998-01-01

We have expressed recombinant NR1a/NR2A and NR1a/NR2D N-methyl-D-aspartate (NMDA) receptor channels in Xenopus oocytes and made recordings of single-channel and macroscopic currents in outside-out membrane patches. For each receptor type we measured (a) the individual single-channel activations evoked by low glutamate concentrations in steady-state recordings, and (b) the macroscopic responses elicited by brief concentration jumps with high agonist concentrations, and we explore the relationship between these two sorts of observation. Low concentration (5–100 nM) steady-state recordings of NR1a/NR2A and NR1a/NR2D single-channel activity generated shut-time distributions that were best fitted with a mixture of five and six exponential components, respectively. Individual activations of either receptor type were resolved as bursts of openings, which we refer to as ‘super-clusters’. During a single activation, NR1a/NR2A receptors were open for 36 % of the time, but NR1a/NR2D receptors were open for only 4 % of the time. For both, distributions of super-cluster durations were best fitted with a mixture of six exponential components. Their overall mean durations were 35.8 and 1602 ms, respectively. Steady-state super-clusters were aligned on their first openings and averaged. The average was well fitted by a sum of exponentials with time constants taken from fits to super-cluster length distributions. It is shown that this is what would be expected for a channel that shows simple Markovian behaviour. The current through NR1a/NR2A channels following a concentration jump from zero to 1 mM glutamate for 1 ms was well fitted by three exponential components with time constants of 13 ms (rising phase), 70 ms and 350 ms (decaying phase). Similar concentration jumps on NR1a/NR2D channels were well fitted by two exponentials with means of 45 ms (rising phase) and 4408 ms (decaying phase) components. During prolonged exposure to glutamate, NR1a/NR2A channels desensitized with a time constant of 649 ms, while NR1a/NR2D channels exhibited no apparent desensitization. We show that under certain conditions, the time constants for the macroscopic jump response should be the same as those for the distribution of super-cluster lengths, though the resolution of the latter is so much greater that it cannot be expected that all the components will be resolvable in a macroscopic current. Good agreement was found for jumps on NR1a/NR2D receptors, and for some jump experiments on NR1a/NR2A. However, the latter were rather variable and some were slower than predicted. Slow decays were associated with patches that had large currents. PMID:9625862

None of the Above

ERIC Educational Resources Information Center

Ray, Mark

2013-01-01

The exponential influx of digital content and mobile devices into schools begs for school librarians to engage in discussions and decision making about the selection, classification, management, and distribution of content ranging from e-books to open educational resources. As information professionals, school librarians should channel their inner…

Inhomogeneous growth of fluctuations of concentration of inertial particles in channel turbulence

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Schmidt, Lukas; Ditlevsen, Peter; van Reeuwijk, Maarten; Holzner, Markus

2018-06-01

We study the growth of concentration fluctuations of weakly inertial particles in the turbulent channel flow starting with a smooth initial distribution. The steady-state concentration is singular and multifractal so the growth describes the increasingly rugged structure of the distribution. We demonstrate that inhomogeneity influences the growth of concentration fluctuations profoundly. For homogeneous turbulence the growth is exponential and is fully determined by Kolmogorov scale eddies.We derive lognormality of the statistics in this case. The growth exponents of the moments are proportional to the sum of Lyapunov exponents, which is quadratic in the small inertia of the particles. In contrast, for inhomogeneous turbulence the growth is linear in inertia. It involves correlations of inertial range and viscous scale eddies that turn the growth into a stretched exponential law with exponent three halves. We demonstrate using direct numerical simulations that the resulting growth rate can differ by orders of magnitude over channel height. This strong variation might have relevance in the planetary boundary layer.

Linearized radiative transfer models for retrieval of cloud parameters from EPIC/DSCOVR measurements

NASA Astrophysics Data System (ADS)

Molina García, Víctor; Sasi, Sruthy; Efremenko, Dmitry S.; Doicu, Adrian; Loyola, Diego

2018-07-01

In this paper, we describe several linearized radiative transfer models which can be used for the retrieval of cloud parameters from EPIC (Earth Polychromatic Imaging Camera) measurements. The approaches under examination are (1) the linearized forward approach, represented in this paper by the linearized discrete ordinate and matrix operator methods with matrix exponential, and (2) the forward-adjoint approach based on the discrete ordinate method with matrix exponential. To enhance the performance of the radiative transfer computations, the correlated k-distribution method and the Principal Component Analysis (PCA) technique are used. We provide a compact description of the proposed methods, as well as a numerical analysis of their accuracy and efficiency when simulating EPIC measurements in the oxygen A-band channel at 764 nm. We found that the computation time of the forward-adjoint approach using the correlated k-distribution method in conjunction with PCA is approximately 13 s for simultaneously computing the derivatives with respect to cloud optical thickness and cloud top height.

The exponential rise of induced seismicity with increasing stress levels in the Groningen gas field and its implications for controlling seismic risk

NASA Astrophysics Data System (ADS)

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

2018-06-01

Induced seismicity typically arises from the progressive activation of recently inactive geological faults by anthropogenic activity. Faults are mechanically and geometrically heterogeneous, so their extremes of stress and strength govern the initial evolution of induced seismicity. We derive a statistical model of Coulomb stress failures and associated aftershocks within the tail of the distribution of fault stress and strength variations to show initial induced seismicity rates will increase as an exponential function of induced stress. Our model provides operational forecasts consistent with the observed space-time-magnitude distribution of earthquakes induced by gas production from the Groningen field in the Netherlands. These probabilistic forecasts also match the observed changes in seismicity following a significant and sustained decrease in gas production rates designed to reduce seismic hazard and risk. This forecast capability allows reliable assessment of alternative control options to better inform future induced seismic risk management decisions.

Controllable excitation of higher-order rogue waves in nonautonomous systems with both varying linear and harmonic external potentials

NASA Astrophysics Data System (ADS)

Jia, Heping; Yang, Rongcao; Tian, Jinping; Zhang, Wenmei

2018-05-01

The nonautonomous nonlinear Schrödinger (NLS) equation with both varying linear and harmonic external potentials is investigated and the semirational rogue wave (RW) solution is presented by similarity transformation. Based on the solution, the interactions between Peregrine soliton and breathers, and the controllability of the semirational RWs in periodic distribution and exponential decreasing nonautonomous systems with both linear and harmonic potentials are studied. It is found that the harmonic potential only influences the constraint condition of the semirational solution, the linear potential is related to the trajectory of the semirational RWs, while dispersion and nonlinearity determine the excitation position of the higher-order RWs. The higher-order RWs can be partly, completely and biperiodically excited in periodic distribution system and the diverse excited patterns can be generated for different parameter relations in exponential decreasing system. The results reveal that the excitation of the higher-order RWs can be controlled in the nonautonomous system by choosing dispersion, nonlinearity and external potentials.

Comparison of Traditional and Open-Access Appointment Scheduling for Exponentially Distributed Service Time.

PubMed

Yan, Chongjun; Tang, Jiafu; Jiang, Bowen; Fung, Richard Y K

2015-01-01

This paper compares the performance measures of traditional appointment scheduling (AS) with those of an open-access appointment scheduling (OA-AS) system with exponentially distributed service time. A queueing model is formulated for the traditional AS system with no-show probability. The OA-AS models assume that all patients who call before the session begins will show up for the appointment on time. Two types of OA-AS systems are considered: with a same-session policy and with a same-or-next-session policy. Numerical results indicate that the superiority of OA-AS systems is not as obvious as those under deterministic scenarios. The same-session system has a threshold of relative waiting cost, after which the traditional system always has higher total costs, and the same-or-next-session system is always preferable, except when the no-show probability or the weight of patients' waiting is low. It is concluded that open-access policies can be viewed as alternative approaches to mitigate the negative effects of no-show patients.

Traction forces during collective cell motion.

PubMed

Gov, N S

2009-08-01

Collective motion of cell cultures is a process of great interest, as it occurs during morphogenesis, wound healing, and tumor metastasis. During these processes cell cultures move due to the traction forces induced by the individual cells on the surrounding matrix. A recent study [Trepat, et al. (2009). Nat. Phys. 5, 426-430] measured for the first time the traction forces driving collective cell migration and found that they arise throughout the cell culture. The leading 5-10 rows of cell do play a major role in directing the motion of the rest of the culture by having a distinct outwards traction. Fluctuations in the traction forces are an order of magnitude larger than the resultant directional traction at the culture edge and, furthermore, have an exponential distribution. Such exponential distributions are observed for the sizes of adhesion domains within cells, the traction forces produced by single cells, and even in nonbiological nonequilibrium systems, such as sheared granular materials. We discuss these observations and their implications for our understanding of cellular flows within a continuous culture.

Inclusive transverse momentum distributions of charged particles in diffractive and non-diffractive photoproduction at HERA

NASA Astrophysics Data System (ADS)

Derrick, M.; Krakauer, D.; Magill, S.; Mikunas, D.; Musgrave, B.; Repond, J.; Stanek, R.; Talaga, R. L.; Zhang, H.; Ayad, R.; Bari, G.; Basile, M.; Bellagamba, L.; Boscherini, D.; Bruni, A.; Bruni, G.; Bruni, P.; Romeo, G. Cara; Castellini, G.; Chiarini, M.; Cifarelli, L.; Cindolo, F.; Contin, A.; Corradi, M.; Gialas, I.; Giusti, P.; Iacobucci, G.; Laurenti, G.; Levi, G.; Margotti, A.; Massam, T.; Nania, R.; Nemoz, C.; Palmonari, F.; Polini, A.; Sartorelli, G.; Timellini, R.; Garcia, Y. Zamora; Zichichi, A.; Bargende, A.; Crittenden, J.; Desch, K.; Diekmann, B.; Doeker, T.; Eckert, M.; Feld, L.; Frey, A.; Geerts, M.; Geitz, G.; Grothe, M.; Haas, T.; Hartmann, H.; Haun, D.; Heinloth, K.; Hilger, E.; Jakob, H.-P.; Katz, U. F.; Mari, S. M.; Mass, A.; Mengel, S.; Mollen, J.; Paul, E.; Rembser, Ch.; Schattevoy, R.; Schramm, D.; Stamm, J.; Wedemeyer, R.; Campbell-Robson, S.; Cassidy, A.; Dyce, N.; Foster, B.; George, S.; Gilmore, R.; Heath, G. P.; Heath, H. F.; Llewellyn, T. J.; Morgado, C. J. S.; Norman, D. J. P.; O'Mara, J. A.; Tapper, R. J.; Wilson, S. S.; Yoshida, R.; Rau, R. R.; Arneodo, M.; Iannotti, L.; Schioppa, M.; Susinno, G.; Bernstein, A.; Caldwell, A.; Cartiglia, N.; Parsons, J. A.; Ritz, S.; Sciulli, F.; Straub, P. B.; Wai, L.; Yang, S.; Zhu, Q.; Borzemski, P.; Chwastowski, J.; Eskreys, A.; Piotrzkowski, K.; Zachara, M.; Zawiejski, L.; Adamczyk, L.; Bednarek, B.; Jeleń, K.; Kisielewska, D.; Kowalski, T.; Rulikowska-Zarębska, E.; Suszycki, L.; Zając, J.; Kotański, A.; Przybycień, M.; Bauerdick, L. A. T.; Behrens, U.; Beier, H.; Bienlein, J. K.; Coldewey, C.; Deppe, O.; Desler, K.; Drews, G.; Flasiński, M.; Gilkinson, D. J.; Glasman, C.; Göttlicher, P.; Große-Knetter, J.; Gutjahr, B.; Hain, W.; Hasell, D.; Heßling, H.; Iga, Y.; Joos, P.; Kasemann, M.; Klanner, R.; Koch, W.; Köpke, L.; Kötz, U.; Kowalski, H.; Labs, L.; Ladage, A.; Löhr, B.; Löwe, M.; Lüke, D.; Mańczak, O.; Monteiro, T.; Ng, J. S. T.; Nickel, S.; Notz, D.; Ohrenberg, K.; Roco, M.; Rohde, M.; Roldán, J.; Schneekloth, U.; Schulz, W.; Selonke, F.; Stiliaris, E.; Surrow, B.; Voß, T.; Westphal, D.; Wolf, G.; Youngman, C.; Zhou, J. F.; Grabosch, H. J.; Kharchilava, A.; Leich, A.; Mattingly, M. C. K.; Meyer, A.; Schlenstedt, S.; Wulff, N.; Barbagli, G.; Pelfer, P.; Anzivino, G.; Maccarrone, G.; de Pasquale, S.; Votano, L.; Bamberger, A.; Eisenhardt, S.; Freidhof, A.; Söldner-Rembold, S.; Schroeder, J.; Trefzger, T.; Brook, N. H.; Bussey, P. J.; Doyle, A. T.; Fleck, J. I.; Saxon, D. H.; Utley, M. L.; Wilson, A. S.; Dannemann, A.; Holm, U.; Horstmann, D.; Neumann, T.; Sinkus, R.; Wick, K.; Badura, E.; Burow, B. D.; Hagge, L.; Lohrmann, E.; Mainusch, J.; Milewski, J.; Nakahata, M.; Pavel, N.; Poelz, G.; Schott, W.; Zetsche, F.; Bacon, T. C.; Butterworth, I.; Gallo, E.; Harris, V. L.; Hung, B. Y. H.; Long, K. R.; Miller, D. B.; Morawitz, P. P. O.; Prinias, A.; Sedgbeer, J. K.; Whitfield, A. F.; Mallik, U.; McCliment, E.; Wang, M. Z.; Wang, S. M.; Wu, J. T.; Zhang, Y.; Cloth, P.; Filges, D.; An, S. H.; Hong, S. M.; Nam, S. W.; Park, S. K.; Suh, M. H.; Yon, S. H.; Imlay, R.; Kartik, S.; Kim, H.-J.; McNeil, R. R.; Metcalf, W.; Nadendla, V. K.; Barreiro, F.; Cases, G.; Graciani, R.; Hernández, J. M.; Hervás, L.; Labarga, L.; Del Peso, J.; Puga, J.; Terron, J.; de Trocóniz, J. F.; Smith, G. R.; Corriveau, F.; Hanna, D. S.; Hartmann, J.; Hung, L. W.; Lim, J. N.; Matthews, C. G.; Patel, P. M.; Sinclair, L. E.; Stairs, D. G.; St. Laurent, M.; Ullmann, R.; Zacek, G.; Bashkirov, V.; Dolgoshein, B. A.; Stifutkin, A.; Bashindzhagyan, G. L.; Ermolov, P. F.; Gladilin, L. K.; Golubkov, Y. A.; Kobrin, V. D.; Kuzmin, V. A.; Proskuryakov, A. S.; Savin, A. A.; Shcheglova, L. M.; Solomin, A. N.; Zotov, N. P.; Botje, M.; Chlebana, F.; Dake, A.; Engelen, J.; de Kamps, M.; Kooijman, P.; Kruse, A.; Tiecke, H.; Verkerke, W.; Vreeswijk, M.; Wiggers, L.; de Wolf, E.; van Woudenberg, R.; Acosta, D.; Bylsma, B.; Durkin, L. S.; Honscheid, K.; Li, C.; Ling, T. Y.; McLean, K. W.; Murray, W. N.; Park, I. H.; Romanowski, T. A.; Seidlein, R.; Bailey, D. S.; Blair, G. A.; Byrne, A.; Cashmore, R. J.; Cooper-Sarkar, A. M.; Daniels, D.; Devenish, R. C. E.; Harnew, N.; Lancaster, M.; Luffman, P. E.; Lindemann, L.; McFall, J. D.; Nath, C.; Noyes, V. A.; Quadt, A.; Uijterwaal, H.; Walczak, R.; Wilson, F. F.; Yip, T.; Abbiendi, G.; Bertolin, A.; Brugnera, R.; Carlin, R.; Dal Corso, F.; de Giorgi, M.; Dosselli, U.; Limentani, S.; Morandin, M.; Posocco, M.; Stanco, L.; Stroili, R.; Voci, C.; Bulmahn, J.; Butterworth, J. M.; Feild, R. G.; Oh, B. Y.; Whitmore, J. J.; D'Agostini, G.; Marini, G.; Nigro, A.; Tassi, E.; Hart, J. C.; McCubbin, N. A.; Prytz, K.; Shah, T. P.; Short, T. L.; Barberis, E.; Dubbs, T.; Heusch, C.; van Hook, M.; Hubbard, B.; Lockman, W.; Rahn, J. T.; Sadrozinski, H. F.-W.; Seiden, A.; Biltzinger, J.; Seifert, R. J.; Schwarzer, O.; Walenta, A. H.; Zech, G.; Abramowicz, H.; Briskin, G.; Dagan, S.; Levy, A.; Hasegawa, T.; Hazumi, M.; Ishii, T.; Kuze, M.; Mine, S.; Nagasawa, Y.; Nakao, M.; Suzuki, I.; Tokushuku, K.; Yamada, S.; Yamazaki, Y.; Chiba, M.; Hamatsu, R.; Hirose, T.; Homma, K.; Kitamura, S.; Nakamitsu, Y.; Yamauchi, K.; Cirio, R.; Costa, M.; Ferrero, M. I.; Lamberti, L.; Maselli, S.; Peroni, C.; Sacchi, R.; Solano, A.; Staiano, A.; Dardo, M.; Bailey, D. C.; Bandyopadhyay, D.; Benard, F.; Brkic, M.; Crombie, M. B.; Gingrich, D. M.; Hartner, G. F.; Joo, K. K.; Levman, G. M.; Martin, J. F.; Orr, R. S.; Sampson, C. R.; Teuscher, R. J.; Catterall, C. D.; Jones, T. W.; Kaziewicz, P. B.; Lane, J. B.; Saunders, R. L.; Shulman, J.; Blankenship, K.; Lu, B.; Mo, L. W.; Bogusz, W.; Charchula, K.; Ciborowski, J.; Gajewski, J.; Grzelak, G.; Kasprzak, M.; Krzyżanowski, M.; Muchorowski, K.; Nowak, R. J.; Pawlak, J. M.; Tymieniecka, T.; Wróblewski, A. K.; Zakrzewski, J. A.; Żarnecki, A. F.; Adamus, M.; Eisenberg, Y.; Karshon, U.; Revel, D.; Zer-Zion, D.; Ali, I.; Badgett, W. F.; Behrens, B.; Dasu, S.; Fordham, C.; Foudas, C.; Goussiou, A.; Loveless, R. J.; Reeder, D. D.; Silverstein, S.; Smith, W. H.; Vaiciulis, A.; Wodarczyk, M.; Tsurugai, T.; Bhadra, S.; Cardy, M. L.; Fagerstroem, C.-P.; Frisken, W. R.; Furutani, K. M.; Khakzad, M.; Schmidke, W. B.

1995-06-01

Inclusive transverse momentum spectra of charged particles in photoproduction events in the laboratory pseudorapidity range -1.2<η<1.4 have been measured up to p T =8 GeV usign the ZEUS detector. Diffractive and non-diffractive reactions have been selected with an average γ p centre of mass (c.m.) energy of < W>=180 GeV. For diffractive reactions, the p T spectra of the photon dissociation events have been measured in two intervals of the dissociated photon mass with mean values < M X >=5 GeV and 10 GeV. The inclusive transverse momentum spectra fall exponentially in the low p T region. The non-diffractive data show a pronounced high p T tail departing from the exponential shape. The p T distributions are compared to lower energy photoproduction data and to hadron-hadron collisions at a similar c.m. energy. The data are also compared to the results of a next-to-leading order QCD calculation.

{phi} meson production in Au + Au and p + p collisions at {radical}s{sub NN}=200 GeV

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

Adams, J.; Adler, C.; Aggarwal, M.M.

2004-06-01

We report the STAR measurement of {psi} meson production in Au + Au and p + p collisions at {radical}s{sub NN} = 200 GeV. Using the event mixing technique, the {psi} spectra and yields are obtained at midrapidity for five centrality bins in Au+Au collisions and for non-singly-diffractive p+p collisions. It is found that the {psi} transverse momentum distributions from Au+Au collisions are better fitted with a single-exponential while the p+p spectrum is better described by a double-exponential distribution. The measured nuclear modification factors indicate that {psi} production in central Au+Au collisions is suppressed relative to peripheral collisions when scaledmore » by the number of binary collisions (). The systematics of versus centrality and the constant {psi}/K{sup -} ratio versus beam species, centrality, and collision energy rule out kaon coalescence as the dominant mechanism for {psi} production.« less

Work fluctuations for Bose particles in grand canonical initial states.

PubMed

Yi, Juyeon; Kim, Yong Woon; Talkner, Peter

2012-05-01

We consider bosons in a harmonic trap and investigate the fluctuations of the work performed by an adiabatic change of the trap curvature. Depending on the reservoir conditions such as temperature and chemical potential that provide the initial equilibrium state, the exponentiated work average (EWA) defined in the context of the Crooks relation and the Jarzynski equality may diverge if the trap becomes wider. We investigate how the probability distribution function (PDF) of the work signals this divergence. It is shown that at low temperatures the PDF is highly asymmetric with a steep fall-off at one side and an exponential tail at the other side. For high temperatures it is closer to a symmetric distribution approaching a Gaussian form. These properties of the work PDF are discussed in relation to the convergence of the EWA and to the existence of the hypothetical equilibrium state to which those thermodynamic potential changes refer that enter both the Crooks relation and the Jarzynski equality.

A computer program for thermal radiation from gaseous rocket exhuast plumes (GASRAD)

NASA Technical Reports Server (NTRS)

Reardon, J. E.; Lee, Y. C.

1979-01-01

A computer code is presented for predicting incident thermal radiation from defined plume gas properties in either axisymmetric or cylindrical coordinate systems. The radiation model is a statistical band model for exponential line strength distribution with Lorentz/Doppler line shapes for 5 gaseous species (H2O, CO2, CO, HCl and HF) and an appoximate (non-scattering) treatment of carbon particles. The Curtis-Godson approximation is used for inhomogeneous gases, but a subroutine is available for using Young's intuitive derivative method for H2O with Lorentz line shape and exponentially-tailed-inverse line strength distribution. The geometry model provides integration over a hemisphere with up to 6 individually oriented identical axisymmetric plumes, a single 3-D plume, Shading surfaces may be used in any of 7 shapes, and a conical limit may be defined for the plume to set individual line-of-signt limits. Intermediate coordinate systems may specified to simplify input of plumes and shading surfaces.

The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

NASA Astrophysics Data System (ADS)

Garavaglia, Alessandro; van der Hofstad, Remco; Woeginger, Gerhard

2017-09-01

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.

Statistics of Optical Coherence Tomography Data From Human Retina

PubMed Central

de Juan, Joaquín; Ferrone, Claudia; Giannini, Daniela; Huang, David; Koch, Giorgio; Russo, Valentina; Tan, Ou; Bruni, Carlo

2010-01-01

Optical coherence tomography (OCT) has recently become one of the primary methods for noninvasive probing of the human retina. The pseudoimage formed by OCT (the so-called B-scan) varies probabilistically across pixels due to complexities in the measurement technique. Hence, sensitive automatic procedures of diagnosis using OCT may exploit statistical analysis of the spatial distribution of reflectance. In this paper, we perform a statistical study of retinal OCT data. We find that the stretched exponential probability density function can model well the distribution of intensities in OCT pseudoimages. Moreover, we show a small, but significant correlation between neighbor pixels when measuring OCT intensities with pixels of about 5 µm. We then develop a simple joint probability model for the OCT data consistent with known retinal features. This model fits well the stretched exponential distribution of intensities and their spatial correlation. In normal retinas, fit parameters of this model are relatively constant along retinal layers, but varies across layers. However, in retinas with diabetic retinopathy, large spikes of parameter modulation interrupt the constancy within layers, exactly where pathologies are visible. We argue that these results give hope for improvement in statistical pathology-detection methods even when the disease is in its early stages. PMID:20304733

Goodness of fit of probability distributions for sightings as species approach extinction.

PubMed

Vogel, Richard M; Hosking, Jonathan R M; Elphick, Chris S; Roberts, David L; Reed, J Michael

2009-04-01

Estimating the probability that a species is extinct and the timing of extinctions is useful in biological fields ranging from paleoecology to conservation biology. Various statistical methods have been introduced to infer the time of extinction and extinction probability from a series of individual sightings. There is little evidence, however, as to which of these models provide adequate fit to actual sighting records. We use L-moment diagrams and probability plot correlation coefficient (PPCC) hypothesis tests to evaluate the goodness of fit of various probabilistic models to sighting data collected for a set of North American and Hawaiian bird populations that have either gone extinct, or are suspected of having gone extinct, during the past 150 years. For our data, the uniform, truncated exponential, and generalized Pareto models performed moderately well, but the Weibull model performed poorly. Of the acceptable models, the uniform distribution performed best based on PPCC goodness of fit comparisons and sequential Bonferroni-type tests. Further analyses using field significance tests suggest that although the uniform distribution is the best of those considered, additional work remains to evaluate the truncated exponential model more fully. The methods we present here provide a framework for evaluating subsequent models.

The perturbed Sparre Andersen model with a threshold dividend strategy

NASA Astrophysics Data System (ADS)

Gao, Heli; Yin, Chuancun

2008-10-01

In this paper, we consider a Sparre Andersen model perturbed by diffusion with generalized Erlang(n)-distributed inter-claim times and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the mth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case where the inter-claim times are Erlang(2) distributed and the claim size distribution is exponential is considered in some details.

Measuring helium bubble diameter distributions in tungsten with grazing incidence small angle x-ray scattering (GISAXS)

NASA Astrophysics Data System (ADS)

Thompson, M.; Kluth, P.; Doerner, R. P.; Kirby, N.; Riley, D.; Corr, C. S.

2016-02-01

Grazing incidence small angle x-ray scattering was performed on tungsten samples exposed to helium plasma in the MAGPIE and Pisces-A linear plasma devices to measure the size distributions of resulting helium nano-bubbles. Nano-bubbles were fitted assuming spheroidal particles and an exponential diameter distribution. These particles had mean diameters between 0.36 and 0.62 nm. Pisces-A exposed samples showed more complex patterns, which may suggest the formation of faceted nano-bubbles or nano-scale surface structures.

Time-Frequency Signal Representations Using Interpolations in Joint-Variable Domains

DTIC Science & Technology

2016-06-14

distribution kernels,” IEEE Trans. Signal Process., vol. 42, no. 5, pp. 1156–1165, May 1994. [25] G. S. Cunningham and W. J. Williams , “Kernel...interpolated data. For comparison, we include sparse reconstruction and WVD and Choi– Williams distribution (CWD) [23], which are directly applied to...Prentice-Hall, 1995. [23] H. I. Choi and W. J. Williams , “Improved time-frequency representa- tion of multicomponent signals using exponential kernels

A Random Walk Picture of Basketball

NASA Astrophysics Data System (ADS)

Gabel, Alan; Redner, Sidney

2012-02-01

We analyze NBA basketball play-by-play data and found that scoring is well described by a weakly-biased, anti-persistent, continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between events. We account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead.

Size-Frequency Distributions of Rocks on Mars and Earth Analog Sites: Implications for Future Landed Missions

NASA Technical Reports Server (NTRS)

Golombeck, M.; Rapp, D.

1996-01-01

The size-frequency distribution of rocks and the Vicking landing sites and a variety of rocky locations on the Earth that formed from a number of geologic processes all have the general shape of simple exponential curves, which have been combined with remote sensing data and models on rock abundance to predict the frequency of boulders potentially hazardous to future Mars landers and rovers.

Similarity solutions for unsteady flow behind an exponential shock in a self-gravitating non-ideal gas with azimuthal magnetic field

NASA Astrophysics Data System (ADS)

Nath, G.; Pathak, R. P.; Dutta, Mrityunjoy

2018-01-01

Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical or spherical) moving with time according to an exponential law is obtained. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The effects of variation of ambient magnetic field, non-idealness of the gas, adiabatic exponent and gravitational parameter are worked out in detail. It is shown that the increase in the non-idealness of the gas or the adiabatic exponent of the gas or presence of magnetic field have decaying effect on the shock wave. Consideration of the isothermal flow and the self-gravitational field increase the shock strength. Also, the consideration of isothermal flow or the presence of magnetic field removes the singularity in the density distribution, which arises in the case of adiabatic flow. The result of our study may be used to interpret measurements carried out by space craft in the solar wind and in neighborhood of the Earth's magnetosphere.

Mathematical Modeling of Extinction of Inhomogeneous Populations

PubMed Central

Karev, G.P.; Kareva, I.

2016-01-01

Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117

Non-Gaussian analysis of diffusion weighted imaging in head and neck at 3T: a pilot study in patients with nasopharyngeal carcinoma.

PubMed

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S P; Bhatia, Kunwar S; Wang, Yi-Xiang J; Ahuja, Anil T; King, Ann D

2014-01-01

To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm(2). DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization.

Some case studies of skewed (and other ab-normal) data distributions arising in low-level environmental research.

PubMed

Currie, L A

2001-07-01

Three general classes of skewed data distributions have been encountered in research on background radiation, chemical and radiochemical blanks, and low levels of 85Kr and 14C in the atmosphere and the cryosphere. The first class of skewed data can be considered to be theoretically, or fundamentally skewed. It is typified by the exponential distribution of inter-arrival times for nuclear counting events for a Poisson process. As part of a study of the nature of low-level (anti-coincidence) Geiger-Muller counter background radiation, tests were performed on the Poisson distribution of counts, the uniform distribution of arrival times, and the exponential distribution of inter-arrival times. The real laboratory system, of course, failed the (inter-arrival time) test--for very interesting reasons, linked to the physics of the measurement process. The second, computationally skewed, class relates to skewness induced by non-linear transformations. It is illustrated by non-linear concentration estimates from inverse calibration, and bivariate blank corrections for low-level 14C-12C aerosol data that led to highly asymmetric uncertainty intervals for the biomass carbon contribution to urban "soot". The third, environmentally, skewed, data class relates to a universal problem for the detection of excursions above blank or baseline levels: namely, the widespread occurrence of ab-normal distributions of environmental and laboratory blanks. This is illustrated by the search for fundamental factors that lurk behind skewed frequency distributions of sulfur laboratory blanks and 85Kr environmental baselines, and the application of robust statistical procedures for reliable detection decisions in the face of skewed isotopic carbon procedural blanks with few degrees of freedom.

Tailpulse signal generator

DOEpatents

Baker, John [Walnut Creek, CA; Archer, Daniel E [Knoxville, TN; Luke, Stanley John [Pleasanton, CA; Decman, Daniel J [Livermore, CA; White, Gregory K [Livermore, CA

2009-06-23

A tailpulse signal generating/simulating apparatus, system, and method designed to produce electronic pulses which simulate tailpulses produced by a gamma radiation detector, including the pileup effect caused by the characteristic exponential decay of the detector pulses, and the random Poisson distribution pulse timing for radioactive materials. A digital signal process (DSP) is programmed and configured to produce digital values corresponding to pseudo-randomly selected pulse amplitudes and pseudo-randomly selected Poisson timing intervals of the tailpulses. Pulse amplitude values are exponentially decayed while outputting the digital value to a digital to analog converter (DAC). And pulse amplitudes of new pulses are added to decaying pulses to simulate the pileup effect for enhanced realism in the simulation.

Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication

NASA Astrophysics Data System (ADS)

Guérin, Philippe Allard; Feix, Adrien; Araújo, Mateus; Brukner, Časlav

2016-09-01

In communication complexity, a number of distant parties have the task of calculating a distributed function of their inputs, while minimizing the amount of communication between them. It is known that with quantum resources, such as entanglement and quantum channels, one can obtain significant reductions in the communication complexity of some tasks. In this work, we study the role of the quantum superposition of the direction of communication as a resource for communication complexity. We present a tripartite communication task for which such a superposition allows for an exponential saving in communication, compared to one-way quantum (or classical) communication; the advantage also holds when we allow for protocols with bounded error probability.

Deformed exponentials and portfolio selection

NASA Astrophysics Data System (ADS)

Rodrigues, Ana Flávia P.; Guerreiro, Igor M.; Cavalcante, Charles Casimiro

In this paper, we present a method for portfolio selection based on the consideration on deformed exponentials in order to generalize the methods based on the gaussianity of the returns in portfolio, such as the Markowitz model. The proposed method generalizes the idea of optimizing mean-variance and mean-divergence models and allows a more accurate behavior for situations where heavy-tails distributions are necessary to describe the returns in a given time instant, such as those observed in economic crises. Numerical results show the proposed method outperforms the Markowitz portfolio for the cumulated returns with a good convergence rate of the weights for the assets which are searched by means of a natural gradient algorithm.

TIME SHARING WITH AN EXPLICIT PRIORITY QUEUING DISCIPLINE.

DTIC Science & Technology

exponentially distributed service times and an ordered priority queue. Each new arrival buys a position in this queue by offering a non-negative bribe to the...parameters is investigated through numerical examples. Finally, to maximize the expected revenue per unit time accruing from bribes , an optimization

Noise in Attractor Networks in the Brain Produced by Graded Firing Rate Representations

PubMed Central

Webb, Tristan J.; Rolls, Edmund T.; Deco, Gustavo; Feng, Jianfeng

2011-01-01

Representations in the cortex are often distributed with graded firing rates in the neuronal populations. The firing rate probability distribution of each neuron to a set of stimuli is often exponential or gamma. In processes in the brain, such as decision-making, that are influenced by the noise produced by the close to random spike timings of each neuron for a given mean rate, the noise with this graded type of representation may be larger than with the binary firing rate distribution that is usually investigated. In integrate-and-fire simulations of an attractor decision-making network, we show that the noise is indeed greater for a given sparseness of the representation for graded, exponential, than for binary firing rate distributions. The greater noise was measured by faster escaping times from the spontaneous firing rate state when the decision cues are applied, and this corresponds to faster decision or reaction times. The greater noise was also evident as less stability of the spontaneous firing state before the decision cues are applied. The implication is that spiking-related noise will continue to be a factor that influences processes such as decision-making, signal detection, short-term memory, and memory recall even with the quite large networks found in the cerebral cortex. In these networks there are several thousand recurrent collateral synapses onto each neuron. The greater noise with graded firing rate distributions has the advantage that it can increase the speed of operation of cortical circuitry. PMID:21931607

Distribution Functions of Sizes and Fluxes Determined from Supra-Arcade Downflows

NASA Technical Reports Server (NTRS)

McKenzie, D.; Savage, S.

2011-01-01

The frequency distributions of sizes and fluxes of supra-arcade downflows (SADs) provide information about the process of their creation. For example, a fractal creation process may be expected to yield a power-law distribution of sizes and/or fluxes. We examine 120 cross-sectional areas and magnetic flux estimates found by Savage & McKenzie for SADs, and find that (1) the areas are consistent with a log-normal distribution and (2) the fluxes are consistent with both a log-normal and an exponential distribution. Neither set of measurements is compatible with a power-law distribution nor a normal distribution. As a demonstration of the applicability of these findings to improved understanding of reconnection, we consider a simple SAD growth scenario with minimal assumptions, capable of producing a log-normal distribution.

Variability of displacement at a point: Implications for earthquake‐size distribution and rupture hazard on faults

USGS Publications Warehouse

Hecker, Suzanne; Abrahamson, N.A.; Wooddell, Kathryn

2013-01-01

To investigate the nature of earthquake‐magnitude distributions on faults, we compare the interevent variability of surface displacement at a point on a fault from a composite global data set of paleoseismic observations with the variability expected from two prevailing magnitude–frequency distributions: the truncated‐exponential model and the characteristic‐earthquake model. We use forward modeling to predict the coefficient of variation (CV) for the alternative earthquake distributions, incorporating factors that would effect observations of displacement at a site. The characteristic‐earthquake model (with a characteristic‐magnitude range of ±0.25) produces CV values consistent with the data (CV∼0.5) only if the variability for a given earthquake magnitude is small. This condition implies that rupture patterns on a fault are stable, in keeping with the concept behind the model. This constraint also bears upon fault‐rupture hazard analysis, which, for lack of point‐specific information, has used global scaling relations to infer variability in average displacement for a given‐size earthquake. Exponential distributions of earthquakes (from M 5 to the maximum magnitude) give rise to CV values that are significantly larger than the empirical constraint. A version of the model truncated at M 7, however, yields values consistent with a larger CV (∼0.6) determined for small‐displacement sites. Although this result allows for a difference in the magnitude distribution of smaller surface‐rupturing earthquakes, it may reflect, in part, less stability in the displacement profile of smaller ruptures and/or the tails of larger ruptures.

Complex Network Theory Applied to the Growth of Kuala Lumpur's Public Urban Rail Transit Network.

PubMed

Ding, Rui; Ujang, Norsidah; Hamid, Hussain Bin; Wu, Jianjun

2015-01-01

Recently, the number of studies involving complex network applications in transportation has increased steadily as scholars from various fields analyze traffic networks. Nonetheless, research on rail network growth is relatively rare. This research examines the evolution of the Public Urban Rail Transit Networks of Kuala Lumpur (PURTNoKL) based on complex network theory and covers both the topological structure of the rail system and future trends in network growth. In addition, network performance when facing different attack strategies is also assessed. Three topological network characteristics are considered: connections, clustering and centrality. In PURTNoKL, we found that the total number of nodes and edges exhibit a linear relationship and that the average degree stays within the interval [2.0488, 2.6774] with heavy-tailed distributions. The evolutionary process shows that the cumulative probability distribution (CPD) of degree and the average shortest path length show good fit with exponential distribution and normal distribution, respectively. Moreover, PURTNoKL exhibits clear cluster characteristics; most of the nodes have a 2-core value, and the CPDs of the centrality's closeness and betweenness follow a normal distribution function and an exponential distribution, respectively. Finally, we discuss four different types of network growth styles and the line extension process, which reveal that the rail network's growth is likely based on the nodes with the biggest lengths of the shortest path and that network protection should emphasize those nodes with the largest degrees and the highest betweenness values. This research may enhance the networkability of the rail system and better shape the future growth of public rail networks.

Lindley frailty model for a class of compound Poisson processes

NASA Astrophysics Data System (ADS)

Kadilar, Gamze Özel; Ata, Nihal

2013-10-01

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

How required reserve ratio affects distribution and velocity of money

NASA Astrophysics Data System (ADS)

Xi, Ning; Ding, Ning; Wang, Yougui

2005-11-01

In this paper the dependence of wealth distribution and the velocity of money on the required reserve ratio is examined based on a random transfer model of money and computer simulations. A fractional reserve banking system is introduced to the model where money creation can be achieved by bank loans and the monetary aggregate is determined by the monetary base and the required reserve ratio. It is shown that monetary wealth follows asymmetric Laplace distribution and latency time of money follows exponential distribution. The expression of monetary wealth distribution and that of the velocity of money in terms of the required reserve ratio are presented in a good agreement with simulation results.

Probabilistic properties of injection induced seismicity - implications for the seismic hazard analysis

NASA Astrophysics Data System (ADS)

Lasocki, Stanislaw; Urban, Pawel; Kwiatek, Grzegorz; Martinez-Garzón, Particia

2017-04-01

Injection induced seismicity (IIS) is an undesired dynamic rockmass response to massive fluid injections. This includes reactions, among others, to hydro-fracturing for shale gas exploitation. Complexity and changeability of technological factors that induce IIS, may result in significant deviations of the observed distributions of seismic process parameters from the models, which perform well in natural, tectonic seismic processes. Classic formulations of probabilistic seismic hazard analysis in natural seismicity assume the seismic marked point process to be a stationary Poisson process, whose marks - magnitudes are governed by a Gutenberg-Richter born exponential distribution. It is well known that the use of an inappropriate earthquake occurrence model and/or an inappropriate of magnitude distribution model leads to significant systematic errors of hazard estimates. It is therefore of paramount importance to check whether the mentioned, commonly used in natural seismicity assumptions on the seismic process, can be safely used in IIS hazard problems or not. Seismicity accompanying shale gas operations is widely studied in the framework of the project "Shale Gas Exploration and Exploitation Induced Risks" (SHEER). Here we present results of SHEER project investigations of such seismicity from Oklahoma and of a proxy of such seismicity - IIS data from The Geysers geothermal field. We attempt to answer to the following questions: • Do IIS earthquakes follow the Gutenberg-Richter distribution law, so that the magnitude distribution can be modelled by an exponential distribution? • Is the occurrence process of IIS earthquakes Poissonian? Is it segmentally Poissonian? If yes, how are these segments linked to cycles of technological operations? Statistical tests indicate that the Gutenberg-Richter relation born exponential distribution model for magnitude is, in general, inappropriate. The magnitude distribution can be complex, multimodal, with no ready-to-use functional model. In this connection, we recommend to use in hazard analyses non-parametric, kernel estimators of magnitude distribution. The earthquake occurrence process of IIS is not a Poisson process. When earthquakes' occurrences are influenced by a multitude of inducing factors, the interevent time distribution can be modelled by the Weibull distribution supporting a negative ageing property of the process. When earthquake occurrences are due to a specific injection activity, the earthquake rate directly depends on the injection rate and responds immediately to the changes of the injection rate. Furthermore, this response is not limited only to correlated variations of the seismic activity but it also concerns significant changes of the shape of interevent time distribution. Unlike the event rate, the shape of magnitude distribution does not exhibit correlation with the injection rate. This work was supported within SHEER: "Shale Gas Exploration and Exploitation Induced Risks" project funded from Horizon 2020 - R&I Framework Programme, call H2020-LCE 16-2014-1 and within statutory activities No3841/E-41/S/2016 of Ministry of Science and Higher Education of Poland.

Revealing the spatial region of a future fracture nucleation in heterogeneous materials at the initial deformation stage

NASA Astrophysics Data System (ADS)

Damaskinskaya, Ekaterina; Hilarov, Vladimir; Frolov, Dmitriy

2016-11-01

The energy distributions of acoustic emission (AE) signals have been analyzed on two scaling levels corresponding to deformation of granite samples and processes on a commercial mining enterprise. It is established that, in cases of localized fracture, the energy distribution of AE signals has shape described by a power law, while a dispersed fracture is characterized by an exponential energy distribution of the AE signals. Analysis of the functional form of the energy distribution performed at the initial stage of loading allows one to recognize a spatial region in the sample where localization of the defect formation will subsequently take place.

Multivariate Analysis and Its Applications

DTIC Science & Technology

1989-02-14

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

Particle yields from numerical simulations

NASA Astrophysics Data System (ADS)

Homor, Marietta M.; Jakovác, Antal

2018-04-01

In this paper we use numerical field theoretical simulations to calculate particle yields. We demonstrate that in the model of local particle creation the deviation from the pure exponential distribution is natural even in equilibrium, and an approximate Tsallis-Pareto-like distribution function can be well fitted to the calculated yields, in accordance with the experimental observations. We present numerical simulations in the classical Φ4 model as well as in the SU(3) quantum Yang-Mills theory to clarify this issue.

Distributed energy store railgun - The limiting case

NASA Astrophysics Data System (ADS)

Marshall, Richard A.

1991-01-01

When the limiting case of a distributed energy store railgun is analyzed, (i.e., the case where the space between adjacent energy stores become indefinitely small) three important results are obtained. First, the shape of the current pulse delivered by each store is sinusoidal with an exponential tail. Second, the rail-to-rail voltage behind the rearmost active store approaches zero. Third, it is not possible to choose parameters in such a way that capacitor crowbars can be eliminated.

Understanding taxi travel patterns

NASA Astrophysics Data System (ADS)

Cai, Hua; Zhan, Xiaowei; Zhu, Ji; Jia, Xiaoping; Chiu, Anthony S. F.; Xu, Ming

2016-09-01

Taxis play important roles in modern urban transportation systems, especially in mega cities. While providing necessary amenities, taxis also significantly contribute to traffic congestion, urban energy consumption, and air pollution. Understanding the travel patterns of taxis is thus important for addressing many urban sustainability challenges. Previous research has primarily focused on examining the statistical properties of passenger trips, which include only taxi trips occupied with passengers. However, unoccupied trips are also important for urban sustainability issues because they represent potential opportunities to improve the efficiency of the transportation system. Therefore, we need to understand the travel patterns of taxis as an integrated system, instead of focusing only on the occupied trips. In this study we examine GPS trajectory data of 11,880 taxis in Beijing, China for a period of three weeks. Our results show that taxi travel patterns share similar traits with travel patterns of individuals but also exhibit differences. Trip displacement distribution of taxi travels is statistically greater than the exponential distribution and smaller than the truncated power-law distribution. The distribution of short trips (less than 30 miles) can be best fitted with power-law while long trips follow exponential decay. We use radius of gyration to characterize individual taxi's travel distance and find that it does not follow a truncated power-law as observed in previous studies. Spatial and temporal regularities exist in taxi travels. However, with increasing spatial coverage, taxi trips can exhibit dual high probability density centers.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Frequency Selection for Multi-frequency Acoustic Measurement of Suspended Sediment

NASA Astrophysics Data System (ADS)

Chen, X.; HO, H.; Fu, X.

2017-12-01

Multi-frequency acoustic measurement of suspended sediment has found successful applications in marine and fluvial environments. Difficult challenges remain in regard to improving its effectiveness and efficiency when applied to high concentrations and wide size distributions in rivers. We performed a multi-frequency acoustic scattering experiment in a cylindrical tank with a suspension of natural sands. The sands range from 50 to 600 μm in diameter with a lognormal size distribution. The bulk concentration of suspended sediment varied from 1.0 to 12.0 g/L. We found that the commonly used linear relationship between the intensity of acoustic backscatter and suspended sediment concentration holds only at sufficiently low concentrations, for instance below 3.0 g/L. It fails at a critical value of concentration that depends on measurement frequency and the distance between the transducer and the target point. Instead, an exponential relationship was found to work satisfactorily throughout the entire range of concentration. The coefficient and exponent of the exponential function changed, however, with the measuring frequency and distance. Considering the increased complexity of inverting the concentration values when an exponential relationship prevails, we further analyzed the relationship between measurement error and measuring frequency. It was also found that the inversion error may be effectively controlled within 5% if the frequency is properly set. Compared with concentration, grain size was found to heavily affect the selection of optimum frequency. A regression relationship for optimum frequency versus grain size was developed based on the experimental results.

Quantitative differentiation of breast lesions at 3T diffusion-weighted imaging (DWI) using the ratio of distributed diffusion coefficient (DDC).

PubMed

Ertas, Gokhan; Onaygil, Can; Akin, Yasin; Kaya, Handan; Aribal, Erkin

2016-12-01

To investigate the accuracy of diffusion coefficients and diffusion coefficient ratios of breast lesions and of glandular breast tissue from mono- and stretched-exponential models for quantitative diagnosis in diffusion-weighted magnetic resonance imaging (MRI). We analyzed pathologically confirmed 170 lesions (85 benign and 85 malignant) imaged using a 3.0T MR scanner. Small regions of interest (ROIs) focusing on the highest signal intensity for lesions and also for glandular tissue of contralateral breast were obtained. Apparent diffusion coefficient (ADC) and distributed diffusion coefficient (DDC) were estimated by performing nonlinear fittings using mono- and stretched-exponential models, respectively. Coefficient ratios were calculated by dividing the lesion coefficient by the glandular tissue coefficient. A stretched exponential model provides significantly better fits then the monoexponential model (P < 0.001): 65% of the better fits for glandular tissue and 71% of the better fits for lesion. High correlation was found in diffusion coefficients (0.99-0.81 and coefficient ratios (0.94) between the models. The highest diagnostic accuracy was found by the DDC ratio (area under the curve [AUC] = 0.93) when compared with lesion DDC, ADC ratio, and lesion ADC (AUC = 0.91, 0.90, 0.90) but with no statistically significant difference (P > 0.05). At optimal thresholds, the DDC ratio achieves 93% sensitivity, 80% specificity, and 87% overall diagnostic accuracy, while ADC ratio leads to 89% sensitivity, 78% specificity, and 83% overall diagnostic accuracy. The stretched exponential model fits better with signal intensity measurements from both lesion and glandular tissue ROIs. Although the DDC ratio estimated by using the model shows a higher diagnostic accuracy than the ADC ratio, lesion DDC, and ADC, it is not statistically significant. J. Magn. Reson. Imaging 2016;44:1633-1641. © 2016 International Society for Magnetic Resonance in Medicine.

Intravoxel water diffusion heterogeneity MR imaging of nasopharyngeal carcinoma using stretched exponential diffusion model.

PubMed

Lai, Vincent; Lee, Victor Ho Fun; Lam, Ka On; Sze, Henry Chun Kin; Chan, Queenie; Khong, Pek Lan

2015-06-01

To determine the utility of stretched exponential diffusion model in characterisation of the water diffusion heterogeneity in different tumour stages of nasopharyngeal carcinoma (NPC). Fifty patients with newly diagnosed NPC were prospectively recruited. Diffusion-weighted MR imaging was performed using five b values (0-2,500 s/mm(2)). Respective stretched exponential parameters (DDC, distributed diffusion coefficient; and alpha (α), water heterogeneity) were calculated. Patients were stratified into low and high tumour stage groups based on the American Joint Committee on Cancer (AJCC) staging for determination of the predictive powers of DDC and α using t test and ROC curve analyses. The mean ± standard deviation values were DDC = 0.692 ± 0.199 (×10(-3) mm(2)/s) for low stage group vs 0.794 ± 0.253 (×10(-3) mm(2)/s) for high stage group; α = 0.792 ± 0.145 for low stage group vs 0.698 ± 0.155 for high stage group. α was significantly lower in the high stage group while DDC was negatively correlated. DDC and α were both reliable independent predictors (p < 0.001), with α being more powerful. Optimal cut-off values were (sensitivity, specificity, positive likelihood ratio, negative likelihood ratio) DDC = 0.692 × 10(-3) mm(2)/s (94.4 %, 64.3 %, 2.64, 0.09), α = 0.720 (72.2 %, 100 %, -, 0.28). The heterogeneity index α is robust and can potentially help in staging and grading prediction in NPC. • Stretched exponential diffusion models can help in tissue characterisation in nasopharyngeal carcinoma • α and distributed diffusion coefficient (DDC) are negatively correlated • α is a robust heterogeneity index marker • α can potentially help in staging and grading prediction.

Moving Average Models with Bivariate Exponential and Geometric Distributions.

DTIC Science & Technology

1985-03-01

ordinary time series and of point processes. Developments in Statistics, Vol. 1, P.R. Krishnaiah , ed. Academic Press, New York. [9] Esary, J.D. and...valued and discrete - valued time series with ARMA correlation structure. Multivariate Analysis V, P.R. Krishnaiah , ed. North-Holland. 151-166. [28

Social Enterprises and Social Sector Workforces: Workforce Initiatives Discussion Paper #3

ERIC Educational Resources Information Center

Academy for Educational Development, 2011

2011-01-01

Increasing evidence shows that investing in social sector supply, service, and value chains has exponentially stronger development impact than investments in other sectors. There are often severely lacking social services such as child care, elder care, health care delivery, prescription drug distribution, home schooling, and private sector…

Global diversity and geography of soil fungi

Treesearch

Leho Tedersoo; Mohammad Bahram; Sergei Põlme; Urmas Kõljalg; Nourou S. Yorou; Ravi Wijesundera; Luis Villarreal Ruiz; Aida M. Vasco-Palacios; Pham Quang Thu; Ave Suija; Matthew E. Smith; Cathy Sharp; Erki Saluveer; Alessandro Saitta; Miguel Rosas; Taavi Riit; David Ratkowsky; Karin Pritsch; Kadri Põldmaa; Meike Piepenbring; Cherdchai Phosri; Marko Peterson; Kaarin Parts; Kadri Pärtel; Eveli Otsing; Eduardo Nouhra; André L. Njouonkou; R. Henrik Nilsson; Luis N. Morgado; Jordan Mayor; Tom W. May; Luiza Majukim; D. Jean Lodge; Su See Lee; Karl-Henrik Larsson; Petr Kohout; Kentaro Hosaka; Indrek Hiiesalu; Terry W. Henkel; Helery Harend; Liang-dong Guo; Alina Greslebin; Gwen Gretlet; Jozsef Geml; Genevieve Gates; William Dunstan; Chris Dunk; Rein Drenkhan; John Dearnaley; André De Kesel; Tan Dang; Xin Chen; Franz Buegger; Francis Q. Brearley; Gregory Bonito; Sten Anslan; Sandra Abell; Kessy Abarenkov

2014-01-01

Fungi play major roles in ecosystem processes, but the determinants of fungal diversity and biogeographic patterns remain poorly understood. Using DNA metabarcoding data from hundreds of globally distributed soil samples,we demonstrate that fungal richness is decoupled from plant diversity.The plant-to-fungus richness ratio declines exponentially toward the poles....

Kinetic market models with single commodity having price fluctuations

NASA Astrophysics Data System (ADS)

Chatterjee, A.; Chakrabarti, B. K.

2006-12-01

We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of trading or exchange of money and commodity proceeds, with local (in time) fluctuations in the price of the commodity. These distributions are studied in markets with agents having uniform and random saving factors. The self-organizing features in money distribution are similar to the cases without any commodity (or with consumable commodities), while the commodity distribution shows an exponential decay. The wealth distribution shows interesting behavior: gamma like distribution for uniform saving propensity and has the same power-law tail, as that of the money distribution, for a market with agents having random saving propensity.

Rainfall continuous time stochastic simulation for a wet climate in the Cantabric Coast

NASA Astrophysics Data System (ADS)

Rebole, Juan P.; Lopez, Jose J.; Garcia-Guzman, Adela

2010-05-01

Rain is the result of a series of complex atmospheric processes which are influenced by numerous factors. This complexity makes its simulation practically unfeasible from a physical basis, advising the use of stochastic diagrams. These diagrams, which are based on observed characteristics (Todorovic and Woolhiser, 1975), allow the introduction of renewal alternating processes, that account for the occurrence of rainfall at different time lapses (Markov chains are a particular case, where lapses can be described by exponential distributions). Thus, a sequential rainfall process can be defined as a temporal series in which rainfall events (periods in which rainfall is recorded) alternate with non rain events (periods in which no rainfall is recorded). The variables of a temporal rain sequence have been characterized (duration of the rainfall event, duration of the non rainfall event, average intensity of the rain in the rain event, and a temporal distribution of the amount of rain in the rain event) in a wet climate such as that of the coastal area of Guipúzcoa. The study has been performed from two series recorded at the meteorological stations of Igueldo-San Sebastián and Fuenterrabia / Airport (data every ten minutes and for its hourly aggregation). As a result of this work, the variables satisfactorily fitted the following distribution functions: the duration of the rain event to a exponential function; the duration of the dry event to a truncated exponential mixed distribution; the average intensity to a Weibull distribution; and the distribution of the rain fallen to the Beta distribution. The characterization was made for an hourly aggregation of the recorded interval of ten minutes. The parameters of the fitting functions were better obtained by means of the maximum likelihood method than the moment method. The parameters obtained from the characterization were used to develop a stochastic rainfall process simulation model by means of a three states Markov chain (Hutchinson, 1990), performed in an hourly basis by García-Guzmán (1993) and Castro et al. (1997, 2005 ). Simulation process results were valid in the hourly case for all the four described variables, with a slightly better response in Fuenterrabia than in Igueldo. In summary, all the variables were better simulated in Fuenterrabia than in Igueldo. Fuenterrabia data series is shorter and with longer sequences without missing data, compared to Igueldo. The latter shows higher number of missing data events, whereas its mean duration is longer in Fuenterrabia.

Decaying two-dimensional turbulence in a circular container.

PubMed

Schneider, Kai; Farge, Marie

2005-12-09

We present direct numerical simulations of two-dimensional decaying turbulence at initial Reynolds number 5 x 10(4) in a circular container with no-slip boundary conditions. Starting with random initial conditions the flow rapidly exhibits self-organization into coherent vortices. We study their formation and the role of the viscous boundary layer on the production and decay of integral quantities. The no-slip wall produces vortices which are injected into the bulk flow and tend to compensate the enstrophy dissipation. The self-organization of the flow is reflected by the transition of the initially Gaussian vorticity probability density function (PDF) towards a distribution with exponential tails. Because of the presence of coherent vortices the pressure PDF become strongly skewed with exponential tails for negative values.

Exponential lag function projective synchronization of memristor-based multidirectional associative memory neural networks via hybrid control

NASA Astrophysics Data System (ADS)

Yuan, Manman; Wang, Weiping; Luo, Xiong; Li, Lixiang; Kurths, Jürgen; Wang, Xiao

2018-03-01

This paper is concerned with the exponential lag function projective synchronization of memristive multidirectional associative memory neural networks (MMAMNNs). First, we propose a new model of MMAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying discrete delays and distributed time delays. Second, we design two kinds of hybrid controllers. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the controllers are carefully designed to confirm the process of different types of synchronization in the MMAMNNs. Third, sufficient criteria guaranteeing the synchronization of system are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

Non-Gaussian Analysis of Diffusion Weighted Imaging in Head and Neck at 3T: A Pilot Study in Patients with Nasopharyngeal Carcinoma

PubMed Central

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S. P.; Bhatia, Kunwar S.; Wang, Yi-Xiang J.; Ahuja, Anil T.; King, Ann D.

2014-01-01

Purpose To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). Materials and Methods After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm2. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Results Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Conclusion Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization. PMID:24466318

Referee Networks and Their Spectral Properties

NASA Astrophysics Data System (ADS)

Slanina, F.; Zhang, Y.-Ch.

2005-09-01

The bipartite graph connecting products and reviewers of that product is studied empirically in the case of amazon.com. We find that the network has power-law degree distribution on the side of reviewers, while on the side of products the distribution is better fitted by stretched exponential. The spectrum of normalised adjacency matrix shows power-law tail in the density of states. Establishing the community structures by finding localised eigenstates is not straightforward as the localised and delocalised states are mixed throughout the whole support of the spectrum.

Transient statistics in stabilizing periodic orbits

NASA Astrophysics Data System (ADS)

Meucci, R.; Gadomski, W.; Ciofini, M.; Arecchi, F. T.

1995-11-01

The statistics of chaotic and periodic transient time intervals preceding the stabilization of a given periodic orbit have been experimentally studied in a CO2 laser with modulated losses, subjected to a small subharmonic perturbation. As predicted by the theory, an exponential tail has been found in the probability distribution of chaotic transients. Furthermore, a fine periodic structure in the distributions of the periodic transients, resulting from the interaction of the control signal and the local structure of the chaotic attractor, has been revealed.

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

NASA Astrophysics Data System (ADS)

Gunaratne, Gemunu H.; McCauley, Joseph L.

2005-05-01

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

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.

The mathematical relationship between Zipf’s law and the hierarchical scaling law

NASA Astrophysics Data System (ADS)

Chen, Yanguang

2012-06-01

The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their relationship has never been revealed by strict mathematical proof. In this paper, the Zipf's distribution of cities is abstracted as a q-sequence. Based on this sequence, a self-similar hierarchy consisting of many levels is defined and the numbers of cities in different levels form a geometric sequence. An exponential distribution of the average size of cities is derived from the hierarchy. Thus we have two exponential functions, from which follows a hierarchical scaling equation. The results can be statistically verified by simple mathematical experiments and observational data of cities. A theoretical foundation is then laid for the conversion from Zipf's law to the hierarchical scaling law, and the latter can show more information about city development than the former. Moreover, the self-similar hierarchy provides a new perspective for studying networks of cities as complex systems. A series of mathematical rules applied to cities such as the allometric growth law, the 2n principle and Pareto's law can be associated with one another by the hierarchical organization.

The Trend Odds Model for Ordinal Data‡

PubMed Central

Capuano, Ana W.; Dawson, Jeffrey D.

2013-01-01

Ordinal data appear in a wide variety of scientific fields. These data are often analyzed using ordinal logistic regression models that assume proportional odds. When this assumption is not met, it may be possible to capture the lack of proportionality using a constrained structural relationship between the odds and the cut-points of the ordinal values (Peterson and Harrell, 1990). We consider a trend odds version of this constrained model, where the odds parameter increases or decreases in a monotonic manner across the cut-points. We demonstrate algebraically and graphically how this model is related to latent logistic, normal, and exponential distributions. In particular, we find that scale changes in these potential latent distributions are consistent with the trend odds assumption, with the logistic and exponential distributions having odds that increase in a linear or nearly linear fashion. We show how to fit this model using SAS Proc Nlmixed, and perform simulations under proportional odds and trend odds processes. We find that the added complexity of the trend odds model gives improved power over the proportional odds model when there are moderate to severe departures from proportionality. A hypothetical dataset is used to illustrate the interpretation of the trend odds model, and we apply this model to a Swine Influenza example where the proportional odds assumption appears to be violated. PMID:23225520

The trend odds model for ordinal data.

PubMed

Capuano, Ana W; Dawson, Jeffrey D

2013-06-15

Ordinal data appear in a wide variety of scientific fields. These data are often analyzed using ordinal logistic regression models that assume proportional odds. When this assumption is not met, it may be possible to capture the lack of proportionality using a constrained structural relationship between the odds and the cut-points of the ordinal values. We consider a trend odds version of this constrained model, wherein the odds parameter increases or decreases in a monotonic manner across the cut-points. We demonstrate algebraically and graphically how this model is related to latent logistic, normal, and exponential distributions. In particular, we find that scale changes in these potential latent distributions are consistent with the trend odds assumption, with the logistic and exponential distributions having odds that increase in a linear or nearly linear fashion. We show how to fit this model using SAS Proc NLMIXED and perform simulations under proportional odds and trend odds processes. We find that the added complexity of the trend odds model gives improved power over the proportional odds model when there are moderate to severe departures from proportionality. A hypothetical data set is used to illustrate the interpretation of the trend odds model, and we apply this model to a swine influenza example wherein the proportional odds assumption appears to be violated. Copyright © 2012 John Wiley & Sons, Ltd.

Driven fragmentation of granular gases.

PubMed

Cruz Hidalgo, Raúl; Pagonabarraga, Ignacio

2008-06-01

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

A new approach to interpretation of heterogeneity of fluorescence decay in complex biological systems

NASA Astrophysics Data System (ADS)

Wlodarczyk, Jakub; Kierdaszuk, Borys

2005-08-01

Decays of tyrosine fluorescence in protein-ligand complexes are described by a model of continuous distribution of fluorescence lifetimes. Resulted analytical power-like decay function provides good fits to highly complex fluorescence kinetics. Moreover, this is a manifestation of so-called Tsallis q-exponential function, which is suitable for description of the systems with long-range interactions, memory effect, as well as with fluctuations of the characteristic lifetime of fluorescence. The proposed decay functions were applied to analysis of fluorescence decays of tyrosine in a protein, i.e. the enzyme purine nucleoside phosphorylase from E. coli (the product of the deoD gene), free in aqueous solution and in a complex with formycin A (an inhibitor) and orthophosphate (a co-substrate). The power-like function provides new information about enzyme-ligand complex formation based on the physically justified heterogeneity parameter directly related to the lifetime distribution. A measure of the heterogeneity parameter in the enzyme systems is provided by a variance of fluorescence lifetime distribution. The possible number of deactivation channels and excited state mean lifetime can be easily derived without a priori knowledge of the complexity of studied system. Moreover, proposed model is simpler then traditional multi-exponential one, and better describes heterogeneous nature of studied systems.

Applicaton of the Calculating Formula for Mean Neutron Exposure on Barium stars

NASA Astrophysics Data System (ADS)

Zhang, F. H.; Zhang, L.; Cui, W. Y.; Zhang, B.

2017-11-01

Latest studies have shown that, in the s-process nucleosynthesis model for the low-mass asymptotic giant branch (AGB) star with (13C) pocket radiative burning during the interpulse period, the distribution of neutron exposures in the nucleosynthesis region can be regarded as an exponential function, and the relation between the mean neutron exposure (τ0) and the model parameters is (τ0} = - Δ τ/ln [q/(1 - r + q)]), in which (Δ τ) is the exposure value of each neutron irradiation, (r) is the overlap factor, and (q) is the mass ratio of the (13C) shell to the He intershell. In this paper the formula is applied to 26 samples of barium stars to test its reliability, and furthermore the neutron exposure nature in the AGB companion stars of 26 barium stars are analyzed. The results show that, the formula is reliable; in the AGB companion stars of 26 barium stars, at least 8 stars definitely have and 12 stars are highly likely to have exponential distribution of neutron exposures, while 4 stars tend to experience single neutron exposure; most of the AGB companion stars may have experienced fewer times of neutron irradiations before the element abundance distribution of the s-process comes to asymptotic condition.

Explicit equilibria in a kinetic model of gambling

NASA Astrophysics Data System (ADS)

Bassetti, F.; Toscani, G.

2010-06-01

We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the agents. For this equation the analytical form of the steady states is found for various realizations of the random fraction of the sum which is shared to the agents. Among others, the exponential distribution appears as steady state in case of a uniformly distributed random fraction, while Gamma distribution appears for a random fraction which is Beta distributed. The case in which the gambling game is only conservative-in-the-mean is shown to lead to an explicit heavy tailed distribution.

Scoring Methods in the International Land Benchmarking (ILAMB) Package

NASA Astrophysics Data System (ADS)

Collier, N.; Hoffman, F. M.; Keppel-Aleks, G.; Lawrence, D. M.; Mu, M.; Riley, W. J.; Randerson, J. T.

2017-12-01

The International Land Model Benchmarking (ILAMB) project is a model-data intercomparison and integration project designed to improve the performance of the land component of Earth system models. This effort is disseminated in the form of a python package which is openly developed (https://bitbucket.org/ncollier/ilamb). ILAMB is more than a workflow system that automates the generation of common scalars and plot comparisons to observational data. We aim to provide scientists and model developers with a tool to gain insight into model behavior. Thus, a salient feature of the ILAMB package is our synthesis methodology, which provides users with a high-level understanding of model performance. Within ILAMB, we calculate a non-dimensional score of a model's performance in a given dimension of the physics, chemistry, or biology with respect to an observational dataset. For example, we compare the Fluxnet-MTE Gross Primary Productivity (GPP) product against model output in the corresponding historical period. We compute common statistics such as the bias, root mean squared error, phase shift, and spatial distribution. We take these measures and find relative errors by normalizing the values, and then use the exponential to map this relative error to the unit interval. This allows for the scores to be combined into an overall score representing multiple aspects of model performance. In this presentation we give details of this process as well as a proposal for tuning the exponential mapping to make scores more cross comparable. However, as many models are calibrated using these scalar measures with respect to observational datasets, we also score the relationships among relevant variables in the model. For example, in the case of GPP, we also consider its relationship to precipitation, evapotranspiration, and temperature. We do this by creating a mean response curve and a two-dimensional distribution based on the observational data and model results. The response curves are then scored using a relative measure of the root mean squared error and the exponential as before. The distributions are scored using the so-called Hellinger distance, a statistical measure for how well one distribution is represented by another, and included in the model's overall score.

Peculiar spectral statistics of ensembles of trees and star-like graphs

NASA Astrophysics Data System (ADS)

Kovaleva, V.; Maximov, Yu; Nechaev, S.; Valba, O.

2017-07-01

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the ‘Lifshitz singularity’ emerging in the one-dimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However, the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, reflecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of an ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.

Stochastic modelling of intermittent fluctuations in the scrape-off layer: Correlations, distributions, level crossings, and moment estimation

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

Garcia, O. E., E-mail: odd.erik.garcia@uit.no; Kube, R.; Theodorsen, A.

A stochastic model is presented for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas. The fluctuations in the plasma density are modeled by a super-position of uncorrelated pulses with fixed shape and duration, describing radial motion of blob-like structures. In the case of an exponential pulse shape and exponentially distributed pulse amplitudes, predictions are given for the lowest order moments, probability density function, auto-correlation function, level crossings, and average times for periods spent above and below a given threshold level. Also, the mean squared errors on estimators of sample mean and variance for realizations of the process bymore » finite time series are obtained. These results are discussed in the context of single-point measurements of fluctuations in the scrape-off layer, broad density profiles, and implications for plasma–wall interactions due to the transient transport events in fusion grade plasmas. The results may also have wide applications for modelling fluctuations in other magnetized plasmas such as basic laboratory experiments and ionospheric irregularities.« less

Model-based analysis of multi-shell diffusion MR data for tractography: How to get over fitting problems

PubMed Central

Jbabdi, Saad; Sotiropoulos, Stamatios N; Savio, Alexander M; Graña, Manuel; Behrens, Timothy EJ

2012-01-01

In this article, we highlight an issue that arises when using multiple b-values in a model-based analysis of diffusion MR data for tractography. The non-mono-exponential decay, commonly observed in experimental data, is shown to induce over-fitting in the distribution of fibre orientations when not considered in the model. Extra fibre orientations perpendicular to the main orientation arise to compensate for the slower apparent signal decay at higher b-values. We propose a simple extension to the ball and stick model based on a continuous Gamma distribution of diffusivities, which significantly improves the fitting and reduces the over-fitting. Using in-vivo experimental data, we show that this model outperforms a simpler, noise floor model, especially at the interfaces between brain tissues, suggesting that partial volume effects are a major cause of the observed non-mono-exponential decay. This model may be helpful for future data acquisition strategies that may attempt to combine multiple shells to improve estimates of fibre orientations in white matter and near the cortex. PMID:22334356

Probability evolution method for exit location distribution

NASA Astrophysics Data System (ADS)

Zhu, Jinjie; Chen, Zhen; Liu, Xianbin

2018-03-01

The exit problem in the framework of the large deviation theory has been a hot topic in the past few decades. The most probable escape path in the weak-noise limit has been clarified by the Freidlin-Wentzell action functional. However, noise in real physical systems cannot be arbitrarily small while noise with finite strength may induce nontrivial phenomena, such as noise-induced shift and noise-induced saddle-point avoidance. Traditional Monte Carlo simulation of noise-induced escape will take exponentially large time as noise approaches zero. The majority of the time is wasted on the uninteresting wandering around the attractors. In this paper, a new method is proposed to decrease the escape simulation time by an exponentially large factor by introducing a series of interfaces and by applying the reinjection on them. This method can be used to calculate the exit location distribution. It is verified by examining two classical examples and is compared with theoretical predictions. The results show that the method performs well for weak noise while may induce certain deviations for large noise. Finally, some possible ways to improve our method are discussed.

Peculiar spectral statistics of ensembles of trees and star-like graphs

DOE PAGES

Kovaleva, V.; Maximov, Yu; Nechaev, S.; ...

2017-07-11

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the \\Lifshitz singularity" emerging in the onedimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However,more » the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, re ecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.« less

Intervention-Based Stochastic Disease Eradication

NASA Astrophysics Data System (ADS)

Billings, Lora; Mier-Y-Teran-Romero, Luis; Lindley, Brandon; Schwartz, Ira

2013-03-01

Disease control is of paramount importance in public health with infectious disease extinction as the ultimate goal. Intervention controls, such as vaccination of susceptible individuals and/or treatment of infectives, are typically based on a deterministic schedule, such as periodically vaccinating susceptible children based on school calendars. In reality, however, such policies are administered as a random process, while still possessing a mean period. Here, we consider the effect of randomly distributed intervention as disease control on large finite populations. We show explicitly how intervention control, based on mean period and treatment fraction, modulates the average extinction times as a function of population size and the speed of infection. In particular, our results show an exponential improvement in extinction times even though the controls are implemented using a random Poisson distribution. Finally, we discover those parameter regimes where random treatment yields an exponential improvement in extinction times over the application of strictly periodic intervention. The implication of our results is discussed in light of the availability of limited resources for control. Supported by the National Institute of General Medical Sciences Award No. R01GM090204

Statistical steady states in turbulent droplet condensation

NASA Astrophysics Data System (ADS)

Bec, Jeremie; Krstulovic, Giorgio; Siewert, Christoph

2017-11-01

We investigate the general problem of turbulent condensation. Using direct numerical simulations we show that the fluctuations of the supersaturation field offer different conditions for the growth of droplets which evolve in time due to turbulent transport and mixing. This leads to propose a Lagrangian stochastic model consisting of a set of integro-differential equations for the joint evolution of the squared radius and the supersaturation along droplet trajectories. The model has two parameters fixed by the total amount of water and the thermodynamic properties, as well as the Lagrangian integral timescale of the turbulent supersaturation. The model reproduces very well the droplet size distributions obtained from direct numerical simulations and their time evolution. A noticeable result is that, after a stage where the squared radius simply diffuses, the system converges exponentially fast to a statistical steady state independent of the initial conditions. The main mechanism involved in this convergence is a loss of memory induced by a significant number of droplets undergoing a complete evaporation before growing again. The statistical steady state is characterised by an exponential tail in the droplet mass distribution.

Peculiar spectral statistics of ensembles of trees and star-like graphs

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

Kovaleva, V.; Maximov, Yu; Nechaev, S.

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the \\Lifshitz singularity" emerging in the onedimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However,more » the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, re ecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.« less

Reliability demonstration test for load-sharing systems with exponential and Weibull components

PubMed Central

Hu, Qingpei; Yu, Dan; Xie, Min

2017-01-01

Conducting a Reliability Demonstration Test (RDT) is a crucial step in production. Products are tested under certain schemes to demonstrate whether their reliability indices reach pre-specified thresholds. Test schemes for RDT have been studied in different situations, e.g., lifetime testing, degradation testing and accelerated testing. Systems designed with several structures are also investigated in many RDT plans. Despite the availability of a range of test plans for different systems, RDT planning for load-sharing systems hasn’t yet received the attention it deserves. In this paper, we propose a demonstration method for two specific types of load-sharing systems with components subject to two distributions: exponential and Weibull. Based on the assumptions and interpretations made in several previous works on such load-sharing systems, we set the mean time to failure (MTTF) of the total system as the demonstration target. We represent the MTTF as a summation of mean time between successive component failures. Next, we introduce generalized test statistics for both the underlying distributions. Finally, RDT plans for the two types of systems are established on the basis of these test statistics. PMID:29284030

Reliability demonstration test for load-sharing systems with exponential and Weibull components.

PubMed

Xu, Jianyu; Hu, Qingpei; Yu, Dan; Xie, Min

2017-01-01

Conducting a Reliability Demonstration Test (RDT) is a crucial step in production. Products are tested under certain schemes to demonstrate whether their reliability indices reach pre-specified thresholds. Test schemes for RDT have been studied in different situations, e.g., lifetime testing, degradation testing and accelerated testing. Systems designed with several structures are also investigated in many RDT plans. Despite the availability of a range of test plans for different systems, RDT planning for load-sharing systems hasn't yet received the attention it deserves. In this paper, we propose a demonstration method for two specific types of load-sharing systems with components subject to two distributions: exponential and Weibull. Based on the assumptions and interpretations made in several previous works on such load-sharing systems, we set the mean time to failure (MTTF) of the total system as the demonstration target. We represent the MTTF as a summation of mean time between successive component failures. Next, we introduce generalized test statistics for both the underlying distributions. Finally, RDT plans for the two types of systems are established on the basis of these test statistics.

Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains: the role of mixing statistics and frame shift of neighboring genes.

PubMed

Cocho, Germinal; Miramontes, Pedro; Mansilla, Ricardo; Li, Wentian

2014-12-01

We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies. Copyright © 2014 Elsevier Ltd. All rights reserved.

From the Cover: The growth of business firms: Theoretical framework and empirical evidence

NASA Astrophysics Data System (ADS)

Fu, Dongfeng; Pammolli, Fabio; Buldyrev, S. V.; Riccaboni, Massimo; Matia, Kaushik; Yamasaki, Kazuko; Stanley, H. Eugene

2005-12-01

We introduce a model of proportional growth to explain the distribution Pg(g) of business-firm growth rates. The model predicts that Pg(g) is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent = 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the predictions of the model agree with empirical growth distributions and size-variance relationships. proportional growth | preferential attachment | Laplace distribution

Distributed convex optimisation with event-triggered communication in networked systems

NASA Astrophysics Data System (ADS)

Liu, Jiayun; Chen, Weisheng

2016-12-01

This paper studies the distributed convex optimisation problem over directed networks. Motivated by practical considerations, we propose a novel distributed zero-gradient-sum optimisation algorithm with event-triggered communication. Therefore, communication and control updates just occur at discrete instants when some predefined condition satisfies. Thus, compared with the time-driven distributed optimisation algorithms, the proposed algorithm has the advantages of less energy consumption and less communication cost. Based on Lyapunov approaches, we show that the proposed algorithm makes the system states asymptotically converge to the solution of the problem exponentially fast and the Zeno behaviour is excluded. Finally, simulation example is given to illustrate the effectiveness of the proposed algorithm.

Decision Models for Determining the Optimal Life Test Sampling Plans

NASA Astrophysics Data System (ADS)

Nechval, Nicholas A.; Nechval, Konstantin N.; Purgailis, Maris; Berzins, Gundars; Strelchonok, Vladimir F.

2010-11-01

Life test sampling plan is a technique, which consists of sampling, inspection, and decision making in determining the acceptance or rejection of a batch of products by experiments for examining the continuous usage time of the products. In life testing studies, the lifetime is usually assumed to be distributed as either a one-parameter exponential distribution, or a two-parameter Weibull distribution with the assumption that the shape parameter is known. Such oversimplified assumptions can facilitate the follow-up analyses, but may overlook the fact that the lifetime distribution can significantly affect the estimation of the failure rate of a product. Moreover, sampling costs, inspection costs, warranty costs, and rejection costs are all essential, and ought to be considered in choosing an appropriate sampling plan. The choice of an appropriate life test sampling plan is a crucial decision problem because a good plan not only can help producers save testing time, and reduce testing cost; but it also can positively affect the image of the product, and thus attract more consumers to buy it. This paper develops the frequentist (non-Bayesian) decision models for determining the optimal life test sampling plans with an aim of cost minimization by identifying the appropriate number of product failures in a sample that should be used as a threshold in judging the rejection of a batch. The two-parameter exponential and Weibull distributions with two unknown parameters are assumed to be appropriate for modelling the lifetime of a product. A practical numerical application is employed to demonstrate the proposed approach.

Modelling control of epidemics spreading by long-range interactions.

PubMed

Dybiec, Bartłomiej; Kleczkowski, Adam; Gilligan, Christopher A

2009-10-06

We have studied the spread of epidemics characterized by a mixture of local and non-local interactions. The infection spreads on a two-dimensional lattice with the fixed nearest neighbour connections. In addition, long-range dynamical links are formed by moving agents (vectors). Vectors perform random walks, with step length distributed according to a thick-tail distribution. Two distributions are considered in this paper, an alpha-stable distribution describing self-similar vector movement, yet characterized by an infinite variance and an exponential power characterized by a large but finite variance. Such long-range interactions are hard to track and make control of epidemics very difficult. We also allowed for cryptic infection, whereby an infected individual on the lattice can be infectious prior to showing any symptoms of infection or disease. To account for such cryptic spread, we considered a control strategy in which not only detected, i.e. symptomatic, individuals but also all individuals within a certain control neighbourhood are treated upon the detection of disease. We show that it is possible to eradicate the disease by using such purely local control measures, even in the presence of long-range jumps. In particular, we show that the success of local control and the choice of the optimal strategy depend in a non-trivial way on the dispersal patterns of the vectors. By characterizing these patterns using the stability index of the alpha-stable distribution to change the power-law behaviour or the exponent characterizing the decay of an exponential power distribution, we show that infection can be successfully contained using relatively small control neighbourhoods for two limiting cases for long-distance dispersal and for vectors that are much more limited in their dispersal range.

Probing the stochastic property of endoreduplication in cell size determination of Arabidopsis thaliana leaf epidermal tissue

PubMed Central

2017-01-01

Cell size distribution is highly reproducible, whereas the size of individual cells often varies greatly within a tissue. This is obvious in a population of Arabidopsis thaliana leaf epidermal cells, which ranged from 1,000 to 10,000 μm2 in size. Endoreduplication is a specialized cell cycle in which nuclear genome size (ploidy) is doubled in the absence of cell division. Although epidermal cells require endoreduplication to enhance cellular expansion, the issue of whether this mechanism is sufficient for explaining cell size distribution remains unclear due to a lack of quantitative understanding linking the occurrence of endoreduplication with cell size diversity. Here, we addressed this question by quantitatively summarizing ploidy profile and cell size distribution using a simple theoretical framework. We first found that endoreduplication dynamics is a Poisson process through cellular maturation. This finding allowed us to construct a mathematical model to predict the time evolution of a ploidy profile with a single rate constant for endoreduplication occurrence in a given time. We reproduced experimentally measured ploidy profile in both wild-type leaf tissue and endoreduplication-related mutants with this analytical solution, further demonstrating the probabilistic property of endoreduplication. We next extended the mathematical model by incorporating the element that cell size is determined according to ploidy level to examine cell size distribution. This analysis revealed that cell size is exponentially enlarged 1.5 times every endoreduplication round. Because this theoretical simulation successfully recapitulated experimentally observed cell size distributions, we concluded that Poissonian endoreduplication dynamics and exponential size-boosting are the sources of the broad cell size distribution in epidermal tissue. More generally, this study contributes to a quantitative understanding whereby stochastic dynamics generate steady-state biological heterogeneity. PMID:28926847

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

PubMed

Lin, Guoxing

2016-11-21

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

2D modelling of the light distribution of early-type galaxies in a volume-limited sample - II. Results for real galaxies

NASA Astrophysics Data System (ADS)

D'Onofrio, M.

2001-10-01

In this paper we analyse the results of the two-dimensional (2D) fit of the light distribution of 73 early-type galaxies belonging to the Virgo and Fornax clusters, a sample volume- and magnitude-limited down to MB=-17.3, and highly homogeneous. In our previous paper (Paper I) we have presented the adopted 2D models of the surface-brightness distribution - namely the r1/n and (r1/n+exp) models - we have discussed the main sources of error affecting the structural parameters, and we have tested the ability of the chosen minimization algorithm (MINUIT) in determining the fitting parameters using a sample of artificial galaxies. We show that, with the exception of 11 low-luminosity E galaxies, the best fit of the real galaxy sample is always achieved with the two-component (r1/n+exp) model. The improvement in the χ2 due to the addition of the exponential component is found to be statistically significant. The best fit is obtained with the exponent n of the generalized r1/n Sersic law different from the classical de Vaucouleurs value of 4. Nearly 42 per cent of the sample have n<2, suggesting the presence of exponential `bulges' also in early-type galaxies. 20 luminous E galaxies are fitted by the two-component model, with a small central exponential structure (`disc') and an outer big spheroid with n>4. We believe that this is probably due to their resolved core. The resulting scalelengths Rh and Re of each component peak approximately at ~1 and ~2kpc, respectively, although with different variances in their distributions. The ratio Re/Rh peaks at ~0.5, a value typical for normal lenticular galaxies. The first component, represented by the r1/n law, is probably made of two distinct families, `ordinary' and `bright', on the basis of their distribution in the μe-log(Re) plane, a result already suggested by Capaccioli, Caon and D'Onofrio. The bulges of spirals and S0 galaxies belong to the `ordinary' family, while the large spheroids of luminous E galaxies form the `bright' family. The second component, represented by the exponential law, also shows a wide distribution in the μ0c-log(Rh) plane. Small discs (or cores) have short scalelengths and high central surface brightness, while normal lenticulars and spiral galaxies generally have scalelengths higher than 0.5kpc and central surface brightness brighter than 20magarcsec-2 (in the B band). The scalelengths Re and Rh of the `bulge' and `disc' components are probably correlated, indicating that a self-regulating mechanism of galaxy formation may be at work. Alternatively, two regions of the Re-Rh plane are avoided by galaxies due to dynamical instability effects. The bulge-to-disc (B/D) ratio seems to vary uniformly along the Hubble sequence, going from late-type spirals to E galaxies. At the end of the sequence the ratio between the large spheroidal component and the small inner core can reach B/D~100.

The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

NASA Technical Reports Server (NTRS)

Koshak, William; Solakiewicz, Richard

2012-01-01

The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.

Higher-order phase transitions on financial markets

NASA Astrophysics Data System (ADS)

Kasprzak, A.; Kutner, R.; Perelló, J.; Masoliver, J.

2010-08-01

Statistical and thermodynamic properties of the anomalous multifractal structure of random interevent (or intertransaction) times were thoroughly studied by using the extended continuous-time random walk (CTRW) formalism of Montroll, Weiss, Scher, and Lax. Although this formalism is quite general (and can be applied to any interhuman communication with nontrivial priority), we consider it in the context of a financial market where heterogeneous agent activities can occur within a wide spectrum of time scales. As the main general consequence, we found (by additionally using the Saddle-Point Approximation) the scaling or power-dependent form of the partition function, Z(q'). It diverges for any negative scaling powers q' (which justifies the name anomalous) while for positive ones it shows the scaling with the general exponent τ(q'). This exponent is the nonanalytic (singular) or noninteger power of q', which is one of the pilar of higher-order phase transitions. In definition of the partition function we used the pausing-time distribution (PTD) as the central one, which takes the form of convolution (or superstatistics used, e.g. for describing turbulence as well as the financial market). Its integral kernel is given by the stretched exponential distribution (often used in disordered systems). This kernel extends both the exponential distribution assumed in the original version of the CTRW formalism (for description of the transient photocurrent measured in amorphous glassy material) as well as the Gaussian one sometimes used in this context (e.g. for diffusion of hydrogen in amorphous metals or for aging effects in glasses). Our most important finding is the third- and higher-order phase transitions, which can be roughly interpreted as transitions between the phase where high frequency trading is most visible and the phase defined by low frequency trading. The specific order of the phase transition directly depends upon the shape exponent α defining the stretched exponential integral kernel. On this basis a simple practical hint for investors was formulated.

How do output growth-rate distributions look like? Some cross-country, time-series evidence

NASA Astrophysics Data System (ADS)

Fagiolo, G.; Napoletano, M.; Roventini, A.

2007-05-01

This paper investigates the statistical properties of within-country gross domestic product (GDP) and industrial production (IP) growth-rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether also within-country, time-series GDP and IP growth rates can be approximated by tent-shaped distributions. We fit output growth rates with the exponential-power (Subbotin) family of densities, which includes as particular cases both Gaussian and Laplace distributions. We find that, for a large number of OECD (Organization for Economic Cooperation and Development) countries including the US, both GDP and IP growth rates are Laplace distributed. Moreover, we show that fat-tailed distributions robustly emerge even after controlling for outliers, autocorrelation and heteroscedasticity.

Effect of temperature on life history parameters of adult Culicoides sonorensis (Diptera: Ceratopogonidae) in relation to geographic origin and vectorial capacity for bluetongue virus.

PubMed

Lysyk, T J; Danyk, T

2007-09-01

The effect of temperature on survival, oviposition, gonotrophic development, and a life history factor of vectorial capacity were examined in adult Culicoides sonorensis (Wirth & Jones) (Diptera: Ceratopogonidae) that originated from two geographic locations. Flies originating from the United States (Colorado) had slightly reduced survival after a bloodmeal compared with wild flies collected in southern Alberta (AB), Canada. Survival of AB flies declined in a curvilinear manner with temperature, whereas survival of U.S. flies showed a linear response to temperature. The survivorship curve of the AB flies more closely followed a Weibull distribution than an exponential, indicating survival was age-dependent. Survivorship of the U.S. flies followed an exponential distribution. Females from both sources laid similar numbers of eggs throughout their life. The first eggs were laid by females from both sources at 31.9 degree-day (DD)9.3. Dissections of blood-fed flies reared at various temperatures indicated that flies from both sources were 90% gravid at 32 DD9.3. Relationships among temperature and life history components of vectorial capacity were similar among flies from the two sources and indicated that vectorial capacity would be approximately 1.8-2.6-fold greater in a southern U.S. climate compared with southwestern Canada due solely to the effects of temperature on the life history of C. sonorensis. Using life history estimates derived from Weibull model had little effect on estimating vectorial capacity, whereas using estimates derived from the exponential model slightly overestimated vectorial capacity.

Robust Image Regression Based on the Extended Matrix Variate Power Exponential Distribution of Dependent Noise.

PubMed

Luo, Lei; Yang, Jian; Qian, Jianjun; Tai, Ying; Lu, Gui-Fu

2017-09-01

Dealing with partial occlusion or illumination is one of the most challenging problems in image representation and classification. In this problem, the characterization of the representation error plays a crucial role. In most current approaches, the error matrix needs to be stretched into a vector and each element is assumed to be independently corrupted. This ignores the dependence between the elements of error. In this paper, it is assumed that the error image caused by partial occlusion or illumination changes is a random matrix variate and follows the extended matrix variate power exponential distribution. This has the heavy tailed regions and can be used to describe a matrix pattern of l×m dimensional observations that are not independent. This paper reveals the essence of the proposed distribution: it actually alleviates the correlations between pixels in an error matrix E and makes E approximately Gaussian. On the basis of this distribution, we derive a Schatten p -norm-based matrix regression model with L q regularization. Alternating direction method of multipliers is applied to solve this model. To get a closed-form solution in each step of the algorithm, two singular value function thresholding operators are introduced. In addition, the extended Schatten p -norm is utilized to characterize the distance between the test samples and classes in the design of the classifier. Extensive experimental results for image reconstruction and classification with structural noise demonstrate that the proposed algorithm works much more robustly than some existing regression-based methods.

Empirical study of recent Chinese stock market

NASA Astrophysics Data System (ADS)

Jiang, J.; Li, W.; Cai, X.; Wang, Qiuping A.

2009-05-01

We investigate the statistical properties of the empirical data taken from the Chinese stock market during the time period from January, 2006 to July, 2007. By using the methods of detrended fluctuation analysis (DFA) and calculating correlation coefficients, we acquire the evidence of strong correlations among different stock types, stock index, stock volume turnover, A share (B share) seat number, and GDP per capita. In addition, we study the behavior of “volatility”, which is now defined as the difference between the new account numbers for two consecutive days. It is shown that the empirical power-law of the number of aftershock events exceeding the selected threshold is analogous to the Omori law originally observed in geophysics. Furthermore, we find that the cumulative distributions of stock return, trade volume and trade number are all exponential-like, which does not belong to the universality class of such distributions found by Xavier Gabaix et al. [Xavier Gabaix, Parameswaran Gopikrishnan, Vasiliki Plerou, H. Eugene Stanley, Nature, 423 (2003)] for major western markets. Through the comparison, we draw a conclusion that regardless of developed stock markets or emerging ones, “cubic law of returns” is valid only in the long-term absolute return, and in the short-term one, the distributions are exponential-like. Specifically, the distributions of both trade volume and trade number display distinct decaying behaviors in two separate regimes. Lastly, the scaling behavior of the relation is analyzed between dispersion and the mean monthly trade value for each administrative area in China.

Beyond the power law: Uncovering stylized facts in interbank networks

NASA Astrophysics Data System (ADS)

Vandermarliere, Benjamin; Karas, Alexei; Ryckebusch, Jan; Schoors, Koen

2015-06-01

We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over August 1998-October 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio) and edge weights (loan size and counterparty exposure). We search for the theoretical distribution that fits the data best and report the "best" fit parameters. We observe that all studied distributions are heavy tailed. The fat tail typically contains 20% of the data and can be mostly described well by a truncated power law. Also the power law, stretched exponential and log-normal provide reasonably good fits to the tails of the data. In most cases, however, separating the bulk and tail parts of the data is hard, so we proceed to study the full range of the events. We find that the stretched exponential and the log-normal distributions fit the full range of the data best. These conclusions are robust to (1) whether we aggregate the data over a week, month, quarter or year; (2) whether we look at the "growth" versus "maturity" phases of interbank market development; and (3) with minor exceptions, whether we look at the "normal" versus "crisis" operation periods. In line with prior research, we find that the network topology changes greatly as the interbank market moves from a "normal" to a "crisis" operation period.

The probability distribution model of air pollution index and its dominants in Kuala Lumpur

NASA Astrophysics Data System (ADS)

AL-Dhurafi, Nasr Ahmed; Razali, Ahmad Mahir; Masseran, Nurulkamal; Zamzuri, Zamira Hasanah

2016-11-01

This paper focuses on the statistical modeling for the distributions of air pollution index (API) and its sub-indexes data observed at Kuala Lumpur in Malaysia. Five pollutants or sub-indexes are measured including, carbon monoxide (CO); sulphur dioxide (SO2); nitrogen dioxide (NO2), and; particulate matter (PM10). Four probability distributions are considered, namely log-normal, exponential, Gamma and Weibull in search for the best fit distribution to the Malaysian air pollutants data. In order to determine the best distribution for describing the air pollutants data, five goodness-of-fit criteria's are applied. This will help in minimizing the uncertainty in pollution resource estimates and improving the assessment phase of planning. The conflict in criterion results for selecting the best distribution was overcome by using the weight of ranks method. We found that the Gamma distribution is the best distribution for the majority of air pollutants data in Kuala Lumpur.

Probabilistic structural analysis of a truss typical for space station

NASA Technical Reports Server (NTRS)

Pai, Shantaram S.

1990-01-01

A three-bay, space, cantilever truss is probabilistically evaluated using the computer code NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) to identify and quantify the uncertainties and respective sensitivities associated with corresponding uncertainties in the primitive variables (structural, material, and loads parameters) that defines the truss. The distribution of each of these primitive variables is described in terms of one of several available distributions such as the Weibull, exponential, normal, log-normal, etc. The cumulative distribution function (CDF's) for the response functions considered and sensitivities associated with the primitive variables for given response are investigated. These sensitivities help in determining the dominating primitive variables for that response.

Universal scaling law in human behavioral organization.

PubMed

Nakamura, Toru; Kiyono, Ken; Yoshiuchi, Kazuhiro; Nakahara, Rika; Struzik, Zbigniew R; Yamamoto, Yoshiharu

2007-09-28

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression.

Universal Scaling Law in Human Behavioral Organization

NASA Astrophysics Data System (ADS)

Nakamura, Toru; Kiyono, Ken; Yoshiuchi, Kazuhiro; Nakahara, Rika; Struzik, Zbigniew R.; Yamamoto, Yoshiharu

2007-09-01

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression.

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

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

Knessl, C.; Tier, C.

1999-10-01

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

The growth of business firms: theoretical framework and empirical evidence.

PubMed

Fu, Dongfeng; Pammolli, Fabio; Buldyrev, S V; Riccaboni, Massimo; Matia, Kaushik; Yamasaki, Kazuko; Stanley, H Eugene

2005-12-27

We introduce a model of proportional growth to explain the distribution P(g)(g) of business-firm growth rates. The model predicts that P(g)(g) is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent zeta = 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the predictions of the model agree with empirical growth distributions and size-variance relationships.

Neutron skyshine measurements at Fermilab.

PubMed

Cossairt, J D; Coulson, L V

1985-02-01

Neutron skyshine has been a significant source of environmental radiation exposure at many high-energy proton accelerators. A particularly troublesome source of skyshine neutrons has existed at Fermilab during operation of the 400-GeV high-energy physics program. This paper reports on several measurements of this source made with a DePangher precision long counter at large distances. The spatial distribution of the neutron skyshine can approximately be described as an inverse square law dependence multiplied by an exponential with an approximate attenuation length of 1200 +/- 300 m. The absolute magnitude of the distributions can be matched directly to the conventionally measured absorbed dose distribution near the source.

Transfer potentials shape and equilibrate monetary systems

NASA Astrophysics Data System (ADS)

Fischer, Robert; Braun, Dieter

2003-04-01

We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economist's quantity theory ( MV= PQ). To match the resulting quantity of money with the model assumption of a constant price, we have to impose boundary conditions. They either restrict specific transfers globally or impose transfers locally. Both connect through a general framework of transfer potentials. We show that either restricted or imposed transfers can shape Gaussian, tent-shape exponential, Boltzmann-exponential, pareto or periodic equilibrium distributions. We derive the master equation and find its general time-dependent approximate solution. An equivalent of quantity theory for random money transfer under the boundary conditions of transfer potentials is given.

Radioactivity Registered With a Small Number of Events

NASA Astrophysics Data System (ADS)

Zlokazov, Victor; Utyonkov, Vladimir

2018-02-01

The synthesis of superheavy elements asks for the analysis of low statistics experimental data presumably obeying an unknown exponential distribution and to take the decision whether they originate from one source or have admixtures. Here we analyze predictions following from non-parametrical methods, employing only such fundamental sample properties as the sample mean, the median and the mode.

Biodegradation of Dense Non-Aqueous Phase Liquids (DNAPL) Through Bioaugmentation of Source Areas - Dover National Test Site, Dover, Delaware

DTIC Science & Technology

2008-08-01

the distribution of DNAPL. The OSU research team evaluated the use of radon as a partitioning groundwater tracer. The DNAPL release fulfilled one...close to the source area generated more PCE equivalent mass over time. The exponential decay from the fitted line (predicted PCE, orange line in each

Power function decay of hydraulic conductivity for a TOPMODEL-based infiltration routine

NASA Astrophysics Data System (ADS)

Wang, Jun; Endreny, Theodore A.; Hassett, James M.

2006-11-01

TOPMODEL rainfall-runoff hydrologic concepts are based on soil saturation processes, where soil controls on hydrograph recession have been represented by linear, exponential, and power function decay with soil depth. Although these decay formulations have been incorporated into baseflow decay and topographic index computations, only the linear and exponential forms have been incorporated into infiltration subroutines. This study develops a power function formulation of the Green and Ampt infiltration equation for the case where the power n = 1 and 2. This new function was created to represent field measurements in the New York City, USA, Ward Pound Ridge drinking water supply area, and provide support for similar sites reported by other researchers. Derivation of the power-function-based Green and Ampt model begins with the Green and Ampt formulation used by Beven in deriving an exponential decay model. Differences between the linear, exponential, and power function infiltration scenarios are sensitive to the relative difference between rainfall rates and hydraulic conductivity. Using a low-frequency 30 min design storm with 4.8 cm h-1 rain, the n = 2 power function formulation allows for a faster decay of infiltration and more rapid generation of runoff. Infiltration excess runoff is rare in most forested watersheds, and advantages of the power function infiltration routine may primarily include replication of field-observed processes in urbanized areas and numerical consistency with power function decay of baseflow and topographic index distributions. Equation development is presented within a TOPMODEL-based Ward Pound Ridge rainfall-runoff simulation. Copyright

On the origin of non-exponential fluorescence decays in enzyme-ligand complex

NASA Astrophysics Data System (ADS)

Wlodarczyk, Jakub; Kierdaszuk, Borys

2004-05-01

Complex fluorescence decays have usually been analyzed with the aid of a multi-exponential model, but interpretation of the individual exponential terms has not been adequately characterized. In such cases the intensity decays were also analyzed in terms of the continuous lifetime distribution as a consequence of an interaction of fluorophore with environment, conformational heterogeneity or their dynamical nature. We show that non-exponential fluorescence decay of the enzyme-ligand complexes may results from time dependent energy transport. The latter, to our opinion, may be accounted for by electron transport from the protein tyrosines to their neighbor residues. We introduce the time-dependent hopping rate in the form v(t)~(a+bt)-1. This in turn leads to the luminescence decay function in the form I(t)=Ioexp(-t/τ1)(1+lt/γτ2)-γ. Such a decay function provides good fits to highly complex fluorescence decays. The power-like tail implies the time hierarchy in migration energy process due to the hierarchical energy-level structure. Moreover, such a power-like term is a manifestation of so called Tsallis nonextensive statistic and is suitable for description of the systems with long-range interactions, memory effect as well as with fluctuations of characteristic lifetime of fluorescence. The proposed decay function was applied in analysis of fluorescence decays of tyrosine protein, i.e. the enzyme purine nucleoside phosphorylase from E. coli in a complex with formycin A (an inhibitor) and orthophosphate (a co-substrate).

A Study of the Application of the Lognormal and Gamma Distributions to Corrective Maintenance Repair Time Data.

DTIC Science & Technology

1982-10-01

K-S A R A j 1 10 23 R 3 8 11 16 18 For the lognormal methods the test methods sometimes give different results. The K-S test and the chi-square...significant difference among the three test methods . A previous study has been done using 24 data sets of electronic systems and equipments, using only the W...are suitable descriptors for corrective maintenance repair times, and to estimate the difference caused in assuming an exponential distribution for

Dependence of Strain Distribution on In Content in InGaN/GaN Quantum Wires and Spherical Quantum Dots

NASA Astrophysics Data System (ADS)

Sharma, Akant Sagar; Dhar, S.

2018-02-01

The distribution of strain, developed in zero-dimensional quantum spherical dots and one-dimensional cylindrical quantum wires of an InGaN/GaN system is calculated as functions of radius of the structure and indium mole fraction. The strain shows strong dependence on indium mole fraction at small distances from the center. The strain associated with both the structures is found to decrease exponentially with the increase in dot or cylinder radius and increases linearly with indium content.

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

DTIC Science & Technology

1980-06-01

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

The asymptotic behavior in a reversible random coagulation-fragmentation polymerization process with sub-exponential decay

NASA Astrophysics Data System (ADS)

Dong, Siqun; Zhao, Dianli

2018-01-01

This paper studies the subcritical, near-critical and supercritical asymptotic behavior of a reversible random coagulation-fragmentation polymerization process as N → ∞, with the number of distinct ways to form a k-clusters from k units satisfying f(k) =(1 + o (1)) cr-ke-kαk-β, where 0 < α < 1 and β > 0. When the cluster size is small, its distribution is proved to converge to the Gaussian distribution. For the medium clusters, its distribution will converge to Poisson distribution in supercritical stage, and no large clusters exist in this stage. Furthermore, the largest length of polymers of size N is of order ln N in the subcritical stage under α ⩽ 1 / 2.

Superstatistics model for T₂ distribution in NMR experiments on porous media.

PubMed

Correia, M D; Souza, A M; Sinnecker, J P; Sarthour, R S; Santos, B C C; Trevizan, W; Oliveira, I S

2014-07-01

We propose analytical functions for T2 distribution to describe transverse relaxation in high- and low-fields NMR experiments on porous media. The method is based on a superstatistics theory, and allows to find the mean and standard deviation of T2, directly from measurements. It is an alternative to multiexponential models for data decay inversion in NMR experiments. We exemplify the method with q-exponential functions and χ(2)-distributions to describe, respectively, data decay and T2 distribution on high-field experiments of fully water saturated glass microspheres bed packs, sedimentary rocks from outcrop and noisy low-field experiment on rocks. The method is general and can also be applied to biological systems. Copyright © 2014 Elsevier Inc. All rights reserved.

Dynamical Aspects of Quasifission Process in Heavy-Ion Reactions

NASA Astrophysics Data System (ADS)

Knyazheva, G. N.; Itkis, I. M.; Kozulin, E. M.

2015-06-01

The study of mass-energy distributions of binary fragments obtained in the reactions of 36S, 48Ca, 58Fe and 64Ni ions with the 232Th, 238U, 244Pu and 248Cm at energies below and above the Coulomb barrier is presented. For all the reactions the main component of the distributions corresponds to asymmetrical mass division typical for asymmetric quasifission process. To describe the quasifission mass distribution the simple method has been proposed. This method is based on the driving potential of the system and time dependent mass drift. This procedure allows to estimate QF time scale from the measured mass distributions. It has been found that the QF time exponentially decreases when the reaction Coulomb factor Z1Z2 increases.

The Italian primary school-size distribution and the city-size: a complex nexus

NASA Astrophysics Data System (ADS)

Belmonte, Alessandro; di Clemente, Riccardo; Buldyrev, Sergey V.

2014-06-01

We characterize the statistical law according to which Italian primary school-size distributes. We find that the school-size can be approximated by a log-normal distribution, with a fat lower tail that collects a large number of very small schools. The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF. These distributions are similar to those observed for firms and are consistent with a Bose-Einstein preferential attachment process. The body of the distribution features a bimodal shape suggesting some source of heterogeneity in the school organization that we uncover by an in-depth analysis of the relation between schools-size and city-size. We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy. Different regional policies are also discussed shedding lights on the relation between policy and geographical features.

Distribution of tsunami interevent times

NASA Astrophysics Data System (ADS)

Geist, Eric L.; Parsons, Tom

2008-01-01

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

Wildfires in Siberian Mountain Forest

NASA Astrophysics Data System (ADS)

Kharuk, V.; Ponomarev, E. I.; Antamoshkina, O.

2017-12-01

The annual burned area in Russia was estimated as 0.55 to 20 Mha with >70% occurred in Siberia. We analyzed Siberian wildfires distribution with respect to elevation, slope steepness and exposure. In addition, wildfires temporal dynamic and latitudinal range were analyzed. We used daily thermal anomalies derived from NOAA/AVHRR and Terra/MODIS satellites (1990-2016). Fire return intervals were (FRI) calculated based on the dendrochronology analysis of samples taken from trees with burn marks. Spatial distribution of wildfires dependent on topo features: relative burned area increase with elevation increase (ca. 1100 m), switching to following decrease. The wildfires frequency exponentially decreased within lowlands - highlands transition. Burned area is increasing with slope steepness increase (up to 5-10°). Fire return intervals (FRI) on the southfacing slopes are about 30% longer than on the north facing. Wildfire re-occurrence is decreasing exponentially: 90% of burns were caused by single fires, 8.5% by double fires, 1% burned three times, and on about 0.05% territory wildfires occurred four times (observed period: 75 yr.). Wildfires area and number, as well as FRI, also dependent on latitude: relative burned area increasing exponentially in norward direction, whereas relative fire number is exponentially decreasing. FRI increases in the northward direction: from 80 years at 62°N to 200 years at the Arctic Circle, and to 300 years at the northern limit of closed forests ( 71+°N). Fire frequency, fire danger period and FRI are strongly correlated with incoming solar radiation (r = 0.81 - 0.95). In 21-s century, a positive trend of wildfires number and area observed in mountain areas in all Siberia. Thus, burned area and number of fires in Siberia are significantly increased since 1990th (R2 =0.47, R2 =0.69, respectively), and that increase correlated with air temperatures and climate aridity increases. However, wildfires are essential for supporting fire-resistant species (e.g., Larix sibirica, L, dahurica and Pinus silvestris) reforestation and completion with non-fire-resistant species. This work was supported by the Russian Foundation for Basic Research, the Government of the Krasnoyarsk krai, the Krasnoyarsk Fund for Support of Scientific and Technological Activities (N 17-41-240475)

Path statistics, memory, and coarse-graining of continuous-time random walks on networks

PubMed Central

Kion-Crosby, Willow; Morozov, Alexandre V.

2015-01-01

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs. PMID:26646868

Observations of sea ice ridging in the Weddell Sea

NASA Astrophysics Data System (ADS)

Granberg, Hardy B.; Leppaäranta, Matti

1999-11-01

Sea ice surface topography data were obtained by helicopter-borne laser profiling during the First Finnish Antarctic Expedition (FINNARP-89). The measurements were made near the ice margin at about 73°S, 27°W in the eastern Weddell Sea on December 31, 1989, and January 1, 1990. Five transects, ranging in length from 127 to 163 km and covering a total length of 724 km, are analyzed. With a lower cutoff of 0.91 m the overall ridge frequency was 8.4 ridges/km and the average ridge height was 1.32 m. The spatial variations in ridging were large; for 36 individual 20-km segments the frequencies were 2-16 ridges/km and the mean heights were 1.16-1.56 m. The frequencies and mean heights were weakly correlated. The distributions of the ridge heights followed the exponential distribution; the spacings did not pass tests for either the exponential or the lognormal distribution, but the latter was much closer. In the 20-km segments the areally averaged thickness of ridged ice was 0.51±0.28 m, ranging from 0.10 to 1.15 m. The observed ridge size and frequency are greater than those known for the Ross Sea. Compared with the central Arctic, the Weddell Sea ridging frequencies are similar but the ridge heights are smaller, possibly as a result of differences in snow accumulation.

A kinetic approach to some quasi-linear laws of macroeconomics

NASA Astrophysics Data System (ADS)

Gligor, M.; Ignat, M.

2002-11-01

Some previous works have presented the data on wealth and income distributions in developed countries and have found that the great majority of population is described by an exponential distribution, which results in idea that the kinetic approach could be adequate to describe this empirical evidence. The aim of our paper is to extend this framework by developing a systematic kinetic approach of the socio-economic systems and to explain how linear laws, modelling correlations between macroeconomic variables, may arise in this context. Firstly we construct the Boltzmann kinetic equation for an idealised system composed by many individuals (workers, officers, business men, etc.), each of them getting a certain income and spending money for their needs. To each individual a certain time variable amount of money is associated this meaning him/her phase space coordinate. In this way the exponential distribution of money in a closed economy is explicitly found. The extension of this result, including states near the equilibrium, give us the possibility to take into account the regular increase of the total amount of money, according to the modern economic theories. The Kubo-Green-Onsager linear response theory leads us to a set of linear equations between some macroeconomic variables. Finally, the validity of such laws is discussed in relation with the time reversal symmetry and is tested empirically using some macroeconomic time series.

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

PubMed

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

2003-01-01

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

Stretched exponential dynamics of coupled logistic maps on a small-world network

NASA Astrophysics Data System (ADS)

Mahajan, Ashwini V.; Gade, Prashant M.

2018-02-01

We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in a coarse grained sense acts as an excellent order parameter to study this transition. We investigate the phase diagram by varying coupling strength and small-world rewiring probability p of nonlocal connections. The persistent region is a compact region bounded by two critical lines where band-merging crisis occurs. On one critical line, the persistent sites shows a nonexponential (stretched exponential) decay for all p while for another one, it shows crossover from nonexponential to exponential behavior as p → 1 . With an effectively antiferromagnetic coupling, coupling to two neighbors on either side leads to exchange frustration. Apart from exchange frustration, non-bipartite topology and nonlocal couplings in a small-world network could be a reason for anomalous relaxation. The distribution of trap times in asymptotic regime has a long tail as well. The dependence of temporal evolution of persistence on initial conditions is studied and a scaling form for persistence after waiting time is proposed. We present a simple possible model for this behavior.

Spectral Gap Estimates in Mean Field Spin Glasses

NASA Astrophysics Data System (ADS)

Ben Arous, Gérard; Jagannath, Aukosh

2018-05-01

We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the spectral gap is exponentially small, and thus that mixing is exponentially slow. We then exhibit sufficient conditions on the equilibrium Gibbs measure which guarantee the existence of these barriers, using the notion of replicon eigenvalue and 2D Guerra Talagrand bounds. We show how these sufficient conditions cover large classes of Ising spin models for reversible nearest-neighbor dynamics and spherical models for Langevin dynamics. Finally, in the case of Ising spins, Panchenko's recent rigorous calculation (Panchenko in Ann Probab 46(2):865-896, 2018) of the free energy for a system of "two real replica" enables us to prove a quenched LDP for the overlap distribution, which gives us a wider criterion for slow mixing directly related to the Franz-Parisi-Virasoro approach (Franz et al. in J Phys I 2(10):1869-1880, 1992; Kurchan et al. J Phys I 3(8):1819-1838, 1993). This condition holds in a wider range of temperatures.

Floquet states of a kicked particle in a singular potential: Exponential and power-law profiles

NASA Astrophysics Data System (ADS)

Paul, Sanku; Santhanam, M. S.

2018-03-01

It is well known that, in the chaotic regime, all the Floquet states of kicked rotor system display an exponential profile resulting from dynamical localization. If the kicked rotor is placed in an additional stationary infinite potential well, its Floquet states display power-law profile. It has also been suggested in general that the Floquet states of periodically kicked systems with singularities in the potential would have power-law profile. In this work, we study the Floquet states of a kicked particle in finite potential barrier. By varying the height of finite potential barrier, the nature of transition in the Floquet state from exponential to power-law decay profile is studied. We map this system to a tight-binding model and show that the nature of decay profile depends on energy band spanned by the Floquet states (in unperturbed basis) relative to the potential height. This property can also be inferred from the statistics of Floquet eigenvalues and eigenvectors. This leads to an unusual scenario in which the level spacing distribution, as a window in to the spectral correlations, is not a unique characteristic for the entire system.

Size-dependent standard deviation for growth rates: Empirical results and theoretical modeling

NASA Astrophysics Data System (ADS)

Podobnik, Boris; Horvatic, Davor; Pammolli, Fabio; Wang, Fengzhong; Stanley, H. Eugene; Grosse, I.

2008-05-01

We study annual logarithmic growth rates R of various economic variables such as exports, imports, and foreign debt. For each of these variables we find that the distributions of R can be approximated by double exponential (Laplace) distributions in the central parts and power-law distributions in the tails. For each of these variables we further find a power-law dependence of the standard deviation σ(R) on the average size of the economic variable with a scaling exponent surprisingly close to that found for the gross domestic product (GDP) [Phys. Rev. Lett. 81, 3275 (1998)]. By analyzing annual logarithmic growth rates R of wages of 161 different occupations, we find a power-law dependence of the standard deviation σ(R) on the average value of the wages with a scaling exponent β≈0.14 close to those found for the growth of exports, imports, debt, and the growth of the GDP. In contrast to these findings, we observe for payroll data collected from 50 states of the USA that the standard deviation σ(R) of the annual logarithmic growth rate R increases monotonically with the average value of payroll. However, also in this case we observe a power-law dependence of σ(R) on the average payroll with a scaling exponent β≈-0.08 . Based on these observations we propose a stochastic process for multiple cross-correlated variables where for each variable (i) the distribution of logarithmic growth rates decays exponentially in the central part, (ii) the distribution of the logarithmic growth rate decays algebraically in the far tails, and (iii) the standard deviation of the logarithmic growth rate depends algebraically on the average size of the stochastic variable.

The absolute magnitude distribution of cold classical Kuiper belt objects

NASA Astrophysics Data System (ADS)

Petit, Jean-Marc; Bannister, Michele T.; Alexandersen, Mike; Chen, Ying-Tung; Gladman, Brett; Gwyn, Stephen; Kavelaars, JJ; Volk, Kathryn

2016-10-01

We report measurements of the low inclination component of the main Kuiper Belt showing a size freqency distribution very steep for sizes larger than H_r ~ 6.5-7.0 and then a flattening to shallower slope that is still steeper than the collisional equilibrium slope.The Outer Solar System Origins Survey (OSSOS) is ongoing and is expected to detect over 500 TNOs in a precisely calibrated and characterized survey. Combining our current sample with CFEPS and the Alexandersen et al. (2015) survey, we analyse a sample of ~180 low inclination main classical (cold) TNOs, with absolute magnitude H_r (SDSS r' like flter) in the range 5 to 8.8. We confirm that the H_r distribution can be approximated by an exponential with a very steep slope (>1) at the bright end of the distribution, as has been recognized long ago. A transition to a shallower slope occurs around H_r ~ 6.5 - 7.0, an H_r mag identified by Fraster et al (2014). Faintward of this transition, we find a second exponential to be a good approximation at least until H_r ~ 8.5, but with a slope significantly steeper than the one proposed by Fraser et al. (2014) or even the collisional equilibrium value of 0.5.The transition in the cold TNO H_r distribution thus appears to occur at larger sizes than is observed in the high inclination main classical (hot) belt, an important indicator of a different cosmogony for these two sub-components of the main classical Kuiper belt. Given the largish slope faintward of the transition, the cold population with ~100 km diameter may dominate the mass of the Kuiper belt in the 40 AU < a < 47 au region.

A Validation Study of the Rank-Preserving Structural Failure Time Model: Confidence Intervals and Unique, Multiple, and Erroneous Solutions.

PubMed

Ouwens, Mario; Hauch, Ole; Franzén, Stefan

2018-05-01

The rank-preserving structural failure time model (RPSFTM) is used for health technology assessment submissions to adjust for switching patients from reference to investigational treatment in cancer trials. It uses counterfactual survival (survival when only reference treatment would have been used) and assumes that, at randomization, the counterfactual survival distribution for the investigational and reference arms is identical. Previous validation reports have assumed that patients in the investigational treatment arm stay on therapy throughout the study period. To evaluate the validity of the RPSFTM at various levels of crossover in situations in which patients are taken off the investigational drug in the investigational arm. The RPSFTM was applied to simulated datasets differing in percentage of patients switching, time of switching, underlying acceleration factor, and number of patients, using exponential distributions for the time on investigational and reference treatment. There were multiple scenarios in which two solutions were found: one corresponding to identical counterfactual distributions, and the other to two different crossing counterfactual distributions. The same was found for the hazard ratio (HR). Unique solutions were observed only when switching patients were on investigational treatment for <40% of the time that patients in the investigational arm were on treatment. Distributions other than exponential could have been used for time on treatment. An HR equal to 1 is a necessary but not always sufficient condition to indicate acceleration factors associated with equal counterfactual survival. Further assessment to distinguish crossing counterfactual curves from equal counterfactual curves is especially needed when the time that switchers stay on investigational treatment is relatively long compared to the time direct starters stay on investigational treatment.

Size-dependent standard deviation for growth rates: empirical results and theoretical modeling.

PubMed

Podobnik, Boris; Horvatic, Davor; Pammolli, Fabio; Wang, Fengzhong; Stanley, H Eugene; Grosse, I

2008-05-01

We study annual logarithmic growth rates R of various economic variables such as exports, imports, and foreign debt. For each of these variables we find that the distributions of R can be approximated by double exponential (Laplace) distributions in the central parts and power-law distributions in the tails. For each of these variables we further find a power-law dependence of the standard deviation sigma(R) on the average size of the economic variable with a scaling exponent surprisingly close to that found for the gross domestic product (GDP) [Phys. Rev. Lett. 81, 3275 (1998)]. By analyzing annual logarithmic growth rates R of wages of 161 different occupations, we find a power-law dependence of the standard deviation sigma(R) on the average value of the wages with a scaling exponent beta approximately 0.14 close to those found for the growth of exports, imports, debt, and the growth of the GDP. In contrast to these findings, we observe for payroll data collected from 50 states of the USA that the standard deviation sigma(R) of the annual logarithmic growth rate R increases monotonically with the average value of payroll. However, also in this case we observe a power-law dependence of sigma(R) on the average payroll with a scaling exponent beta approximately -0.08 . Based on these observations we propose a stochastic process for multiple cross-correlated variables where for each variable (i) the distribution of logarithmic growth rates decays exponentially in the central part, (ii) the distribution of the logarithmic growth rate decays algebraically in the far tails, and (iii) the standard deviation of the logarithmic growth rate depends algebraically on the average size of the stochastic variable.

Statistical physics approaches to quantifying sleep-stage transitions

NASA Astrophysics Data System (ADS)

Lo, Chung-Chuan

Sleep can be viewed as a sequence of transitions in a very complex neuronal system. Traditionally, studies of the dynamics of sleep control have focused on the circadian rhythm of sleep-wake transitions or on the ultradian rhythm of the sleep cycle. However, very little is known about the mechanisms responsible for the time structure or even the statistics of the rapid sleep-stage transitions that appear without periodicity. I study the time dynamics of sleep-wake transitions for different species, including humans, rats, and mice, and find that the wake and sleep episodes exhibit completely different behaviors: the durations of wake episodes are characterized by a scale-free power-law distribution, while the durations of sleep episodes have an exponential distribution with a characteristic time scale. The functional forms of the distributions of the sleep and wake durations hold for human subjects of different ages and for subjects with sleep apnea. They also hold for all the species I investigate. Surprisingly, all species have the same power-law exponent for the distribution of wake durations, but the exponential characteristic time of the distribution of sleep durations changes across species. I develop a stochastic model which accurately reproduces our empirical findings. The model suggests that the difference between the dynamics of the sleep and wake states arises from the constraints on the number of microstates in the sleep-wake system. I develop a measure of asymmetry in sleep-stage transitions using a transition probability matrix. I find that both normal and sleep apnea subjects are characterized by two types of asymmetric sleep-stage transition paths, and that the sleep apnea group exhibits less asymmetry in the sleep-stage transitions.

Analysis of volumetric response of pituitary adenomas receiving adjuvant CyberKnife stereotactic radiosurgery with the application of an exponential fitting model.

PubMed

Yu, Yi-Lin; Yang, Yun-Ju; Lin, Chin; Hsieh, Chih-Chuan; Li, Chiao-Zhu; Feng, Shao-Wei; Tang, Chi-Tun; Chung, Tzu-Tsao; Ma, Hsin-I; Chen, Yuan-Hao; Ju, Da-Tong; Hueng, Dueng-Yuan

2017-01-01

Tumor control rates of pituitary adenomas (PAs) receiving adjuvant CyberKnife stereotactic radiosurgery (CK SRS) are high. However, there is currently no uniform way to estimate the time course of the disease. The aim of this study was to analyze the volumetric responses of PAs after CK SRS and investigate the application of an exponential decay model in calculating an accurate time course and estimation of the eventual outcome.A retrospective review of 34 patients with PAs who received adjuvant CK SRS between 2006 and 2013 was performed. Tumor volume was calculated using the planimetric method. The percent change in tumor volume and tumor volume rate of change were compared at median 4-, 10-, 20-, and 36-month intervals. Tumor responses were classified as: progression for >15% volume increase, regression for ≤15% decrease, and stabilization for ±15% of the baseline volume at the time of last follow-up. For each patient, the volumetric change versus time was fitted with an exponential model.The overall tumor control rate was 94.1% in the 36-month (range 18-87 months) follow-up period (mean volume change of -43.3%). Volume regression (mean decrease of -50.5%) was demonstrated in 27 (79%) patients, tumor stabilization (mean change of -3.7%) in 5 (15%) patients, and tumor progression (mean increase of 28.1%) in 2 (6%) patients (P = 0.001). Tumors that eventually regressed or stabilized had a temporary volume increase of 1.07% and 41.5% at 4 months after CK SRS, respectively (P = 0.017). The tumor volume estimated using the exponential fitting equation demonstrated high positive correlation with the actual volume calculated by magnetic resonance imaging (MRI) as tested by Pearson correlation coefficient (0.9).Transient progression of PAs post-CK SRS was seen in 62.5% of the patients receiving CK SRS, and it was not predictive of eventual volume regression or progression. A three-point exponential model is of potential predictive value according to relative distribution. An exponential decay model can be used to calculate the time course of tumors that are ultimately controlled.

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.

Is the Milky Way's hot halo convectively unstable?

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

Henley, David B.; Shelton, Robin L., E-mail: dbh@physast.uga.edu

2014-03-20

We investigate the convective stability of two popular types of model of the gas distribution in the hot Galactic halo. We first consider models in which the halo density and temperature decrease exponentially with height above the disk. These halo models were created to account for the fact that, on some sight lines, the halo's X-ray emission lines and absorption lines yield different temperatures, implying that the halo is non-isothermal. We show that the hot gas in these exponential models is convectively unstable if γ < 3/2, where γ is the ratio of the temperature and density scale heights. Usingmore » published measurements of γ and its uncertainty, we use Bayes' theorem to infer posterior probability distributions for γ, and hence the probability that the halo is convectively unstable for different sight lines. We find that, if these exponential models are good descriptions of the hot halo gas, at least in the first few kiloparsecs from the plane, the hot halo is reasonably likely to be convectively unstable on two of the three sight lines for which scale height information is available. We also consider more extended models of the halo. While isothermal halo models are convectively stable if the density decreases with distance from the Galaxy, a model of an extended adiabatic halo in hydrostatic equilibrium with the Galaxy's dark matter is on the boundary between stability and instability. However, we find that radiative cooling may perturb this model in the direction of convective instability. If the Galactic halo is indeed convectively unstable, this would argue in favor of supernova activity in the Galactic disk contributing to the heating of the hot halo gas.« less

Determining the turnover time of groundwater systems with the aid of environmental tracers. 1. Models and their applicability

NASA Astrophysics Data System (ADS)

Małoszewski, P.; Zuber, A.

1982-06-01

Three new lumped-parameter models have been developed for the interpretation of environmental radioisotope data in groundwater systems. Two of these models combine other simpler models, i.e. the piston flow model is combined either with the exponential model (exponential distribution of transit times) or with the linear model (linear distribution of transit times). The third model is based on a new solution to the dispersion equation which more adequately represents the real systems than the conventional solution generally applied so far. The applicability of models was tested by the reinterpretation of several known case studies (Modry Dul, Cheju Island, Rasche Spring and Grafendorf). It has been shown that two of these models, i.e. the exponential-piston flow model and the dispersive model give better fitting than other simpler models. Thus, the obtained values of turnover times are more reliable, whereas the additional fitting parameter gives some information about the structure of the system. In the examples considered, in spite of a lower number of fitting parameters, the new models gave practically the same fitting as the multiparameter finite state mixing-cell models. It has been shown that in the case of a constant tracer input a prior physical knowledge of the groundwater system is indispensable for determining the turnover time. The piston flow model commonly used for age determinations by the 14C method is an approximation applicable only in the cases of low dispersion. In some cases the stable-isotope method aids in the interpretation of systems containing mixed waters of different ages. However, when 14C method is used for mixed-water systems a serious mistake may arise by neglecting the different bicarbonate contents in particular water components.

Naval Research Logistics Quarterly. Volume 29, Number 4, December 1982,

DTIC Science & Technology

1982-12-01

1982, pp. 247-256. HURTER, A.P., JR. and E.R. Venta , "Production-Location Problems," Vol. 29, No. 2, June 1982, pp. 279-290. JARVIS, J. and R.G...4 Hyper-Exponential and the Erland Failure Distribution," Vol. 29, No. 4, December 1982, pp. VENTA , E.R. and A.P. Hurter, Jr., "Production-Location

Making statistical inferences about software reliability

NASA Technical Reports Server (NTRS)

Miller, Douglas R.

1988-01-01

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

A Model and a Metric for the Analysis of Status Attainment Processes. Discussion Paper No. 492-78.

ERIC Educational Resources Information Center

Sorensen, Aage B.

This paper proposes a theory of the status attainment process, and specifies it in a mathematical model. The theory justifies a transformation of the conventional status scores to a metric that produces a exponential distribution of attainments, and a transformation of educational attainments to a metric that reflects the competitive advantage…

PLEMT: A NOVEL PSEUDOLIKELIHOOD BASED EM TEST FOR HOMOGENEITY IN GENERALIZED EXPONENTIAL TILT MIXTURE MODELS.

PubMed

Hong, Chuan; Chen, Yong; Ning, Yang; Wang, Shuang; Wu, Hao; Carroll, Raymond J

2017-01-01

Motivated by analyses of DNA methylation data, we propose a semiparametric mixture model, namely the generalized exponential tilt mixture model, to account for heterogeneity between differentially methylated and non-differentially methylated subjects in the cancer group, and capture the differences in higher order moments (e.g. mean and variance) between subjects in cancer and normal groups. A pairwise pseudolikelihood is constructed to eliminate the unknown nuisance function. To circumvent boundary and non-identifiability problems as in parametric mixture models, we modify the pseudolikelihood by adding a penalty function. In addition, the test with simple asymptotic distribution has computational advantages compared with permutation-based test for high-dimensional genetic or epigenetic data. We propose a pseudolikelihood based expectation-maximization test, and show the proposed test follows a simple chi-squared limiting distribution. Simulation studies show that the proposed test controls Type I errors well and has better power compared to several current tests. In particular, the proposed test outperforms the commonly used tests under all simulation settings considered, especially when there are variance differences between two groups. The proposed test is applied to a real data set to identify differentially methylated sites between ovarian cancer subjects and normal subjects.

Universal behavior of the interoccurrence times between losses in financial markets: independence of the time resolution.

PubMed

Ludescher, Josef; Bunde, Armin

2014-12-01

We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution P(Q)(r) of the interoccurrence times r between losses below a negative threshold -Q, for fixed mean interoccurrence times R(Q) in multiples of the corresponding time resolutions, can be described on all time scales by the same q exponentials, P(Q)(r)∝1/{[1+(q-1)βr](1/(q-1))}. We propose that the asset- and time-scale-independent analytic form of P(Q)(r) can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution P(Q)(r) as well as the autocorrelation C(Q)(s) of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the q-exponential form of P(Q)(r) and the power-law decay of C(Q)(s).

Thermally Stimulated Currents in Nanocrystalline Titania

PubMed Central

Bruzzi, Mara; Mori, Riccardo; Baldi, Andrea; Cavallaro, Alessandro; Scaringella, Monica

2018-01-01

A thorough study on the distribution of defect-related active energy levels has been performed on nanocrystalline TiO2. Films have been deposited on thick-alumina printed circuit boards equipped with electrical contacts, heater and temperature sensors, to carry out a detailed thermally stimulated currents analysis on a wide temperature range (5–630 K), in view to evidence contributions from shallow to deep energy levels within the gap. Data have been processed by numerically modelling electrical transport. The model considers both free and hopping contribution to conduction, a density of states characterized by an exponential tail of localized states below the conduction band and the convolution of standard Thermally Stimulated Currents (TSC) emissions with gaussian distributions to take into account the variability in energy due to local perturbations in the highly disordered network. Results show that in the low temperature range, up to 200 K, hopping within the exponential band tail represents the main contribution to electrical conduction. Above room temperature, electrical conduction is dominated by free carriers contribution and by emissions from deep energy levels, with a defect density ranging within 1014–1018 cm−3, associated with physio- and chemi-sorbed water vapour, OH groups and to oxygen vacancies. PMID:29303976

A NEW METHOD OF PEAK DETECTION FOR ANALYSIS OF COMPREHENSIVE TWO-DIMENSIONAL GAS CHROMATOGRAPHY MASS SPECTROMETRY DATA.

PubMed

Kim, Seongho; Ouyang, Ming; Jeong, Jaesik; Shen, Changyu; Zhang, Xiang

2014-06-01

We develop a novel peak detection algorithm for the analysis of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC×GC-TOF MS) data using normal-exponential-Bernoulli (NEB) and mixture probability models. The algorithm first performs baseline correction and denoising simultaneously using the NEB model, which also defines peak regions. Peaks are then picked using a mixture of probability distribution to deal with the co-eluting peaks. Peak merging is further carried out based on the mass spectral similarities among the peaks within the same peak group. The algorithm is evaluated using experimental data to study the effect of different cut-offs of the conditional Bayes factors and the effect of different mixture models including Poisson, truncated Gaussian, Gaussian, Gamma, and exponentially modified Gaussian (EMG) distributions, and the optimal version is introduced using a trial-and-error approach. We then compare the new algorithm with two existing algorithms in terms of compound identification. Data analysis shows that the developed algorithm can detect the peaks with lower false discovery rates than the existing algorithms, and a less complicated peak picking model is a promising alternative to the more complicated and widely used EMG mixture models.

Thermally Stimulated Currents in Nanocrystalline Titania.

PubMed

Bruzzi, Mara; Mori, Riccardo; Baldi, Andrea; Carnevale, Ennio Antonio; Cavallaro, Alessandro; Scaringella, Monica

2018-01-05

A thorough study on the distribution of defect-related active energy levels has been performed on nanocrystalline TiO₂. Films have been deposited on thick-alumina printed circuit boards equipped with electrical contacts, heater and temperature sensors, to carry out a detailed thermally stimulated currents analysis on a wide temperature range (5-630 K), in view to evidence contributions from shallow to deep energy levels within the gap. Data have been processed by numerically modelling electrical transport. The model considers both free and hopping contribution to conduction, a density of states characterized by an exponential tail of localized states below the conduction band and the convolution of standard Thermally Stimulated Currents (TSC) emissions with gaussian distributions to take into account the variability in energy due to local perturbations in the highly disordered network. Results show that in the low temperature range, up to 200 K, hopping within the exponential band tail represents the main contribution to electrical conduction. Above room temperature, electrical conduction is dominated by free carriers contribution and by emissions from deep energy levels, with a defect density ranging within 10 14 -10 18 cm -3 , associated with physio- and chemi-sorbed water vapour, OH groups and to oxygen vacancies.

Distributed seeding for narrow-line width hard x-ray free-electron lasers

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

Nguyen, Dinh Cong; Anisimov, Petr Mikhaylovich; Buechler, Cynthia Eileen

2015-09-09

We describe a new FEL line-narrowing technique called distributed seeding (DS), using Si(111) Bragg crystal monochromators to enhance the spectral brightness of the MaRIE hard X-ray freeelectron laser. DS differs from self-seeding in three important aspects. First, DS relies on spectral filtering of the radiation at multiple locations along the undulator, with a monochromator located every few power gain lengths. Second, DS performs filtering early in the exponential gain region before SASE spikes start to appear in the radiation longitudinal profile. Third, DS provides the option to select a wavelength longer than the peak of the SASE gain curve, whichmore » leads to improved spectral contrast of the seeded FEL over the SASE background. Timedependent Genesis simulations show the power-vs-z growth curves for DS exhibit behaviors of a seeded FEL amplifier, such as exponential growth region immediately after the filters. Of the seeding approaches considered, the two-stage DS spectra produce the highest contrast of seeded FEL over the SASE background and that the three-stage DS provides the narrowest linewidth with a relative spectral FWHM of 8 X 10 -5 .« less

Universal behavior of the interoccurrence times between losses in financial markets: Independence of the time resolution

NASA Astrophysics Data System (ADS)

Ludescher, Josef; Bunde, Armin

2014-12-01

We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution PQ(r ) of the interoccurrence times r between losses below a negative threshold -Q , for fixed mean interoccurrence times RQ in multiples of the corresponding time resolutions, can be described on all time scales by the same q exponentials, PQ(r ) ∝1 /{[1+(q -1 ) β r ] 1 /(q -1 )} . We propose that the asset- and time-scale-independent analytic form of PQ(r ) can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution PQ(r ) as well as the autocorrelation CQ(s ) of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the q -exponential form of PQ(r ) and the power-law decay of CQ(s ) .

Transformations of the distribution of nuclei formed in a nucleation pulse: Interface-limited growth.

PubMed

Shneidman, Vitaly A

2009-10-28

A typical nucleation-growth process is considered: a system is quenched into a supersaturated state with a small critical radius r( *) (-) and is allowed to nucleate during a finite time interval t(n), after which the supersaturation is abruptly reduced to a fixed value with a larger critical radius r( *) (+). The size-distribution of nucleated particles f(r,t) further evolves due to their deterministic growth and decay for r larger or smaller than r( *) (+), respectively. A general analytic expressions for f(r,t) is obtained, and it is shown that after a large growth time t this distribution approaches an asymptotic shape determined by two dimensionless parameters, lambda related to t(n), and Lambda=r( *) (+)/r( *) (-). This shape is strongly asymmetric with an exponential and double-exponential cutoffs at small and large sizes, respectively, and with a broad near-flat top in case of a long pulse. Conversely, for a short pulse the distribution acquires a distinct maximum at r=r(max)(t) and approaches a universal shape exp[zeta-e(zeta)], with zeta proportional to r-r(max), independent of the pulse duration. General asymptotic predictions are examined in terms of Zeldovich-Frenkel nucleation model where the entire transient behavior can be described in terms of the Lambert W function. Modifications for the Turnbull-Fisher model are also considered, and analytics is compared with exact numerics. Results are expected to have direct implementations in analysis of two-step annealing crystallization experiments, although other applications might be anticipated due to universality of the nucleation pulse technique.

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.

Bloch-Nordsieck thermometers: one-loop exponentiation in finite temperature QED

NASA Astrophysics Data System (ADS)

Gupta, Sourendu; Indumathi, D.; Mathews, Prakash; Ravindran, V.

1996-02-01

We study the scattering of hard external particles in a heat bath in a real-time formalism for finite temperature QED. We investigate the distribution of the 4-momentum difference of initial and final hard particles in a fully covariant manner when the scale of the process, Q, is much larger than the temperature, T. Our computations are valid for all T subject to this constraint. We exponentiate the leading infra-red term at one-loop order through a resummation of soft (thermal) photon emissions and absorptions. For T > 0, we find that tensor structures arise which are not present at T = 0. These cant' thermal signatures. As a result, external particles can serve as thermometers introduced into the heat bath. We investigate the phase space origin of log( Q/ m) and log ( Q/ T) teens.

Size and DNA distributions of electrophoretically separated cultured human kidney cells

NASA Technical Reports Server (NTRS)

Kunze, M. E.; Plank, L. D.; Todd, P. W.

1985-01-01

Electrophoretic purification of purifying cultured cells according to function presumes that the size of cycle phase of a cell is not an overriding determinant of its electrophoretic velocity in an electrophoretic separator. The size distributions and DNA distributions of fractions of cells purified by density gradient electrophoresis were determined. No systematic dependence of electrophoretic migration upward in a density gradient column upon either size or DNA content were found. It was found that human leukemia cell populations, which are more uniform function and found in all phases of the cell cycle during exponential growth, separated on a vertical sensity gradient electrophoresis column according to their size, which is shown to be strictly cell cycle dependent.

Multifractal Approach to Time Clustering of Earthquakes. Application to Mt. Vesuvio Seismicity

NASA Astrophysics Data System (ADS)

Codano, C.; Alonzo, M. L.; Vilardo, G.

The clustering structure of the Vesuvian earthquakes occurring is investigated by means of statistical tools: the inter-event time distribution, the running mean and the multifractal analysis. The first cannot clearly distinguish between a Poissonian process and a clustered one due to the difficulties of clearly distinguishing between an exponential distribution and a power law one. The running mean test reveals the clustering of the earthquakes, but looses information about the structure of the distribution at global scales. The multifractal approach can enlighten the clustering at small scales, while the global behaviour remains Poissonian. Subsequently the clustering of the events is interpreted in terms of diffusive processes of the stress in the earth crust.

Log-amplitude statistics for Beck-Cohen superstatistics

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Konno, Hidetoshi

2013-05-01

As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ2, inverse χ2, and log-normal superstatistical distributions. Furthermore, we show that χ2 and inverse χ2 superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ2 superstatistical distribution with degree 2.

Frequency distributions and correlations of solar X-ray flare parameters

NASA Technical Reports Server (NTRS)

Crosby, Norma B.; Aschwanden, Markus J.; Dennis, Brian R.

1993-01-01

Frequency distributions of flare parameters are determined from over 12,000 solar flares. The flare duration, the peak counting rate, the peak hard X-ray flux, the total energy in electrons, and the peak energy flux in electrons are among the parameters studied. Linear regression fits, as well as the slopes of the frequency distributions, are used to determine the correlations between these parameters. The relationship between the variations of the frequency distributions and the solar activity cycle is also investigated. Theoretical models for the frequency distribution of flare parameters are dependent on the probability of flaring and the temporal evolution of the flare energy build-up. The results of this study are consistent with stochastic flaring and exponential energy build-up. The average build-up time constant is found to be 0.5 times the mean time between flares.

A growth model for directed complex networks with power-law shape in the out-degree distribution

PubMed Central

Esquivel-Gómez, J.; Stevens-Navarro, E.; Pineda-Rico, U.; Acosta-Elias, J.

2015-01-01

Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1. PMID:25567141

Analytic score distributions for a spatially continuous tridirectional Monte Carol transport problem

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

Booth, T.E.

1996-01-01

The interpretation of the statistical error estimates produced by Monte Carlo transport codes is still somewhat of an art. Empirically, there are variance reduction techniques whose error estimates are almost always reliable, and there are variance reduction techniques whose error estimates are often unreliable. Unreliable error estimates usually result from inadequate large-score sampling from the score distribution`s tail. Statisticians believe that more accurate confidence interval statements are possible if the general nature of the score distribution can be characterized. Here, the analytic score distribution for the exponential transform applied to a simple, spatially continuous Monte Carlo transport problem is provided.more » Anisotropic scattering and implicit capture are included in the theory. In large part, the analytic score distributions that are derived provide the basis for the ten new statistical quality checks in MCNP.« less

On the efficacy of procedures to normalize Ex-Gaussian distributions.

PubMed

Marmolejo-Ramos, Fernando; Cousineau, Denis; Benites, Luis; Maehara, Rocío

2014-01-01

Reaction time (RT) is one of the most common types of measure used in experimental psychology. Its distribution is not normal (Gaussian) but resembles a convolution of normal and exponential distributions (Ex-Gaussian). One of the major assumptions in parametric tests (such as ANOVAs) is that variables are normally distributed. Hence, it is acknowledged by many that the normality assumption is not met. This paper presents different procedures to normalize data sampled from an Ex-Gaussian distribution in such a way that they are suitable for parametric tests based on the normality assumption. Using simulation studies, various outlier elimination and transformation procedures were tested against the level of normality they provide. The results suggest that the transformation methods are better than elimination methods in normalizing positively skewed data and the more skewed the distribution then the transformation methods are more effective in normalizing such data. Specifically, transformation with parameter lambda -1 leads to the best results.

Increased intra-individual reaction time variability in attention-deficit/hyperactivity disorder across response inhibition tasks with different cognitive demands.

PubMed

Vaurio, Rebecca G; Simmonds, Daniel J; Mostofsky, Stewart H

2009-10-01

One of the most consistent findings in children with ADHD is increased moment-to-moment variability in reaction time (RT). The source of increased RT variability can be examined using ex-Gaussian analyses that divide variability into normal and exponential components and Fast Fourier transform (FFT) that allow for detailed examination of the frequency of responses in the exponential distribution. Prior studies of ADHD using these methods have produced variable results, potentially related to differences in task demand. The present study sought to examine the profile of RT variability in ADHD using two Go/No-go tasks with differing levels of cognitive demand. A total of 140 children (57 with ADHD and 83 typically developing controls), ages 8-13 years, completed both a "simple" Go/No-go task and a more "complex" Go/No-go task with increased working memory load. Repeated measures ANOVA of ex-Gaussian functions revealed for both tasks children with ADHD demonstrated increased variability in both the normal/Gaussian (significantly elevated sigma) and the exponential (significantly elevated tau) components. In contrast, FFT analysis of the exponential component revealed a significant task x diagnosis interaction, such that infrequent slow responses in ADHD differed depending on task demand (i.e., for the simple task, increased power in the 0.027-0.074 Hz frequency band; for the complex task, decreased power in the 0.074-0.202 Hz band). The ex-Gaussian findings revealing increased variability in both the normal (sigma) and exponential (tau) components for the ADHD group, suggest that both impaired response preparation and infrequent "lapses in attention" contribute to increased variability in ADHD. FFT analyses reveal that the periodicity of intermittent lapses of attention in ADHD varies with task demand. The findings provide further support for intra-individual variability as a candidate intermediate endophenotype of ADHD.

Transmission of electric fields due to distributed cloud charges in the atmosphere-ionosphere system

NASA Astrophysics Data System (ADS)

Paul, Suman; De, S. S.; Haldar, D. K.; Guha, G.

2017-10-01

The transmission of electric fields in the lower atmosphere by thunder clouds with a suitable charge distribution profile has been modeled. The electromagnetic responses of the atmosphere are presented through Maxwell's equations together with a time-varying source charge distribution. The conductivities are taken to be exponentially graded function of altitude. The radial and vertical electric field components are derived for isotropic, anisotropic and thundercloud regions. The analytical solutions for the total Maxwell's current which flows from the cloud into the ionosphere under DC and quasi-static conditions are obtained for isotropic region. We found that the effect of charge distribution in thunderclouds produced by lightning discharges diminishes rapidly with increasing altitudes. Also, it is found that time to reach Maxwell's currents a maximum is higher for higher altitudes.

How Many Conformations Need To Be Sampled To Obtain Converged QM/MM Energies? The Curse of Exponential Averaging.

PubMed

Ryde, Ulf

2017-11-14

Combined quantum mechanical and molecular mechanical (QM/MM) calculations is a popular approach to study enzymatic reactions. They are often based on a set of minimized structures obtained on snapshots from a molecular dynamics simulation to include some dynamics of the enzyme. It has been much discussed how the individual energies should be combined to obtain a final estimate of the energy, but the current consensus seems to be to use an exponential average. Then, the question is how many snapshots are needed to reach a reliable estimate of the energy. In this paper, I show that the question can be easily be answered if it is assumed that the energies follow a Gaussian distribution. Then, the outcome can be simulated based on a single parameter, σ, the standard deviation of the QM/MM energies from the various snapshots, and the number of required snapshots can be estimated once the desired accuracy and confidence of the result has been specified. Results for various parameters are presented, and it is shown that many more snapshots are required than is normally assumed. The number can be reduced by employing a cumulant approximation to second order. It is shown that most convergence criteria work poorly, owing to the very bad conditioning of the exponential average when σ is large (more than ∼7 kJ/mol), because the energies that contribute most to the exponential average have a very low probability. On the other hand, σ serves as an excellent convergence criterion.

Disentangling inhibition-based and retrieval-based aftereffects of distractors: Cognitive versus motor processes.

PubMed

Singh, Tarini; Laub, Ruth; Burgard, Jan Pablo; Frings, Christian

2018-05-01

Selective attention refers to the ability to selectively act upon relevant information at the expense of irrelevant information. Yet, in many experimental tasks, what happens to the representation of the irrelevant information is still debated. Typically, 2 approaches to distractor processing have been suggested, namely distractor inhibition and distractor-based retrieval. However, it is also typical that both processes are hard to disentangle. For instance, in the negative priming literature (for a review Frings, Schneider, & Fox, 2015) this has been a continuous debate since the early 1980s. In the present study, we attempted to prove that both processes exist, but that they reflect distractor processing at different levels of representation. Distractor inhibition impacts stimulus representation, whereas distractor-based retrieval impacts mainly motor processes. We investigated both processes in a distractor-priming task, which enables an independent measurement of both processes. For our argument that both processes impact different levels of distractor representation, we estimated the exponential parameter (τ) and Gaussian components (μ, σ) of the exponential Gaussian reaction-time (RT) distribution, which have previously been used to independently test the effects of cognitive and motor processes (e.g., Moutsopoulou & Waszak, 2012). The distractor-based retrieval effect was evident for the Gaussian component, which is typically discussed as reflecting motor processes, but not for the exponential parameter, whereas the inhibition component was evident for the exponential parameter, which is typically discussed as reflecting cognitive processes, but not for the Gaussian parameter. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

The Martian twilight

NASA Technical Reports Server (NTRS)

Kahn, R.; Goody, R.; Pollack, J.

1981-01-01

The changing sky brightness during the Martian twilight as measured by the Viking lander cameras is shown to be consistent with data obtained from sky brightness measurements. An exponential distribution of dust with a scale height of 10 km, equal to the atmospheric scale height, is consistent with the shape of the light curve. Multiple scattering resulting from the forward scattering peak of large particles makes a major contribution to the intensity of the twilight. The spectral distribution of light in the twilight sky may require slightly different optical properties for the scattering particles at high levels from those of the aerosol at lower levels.

Contact-metal dependent current injection in pentacene thin-film transistors

NASA Astrophysics Data System (ADS)

Wang, S. D.; Minari, T.; Miyadera, T.; Tsukagoshi, K.; Aoyagi, Y.

2007-11-01

Contact-metal dependent current injection in top-contact pentacene thin-film transistors is analyzed, and the local mobility in the contact region was found to follow the Meyer-Neldel rule. An exponential trap distribution, rather than the metal/organic hole injection barrier, is proposed to be the dominant factor of the contact resistance in pentacene thin-film transistors. The variable temperature measurements revealed a much narrower trap distribution in the copper contact compared with the corresponding gold contact, and this is the origin of the smaller contact resistance for copper despite a lower work function.

Dynamics of behavioral organization and its alteration in major depression

NASA Astrophysics Data System (ADS)

Nakamura, Toru; Kiyono, Ken; Yoshiuchi, Kazuhiro; Nakahara, Rika; Struzik, Zbigniew R.; Yamamoto, Yoshiharu

2007-07-01

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity counts successively above a predefined threshold follow a stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the contrary, resting period durations below the threshold for both groups obey a scale free power law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find underlying robust laws governing human behavioral organization, with a parameter altered in depression.

Spatio-temporal analysis of aftershock sequences in terms of Non Extensive Statistical Physics.

NASA Astrophysics Data System (ADS)

Chochlaki, Kalliopi; Vallianatos, Filippos

2017-04-01

Earth's seismicity is considered as an extremely complicated process where long-range interactions and fracturing exist (Vallianatos et al., 2016). For this reason, in order to analyze it, we use an innovative methodological approach, introduced by Tsallis (Tsallis, 1988; 2009), named Non Extensive Statistical Physics. This approach introduce a generalization of the Boltzmann-Gibbs statistical mechanics and it is based on the definition of Tsallis entropy Sq, which maximized leads the the so-called q-exponential function that expresses the probability distribution function that maximizes the Sq. In the present work, we utilize the concept of Non Extensive Statistical Physics in order to analyze the spatiotemporal properties of several aftershock series. Marekova (Marekova, 2014) suggested that the probability densities of the inter-event distances between successive aftershocks follow a beta distribution. Using the same data set we analyze the inter-event distance distribution of several aftershocks sequences in different geographic regions by calculating non extensive parameters that determine the behavior of the system and by fitting the q-exponential function, which expresses the degree of non-extentivity of the investigated system. Furthermore, the inter-event times distribution of the aftershocks as well as the frequency-magnitude distribution has been analyzed. The results supports the applicability of Non Extensive Statistical Physics ideas in aftershock sequences where a strong correlation exists along with memory effects. References C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1988) 479-487. doi:10.1007/BF01016429 C. Tsallis, Introduction to nonextensive statistical mechanics: Approaching a complex world, 2009. doi:10.1007/978-0-387-85359-8. E. Marekova, Analysis of the spatial distribution between successive earthquakes in aftershocks series, Annals of Geophysics, 57, 5, doi:10.4401/ag-6556, 2014 F. Vallianatos, G. Papadakis, G. Michas, Generalized statistical mechanics approaches to earthquakes and tectonics. Proc. R. Soc. A, 472, 20160497, 2016.

Shifts in Summertime Precipitation Accumulation Distributions over the US

NASA Astrophysics Data System (ADS)

Martinez-Villalobos, C.; Neelin, J. D.

2016-12-01

Precipitation accumulations, i.e., the amount of precipitation integrated over the course of an event, is a variable with both important physical and societal implications. Previous observational studies show that accumulation distributions have a characteristic shape, with an approximately power law decrease at first, followed by a sharp decrease at a characteristic large event cutoff scale. This cutoff scale is important as it limits the biggest accumulation events. Stochastic prototypes show that the resulting distributions, and importantly the large event cutoff scale, can be understood as a result of the interplay between moisture loss by precipitation and changes in moisture sinks/sources due to fluctuations in moisture divergence over the course of a precipitation event. The strength of this fluctuating moisture sink/source term is expected to increase under global warming, with both theory and climate model simulations predicting a concomitant increase in the large event cutoff scale. This cutoff scale increase has important consequences as it implies an approximately exponential increase for the largest accumulation events. Given its importance, in this study we characterize and track changes in the distribution of precipitation events accumulations over the contiguous US. Accumulation distributions are calculated using hourly precipitation data from 1700 stations, covering the 1974-2013 period over May-October. The resulting distributions largely follow the aforementioned shape, with individual cutoff scales depending on the local climate. An increase in the large event cutoff scale over this period is observed over several regions over the US, most notably over the eastern third of the US. In agreement with the increase in the cutoff, almost exponential increases in the highest accumulation percentiles occur over these regions, with increases in the 99.9 percentile in the Northeast of 70% for example. The relationship to changes in daily precipitation that have previously been noted and to changes in the moisture budget over this period are examined.

Shifts in Summertime Precipitation Accumulation Distributions over the US

NASA Astrophysics Data System (ADS)

Martinez-Villalobos, C.; Neelin, J. D.

2017-12-01

Precipitation accumulations, i.e., the amount of precipitation integrated over the course of an event, is a variable with both important physical and societal implications. Previous observational studies show that accumulation distributions have a characteristic shape, with an approximately power law decrease at first, followed by a sharp decrease at a characteristic large event cutoff scale. This cutoff scale is important as it limits the biggest accumulation events. Stochastic prototypes show that the resulting distributions, and importantly the large event cutoff scale, can be understood as a result of the interplay between moisture loss by precipitation and changes in moisture sinks/sources due to fluctuations in moisture divergence over the course of a precipitation event. The strength of this fluctuating moisture sink/source term is expected to increase under global warming, with both theory and climate model simulations predicting a concomitant increase in the large event cutoff scale. This cutoff scale increase has important consequences as it implies an approximately exponential increase for the largest accumulation events. Given its importance, in this study we characterize and track changes in the distribution of precipitation events accumulations over the contiguous US. Accumulation distributions are calculated using hourly precipitation data from 1700 stations, covering the 1974-2013 period over May-October. The resulting distributions largely follow the aforementioned shape, with individual cutoff scales depending on the local climate. An increase in the large event cutoff scale over this period is observed over several regions over the US, most notably over the eastern third of the US. In agreement with the increase in the cutoff, almost exponential increases in the highest accumulation percentiles occur over these regions, with increases in the 99.9 percentile in the Northeast of 70% for example. The relationship to changes in daily precipitation that have previously been noted and to changes in the moisture budget over this period are examined.

Scalable Rapidly Deployable Convex Optimization for Data Analytics

DTIC Science & Technology

SOCPs , SDPs, exponential cone programs, and power cone programs. CVXPY supports basic methods for distributed optimization, on...multiple heterogenous platforms. We have also done basic research in various application areas , using CVXPY , to demonstrate its usefulness. See attached report for publication information....Over the period of the contract we have developed the full stack for wide use of convex optimization, in machine learning and many other areas .

Mathematical modeling of inhalation exposure

NASA Technical Reports Server (NTRS)

Fiserova-Bergerova, V.

1976-01-01

The paper presents a mathematical model of inhalation exposure in which uptake, distribution and excretion are described by exponential functions, while rate constants are determined by tissue volumes, blood perfusion and by the solubility of vapors (partition coefficients). In the model, tissues are grouped into four pharmokinetic compartments. The model is used to study continuous and interrupted chronic exposures and is applied to the inhalation of Forane and methylene chloride.

Leveraging the Cloud for Integrated Network Experimentation

DTIC Science & Technology

2014-03-01

kernel settings, or any of the low-level subcomponents. 3. Scalable Solutions: Businesses can build scalable solutions for their clients , ranging from...values. These values 13 can assume several distributions that include normal, Pareto , uniform, exponential and Poisson, among others [21]. Additionally, D...communication, the web client establishes a connection to the server before traffic begins to flow. Web servers do not initiate connections to clients in

Group Recommendation in Social Networks

DTIC Science & Technology

2011-01-01

APPROVAL SHEET Title of Thesis: Group recognition in social networks Name of Candidate: Nagapradeep Chinnam Master of...2011 4. TITLE AND SUBTITLE Group recognition in social networks 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT Recent years have seen an exponential growth in the use of social

Coupled large eddy simulation and discrete element model of bedload motion

NASA Astrophysics Data System (ADS)

Furbish, D.; Schmeeckle, M. W.

2011-12-01

We combine a three-dimensional large eddy simulation of turbulence to a three-dimensional discrete element model of turbulence. The large eddy simulation of the turbulent fluid is extended into the bed composed of non-moving particles by adding resistance terms to the Navier-Stokes equations in accordance with the Darcy-Forchheimer law. This allows the turbulent velocity and pressure fluctuations to penetrate the bed of discrete particles, and this addition of a porous zone results in turbulence structures above the bed that are similar to previous experimental and numerical results for hydraulically-rough beds. For example, we reproduce low-speed streaks that are less coherent than those over smooth-beds due to the episodic outflow of fluid from the bed. Local resistance terms are also added to the Navier-Stokes equations to account for the drag of individual moving particles. The interaction of the spherical particles utilizes a standard DEM soft-sphere Hertz model. We use only a simple drag model to calculate the fluid forces on the particles. The model reproduces an exponential distribution of bedload particle velocities that we have found experimentally using high-speed video of a flat bed of moving sand in a recirculating water flume. The exponential distribution of velocity results from the motion of many particles that are nearly constantly in contact with other bed particles and come to rest after short distances, in combination with a relatively few particles that are entrained further above the bed and have velocities approaching that of the fluid. Entrainment and motion "hot spots" are evident that are not perfectly correlated with the local, instantaneous fluid velocity. Zones of the bed that have recently experienced motion are more susceptible to motion because of the local configuration of particle contacts. The paradigm of a characteristic saltation hop length in riverine bedload transport has infused many aspects of geomorphic thought, including even bedrock erosion. In light of our theoretical, experimental, and numerical findings supporting the exponential distribution of bedload particle motion, the idea of a characteristic saltation hop should be scrapped or substantially modified.

Comparing Exponential and Exponentiated Models of Drug Demand in Cocaine Users

PubMed Central

Strickland, Justin C.; Lile, Joshua A.; Rush, Craig R.; Stoops, William W.

2016-01-01

Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model, but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use), whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values impact demand parameters and their association with drug-use outcomes when using the exponential model, but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency, in addition to demonstrating construct validity and generalizability. PMID:27929347

Comparing exponential and exponentiated models of drug demand in cocaine users.

PubMed

Strickland, Justin C; Lile, Joshua A; Rush, Craig R; Stoops, William W

2016-12-01

Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, or 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use) whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values affects demand parameters and their association with drug-use outcomes when using the exponential model but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency and demonstrating construct validity and generalizability. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Light distribution in plant canopies: A comparison between 1-D multi-layer modeling approach and 3-D ray tracing

NASA Astrophysics Data System (ADS)

Srinivasan, V.; Yiwen, X.; Ellis, A.; Christensen, A.; Borkiewic, K.; Cox, D.; Hart, J.; Long, S.; Marshall-Colon, A.

2016-12-01

The distribution of absorbed solar radiation in the photosynthetically active region wavelength (PAR) within plant canopies plays a critical role in determining photosynthetic carbon uptake and its associated transpiration. The vertical distribution of leaf area, leaf angles, leaf absorptivity and reflectivity within the canopy, affect the distribution of PAR absorbed throughout the canopy. While the upper canopy sunlit leaves absorb most of the incoming PAR and hence contribute most towards total canopy carbon uptake, the lower canopy shaded leaves which receive mostly lower intensity diffuse PAR make significant contributions towards plant carbon uptake. Most detailed vegetation models use a 1-D vertical multi-layer approach to model the sunlight and shaded canopy leaf fractions, and quantify the direct and diffuse radiation absorbed by the respective leaf fractions. However, this approach is only applicable under canopy closure conditions, and furthermore it fails to accurately capture the effects of diurnally varying leaf angle distributions in some plant canopies. Here, we show by using a 3-D ray tracing model which uses an explicit 3-D canopy structure that enforces no conditions about canopy closure, that the effects of diurnal variation of canopy leaf angle distributions better match with observed data. Our comparative analysis performed on soybean crop canopies between 3-D ray tracing model and the multi-layer model shows that the distribution of absorbed direct PAR is not exponential while, the distribution of absorbed diffuse PAR radiation within plant canopies is exponential. These results show the multi-layer model to significantly over-predict canopy PAR absorbed, and in turn significantly overestimate photosynthetic carbon uptake by up to 13% and canopy transpiration by 7% under mid-day sun conditions as verified through our canopy chamber experiments. Our results indicate that current detailed 1-D multi-layer canopy radiation attenuation models significantly over predict canopy radiation absorption and its associated canopy photosynthetic and transpiration fluxes, and use of a 3-D ray tracing model provides more realistic predictions of leaf canopy integrated fluxes of carbon and water.

Numerical and machine learning simulation of parametric distributions of groundwater residence time in streams and wells

NASA Astrophysics Data System (ADS)

Starn, J. J.; Belitz, K.; Carlson, C.

2017-12-01

Groundwater residence-time distributions (RTDs) are critical for assessing susceptibility of water resources to contamination. This novel approach for estimating regional RTDs was to first simulate groundwater flow using existing regional digital data sets in 13 intermediate size watersheds (each an average of 7,000 square kilometers) that are representative of a wide range of glacial systems. RTDs were simulated with particle tracking. We refer to these models as "general models" because they are based on regional, as opposed to site-specific, digital data. Parametric RTDs were created from particle RTDs by fitting 1- and 2-component Weibull, gamma, and inverse Gaussian distributions, thus reducing a large number of particle travel times to 3 to 7 parameters (shape, location, and scale for each component plus a mixing fraction) for each modeled area. The scale parameter of these distributions is related to the mean exponential age; the shape parameter controls departure from the ideal exponential distribution and is partly a function of interaction with bedrock and with drainage density. Given the flexible shape and mathematical similarity of these distributions, any of them are potentially a good fit to particle RTDs. The 1-component gamma distribution provided a good fit to basin-wide particle RTDs. RTDs at monitoring wells and streams often have more complicated shapes than basin-wide RTDs, caused in part by heterogeneity in the model, and generally require 2-component distributions. A machine learning model was trained on the RTD parameters using features derived from regionally available watershed characteristics such as recharge rate, material thickness, and stream density. RTDs appeared to vary systematically across the landscape in relation to watershed features. This relation was used to produce maps of useful metrics with respect to risk-based thresholds, such as the time to first exceedance, time to maximum concentration, time above the threshold (exposure time), and the time until last exceedance; thus, the parameters of groundwater residence time are measures of the intrinsic susceptibility of groundwater to contamination.

Development of a time-trend model for analyzing and predicting case-pattern of Lassa fever epidemics in Liberia, 2013-2017.

PubMed

Olugasa, Babasola O; Odigie, Eugene A; Lawani, Mike; Ojo, Johnson F

2015-01-01

The objective was to develop a case-pattern model for Lassa fever (LF) among humans and derive predictors of time-trend point distribution of LF cases in Liberia in view of the prevailing under-reporting and public health challenge posed by the disease in the country. A retrospective 5 years data of LF distribution countrywide among humans were used to train a time-trend model of the disease in Liberia. A time-trend quadratic model was selected due to its goodness-of-fit (R2 = 0.89, and P < 0.05) and best performance compared to linear and exponential models. Parameter predictors were run on least square method to predict LF cases for a prospective 5 years period, covering 2013-2017. The two-stage predictive model of LF case-pattern between 2013 and 2017 was characterized by a prospective decline within the South-coast County of Grand Bassa over the forecast period and an upward case-trend within the Northern County of Nimba. Case specific exponential increase was predicted for the first 2 years (2013-2014) with a geometric increase over the next 3 years (2015-2017) in Nimba County. This paper describes a translational application of the space-time distribution pattern of LF epidemics, 2008-2012 reported in Liberia, on which a predictive model was developed. We proposed a computationally feasible two-stage space-time permutation approach to estimate the time-trend parameters and conduct predictive inference on LF in Liberia.

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

NASA Astrophysics Data System (ADS)

Dinh, Khanh N.; Sidje, Roger B.

2017-12-01

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

δ-exceedance records and random adaptive walks

NASA Astrophysics Data System (ADS)

Park, Su-Chan; Krug, Joachim

2016-08-01

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

The resolved star formation history of M51a through successive Bayesian marginalization

NASA Astrophysics Data System (ADS)

Martínez-García, Eric E.; Bruzual, Gustavo; Magris C., Gladis; González-Lópezlira, Rosa A.

2018-02-01

We have obtained the time and space-resolved star formation history (SFH) of M51a (NGC 5194) by fitting Galaxy Evolution Explorer (GALEX), Sloan Digital Sky Survey and near-infrared pixel-by-pixel photometry to a comprehensive library of stellar population synthesis models drawn from the Synthetic Spectral Atlas of Galaxies (SSAG). We fit for each space-resolved element (pixel) an independent model where the SFH is averaged in 137 age bins, each one 100 Myr wide. We used the Bayesian Successive Priors (BSP) algorithm to mitigate the bias in the present-day spatial mass distribution. We test BSP with different prior probability distribution functions (PDFs); this exercise suggests that the best prior PDF is the one concordant with the spatial distribution of the stellar mass as inferred from the near-infrared images. We also demonstrate that varying the implicit prior PDF of the SFH in SSAG does not affect the results. By summing the contributions to the global star formation rate of each pixel, at each age bin, we have assembled the resolved SFH of the whole galaxy. According to these results, the star formation rate of M51a was exponentially increasing for the first 10 Gyr after the big bang, and then turned into an exponentially decreasing function until the present day. Superimposed, we find a main burst of star formation at t ≈ 11.9 Gyr after the big bang.

Marangoni convection in Casson liquid flow due to an infinite disk with exponential space dependent heat source and cross-diffusion effects

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.; Shashikumar, N. S.; Hayat, T.; Alsaedi, A.

2018-06-01

Present work aims to investigate the features of the exponential space dependent heat source (ESHS) and cross-diffusion effects in Marangoni convective heat mass transfer flow due to an infinite disk. Flow analysis is comprised with magnetohydrodynamics (MHD). The effects of Joule heating, viscous dissipation and solar radiation are also utilized. The thermal and solute field on the disk surface varies in a quadratic manner. The ordinary differential equations have been obtained by utilizing Von Kármán transformations. The resulting problem under consideration is solved numerically via Runge-Kutta-Fehlberg based shooting scheme. The effects of involved pertinent flow parameters are explored by graphical illustrations. Results point out that the ESHS effect dominates thermal dependent heat source effect on thermal boundary layer growth. The concentration and temperature distributions and their associated layer thicknesses are enhanced by Marangoni effect.

Reliability analysis using an exponential power model with bathtub-shaped failure rate function: a Bayes study.

PubMed

Shehla, Romana; Khan, Athar Ali

2016-01-01

Models with bathtub-shaped hazard function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this paper, the exponential power model capable of assuming increasing as well as bathtub-shape, is studied. This article makes a Bayesian study of the same model and simultaneously shows how posterior simulations based on Markov chain Monte Carlo algorithms can be straightforward and routine in R. The study is carried out for complete as well as censored data, under the assumption of weakly-informative priors for the parameters. In addition to this, inference interest focuses on the posterior distribution of non-linear functions of the parameters. Also, the model has been extended to include continuous explanatory variables and R-codes are well illustrated. Two real data sets are considered for illustrative purposes.

Tempered fractional calculus

NASA Astrophysics Data System (ADS)

Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

2015-07-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS.

PubMed

Meerschaert, Mark M; Sabzikar, Farzad; Chen, Jinghua

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS

PubMed Central

MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA

2014-01-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series. PMID:26085690

Tempered fractional calculus

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

Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu; Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu; Chen, Jinghua, E-mail: cjhdzdz@163.com

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a temperedmore » fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.« less

Thermodynamics and glassy phase transition of regular black holes

NASA Astrophysics Data System (ADS)

Javed, Wajiha; Yousaf, Z.; Akhtar, Zunaira

2018-05-01

This paper is aimed to study thermodynamical properties of phase transition for regular charged black holes (BHs). In this context, we have considered two different forms of BH metrics supplemented with exponential and logistic distribution functions and investigated the recent expansion of phase transition through grand canonical ensemble. After exploring the corresponding Ehrenfest’s equation, we found the second-order background of phase transition at critical points. In order to check the critical behavior of regular BHs, we have evaluated some corresponding explicit relations for the critical temperature, pressure and volume and draw certain graphs with constant values of Smarr’s mass. We found that for the BH metric with exponential configuration function, the phase transition curves are divergent near the critical points, while glassy phase transition has been observed for the Ayón-Beato-García-Bronnikov (ABGB) BH in n = 5 dimensions.

Improving deep convolutional neural networks with mixed maxout units.

PubMed

Zhao, Hui-Zhen; Liu, Fu-Xian; Li, Long-Yue

2017-01-01

Motivated by insights from the maxout-units-based deep Convolutional Neural Network (CNN) that "non-maximal features are unable to deliver" and "feature mapping subspace pooling is insufficient," we present a novel mixed variant of the recently introduced maxout unit called a mixout unit. Specifically, we do so by calculating the exponential probabilities of feature mappings gained by applying different convolutional transformations over the same input and then calculating the expected values according to their exponential probabilities. Moreover, we introduce the Bernoulli distribution to balance the maximum values with the expected values of the feature mappings subspace. Finally, we design a simple model to verify the pooling ability of mixout units and a Mixout-units-based Network-in-Network (NiN) model to analyze the feature learning ability of the mixout models. We argue that our proposed units improve the pooling ability and that mixout models can achieve better feature learning and classification performance.

Charge Transport Properties in Disordered Organic Semiconductor as a Function of Charge Density: Monte Carlo Simulation

NASA Astrophysics Data System (ADS)

Shukri, Seyfan Kelil

2017-01-01

We have done Kinetic Monte Carlo (KMC) simulations to investigate the effect of charge carrier density on the electrical conductivity and carrier mobility in disordered organic semiconductors using a lattice model. The density of state (DOS) of the system are considered to be Gaussian and exponential. Our simulations reveal that the mobility of the charge carrier increases with charge carrier density for both DOSs. In contrast, the mobility of charge carriers decreases as the disorder increases. In addition the shape of the DOS has a significance effect on the charge transport properties as a function of density which are clearly seen. On the other hand, for the same distribution width and at low carrier density, the change occurred on the conductivity and mobility for a Gaussian DOS is more pronounced than that for the exponential DOS.

Statistics of equivalent width data and new oscillator strengths for Si II, Fe II, and Mn II. [in interstellar medium

NASA Technical Reports Server (NTRS)

Van Buren, Dave

1986-01-01

Equivalent width data from Copernicus and IUE appear to have an exponential, rather than a Gaussian distribution of errors. This is probably because there is one dominant source of error: the assignment of the background continuum shape. The maximum likelihood method of parameter estimation is presented for the case of exponential statistics, in enough generality for application to many problems. The method is applied to global fitting of Si II, Fe II, and Mn II oscillator strengths and interstellar gas parameters along many lines of sight. The new values agree in general with previous determinations but are usually much more tightly constrained. Finally, it is shown that care must be taken in deriving acceptable regions of parameter space because the probability contours are not generally ellipses whose axes are parallel to the coordinate axes.

Performance analysis for mixed FSO/RF Nakagami-m and Exponentiated Weibull dual-hop airborne systems

NASA Astrophysics Data System (ADS)

Jing, Zhao; Shang-hong, Zhao; Wei-hu, Zhao; Ke-fan, Chen

2017-06-01

In this paper, the performances of mixed free-space optical (FSO)/radio frequency (RF) systems are presented based on the decode-and-forward relaying. The Exponentiated Weibull fading channel with pointing error effect is adopted for the atmospheric fluctuation of FSO channel and the RF link undergoes the Nakagami-m fading. We derived the analytical expression for cumulative distribution function (CDF) of equivalent signal-to-noise ratio (SNR). The novel mathematical presentations of outage probability and average bit-error-rate (BER) are developed based on the Meijer's G function. The analytical results show an accurately match to the Monte-Carlo simulation results. The outage and BER performance for the mixed system by decode-and-forward relay are investigated considering atmospheric turbulence and pointing error condition. The effect of aperture averaging is evaluated in all atmospheric turbulence conditions as well.

Isolation of a variant of Candida albicans.

PubMed Central

Buckley, H R; Price, M R; Daneo-Moore, L

1982-01-01

During the course of Candida albicans antigen production, a variant of this organism was encountered which did not produce hyphae at 37 degrees C. Presented here are some of the characteristics of this variant. It produces hyphae at 25 degrees C on cornmeal agar and synthetic medium plus N-acetylglucosamine and Tween 80. At 37 degrees C, it does not produce hyphae on these media, although C. albicans normally does produce hyphae under these circumstances. In liquid synthetic medium, this variant does not produce hyphae at 37 degrees C. The variant strain was analyzed for DNA, RNA, protein content, and particle size. After 50 to 70 h in balanced exponential-phase growth, particle size distribution was narrow, and there were no differences in the DNA, RNA, or protein content per particle in the two strains. When balanced exponential-phase cultures were brought into stationary phase, both strains contained the same amount of DNA per cell. Images PMID:6752021

Isolation of a variant of Candida albicans.

PubMed

Buckley, H R; Price, M R; Daneo-Moore, L

1982-09-01

During the course of Candida albicans antigen production, a variant of this organism was encountered which did not produce hyphae at 37 degrees C. Presented here are some of the characteristics of this variant. It produces hyphae at 25 degrees C on cornmeal agar and synthetic medium plus N-acetylglucosamine and Tween 80. At 37 degrees C, it does not produce hyphae on these media, although C. albicans normally does produce hyphae under these circumstances. In liquid synthetic medium, this variant does not produce hyphae at 37 degrees C. The variant strain was analyzed for DNA, RNA, protein content, and particle size. After 50 to 70 h in balanced exponential-phase growth, particle size distribution was narrow, and there were no differences in the DNA, RNA, or protein content per particle in the two strains. When balanced exponential-phase cultures were brought into stationary phase, both strains contained the same amount of DNA per cell.

Auxiliary Parameter MCMC for Exponential Random Graph Models

NASA Astrophysics Data System (ADS)

Byshkin, Maksym; Stivala, Alex; Mira, Antonietta; Krause, Rolf; Robins, Garry; Lomi, Alessandro

2016-11-01

Exponential random graph models (ERGMs) are a well-established family of statistical models for analyzing social networks. Computational complexity has so far limited the appeal of ERGMs for the analysis of large social networks. Efficient computational methods are highly desirable in order to extend the empirical scope of ERGMs. In this paper we report results of a research project on the development of snowball sampling methods for ERGMs. We propose an auxiliary parameter Markov chain Monte Carlo (MCMC) algorithm for sampling from the relevant probability distributions. The method is designed to decrease the number of allowed network states without worsening the mixing of the Markov chains, and suggests a new approach for the developments of MCMC samplers for ERGMs. We demonstrate the method on both simulated and actual (empirical) network data and show that it reduces CPU time for parameter estimation by an order of magnitude compared to current MCMC methods.

Nuclear counting filter based on a centered Skellam test and a double exponential smoothing

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

Coulon, Romain; Kondrasovs, Vladimir; Dumazert, Jonathan

2015-07-01

Online nuclear counting represents a challenge due to the stochastic nature of radioactivity. The count data have to be filtered in order to provide a precise and accurate estimation of the count rate, this with a response time compatible with the application in view. An innovative filter is presented in this paper addressing this issue. It is a nonlinear filter based on a Centered Skellam Test (CST) giving a local maximum likelihood estimation of the signal based on a Poisson distribution assumption. This nonlinear approach allows to smooth the counting signal while maintaining a fast response when brutal change activitymore » occur. The filter has been improved by the implementation of a Brown's double Exponential Smoothing (BES). The filter has been validated and compared to other state of the art smoothing filters. The CST-BES filter shows a significant improvement compared to all tested smoothing filters. (authors)« less

Self Organized Criticality as a new paradigm of sleep regulation

NASA Astrophysics Data System (ADS)

Ivanov, Plamen Ch.; Bartsch, Ronny P.

2012-02-01

Humans and animals often exhibit brief awakenings from sleep (arousals), which are traditionally viewed as random disruptions of sleep caused by external stimuli or pathologic perturbations. However, our recent findings show that arousals exhibit complex temporal organization and scale-invariant behavior, characterized by a power-law probability distribution for their durations, while sleep stage durations exhibit exponential behavior. The co-existence of both scale-invariant and exponential processes generated by a single regulatory mechanism has not been observed in physiological systems until now. Such co-existence resembles the dynamical features of non-equilibrium systems exhibiting self-organized criticality (SOC). Our empirical analysis and modeling approaches based on modern concepts from statistical physics indicate that arousals are an integral part of sleep regulation and may be necessary to maintain and regulate healthy sleep by releasing accumulated excitations in the regulatory neuronal networks, following a SOC-type temporal organization.

Experimental tests of truncated diffusion in fault damage zones

NASA Astrophysics Data System (ADS)

Suzuki, Anna; Hashida, Toshiyuki; Li, Kewen; Horne, Roland N.

2016-11-01

Fault zones affect the flow paths of fluids in groundwater aquifers and geological reservoirs. Fault-related fracture damage decreases to background levels with increasing distance from the fault core according to a power law. This study investigated mass transport in such a fault-related structure using nonlocal models. A column flow experiment is conducted to create a permeability distribution that varies with distance from a main conduit. The experimental tracer response curve is preasymptotic and implies subdiffusive transport, which is slower than the normal Fickian diffusion. If the surrounding area is a finite domain, an upper truncated behavior in tracer response (i.e., exponential decline at late times) is observed. The tempered anomalous diffusion (TAD) model captures the transition from subdiffusive to Fickian transport, which is characterized by a smooth transition from power-law to an exponential decline in the late-time breakthrough curves.

Intermittent fluctuations in the Alcator C-Mod scrape-off layer for ohmic and high confinement mode plasmas

NASA Astrophysics Data System (ADS)

Garcia, O. E.; Kube, R.; Theodorsen, A.; LaBombard, B.; Terry, J. L.

2018-05-01

Plasma fluctuations in the scrape-off layer of the Alcator C-Mod tokamak in ohmic and high confinement modes have been analyzed using gas puff imaging data. In all cases investigated, the time series of emission from a single spatially resolved view into the gas puff are dominated by large-amplitude bursts, attributed to blob-like filament structures moving radially outwards and poloidally. There is a remarkable similarity of the fluctuation statistics in ohmic plasmas and in edge localized mode-free and enhanced D-alpha high confinement mode plasmas. Conditionally averaged waveforms have a two-sided exponential shape with comparable temporal scales and asymmetry, while the burst amplitudes and the waiting times between them are exponentially distributed. The probability density functions and the frequency power spectral densities are similar for all these confinement modes. These results provide strong evidence in support of a stochastic model describing the plasma fluctuations in the scrape-off layer as a super-position of uncorrelated exponential pulses. Predictions of this model are in excellent agreement with experimental measurements in both ohmic and high confinement mode plasmas. The stochastic model thus provides a valuable tool for predicting fluctuation-induced plasma-wall interactions in magnetically confined fusion plasmas.

Stellar Surface Brightness Profiles of Dwarf Galaxies

NASA Astrophysics Data System (ADS)

Herrmann, K. A.

2014-03-01

Radial stellar surface brightness profiles of spiral galaxies can be classified into three types: (I) single exponential, or the light falls off with one exponential out to a break radius and then falls off (II) more steeply (“truncated”), or (III) less steeply (“anti-truncated”). Why there are three different radial profile types is still a mystery, including why light falls off as an exponential at all. Profile breaks are also found in dwarf disks, but some dwarf Type IIs are flat or increasing (FI) out to a break before falling off. I have been re-examining the multi-wavelength stellar disk profiles of 141 dwarf galaxies, primarily from Hunter & Elmegreen (2004, 2006). Each dwarf has data in up to 11 wavelength bands: FUV and NUV from GALEX, UBVJHK and Hα from ground-based observations, and 3.6 and 4.5μm from Spitzer. Here I highlight some results from a semi-automatic fitting of this data set including: (1) statistics of break locations and other properties as a function of wavelength and profile type, (2) color trends and radial mass distribution as a function of profile type, and (3) the relationship of the break radius to the kinematics and density profiles of atomic hydrogen gas in the 40 dwarfs of the LITTLE THINGS subsample.

Two Components of Voltage-Dependent Inactivation in Cav1.2 Channels Revealed by Its Gating Currents

PubMed Central

Ferreira, Gonzalo; Ríos, Eduardo; Reyes, Nicolás

2003-01-01

Voltage-dependent inactivation (VDI) was studied through its effects on the voltage sensor in Cav1.2 channels expressed in tsA 201 cells. Two kinetically distinct phases of VDI in onset and recovery suggest the presence of dual VDI processes. Upon increasing duration of conditioning depolarizations, the half-distribution potential (V1/2) of intramembranous mobile charge was negatively shifted as a sum of two exponential terms, with time constants 0.5 s and 4 s, and relative amplitudes near 50% each. This kinetics behavior was consistent with that of increment of maximal charge related to inactivation (Qn). Recovery from inactivation was also accompanied by a reduction of Qn that varied with recovery time as a sum of two exponentials. The amplitudes of corresponding exponential terms were strongly correlated in onset and recovery, indicating that channels recover rapidly from fast VDI and slowly from slow VDI. Similar to charge “immobilization,” the charge moved in the repolarization (OFF) transient became slower during onset of fast VDI. Slow VDI had, instead, hallmarks of interconversion of charge. Confirming the mechanistic duality, fast VDI virtually disappeared when Li+ carried the current. A nine-state model with parallel fast and slow inactivation pathways from the open state reproduces most of the observations. PMID:12770874