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.

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.

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

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.

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.

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.

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.

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.

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

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.

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…

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.

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

A scaling law for random walks on networks

PubMed Central

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-01-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics. PMID:25311870

A scaling law for random walks on networks

NASA Astrophysics Data System (ADS)

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

A scaling law for random walks on networks.

PubMed

Perkins, Theodore J; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-14

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

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.

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

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.

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.

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.

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.

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.

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.

Exploration properties of biased evanescent random walkers on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Esguerra, Jose Perico; Reyes, Jelian

2017-08-01

We investigate the combined effects of bias and evanescence on the characteristics of random walks on a one-dimensional lattice. We calculate the time-dependent return probability, eventual return probability, conditional mean return time, and the time-dependent mean number of visited sites of biased immortal and evanescent discrete-time random walkers on a one-dimensional lattice. We then extend the calculations to the case of a continuous-time step-coupled biased evanescent random walk on a one-dimensional lattice with an exponential waiting time distribution.

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.

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).

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 ) .

Exponential gain of randomness certified by quantum contextuality

NASA Astrophysics Data System (ADS)

Um, Mark; Zhang, Junhua; Wang, Ye; Wang, Pengfei; Kim, Kihwan

2017-04-01

We demonstrate the protocol of exponential gain of randomness certified by quantum contextuality in a trapped ion system. The genuine randomness can be produced by quantum principle and certified by quantum inequalities. Recently, randomness expansion protocols based on inequality of Bell-text and Kochen-Specker (KS) theorem, have been demonstrated. These schemes have been theoretically innovated to exponentially expand the randomness and amplify the randomness from weak initial random seed. Here, we report the experimental evidence of such exponential expansion of randomness. In the experiment, we use three states of a 138Ba + ion between a ground state and two quadrupole states. In the 138Ba + ion system, we do not have detection loophole and we apply a methods to rule out certain hidden variable models that obey a kind of extended noncontextuality.

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.

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.

Saddlepoint approximation to the distribution of the total distance of the continuous time random walk

NASA Astrophysics Data System (ADS)

Gatto, Riccardo

2017-12-01

This article considers the random walk over Rp, with p ≥ 2, where a given particle starts at the origin and moves stepwise with uniformly distributed step directions and step lengths following a common distribution. Step directions and step lengths are independent. The case where the number of steps of the particle is fixed and the more general case where it follows an independent continuous time inhomogeneous counting process are considered. Saddlepoint approximations to the distribution of the distance from the position of the particle to the origin are provided. Despite the p-dimensional nature of the random walk, the computations of the saddlepoint approximations are one-dimensional and thus simple. Explicit formulae are derived with dimension p = 3: for uniformly and exponentially distributed step lengths, for fixed and for Poisson distributed number of steps. In these situations, the high accuracy of the saddlepoint approximations is illustrated by numerical comparisons with Monte Carlo simulation. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

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.

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.

Reducing financial avalanches by random investments

NASA Astrophysics Data System (ADS)

Biondo, Alessio Emanuele; Pluchino, Alessandro; Rapisarda, Andrea; Helbing, Dirk

2013-12-01

Building on similarities between earthquakes and extreme financial events, we use a self-organized criticality-generating model to study herding and avalanche dynamics in financial markets. We consider a community of interacting investors, distributed in a small-world network, who bet on the bullish (increasing) or bearish (decreasing) behavior of the market which has been specified according to the S&P 500 historical time series. Remarkably, we find that the size of herding-related avalanches in the community can be strongly reduced by the presence of a relatively small percentage of traders, randomly distributed inside the network, who adopt a random investment strategy. Our findings suggest a promising strategy to limit the size of financial bubbles and crashes. We also obtain that the resulting wealth distribution of all traders corresponds to the well-known Pareto power law, while that of random traders is exponential. In other words, for technical traders, the risk of losses is much greater than the probability of gains compared to those of random traders.

Reducing financial avalanches by random investments.

PubMed

Biondo, Alessio Emanuele; Pluchino, Alessandro; Rapisarda, Andrea; Helbing, Dirk

2013-12-01

Building on similarities between earthquakes and extreme financial events, we use a self-organized criticality-generating model to study herding and avalanche dynamics in financial markets. We consider a community of interacting investors, distributed in a small-world network, who bet on the bullish (increasing) or bearish (decreasing) behavior of the market which has been specified according to the S&P 500 historical time series. Remarkably, we find that the size of herding-related avalanches in the community can be strongly reduced by the presence of a relatively small percentage of traders, randomly distributed inside the network, who adopt a random investment strategy. Our findings suggest a promising strategy to limit the size of financial bubbles and crashes. We also obtain that the resulting wealth distribution of all traders corresponds to the well-known Pareto power law, while that of random traders is exponential. In other words, for technical traders, the risk of losses is much greater than the probability of gains compared to those of random traders.

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.

Random walk numerical simulation for hopping transport at finite carrier concentrations: diffusion coefficient and transport energy concept.

PubMed

Gonzalez-Vazquez, J P; Anta, Juan A; Bisquert, Juan

2009-11-28

The random walk numerical simulation (RWNS) method is used to compute diffusion coefficients for hopping transport in a fully disordered medium at finite carrier concentrations. We use Miller-Abrahams jumping rates and an exponential distribution of energies to compute the hopping times in the random walk simulation. The computed diffusion coefficient shows an exponential dependence with respect to Fermi-level and Arrhenius behavior with respect to temperature. This result indicates that there is a well-defined transport level implicit to the system dynamics. To establish the origin of this transport level we construct histograms to monitor the energies of the most visited sites. In addition, we construct "corrected" histograms where backward moves are removed. Since these moves do not contribute to transport, these histograms provide a better estimation of the effective transport level energy. The analysis of this concept in connection with the Fermi-level dependence of the diffusion coefficient and the regime of interest for the functioning of dye-sensitised solar cells is thoroughly discussed.

Coherent wave transmission in quasi-one-dimensional systems with Lévy disorder

NASA Astrophysics Data System (ADS)

Amanatidis, Ilias; Kleftogiannis, Ioannis; Falceto, Fernando; Gopar, Víctor A.

2017-12-01

We study the random fluctuations of the transmission in disordered quasi-one-dimensional systems such as disordered waveguides and/or quantum wires whose random configurations of disorder are characterized by density distributions with a long tail known as Lévy distributions. The presence of Lévy disorder leads to large fluctuations of the transmission and anomalous localization, in relation to the standard exponential localization (Anderson localization). We calculate the complete distribution of the transmission fluctuations for a different number of transmission channels in the presence and absence of time-reversal symmetry. Significant differences in the transmission statistics between disordered systems with Anderson and anomalous localizations are revealed. The theoretical predictions are independently confirmed by tight-binding numerical simulations.

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.

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

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.

Modeling of magnitude distributions by the generalized truncated exponential distribution

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2015-01-01

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

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States.

PubMed

Steimer, Andreas; Schindler, Kaspar

2015-01-01

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon's implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike's preceding ISI. As we show, the EIF's exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron's ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

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.

Characterizing ISI and sub-threshold membrane potential distributions: Ensemble of IF neurons with random squared-noise intensity.

PubMed

Kumar, Sanjeev; Karmeshu

2018-04-01

A theoretical investigation is presented that characterizes the emerging sub-threshold membrane potential and inter-spike interval (ISI) distributions of an ensemble of IF neurons that group together and fire together. The squared-noise intensity σ 2 of the ensemble of neurons is treated as a random variable to account for the electrophysiological variations across population of nearly identical neurons. Employing superstatistical framework, both ISI distribution and sub-threshold membrane potential distribution of neuronal ensemble are obtained in terms of generalized K-distribution. The resulting distributions exhibit asymptotic behavior akin to stretched exponential family. Extensive simulations of the underlying SDE with random σ 2 are carried out. The results are found to be in excellent agreement with the analytical results. The analysis has been extended to cover the case corresponding to independent random fluctuations in drift in addition to random squared-noise intensity. The novelty of the proposed analytical investigation for the ensemble of IF neurons is that it yields closed form expressions of probability distributions in terms of generalized K-distribution. Based on a record of spiking activity of thousands of neurons, the findings of the proposed model are validated. The squared-noise intensity σ 2 of identified neurons from the data is found to follow gamma distribution. The proposed generalized K-distribution is found to be in excellent agreement with that of empirically obtained ISI distribution of neuronal ensemble. Copyright © 2018 Elsevier B.V. All rights reserved.

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

USGS Publications Warehouse

Kirby, W.

1983-01-01

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

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

USGS Publications Warehouse

Kirby, W.H.

1980-01-01

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

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

NASA Technical Reports Server (NTRS)

Peters, C. (Principal Investigator)

1980-01-01

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

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.

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.

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.

Robust reliable sampled-data control for switched systems with application to flight control

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Joby, Maya; Shi, P.; Mathiyalagan, K.

2016-11-01

This paper addresses the robust reliable stabilisation problem for a class of uncertain switched systems with random delays and norm bounded uncertainties. The main aim of this paper is to obtain the reliable robust sampled-data control design which involves random time delay with an appropriate gain control matrix for achieving the robust exponential stabilisation for uncertain switched system against actuator failures. In particular, the involved delays are assumed to be randomly time-varying which obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and employing an average-dwell time approach, a new set of criteria is derived for ensuring the robust exponential stability of the closed-loop switched system. More precisely, the Schur complement and Jensen's integral inequality are used in derivation of stabilisation criteria. By considering the relationship among the random time-varying delay and its lower and upper bounds, a new set of sufficient condition is established for the existence of reliable robust sampled-data control in terms of solution to linear matrix inequalities (LMIs). Finally, an illustrative example based on the F-18 aircraft model is provided to show the effectiveness of the proposed design procedures.

An invariance property of generalized Pearson random walks in bounded geometries

NASA Astrophysics Data System (ADS)

Mazzolo, Alain

2009-03-01

Invariance properties of random walks in bounded domains are a topic of growing interest since they contribute to improving our understanding of diffusion in confined geometries. Recently, limited to Pearson random walks with exponentially distributed straight paths, it has been shown that under isotropic uniform incidence, the average length of the trajectories through the domain is independent of the random walk characteristic and depends only on the ratio of the volume's domain over its surface. In this paper, thanks to arguments of integral geometry, we generalize this property to any isotropic bounded stochastic process and we give the conditions of its validity for isotropic unbounded stochastic processes. The analytical form for the traveled distance from the boundary to the first scattering event that ensures the validity of the Cauchy formula is also derived. The generalization of the Cauchy formula is an analytical constraint that thus concerns a very wide range of stochastic processes, from the original Pearson random walk to a Rayleigh distribution of the displacements, covering many situations of physical importance.

Quantum random access memory.

PubMed

Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo

2008-04-25

A random access memory (RAM) uses n bits to randomly address N=2(n) distinct memory cells. A quantum random access memory (QRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that exponentially reduces the requirements for a memory call: O(logN) switches need be thrown instead of the N used in conventional (classical or quantum) RAM designs. This yields a more robust QRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing. A quantum optical implementation is presented.

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.

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.

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

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.

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

A New Insight into the Earthquake Recurrence Studies from the Three-parameter Generalized Exponential Distributions

NASA Astrophysics Data System (ADS)

Pasari, S.; Kundu, D.; Dikshit, O.

2012-12-01

Earthquake recurrence interval is one of the important ingredients towards probabilistic seismic hazard assessment (PSHA) for any location. Exponential, gamma, Weibull and lognormal distributions are quite established probability models in this recurrence interval estimation. However, they have certain shortcomings too. Thus, it is imperative to search for some alternative sophisticated distributions. In this paper, we introduce a three-parameter (location, scale and shape) exponentiated exponential distribution and investigate the scope of this distribution as an alternative of the afore-mentioned distributions in earthquake recurrence studies. This distribution is a particular member of the exponentiated Weibull distribution. Despite of its complicated form, it is widely accepted in medical and biological applications. Furthermore, it shares many physical properties with gamma and Weibull family. Unlike gamma distribution, the hazard function of generalized exponential distribution can be easily computed even if the shape parameter is not an integer. To contemplate the plausibility of this model, a complete and homogeneous earthquake catalogue of 20 events (M ≥ 7.0) spanning for the period 1846 to 1995 from North-East Himalayan region (20-32 deg N and 87-100 deg E) has been used. The model parameters are estimated using maximum likelihood estimator (MLE) and method of moment estimator (MOME). No geological or geophysical evidences have been considered in this calculation. The estimated conditional probability reaches quite high after about a decade for an elapsed time of 17 years (i.e. 2012). Moreover, this study shows that the generalized exponential distribution fits the above data events more closely compared to the conventional models and hence it is tentatively concluded that generalized exponential distribution can be effectively considered in earthquake recurrence studies.

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

PubMed Central

Steimer, Andreas; Schindler, Kaspar

2015-01-01

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation. PMID:26203657

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).

Dynamical Localization for Unitary Anderson Models

NASA Astrophysics Data System (ADS)

Hamza, Eman; Joye, Alain; Stolz, Günter

2009-11-01

This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary operator and a random unitary operator. The deterministic operator has a band structure, is absolutely continuous and plays the role of the discrete Laplacian. The random operator is diagonal with elements given by i.i.d. random phases distributed according to some absolutely continuous measure and plays the role of the random potential. In dimension one, these operators belong to the family of CMV-matrices in the theory of orthogonal polynomials on the unit circle. We implement the method of Aizenman-Molchanov to prove exponential decay of the fractional moments of the Green function for the unitary Anderson model in the following three regimes: In any dimension, throughout the spectrum at large disorder and near the band edges at arbitrary disorder and, in dimension one, throughout the spectrum at arbitrary disorder. We also prove that exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies spectral localization. These results complete the analogy with the self-adjoint case where dynamical localization is known to be true in the same three regimes.

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.

A mixing evolution model for bidirectional microblog user networks

NASA Astrophysics Data System (ADS)

Yuan, Wei-Guo; Liu, Yun

2015-08-01

Microblogs have been widely used as a new form of online social networking. Based on the user profile data collected from Sina Weibo, we find that the number of microblog user bidirectional friends approximately corresponds with the lognormal distribution. We then build two microblog user networks with real bidirectional relationships, both of which have not only small-world and scale-free but also some special properties, such as double power-law degree distribution, disassortative network, hierarchical and rich-club structure. Moreover, by detecting the community structures of the two real networks, we find both of their community scales follow an exponential distribution. Based on the empirical analysis, we present a novel evolution network model with mixed connection rules, including lognormal fitness preferential and random attachment, nearest neighbor interconnected in the same community, and global random associations in different communities. The simulation results show that our model is consistent with real network in many topology features.

Resistance distribution in the hopping percolation model.

PubMed

Strelniker, Yakov M; Havlin, Shlomo; Berkovits, Richard; Frydman, Aviad

2005-07-01

We study the distribution function P (rho) of the effective resistance rho in two- and three-dimensional random resistor networks of linear size L in the hopping percolation model. In this model each bond has a conductivity taken from an exponential form sigma proportional to exp (-kappar) , where kappa is a measure of disorder and r is a random number, 0< or = r < or =1 . We find that in both the usual strong-disorder regime L/ kappa(nu) >1 (not sensitive to removal of any single bond) and the extreme-disorder regime L/ kappa(nu) <1 (very sensitive to such a removal) the distribution depends only on L/kappa(nu) and can be well approximated by a log-normal function with dispersion b kappa(nu) /L , where b is a coefficient which depends on the type of lattice, and nu is the correlation critical exponent.

Exponential Sum-Fitting of Dwell-Time Distributions without Specifying Starting Parameters

PubMed Central

Landowne, David; Yuan, Bin; Magleby, Karl L.

2013-01-01

Fitting dwell-time distributions with sums of exponentials is widely used to characterize histograms of open- and closed-interval durations recorded from single ion channels, as well as for other physical phenomena. However, it can be difficult to identify the contributing exponential components. Here we extend previous methods of exponential sum-fitting to present a maximum-likelihood approach that consistently detects all significant exponentials without the need for user-specified starting parameters. Instead of searching for exponentials, the fitting starts with a very large number of initial exponentials with logarithmically spaced time constants, so that none are missed. Maximum-likelihood fitting then determines the areas of all the initial exponentials keeping the time constants fixed. In an iterative manner, with refitting after each step, the analysis then removes exponentials with negligible area and combines closely spaced adjacent exponentials, until only those exponentials that make significant contributions to the dwell-time distribution remain. There is no limit on the number of significant exponentials and no starting parameters need be specified. We demonstrate fully automated detection for both experimental and simulated data, as well as for classical exponential-sum-fitting problems. PMID:23746510

A Simulation of the ECSS Help Desk with the Erlang a Model

DTIC Science & Technology

2011-03-01

a popular distribution is the exponential distribution as shown in Figure 3. Figure 3: Exponential Distribution ( Bourke , 2001) Exponential...System Sciences, Vol 8, 235B. Bourke , P. (2001, January). Miscellaneous Functions. Retrieved January 22, 2011, from http://local.wasp.uwa.edu.au

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.

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.

Power law versus exponential state transition dynamics: application to sleep-wake architecture.

PubMed

Chu-Shore, Jesse; Westover, M Brandon; Bianchi, Matt T

2010-12-02

Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot. To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the "incorrect" model over a range of parameters. The "zone of mimicry" of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions. Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.

Observation of arrival times of EAS with energies or = 6 x 10 (14) eV

NASA Technical Reports Server (NTRS)

Sun, L.

1985-01-01

The Earth's atmosphere is continually being bombarded by primary cosmic ray particles which are generally believed to be high-energy nuclei. The fact that the majority of cosmic ray primaries are charged particles and that space is permeated with random magnetic fields, means that the particles do not travel in straight lines. The arrival time distribution of EAS may also transfer some information about the primary particles. Actually, if the particles come to our Earth in a completely random process, the arrival time distribution of pairs of successive particles should fit an exponential law. The work reported here was arried out at Sydney University from May 1982 to January 1983. All the data are used to plot the arrival-time distribution of the events, that is, the distribution of time-separation between consecutive events on a 1 minute bin size. During this period more than 2300 showers were recorded. The results are discussed and compared with that of some other experiments.

Temporal complexity in emission from Anderson localized lasers

NASA Astrophysics Data System (ADS)

Kumar, Randhir; Balasubrahmaniyam, M.; Alee, K. Shadak; Mujumdar, Sushil

2017-12-01

Anderson localization lasers exploit resonant cavities formed due to structural disorder. The inherent randomness in the structure of these cavities realizes a probability distribution in all cavity parameters such as quality factors, mode volumes, mode structures, and so on, implying resultant statistical fluctuations in the temporal behavior. Here we provide direct experimental measurements of temporal width distributions of Anderson localization lasing pulses in intrinsically and extrinsically disordered coupled-microresonator arrays. We first illustrate signature exponential decays in the spatial intensity distributions of the lasing modes that quantify their localized character, and then measure the temporal width distributions of the pulsed emission over several configurations. We observe a dependence of temporal widths on the disorder strength, wherein the widths show a single-peaked, left-skewed distribution in extrinsic disorder and a dual-peaked distribution in intrinsic disorder. We propose a model based on coupled rate equations for an emitter and an Anderson cavity with a random mode structure, which gives excellent quantitative and qualitative agreement with the experimental observations. The experimental and theoretical analyses bring to the fore the temporal complexity in Anderson-localization-based lasing systems.

On the gap between an empirical distribution and an exponential distribution of waiting times for price changes in a financial market

NASA Astrophysics Data System (ADS)

Sazuka, Naoya

2007-03-01

We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high-frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between trades are not exponentially distributed. Here we show that our data is well approximated by a Weibull distribution rather than an exponential distribution in the non-asymptotic regime. Moreover, we quantitatively evaluate how much an empirical data is far from an exponential distribution using a Weibull fit. Finally, we discuss a transition between a Weibull-law and a power-law in the long time asymptotic regime.

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

NASA Astrophysics Data System (ADS)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

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

PubMed

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

2012-01-01

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

Complex growing networks with intrinsic vertex fitness

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

Bedogne, C.; Rodgers, G. J.

2006-10-15

One of the major questions in complex network research is to identify the range of mechanisms by which a complex network can self organize into a scale-free state. In this paper we investigate the interplay between a fitness linking mechanism and both random and preferential attachment. In our models, each vertex is assigned a fitness x, drawn from a probability distribution {rho}(x). In Model A, at each time step a vertex is added and joined to an existing vertex, selected at random, with probability p and an edge is introduced between vertices with fitnesses x and y, with a ratemore » f(x,y), with probability 1-p. Model B differs from Model A in that, with probability p, edges are added with preferential attachment rather than randomly. The analysis of Model A shows that, for every fixed fitness x, the network's degree distribution decays exponentially. In Model B we recover instead a power-law degree distribution whose exponent depends only on p, and we show how this result can be generalized. The properties of a number of particular networks are examined.« less

Incorporation of nonlinear thermorheological complexity into the phenomenologies of structural relaxation.

PubMed

Hodge, Ian M

2005-09-22

A distribution of activation energies is introduced into the nonlinear Adam-Gibbs ("Hodge-Scherer") phenomenology for structural relaxation. The resulting dependencies of the stretched exponential beta parameter on thermodynamic temperature and fictive temperature (nonlinear thermorheological complexity) are derived. No additional adjustable parameters are introduced, and contact is made with the predictions of the random first-order transition theory of aging of Lubchenko and Wolynes [J. Chem. Physics121, 2852 (2004)].

Inflation with a graceful exit in a random landscape

NASA Astrophysics Data System (ADS)

Pedro, F. G.; Westphal, A.

2017-03-01

We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N ≪ 10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.

Stationary Random Metrics on Hierarchical Graphs Via {(min,+)}-type Recursive Distributional Equations

NASA Astrophysics Data System (ADS)

Khristoforov, Mikhail; Kleptsyn, Victor; Triestino, Michele

2016-07-01

This paper is inspired by the problem of understanding in a mathematical sense the Liouville quantum gravity on surfaces. Here we show how to define a stationary random metric on self-similar spaces which are the limit of nice finite graphs: these are the so-called hierarchical graphs. They possess a well-defined level structure and any level is built using a simple recursion. Stopping the construction at any finite level, we have a discrete random metric space when we set the edges to have random length (using a multiplicative cascade with fixed law {m}). We introduce a tool, the cut-off process, by means of which one finds that renormalizing the sequence of metrics by an exponential factor, they converge in law to a non-trivial metric on the limit space. Such limit law is stationary, in the sense that glueing together a certain number of copies of the random limit space, according to the combinatorics of the brick graph, the obtained random metric has the same law when rescaled by a random factor of law {m} . In other words, the stationary random metric is the solution of a distributional equation. When the measure m has continuous positive density on {mathbf{R}+}, the stationary law is unique up to rescaling and any other distribution tends to a rescaled stationary law under the iterations of the hierarchical transformation. We also investigate topological and geometric properties of the random space when m is log-normal, detecting a phase transition influenced by the branching random walk associated to the multiplicative cascade.

Explaining mortality rate plateaus

PubMed Central

Weitz, Joshua S.; Fraser, Hunter B.

2001-01-01

We propose a stochastic model of aging to explain deviations from exponential growth in mortality rates commonly observed in empirical studies. Mortality rate plateaus are explained as a generic consequence of considering death in terms of first passage times for processes undergoing a random walk with drift. Simulations of populations with age-dependent distributions of viabilities agree with a wide array of experimental results. The influence of cohort size is well accounted for by the stochastic nature of the model. PMID:11752476

Stochastic modelling of a single ion channel: an alternating renewal approach with application to limited time resolution.

PubMed

Milne, R K; Yeo, G F; Edeson, R O; Madsen, B W

1988-04-22

Stochastic models of ion channels have been based largely on Markov theory where individual states and transition rates must be specified, and sojourn-time densities for each state are constrained to be exponential. This study presents an approach based on random-sum methods and alternating-renewal theory, allowing individual states to be grouped into classes provided the successive sojourn times in a given class are independent and identically distributed. Under these conditions Markov models form a special case. The utility of the approach is illustrated by considering the effects of limited time resolution (modelled by using a discrete detection limit, xi) on the properties of observable events, with emphasis on the observed open-time (xi-open-time). The cumulants and Laplace transform for a xi-open-time are derived for a range of Markov and non-Markov models; several useful approximations to the xi-open-time density function are presented. Numerical studies show that the effects of limited time resolution can be extreme, and also highlight the relative importance of the various model parameters. The theory could form a basis for future inferential studies in which parameter estimation takes account of limited time resolution in single channel records. Appendixes include relevant results concerning random sums and a discussion of the role of exponential distributions in Markov models.

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.

Decay of random correlation functions for unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Benedicks, Michael; Maume-Deschamps, Véronique

2000-10-01

Since the pioneering results of Jakobson and subsequent work by Benedicks-Carleson and others, it is known that quadratic maps tfa( χ) = a - χ2 admit a unique absolutely continuous invariant measure for a positive measure set of parameters a. For topologically mixing tfa, Young and Keller-Nowicki independently proved exponential decay of correlation functions for this a.c.i.m. and smooth observables. We consider random compositions of small perturbations tf + ωt, with tf = tfa or another unimodal map satisfying certain nonuniform hyperbolicity axioms, and ωt chosen independently and identically in [-ɛ, ɛ]. Baladi-Viana showed exponential mixing of the associated Markov chain, i.e., averaging over all random itineraries. We obtain stretched exponential bounds for the random correlation functions of Lipschitz observables for the sample measure μωof almost every itinerary.

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

NASA Astrophysics Data System (ADS)

Low, Yeh Ching; Ong, Seng Huat

2016-06-01

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

Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: a basis for q-exponential distributions.

PubMed

Abe, Sumiyoshi

2002-10-01

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Rényi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.

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

Treesearch

Paul A. Murphy; Robert M. Farrar

1981-01-01

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

Subcritical Multiplicative Chaos for Regularized Counting Statistics from Random Matrix Theory

NASA Astrophysics Data System (ADS)

Lambert, Gaultier; Ostrovsky, Dmitry; Simm, Nick

2018-05-01

For an {N × N} Haar distributed random unitary matrix U N , we consider the random field defined by counting the number of eigenvalues of U N in a mesoscopic arc centered at the point u on the unit circle. We prove that after regularizing at a small scale {ɛN > 0}, the renormalized exponential of this field converges as N \\to ∞ to a Gaussian multiplicative chaos measure in the whole subcritical phase. We discuss implications of this result for obtaining a lower bound on the maximum of the field. We also show that the moments of the total mass converge to a Selberg-like integral and by taking a further limit as the size of the arc diverges, we establish part of the conjectures in Ostrovsky (Nonlinearity 29(2):426-464, 2016). By an analogous construction, we prove that the multiplicative chaos measure coming from the sine process has the same distribution, which strongly suggests that this limiting object should be universal. Our approach to the L 1-phase is based on a generalization of the construction in Berestycki (Electron Commun Probab 22(27):12, 2017) to random fields which are only asymptotically Gaussian. In particular, our method could have applications to other random fields coming from either random matrix theory or a different context.

Distributed Secure Coordinated Control for Multiagent Systems Under Strategic Attacks.

PubMed

Feng, Zhi; Wen, Guanghui; Hu, Guoqiang

2017-05-01

This paper studies a distributed secure consensus tracking control problem for multiagent systems subject to strategic cyber attacks modeled by a random Markov process. A hybrid stochastic secure control framework is established for designing a distributed secure control law such that mean-square exponential consensus tracking is achieved. A connectivity restoration mechanism is considered and the properties on attack frequency and attack length rate are investigated, respectively. Based on the solutions of an algebraic Riccati equation and an algebraic Riccati inequality, a procedure to select the control gains is provided and stability analysis is studied by using Lyapunov's method.. The effect of strategic attacks on discrete-time systems is also investigated. Finally, numerical examples are provided to illustrate the effectiveness of theoretical analysis.

Long period pseudo random number sequence generator

NASA Technical Reports Server (NTRS)

Wang, Charles C. (Inventor)

1989-01-01

A circuit for generating a sequence of pseudo random numbers, (A sub K). There is an exponentiator in GF(2 sup m) for the normal basis representation of elements in a finite field GF(2 sup m) each represented by m binary digits and having two inputs and an output from which the sequence (A sub K). Of pseudo random numbers is taken. One of the two inputs is connected to receive the outputs (E sub K) of maximal length shift register of n stages. There is a switch having a pair of inputs and an output. The switch outputs is connected to the other of the two inputs of the exponentiator. One of the switch inputs is connected for initially receiving a primitive element (A sub O) in GF(2 sup m). Finally, there is a delay circuit having an input and an output. The delay circuit output is connected to the other of the switch inputs and the delay circuit input is connected to the output of the exponentiator. Whereby after the exponentiator initially receives the primitive element (A sub O) in GF(2 sup m) through the switch, the switch can be switched to cause the exponentiator to receive as its input a delayed output A(K-1) from the exponentiator thereby generating (A sub K) continuously at the output of the exponentiator. The exponentiator in GF(2 sup m) is novel and comprises a cyclic-shift circuit; a Massey-Omura multiplier; and, a control logic circuit all operably connected together to perform the function U(sub i) = 92(sup i) (for n(sub i) = 1 or 1 (for n(subi) = 0).

Bayesian exponential random graph modelling of interhospital patient referral networks.

PubMed

Caimo, Alberto; Pallotti, Francesca; Lomi, Alessandro

2017-08-15

Using original data that we have collected on referral relations between 110 hospitals serving a large regional community, we show how recently derived Bayesian exponential random graph models may be adopted to illuminate core empirical issues in research on relational coordination among healthcare organisations. We show how a rigorous Bayesian computation approach supports a fully probabilistic analytical framework that alleviates well-known problems in the estimation of model parameters of exponential random graph models. We also show how the main structural features of interhospital patient referral networks that prior studies have described can be reproduced with accuracy by specifying the system of local dependencies that produce - but at the same time are induced by - decentralised collaborative arrangements between hospitals. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

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

NASA Astrophysics Data System (ADS)

Iskandar, I.

2018-03-01

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

Does the Australian desert ant Melophorus bagoti approximate a Lévy search by an intrinsic bi-modal walk?

PubMed

Reynolds, Andy M; Schultheiss, Patrick; Cheng, Ken

2014-01-07

We suggest that the Australian desert ant Melophorus bagoti approximates a Lévy search pattern by using an intrinsic bi-exponential walk and does so when a Lévy search pattern is advantageous. When attempting to locate its nest, M. bagoti adopt a stereotypical search pattern. These searches begin at the location where the ant expects to find the nest, and comprise loops that start and end at this location, and are directed in different azimuthal directions. Loop lengths are exponentially distributed when searches are in visually familiar surroundings and are well described by a mixture of two exponentials when searches are in unfamiliar landscapes. The latter approximates a power-law distribution, the hallmark of a Lévy search. With the aid of a simple analytically tractable theory, we show that an exponential loop-length distribution is advantageous when the distance to the nest can be estimated with some certainty and that a bi-exponential distribution is advantageous when there is considerable uncertainty regarding the nest location. The best bi-exponential search patterns are shown to be those that come closest to approximating advantageous Lévy looping searches. The bi-exponential search patterns of M. bagoti are found to approximate advantageous Lévy search patterns. Copyright © 2013. Published by Elsevier Ltd.

The Extended Erlang-Truncated Exponential distribution: Properties and application to rainfall data.

PubMed

Okorie, I E; Akpanta, A C; Ohakwe, J; Chikezie, D C

2017-06-01

The Erlang-Truncated Exponential ETE distribution is modified and the new lifetime distribution is called the Extended Erlang-Truncated Exponential EETE distribution. Some statistical and reliability properties of the new distribution are given and the method of maximum likelihood estimate was proposed for estimating the model parameters. The usefulness and flexibility of the EETE distribution was illustrated with an uncensored data set and its fit was compared with that of the ETE and three other three-parameter distributions. Results based on the minimized log-likelihood ([Formula: see text]), Akaike information criterion (AIC), Bayesian information criterion (BIC) and the generalized Cramér-von Mises [Formula: see text] statistics shows that the EETE distribution provides a more reasonable fit than the one based on the other competing distributions.

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.

Random Walks on Homeo( S 1)

NASA Astrophysics Data System (ADS)

Malicet, Dominique

2017-12-01

In this paper, we study random walks {g_n=f_{n-1}\\ldots f_0} on the group Homeo ( S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure {ν}. We prove that under the only condition that there is no probability measure invariant by {ν}-almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on {ν} were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k 's. We deduce various dynamical consequences on the random walk ( g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana's invariance principle, working for continuous cocycles on a space fibred in circles.

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

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.

Compiling probabilistic, bio-inspired circuits on a field programmable analog array

PubMed Central

Marr, Bo; Hasler, Jennifer

2014-01-01

A field programmable analog array (FPAA) is presented as an energy and computational efficiency engine: a mixed mode processor for which functions can be compiled at significantly less energy costs using probabilistic computing circuits. More specifically, it will be shown that the core computation of any dynamical system can be computed on the FPAA at significantly less energy per operation than a digital implementation. A stochastic system that is dynamically controllable via voltage controlled amplifier and comparator thresholds is implemented, which computes Bernoulli random variables. From Bernoulli variables it is shown exponentially distributed random variables, and random variables of an arbitrary distribution can be computed. The Gillespie algorithm is simulated to show the utility of this system by calculating the trajectory of a biological system computed stochastically with this probabilistic hardware where over a 127X performance improvement over current software approaches is shown. The relevance of this approach is extended to any dynamical system. The initial circuits and ideas for this work were generated at the 2008 Telluride Neuromorphic Workshop. PMID:24847199

Essays on the statistical mechanics of the labor market and implications for the distribution of earned income

NASA Astrophysics Data System (ADS)

Schneider, Markus P. A.

This dissertation contributes to two areas in economics: the understanding of the distribution of earned income and to Bayesian analysis of distributional data. Recently, physicists claimed that the distribution of earned income is exponential (see Yakovenko, 2009). The first chapter explores the perspective that the economy is a statistical mechanical system and the implication for labor market outcomes is considered critically. The robustness of the empirical results that lead to the physicists' claims, the significance of the exponential distribution in statistical mechanics, and the case for a conservation law in economics are discussed. The conclusion reached is that physicists' conception of the economy is too narrow even within their chosen framework, but that their overall approach is insightful. The dual labor market theory of segmented labor markets is invoked to understand why the observed distribution may be a mixture of distributional components, corresponding to different generating mechanisms described in Reich et al. (1973). The application of informational entropy in chapter II connects this work to Bayesian analysis and maximum entropy econometrics. The analysis follows E. T. Jaynes's treatment of Wolf's dice data, but is applied to the distribution of earned income based on CPS data. The results are calibrated to account for rounded survey responses using a simple simulation, and answer the graphical analyses by physicists. The results indicate that neither the income distribution of all respondents nor of the subpopulation used by physicists appears to be exponential. The empirics do support the claim that a mixture with exponential and log-normal distributional components ts the data. In the final chapter, a log-linear model is used to fit the exponential to the earned income distribution. Separating the CPS data by gender and marital status reveals that the exponential is only an appropriate model for a limited number of subpopulations, namely the never married and women. The estimated parameter for never-married men's incomes is significantly different from the parameter estimated for never-married women, implying that either the combined distribution is not exponential or that the individual distributions are not exponential. However, it substantiates the existence of a persistent gender income gap among the never-married. References: Reich, M., D. M. Gordon, and R. C. Edwards (1973). A Theory of Labor Market Segmentation. Quarterly Journal of Economics 63, 359-365. Yakovenko, V. M. (2009). Econophysics, Statistical Mechanics Approach to. In R. A. Meyers (Ed.), Encyclopedia of Complexity and System Science. Springer.

Persistent random walk of cells involving anomalous effects and random death

NASA Astrophysics Data System (ADS)

Fedotov, Sergei; Tan, Abby; Zubarev, Andrey

2015-04-01

The purpose of this paper is to implement a random death process into a persistent random walk model which produces sub-ballistic superdiffusion (Lévy walk). We develop a stochastic two-velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction. It is assumed that the switching rate is a decreasing function of residence (running) time. This assumption leads to the power law for the velocity switching time distribution. This describes the anomalous persistence of cell motility: the longer the cell moves in one direction, the smaller the switching probability to another direction becomes. We derive master equations for the cell densities with the generalized switching terms involving the tempered fractional material derivatives. We show that the random death of cells has an important implication for the transport process through tempering of the superdiffusive process. In the long-time limit we write stationary master equations in terms of exponentially truncated fractional derivatives in which the rate of death plays the role of tempering of a Lévy jump distribution. We find the upper and lower bounds for the stationary profiles corresponding to the ballistic transport and diffusion with the death-rate-dependent diffusion coefficient. Monte Carlo simulations confirm these bounds.

Random field assessment of nanoscopic inhomogeneity of bone

PubMed Central

Dong, X. Neil; Luo, Qing; Sparkman, Daniel M.; Millwater, Harry R.; Wang, Xiaodu

2010-01-01

Bone quality is significantly correlated with the inhomogeneous distribution of material and ultrastructural properties (e.g., modulus and mineralization) of the tissue. Current techniques for quantifying inhomogeneity consist of descriptive statistics such as mean, standard deviation and coefficient of variation. However, these parameters do not describe the spatial variations of bone properties. The objective of this study was to develop a novel statistical method to characterize and quantitatively describe the spatial variation of bone properties at ultrastructural levels. To do so, a random field defined by an exponential covariance function was used to present the spatial uncertainty of elastic modulus by delineating the correlation of the modulus at different locations in bone lamellae. The correlation length, a characteristic parameter of the covariance function, was employed to estimate the fluctuation of the elastic modulus in the random field. Using this approach, two distribution maps of the elastic modulus within bone lamellae were generated using simulation and compared with those obtained experimentally by a combination of atomic force microscopy and nanoindentation techniques. The simulation-generated maps of elastic modulus were in close agreement with the experimental ones, thus validating the random field approach in defining the inhomogeneity of elastic modulus in lamellae of bone. Indeed, generation of such random fields will facilitate multi-scale modeling of bone in more pragmatic details. PMID:20817128

Bandwagon effects and error bars in particle physics

NASA Astrophysics Data System (ADS)

Jeng, Monwhea

2007-02-01

We study historical records of experiments on particle masses, lifetimes, and widths, both for signs of expectation bias, and to compare actual errors with reported error bars. We show that significant numbers of particle properties exhibit "bandwagon effects": reported values show trends and clustering as a function of the year of publication, rather than random scatter about the mean. While the total amount of clustering is significant, it is also fairly small; most individual particle properties do not display obvious clustering. When differences between experiments are compared with the reported error bars, the deviations do not follow a normal distribution, but instead follow an exponential distribution for up to ten standard deviations.

A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths

NASA Astrophysics Data System (ADS)

Le Caër, Gérard

2010-08-01

A constrained diffusive random walk of n steps in ℝ d and a random flight in ℝ d , which are equivalent, were investigated independently in recent papers (J. Stat. Phys. 127:813, 2007; J. Theor. Probab. 20:769, 2007, and J. Stat. Phys. 131:1039, 2008). The n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation. Conditioned on the sum of their lengths being equal to a given value l, closed-form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d=1,2,4. Uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2D and of two steps in 4D. The previous walk is generalized by considering step lengths which have independent and identical gamma distributions with a shape parameter q>0. Given the total walk length being equal to 1, the step lengths have a Dirichlet distribution whose parameters are all equal to q. The walk and the flight above correspond to q=1. Simple analytical expressions are obtained for any d≥2 and n≥2 for the endpoint distributions of two families of walks whose q are integers or half-integers which depend solely on d. These endpoint distributions have a simple geometrical interpretation. Expressed for a two-step planar walk whose q=1, it means that the distribution of the endpoint on a disc of radius 1 is identical to the distribution of the projection on the disc of a point M uniformly distributed over the surface of the 3D unit sphere. Five additional walks, with a uniform distribution of the endpoint in the inside of a ball, are found from known finite integrals of products of powers and Bessel functions of the first kind. They include four different walks in ℝ3, two of two steps and two of three steps, and one walk of two steps in ℝ4. Pearson-Liouville random walks, obtained by distributing the total lengths of the previous Pearson-Dirichlet walks according to some specified probability law are finally discussed. Examples of unconstrained random walks, whose step lengths are gamma distributed, are more particularly considered.

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

Monte Carlo Sampling in Fractal Landscapes

NASA Astrophysics Data System (ADS)

Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.

2013-05-01

We design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems. We show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest Lyapunov exponent of the chaotic system. We propose a generalization of the Wang-Landau algorithm which constructs not only the density of states (transient time distribution) but also the correct step length. As a result, we obtain a flat-histogram Monte Carlo method which samples fractal landscapes in polynomial time, a dramatic improvement over the exponential scaling of traditional uniform-sampling methods. Our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions.

Multiserver Queueing Model subject to Single Exponential Vacation

NASA Astrophysics Data System (ADS)

Vijayashree, K. V.; Janani, B.

2018-04-01

A multi-server queueing model subject to single exponential vacation is considered. The arrivals are allowed to join the queue according to a Poisson distribution and services takes place according to an exponential distribution. Whenever the system becomes empty, all the servers goes for a vacation and returns back after a fixed interval of time. The servers then starts providing service if there are waiting customers otherwise they will wait to complete the busy period. The vacation times are also assumed to be exponentially distributed. In this paper, the stationary and transient probabilities for the number of customers during ideal and functional state of the server are obtained explicitly. Also, numerical illustrations are added to visualize the effect of various parameters.

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

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Cocco, Simona; Monasson, Rémi

2015-11-01

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

Analysis of backward error recovery for concurrent processes with recovery blocks

NASA Technical Reports Server (NTRS)

Shin, K. G.; Lee, Y. H.

1982-01-01

Three different methods of implementing recovery blocks (RB's). These are the asynchronous, synchronous, and the pseudo recovery point implementations. Pseudo recovery points so that unbounded rollback may be avoided while maintaining process autonomy are proposed. Probabilistic models for analyzing these three methods under standard assumptions in computer performance analysis, i.e., exponential distributions for related random variables were developed. The interval between two successive recovery lines for asynchronous RB's mean loss in computation power for the synchronized method, and additional overhead and rollback distance in case PRP's are used were estimated.

Random local temporal structure of category fluency responses.

PubMed

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

2012-04-01

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

Multivariate generalized hidden Markov regression models with random covariates: Physical exercise in an elderly population.

PubMed

Punzo, Antonio; Ingrassia, Salvatore; Maruotti, Antonello

2018-04-22

A time-varying latent variable model is proposed to jointly analyze multivariate mixed-support longitudinal data. The proposal can be viewed as an extension of hidden Markov regression models with fixed covariates (HMRMFCs), which is the state of the art for modelling longitudinal data, with a special focus on the underlying clustering structure. HMRMFCs are inadequate for applications in which a clustering structure can be identified in the distribution of the covariates, as the clustering is independent from the covariates distribution. Here, hidden Markov regression models with random covariates are introduced by explicitly specifying state-specific distributions for the covariates, with the aim of improving the recovering of the clusters in the data with respect to a fixed covariates paradigm. The hidden Markov regression models with random covariates class is defined focusing on the exponential family, in a generalized linear model framework. Model identifiability conditions are sketched, an expectation-maximization algorithm is outlined for parameter estimation, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients, as well as of the hidden path parameters, are evaluated through simulation experiments and compared with those of HMRMFCs. The method is applied to physical activity data. Copyright © 2018 John Wiley & Sons, Ltd.

A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang Sang; Marsden, Jerrold E.

2010-09-01

We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

Randomized central limit theorems: A unified theory.

PubMed

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

Randomized central limit theorems: A unified theory

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

A Simulation Study Comparing Epidemic Dynamics on Exponential Random Graph and Edge-Triangle Configuration Type Contact Network Models

PubMed Central

Rolls, David A.; Wang, Peng; McBryde, Emma; Pattison, Philippa; Robins, Garry

2015-01-01

We compare two broad types of empirically grounded random network models in terms of their abilities to capture both network features and simulated Susceptible-Infected-Recovered (SIR) epidemic dynamics. The types of network models are exponential random graph models (ERGMs) and extensions of the configuration model. We use three kinds of empirical contact networks, chosen to provide both variety and realistic patterns of human contact: a highly clustered network, a bipartite network and a snowball sampled network of a “hidden population”. In the case of the snowball sampled network we present a novel method for fitting an edge-triangle model. In our results, ERGMs consistently capture clustering as well or better than configuration-type models, but the latter models better capture the node degree distribution. Despite the additional computational requirements to fit ERGMs to empirical networks, the use of ERGMs provides only a slight improvement in the ability of the models to recreate epidemic features of the empirical network in simulated SIR epidemics. Generally, SIR epidemic results from using configuration-type models fall between those from a random network model (i.e., an Erdős-Rényi model) and an ERGM. The addition of subgraphs of size four to edge-triangle type models does improve agreement with the empirical network for smaller densities in clustered networks. Additional subgraphs do not make a noticeable difference in our example, although we would expect the ability to model cliques to be helpful for contact networks exhibiting household structure. PMID:26555701

Source-Independent Quantum Random Number Generation

NASA Astrophysics Data System (ADS)

Cao, Zhu; Zhou, Hongyi; Yuan, Xiao; Ma, Xiongfeng

2016-01-01

Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts—a randomness source and its readout. The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness. However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output. To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted. In our randomness analysis, we make no assumptions about the dimension of the source. For instance, multiphoton emissions are allowed in optical implementations. Our analysis takes into account the finite-key effect with the composable security definition. In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit. In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 ×103 bit /s .

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

NASA Astrophysics Data System (ADS)

Li, Zhi; Brissette, Fancois; Chen, Jie

2013-04-01

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

Persistence of exponential bed thickness distributions in the stratigraphic record: Experiments and theory

NASA Astrophysics Data System (ADS)

Straub, K. M.; Ganti, V. K.; Paola, C.; Foufoula-Georgiou, E.

2010-12-01

Stratigraphy preserved in alluvial basins houses the most complete record of information necessary to reconstruct past environmental conditions. Indeed, the character of the sedimentary record is inextricably related to the surface processes that formed it. In this presentation we explore how the signals of surface processes are recorded in stratigraphy through the use of physical and numerical experiments. We focus on linking surface processes to stratigraphy in 1D by quantifying the probability distributions of processes that govern the evolution of depositional systems to the probability distribution of preserved bed thicknesses. In this study we define a bed as a package of sediment bounded above and below by erosional surfaces. In a companion presentation we document heavy-tailed statistics of erosion and deposition from high-resolution temporal elevation data recorded during a controlled physical experiment. However, the heavy tails in the magnitudes of erosional and depositional events are not preserved in the experimental stratigraphy. Similar to many bed thickness distributions reported in field studies we find that an exponential distribution adequately describes the thicknesses of beds preserved in our experiment. We explore the generation of exponential bed thickness distributions from heavy-tailed surface statistics using 1D numerical models. These models indicate that when the full distribution of elevation fluctuations (both erosional and depositional events) is symmetrical, the resulting distribution of bed thicknesses is exponential in form. Finally, we illustrate that a predictable relationship exists between the coefficient of variation of surface elevation fluctuations and the scale-parameter of the resulting exponential distribution of bed thicknesses.

Exponential model normalization for electrical capacitance tomography with external electrodes under gap permittivity conditions

NASA Astrophysics Data System (ADS)

Baidillah, Marlin R.; Takei, Masahiro

2017-06-01

A nonlinear normalization model which is called exponential model for electrical capacitance tomography (ECT) with external electrodes under gap permittivity conditions has been developed. The exponential model normalization is proposed based on the inherently nonlinear relationship characteristic between the mixture permittivity and the measured capacitance due to the gap permittivity of inner wall. The parameters of exponential equation are derived by using an exponential fitting curve based on the simulation and a scaling function is added to adjust the experiment system condition. The exponential model normalization was applied to two dimensional low and high contrast dielectric distribution phantoms by using simulation and experimental studies. The proposed normalization model has been compared with other normalization models i.e. Parallel, Series, Maxwell and Böttcher models. Based on the comparison of image reconstruction results, the exponential model is reliable to predict the nonlinear normalization of measured capacitance in term of low and high contrast dielectric distribution.

Fragment size distribution statistics in dynamic fragmentation of laser shock-loaded tin

NASA Astrophysics Data System (ADS)

He, Weihua; Xin, Jianting; Zhao, Yongqiang; Chu, Genbai; Xi, Tao; Shui, Min; Lu, Feng; Gu, Yuqiu

2017-06-01

This work investigates the geometric statistics method to characterize the size distribution of tin fragments produced in the laser shock-loaded dynamic fragmentation process. In the shock experiments, the ejection of the tin sample with etched V-shape groove in the free surface are collected by the soft recovery technique. Subsequently, the produced fragments are automatically detected with the fine post-shot analysis techniques including the X-ray micro-tomography and the improved watershed method. To characterize the size distributions of the fragments, a theoretical random geometric statistics model based on Poisson mixtures is derived for dynamic heterogeneous fragmentation problem, which reveals linear combinational exponential distribution. The experimental data related to fragment size distributions of the laser shock-loaded tin sample are examined with the proposed theoretical model, and its fitting performance is compared with that of other state-of-the-art fragment size distribution models. The comparison results prove that our proposed model can provide far more reasonable fitting result for the laser shock-loaded tin.

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.

Landscape movements of Anopheles gambiae malaria vector mosquitoes in rural Gambia.

PubMed

Thomas, Christopher J; Cross, Dónall E; Bøgh, Claus

2013-01-01

For malaria control in Africa it is crucial to characterise the dispersal of its most efficient vector, Anopheles gambiae, in order to target interventions and assess their impact spatially. Our study is, we believe, the first to present a statistical model of dispersal probability against distance from breeding habitat to human settlements for this important disease vector. We undertook post-hoc analyses of mosquito catches made in The Gambia to derive statistical dispersal functions for An. gambiae sensu lato collected in 48 villages at varying distances to alluvial larval habitat along the River Gambia. The proportion dispersing declined exponentially with distance, and we estimated that 90% of movements were within 1.7 km. Although a 'heavy-tailed' distribution is considered biologically more plausible due to active dispersal by mosquitoes seeking blood meals, there was no statistical basis for choosing it over a negative exponential distribution. Using a simple random walk model with daily survival and movements previously recorded in Burkina Faso, we were able to reproduce the dispersal probabilities observed in The Gambia. Our results provide an important quantification of the probability of An. gambiae s.l. dispersal in a rural African setting typical of many parts of the continent. However, dispersal will be landscape specific and in order to generalise to other spatial configurations of habitat and hosts it will be necessary to produce tractable models of mosquito movements for operational use. We show that simple random walk models have potential. Consequently, there is a pressing need for new empirical studies of An. gambiae survival and movements in different settings to drive this development.

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.

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...

Enhancing the Selection of Backoff Interval Using Fuzzy Logic over Wireless Ad Hoc Networks

PubMed Central

Ranganathan, Radha; Kannan, Kathiravan

2015-01-01

IEEE 802.11 is the de facto standard for medium access over wireless ad hoc network. The collision avoidance mechanism (i.e., random binary exponential backoff—BEB) of IEEE 802.11 DCF (distributed coordination function) is inefficient and unfair especially under heavy load. In the literature, many algorithms have been proposed to tune the contention window (CW) size. However, these algorithms make every node select its backoff interval between [0, CW] in a random and uniform manner. This randomness is incorporated to avoid collisions among the nodes. But this random backoff interval can change the optimal order and frequency of channel access among competing nodes which results in unfairness and increased delay. In this paper, we propose an algorithm that schedules the medium access in a fair and effective manner. This algorithm enhances IEEE 802.11 DCF with additional level of contention resolution that prioritizes the contending nodes according to its queue length and waiting time. Each node computes its unique backoff interval using fuzzy logic based on the input parameters collected from contending nodes through overhearing. We evaluate our algorithm against IEEE 802.11, GDCF (gentle distributed coordination function) protocols using ns-2.35 simulator and show that our algorithm achieves good performance. PMID:25879066

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.

Random field assessment of nanoscopic inhomogeneity of bone.

PubMed

Dong, X Neil; Luo, Qing; Sparkman, Daniel M; Millwater, Harry R; Wang, Xiaodu

2010-12-01

Bone quality is significantly correlated with the inhomogeneous distribution of material and ultrastructural properties (e.g., modulus and mineralization) of the tissue. Current techniques for quantifying inhomogeneity consist of descriptive statistics such as mean, standard deviation and coefficient of variation. However, these parameters do not describe the spatial variations of bone properties. The objective of this study was to develop a novel statistical method to characterize and quantitatively describe the spatial variation of bone properties at ultrastructural levels. To do so, a random field defined by an exponential covariance function was used to represent the spatial uncertainty of elastic modulus by delineating the correlation of the modulus at different locations in bone lamellae. The correlation length, a characteristic parameter of the covariance function, was employed to estimate the fluctuation of the elastic modulus in the random field. Using this approach, two distribution maps of the elastic modulus within bone lamellae were generated using simulation and compared with those obtained experimentally by a combination of atomic force microscopy and nanoindentation techniques. The simulation-generated maps of elastic modulus were in close agreement with the experimental ones, thus validating the random field approach in defining the inhomogeneity of elastic modulus in lamellae of bone. Indeed, generation of such random fields will facilitate multi-scale modeling of bone in more pragmatic details. Copyright © 2010 Elsevier Inc. 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

Epidemics in networks: a master equation approach

NASA Astrophysics Data System (ADS)

Cotacallapa, M.; Hase, M. O.

2016-02-01

A problem closely related to epidemiology, where a subgraph of ‘infected’ links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link is able to propagate a disease/information. The relaxation timescale of this random variable is examined in both annealed and quenched limits, and the effectiveness of propagation of disease/information is analyzed. The dynamics of the model is governed by a master equation and two types of underlying network are considered: one is scale-free and the other has exponential degree distribution. We have shown that the relaxation timescale of the contagion variable has a major influence on the topology of the subgraph of infected links, which determines the efficiency of spreading of disease/information over the network.

Self-excitation of a nonlinear scalar field in a random medium

PubMed Central

Zeldovich, Ya. B.; Molchanov, S. A.; Ruzmaikin, A. A.; Sokoloff, D. D.

1987-01-01

We discuss the evolution in time of a scalar field under the influence of a random potential and diffusion. The cases of a short-correlation in time and of stationary potentials are considered. In a linear approximation and for sufficiently weak diffusion, the statistical moments of the field grow exponentially in time at growth rates that progressively increase with the order of the moment; this indicates the intermittent nature of the field. Nonlinearity halts this growth and in some cases can destroy the intermittency. However, in many nonlinear situations the intermittency is preserved: high, persistent peaks of the field exist against the background of a smooth field distribution. These widely spaced peaks may make a major contribution to the average characteristics of the field. PMID:16593872

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

Rational decisions, random matrices and spin glasses

NASA Astrophysics Data System (ADS)

Galluccio, Stefano; Bouchaud, Jean-Philippe; Potters, Marc

We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of optimal solutions is generally exponentially large, and each of them is fragile: rationality is in this case of limited use. In addition, this problem is related to spin glasses with Lévy-like (long-ranged) couplings, for which we show that the ground state is not exponentially degenerate.

Effects of random initial conditions on the dynamical scaling behaviors of a fixed-energy Manna sandpile model in one dimension

NASA Astrophysics Data System (ADS)

Kwon, Sungchul; Kim, Jin Min

2015-01-01

For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the effects of random initial conditions on the dynamical scaling behavior of an order parameter. In the FE Manna model, the density ρ of total particles is conserved, and an absorbing phase transition occurs at ρc as ρ varies. In this work, we show that, for a given ρ , random initial distributions of particles lead to the domain structure in which domains with particle densities higher and lower than ρc alternate with each other. In the domain structure, the dominant length scale is the average domain length, which increases via the coalescence of adjacent domains. At ρc, the domain structure slows down the decay of an order parameter and also causes anomalous finite-size effects, i.e., power-law decay followed by an exponential one before the quasisteady state. As a result, the interplay of particle conservation and random initial conditions causes the domain structure, which is the origin of the anomalous dynamical scaling behaviors for random initial conditions.

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

NASA Astrophysics Data System (ADS)

Sposini, Vittoria; Chechkin, Aleksei V.; Seno, Flavio; Pagnini, Gianni; Metzler, Ralf

2018-04-01

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.

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.

Multirate parallel distributed compensation of a cluster in wireless sensor and actor networks

NASA Astrophysics Data System (ADS)

Yang, Chun-xi; Huang, Ling-yun; Zhang, Hao; Hua, Wang

2016-01-01

The stabilisation problem for one of the clusters with bounded multiple random time delays and packet dropouts in wireless sensor and actor networks is investigated in this paper. A new multirate switching model is constructed to describe the feature of this single input multiple output linear system. According to the difficulty of controller design under multi-constraints in multirate switching model, this model can be converted to a Takagi-Sugeno fuzzy model. By designing a multirate parallel distributed compensation, a sufficient condition is established to ensure this closed-loop fuzzy control system to be globally exponentially stable. The solution of the multirate parallel distributed compensation gains can be obtained by solving an auxiliary convex optimisation problem. Finally, two numerical examples are given to show, compared with solving switching controller, multirate parallel distributed compensation can be obtained easily. Furthermore, it has stronger robust stability than arbitrary switching controller and single-rate parallel distributed compensation under the same conditions.

Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.

PubMed

Jin, Ick Hoon; Yuan, Ying; Liang, Faming

2013-10-01

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

Role of exponential type random invexities for asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming.

PubMed

Verma, Ram U; Seol, Youngsoo

2016-01-01

First a new notion of the random exponential Hanson-Antczak type [Formula: see text]-V-invexity is introduced, which generalizes most of the existing notions in the literature, second a random function [Formula: see text] of the second order is defined, and finally a class of asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming is established. Furthermore, several sets of asymptotic sufficiency results in which various generalized exponential type [Formula: see text]-V-invexity assumptions are imposed on certain vector functions whose components are the individual as well as some combinations of the problem functions are examined and proved. To the best of our knowledge, all the established results on the semi-infinite aspects of the multi-objective fractional programming are new, which is a significantly new emerging field of the interdisciplinary research in nature. We also observed that the investigated results can be modified and applied to several special classes of nonlinear programming problems.

Metastable dynamical patterns and their stabilization in arrays of bidirectionally coupled sigmoidal neurons

NASA Astrophysics Data System (ADS)

Horikawa, Yo

2013-12-01

Transient patterns in a bistable ring of bidirectionally coupled sigmoidal neurons were studied. When the system had a pair of spatially uniform steady solutions, the instability of unstable spatially nonuniform steady solutions decreased exponentially with the number of neurons because of the symmetry of the system. As a result, transient spatially nonuniform patterns showed dynamical metastability: Their duration increased exponentially with the number of neurons and the duration of randomly generated patterns obeyed a power-law distribution. However, these metastable dynamical patterns were easily stabilized in the presence of small variations in coupling strength. Metastable rotating waves and their pinning in the presence of asymmetry in the direction of coupling and the disappearance of metastable dynamical patterns due to asymmetry in the output function of a neuron were also examined. Further, in a two-dimensional array of neurons with nearest-neighbor coupling, intrinsically one-dimensional patterns were dominant in transients, and self-excitation in these neurons affected the metastable dynamical patterns.

Time prediction of failure a type of lamps by using general composite hazard rate model

NASA Astrophysics Data System (ADS)

Riaman; Lesmana, E.; Subartini, B.; Supian, S.

2018-03-01

This paper discusses the basic survival model estimates to obtain the average predictive value of lamp failure time. This estimate is for the parametric model, General Composite Hazard Level Model. The random time variable model used is the exponential distribution model, as the basis, which has a constant hazard function. In this case, we discuss an example of survival model estimation for a composite hazard function, using an exponential model as its basis. To estimate this model is done by estimating model parameters, through the construction of survival function and empirical cumulative function. The model obtained, will then be used to predict the average failure time of the model, for the type of lamp. By grouping the data into several intervals and the average value of failure at each interval, then calculate the average failure time of a model based on each interval, the p value obtained from the tes result is 0.3296.

Mutant number distribution in an exponentially growing population

NASA Astrophysics Data System (ADS)

Keller, Peter; Antal, Tibor

2015-01-01

We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.

Stability analysis for discrete-time stochastic memristive neural networks with both leakage and probabilistic delays.

PubMed

Liu, Hongjian; Wang, Zidong; Shen, Bo; Huang, Tingwen; Alsaadi, Fuad E

2018-06-01

This paper is concerned with the globally exponential stability problem for a class of discrete-time stochastic memristive neural networks (DSMNNs) with both leakage delays as well as probabilistic time-varying delays. For the probabilistic delays, a sequence of Bernoulli distributed random variables is utilized to determine within which intervals the time-varying delays fall at certain time instant. The sector-bounded activation function is considered in the addressed DSMNN. By taking into account the state-dependent characteristics of the network parameters and choosing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are established under which the underlying DSMNN is globally exponentially stable in the mean square. The derived conditions are made dependent on both the leakage and the probabilistic delays, and are therefore less conservative than the traditional delay-independent criteria. A simulation example is given to show the effectiveness of the proposed stability criterion. Copyright © 2018 Elsevier Ltd. All rights reserved.

Extreme Threshold Failures Within a Heterogeneous Elastic Thin Sheet and the Spatial-Temporal Development of Induced Seismicity Within the Groningen Gas Field

NASA Astrophysics Data System (ADS)

Bourne, S. J.; Oates, S. J.

2017-12-01

Measurements of the strains and earthquakes induced by fluid extraction from a subsurface reservoir reveal a transient, exponential-like increase in seismicity relative to the volume of fluids extracted. If the frictional strength of these reactivating faults is heterogeneously and randomly distributed, then progressive failures of the weakest fault patches account in a general manner for this initial exponential-like trend. Allowing for the observable elastic and geometric heterogeneity of the reservoir, the spatiotemporal evolution of induced seismicity over 5 years is predictable without significant bias using a statistical physics model of poroelastic reservoir deformations inducing extreme threshold frictional failures of previously inactive faults. This model is used to forecast the temporal and spatial probability density of earthquakes within the Groningen natural gas reservoir, conditional on future gas production plans. Probabilistic seismic hazard and risk assessments based on these forecasts inform the current gas production policy and building strengthening plans.

Stochastic scheduling on a repairable manufacturing system

NASA Astrophysics Data System (ADS)

Li, Wei; Cao, Jinhua

1995-08-01

In this paper, we consider some stochastic scheduling problems with a set of stochastic jobs on a manufacturing system with a single machine that is subject to multiple breakdowns and repairs. When the machine processing a job fails, the job processing must restart some time later when the machine is repaired. For this typical manufacturing system, we find the optimal policies that minimize the following objective functions: (1) the weighed sum of the completion times; (2) the weighed number of late jobs having constant due dates; (3) the weighted number of late jobs having random due dates exponentially distributed, which generalize some previous results.

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-10-01

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s < 1, the disease of stochastic autonomous SVIR model will die out exponentially; if R˜0s > 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

Network topology and resilience analysis of South Korean power grid

NASA Astrophysics Data System (ADS)

Kim, Dong Hwan; Eisenberg, Daniel A.; Chun, Yeong Han; Park, Jeryang

2017-01-01

In this work, we present topological and resilience analyses of the South Korean power grid (KPG) with a broad voltage level. While topological analysis of KPG only with high-voltage infrastructure shows an exponential degree distribution, providing another empirical evidence of power grid topology, the inclusion of low voltage components generates a distribution with a larger variance and a smaller average degree. This result suggests that the topology of a power grid may converge to a highly skewed degree distribution if more low-voltage data is considered. Moreover, when compared to ER random and BA scale-free networks, the KPG has a lower efficiency and a higher clustering coefficient, implying that highly clustered structure does not necessarily guarantee a functional efficiency of a network. Error and attack tolerance analysis, evaluated with efficiency, indicate that the KPG is more vulnerable to random or degree-based attacks than betweenness-based intentional attack. Cascading failure analysis with recovery mechanism demonstrates that resilience of the network depends on both tolerance capacity and recovery initiation time. Also, when the two factors are fixed, the KPG is most vulnerable among the three networks. Based on our analysis, we propose that the topology of power grids should be designed so the loads are homogeneously distributed, or functional hubs and their neighbors have high tolerance capacity to enhance resilience.

Nonstandard convergence to jamming in random sequential adsorption: The case of patterned one-dimensional substrates

NASA Astrophysics Data System (ADS)

Verma, Arjun; Privman, Vladimir

2018-02-01

We study approach to the large-time jammed state of the deposited particles in the model of random sequential adsorption. The convergence laws are usually derived from the argument of Pomeau which includes the assumption of the dominance, at large enough times, of small landing regions into each of which only a single particle can be deposited without overlapping earlier deposited particles and which, after a certain time are no longer created by depositions in larger gaps. The second assumption has been that the size distribution of gaps open for particle-center landing in this large-time small-gaps regime is finite in the limit of zero gap size. We report numerical Monte Carlo studies of a recently introduced model of random sequential adsorption on patterned one-dimensional substrates that suggest that the second assumption must be generalized. We argue that a region exists in the parameter space of the studied model in which the gap-size distribution in the Pomeau large-time regime actually linearly vanishes at zero gap sizes. In another region, the distribution develops a threshold property, i.e., there are no small gaps below a certain gap size. We discuss the implications of these findings for new asymptotic power-law and exponential-modified-by-a-power-law convergences to jamming in irreversible one-dimensional deposition.

Crowding Effects in Vehicular Traffic

PubMed Central

Combinido, Jay Samuel L.; Lim, May T.

2012-01-01

While the impact of crowding on the diffusive transport of molecules within a cell is widely studied in biology, it has thus far been neglected in traffic systems where bulk behavior is the main concern. Here, we study the effects of crowding due to car density and driving fluctuations on the transport of vehicles. Using a microscopic model for traffic, we found that crowding can push car movement from a superballistic down to a subdiffusive state. The transition is also associated with a change in the shape of the probability distribution of positions from a negatively-skewed normal to an exponential distribution. Moreover, crowding broadens the distribution of cars’ trap times and cluster sizes. At steady state, the subdiffusive state persists only when there is a large variability in car speeds. We further relate our work to prior findings from random walk models of transport in cellular systems. PMID:23139762

Rockfall travel distances theoretical distributions

NASA Astrophysics Data System (ADS)

Jaboyedoff, Michel; Derron, Marc-Henri; Pedrazzini, Andrea

2017-04-01

The probability of propagation of rockfalls is a key part of hazard assessment, because it permits to extrapolate the probability of propagation of rockfall either based on partial data or simply theoretically. The propagation can be assumed frictional which permits to describe on average the propagation by a line of kinetic energy which corresponds to the loss of energy along the path. But loss of energy can also be assumed as a multiplicative process or a purely random process. The distributions of the rockfall block stop points can be deduced from such simple models, they lead to Gaussian, Inverse-Gaussian, Log-normal or exponential negative distributions. The theoretical background is presented, and the comparisons of some of these models with existing data indicate that these assumptions are relevant. The results are either based on theoretical considerations or by fitting results. They are potentially very useful for rockfall hazard zoning and risk assessment. This approach will need further investigations.

Entropy of spatial network ensembles

NASA Astrophysics Data System (ADS)

Coon, Justin P.; Dettmann, Carl P.; Georgiou, Orestis

2018-04-01

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly in space and links formed independently between pairs of nodes with probability given by a specified function (the "pair connection function") of their mutual distance. We consider the general case where randomness arises in node positions as well as pairwise connections (i.e., for a given pair distance, the corresponding edge state is a random variable). Classical random geometric graph and exponential graph models can be recovered in certain limits. We derive a simple bound for the entropy of a spatial network ensemble and calculate the conditional entropy of an ensemble given the node location distribution for hard and soft (probabilistic) pair connection functions. Under this formalism, we derive the connection function that yields maximum entropy under general constraints. Finally, we apply our analytical framework to study two practical examples: ad hoc wireless networks and the US flight network. Through the study of these examples, we illustrate that both exhibit properties that are indicative of nearly maximally entropic ensembles.

Intermittent Lagrangian velocities and accelerations in three-dimensional porous medium flow.

PubMed

Holzner, M; Morales, V L; Willmann, M; Dentz, M

2015-07-01

Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors.

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.

Lithium ion dynamics in Li2S+GeS2+GeO2 glasses studied using (7)Li NMR field-cycling relaxometry and line-shape analysis.

PubMed

Gabriel, Jan; Petrov, Oleg V; Kim, Youngsik; Martin, Steve W; Vogel, Michael

2015-09-01

We use (7)Li NMR to study the ionic jump motion in ternary 0.5Li2S+0.5[(1-x)GeS2+xGeO2] glassy lithium ion conductors. Exploring the "mixed glass former effect" in this system led to the assumption of a homogeneous and random variation of diffusion barriers in this system. We exploit that combining traditional line-shape analysis with novel field-cycling relaxometry, it is possible to measure the spectral density of the ionic jump motion in broad frequency and temperature ranges and, thus, to determine the distribution of activation energies. Two models are employed to parameterize the (7)Li NMR data, namely, the multi-exponential autocorrelation function model and the power-law waiting times model. Careful evaluation of both of these models indicates a broadly inhomogeneous energy landscape for both the single (x=0.0) and the mixed (x=0.1) network former glasses. The multi-exponential autocorrelation function model can be well described by a Gaussian distribution of activation barriers. Applicability of the methods used and their sensitivity to microscopic details of ionic motion are discussed. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

Solution of the finite Milne problem in stochastic media with RVT Technique

NASA Astrophysics Data System (ADS)

Slama, Howida; El-Bedwhey, Nabila A.; El-Depsy, Alia; Selim, Mustafa M.

2017-12-01

This paper presents the solution to the Milne problem in the steady state with isotropic scattering phase function. The properties of the medium are considered as stochastic ones with Gaussian or exponential distributions and hence the problem treated as a stochastic integro-differential equation. To get an explicit form for the radiant energy density, the linear extrapolation distance, reflectivity and transmissivity in the deterministic case the problem is solved using the Pomraning-Eddington method. The obtained solution is found to be dependent on the optical space variable and thickness of the medium which are considered as random variables. The random variable transformation (RVT) technique is used to find the first probability density function (1-PDF) of the solution process. Then the stochastic linear extrapolation distance, reflectivity and transmissivity are calculated. For illustration, numerical results with conclusions are provided.

Reconfiguration and Search of Social Networks

PubMed Central

Zhang, Lianming; Peng, Aoyuan

2013-01-01

Social networks tend to exhibit some topological characteristics different from regular networks and random networks, such as shorter average path length and higher clustering coefficient, and the node degree of the majority of social networks obeys exponential distribution. Based on the topological characteristics of the real social networks, a new network model which suits to portray the structure of social networks was proposed, and the characteristic parameters of the model were calculated. To find out the relationship between two people in the social network, and using the local information of the social network and the parallel mechanism, a hybrid search strategy based on k-walker random and a high degree was proposed. Simulation results show that the strategy can significantly reduce the average number of search steps, so as to effectively improve the search speed and efficiency. PMID:24574861

Effects of random aspects of cutting tool wear on surface roughness and tool life

NASA Astrophysics Data System (ADS)

Nabil, Ben Fredj; Mabrouk, Mohamed

2006-10-01

The effects of random aspects of cutting tool flank wear on surface roughness and on tool lifetime, when turning the AISI 1045 carbon steel, were studied in this investigation. It was found that standard deviations corresponding to tool flank wear and to the surface roughness increase exponentially with cutting time. Under cutting conditions that correspond to finishing operations, no significant differences were found between the calculated values of the capability index C p at the steady-state region of the tool flank wear, using the best-fit method or the Box-Cox transformation, or by making the assumption that the surface roughness data are normally distributed. Hence, a method to establish cutting tool lifetime could be established that simultaneously respects the desired average of surface roughness and the required capability index.

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.

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.

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).

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

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

Drude weight fluctuations in many-body localized systems

NASA Astrophysics Data System (ADS)

Filippone, Michele; Brouwer, Piet W.; Eisert, Jens; von Oppen, Felix

2016-11-01

We numerically investigate the distribution of Drude weights D of many-body states in disordered one-dimensional interacting electron systems across the transition to a many-body localized phase. Drude weights are proportional to the spectral curvatures induced by magnetic fluxes in mesoscopic rings. They offer a method to relate the transition to the many-body localized phase to transport properties. In the delocalized regime, we find that the Drude weight distribution at a fixed disorder configuration agrees well with the random-matrix-theory prediction P (D ) ∝(γ2+D2) -3 /2 , although the distribution width γ strongly fluctuates between disorder realizations. A crossover is observed towards a distribution with different large-D asymptotics deep in the many-body localized phase, which however differs from the commonly expected Cauchy distribution. We show that the average distribution width <γ >, rescaled by L Δ ,Δ being the average level spacing in the middle of the spectrum and L the systems size, is an efficient probe of the many-body localization transition, as it increases (vanishes) exponentially in the delocalized (localized) phase.

Feasibility of quasi-random band model in evaluating atmospheric radiance

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Mirakhur, N.

1980-01-01

The use of the quasi-random band model in evaluating upwelling atmospheric radiation is investigated. The spectral transmittance and total band adsorptance are evaluated for selected molecular bands by using the line by line model, quasi-random band model, exponential sum fit method, and empirical correlations, and these are compared with the available experimental results. The atmospheric transmittance and upwelling radiance were calculated by using the line by line and quasi random band models and were compared with the results of an existing program called LOWTRAN. The results obtained by the exponential sum fit and empirical relations were not in good agreement with experimental results and their use cannot be justified for atmospheric studies. The line by line model was found to be the best model for atmospheric applications, but it is not practical because of high computational costs. The results of the quasi random band model compare well with the line by line and experimental results. The use of the quasi random band model is recommended for evaluation of the atmospheric radiation.

Quantitative characterization and modeling of lithologic heterogeneity

NASA Astrophysics Data System (ADS)

Deshpande, Anil

The fundamental goal of this thesis is to gain a better understanding of the vertical and lateral stratigraphic heterogeneities in sedimentary deposits. Two approaches are taken: Statistical characterization of lithologic variation recorded by geophysical data such as reflection seismic and wireline logs, and stochastic forward modeling of sediment accumulation in basins. Analysis of reflection seismic and wireline log data from Pleistocene fluvial and deltaic deposits in the Eugene Island 330 field, offshore Gulf of Mexico reveal scale-invariant statistics and strong anisotropy in rock properties. Systematic quantification of lateral lithologic heterogeneity within a stratigraphic framework, using reflection seismic data, indicates that fluvial and deltaic depositional systems exhibit statistical behavior related to stratigraphic fabric. Well log and seismic data profiles show a decay in power spectra with wavenumber, k, according to ksp{-beta} with beta between 1 and 2.3. The question of how surface processes are recorded in bed thickness distributions as a function of basin accommodation space is addressed with stochastic sedimentation model. In zones of high accommodation, random, uncorrelated, driving events produce a range of spatially correlated lithology fields. In zones of low accommodation, bed thickness distributions deviate from the random forcing imposed (an exponential thickness distribution). Model results are similar to that of a shallowing upward parasequence recorded in 15 meters of offshore Gulf of Mexico Pleistocene core. These data record a deviation from exponentially distributed bed thicknesses from the deeper water part of the cycle to the shallow part of the cycle where bed amalgamation dominates. Finally, a stochastic basin-fill model is used to explore the primary controls on stratigraphic architecture of turbidite channel-fill in the South Timbalier 295 field, offshore Louisiana Gulf Coast. Spatial and temporal changes in topography and subsidence rate are shown to be the main controls on turbidite channel stacking pattern within this basin. The model predicts the deposition of thick, amalgamated turbidite channel sands in the basin during a period of high initial subsidence followed by deposition of thinner, less connected sands when basin subsidence rate and accommodation space are low.

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.

Vacuum statistics and stability in axionic landscapes

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

Masoumi, Ali; Vilenkin, Alexander, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu

2016-03-01

We investigate vacuum statistics and stability in random axionic landscapes. For this purpose we developed an algorithm for a quick evaluation of the tunneling action, which in most cases is accurate within 10%. We find that stability of a vacuum is strongly correlated with its energy density, with lifetime rapidly growing as the energy density is decreased. On the other hand, the probability P(B) for a vacuum to have a tunneling action B greater than a given value declines as a slow power law in B. This is in sharp contrast with the studies of random quartic potentials, which foundmore » a fast exponential decline of P(B). Our results suggest that the total number of relatively stable vacua (say, with B>100) grows exponentially with the number of fields N and can get extremely large for N∼> 100. The problem with this kind of model is that the stable vacua are concentrated near the absolute minimum of the potential, so the observed value of the cosmological constant cannot be explained without fine-tuning. To address this difficulty, we consider a modification of the model, where the axions acquire a quadratic mass term, due to their mixing with 4-form fields. This results in a larger landscape with a much broader distribution of vacuum energies. The number of relatively stable vacua in such models can still be extremely large.« less

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.

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

NASA Astrophysics Data System (ADS)

Sergeenko, N. P.

2017-11-01

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

Chemical Continuous Time Random Walks

NASA Astrophysics Data System (ADS)

Aquino, T.; Dentz, M.

2017-12-01

Traditional methods for modeling solute transport through heterogeneous media employ Eulerian schemes to solve for solute concentration. More recently, Lagrangian methods have removed the need for spatial discretization through the use of Monte Carlo implementations of Langevin equations for solute particle motions. While there have been recent advances in modeling chemically reactive transport with recourse to Lagrangian methods, these remain less developed than their Eulerian counterparts, and many open problems such as efficient convergence and reconstruction of the concentration field remain. We explore a different avenue and consider the question: In heterogeneous chemically reactive systems, is it possible to describe the evolution of macroscopic reactant concentrations without explicitly resolving the spatial transport? Traditional Kinetic Monte Carlo methods, such as the Gillespie algorithm, model chemical reactions as random walks in particle number space, without the introduction of spatial coordinates. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. In real systems, transport limitations lead to incomplete mixing and decreased reaction efficiency. We introduce an arbitrary inter-reaction time distribution, which may account for the impact of incomplete mixing. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical Master equation and formulate a generalized Gillespie algorithm. We then determine the modified chemical rate laws for different inter-reaction time distributions. We trace Michaelis-Menten-type kinetics back to finite-mean delay times, and predict time-nonlocal macroscopic reaction kinetics as a consequence of broadly distributed delays. Non-Markovian kinetics exhibit weak ergodicity breaking and show key features of reactions under local non-equilibrium.

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

NASA Astrophysics Data System (ADS)

Leonenko, N. N.; Ruiz-Medina, M. D.

2006-07-01

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

The complex network of the Brazilian Popular Music

NASA Astrophysics Data System (ADS)

de Lima e Silva, D.; Medeiros Soares, M.; Henriques, M. V. C.; Schivani Alves, M. T.; de Aguiar, S. G.; de Carvalho, T. P.; Corso, G.; Lucena, L. S.

2004-02-01

We study the Brazilian Popular Music in a network perspective. We call the Brazilian Popular Music Network, BPMN, the graph where the vertices are the song writers and the links are determined by the existence of at least a common singer. The linking degree distribution of such graph shows power law and exponential regions. The exponent of the power law is compatible with the values obtained by the evolving network algorithms seen in the literature. The average path length of the BPMN is similar to the correspondent random graph, its clustering coefficient, however, is significantly larger. These results indicate that the BPMN forms a small-world network.

An analytic solution of the stochastic storage problem applicable to soil water

USGS Publications Warehouse

Milly, P.C.D.

1993-01-01

The accumulation of soil water during rainfall events and the subsequent depletion of soil water by evaporation between storms can be described, to first order, by simple accounting models. When the alternating supplies (precipitation) and demands (potential evaporation) are viewed as random variables, it follows that soil-water storage, evaporation, and runoff are also random variables. If the forcing (supply and demand) processes are stationary for a sufficiently long period of time, an asymptotic regime should eventually be reached where the probability distribution functions of storage, evaporation, and runoff are stationary and uniquely determined by the distribution functions of the forcing. Under the assumptions that the potential evaporation rate is constant, storm arrivals are Poisson-distributed, rainfall is instantaneous, and storm depth follows an exponential distribution, it is possible to derive the asymptotic distributions of storage, evaporation, and runoff analytically for a simple balance model. A particular result is that the fraction of rainfall converted to runoff is given by (1 - R−1)/(eα(1−R−1) − R−1), in which R is the ratio of mean potential evaporation to mean rainfall and a is the ratio of soil water-holding capacity to mean storm depth. The problem considered here is analogous to the well-known problem of storage in a reservoir behind a dam, for which the present work offers a new solution for reservoirs of finite capacity. A simple application of the results of this analysis suggests that random, intraseasonal fluctuations of precipitation cannot by themselves explain the observed dependence of the annual water balance on annual totals of precipitation and potential evaporation.

Exponential vanishing of the ground-state gap of the quantum random energy model via adiabatic quantum computing

NASA Astrophysics Data System (ADS)

Adame, J.; Warzel, S.

2015-11-01

In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.

Exponential vanishing of the ground-state gap of the quantum random energy model via adiabatic quantum computing

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

Adame, J.; Warzel, S., E-mail: warzel@ma.tum.de

In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.

Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model.

PubMed

Borges, F S; Protachevicz, P R; Lameu, E L; Bonetti, R C; Iarosz, K C; Caldas, I L; Baptista, M S; Batista, A M

2017-06-01

We have studied neuronal synchronisation in a random network of adaptive exponential integrate-and-fire neurons. We study how spiking or bursting synchronous behaviour appears as a function of the coupling strength and the probability of connections, by constructing parameter spaces that identify these synchronous behaviours from measurements of the inter-spike interval and the calculation of the order parameter. Moreover, we verify the robustness of synchronisation by applying an external perturbation to each neuron. The simulations show that bursting synchronisation is more robust than spike synchronisation. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

[A modification of the Gompertz plot resulting from the age index by Ries and an approximation of the survivorship curve (author's transl)].

PubMed

Lohmann, W

1978-01-01

The shape of the survivorship curve can easily be interpreted on condition that the probability of death is proportional to an exponentially rising function of ageing. According to the formation of a sum for determining of the age index by Ries it was investigated to what extent the survivorship curve may be approximated by a sum of exponentials. It follows that the difference between the pure exponential function and a sum of exponentials by using possible values is lying within the random variation. Because the probability of death for different diseases is variable, the new statement is a better one.

Gravitational Effects on Closed-Cellular-Foam Microstructure

NASA Technical Reports Server (NTRS)

Noever, David A.; Cronise, Raymond J.; Wessling, Francis C.; McMannus, Samuel P.; Mathews, John; Patel, Darayas

1996-01-01

Polyurethane foam has been produced in low gravity for the first time. The cause and distribution of different void or pore sizes are elucidated from direct comparison of unit-gravity and low-gravity samples. Low gravity is found to increase the pore roundness by 17% and reduce the void size by 50%. The standard deviation for pores becomes narrower (a more homogeneous foam is produced) in low gravity. Both a Gaussian and a Weibull model fail to describe the statistical distribution of void areas, and hence the governing dynamics do not combine small voids in either a uniform or a dependent fashion to make larger voids. Instead, the void areas follow an exponential law, which effectively randomizes the production of void sizes in a nondependent fashion consistent more with single nucleation than with multiple or combining events.

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.

An evolving model of online bipartite networks

NASA Astrophysics Data System (ADS)

Zhang, Chu-Xu; Zhang, Zi-Ke; Liu, Chuang

2013-12-01

Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models, resulting in either power-law or exponential degree distributions. However, many empirical results show that the user degree distribution actually follows a shifted power-law distribution, the so-called Mandelbrot’s law, which cannot be fully described by previous models. In this paper, we propose an evolving model, considering two different user behaviors: random and preferential attachment. Extensive empirical results on two real bipartite networks, Delicious and CiteULike, show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions. In addition, we introduce a structural parameter p, to demonstrate that the hybrid user behavior leads to the shifted power-law degree distribution, and the region of power-law tail will increase with the increment of p. The proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks.

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.

The random coding bound is tight for the average code.

NASA Technical Reports Server (NTRS)

Gallager, R. G.

1973-01-01

The random coding bound of information theory provides a well-known upper bound to the probability of decoding error for the best code of a given rate and block length. The bound is constructed by upperbounding the average error probability over an ensemble of codes. The bound is known to give the correct exponential dependence of error probability on block length for transmission rates above the critical rate, but it gives an incorrect exponential dependence at rates below a second lower critical rate. Here we derive an asymptotic expression for the average error probability over the ensemble of codes used in the random coding bound. The result shows that the weakness of the random coding bound at rates below the second critical rate is due not to upperbounding the ensemble average, but rather to the fact that the best codes are much better than the average at low rates.

Microfracture spacing distributions and the evolution of fracture patterns in sandstones

NASA Astrophysics Data System (ADS)

Hooker, J. N.; Laubach, S. E.; Marrett, R.

2018-03-01

Natural fracture patterns in sandstone were sampled using scanning electron microscope-based cathodoluminescence (SEM-CL) imaging. All fractures are opening-mode and are fully or partially sealed by quartz cement. Most sampled fractures are too small to be height-restricted by sedimentary layers. At very low strains (<∼0.001), fracture spatial distributions are indistinguishable from random, whereas at higher strains, fractures are generally statistically clustered. All 12 large (N > 100) datasets show spacings that are best fit by log-normal size distributions, compared to exponential, power law, or normal distributions. The clustering of fractures suggests that the locations of natural factures are not determined by a random process. To investigate natural fracture localization, we reconstructed the opening history of a cluster of fractures within the Huizachal Group in northeastern Mexico, using fluid inclusions from synkinematic cements and thermal-history constraints. The largest fracture, which is the only fracture in the cluster visible to the naked eye, among 101 present, opened relatively late in the sequence. This result suggests that the growth of sets of fractures is a self-organized process, in which small, initially isolated fractures grow and progressively interact, with preferential growth of a subset of fractures developing at the expense of growth of the rest. Size-dependent sealing of fractures within sets suggests that synkinematic cementation may contribute to fracture clustering.

Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation.

PubMed

Anta, Juan A; Mora-Seró, Iván; Dittrich, Thomas; Bisquert, Juan

2008-08-14

We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.

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.

High activity and Levy searches: jellyfish can search the water column like fish.

PubMed

Hays, Graeme C; Bastian, Thomas; Doyle, Thomas K; Fossette, Sabrina; Gleiss, Adrian C; Gravenor, Michael B; Hobson, Victoria J; Humphries, Nicolas E; Lilley, Martin K S; Pade, Nicolas G; Sims, David W

2012-02-07

Over-fishing may lead to a decrease in fish abundance and a proliferation of jellyfish. Active movements and prey search might be thought to provide a competitive advantage for fish, but here we use data-loggers to show that the frequently occurring coastal jellyfish (Rhizostoma octopus) does not simply passively drift to encounter prey. Jellyfish (327 days of data from 25 jellyfish with depth collected every 1 min) showed very dynamic vertical movements, with their integrated vertical movement averaging 619.2 m d(-1), more than 60 times the water depth where they were tagged. The majority of movement patterns were best approximated by exponential models describing normal random walks. However, jellyfish also showed switching behaviour from exponential patterns to patterns best fitted by a truncated Lévy distribution with exponents (mean μ=1.96, range 1.2-2.9) close to the theoretical optimum for searching for sparse prey (μopt≈2.0). Complex movements in these 'simple' animals may help jellyfish to compete effectively with fish for plankton prey, which may enhance their ability to increase in dominance in perturbed ocean systems.

Observer-based sliding mode control of Markov jump systems with random sensor delays and partly unknown transition rates

NASA Astrophysics Data System (ADS)

Yao, Deyin; Lu, Renquan; Xu, Yong; Ren, Hongru

2017-10-01

In this paper, the sliding mode control problem of Markov jump systems (MJSs) with unmeasured state, partly unknown transition rates and random sensor delays is probed. In the practical engineering control, the exact information of transition rates is hard to obtain and the measurement channel is supposed to subject to random sensor delay. Design a Luenberger observer to estimate the unmeasured system state, and an integral sliding mode surface is constructed to ensure the exponential stability of MJSs. A sliding mode controller based on estimator is proposed to drive the system state onto the sliding mode surface and render the sliding mode dynamics exponentially mean-square stable with H∞ performance index. Finally, simulation results are provided to illustrate the effectiveness of the proposed results.

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.

Nonlinear dynamic evolution and control in CCFN with mixed attachment mechanisms

NASA Astrophysics Data System (ADS)

Wang, Jianrong; Wang, Jianping; Han, Dun

2017-01-01

In recent years, wireless communication plays an important role in our lives. Cooperative communication, is used by a mobile station with single antenna to share with each other forming a virtual MIMO antenna system, will become a development with a diversity gain for wireless communication in tendency future. In this paper, a fitness model of evolution network based on complex networks with mixed attachment mechanisms is devised in order to study an actual network-CCFN (cooperative communication fitness network). Firstly, the evolution of CCFN is given by four cases with different probabilities, and the rate equations of nodes degree are presented to analyze the evolution of CCFN. Secondly, the degree distribution is analyzed by calculating the rate equation and numerical simulation with the examples of four fitness distributions such as power law, uniform fitness distribution, exponential fitness distribution and Rayleigh fitness distribution. Finally, the robustness of CCFN is studied by numerical simulation with four fitness distributions under random attack and intentional attack to analyze the effects of degree distribution, average path length and average degree. The results of this paper offers insights for building CCFN systems in order to program communication resources.

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.

A General Exponential Framework for Dimensionality Reduction.

PubMed

Wang, Su-Jing; Yan, Shuicheng; Yang, Jian; Zhou, Chun-Guang; Fu, Xiaolan

2014-02-01

As a general framework, Laplacian embedding, based on a pairwise similarity matrix, infers low dimensional representations from high dimensional data. However, it generally suffers from three issues: 1) algorithmic performance is sensitive to the size of neighbors; 2) the algorithm encounters the well known small sample size (SSS) problem; and 3) the algorithm de-emphasizes small distance pairs. To address these issues, here we propose exponential embedding using matrix exponential and provide a general framework for dimensionality reduction. In the framework, the matrix exponential can be roughly interpreted by the random walk over the feature similarity matrix, and thus is more robust. The positive definite property of matrix exponential deals with the SSS problem. The behavior of the decay function of exponential embedding is more significant in emphasizing small distance pairs. Under this framework, we apply matrix exponential to extend many popular Laplacian embedding algorithms, e.g., locality preserving projections, unsupervised discriminant projections, and marginal fisher analysis. Experiments conducted on the synthesized data, UCI, and the Georgia Tech face database show that the proposed new framework can well address the issues mentioned above.

Markov chain formalism for generalized radiative transfer in a plane-parallel medium, accounting for polarization

NASA Astrophysics Data System (ADS)

Xu, Feng; Davis, Anthony B.; Diner, David J.

2016-11-01

A Markov chain formalism is developed for computing the transport of polarized radiation according to Generalized Radiative Transfer (GRT) theory, which was developed recently to account for unresolved random fluctuations of scattering particle density and can also be applied to unresolved spectral variability of gaseous absorption as an improvement over the standard correlated-k method. Using Gamma distribution to describe the probability density function of the extinction or absorption coefficient, a shape parameter a that quantifies the variability is introduced, defined as the mean extinction or absorption coefficient squared divided by its variance. It controls the decay rate of a power-law transmission that replaces the usual exponential Beer-Lambert-Bouguer law. Exponential transmission, hence classic RT, is recovered when a→∞. The new approach is verified to high accuracy against numerical benchmark results obtained with a custom Monte Carlo method. For a<∞, angular reciprocity is violated to a degree that increases with the spatial variability, as observed for finite portions of real-world cloudy scenes. While the degree of linear polarization in liquid water cloudbows, supernumerary bows, and glories is affected by spatial heterogeneity, the positions in scattering angle of these features are relatively unchanged. As a result, a single-scattering model based on the assumption of subpixel homogeneity can still be used to derive droplet size distributions from polarimetric measurements of extended stratocumulus clouds.

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.

Sequentially switching cell assemblies in random inhibitory networks of spiking neurons in the striatum.

PubMed

Ponzi, Adam; Wickens, Jeff

2010-04-28

The striatum is composed of GABAergic medium spiny neurons with inhibitory collaterals forming a sparse random asymmetric network and receiving an excitatory glutamatergic cortical projection. Because the inhibitory collaterals are sparse and weak, their role in striatal network dynamics is puzzling. However, here we show by simulation of a striatal inhibitory network model composed of spiking neurons that cells form assemblies that fire in sequential coherent episodes and display complex identity-temporal spiking patterns even when cortical excitation is simply constant or fluctuating noisily. Strongly correlated large-scale firing rate fluctuations on slow behaviorally relevant timescales of hundreds of milliseconds are shown by members of the same assembly whereas members of different assemblies show strong negative correlation, and we show how randomly connected spiking networks can generate this activity. Cells display highly irregular spiking with high coefficients of variation, broadly distributed low firing rates, and interspike interval distributions that are consistent with exponentially tailed power laws. Although firing rates vary coherently on slow timescales, precise spiking synchronization is absent in general. Our model only requires the minimal but striatally realistic assumptions of sparse to intermediate random connectivity, weak inhibitory synapses, and sufficient cortical excitation so that some cells are depolarized above the firing threshold during up states. Our results are in good qualitative agreement with experimental studies, consistent with recently determined striatal anatomy and physiology, and support a new view of endogenously generated metastable state switching dynamics of the striatal network underlying its information processing operations.

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.

Response kinetics of tethered bacteria to stepwise changes in nutrient concentration.

PubMed

Chernova, Anna A; Armitage, Judith P; Packer, Helen L; Maini, Philip K

2003-09-01

We examined the changes in swimming behaviour of the bacterium Rhodobacter sphaeroides in response to stepwise changes in a nutrient (propionate), following the pre-stimulus motion, the initial response and the adaptation to the sustained concentration of the chemical. This was carried out by tethering motile cells by their flagella to glass slides and following the rotational behaviour of their cell bodies in response to the nutrient change. Computerised motion analysis was used to analyse the behaviour. Distributions of run and stop times were obtained from rotation data for tethered cells. Exponential and Weibull fits for these distributions, and variability in individual responses are discussed. In terms of parameters derived from the run and stop time distributions, we compare the responses to stepwise changes in the nutrient concentration and the long-term behaviour of 84 cells under 12 propionate concentration levels from 1 nM to 25 mM. We discuss traditional assumptions for the random walk approximation to bacterial swimming and compare them with the observed R. sphaeroides motile behaviour.

A statistical analysis of product prices in online markets

NASA Astrophysics Data System (ADS)

Mizuno, T.; Watanabe, T.

2010-08-01

We empirically investigate fluctuations in product prices in online markets by using a tick-by-tick price data collected from a Japanese price comparison site, and find some similarities and differences between product and asset prices. The average price of a product across e-retailers behaves almost like a random walk, although the probability of price increase/decrease is higher conditional on the multiple events of price increase/decrease. This is quite similar to the property reported by previous studies about asset prices. However, we fail to find a long memory property in the volatility of product price changes. Also, we find that the price change distribution for product prices is close to an exponential distribution, rather than a power law distribution. These two findings are in a sharp contrast with the previous results regarding asset prices. We propose an interpretation that these differences may stem from the absence of speculative activities in product markets; namely, e-retailers seldom repeat buy and sell of a product, unlike traders in asset markets.

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.

A clinical trial design using the concept of proportional time using the generalized gamma ratio distribution.

PubMed

Phadnis, Milind A; Wetmore, James B; Mayo, Matthew S

2017-11-20

Traditional methods of sample size and power calculations in clinical trials with a time-to-event end point are based on the logrank test (and its variations), Cox proportional hazards (PH) assumption, or comparison of means of 2 exponential distributions. Of these, sample size calculation based on PH assumption is likely the most common and allows adjusting for the effect of one or more covariates. However, when designing a trial, there are situations when the assumption of PH may not be appropriate. Additionally, when it is known that there is a rapid decline in the survival curve for a control group, such as from previously conducted observational studies, a design based on the PH assumption may confer only a minor statistical improvement for the treatment group that is neither clinically nor practically meaningful. For such scenarios, a clinical trial design that focuses on improvement in patient longevity is proposed, based on the concept of proportional time using the generalized gamma ratio distribution. Simulations are conducted to evaluate the performance of the proportional time method and to identify the situations in which such a design will be beneficial as compared to the standard design using a PH assumption, piecewise exponential hazards assumption, and specific cases of a cure rate model. A practical example in which hemorrhagic stroke patients are randomized to 1 of 2 arms in a putative clinical trial demonstrates the usefulness of this approach by drastically reducing the number of patients needed for study enrollment. Copyright © 2017 John Wiley & Sons, Ltd.

Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field

NASA Astrophysics Data System (ADS)

Susa, Yuki; Yamashiro, Yu; Yamamoto, Masayuki; Nishimori, Hidetoshi

2018-02-01

We show, for quantum annealing, that a certain type of inhomogeneous driving of the transverse field erases first-order quantum phase transitions in the p-body interacting mean-field-type model with and without longitudinal random field. Since a first-order phase transition poses a serious difficulty for quantum annealing (adiabatic quantum computing) due to the exponentially small energy gap, the removal of first-order transitions means an exponential speedup of the annealing process. The present method may serve as a simple protocol for the performance enhancement of quantum annealing, complementary to non-stoquastic Hamiltonians.

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.

Optimal search strategies of space-time coupled random walkers with finite lifetimes

NASA Astrophysics Data System (ADS)

Campos, D.; Abad, E.; Méndez, V.; Yuste, S. B.; Lindenberg, K.

2015-05-01

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers." A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate ωm. While still alive, the creeper has a finite mean frequency ω of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an ωm-dependent optimal frequency ω =ωopt that maximizes the probability of eventual target detection. We work primarily in one-dimensional (d =1 ) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in d =2 domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the d =1 case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.

Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility

NASA Astrophysics Data System (ADS)

Sokolov, Valentin V.; Zhirov, Oleg V.; Kharkov, Yaroslav A.

The extraordinary complexity of classical trajectories of typical nonlinear systems that manifest stochastic behavior is intimately connected with exponential sensitivity to small variations of initial conditions and/or weak external perturbations. In rigorous terms, such classical systems are characterized by positive algorithmic complexity described by the Lyapunov exponent or, alternatively, by the Kolmogorov-Sinai entropy. The said implies that, in spite of the fact that, formally, any however complex trajectory of a perfectly isolated (closed) system is unique and differentiable for any certain initial conditions and the motion is perfectly reversible, it is impractical to treat that sort of classical systems as closed ones. Inevitably, arbitrary weak influence of an environment crucially impacts the dynamics. This influence, that can be considered as a noise, rapidly effaces the memory of initial conditions and turns the motion into an irreversible random process. In striking contrast, the quantum mechanics of the classically chaotic systems exhibit much weaker sensitivity and strong memory of the initial state. Qualitatively, this crucial difference could be expected in view of a much simpler structure of quantum states as compared to the extraordinary complexity of random and unpredictable classical trajectories. However the very notion of trajectories is absent in quantum mechanics so that the concept of exponential instability seems to be irrelevant in this case. The problem of a quantitative measure of complexity of a quantum state of motion, that is a very important and nontrivial issue of the theory of quantum dynamical chaos, is the one of our concern. With such a measure in hand, we quantitatively analyze the stability and reversibility of quantum dynamics in the presence of external noise. To solve this problem we point out that individual classical trajectories are of minor interest if the motion is chaotic. Properties of all of them are alike in this case and rather the behavior of their manifolds carries really valuable information. Therefore the phase-space methods and, correspondingly, the Liouville form of the classical mechanics become the most adequate. It is very important that, opposite to the classical trajectories, the classical phase space distribution and the Liouville equation have direct quantum analogs. Hence, the analogy and difference of classical and quantum dynamics can be traced by comparing the classical (W(c)(I,θ;t)) and quantum (Wigner function W(I,θ;t)) phase space distributions both expressed in identical phase-space variables but ruled by different(!) linear equations. The paramount property of the classical dynamical chaos is the exponentially fast structuring of the system's phase space on finer and finer scales. On the contrary, degree of structuring of the corresponding Wigner function is restricted by the quantization of the phase space. This makes Wigner function more coarse and relatively "simple" as compared to its classical counterpart. Fourier analysis affords quite suitable ground for analyzing complexity of a phase space distribution, that is equally valid in classical and quantum cases. We demonstrate that the typical number of Fourier harmonics is indeed a relevant measure of complexity of states of motion in both classical as well as quantum cases. This allowed us to investigate in detail and introduce a quantitative measure of sensitivity to an external noisy environment and formulate the conditions under which the quantum motion remains reversible. It turns out that while the mean number of harmonics of the classical phase-space distribution of a non-integrable system grows with time exponentially during the whole time of the motion, the time of exponential upgrowth of this number in the case of the corresponding quantum Wigner function is restricted only to the Ehrenfest interval 0 < t < tE - just the interval within which the Wigner function still satisfies the classical Liouville equation. We showed that the number of harmonics increases beyond this interval algebraically. This fact gains a crucial importance when the Ehrenfest time is so short that the exponential regime has no time to show up. Under this condition the quantum motion turns out to be quite stable and reversible.

Study the fragment size distribution in dynamic fragmentation of laser shock loding tin

NASA Astrophysics Data System (ADS)

He, Weihua; Xin, Jianting; Chu, Genbai; Shui, Min; Xi, Tao; Zhao, Yongqiang; Gu, Yuqiu

2017-06-01

Characterizing the distribution of fragment size produced from dynamic fragmentation process is very important for fundamental science like predicting material dymanic response performance and for a variety of engineering applications. However, only a few data about fragment mass or size have been obtained due to its great challenge in its dynamic measurement. This paper would focus on investigating the fragment size distribution from the dynamic fragmentation of laser shock-loaded metal. Material ejection of tin sample with wedge shape groove in the free surface is collected with soft recovery technique. Via fine post-shot analysis techniques including X-ray micro-tomography and the improved watershed method, it is found that fragments can be well detected. To characterize their size distributions, a random geometric statistics method based on Poisson mixtures was derived for dynamic heterogeneous fragmentation problem, which leads to a linear combinational exponential distribution. Finally we examined the size distribution of laser shock-loaded tin with the derived model, and provided comparisons with other state-of-art models. The resulting comparisons prove that our proposed model can provide more reasonable fitting result for laser shock-loaded metal.

Geometrical effects on the electron residence time in semiconductor nano-particles.

PubMed

Koochi, Hakimeh; Ebrahimi, Fatemeh

2014-09-07

We have used random walk (RW) numerical simulations to investigate the influence of the geometry on the statistics of the electron residence time τ(r) in a trap-limited diffusion process through semiconductor nano-particles. This is an important parameter in coarse-grained modeling of charge carrier transport in nano-structured semiconductor films. The traps have been distributed randomly on the surface (r(2) model) or through the whole particle (r(3) model) with a specified density. The trap energies have been taken from an exponential distribution and the traps release time is assumed to be a stochastic variable. We have carried out (RW) simulations to study the effect of coordination number, the spatial arrangement of the neighbors and the size of nano-particles on the statistics of τ(r). It has been observed that by increasing the coordination number n, the average value of electron residence time, τ̅(r) rapidly decreases to an asymptotic value. For a fixed coordination number n, the electron's mean residence time does not depend on the neighbors' spatial arrangement. In other words, τ̅(r) is a porosity-dependence, local parameter which generally varies remarkably from site to site, unless we are dealing with highly ordered structures. We have also examined the effect of nano-particle size d on the statistical behavior of τ̅(r). Our simulations indicate that for volume distribution of traps, τ̅(r) scales as d(2). For a surface distribution of traps τ(r) increases almost linearly with d. This leads to the prediction of a linear dependence of the diffusion coefficient D on the particle size d in ordered structures or random structures above the critical concentration which is in accordance with experimental observations.

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.

Dynamic design of ecological monitoring networks for non-Gaussian spatio-temporal data

USGS Publications Warehouse

Wikle, C.K.; Royle, J. Andrew

2005-01-01

Many ecological processes exhibit spatial structure that changes over time in a coherent, dynamical fashion. This dynamical component is often ignored in the design of spatial monitoring networks. Furthermore, ecological variables related to processes such as habitat are often non-Gaussian (e.g. Poisson or log-normal). We demonstrate that a simulation-based design approach can be used in settings where the data distribution is from a spatio-temporal exponential family. The key random component in the conditional mean function from this distribution is then a spatio-temporal dynamic process. Given the computational burden of estimating the expected utility of various designs in this setting, we utilize an extended Kalman filter approximation to facilitate implementation. The approach is motivated by, and demonstrated on, the problem of selecting sampling locations to estimate July brood counts in the prairie pothole region of the U.S.

Effect of extreme data loss on heart rate signals quantified by entropy analysis

NASA Astrophysics Data System (ADS)

Li, Yu; Wang, Jun; Li, Jin; Liu, Dazhao

2015-02-01

The phenomenon of data loss always occurs in the analysis of large databases. Maintaining the stability of analysis results in the event of data loss is very important. In this paper, we used a segmentation approach to generate a synthetic signal that is randomly wiped from data according to the Gaussian distribution and the exponential distribution of the original signal. Then, the logistic map is used as verification. Finally, two methods of measuring entropy-base-scale entropy and approximate entropy-are comparatively analyzed. Our results show the following: (1) Two key parameters-the percentage and the average length of removed data segments-can change the sequence complexity according to logistic map testing. (2) The calculation results have preferable stability for base-scale entropy analysis, which is not sensitive to data loss. (3) The loss percentage of HRV signals should be controlled below the range (p = 30 %), which can provide useful information in clinical applications.

General simulation algorithm for autocorrelated binary processes.

PubMed

Serinaldi, Francesco; Lombardo, Federico

2017-02-01

The apparent ubiquity of binary random processes in physics and many other fields has attracted considerable attention from the modeling community. However, generation of binary sequences with prescribed autocorrelation is a challenging task owing to the discrete nature of the marginal distributions, which makes the application of classical spectral techniques problematic. We show that such methods can effectively be used if we focus on the parent continuous process of beta distributed transition probabilities rather than on the target binary process. This change of paradigm results in a simulation procedure effectively embedding a spectrum-based iterative amplitude-adjusted Fourier transform method devised for continuous processes. The proposed algorithm is fully general, requires minimal assumptions, and can easily simulate binary signals with power-law and exponentially decaying autocorrelation functions corresponding, for instance, to Hurst-Kolmogorov and Markov processes. An application to rainfall intermittency shows that the proposed algorithm can also simulate surrogate data preserving the empirical autocorrelation.

Extreme event statistics in a drifting Markov chain

NASA Astrophysics Data System (ADS)

Kindermann, Farina; Hohmann, Michael; Lausch, Tobias; Mayer, Daniel; Schmidt, Felix; Widera, Artur

2017-07-01

We analyze extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one-dimensional periodic potential. Based on more than 500 individual atomic traces we verify the applicability of the Sparre Andersen theorem to our system despite the presence of a drift. We present detailed analysis of four different rare-event statistics for our system: the distributions of extreme values, of record values, of extreme value occurrence in the chain, and of the number of records in the chain. We observe that, for our data, the shape of the extreme event distributions is dominated by the underlying exponential distance distribution extracted from the atomic traces. Furthermore, we find that even small drifts influence the statistics of extreme events and record values, which is supported by numerical simulations, and we identify cases in which the drift can be determined without information about the underlying random variable distributions. Our results facilitate the use of extreme event statistics as a signal for small drifts in correlated trajectories.

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.

Dynamical Localization for Discrete Anderson Dirac Operators

NASA Astrophysics Data System (ADS)

Prado, Roberto A.; de Oliveira, César R.; Carvalho, Silas L.

2017-04-01

We establish dynamical localization for random Dirac operators on the d-dimensional lattice, with d\\in { 1, 2, 3} , in the three usual regimes: large disorder, band edge and 1D. These operators are discrete versions of the continuous Dirac operators and consist in the sum of a discrete free Dirac operator with a random potential. The potential is a diagonal matrix formed by different scalar potentials, which are sequences of independent and identically distributed random variables according to an absolutely continuous probability measure with bounded density and of compact support. We prove the exponential decay of fractional moments of the Green function for such models in each of the above regimes, i.e., (j) throughout the spectrum at larger disorder, (jj) for energies near the band edges at arbitrary disorder and (jjj) in dimension one, for all energies in the spectrum and arbitrary disorder. Dynamical localization in theses regimes follows from the fractional moments method. The result in the one-dimensional regime contrast with one that was previously obtained for 1D Dirac model with Bernoulli potential.

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

NASA Technical Reports Server (NTRS)

Smelyanskiy, V. N.; Toussaint, U. V.; Timucin, D. A.

2002-01-01

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

NASA Technical Reports Server (NTRS)

Smelyanskiy, Vadius; vonToussaint, Udo V.; Timucin, Dogan A.; Clancy, Daniel (Technical Monitor)

2002-01-01

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

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.

At least some errors are randomly generated (Freud was wrong)

NASA Technical Reports Server (NTRS)

Sellen, A. J.; Senders, J. W.

1986-01-01

An experiment was carried out to expose something about human error generating mechanisms. In the context of the experiment, an error was made when a subject pressed the wrong key on a computer keyboard or pressed no key at all in the time allotted. These might be considered, respectively, errors of substitution and errors of omission. Each of seven subjects saw a sequence of three digital numbers, made an easily learned binary judgement about each, and was to press the appropriate one of two keys. Each session consisted of 1,000 presentations of randomly permuted, fixed numbers broken into 10 blocks of 100. One of two keys should have been pressed within one second of the onset of each stimulus. These data were subjected to statistical analyses in order to probe the nature of the error generating mechanisms. Goodness of fit tests for a Poisson distribution for the number of errors per 50 trial interval and for an exponential distribution of the length of the intervals between errors were carried out. There is evidence for an endogenous mechanism that may best be described as a random error generator. Furthermore, an item analysis of the number of errors produced per stimulus suggests the existence of a second mechanism operating on task driven factors producing exogenous errors. Some errors, at least, are the result of constant probability generating mechanisms with error rate idiosyncratically determined for each subject.

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.

Two-time scale subordination in physical processes with long-term memory

NASA Astrophysics Data System (ADS)

Stanislavsky, Aleksander; Weron, Karina

2008-03-01

We describe dynamical processes in continuous media with a long-term memory. Our consideration is based on a stochastic subordination idea and concerns two physical examples in detail. First we study a temporal evolution of the species concentration in a trapping reaction in which a diffusing reactant is surrounded by a sea of randomly moving traps. The analysis uses the random-variable formalism of anomalous diffusive processes. We find that the empirical trapping-reaction law, according to which the reactant concentration decreases in time as a product of an exponential and a stretched exponential function, can be explained by a two-time scale subordination of random processes. Another example is connected with a state equation for continuous media with memory. If the pressure and the density of a medium are subordinated in two different random processes, then the ordinary state equation becomes fractional with two-time scales. This allows one to arrive at the Bagley-Torvik type of state equation.

Quantifying Uncertainties in N2O Emission Due to N Fertilizer Application in Cultivated Areas

PubMed Central

Philibert, Aurore; Loyce, Chantal; Makowski, David

2012-01-01

Nitrous oxide (N2O) is a greenhouse gas with a global warming potential approximately 298 times greater than that of CO2. In 2006, the Intergovernmental Panel on Climate Change (IPCC) estimated N2O emission due to synthetic and organic nitrogen (N) fertilization at 1% of applied N. We investigated the uncertainty on this estimated value, by fitting 13 different models to a published dataset including 985 N2O measurements. These models were characterized by (i) the presence or absence of the explanatory variable “applied N”, (ii) the function relating N2O emission to applied N (exponential or linear function), (iii) fixed or random background (i.e. in the absence of N application) N2O emission and (iv) fixed or random applied N effect. We calculated ranges of uncertainty on N2O emissions from a subset of these models, and compared them with the uncertainty ranges currently used in the IPCC-Tier 1 method. The exponential models outperformed the linear models, and models including one or two random effects outperformed those including fixed effects only. The use of an exponential function rather than a linear function has an important practical consequence: the emission factor is not constant and increases as a function of applied N. Emission factors estimated using the exponential function were lower than 1% when the amount of N applied was below 160 kg N ha−1. Our uncertainty analysis shows that the uncertainty range currently used by the IPCC-Tier 1 method could be reduced. PMID:23226430

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.

Diameter distribution in a Brazilian tropical dry forest domain: predictions for the stand and species.

PubMed

Lima, Robson B DE; Bufalino, Lina; Alves, Francisco T; Silva, José A A DA; Ferreira, Rinaldo L C

2017-01-01

Currently, there is a lack of studies on the correct utilization of continuous distributions for dry tropical forests. Therefore, this work aims to investigate the diameter structure of a brazilian tropical dry forest and to select suitable continuous distributions by means of statistic tools for the stand and the main species. Two subsets were randomly selected from 40 plots. Diameter at base height was obtained. The following functions were tested: log-normal; gamma; Weibull 2P and Burr. The best fits were selected by Akaike's information validation criterion. Overall, the diameter distribution of the dry tropical forest was better described by negative exponential curves and positive skewness. The forest studied showed diameter distributions with decreasing probability for larger trees. This behavior was observed for both the main species and the stand. The generalization of the function fitted for the main species show that the development of individual models is needed. The Burr function showed good flexibility to describe the diameter structure of the stand and the behavior of Mimosa ophthalmocentra and Bauhinia cheilantha species. For Poincianella bracteosa, Aspidosperma pyrifolium and Myracrodum urundeuva better fitting was obtained with the log-normal function.

Brittle-to-ductile transition in a fiber bundle with strong heterogeneity.

PubMed

Kovács, Kornél; Hidalgo, Raul Cruz; Pagonabarraga, Ignacio; Kun, Ferenc

2013-04-01

We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0≤α≤1 of the bundle is strong and it is represented by unbreakable fibers, while fibers of the weak component have randomly distributed failure strength. Computer simulations revealed that there exists a critical composition α(c) which separates two qualitatively different behaviors: Below the critical point, the failure of the bundle is brittle, characterized by an abrupt damage growth within the breakable part of the system. Above α(c), however, the macroscopic response becomes ductile, providing stability during the entire breaking process. The transition occurs at an astonishingly low fraction of strong fibers which can have importance for applications. We show that in the ductile phase, the size distribution of breaking bursts has a power law functional form with an exponent μ=2 followed by an exponential cutoff. In the brittle phase, the power law also prevails but with a higher exponent μ=9/2. The transition between the two phases shows analogies to continuous phase transitions. Analyzing the microstructure of the damage, it was found that at the beginning of the fracture process cracks nucleate randomly, while later on growth and coalescence of cracks dominate, which give rise to power law distributed crack sizes.

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

Fieth, Pascal; Hartmann, Alexander K.

2016-08-01

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

Fossil preservation and the stratigraphic ranges of taxa

NASA Technical Reports Server (NTRS)

Foote, M.; Raup, D. M.

1996-01-01

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

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.

Enhancing Multimedia Imbalanced Concept Detection Using VIMP in Random Forests.

PubMed

Sadiq, Saad; Yan, Yilin; Shyu, Mei-Ling; Chen, Shu-Ching; Ishwaran, Hemant

2016-07-01

Recent developments in social media and cloud storage lead to an exponential growth in the amount of multimedia data, which increases the complexity of managing, storing, indexing, and retrieving information from such big data. Many current content-based concept detection approaches lag from successfully bridging the semantic gap. To solve this problem, a multi-stage random forest framework is proposed to generate predictor variables based on multivariate regressions using variable importance (VIMP). By fine tuning the forests and significantly reducing the predictor variables, the concept detection scores are evaluated when the concept of interest is rare and imbalanced, i.e., having little collaboration with other high level concepts. Using classical multivariate statistics, estimating the value of one coordinate using other coordinates standardizes the covariates and it depends upon the variance of the correlations instead of the mean. Thus, conditional dependence on the data being normally distributed is eliminated. Experimental results demonstrate that the proposed framework outperforms those approaches in the comparison in terms of the Mean Average Precision (MAP) values.

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.

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.

Development of a methodology to evaluate material accountability in pyroprocess

NASA Astrophysics Data System (ADS)

Woo, Seungmin

This study investigates the effect of the non-uniform nuclide composition in spent fuel on material accountancy in the pyroprocess. High-fidelity depletion simulations are performed using the Monte Carlo code SERPENT in order to determine nuclide composition as a function of axial and radial position within fuel rods and assemblies, and burnup. For improved accuracy, the simulations use short burnups step (25 days or less), Xe-equilibrium treatment (to avoid oscillations over burnup steps), axial moderator temperature distribution, and 30 axial meshes. Analytical solutions of the simplified depletion equations are built to understand the axial non-uniformity of nuclide composition in spent fuel. The cosine shape of axial neutron flux distribution dominates the axial non-uniformity of the nuclide composition. Combined cross sections and time also generate axial non-uniformity, as the exponential term in the analytical solution consists of the neutron flux, cross section and time. The axial concentration distribution for a nuclide having the small cross section gets steeper than that for another nuclide having the great cross section because the axial flux is weighted by the cross section in the exponential term in the analytical solution. Similarly, the non-uniformity becomes flatter as increasing burnup, because the time term in the exponential increases. Based on the developed numerical recipes and decoupling of the results between the axial distributions and the predetermined representative radial distributions by matching the axial height, the axial and radial composition distributions for representative spent nuclear fuel assemblies, the Type-0, -1, and -2 assemblies after 1, 2, and 3 depletion cycles, is obtained. These data are appropriately modified to depict processing for materials in the head-end process of pyroprocess that is chopping, voloxidation and granulation. The expectation and standard deviation of the Pu-to-244Cm-ratio by the single granule sampling calculated by the central limit theorem and the Geary-Hinkley transformation. Then, the uncertainty propagation through the key-pyroprocess is conducted to analyze the Material Unaccounted For (MUF), which is a random variable defined as a receipt minus a shipment of a process, in the system. The random variable, LOPu, is defined for evaluating the non-detection probability at each Key Measurement Point (KMP) as the original Pu mass minus the Pu mass after a missing scenario. A number of assemblies for the LOPu to be 8 kg is considered in this calculation. The probability of detection for the 8 kg LOPu is evaluated with respect the size of granule and powder using the event tree analysis and the hypothesis testing method. We can observe there are possible cases showing the probability of detection for the 8 kg LOPu less than 95%. In order to enhance the detection rate, a new Material Balance Area (MBA) model is defined for the key-pyroprocess. The probabilities of detection for all spent fuel types based on the new MBA model are greater than 99%. Furthermore, it is observed that the probability of detection significantly increases by increasing granule sample sizes to evaluate the Pu-to-244Cm-ratio before the key-pyroprocess. Based on these observations, even though the Pu material accountability in pyroprocess is affected by the non-uniformity of nuclide composition when the Pu-to-244Cm-ratio method is being applied, that is surmounted by decreasing the uncertainty of measured ratio by increasing sample sizes and modifying the MBAs and KMPs. (Abstract shortened by ProQuest.).

Resolvent-Techniques for Multiple Exercise Problems

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

Christensen, Sören, E-mail: christensen@math.uni-kiel.de; Lempa, Jukka, E-mail: jukka.lempa@hioa.no

2015-02-15

We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristicsmore » of the problems can be identified more explicitly. We illustrate the main results with explicit examples.« less

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.

Rigorous Results for the Distribution of Money on Connected Graphs

NASA Astrophysics Data System (ADS)

Lanchier, Nicolas; Reed, Stephanie

2018-05-01

This paper is concerned with general spatially explicit versions of three stochastic models for the dynamics of money that have been introduced and studied numerically by statistical physicists: the uniform reshuffling model, the immediate exchange model and the model with saving propensity. All three models consist of systems of economical agents that consecutively engage in pairwise monetary transactions. Computer simulations performed in the physics literature suggest that, when the number of agents and the average amount of money per agent are large, the limiting distribution of money as time goes to infinity approaches the exponential distribution for the first model, the gamma distribution with shape parameter two for the second model and a distribution similar but not exactly equal to a gamma distribution whose shape parameter depends on the saving propensity for the third model. The main objective of this paper is to give rigorous proofs of these conjectures and also extend these conjectures to generalizations of the first two models and a variant of the third model that include local rather than global interactions, i.e., instead of choosing the two interacting agents uniformly at random from the system, the agents are located on the vertex set of a general connected graph and can only interact with their neighbors.

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.

Universality of accelerating change

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Shlesinger, Michael F.

2018-03-01

On large time scales the progress of human technology follows an exponential growth trend that is termed accelerating change. The exponential growth trend is commonly considered to be the amalgamated effect of consecutive technology revolutions - where the progress carried in by each technology revolution follows an S-curve, and where the aging of each technology revolution drives humanity to push for the next technology revolution. Thus, as a collective, mankind is the 'intelligent designer' of accelerating change. In this paper we establish that the exponential growth trend - and only this trend - emerges universally, on large time scales, from systems that combine together two elements: randomness and amalgamation. Hence, the universal generation of accelerating change can be attained by systems with no 'intelligent designer'.

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.

Exploring conservative islands using correlated and uncorrelated noise

NASA Astrophysics Data System (ADS)

da Silva, Rafael M.; Manchein, Cesar; Beims, Marcus W.

2018-02-01

In this work, noise is used to analyze the penetration of regular islands in conservative dynamical systems. For this purpose we use the standard map choosing nonlinearity parameters for which a mixed phase space is present. The random variable which simulates noise assumes three distributions, namely equally distributed, normal or Gaussian, and power law (obtained from the same standard map but for other parameters). To investigate the penetration process and explore distinct dynamical behaviors which may occur, we use recurrence time statistics (RTS), Lyapunov exponents and the occupation rate of the phase space. Our main findings are as follows: (i) the standard deviations of the distributions are the most relevant quantity to induce the penetration; (ii) the penetration of islands induce power-law decays in the RTS as a consequence of enhanced trapping; (iii) for the power-law correlated noise an algebraic decay of the RTS is observed, even though sticky motion is absent; and (iv) although strong noise intensities induce an ergodic-like behavior with exponential decays of RTS, the largest Lyapunov exponent is reminiscent of the regular islands.

Polynomials with Restricted Coefficients and Their Applications

DTIC Science & Technology

1987-01-01

sums of exponentials of quadratics, he reduced such ýzums to exponentials of linears (geometric sums!) by simplg multiplying by their conjugates...n, the same algebraic manipulations as before lead to rn V`-~ v ie ? --8-- el4V’ .fk ts with 𔄃 = a+(2r+l)t, A = a+(2r+2m+l)t. To estimate the right...coefficients. These random polynomials represent the deviation in frequency response of a linear , equispaced antenna array cauised by coefficient

Rapid growth of seed black holes in the early universe by supra-exponential accretion.

PubMed

Alexander, Tal; Natarajan, Priyamvada

2014-09-12

Mass accretion by black holes (BHs) is typically capped at the Eddington rate, when radiation's push balances gravity's pull. However, even exponential growth at the Eddington-limited e-folding time t(E) ~ few × 0.01 billion years is too slow to grow stellar-mass BH seeds into the supermassive luminous quasars that are observed when the universe is 1 billion years old. We propose a dynamical mechanism that can trigger supra-exponential accretion in the early universe, when a BH seed is bound in a star cluster fed by the ubiquitous dense cold gas flows. The high gas opacity traps the accretion radiation, while the low-mass BH's random motions suppress the formation of a slowly draining accretion disk. Supra-exponential growth can thus explain the puzzling emergence of supermassive BHs that power luminous quasars so soon after the Big Bang. Copyright © 2014, American Association for the Advancement of Science.

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.

Diffusion and Localization of Relative Strategy Scores in The Minority Game

NASA Astrophysics Data System (ADS)

Granath, Mats; Perez-Diaz, Alvaro

2016-10-01

We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase (α ≡ P/N≳ 1) of the basic Minority Game using sign-payoff, with N agents holding two strategies over P histories. We formulate a statistical model that makes use of the gauge freedom with respect to the ordering of an agent's strategies to quantify the correlation between the attendance and the distribution of strategies. The relative score xin Z of the two strategies of an agent is described in terms of a one dimensional random walk with asymmetric jump probabilities, leading either to a static and asymmetric exponential distribution centered at x=0 for fickle agents or to diffusion with a positive or negative drift for frozen agents. In terms of scaled coordinates x/√{N} and t / N the distributions are uniquely given by α and in quantitative agreement with direct simulations of the game. As the model avoids the reformulation in terms of a constrained minimization problem it can be used for arbitrary payoff functions with little calculational effort and provides a transparent and simple formulation of the dynamics of the basic Minority Game in the asymmetric phase.

Critical thresholds for eventual extinction in randomly disturbed population growth models.

PubMed

Peckham, Scott D; Waymire, Edward C; De Leenheer, Patrick

2018-02-16

This paper considers several single species growth models featuring a carrying capacity, which are subject to random disturbances that lead to instantaneous population reduction at the disturbance times. This is motivated in part by growing concerns about the impacts of climate change. Our main goal is to understand whether or not the species can persist in the long run. We consider the discrete-time stochastic process obtained by sampling the system immediately after the disturbances, and find various thresholds for several modes of convergence of this discrete process, including thresholds for the absence or existence of a positively supported invariant distribution. These thresholds are given explicitly in terms of the intensity and frequency of the disturbances on the one hand, and the population's growth characteristics on the other. We also perform a similar threshold analysis for the original continuous-time stochastic process, and obtain a formula that allows us to express the invariant distribution for this continuous-time process in terms of the invariant distribution of the discrete-time process, and vice versa. Examples illustrate that these distributions can differ, and this sends a cautionary message to practitioners who wish to parameterize these and related models using field data. Our analysis relies heavily on a particular feature shared by all the deterministic growth models considered here, namely that their solutions exhibit an exponentially weighted averaging property between a function of the initial condition, and the same function applied to the carrying capacity. This property is due to the fact that these systems can be transformed into affine systems.

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.

Statics and Dynamics of Selfish Interactions in Distributed Service Systems

PubMed Central

Altarelli, Fabrizio; Braunstein, Alfredo; Dall’Asta, Luca

2015-01-01

We study a class of games which models the competition among agents to access some service provided by distributed service units and which exhibits congestion and frustration phenomena when service units have limited capacity. We propose a technique, based on the cavity method of statistical physics, to characterize the full spectrum of Nash equilibria of the game. The analysis reveals a large variety of equilibria, with very different statistical properties. Natural selfish dynamics, such as best-response, usually tend to large-utility equilibria, even though those of smaller utility are exponentially more numerous. Interestingly, the latter actually can be reached by selecting the initial conditions of the best-response dynamics close to the saturation limit of the service unit capacities. We also study a more realistic stochastic variant of the game by means of a simple and effective approximation of the average over the random parameters, showing that the properties of the average-case Nash equilibria are qualitatively similar to the deterministic ones. PMID:26177449

Large deviations and mixing for dissipative PDEs with unbounded random kicks

NASA Astrophysics Data System (ADS)

Jakšić, V.; Nersesyan, V.; Pillet, C.-A.; Shirikyan, A.

2018-02-01

We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic dynamics and a non-degeneracy condition for the driving random force, we discuss the existence and uniqueness of a stationary measure and its exponential stability in the Kantorovich-Wasserstein metric. We next turn to the large deviations principle (LDP) and establish its validity for the occupation measures of the Markov processes in question. The proof is based on Kifer’s criterion for non-compact spaces, a result on large-time asymptotics for generalised Markov semigroup, and a coupling argument. These tools combined together constitute a new approach to LDP for infinite-dimensional processes without strong Feller property in a non-compact space. The results obtained can be applied to the two-dimensional Navier-Stokes system in a bounded domain and to the complex Ginzburg-Landau equation.

Stability of the Markov operator and synchronization of Markovian random products

NASA Astrophysics Data System (ADS)

Díaz, Lorenzo J.; Matias, Edgar

2018-05-01

We study Markovian random products on a large class of ‘m-dimensional’ connected compact metric spaces (including products of closed intervals and trees). We introduce a splitting condition, generalizing the classical one by Dubins and Freedman, and prove that this condition implies the asymptotic stability of the corresponding Markov operator and (exponentially fast) synchronization.

On the identification of Dragon Kings among extreme-valued outliers

NASA Astrophysics Data System (ADS)

Riva, M.; Neuman, S. P.; Guadagnini, A.

2013-07-01

Extreme values of earth, environmental, ecological, physical, biological, financial and other variables often form outliers to heavy tails of empirical frequency distributions. Quite commonly such tails are approximated by stretched exponential, log-normal or power functions. Recently there has been an interest in distinguishing between extreme-valued outliers that belong to the parent population of most data in a sample and those that do not. The first type, called Gray Swans by Nassim Nicholas Taleb (often confused in the literature with Taleb's totally unknowable Black Swans), is drawn from a known distribution of the tails which can thus be extrapolated beyond the range of sampled values. However, the magnitudes and/or space-time locations of unsampled Gray Swans cannot be foretold. The second type of extreme-valued outliers, termed Dragon Kings by Didier Sornette, may in his view be sometimes predicted based on how other data in the sample behave. This intriguing prospect has recently motivated some authors to propose statistical tests capable of identifying Dragon Kings in a given random sample. Here we apply three such tests to log air permeability data measured on the faces of a Berea sandstone block and to synthetic data generated in a manner statistically consistent with these measurements. We interpret the measurements to be, and generate synthetic data that are, samples from α-stable sub-Gaussian random fields subordinated to truncated fractional Gaussian noise (tfGn). All these data have frequency distributions characterized by power-law tails with extreme-valued outliers about the tail edges.

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.

Answer (in part) blowing in the wind. Comment on "Liberating Lévy walk research from the shackles of optimal foraging" by A. Reynolds

NASA Astrophysics Data System (ADS)

Cheng, Ken

2015-09-01

In a perspective in this issue based on thorough review, Andy Reynolds [1] tackles the issue of how the by now ubiquitously found Lévy walks can be generated, by animals, by organisms other than animals, and other forms of life below the level of organisms, such as cells. The answer comes not in a single whole cloth, but rather in a patchwork of generating factors. Lévy-like movements arise in objects blowing in the wind, or from travelers encountering turbulence in the seas or being repelled by boundaries. A variety of desiderata in movements, not related to achieving optimal foraging, may also engender Lévy-like movements. These include avoiding other organisms or not crossing one's traveled path. Adding to that plethora are ways in which variations on the theme of garden-variety random walks can at least approach a Lévy walk, if not capturing the mathematical form perfectly. Such variations include executing random walks on multiple scales, a strategy exhibited by desert ants [2,3], mussels [4], and quite likely extant hunter-gatherer humans as well [5]. It is possible that fossil tracks over 50 million years old also show this strategy, as the curve fitting with multiple random walks, characterized by multiple exponential distributions, is as good or better than curve fits having the power-law distribution characteristic of Lévy walks [6]. Another variation is to have a random walk search whose scale is expanding over time. In great detail and based on extensive literature - the review has over 200 references - a range of other ways in which Lévy-like movements might come about are also discussed.

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.

Geometrical effects on the electron residence time in semiconductor nano-particles

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

Koochi, Hakimeh; Ebrahimi, Fatemeh, E-mail: f-ebrahimi@birjand.ac.ir; Solar Energy Research Group, University of Birjand, Birjand

2014-09-07

We have used random walk (RW) numerical simulations to investigate the influence of the geometry on the statistics of the electron residence time τ{sub r} in a trap-limited diffusion process through semiconductor nano-particles. This is an important parameter in coarse-grained modeling of charge carrier transport in nano-structured semiconductor films. The traps have been distributed randomly on the surface (r{sup 2} model) or through the whole particle (r{sup 3} model) with a specified density. The trap energies have been taken from an exponential distribution and the traps release time is assumed to be a stochastic variable. We have carried out (RW)more » simulations to study the effect of coordination number, the spatial arrangement of the neighbors and the size of nano-particles on the statistics of τ{sub r}. It has been observed that by increasing the coordination number n, the average value of electron residence time, τ{sup ¯}{sub r} rapidly decreases to an asymptotic value. For a fixed coordination number n, the electron's mean residence time does not depend on the neighbors' spatial arrangement. In other words, τ{sup ¯}{sub r} is a porosity-dependence, local parameter which generally varies remarkably from site to site, unless we are dealing with highly ordered structures. We have also examined the effect of nano-particle size d on the statistical behavior of τ{sup ¯}{sub r}. Our simulations indicate that for volume distribution of traps, τ{sup ¯}{sub r} scales as d{sup 2}. For a surface distribution of traps τ{sup ¯}{sub r} increases almost linearly with d. This leads to the prediction of a linear dependence of the diffusion coefficient D on the particle size d in ordered structures or random structures above the critical concentration which is in accordance with experimental observations.« less

Natural Time and Nowcasting Earthquakes: Are Large Global Earthquakes Temporally Clustered?

NASA Astrophysics Data System (ADS)

Luginbuhl, Molly; Rundle, John B.; Turcotte, Donald L.

2018-02-01

The objective of this paper is to analyze the temporal clustering of large global earthquakes with respect to natural time, or interevent count, as opposed to regular clock time. To do this, we use two techniques: (1) nowcasting, a new method of statistically classifying seismicity and seismic risk, and (2) time series analysis of interevent counts. We chose the sequences of M_{λ } ≥ 7.0 and M_{λ } ≥ 8.0 earthquakes from the global centroid moment tensor (CMT) catalog from 2004 to 2016 for analysis. A significant number of these earthquakes will be aftershocks of the largest events, but no satisfactory method of declustering the aftershocks in clock time is available. A major advantage of using natural time is that it eliminates the need for declustering aftershocks. The event count we utilize is the number of small earthquakes that occur between large earthquakes. The small earthquake magnitude is chosen to be as small as possible, such that the catalog is still complete based on the Gutenberg-Richter statistics. For the CMT catalog, starting in 2004, we found the completeness magnitude to be M_{σ } ≥ 5.1. For the nowcasting method, the cumulative probability distribution of these interevent counts is obtained. We quantify the distribution using the exponent, β, of the best fitting Weibull distribution; β = 1 for a random (exponential) distribution. We considered 197 earthquakes with M_{λ } ≥ 7.0 and found β = 0.83 ± 0.08. We considered 15 earthquakes with M_{λ } ≥ 8.0, but this number was considered too small to generate a meaningful distribution. For comparison, we generated synthetic catalogs of earthquakes that occur randomly with the Gutenberg-Richter frequency-magnitude statistics. We considered a synthetic catalog of 1.97 × 10^5 M_{λ } ≥ 7.0 earthquakes and found β = 0.99 ± 0.01. The random catalog converted to natural time was also random. We then generated 1.5 × 10^4 synthetic catalogs with 197 M_{λ } ≥ 7.0 in each catalog and found the statistical range of β values. The observed value of β = 0.83 for the CMT catalog corresponds to a p value of p=0.004 leading us to conclude that the interevent natural times in the CMT catalog are not random. For the time series analysis, we calculated the autocorrelation function for the sequence of natural time intervals between large global earthquakes and again compared with data from 1.5 × 10^4 synthetic catalogs of random data. In this case, the spread of autocorrelation values was much larger, so we concluded that this approach is insensitive to deviations from random behavior.

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.

Vaccination intervention on epidemic dynamics in networks

NASA Astrophysics Data System (ADS)

Peng, Xiao-Long; Xu, Xin-Jian; Fu, Xinchu; Zhou, Tao

2013-02-01

Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabási-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.

Modelling the Probability of Landslides Impacting Road Networks

NASA Astrophysics Data System (ADS)

Taylor, F. E.; Malamud, B. D.

2012-04-01

During a landslide triggering event, the threat of landslides blocking roads poses a risk to logistics, rescue efforts and communities dependant on those road networks. Here we present preliminary results of a stochastic model we have developed to evaluate the probability of landslides intersecting a simple road network during a landslide triggering event and apply simple network indices to measure the state of the road network in the affected region. A 4000 x 4000 cell array with a 5 m x 5 m resolution was used, with a pre-defined simple road network laid onto it, and landslides 'randomly' dropped onto it. Landslide areas (AL) were randomly selected from a three-parameter inverse gamma probability density function, consisting of a power-law decay of about -2.4 for medium and large values of AL and an exponential rollover for small values of AL; the rollover (maximum probability) occurs at about AL = 400 m2 This statistical distribution was chosen based on three substantially complete triggered landslide inventories recorded in existing literature. The number of landslide areas (NL) selected for each triggered event iteration was chosen to have an average density of 1 landslide km-2, i.e. NL = 400 landslide areas chosen randomly for each iteration, and was based on several existing triggered landslide event inventories. A simple road network was chosen, in a 'T' shape configuration, with one road 1 x 4000 cells (5 m x 20 km) in a 'T' formation with another road 1 x 2000 cells (5 m x 10 km). The landslide areas were then randomly 'dropped' over the road array and indices such as the location, size (ABL) and number of road blockages (NBL) recorded. This process was performed 500 times (iterations) in a Monte-Carlo type simulation. Initial results show that for a landslide triggering event with 400 landslides over a 400 km2 region, the number of road blocks per iteration, NBL,ranges from 0 to 7. The average blockage area for the 500 iterations (A¯ BL) is about 3000 m2, which closely matches the value of A¯ L for the triggered landslide inventories. We further find that over the 500 iterations, the probability of a given number of road blocks occurring on any given iteration, p(NBL) as a function of NBL, follows reasonably well a three-parameter inverse gamma probability density distribution with an exponential rollover (i.e., the most frequent value) at NBL = 1.3. In this paper we have begun to calculate the probability of the number of landslides blocking roads during a triggering event, and have found that this follows an inverse-gamma distribution, which is similar to that found for the statistics of landslide areas resulting from triggers. As we progress to model more realistic road networks, this work will aid in both long-term and disaster management for road networks by allowing probabilistic assessment of road network potential damage during different magnitude landslide triggering event scenarios.

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.

In vivo growth of 60 non-screening detected lung cancers: a computed tomography study.

PubMed

Mets, Onno M; Chung, Kaman; Zanen, Pieter; Scholten, Ernst T; Veldhuis, Wouter B; van Ginneken, Bram; Prokop, Mathias; Schaefer-Prokop, Cornelia M; de Jong, Pim A

2018-04-01

Current pulmonary nodule management guidelines are based on nodule volume doubling time, which assumes exponential growth behaviour. However, this is a theory that has never been validated in vivo in the routine-care target population. This study evaluates growth patterns of untreated solid and subsolid lung cancers of various histologies in a non-screening setting.Growth behaviour of pathology-proven lung cancers from two academic centres that were imaged at least three times before diagnosis (n=60) was analysed using dedicated software. Random-intercept random-slope mixed-models analysis was applied to test which growth pattern most accurately described lung cancer growth. Individual growth curves were plotted per pathology subgroup and nodule type.We confirmed that growth in both subsolid and solid lung cancers is best explained by an exponential model. However, subsolid lesions generally progress slower than solid ones. Baseline lesion volume was not related to growth, indicating that smaller lesions do not grow slower compared to larger ones.By showing that lung cancer conforms to exponential growth we provide the first experimental basis in the routine-care setting for the assumption made in volume doubling time analysis. Copyright ©ERS 2018.

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.

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

Using Exponential Random Graph Models to Analyze the Character of Peer Relationship Networks and Their Effects on the Subjective Well-being of Adolescents.

PubMed

Jiao, Can; Wang, Ting; Liu, Jianxin; Wu, Huanjie; Cui, Fang; Peng, Xiaozhe

2017-01-01

The influences of peer relationships on adolescent subjective well-being were investigated within the framework of social network analysis, using exponential random graph models as a methodological tool. The participants in the study were 1,279 students (678 boys and 601 girls) from nine junior middle schools in Shenzhen, China. The initial stage of the research used a peer nomination questionnaire and a subjective well-being scale (used in previous studies) to collect data on the peer relationship networks and the subjective well-being of the students. Exponential random graph models were then used to explore the relationships between students with the aim of clarifying the character of the peer relationship networks and the influence of peer relationships on subjective well being. The results showed that all the adolescent peer relationship networks in our investigation had positive reciprocal effects, positive transitivity effects and negative expansiveness effects. However, none of the relationship networks had obvious receiver effects or leaders. The adolescents in partial peer relationship networks presented similar levels of subjective well-being on three dimensions (satisfaction with life, positive affects and negative affects) though not all network friends presented these similarities. The study shows that peer networks can affect an individual's subjective well-being. However, whether similarities among adolescents are the result of social influences or social choices needs further exploration, including longitudinal studies that investigate the potential processes of subjective well-being similarities among adolescents.

Using Exponential Random Graph Models to Analyze the Character of Peer Relationship Networks and Their Effects on the Subjective Well-being of Adolescents

PubMed Central

Jiao, Can; Wang, Ting; Liu, Jianxin; Wu, Huanjie; Cui, Fang; Peng, Xiaozhe

2017-01-01

The influences of peer relationships on adolescent subjective well-being were investigated within the framework of social network analysis, using exponential random graph models as a methodological tool. The participants in the study were 1,279 students (678 boys and 601 girls) from nine junior middle schools in Shenzhen, China. The initial stage of the research used a peer nomination questionnaire and a subjective well-being scale (used in previous studies) to collect data on the peer relationship networks and the subjective well-being of the students. Exponential random graph models were then used to explore the relationships between students with the aim of clarifying the character of the peer relationship networks and the influence of peer relationships on subjective well being. The results showed that all the adolescent peer relationship networks in our investigation had positive reciprocal effects, positive transitivity effects and negative expansiveness effects. However, none of the relationship networks had obvious receiver effects or leaders. The adolescents in partial peer relationship networks presented similar levels of subjective well-being on three dimensions (satisfaction with life, positive affects and negative affects) though not all network friends presented these similarities. The study shows that peer networks can affect an individual’s subjective well-being. However, whether similarities among adolescents are the result of social influences or social choices needs further exploration, including longitudinal studies that investigate the potential processes of subjective well-being similarities among adolescents. PMID:28450845

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.

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

Hoeffding Type Inequalities and their Applications in Statistics and Operations Research

NASA Astrophysics Data System (ADS)

Daras, Tryfon

2007-09-01

Large Deviation theory is the branch of Probability theory that deals with rare events. Sometimes, these events can be described by the sum of random variables that deviates from its mean more than a "normal" amount. A precise calculation of the probabilities of such events turns out to be crucial in a variety of different contents (e.g. in Probability Theory, Statistics, Operations Research, Statistical Physics, Financial Mathematics e.t.c.). Recent applications of the theory deal with random walks in random environments, interacting diffusions, heat conduction, polymer chains [1]. In this paper we prove an inequality of exponential type, namely theorem 2.1, which gives a large deviation upper bound for a specific sequence of r.v.s. Inequalities of this type have many applications in Combinatorics [2]. The inequality generalizes already proven results of this type, in the case of symmetric probability measures. We get as consequences to the inequality: (a) large deviations upper bounds for exchangeable Bernoulli sequences of random variables, generalizing results proven for independent and identically distributed Bernoulli sequences of r.v.s. and (b) a general form of Bernstein's inequality. We compare the inequality with large deviation results already proven by the author and try to see its advantages. Finally, using the inequality, we solve one of the basic problems of Operations Research (bin packing problem) in the case of exchangeable r.v.s.

Random sampling of elementary flux modes in large-scale metabolic networks.

PubMed

Machado, Daniel; Soons, Zita; Patil, Kiran Raosaheb; Ferreira, Eugénio C; Rocha, Isabel

2012-09-15

The description of a metabolic network in terms of elementary (flux) modes (EMs) provides an important framework for metabolic pathway analysis. However, their application to large networks has been hampered by the combinatorial explosion in the number of modes. In this work, we develop a method for generating random samples of EMs without computing the whole set. Our algorithm is an adaptation of the canonical basis approach, where we add an additional filtering step which, at each iteration, selects a random subset of the new combinations of modes. In order to obtain an unbiased sample, all candidates are assigned the same probability of getting selected. This approach avoids the exponential growth of the number of modes during computation, thus generating a random sample of the complete set of EMs within reasonable time. We generated samples of different sizes for a metabolic network of Escherichia coli, and observed that they preserve several properties of the full EM set. It is also shown that EM sampling can be used for rational strain design. A well distributed sample, that is representative of the complete set of EMs, should be suitable to most EM-based methods for analysis and optimization of metabolic networks. Source code for a cross-platform implementation in Python is freely available at http://code.google.com/p/emsampler. dmachado@deb.uminho.pt Supplementary data are available at Bioinformatics online.

The Supermarket Model with Bounded Queue Lengths in Equilibrium

NASA Astrophysics Data System (ADS)

Brightwell, Graham; Fairthorne, Marianne; Luczak, Malwina J.

2018-04-01

In the supermarket model, there are n queues, each with a single server. Customers arrive in a Poisson process with arrival rate λ n , where λ = λ (n) \\in (0,1) . Upon arrival, a customer selects d=d(n) servers uniformly at random, and joins the queue of a least-loaded server amongst those chosen. Service times are independent exponentially distributed random variables with mean 1. In this paper, we analyse the behaviour of the supermarket model in the regime where λ (n) = 1 - n^{-α } and d(n) = \\lfloor n^β \\rfloor , where α and β are fixed numbers in (0, 1]. For suitable pairs (α , β ) , our results imply that, in equilibrium, with probability tending to 1 as n → ∞, the proportion of queues with length equal to k = \\lceil α /β \\rceil is at least 1-2n^{-α + (k-1)β } , and there are no longer queues. We further show that the process is rapidly mixing when started in a good state, and give bounds on the speed of mixing for more general initial conditions.

MIXREG: a computer program for mixed-effects regression analysis with autocorrelated errors.

PubMed

Hedeker, D; Gibbons, R D

1996-05-01

MIXREG is a program that provides estimates for a mixed-effects regression model (MRM) for normally-distributed response data including autocorrelated errors. This model can be used for analysis of unbalanced longitudinal data, where individuals may be measured at a different number of timepoints, or even at different timepoints. Autocorrelated errors of a general form or following an AR(1), MA(1), or ARMA(1,1) form are allowable. This model can also be used for analysis of clustered data, where the mixed-effects model assumes data within clusters are dependent. The degree of dependency is estimated jointly with estimates of the usual model parameters, thus adjusting for clustering. MIXREG uses maximum marginal likelihood estimation, utilizing both the EM algorithm and a Fisher-scoring solution. For the scoring solution, the covariance matrix of the random effects is expressed in its Gaussian decomposition, and the diagonal matrix reparameterized using the exponential transformation. Estimation of the individual random effects is accomplished using an empirical Bayes approach. Examples illustrating usage and features of MIXREG are provided.

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.

Large and small-scale structures and the dust energy balance problem in spiral galaxies

NASA Astrophysics Data System (ADS)

Saftly, W.; Baes, M.; De Geyter, G.; Camps, P.; Renaud, F.; Guedes, J.; De Looze, I.

2015-04-01

The interstellar dust content in galaxies can be traced in extinction at optical wavelengths, or in emission in the far-infrared. Several studies have found that radiative transfer models that successfully explain the optical extinction in edge-on spiral galaxies generally underestimate the observed FIR/submm fluxes by a factor of about three. In order to investigate this so-called dust energy balance problem, we use two Milky Way-like galaxies produced by high-resolution hydrodynamical simulations. We create mock optical edge-on views of these simulated galaxies (using the radiative transfer code SKIRT), and we then fit the parameters of a basic spiral galaxy model to these images (using the fitting code FitSKIRT). The basic model includes smooth axisymmetric distributions along a Sérsic bulge and exponential disc for the stars, and a second exponential disc for the dust. We find that the dust mass recovered by the fitted models is about three times smaller than the known dust mass of the hydrodynamical input models. This factor is in agreement with previous energy balance studies of real edge-on spiral galaxies. On the other hand, fitting the same basic model to less complex input models (e.g. a smooth exponential disc with a spiral perturbation or with random clumps), does recover the dust mass of the input model almost perfectly. Thus it seems that the complex asymmetries and the inhomogeneous structure of real and hydrodynamically simulated galaxies are a lot more efficient at hiding dust than the rather contrived geometries in typical quasi-analytical models. This effect may help explain the discrepancy between the dust emission predicted by radiative transfer models and the observed emission in energy balance studies for edge-on spiral galaxies.

Local dependence in random graph models: characterization, properties and statistical inference

PubMed Central

Schweinberger, Michael; Handcock, Mark S.

2015-01-01

Summary Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with ‘ground truth’. PMID:26560142

Dynamical properties of the S =1/2 random Heisenberg chain

NASA Astrophysics Data System (ADS)

Shu, Yu-Rong; Dupont, Maxime; Yao, Dao-Xin; Capponi, Sylvain; Sandvik, Anders W.

2018-03-01

We study dynamical properties at finite temperature (T ) of Heisenberg spin chains with random antiferromagnetic exchange couplings, which realize the random singlet phase in the low-energy limit, using three complementary numerical methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Specifically, we investigate the dynamic spin structure factor S (q ,ω ) and its ω →0 limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate 1 /T1 ). Our study reveals a continuous narrow band of low-energy excitations in S (q ,ω ) , extending throughout the q space, instead of being restricted to q ≈0 and q ≈π as found in the uniform system. Close to q =π , the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted q dependence further away from q =π . Furthermore we also find spin diffusion effects close to q =0 that are not contained within the random-singlet theory but give non-negligible contributions to the mean 1 /T1 . To compare with NMR experiments, we consider the distribution of the local relaxation rates 1 /T1 . We show that the local 1 /T1 values are broadly distributed, approximately according to a stretched exponential. The mean 1 /T1 first decreases with T , but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency ω0. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean 1 /T1 has never been experimentally observed. Indeed, we show that the divergence of the mean 1 /T1 is due to rare events in the disordered chains and is concealed in experiments, where the typical 1 /T1 value is accessed.

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.

Complex scaling behavior in animal foraging patterns

NASA Astrophysics Data System (ADS)

Premachandra, Prabhavi Kaushalya

This dissertation attempts to answer questions from two different areas of biology, ecology and neuroscience, using physics-based techniques. In Section 2, suitability of three competing random walk models is tested to describe the emergent movement patterns of two species of primates. The truncated power law (power law with exponential cut off) is the most suitable random walk model that characterizes the emergent movement patterns of these primates. In Section 3, an agent-based model is used to simulate search behavior in different environments (landscapes) to investigate the impact of the resource landscape on the optimal foraging movement patterns of deterministic foragers. It should be noted that this model goes beyond previous work in that it includes parameters such as spatial memory and satiation, which have received little consideration to date in the field of movement ecology. When the food availability is scarce in a tropical forest-like environment with feeding trees distributed in a clumped fashion and the size of those trees are distributed according to a lognormal distribution, the optimal foraging pattern of a generalist who can consume various and abundant food types indeed reaches the Levy range, and hence, show evidence for Levy-flight-like (power law distribution with exponent between 1 and 3) behavior. Section 4 of the dissertation presents an investigation of phase transition behavior in a network of locally coupled self-sustained oscillators as the system passes through various bursting states. The results suggest that a phase transition does not occur for this locally coupled neuronal network. The data analysis in the dissertation adopts a model selection approach and relies on methods based on information theory and maximum likelihood.

A Bayesian, generalized frailty model for comet assays.

PubMed

Ghebretinsae, Aklilu Habteab; Faes, Christel; Molenberghs, Geert; De Boeck, Marlies; Geys, Helena

2013-05-01

This paper proposes a flexible modeling approach for so-called comet assay data regularly encountered in preclinical research. While such data consist of non-Gaussian outcomes in a multilevel hierarchical structure, traditional analyses typically completely or partly ignore this hierarchical nature by summarizing measurements within a cluster. Non-Gaussian outcomes are often modeled using exponential family models. This is true not only for binary and count data, but also for, example, time-to-event outcomes. Two important reasons for extending this family are for (1) the possible occurrence of overdispersion, meaning that the variability in the data may not be adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of a hierarchical structure in the data, owing to clustering in the data. The first issue is dealt with through so-called overdispersion models. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. In the case of time-to-event data, one encounters, for example, the gamma frailty model (Duchateau and Janssen, 2007 ). While both of these issues may occur simultaneously, models combining both are uncommon. Molenberghs et al. ( 2010 ) proposed a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. Here, we use this method to model data from a comet assay with a three-level hierarchical structure. Although a conjugate gamma random effect is used for the overdispersion random effect, both gamma and normal random effects are considered for the hierarchical random effect. Apart from model formulation, we place emphasis on Bayesian estimation. Our proposed method has an upper hand over the traditional analysis in that it (1) uses the appropriate distribution stipulated in the literature; (2) deals with the complete hierarchical nature; and (3) uses all information instead of summary measures. The fit of the model to the comet assay is compared against the background of more conventional model fits. Results indicate the toxicity of 1,2-dimethylhydrazine dihydrochloride at different dose levels (low, medium, and high).

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.

Particle shape inhomogeneity and plasmon-band broadening of solar-control LaB6 nanoparticles

NASA Astrophysics Data System (ADS)

Machida, Keisuke; Adachi, Kenji

2015-07-01

An ensemble inhomogeneity of non-spherical LaB6 nanoparticles dispersion has been analyzed with Mie theory to account for the observed broad plasmon band. LaB6 particle shape has been characterized using small-angle X-ray scattering (SAXS) and electron tomography (ET). SAXS scattering intensity is found to vary exponentially with exponent -3.10, indicating the particle shape of disk toward sphere. ET analysis disclosed dually grouped distribution of nanoparticle dispersion; one is large-sized at small aspect ratio and the other is small-sized with scattered high aspect ratio, reflecting the dual fragmentation modes during the milling process. Mie extinction calculations have been integrated for 100 000 particles of varying aspect ratio, which were produced randomly by using the Box-Muller method. The Mie integration method has produced a broad and smooth absorption band expanded towards low energy, in remarkable agreement with experimental profiles by assuming a SAXS- and ET-derived shape distribution, i.e., a majority of disks with a little incorporation of rods and spheres for the ensemble. The analysis envisages a high potential of LaB6 with further-increased visible transparency and plasmon peak upon controlled particle-shape and its distribution.

Application of a deconvolution method for identifying burst amplitudes and arrival times in Alcator C-Mod far SOL plasma fluctuations

NASA Astrophysics Data System (ADS)

Theodorsen, Audun; Garcia, Odd Erik; Kube, Ralph; Labombard, Brian; Terry, Jim

2017-10-01

In the far scrape-off layer (SOL), radial motion of filamentary structures leads to excess transport of particles and heat. Amplitudes and arrival times of these filaments have previously been studied by conditional averaging in single-point measurements from Langmuir Probes and Gas Puff Imaging (GPI). Conditional averaging can be problematic: the cutoff for large amplitudes is mostly chosen by convention; the conditional windows used may influence the arrival time distribution; and the amplitudes cannot be separated from a background. Previous work has shown that SOL fluctuations are well described by a stochastic model consisting of a super-position of pulses with fixed shape and randomly distributed amplitudes and arrival times. The model can be formulated as a pulse shape convolved with a train of delta pulses. By choosing a pulse shape consistent with the power spectrum of the fluctuation time series, Richardson-Lucy deconvolution can be used to recover the underlying amplitudes and arrival times of the delta pulses. We apply this technique to both L and H-mode GPI data from the Alcator C-Mod tokamak. The pulse arrival times are shown to be uncorrelated and uniformly distributed, consistent with a Poisson process, and the amplitude distribution has an exponential tail.

Penna Bit-String Model with Constant Population

NASA Astrophysics Data System (ADS)

de Oliveira, P. M. C.; de Oliveira, S. Moss; Sá Martins, J. S.

We removed from the Penna model for biological aging any random killing Verhulst factor. Deaths are due only to genetic diseases and the population size is fixed, instead of fluctuating around some constant value. We show that these modifications give qualitatively the same results obtained in an earlier paper, where the random killings (used to avoid an exponential increase of the population) were applied only to newborns.

Time Course of Visual Extrapolation Accuracy

DTIC Science & Technology

1995-09-01

The pond and duckweed problem: Three experiments on the misperception of exponential growth . Acta Psychologica 43, 239-251. Wiener, E.L., 1962...random variation in tracker velocity. Both models predicted changes in hit and false alarm rates well, except in a condition where response asymmetries...systematic velocity error in tracking, only random variation in tracker velocity. Both models predicted changes in hit and false alarm rates well

Bridging the gulf between correlated random walks and Lévy walks: autocorrelation as a source of Lévy walk movement patterns.

PubMed

Reynolds, Andy M

2010-12-06

For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual's trajectory through space is represented by a sequence of distinct, independent randomly oriented 'moves'. It has long been recognized that the transformation of an animal's continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in the literature and are gaining prominence. In these models, velocities evolve as a Markovian process and have exponential autocorrelation. Integration of the velocity process gives the position process. Here, through a simple scaling argument and through an exact analytical analysis, it is shown that autocorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale. This is significant because over recent years there has been an accumulation of evidence from a variety of experimental and theoretical studies that many organisms have movement patterns that can be approximated by LWs, and there is now intense debate about the relative merits of CRWs and LWs as representations of non-orientated animal movement patterns.

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…

A different Deutsch-Jozsa

NASA Astrophysics Data System (ADS)

Bera, Debajyoti

2015-06-01

One of the early achievements of quantum computing was demonstrated by Deutsch and Jozsa (Proc R Soc Lond A Math Phys Sci 439(1907):553, 1992) regarding classification of a particular type of Boolean functions. Their solution demonstrated an exponential speedup compared to classical approaches to the same problem; however, their solution was the only known quantum algorithm for that specific problem so far. This paper demonstrates another quantum algorithm for the same problem, with the same exponential advantage compared to classical algorithms. The novelty of this algorithm is the use of quantum amplitude amplification, a technique that is the key component of another celebrated quantum algorithm developed by Grover (Proceedings of the twenty-eighth annual ACM symposium on theory of computing, ACM Press, New York, 1996). A lower bound for randomized (classical) algorithms is also presented which establishes a sound gap between the effectiveness of our quantum algorithm and that of any randomized algorithm with similar efficiency.

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.

Shallow cumuli ensemble statistics for development of a stochastic parameterization

NASA Astrophysics Data System (ADS)

Sakradzija, Mirjana; Seifert, Axel; Heus, Thijs

2014-05-01

According to a conventional deterministic approach to the parameterization of moist convection in numerical atmospheric models, a given large scale forcing produces an unique response from the unresolved convective processes. This representation leaves out the small-scale variability of convection, as it is known from the empirical studies of deep and shallow convective cloud ensembles, there is a whole distribution of sub-grid states corresponding to the given large scale forcing. Moreover, this distribution gets broader with the increasing model resolution. This behavior is also consistent with our theoretical understanding of a coarse-grained nonlinear system. We propose an approach to represent the variability of the unresolved shallow-convective states, including the dependence of the sub-grid states distribution spread and shape on the model horizontal resolution. Starting from the Gibbs canonical ensemble theory, Craig and Cohen (2006) developed a theory for the fluctuations in a deep convective ensemble. The micro-states of a deep convective cloud ensemble are characterized by the cloud-base mass flux, which, according to the theory, is exponentially distributed (Boltzmann distribution). Following their work, we study the shallow cumulus ensemble statistics and the distribution of the cloud-base mass flux. We employ a Large-Eddy Simulation model (LES) and a cloud tracking algorithm, followed by a conditional sampling of clouds at the cloud base level, to retrieve the information about the individual cloud life cycles and the cloud ensemble as a whole. In the case of shallow cumulus cloud ensemble, the distribution of micro-states is a generalized exponential distribution. Based on the empirical and theoretical findings, a stochastic model has been developed to simulate the shallow convective cloud ensemble and to test the convective ensemble theory. Stochastic model simulates a compound random process, with the number of convective elements drawn from a Poisson distribution, and cloud properties sub-sampled from a generalized ensemble distribution. We study the role of the different cloud subtypes in a shallow convective ensemble and how the diverse cloud properties and cloud lifetimes affect the system macro-state. To what extent does the cloud-base mass flux distribution deviate from the simple Boltzmann distribution and how does it affect the results from the stochastic model? Is the memory, provided by the finite lifetime of individual clouds, of importance for the ensemble statistics? We also test for the minimal information given as an input to the stochastic model, able to reproduce the ensemble mean statistics and the variability in a convective ensemble. An important property of the resulting distribution of the sub-grid convective states is its scale-adaptivity - the smaller the grid-size, the broader the compound distribution of the sub-grid states.

Solar F10.7 radiation - A short term model for Space Station applications

NASA Technical Reports Server (NTRS)

Vedder, John D.; Tabor, Jill L.

1991-01-01

A new method is described for statistically modeling the F10.7 component of solar radiation for 91-day intervals. The resulting model represents this component of the solar flux as a quasi-exponentially correlated, Weibull distributed random variable, and thereby demonstrates excellent agreement with observed F10.7 data. Values of the F10.7 flux are widely used in models of the earth's upper atmosphere because of its high correlation with density fluctuations due to solar heating effects. Because of the direct relation between atmospheric density and drag, a realistic model of the short term fluctuation of the F10.7 flux is important for the design and operation of Space Station Freedom. The method of modeling this flux described in this report should therefore be useful for a variety of Space Station applications.

Memory effects on a resonate-and-fire neuron model subjected to Ornstein-Uhlenbeck noise

NASA Astrophysics Data System (ADS)

Paekivi, S.; Mankin, R.; Rekker, A.

2017-10-01

We consider a generalized Langevin equation with an exponentially decaying memory kernel as a model for the firing process of a resonate-and-fire neuron. The effect of temporally correlated random neuronal input is modeled as Ornstein-Uhlenbeck noise. In the noise-induced spiking regime of the neuron, we derive exact analytical formulas for the dependence of some statistical characteristics of the output spike train, such as the probability distribution of the interspike intervals (ISIs) and the survival probability, on the parameters of the input stimulus. Particularly, on the basis of these exact expressions, we have established sufficient conditions for the occurrence of memory-time-induced transitions between unimodal and multimodal structures of the ISI density and a critical damping coefficient which marks a dynamical transition in the behavior of the system.

Exploring Explanations of Subglacial Bedform Sizes Using Statistical Models.

PubMed

Hillier, John K; Kougioumtzoglou, Ioannis A; Stokes, Chris R; Smith, Michael J; Clark, Chris D; Spagnolo, Matteo S

2016-01-01

Sediments beneath modern ice sheets exert a key control on their flow, but are largely inaccessible except through geophysics or boreholes. In contrast, palaeo-ice sheet beds are accessible, and typically characterised by numerous bedforms. However, the interaction between bedforms and ice flow is poorly constrained and it is not clear how bedform sizes might reflect ice flow conditions. To better understand this link we present a first exploration of a variety of statistical models to explain the size distribution of some common subglacial bedforms (i.e., drumlins, ribbed moraine, MSGL). By considering a range of models, constructed to reflect key aspects of the physical processes, it is possible to infer that the size distributions are most effectively explained when the dynamics of ice-water-sediment interaction associated with bedform growth is fundamentally random. A 'stochastic instability' (SI) model, which integrates random bedform growth and shrinking through time with exponential growth, is preferred and is consistent with other observations of palaeo-bedforms and geophysical surveys of active ice sheets. Furthermore, we give a proof-of-concept demonstration that our statistical approach can bridge the gap between geomorphological observations and physical models, directly linking measurable size-frequency parameters to properties of ice sheet flow (e.g., ice velocity). Moreover, statistically developing existing models as proposed allows quantitative predictions to be made about sizes, making the models testable; a first illustration of this is given for a hypothesised repeat geophysical survey of bedforms under active ice. Thus, we further demonstrate the potential of size-frequency distributions of subglacial bedforms to assist the elucidation of subglacial processes and better constrain ice sheet models.

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.

Wireless cellular networks with Pareto-distributed call holding times

NASA Astrophysics Data System (ADS)

Rodriguez-Dagnino, Ramon M.; Takagi, Hideaki

2001-07-01

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

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.

Harmonic statistics

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-05-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.

Maximum likelihood solution for inclination-only data in paleomagnetism

NASA Astrophysics Data System (ADS)

Arason, P.; Levi, S.

2010-08-01

We have developed a new robust maximum likelihood method for estimating the unbiased mean inclination from inclination-only data. In paleomagnetic analysis, the arithmetic mean of inclination-only data is known to introduce a shallowing bias. Several methods have been introduced to estimate the unbiased mean inclination of inclination-only data together with measures of the dispersion. Some inclination-only methods were designed to maximize the likelihood function of the marginal Fisher distribution. However, the exact analytical form of the maximum likelihood function is fairly complicated, and all the methods require various assumptions and approximations that are often inappropriate. For some steep and dispersed data sets, these methods provide estimates that are significantly displaced from the peak of the likelihood function to systematically shallower inclination. The problem locating the maximum of the likelihood function is partly due to difficulties in accurately evaluating the function for all values of interest, because some elements of the likelihood function increase exponentially as precision parameters increase, leading to numerical instabilities. In this study, we succeeded in analytically cancelling exponential elements from the log-likelihood function, and we are now able to calculate its value anywhere in the parameter space and for any inclination-only data set. Furthermore, we can now calculate the partial derivatives of the log-likelihood function with desired accuracy, and locate the maximum likelihood without the assumptions required by previous methods. To assess the reliability and accuracy of our method, we generated large numbers of random Fisher-distributed data sets, for which we calculated mean inclinations and precision parameters. The comparisons show that our new robust Arason-Levi maximum likelihood method is the most reliable, and the mean inclination estimates are the least biased towards shallow values.

Risk aversion and uncertainty in cost-effectiveness analysis: the expected-utility, moment-generating function approach.

PubMed

Elbasha, Elamin H

2005-05-01

The availability of patient-level data from clinical trials has spurred a lot of interest in developing methods for quantifying and presenting uncertainty in cost-effectiveness analysis (CEA). Although the majority has focused on developing methods for using sample data to estimate a confidence interval for an incremental cost-effectiveness ratio (ICER), a small strand of the literature has emphasized the importance of incorporating risk preferences and the trade-off between the mean and the variance of returns to investment in health and medicine (mean-variance analysis). This paper shows how the exponential utility-moment-generating function approach is a natural extension to this branch of the literature for modelling choices from healthcare interventions with uncertain costs and effects. The paper assumes an exponential utility function, which implies constant absolute risk aversion, and is based on the fact that the expected value of this function results in a convenient expression that depends only on the moment-generating function of the random variables. The mean-variance approach is shown to be a special case of this more general framework. The paper characterizes the solution to the resource allocation problem using standard optimization techniques and derives the summary measure researchers need to estimate for each programme, when the assumption of risk neutrality does not hold, and compares it to the standard incremental cost-effectiveness ratio. The importance of choosing the correct distribution of costs and effects and the issues related to estimation of the parameters of the distribution are also discussed. An empirical example to illustrate the methods and concepts is provided. Copyright 2004 John Wiley & Sons, Ltd

Quasiprobability behind the out-of-time-ordered correlator

NASA Astrophysics Data System (ADS)

Yunger Halpern, Nicole; Swingle, Brian; Dressel, Justin

2018-04-01

Two topics, evolving rapidly in separate fields, were combined recently: the out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC was shown to equal a moment of a summed quasiprobability [Yunger Halpern, Phys. Rev. A 95, 012120 (2017), 10.1103/PhysRevA.95.012120]. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze Yunger Halpern's weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse graining) numerically and analytically: we simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors: the quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. We define an extended KD quasiprobability that generalizes the KD distribution. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.

Crowding Induces Complex Ergodic Diffusion and Dynamic Elongation of Large DNA Molecules

PubMed Central

Chapman, Cole D.; Gorczyca, Stephanie; Robertson-Anderson, Rae M.

2015-01-01

Despite the ubiquity of molecular crowding in living cells, the effects of crowding on the dynamics of genome-sized DNA are poorly understood. Here, we track single, fluorescent-labeled large DNA molecules (11, 115 kbp) diffusing in dextran solutions that mimic intracellular crowding conditions (0–40%), and determine the effects of crowding on both DNA mobility and conformation. Both DNAs exhibit ergodic Brownian motion and comparable mobility reduction in all conditions; however, crowder size (10 vs. 500 kDa) plays a critical role in the underlying diffusive mechanisms and dependence on crowder concentration. Surprisingly, in 10-kDa dextran, crowder influence saturates at ∼20% with an ∼5× drop in DNA diffusion, in stark contrast to exponentially retarded mobility, coupled to weak anomalous subdiffusion, with increasing concentration of 500-kDa dextran. Both DNAs elongate into lower-entropy states (compared to random coil conformations) when crowded, with elongation states that are gamma distributed and fluctuate in time. However, the broadness of the distribution of states and the time-dependence and length scale of elongation length fluctuations depend on both DNA and crowder size with concentration having surprisingly little impact. Results collectively show that mobility reduction and coil elongation of large crowded DNAs are due to a complex interplay between entropic effects and crowder mobility. Although elongation and initial mobility retardation are driven by depletion interactions, subdiffusive dynamics, and the drastic exponential slowing of DNA, up to ∼300×, arise from the reduced mobility of larger crowders. Our results elucidate the highly important and widely debated effects of cellular crowding on genome-sized DNA. PMID:25762333

Infinite-disorder critical points of models with stretched exponential interactions

NASA Astrophysics Data System (ADS)

Juhász, Róbert

2014-09-01

We show that an interaction decaying as a stretched exponential function of distance, J(l)˜ e-cl^a , is able to alter the universality class of short-range systems having an infinite-disorder critical point. To do so, we study the low-energy properties of the random transverse-field Ising chain with the above form of interaction by a strong-disorder renormalization group (SDRG) approach. We find that the critical behavior of the model is controlled by infinite-disorder fixed points different from those of the short-range model if 0 < a < 1/2. In this range, the critical exponents calculated analytically by a simplified SDRG scheme are found to vary with a, while, for a > 1/2, the model belongs to the same universality class as its short-range variant. The entanglement entropy of a block of size L increases logarithmically with L at the critical point but, unlike the short-range model, the prefactor is dependent on disorder in the range 0 < a < 1/2. Numerical results obtained by an improved SDRG scheme are found to be in agreement with the analytical predictions. The same fixed points are expected to describe the critical behavior of, among others, the random contact process with stretched exponentially decaying activation rates.

Predictability of monthly temperature and precipitation using automatic time series forecasting methods

NASA Astrophysics Data System (ADS)

Papacharalampous, Georgia; Tyralis, Hristos; Koutsoyiannis, Demetris

2018-02-01

We investigate the predictability of monthly temperature and precipitation by applying automatic univariate time series forecasting methods to a sample of 985 40-year-long monthly temperature and 1552 40-year-long monthly precipitation time series. The methods include a naïve one based on the monthly values of the last year, as well as the random walk (with drift), AutoRegressive Fractionally Integrated Moving Average (ARFIMA), exponential smoothing state-space model with Box-Cox transformation, ARMA errors, Trend and Seasonal components (BATS), simple exponential smoothing, Theta and Prophet methods. Prophet is a recently introduced model inspired by the nature of time series forecasted at Facebook and has not been applied to hydrometeorological time series before, while the use of random walk, BATS, simple exponential smoothing and Theta is rare in hydrology. The methods are tested in performing multi-step ahead forecasts for the last 48 months of the data. We further investigate how different choices of handling the seasonality and non-normality affect the performance of the models. The results indicate that: (a) all the examined methods apart from the naïve and random walk ones are accurate enough to be used in long-term applications; (b) monthly temperature and precipitation can be forecasted to a level of accuracy which can barely be improved using other methods; (c) the externally applied classical seasonal decomposition results mostly in better forecasts compared to the automatic seasonal decomposition used by the BATS and Prophet methods; and (d) Prophet is competitive, especially when it is combined with externally applied classical seasonal decomposition.

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

Information of group-correlations in Korean financial market

NASA Astrophysics Data System (ADS)

Choi, Jaewon; Lim, Gyuchang; Kim, Soo Yong; Kim, Kyungsik

2011-01-01

We study two sides of the KOSPI, classified as an emerging market. First, the evolutionary property is examined in terms of overlapping matrix and survival ratios. To this end, we apply the random matrix theory (RMT) and the one-factor model to analyzing correlation matrix and finding business clusters. Second, we examine the relations between the market capitalization and the business. For the well-developed markets such as NYSE, the contribution of the firms to the second-largest eigenvector shows an exponential function of the market capitalizations while no clue is observed for the KOSPI. We confirm that the market capitalization is distributed in a power-law with the exponent 1.2 like a Pareto's distribution. Particulary, the KOSPI shows a different behavior compared to the mature market, that is, one or two companies lead a number of companies with the little money and big companies competed to win each other. The clusters also represent by largest eigenstates show a weak affiliation compared to smaller ones. These results imply that the KOSPI is the target for the short-positioned investors.

Distributed synchronization control of complex networks with communication constraints.

PubMed

Xu, Zhenhua; Zhang, Dan; Song, Hongbo

2016-11-01

This paper is concerned with the distributed synchronization control of complex networks with communication constraints. In this work, the controllers communicate with each other through the wireless network, acting as a controller network. Due to the constrained transmission power, techniques such as the packet size reduction and transmission rate reduction schemes are proposed which could help reduce communication load of the controller network. The packet dropout problem is also considered in the controller design since it is often encountered in networked control systems. We show that the closed-loop system can be modeled as a switched system with uncertainties and random variables. By resorting to the switched system approach and some stochastic system analysis method, a new sufficient condition is firstly proposed such that the exponential synchronization is guaranteed in the mean-square sense. The controller gains are determined by using the well-known cone complementarity linearization (CCL) algorithm. Finally, a simulation study is performed, which demonstrates the effectiveness of the proposed design algorithm. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Exponential convergence rate (the spectral convergence) of the fast Padé transform for exact quantification in magnetic resonance spectroscopy.

PubMed

Belkić, Dzevad

2006-12-21

This study deals with the most challenging numerical aspect for solving the quantification problem in magnetic resonance spectroscopy (MRS). The primary goal is to investigate whether it could be feasible to carry out a rigorous computation within finite arithmetics to reconstruct exactly all the machine accurate input spectral parameters of every resonance from a synthesized noiseless time signal. We also consider simulated time signals embedded in random Gaussian distributed noise of the level comparable to the weakest resonances in the corresponding spectrum. The present choice for this high-resolution task in MRS is the fast Padé transform (FPT). All the sought spectral parameters (complex frequencies and amplitudes) can unequivocally be reconstructed from a given input time signal by using the FPT. Moreover, the present computations demonstrate that the FPT can achieve the spectral convergence, which represents the exponential convergence rate as a function of the signal length for a fixed bandwidth. Such an extraordinary feature equips the FPT with the exemplary high-resolution capabilities that are, in fact, theoretically unlimited. This is illustrated in the present study by the exact reconstruction (within machine accuracy) of all the spectral parameters from an input time signal comprised of 25 harmonics, i.e. complex damped exponentials, including those for tightly overlapped and nearly degenerate resonances whose chemical shifts differ by an exceedingly small fraction of only 10(-11) ppm. Moreover, without exhausting even a quarter of the full signal length, the FPT is shown to retrieve exactly all the input spectral parameters defined with 12 digits of accuracy. Specifically, we demonstrate that when the FPT is close to the convergence region, an unprecedented phase transition occurs, since literally a few additional signal points are sufficient to reach the full 12 digit accuracy with the exponentially fast rate of convergence. This is the critical proof-of-principle for the high-resolution power of the FPT for machine accurate input data. Furthermore, it is proven that the FPT is also a highly reliable method for quantifying noise-corrupted time signals reminiscent of those encoded via MRS in clinical neuro-diagnostics.

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.

A new cellular automata model of traffic flow with negative exponential weighted look-ahead potential

NASA Astrophysics Data System (ADS)

Ma, Xiao; Zheng, Wei-Fan; Jiang, Bao-Shan; Zhang, Ji-Ye

2016-10-01

With the development of traffic systems, some issues such as traffic jams become more and more serious. Efficient traffic flow theory is needed to guide the overall controlling, organizing and management of traffic systems. On the basis of the cellular automata model and the traffic flow model with look-ahead potential, a new cellular automata traffic flow model with negative exponential weighted look-ahead potential is presented in this paper. By introducing the negative exponential weighting coefficient into the look-ahead potential and endowing the potential of vehicles closer to the driver with a greater coefficient, the modeling process is more suitable for the driver’s random decision-making process which is based on the traffic environment that the driver is facing. The fundamental diagrams for different weighting parameters are obtained by using numerical simulations which show that the negative exponential weighting coefficient has an obvious effect on high density traffic flux. The complex high density non-linear traffic behavior is also reproduced by numerical simulations. Project supported by the National Natural Science Foundation of China (Grant Nos. 11572264, 11172247, 11402214, and 61373009).

Pilot Study on the Applicability of Variance Reduction Techniques to the Simulation of a Stochastic Combat Model

DTIC Science & Technology

1987-09-01

inverse transform method to obtain unit-mean exponential random variables, where Vi is the jth random number in the sequence of a stream of uniform random...numbers. The inverse transform method is discussed in the simulation textbooks listed in the reference section of this thesis. X(b,c,d) = - P(b,c,d...Defender ,C * P(b,c,d) We again use the inverse transform method to obtain the conditions for an interim event to occur and to induce the change in

Time-dependent breakdown of fiber networks: Uncertainty of lifetime

NASA Astrophysics Data System (ADS)

Mattsson, Amanda; Uesaka, Tetsu

2017-05-01

Materials often fail when subjected to stresses over a prolonged period. The time to failure, also called the lifetime, is known to exhibit large variability of many materials, particularly brittle and quasibrittle materials. For example, a coefficient of variation reaches 100% or even more. Its distribution shape is highly skewed toward zero lifetime, implying a large number of premature failures. This behavior contrasts with that of normal strength, which shows a variation of only 4%-10% and a nearly bell-shaped distribution. The fundamental cause of this large and unique variability of lifetime is not well understood because of the complex interplay between stochastic processes taking place on the molecular level and the hierarchical and disordered structure of the material. We have constructed fiber network models, both regular and random, as a paradigm for general material structures. With such networks, we have performed Monte Carlo simulations of creep failure to establish explicit relationships among fiber characteristics, network structures, system size, and lifetime distribution. We found that fiber characteristics have large, sometimes dominating, influences on the lifetime variability of a network. Among the factors investigated, geometrical disorders of the network were found to be essential to explain the large variability and highly skewed shape of the lifetime distribution. With increasing network size, the distribution asymptotically approaches a double-exponential form. The implication of this result is that, so-called "infant mortality," which is often predicted by the Weibull approximation of the lifetime distribution, may not exist for a large system.

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.

Topology Trivialization and Large Deviations for the Minimum in the Simplest Random Optimization

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.; Le Doussal, Pierre

2014-01-01

Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)-dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust region subproblem" or "constraint least square problem". When both terms in the cost function are random this amounts to studying the ground state energy of the simplest spherical spin glass in a random magnetic field. We first identify and study two distinct large-N scaling regimes in which the linear term (magnetic field) leads to a gradual topology trivialization, i.e. reduction in the total number {N}_{tot} of critical (stationary) points in the cost function landscape. In the first regime {N}_{tot} remains of the order N and the cost function (energy) has generically two almost degenerate minima with the Tracy-Widom (TW) statistics. In the second regime the number of critical points is of the order of unity with a finite probability for a single minimum. In that case the mean total number of extrema (minima and maxima) of the cost function is given by the Laplace transform of the TW density, and the distribution of the global minimum energy is expected to take a universal scaling form generalizing the TW law. Though the full form of that distribution is not yet known to us, one of its far tails can be inferred from the large deviation theory for the global minimum. In the rest of the paper we show how to use the replica method to obtain the probability density of the minimum energy in the large-deviation approximation by finding both the rate function and the leading pre-exponential factor.

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.

Effects of clustered transmission on epidemic growth Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Merler, Stefano

2016-09-01

Characterizing the early growth profile of an epidemic outbreak is key for predicting the likely trajectory of the number of cases and for designing adequate control measures. Epidemic profiles characterized by exponential growth have been widely observed in the past and a grounding theoretical framework for the analysis of infectious disease dynamics was provided by the pioneering work of Kermack and McKendrick [1]. In particular, exponential growth stems from the assumption that pathogens spread in homogeneous mixing populations; that is, individuals of the population mix uniformly and randomly with each other. However, this assumption was readily recognized as highly questionable [2], and sub-exponential profiles of epidemic growth have been observed in a number of epidemic outbreaks, including HIV/AIDS, foot-and-mouth disease, measles and, more recently, Ebola [3,4].

Scaling relationships of channel networks at large scales: Examples from two large-magnitude watersheds in Brittany, France

NASA Astrophysics Data System (ADS)

Crave, A.; Davy, P.

1997-01-01

We present a statistical analysis on two watersheds in French Brittany whose drainage areas are about 10,000 and 2000 km2. The channel system was analysed from the digitised blue lines of the 1:100,000 map and from a 250-m DEM. Link lengths follow an exponential distribution, consistent with the Markovian model of channel branching proposed by Smart (1968). The departure from the exponential distribution for small lengths, that has been extensively discussed before, results from a statistical effect due to the finite number of channels and junctions. The Strahler topology applied on channels defines a self-similar organisation whose similarity dimension is about 1.7, that is clearly smaller than the value of 2 expected for a random organisation. The similarity dimension is consistent with an independent measurement of the Horton ratios of stream numbers and lengths. The variables defined by an upstream integral (drainage area, mainstream length, upstream length) follow power-law distributions limited at large scales by a finite size effect, due to the finite area of the watersheds. A special emphasis is given to the exponent of the drainage area, aA, that has been previously discussed in the context of different aggregation models relevant to channel network growth. We show that aA is consistent with 4/3, a value that was obtained and analytically demonstrated from directed random walk aggregating models, inspired by the model of Scheidegger (1967). The drainage density and mainstream length present no simple scaling with area, except at large areas where they tend to trivial values: constant density and square root of drainage area, respectively. These asymptotic limits necessarily imply that the space dimension of channel networks is 2, equal to the embedding space. The limits are reached for drainage areas larger than 100 km2. For smaller areas, the asymptotic limit represents either a lower bound (drainage density) or an upper bound (mainstream length) of the distributions. Because the fluctuations of the drainage density slowly converge to a finite limit, the system could be adequately described as a fat fractal, where the average drainage density is the sum of a constant plus a fluctuation decreasing as a power law with integrating area. A fat fractal hypothesis could explain why the similarity dimension is not equal to the fractal capacity dimension, as it is for thin fractals. The physical consequences are not yet really understood, but we draw an analogy with a directed aggregating system where the growth process involves both stochastic and deterministic growth. These models are known to be fat fractals, and the deterministic growth, which constitutes a fundamental ingredient of these models, could be attributed in river systems to the role of terrestrial gravity.

Fiber-Type Random Laser Based on a Cylindrical Waveguide with a Disordered Cladding Layer.

PubMed

Zhang, Wei Li; Zheng, Meng Ya; Ma, Rui; Gong, Chao Yang; Yang, Zhao Ji; Peng, Gang Ding; Rao, Yun Jiang

2016-05-25

This letter reports a fiber-type random laser (RL) which is made from a capillary coated with a disordered layer at its internal surface and filled with a gain (laser dye) solution in the core region. This fiber-type optical structure, with the disordered layer providing randomly scattered light into the gain region and the cylindrical waveguide providing confinement of light, assists the formation of random lasing modes and enables a flexible and efficient way of making random lasers. We found that the RL is sensitive to laser dye concentration in the core region and there exists a fine exponential relationship between the lasing intensity and particle concentration in the gain solution. The proposed structure could be a fine platform of realizing random lasing and random lasing based sensing.

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.

Data Assimilation by Ensemble Kalman Filter during One-Dimensional Nonlinear Consolidation in Randomly Heterogeneous Highly Compressible Aquitards

NASA Astrophysics Data System (ADS)

Zapata Norberto, B.; Morales-Casique, E.; Herrera, G. S.

2017-12-01

Severe land subsidence due to groundwater extraction may occur in multiaquifer systems where highly compressible aquitards are present. The highly compressible nature of the aquitards leads to nonlinear consolidation where the groundwater flow parameters are stress-dependent. The case is further complicated by the heterogeneity of the hydrogeologic and geotechnical properties of the aquitards. We explore the effect of realistic vertical heterogeneity of hydrogeologic and geotechnical parameters on the consolidation of highly compressible aquitards by means of 1-D Monte Carlo numerical simulations. 2000 realizations are generated for each of the following parameters: hydraulic conductivity (K), compression index (Cc) and void ratio (e). The correlation structure, the mean and the variance for each parameter were obtained from a literature review about field studies in the lacustrine sediments of Mexico City. The results indicate that among the parameters considered, random K has the largest effect on the ensemble average behavior of the system. Random K leads to the largest variance (and therefore largest uncertainty) of total settlement, groundwater flux and time to reach steady state conditions. We further propose a data assimilation scheme by means of ensemble Kalman filter to estimate the ensemble mean distribution of K, pore-pressure and total settlement. We consider the case where pore-pressure measurements are available at given time intervals. We test our approach by generating a 1-D realization of K with exponential spatial correlation, and solving the nonlinear flow and consolidation problem. These results are taken as our "true" solution. We take pore-pressure "measurements" at different times from this "true" solution. The ensemble Kalman filter method is then employed to estimate ensemble mean distribution of K, pore-pressure and total settlement based on the sequential assimilation of these pore-pressure measurements. The ensemble-mean estimates from this procedure closely approximate those from the "true" solution. This procedure can be easily extended to other random variables such as compression index and void ratio.

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.

Flux line relaxation kinetics following current quenches in disordered type-II superconductors

NASA Astrophysics Data System (ADS)

Chaturvedi, Harshwardhan; Assi, Hiba; Dobramysl, Ulrich; Pleimling, Michel; Täuber, Uwe

We describe the disordered vortex system in type-II superconductors with an elastic line model, whose dynamics we investigate numerically by means of Langevin Molecular Dynamics. A system of driven interacting flux lines in a sample with randomly distributed point pinning centers is subjected to drive quench from a moving non-equilibrium steady state into one of three regimes viz. moving (steady state), pinned (glassy) or depinning (critical). The first yields fast exponential relaxation to the new non-equilibrium stationary state while the second displays algebraically slow relaxation and aging scaling with non-universal exponents. Our most recent work consists of aging and finite temperature scaling studies for drive quenches into the critical depinning regime. This research is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-09ER46613.

Modeling Citation Networks Based on Vigorousness and Dormancy

NASA Astrophysics Data System (ADS)

Wang, Xue-Wen; Zhang, Li-Jie; Yang, Guo-Hong; Xu, Xin-Jian

2013-08-01

In citation networks, the activity of papers usually decreases with age and dormant papers may be discovered and become fashionable again. To model this phenomenon, a competition mechanism is suggested which incorporates two factors: vigorousness and dormancy. Based on this idea, a citation network model is proposed, in which a node has two discrete stage: vigorous and dormant. Vigorous nodes can be deactivated and dormant nodes may be activated and become vigorous. The evolution of the network couples addition of new nodes and state transitions of old ones. Both analytical calculation and numerical simulation show that the degree distribution of nodes in generated networks displays a good right-skewed behavior. Particularly, scale-free networks are obtained as the deactivated vertex is target selected and exponential networks are realized for the random-selected case. Moreover, the measurement of four real-world citation networks achieves a good agreement with the stochastic model.

Agitation, Mixing, and Transfers Induced by Bubbles

NASA Astrophysics Data System (ADS)

Risso, Frédéric

2018-01-01

Bubbly flows involve bubbles randomly distributed within a liquid. At large Reynolds number, they experience an agitation that can combine shear-induced turbulence (SIT), large-scale buoyancy-driven flows, and bubble-induced agitation (BIA). The properties of BIA strongly differ from those of SIT. They have been determined from studies of homogeneous swarms of rising bubbles. Regarding the bubbles, agitation is mainly caused by the wake-induced path instability. Regarding the liquid, two contributions must be distinguished. The first one corresponds to the anisotropic flow disturbances generated near the bubbles, principally in the vertical direction. The second one is the almost isotropic turbulence induced by the flow instability through a population of bubbles, which turns out to be the main cause of horizontal fluctuations. Both contributions generate a k-3 spectral subrange and exponential probability density functions. The subsequent issue will be to understand how BIA interacts with SIT.

Large Fluctuations for Spatial Diffusion of Cold Atoms

NASA Astrophysics Data System (ADS)

Aghion, Erez; Kessler, David A.; Barkai, Eli

2017-06-01

We use a new approach to study the large fluctuations of a heavy-tailed system, where the standard large-deviations principle does not apply. Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example, spreading packets of particles. Mathematically, it concerns the exponential falloff of the density of thin-tailed systems. Here we investigate the spatial density Pt(x ) of laser-cooled atoms, where at intermediate length scales the shape is fat tailed. We focus on the rare events beyond this range, which dominate important statistical properties of the system. Through a novel friction mechanism induced by the laser fields, the density is explored with the recently proposed non-normalized infinite-covariant density approach. The small and large fluctuations give rise to a bifractal nature of the spreading packet. We derive general relations which extend our theory to a class of systems with multifractal moments.

Thermally assisted nanosecond laser generation of ferric nanoparticles

NASA Astrophysics Data System (ADS)

Kurselis, K.; Kozheshkurt, V.; Kiyan, R.; Chichkov, B.; Sajti, L.

2018-03-01

A technique to increase nanosecond laser based production of ferric nanoparticles by elevating temperature of the iron target and controlling its surface exposure to oxygen is reported. High power near-infrared laser ablation of the iron target heated up to 600 °C enhances the particle generation efficiency by more than tenfold exceeding 6 μg/J. Temporal and thermal dependencies of the particle generation process indicate correlation of this enhancement with the oxidative processes that take place on the iron surface during the per spot interpulse delay. Nanoparticles, produced using the heat-assisted ablation technique, are examined using scanning electron and transmission electron microscopy confirming the presence of 1-100 nm nanoparticles with an exponential size distribution that contain multiple randomly oriented magnetite nanocrystallites. The described process enables the application of high power lasers and facilitates precise, uniform, and controllable direct deposition of ferric nanoparticle coatings at the industry-relevant rates.

Sample Size Requirements and Study Duration for Testing Main Effects and Interactions in Completely Randomized Factorial Designs When Time to Event is the Outcome

PubMed Central

Moser, Barry Kurt; Halabi, Susan

2013-01-01

In this paper we develop the methodology for designing clinical trials with any factorial arrangement when the primary outcome is time to event. We provide a matrix formulation for calculating the sample size and study duration necessary to test any effect with a pre-specified type I error rate and power. Assuming that a time to event follows an exponential distribution, we describe the relationships between the effect size, the power, and the sample size. We present examples for illustration purposes. We provide a simulation study to verify the numerical calculations of the expected number of events and the duration of the trial. The change in the power produced by a reduced number of observations or by accruing no patients to certain factorial combinations is also described. PMID:25530661

Weak signal transmission in complex networks and its application in detecting connectivity.

PubMed

Liang, Xiaoming; Liu, Zonghua; Li, Baowen

2009-10-01

We present a network model of coupled oscillators to study how a weak signal is transmitted in complex networks. Through both theoretical analysis and numerical simulations, we find that the response of other nodes to the weak signal decays exponentially with their topological distance to the signal source and the coupling strength between two neighboring nodes can be figured out by the responses. This finding can be conveniently used to detect the topology of unknown network, such as the degree distribution, clustering coefficient and community structure, etc., by repeatedly choosing different nodes as the signal source. Through four typical networks, i.e., the regular one dimensional, small world, random, and scale-free networks, we show that the features of network can be approximately given by investigating many fewer nodes than the network size, thus our approach to detect the topology of unknown network may be efficient in practical situations with large network size.

From plant traits to plant communities: a statistical mechanistic approach to biodiversity.

PubMed

Shipley, Bill; Vile, Denis; Garnier, Eric

2006-11-03

We developed a quantitative method, analogous to those used in statistical mechanics, to predict how biodiversity will vary across environments, which plant species from a species pool will be found in which relative abundances in a given environment, and which plant traits determine community assembly. This provides a scaling from plant traits to ecological communities while bypassing the complications of population dynamics. Our method treats community development as a sorting process involving species that are ecologically equivalent except with respect to particular functional traits, which leads to a constrained random assembly of species; the relative abundance of each species adheres to a general exponential distribution as a function of its traits. Using data for eight functional traits of 30 herbaceous species and community-aggregated values of these traits in 12 sites along a 42-year chronosequence of secondary succession, we predicted 94% of the variance in the relative abundances.

Alternative steady states in ecological networks

NASA Astrophysics Data System (ADS)

Fried, Yael; Shnerb, Nadav M.; Kessler, David A.

2017-07-01

In many natural situations, one observes a local system with many competing species that is coupled by weak immigration to a regional species pool. The dynamics of such a system is dominated by its stable and uninvadable (SU) states. When the competition matrix is random, the number of SUs depends on the average value and variance of its entries. Here we consider the problem in the limit of weak competition and large variance. Using a yes-no interaction model, we show that the number of SUs corresponds to the number of maximum cliques in an Erdös-Rényi network. The number of SUs grows exponentially with the number of species in this limit, unless the network is completely asymmetric. In the asymmetric limit, the number of SUs is O (1 ) . Numerical simulations suggest that these results are valid for models with a continuous distribution of competition terms.

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.

Evolution and History in a new "Mathematical SETI" model

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2014-01-01

In a recent paper (Maccone, 2011 [15]) and in a recent book (Maccone, 2012 [17]), this author proposed a new mathematical model capable of merging SETI and Darwinian Evolution into a single mathematical scheme. This model is based on exponentials and lognormal probability distributions, called "b-lognormals" if they start at any positive time b ("birth") larger than zero. Indeed: 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, as it happened on Earth. In 2008 (Maccone, 2008 [9]) this author firstly provided a statistical generalization of the Drake equation where the number N of communicating ET civilizations in the Galaxy was shown to follow the lognormal probability distribution. This fact 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 if the number of factors is increased at will, i.e. it approaches infinity. Also, in Maccone (2011 [15]), it was shown 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 b-lognormal distributions constrained between the time axis and the exponential growth curve. This was a brand-new result. And one more new and far-reaching idea was to define Darwinian Evolution as a particular realization of a stochastic process called Geometric Brownian Motion (GBM) having the above exponential as its own mean value curve. The b-lognormals may be also be interpreted as the lifespan of any living being, let it be a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization. In Maccone, (2012 [17, Chapters 6, 7, 8 and 11]), as well as in the present paper, we give important exact equations yielding the b-lognormal when its birth time, senility-time (descending inflexion point) and death time (where the tangent at senility intercepts the time axis) are known. These also are brand-new results. In particular, the σ=1 b-lognormals are shown to be related to the golden ratio, so famous in the arts and in architecture, and these special b-lognormals we call "golden b-lognormals". Applying this new mathematical apparatus to Human History leads to the discovery of the exponential trend of progress between Ancient Greece and the current USA Empire as the envelope of the b-lognormals of all Western Civilizations over a period of 2500 years. We then invoke Shannon's Information Theory. The entropy of the obtained b-lognormals turns out to be the index of "development level" reached by each historic civilization. As a consequence, we get a numerical estimate of the entropy difference (i.e. the difference in the evolution levels) between any two civilizations. In particular, this was the case when Spaniards first met with Aztecs in 1519, and we find the relevant entropy difference between Spaniards an Aztecs to be 3.84 bits/individual over a period of about 50 centuries of technological difference. In a similar calculation, the entropy difference between the first living organism on Earth (RNA?) and Humans turns out to equal 25.57 bits/individual over a period of 3.5 billion years of Darwinian Evolution. Finally, we extrapolate our exponentials into the future, which is of course arbitrary, but is the best Humans can do before they get in touch with any alien civilization. The results are appalling: the entropy difference between aliens 1 million years more advanced than Humans is of the order of 1000 bits/individual, while 10,000 bits/individual would be requested to any Civilization wishing to colonize the whole Galaxy (Fermi Paradox). In conclusion, we have derived a mathematical model capable of estimating how much more advanced than humans an alien civilization will be when SETI succeeds.

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.

Model for interevent times with long tails and multifractality in human communications: An application to financial trading

NASA Astrophysics Data System (ADS)

Perelló, Josep; Masoliver, Jaume; Kasprzak, Andrzej; Kutner, Ryszard

2008-09-01

Social, technological, and economic time series are divided by events which are usually assumed to be random, albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics has therefore become a central issue. The approach we present is taken from the continuous-time random-walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the intertransaction time intervals of several financial markets. We observe that empirical data describe a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. A stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.

Tabletop Traffic Jams: Modeling Traffic Jams using Self Propelled Particles

NASA Astrophysics Data System (ADS)

Yadav, Vikrant; Kudrolli, Arshad

2015-03-01

We model behavior of traffic using Self Propelled Particles (SPPs). Granular rods with asymmetric mass distribution confined to move in a circular channel on a vibrated substrate and interact with each other through inelastic collision serve as our model vehicle. Motion of a single vehicle is observed to be composed of 2 parts, a linear velocity in the direction of lighter end of particle and a non-Gaussian random velocity. We find that the collective mean speed of the SPPs is constant over a wide range of line densities before decreasing rapidly as the maximum packing is approached indicating the spontaneous formation of Phantom jams. This decrease in speed is observed to be far greater than any small differences in the mean drift speed of individual SPPs , and occurs as the collision frequency between SPPs increase exponentially with line density. However the random velocity component of SPPs remain super-diffusive over entire range of line densities. While the collective motion at low densities is characterized by caravan following behind the slowest particle leading to clustering, at higher densities we see formation of jamming waves travelling in direction opposite to that of motion of particles.

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.

The Radial Distribution of Star Formation in Galaxies at z ~ 1 from the 3D-HST Survey

NASA Astrophysics Data System (ADS)

Nelson, Erica June; van Dokkum, Pieter G.; Momcheva, Ivelina; Brammer, Gabriel; Lundgren, Britt; Skelton, Rosalind E.; Whitaker, Katherine E.; Da Cunha, Elisabete; Förster Schreiber, Natascha; Franx, Marijn; Fumagalli, Mattia; Kriek, Mariska; Labbe, Ivo; Leja, Joel; Patel, Shannon; Rix, Hans-Walter; Schmidt, Kasper B.; van der Wel, Arjen; Wuyts, Stijn

2013-01-01

The assembly of galaxies can be described by the distribution of their star formation as a function of cosmic time. Thanks to the WFC3 grism on the Hubble Space Telescope (HST) it is now possible to measure this beyond the local Universe. Here we present the spatial distribution of Hα emission for a sample of 54 strongly star-forming galaxies at z ~ 1 in the 3D-HST Treasury survey. By stacking the Hα emission, we find that star formation occurred in approximately exponential distributions at z ~ 1, with a median Sérsic index of n = 1.0 ± 0.2. The stacks are elongated with median axis ratios of b/a = 0.58 ± 0.09 in Hα consistent with (possibly thick) disks at random orientation angles. Keck spectra obtained for a subset of eight of the galaxies show clear evidence for rotation, with inclination corrected velocities of 90-330 km s-1. The most straightforward interpretation of our results is that star formation in strongly star-forming galaxies at z ~ 1 generally occurred in disks. The disks appear to be "scaled-up" versions of nearby spiral galaxies: they have EW(Hα) ~ 100 Å out to the solar orbit and they have star formation surface densities above the threshold for driving galactic scale winds.

The Radial Distribution of Star Formation in Galaxies at Z approximately 1 from the 3D-HST Survey

NASA Technical Reports Server (NTRS)

Nelson, Erica June; vanDokkum, Pieter G.; Momcheva, Ivelina; Brammer, Gabriel; Lundgren, Britt; Skelton, Rosalind E.; Whitaker, Katherine E.; DaCunha, Elisabete; Schreiber, Natascha Foerster; Franx, Marijn;

Exploring Explanations of Subglacial Bedform Sizes Using Statistical Models

PubMed Central

Kougioumtzoglou, Ioannis A.; Stokes, Chris R.; Smith, Michael J.; Clark, Chris D.; Spagnolo, Matteo S.

2016-01-01

Sediments beneath modern ice sheets exert a key control on their flow, but are largely inaccessible except through geophysics or boreholes. In contrast, palaeo-ice sheet beds are accessible, and typically characterised by numerous bedforms. However, the interaction between bedforms and ice flow is poorly constrained and it is not clear how bedform sizes might reflect ice flow conditions. To better understand this link we present a first exploration of a variety of statistical models to explain the size distribution of some common subglacial bedforms (i.e., drumlins, ribbed moraine, MSGL). By considering a range of models, constructed to reflect key aspects of the physical processes, it is possible to infer that the size distributions are most effectively explained when the dynamics of ice-water-sediment interaction associated with bedform growth is fundamentally random. A ‘stochastic instability’ (SI) model, which integrates random bedform growth and shrinking through time with exponential growth, is preferred and is consistent with other observations of palaeo-bedforms and geophysical surveys of active ice sheets. Furthermore, we give a proof-of-concept demonstration that our statistical approach can bridge the gap between geomorphological observations and physical models, directly linking measurable size-frequency parameters to properties of ice sheet flow (e.g., ice velocity). Moreover, statistically developing existing models as proposed allows quantitative predictions to be made about sizes, making the models testable; a first illustration of this is given for a hypothesised repeat geophysical survey of bedforms under active ice. Thus, we further demonstrate the potential of size-frequency distributions of subglacial bedforms to assist the elucidation of subglacial processes and better constrain ice sheet models. PMID:27458921

Dynamics of transit times and StorAge Selection functions in four forested catchments from stable isotope data

NASA Astrophysics Data System (ADS)

Rodriguez, Nicolas B.; McGuire, Kevin J.; Klaus, Julian

2017-04-01

Transit time distributions, residence time distributions and StorAge Selection functions are fundamental integrated descriptors of water storage, mixing, and release in catchments. In this contribution, we determined these time-variant functions in four neighboring forested catchments in H.J. Andrews Experimental Forest, Oregon, USA by employing a two year time series of 18O in precipitation and discharge. Previous studies in these catchments assumed stationary, exponentially distributed transit times, and complete mixing/random sampling to explore the influence of various catchment properties on the mean transit time. Here we relaxed such assumptions to relate transit time dynamics and the variability of StoreAge Selection functions to catchment characteristics, catchment storage, and meteorological forcing seasonality. Conceptual models of the catchments, consisting of two reservoirs combined in series-parallel, were calibrated to discharge and stable isotope tracer data. We assumed randomly sampled/fully mixed conditions for each reservoir, which resulted in an incompletely mixed system overall. Based on the results we solved the Master Equation, which describes the dynamics of water ages in storage and in catchment outflows Consistent between all catchments, we found that transit times were generally shorter during wet periods, indicating the contribution of shallow storage (soil, saprolite) to discharge. During extended dry periods, transit times increased significantly indicating the contribution of deeper storage (bedrock) to discharge. Our work indicated that the strong seasonality of precipitation impacted transit times by leading to a dynamic selection of stored water ages, whereas catchment size was not a control on transit times. In general this work showed the usefulness of using time-variant transit times with conceptual models and confirmed the existence of the catchment age mixing behaviors emerging from other similar studies.

Application of a time-dependent coalescence process for inferring the history of population size changes from DNA sequence data.

PubMed

Polanski, A; Kimmel, M; Chakraborty, R

1998-05-12

Distribution of pairwise differences of nucleotides from data on a sample of DNA sequences from a given segment of the genome has been used in the past to draw inferences about the past history of population size changes. However, all earlier methods assume a given model of population size changes (such as sudden expansion), parameters of which (e.g., time and amplitude of expansion) are fitted to the observed distributions of nucleotide differences among pairwise comparisons of all DNA sequences in the sample. Our theory indicates that for any time-dependent population size, N(tau) (in which time tau is counted backward from present), a time-dependent coalescence process yields the distribution, p(tau), of the time of coalescence between two DNA sequences randomly drawn from the population. Prediction of p(tau) and N(tau) requires the use of a reverse Laplace transform known to be unstable. Nevertheless, simulated data obtained from three models of monotone population change (stepwise, exponential, and logistic) indicate that the pattern of a past population size change leaves its signature on the pattern of DNA polymorphism. Application of the theory to the published mtDNA sequences indicates that the current mtDNA sequence variation is not inconsistent with a logistic growth of the human population.

Superconductor-insulator transition on annealed complex networks.

PubMed

Bianconi, Ginestra

2012-06-01

Cuprates show multiphase and multiscale complexity that has hindered physicists search for the mechanism of high T{c} for many years. Recently the interest has been addressed to a possible optimum inhomogeneity of dopants, defects, and interstitials, and the structural scale invariance of dopants detected by scanning micro-x-ray diffraction has been reported to promote the critical temperature. In order to shed light on critical phenomena on granular materials, here we propose a stylized model capturing the essential characteristics of the superconducting-insulator transition of a highly dynamical, heterogeneous granular material: the random transverse Ising model (RTIM) on annealed complex network. We show that when the networks encode for high heterogeneity of the expected degrees described by a power-law distribution, the critical temperature for the onset of the superconducting phase diverges to infinity as the power-law exponent γ of the expected degree distribution is less than 3, i.e., γ<3. Moreover we investigate the case in which the critical state of the electronic background is triggered by an external parameter g that determines an exponential cutoff in the power-law expected degree distribution characterized by an exponent γ. We find that for g=g{c} the critical temperature for the superconducting-insulator transition has a maximum if γ>3 and diverges if γ<3.

Population Pharmacokinetics of Darbepoetin Alfa in Conjunction with Hypothermia for the Treatment of Neonatal Hypoxic-Ischemic Encephalopathy.

PubMed

Roberts, Jessica K; Stockmann, Chris; Ward, Robert M; Beachy, Joanna; Baserga, Mariana C; Spigarelli, Michael G; Sherwin, Catherine M T

2015-12-01

The aim of this study was to determine the population pharmacokinetics of darbepoetin alfa in hypothermic neonates with hypoxic-ischemic encephalopathy treated with hypothermia. Neonates ≥36 weeks gestation and <12 h postpartum with moderate to severe hypoxic-ischemic encephalopathy who were undergoing hypothermia treatment were recruited in this randomized, multicenter, investigational, new drug pharmacokinetic study. Two intravenous darbepoetin alfa treatment groups were evaluated: 2 and 10 µg/kg. Serum erythropoietin concentrations were measured using an enzyme-linked immunosorbent assay. Monolix 4.3.1 was used to estimate darbepoetin alfa clearance and volume of distribution. Covariates tested included: birthweight, gestational age, postnatal age, postmenstrual age, sex, Sarnat score, and study site. Darbepoetin alfa pharmacokinetics were well described by a one-compartment model with exponential error. Clearance and the volume of distribution were scaled by birthweight (centered on the mean) a priori. Additionally, gestational age (also centered on the mean) significantly affected darbepoetin alfa clearance. Clearance and volume of distribution were estimated as 0.0465 L/h (95% confidence interval 0.0392-0.0537) and 1.58 L (95% confidence interval 1.29-1.87), respectively. A one-compartment model successfully described the pharmacokinetics of darbepoetin alfa among hypothermic neonates treated for hypoxic-ischemic encephalopathy. Clearance decreased with increasing gestational age.

Quantum discord length is enhanced while entanglement length is not by introducing disorder in a spin chain.

PubMed

Sadhukhan, Debasis; Roy, Sudipto Singha; Rakshit, Debraj; Prabhu, R; Sen De, Aditi; Sen, Ujjwal

2016-01-01

Classical correlation functions of ground states typically decay exponentially and polynomially, respectively, for gapped and gapless short-range quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder.

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

Le modèle stochastique SIS pour une épidémie dans un environnement aléatoire.

PubMed

Bacaër, Nicolas

2016-10-01

The stochastic SIS epidemic model in a random environment. In a random environment that is a two-state continuous-time Markov chain, the mean time to extinction of the stochastic SIS epidemic model grows in the supercritical case exponentially with respect to the population size if the two states are favorable, and like a power law if one state is favorable while the other is unfavorable.

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.

Income distribution patterns from a complete social security database

NASA Astrophysics Data System (ADS)

Derzsy, N.; Néda, Z.; Santos, M. A.

2012-11-01

We analyze the income distribution of employees for 9 consecutive years (2001-2009) using a complete social security database for an economically important district of Romania. The database contains detailed information on more than half million taxpayers, including their monthly salaries from all employers where they worked. Besides studying the characteristic distribution functions in the high and low/medium income limits, the database allows us a detailed dynamical study by following the time-evolution of the taxpayers income. To our knowledge, this is the first extensive study of this kind (a previous Japanese taxpayers survey was limited to two years). In the high income limit we prove once again the validity of Pareto’s law, obtaining a perfect scaling on four orders of magnitude in the rank for all the studied years. The obtained Pareto exponents are quite stable with values around α≈2.5, in spite of the fact that during this period the economy developed rapidly and also a financial-economic crisis hit Romania in 2007-2008. For the low and medium income category we confirmed the exponential-type income distribution. Following the income of employees in time, we have found that the top limit of the income distribution is a highly dynamical region with strong fluctuations in the rank. In this region, the observed dynamics is consistent with a multiplicative random growth hypothesis. Contrarily with previous results obtained for the Japanese employees, we find that the logarithmic growth-rate is not independent of the income.

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.

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.

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.

The nucleoid protein Dps binds genomic DNA of Escherichia coli in a non-random manner

PubMed Central

Kondrashov, F. A.; Toshchakov, S. V.; Dominova, I.; Shvyreva, U. S.; Vrublevskaya, V. V.; Morenkov, O. S.; Panyukov, V. V.

2017-01-01

Dps is a multifunctional homododecameric protein that oxidizes Fe2+ ions accumulating them in the form of Fe2O3 within its protein cavity, interacts with DNA tightly condensing bacterial nucleoid upon starvation and performs some other functions. During the last two decades from discovery of this protein, its ferroxidase activity became rather well studied, but the mechanism of Dps interaction with DNA still remains enigmatic. The crucial role of lysine residues in the unstructured N-terminal tails led to the conventional point of view that Dps binds DNA without sequence or structural specificity. However, deletion of dps changed the profile of proteins in starved cells, SELEX screen revealed genomic regions preferentially bound in vitro and certain affinity of Dps for artificial branched molecules was detected by atomic force microscopy. Here we report a non-random distribution of Dps binding sites across the bacterial chromosome in exponentially growing cells and show their enrichment with inverted repeats prone to form secondary structures. We found that the Dps-bound regions overlap with sites occupied by other nucleoid proteins, and contain overrepresented motifs typical for their consensus sequences. Of the two types of genomic domains with extensive protein occupancy, which can be highly expressed or transcriptionally silent only those that are enriched with RNA polymerase molecules were preferentially occupied by Dps. In the dps-null mutant we, therefore, observed a differentially altered expression of several targeted genes and found suppressed transcription from the dps promoter. In most cases this can be explained by the relieved interference with Dps for nucleoid proteins exploiting sequence-specific modes of DNA binding. Thus, protecting bacterial cells from different stresses during exponential growth, Dps can modulate transcriptional integrity of the bacterial chromosome hampering RNA biosynthesis from some genes via competition with RNA polymerase or, vice versa, competing with inhibitors to activate transcription. PMID:28800583

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.

Simulation and study of small numbers of random events

NASA Technical Reports Server (NTRS)

Shelton, R. D.

1986-01-01

Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.

The Effect of Random Error on Diagnostic Accuracy Illustrated with the Anthropometric Diagnosis of Malnutrition

PubMed Central

2016-01-01

Background It is often thought that random measurement error has a minor effect upon the results of an epidemiological survey. Theoretically, errors of measurement should always increase the spread of a distribution. Defining an illness by having a measurement outside an established healthy range will lead to an inflated prevalence of that condition if there are measurement errors. Methods and results A Monte Carlo simulation was conducted of anthropometric assessment of children with malnutrition. Random errors of increasing magnitude were imposed upon the populations and showed that there was an increase in the standard deviation with each of the errors that became exponentially greater with the magnitude of the error. The potential magnitude of the resulting error of reported prevalence of malnutrition were compared with published international data and found to be of sufficient magnitude to make a number of surveys and the numerous reports and analyses that used these data unreliable. Conclusions The effect of random error in public health surveys and the data upon which diagnostic cut-off points are derived to define “health” has been underestimated. Even quite modest random errors can more than double the reported prevalence of conditions such as malnutrition. Increasing sample size does not address this problem, and may even result in less accurate estimates. More attention needs to be paid to the selection, calibration and maintenance of instruments, measurer selection, training & supervision, routine estimation of the likely magnitude of errors using standardization tests, use of statistical likelihood of error to exclude data from analysis and full reporting of these procedures in order to judge the reliability of survey reports. PMID:28030627

Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low temperature phase

NASA Astrophysics Data System (ADS)

Monthus, Cécile; Garel, Thomas

2007-03-01

We consider the low temperature T

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.

Terpolymer polyrotaxanes: a promising supramolecular system as electron-transporting materials for optoelectronics

NASA Astrophysics Data System (ADS)

Farcas, A.; Resmerita, A.-M.; Farcas, F.

2016-12-01

Optical, electrochemical and surface-morphological properties of three terpolymer polyrotaxanes (1a, 1b and 1c) composed of 2,7-dibromo-9,9-dicyanomethylenefluorene encapsulated into γ-cyclodextrin (γCD), β- or γ-persilylated cyclodextrin (PS-γCD, PS-γCD) cavities (acceptor) and 4,4'-dibromo-4''-methyltriphenylamine (donor) randomly distributed into 9,9-dioctylfluorene conjugated chains have been evaluated and compared to those of the reference 1. The role of the encapsulation on the thermal stability, solubility, film forming ability and transparency was also investigated. High fluorescence efficiency, almost identical normalized absorbance maximum in solution and solid-states of 1a, 1b and 1c provides the lower aggregation tendency. The fluorescence lifetimes (τ) of 1a, 1b and 1c follow a mono-exponential decay with a value τ = 1.11, 1.03 and 1.14 ns, compared with the neat 1, where a bi-exponential decay was identified. AFM studies reveal a smooth and homogenous surface morphology for polyrotaxanes than that of the reference. The electrochemical data provided that the investigated compounds exhibited n- and p-doping processes. The HOMO/LUMO energy levels 1a, 1b, 1c and 1 and in combination with the work function of anodic ITO glass substrates coated with poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) (-5.2 eV) and cathodic Ca (-2.8 eV) or Al (-2.2 eV) indicate that the compounds are electrochemically accessible as electron-transporting materials.

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.

Properties of branching exponential flights in bounded domains

NASA Astrophysics Data System (ADS)

Zoia, A.; Dumonteil, E.; Mazzolo, A.

2012-11-01

In a series of recent works, important results have been reported concerning the statistical properties of exponential flights evolving in bounded domains, a widely adopted model for finite-speed transport phenomena (Blanco S. and Fournier R., Europhys. Lett., 61 (2003) 168; Mazzolo A., Europhys. Lett., 68 (2004) 350; Bénichou O. et al., Europhys. Lett., 70 (2005) 42). Motivated by physical and biological systems where random spatial displacements are coupled with Galton-Watson birth-death mechanisms, such as neutron multiplication, diffusion of reproducing bacteria or spread of epidemics, in this letter we extend those results in two directions, via a Feynman-Kac formalism. First, we characterize the occupation statistics of exponential flights in the presence of absorption and branching, and give explicit moment formulas for the total length travelled by the walker and the number of performed collisions in a given domain. Then, we show that the survival and escape probability can be derived as well by resorting to a similar approach.

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

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

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of thismore » object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.« less

What Randomized Benchmarking Actually Measures

DOE PAGES

Proctor, Timothy; Rudinger, Kenneth; Young, Kevin; ...

2017-09-28

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r. For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not amore » well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. Here, these theories allow explicit computation of the error rate that RB measures (r), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.« less

Number Partitioning via Quantum Adiabatic Computation

NASA Technical Reports Server (NTRS)

Smelyanskiy, Vadim N.; Toussaint, Udo

2002-01-01

We study both analytically and numerically the complexity of the adiabatic quantum evolution algorithm applied to random instances of combinatorial optimization problems. We use as an example the NP-complete set partition problem and obtain an asymptotic expression for the minimal gap separating the ground and exited states of a system during the execution of the algorithm. We show that for computationally hard problem instances the size of the minimal gap scales exponentially with the problem size. This result is in qualitative agreement with the direct numerical simulation of the algorithm for small instances of the set partition problem. We describe the statistical properties of the optimization problem that are responsible for the exponential behavior of the algorithm.

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

Stalagmite Survival: 500kyr of Cyclical Growth and Natural Attrition of Stalagmites in Sulawesi

NASA Astrophysics Data System (ADS)

Scroxton, N.; Gagan, M. K.; Dunbar, G. B.; Ayliffe, L. K.; Hantoro, W. S.; Shen, C. C.; Hellstrom, J. C.; Zhao, J. X.; Cheng, H.; Edwards, R. L.; Sun, H.; Rifai, H.

2014-12-01

Numerous speleothem studies have analysed the age distribution of stalagmites harvested from multiple caves and inferred important changes in paleoclimates to explain stalagmite growth phases. However, stalagmites take tens to hundreds of thousands of years to grow, and thus the twin desires to preserve the cave condition for future generations and advance palaeoclimate science are often in conflict. In this study we use U/Th ages from low impact mini-cores extracted in situ from the bases of stalagmites, thus keeping the intrinsic value of the cave intact. Our case study is based on 77 individual stalagmites drilled in situ in thirteen caves located in and around Bantimurung-Bulusaraung National Park, South Sulawesi, Indonesia. The stalagmites grew during discrete time intervals within the last ~530,000 years, and analysis of their age distribution shows an exponential decrease in the number of older stalagmites surviving to the present day. The age distribution indicates that the rate of natural attrition of stalagmites is approximately constant through time, probably in response to a number of natural processes, including downward erosion of the karst terrain, cave collapse, in-cave erosional processes and in-cave sedimentation covering stalagmites. Natural attrition of stalagmites is likely to be a general cave phenomenon, and has important implications for cave conservation because it highlights that random removal of stalagmites without prior knowledge of their ages will result in unnecessary replication and a failure to sample the full length of the available paleoclimate record. Departure from this "normal" exponential profile can be used to infer palaeoclimate information: significant deviations are produced by periods of more frequent stalagmite growth, inferred here to reflect increases in monsoon rainfall over Sulawesi (345-340, 75-70 and 10-5 kyr BP). By adjusting the record to account for stalagmite attrition, more statistically robust paleoclimate information can be inferred. Crucially, these insights on past climates have been obtained entirely from reconnaissance-style basal mini-core ages. This novel technique is therefore suitable for caves where the removal of stalagmites would cause irreparable damage, or jeopardize local cultural and tourism potential.

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.

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.

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.

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2018-05-01

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.

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.

Dynamical implications of sample shape for avalanches in 2-dimensional random-field Ising model with saw-tooth domain wall

NASA Astrophysics Data System (ADS)

Tadić, Bosiljka

2018-03-01

We study dynamics of a built-in domain wall (DW) in 2-dimensional disordered ferromagnets with different sample shapes using random-field Ising model on a square lattice rotated by 45 degrees. The saw-tooth DW of the length Lx is created along one side and swept through the sample by slow ramping of the external field until the complete magnetisation reversal and the wall annihilation at the open top boundary at a distance Ly. By fixing the number of spins N =Lx ×Ly = 106 and the random-field distribution at a value above the critical disorder, we vary the ratio of the DW length to the annihilation distance in the range Lx /Ly ∈ [ 1 / 16 , 16 ] . The periodic boundary conditions are applied in the y-direction so that these ratios comprise different samples, i.e., surfaces of cylinders with the changing perimeter Lx and height Ly. We analyse the avalanches of the DW slips between following field updates, and the multifractal structure of the magnetisation fluctuation time series. Our main findings are that the domain-wall lengths materialised in different sample shapes have an impact on the dynamics at all scales. Moreover, the domain-wall motion at the beginning of the hysteresis loop (HLB) probes the disorder effects resulting in the fluctuations that are significantly different from the large avalanches in the central part of the loop (HLC), where the strong fields dominate. Specifically, the fluctuations in HLB exhibit a wide multi-fractal spectrum, which shifts towards higher values of the exponents when the DW length is reduced. The distributions of the avalanches in this segments of the loops obey power-law decay and the exponential cutoffs with the exponents firmly in the mean-field universality class for long DW. In contrast, the avalanches in the HLC obey Tsallis density distribution with the power-law tails which indicate the new categories of the scale invariant behaviour for different ratios Lx /Ly. The large fluctuations in the HLC, on the other hand, have a rather narrow spectrum which is less sensitive to the length of the wall. These findings shed light to the dynamical criticality of the random-field Ising model at its lower critical dimension; they can be relevant to applications of the dynamics of injected domain walls in two-dimensional nanowires and ferromagnetic films.

Time-dependent solutions for a stochastic model of gene expression with molecule production in the form of a compound Poisson process.

PubMed

Jędrak, Jakub; Ochab-Marcinek, Anna

2016-09-01

We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability distribution and the model parameters depend on time in an arbitrary (e.g., oscillatory) manner, and for arbitrary initial conditions. We show that in the case of periodic external activation and constant protein degradation rate, the response of the gene is analogous to the resistor-capacitor low-pass filter, where slow oscillations of the external driving have a greater effect on gene expression than the fast ones. We also demonstrate that the nth cumulant of the protein number distribution depends on the nth moment of the burst size distribution. We use these results to show that different measures of noise (coefficient of variation, Fano factor, fractional change of variance) may vary in time in a different manner. Therefore, any biological hypothesis of evolutionary optimization based on the nonmonotonic dependence of a chosen measure of noise on time must justify why it assumes that biological evolution quantifies noise in that particular way. Finally, we show that not only for exponentially distributed burst sizes but also for a wider class of burst size distributions (e.g., Dirac delta and gamma) the control of gene expression level by burst frequency modulation gives rise to proportional scaling of variance of the protein number distribution to its mean, whereas the control by amplitude modulation implies proportionality of protein number variance to the mean squared.

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

Incidence of the Bertillon and Gompertz effects on the outcome of clinical trials

NASA Astrophysics Data System (ADS)

Roehner, Bertrand M.

2014-11-01

The accounts of medical trials provide very detailed information about the patients’ health conditions. On the contrary, almost no vital data such as marital status or age distribution are usually given. Yet, some of these factors can have a notable impact on the overall death rate, thereby changing the outcome and conclusions of the trial. This paper focuses on two of these variables. The first is marital status; its effect on life expectancy (which will be referred to as the Bertillon effect) may double death rates in all age intervals. The second variable is the age distribution of the oldest patients. Because of the exponential nature of Gompertz’s law changes in the distribution of ages in the oldest age group can have dramatic consequences on the overall number of deaths. One should recall that the death rate at the age of 82 is 40 times higher than at the age of 37. It will be seen that randomization alone can hardly take care of these problems. Appropriate remedies are easy to formulate however. First, the marital status of patients as well as the age distribution of those over 65 should be documented for both study groups. Then, thanks to these data and based on the Bertillon and Gompertz laws, it will become possible to perform appropriate corrections. Such corrections will notably improve the reliability and accuracy of the conclusions, especially in trials which include a large proportion of elderly subjects.

Poisson-process generalization for the trading waiting-time distribution in a double-auction mechanism

NASA Astrophysics Data System (ADS)

Cincotti, Silvano; Ponta, Linda; Raberto, Marco; Scalas, Enrico

2005-05-01

In this paper, empirical analyses and computational experiments are presented on high-frequency data for a double-auction (book) market. Main objective of the paper is to generalize the order waiting time process in order to properly model such empirical evidences. The empirical study is performed on the best bid and best ask data of 7 U.S. financial markets, for 30-stock time series. In particular, statistical properties of trading waiting times have been analyzed and quality of fits is evaluated by suitable statistical tests, i.e., comparing empirical distributions with theoretical models. Starting from the statistical studies on real data, attention has been focused on the reproducibility of such results in an artificial market. The computational experiments have been performed within the Genoa Artificial Stock Market. In the market model, heterogeneous agents trade one risky asset in exchange for cash. Agents have zero intelligence and issue random limit or market orders depending on their budget constraints. The price is cleared by means of a limit order book. The order generation is modelled with a renewal process. Based on empirical trading estimation, the distribution of waiting times between two consecutive orders is modelled by a mixture of exponential processes. Results show that the empirical waiting-time distribution can be considered as a generalization of a Poisson process. Moreover, the renewal process can approximate real data and implementation on the artificial stocks market can reproduce the trading activity in a realistic way.

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.

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.

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.

Estimating time since infection in early homogeneous HIV-1 samples using a poisson model

PubMed Central

2010-01-01

Background The occurrence of a genetic bottleneck in HIV sexual or mother-to-infant transmission has been well documented. This results in a majority of new infections being homogeneous, i.e., initiated by a single genetic strain. Early after infection, prior to the onset of the host immune response, the viral population grows exponentially. In this simple setting, an approach for estimating evolutionary and demographic parameters based on comparison of diversity measures is a feasible alternative to the existing Bayesian methods (e.g., BEAST), which are instead based on the simulation of genealogies. Results We have devised a web tool that analyzes genetic diversity in acutely infected HIV-1 patients by comparing it to a model of neutral growth. More specifically, we consider a homogeneous infection (i.e., initiated by a unique genetic strain) prior to the onset of host-induced selection, where we can assume a random accumulation of mutations. Previously, we have shown that such a model successfully describes about 80% of sexual HIV-1 transmissions provided the samples are drawn early enough in the infection. Violation of the model is an indicator of either heterogeneous infections or the initiation of selection. Conclusions When the underlying assumptions of our model (homogeneous infection prior to selection and fast exponential growth) are met, we are under a very particular scenario for which we can use a forward approach (instead of backwards in time as provided by coalescent methods). This allows for more computationally efficient methods to derive the time since the most recent common ancestor. Furthermore, the tool performs statistical tests on the Hamming distance frequency distribution, and outputs summary statistics (mean of the best fitting Poisson distribution, goodness of fit p-value, etc). The tool runs within minutes and can readily accommodate the tens of thousands of sequences generated through new ultradeep pyrosequencing technologies. The tool is available on the LANL website. PMID:20973976

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.