Context-Sensitive Detection of Local Community Structure

DTIC Science & Technology

2011-04-01

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

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.

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.

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.

Curvature and temperature of complex networks.

PubMed

Krioukov, Dmitri; Papadopoulos, Fragkiskos; Vahdat, Amin; Boguñá, Marián

2009-09-01

We show that heterogeneous degree distributions in observed scale-free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a physical interpretation of hyperbolic distances as energies of links. The hidden space curvature affects the heterogeneity of the degree distribution, while clustering is a function of temperature. We embed the internet into the hyperbolic plane and find a remarkable congruency between the embedding and our hyperbolic model. Besides proving our model realistic, this embedding may be used for routing with only local information, which holds significant promise for improving the performance of internet routing.

Quantifying patterns of research interest evolution

NASA Astrophysics Data System (ADS)

Jia, Tao; Wang, Dashun; Szymanski, Boleslaw

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

Exponential 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.

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.

Dynamics of epidemic diseases on a growing adaptive network

PubMed Central

Demirel, Güven; Barter, Edmund; Gross, Thilo

2017-01-01

The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Here, we analyze an adaptive network where the degree distribution is not independent of epidemics but is shaped through disease-induced dynamics and mortality in a complex interplay. We study the dynamics of a network that grows according to a preferential attachment rule, while nodes are simultaneously removed from the network due to disease-induced mortality. We investigate the prevalence of the disease using individual-based simulations and a heterogeneous node approximation. Our results suggest that in this system in the thermodynamic limit no epidemic thresholds exist, while the interplay between network growth and epidemic spreading leads to exponential networks for any finite rate of infectiousness when the disease persists. PMID:28186146

Dynamics of epidemic diseases on a growing adaptive network.

PubMed

Demirel, Güven; Barter, Edmund; Gross, Thilo

2017-02-10

The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Here, we analyze an adaptive network where the degree distribution is not independent of epidemics but is shaped through disease-induced dynamics and mortality in a complex interplay. We study the dynamics of a network that grows according to a preferential attachment rule, while nodes are simultaneously removed from the network due to disease-induced mortality. We investigate the prevalence of the disease using individual-based simulations and a heterogeneous node approximation. Our results suggest that in this system in the thermodynamic limit no epidemic thresholds exist, while the interplay between network growth and epidemic spreading leads to exponential networks for any finite rate of infectiousness when the disease persists.

Dynamics of epidemic diseases on a growing adaptive network

NASA Astrophysics Data System (ADS)

Demirel, Güven; Barter, Edmund; Gross, Thilo

2017-02-01

The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Here, we analyze an adaptive network where the degree distribution is not independent of epidemics but is shaped through disease-induced dynamics and mortality in a complex interplay. We study the dynamics of a network that grows according to a preferential attachment rule, while nodes are simultaneously removed from the network due to disease-induced mortality. We investigate the prevalence of the disease using individual-based simulations and a heterogeneous node approximation. Our results suggest that in this system in the thermodynamic limit no epidemic thresholds exist, while the interplay between network growth and epidemic spreading leads to exponential networks for any finite rate of infectiousness when the disease persists.

Empirical investigation of topological and weighted properties of a bus transport network from China

NASA Astrophysics Data System (ADS)

Shu-Min, Feng; Bao-Yu, Hu; Cen, Nie; Xiang-Hao, Shen; Yu-Sheng, Ci

2016-03-01

Many bus transport networks (BTNs) have evolved into directed networks. A new representation model for BTNs is proposed, called directed-space P. The bus transport network of Harbin (BTN-H) is described as a directed and weighted complex network by the proposed representation model and by giving each node weights. The topological and weighted properties are revealed in detail. In-degree and out-degree distributions, in-weight and out-weight distributions are presented as an exponential law, respectively. There is a strong relation between in-weight and in-degree (also between out-weight and out-degree), which can be fitted by a power function. Degree-degree and weight-weight correlations are investigated to reveal that BTN-H has a disassortative behavior as the nodes have relatively high degree (or weight). The disparity distributions of out-degree and in-degree follow an approximate power-law. Besides, the node degree shows a near linear increase with the number of routes that connect to the corresponding station. These properties revealed in this paper can help public transport planners to analyze the status quo of the BTN in nature. Project supported by the National High Technology Research and Development Program of China (Grant No. 2014AA110304).

Log-amplitude statistics for Beck-Cohen superstatistics

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Konno, Hidetoshi

2013-05-01

As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ2, inverse χ2, and log-normal superstatistical distributions. Furthermore, we show that χ2 and inverse χ2 superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ2 superstatistical distribution with degree 2.

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.

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.

Referee Networks and Their Spectral Properties

NASA Astrophysics Data System (ADS)

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

2005-09-01

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

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

PubMed

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

2010-03-10

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

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.

A Unified Framework for Complex Networks with Degree Trichotomy Based on Markov Chains.

PubMed

Hui, David Shui Wing; Chen, Yi-Chao; Zhang, Gong; Wu, Weijie; Chen, Guanrong; Lui, John C S; Li, Yingtao

2017-06-16

This paper establishes a Markov chain model as a unified framework for describing the evolution processes in complex networks. The unique feature of the proposed model is its capability in addressing the formation mechanism that can reflect the "trichotomy" observed in degree distributions, based on which closed-form solutions can be derived. Important special cases of the proposed unified framework are those classical models, including Poisson, Exponential, Power-law distributed networks. Both simulation and experimental results demonstrate a good match of the proposed model with real datasets, showing its superiority over the classical models. Implications of the model to various applications including citation analysis, online social networks, and vehicular networks design, are also discussed in the paper.

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.

Characterizing the topology of probabilistic biological networks.

PubMed

Todor, Andrei; Dobra, Alin; Kahveci, Tamer

2013-01-01

Biological interactions are often uncertain events, that may or may not take place with some probability. This uncertainty leads to a massive number of alternative interaction topologies for each such network. The existing studies analyze the degree distribution of biological networks by assuming that all the given interactions take place under all circumstances. This strong and often incorrect assumption can lead to misleading results. In this paper, we address this problem and develop a sound mathematical basis to characterize networks in the presence of uncertain interactions. Using our mathematical representation, we develop a method that can accurately describe the degree distribution of such networks. We also take one more step and extend our method to accurately compute the joint-degree distributions of node pairs connected by edges. The number of possible network topologies grows exponentially with the number of uncertain interactions. However, the mathematical model we develop allows us to compute these degree distributions in polynomial time in the number of interactions. Our method works quickly even for entire protein-protein interaction (PPI) networks. It also helps us find an adequate mathematical model using MLE. We perform a comparative study of node-degree and joint-degree distributions in two types of biological networks: the classical deterministic networks and the more flexible probabilistic networks. Our results confirm that power-law and log-normal models best describe degree distributions for both probabilistic and deterministic networks. Moreover, the inverse correlation of degrees of neighboring nodes shows that, in probabilistic networks, nodes with large number of interactions prefer to interact with those with small number of interactions more frequently than expected. We also show that probabilistic networks are more robust for node-degree distribution computation than the deterministic ones. all the data sets used, the software implemented and the alignments found in this paper are available at http://bioinformatics.cise.ufl.edu/projects/probNet/.

Shareholding Networks in Japan

NASA Astrophysics Data System (ADS)

Souma, Wataru; Fujiwara, Yoshi; Aoyama, Hideaki

2005-06-01

The Japanese shareholding network existing at the end of March 2002 is studied empirically. The network is constructed from 2,303 listed companies and 53 non-listed financial institutions. We consider this network as a directed graph by drawing edges from shareholders to stock corporations. The lengths of the shareholder lists vary with the companies, and the most comprehensive lists contain the top 30 shareholders. Consequently, the distribution of incoming edges has an upper bound, while that of outgoing edges has no bound. The distribution of outgoing degrees is well explained by the power law function with an exponential tail. The exponent in the power law range is γ = 1.7. To understand these features from the viewpoint of a company's growth, we consider the correlations between the outgoing degree and the company's age, profit, and total assets.

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.

Growing and navigating the small world Web by local content

PubMed Central

Menczer, Filippo

2002-01-01

Can we model the scale-free distribution of Web hypertext degree under realistic assumptions about the behavior of page authors? Can a Web crawler efficiently locate an unknown relevant page? These questions are receiving much attention due to their potential impact for understanding the structure of the Web and for building better search engines. Here I investigate the connection between the linkage and content topology of Web pages. The relationship between a text-induced distance metric and a link-based neighborhood probability distribution displays a phase transition between a region where linkage is not determined by content and one where linkage decays according to a power law. This relationship is used to propose a Web growth model that is shown to accurately predict the distribution of Web page degree, based on textual content and assuming only local knowledge of degree for existing pages. A qualitatively similar phase transition is found between linkage and semantic distance, with an exponential decay tail. Both relationships suggest that efficient paths can be discovered by decentralized Web navigation algorithms based on textual and/or categorical cues. PMID:12381792

Growing and navigating the small world Web by local content

NASA Astrophysics Data System (ADS)

Menczer, Filippo

2002-10-01

Can we model the scale-free distribution of Web hypertext degree under realistic assumptions about the behavior of page authors? Can a Web crawler efficiently locate an unknown relevant page? These questions are receiving much attention due to their potential impact for understanding the structure of the Web and for building better search engines. Here I investigate the connection between the linkage and content topology of Web pages. The relationship between a text-induced distance metric and a link-based neighborhood probability distribution displays a phase transition between a region where linkage is not determined by content and one where linkage decays according to a power law. This relationship is used to propose a Web growth model that is shown to accurately predict the distribution of Web page degree, based on textual content and assuming only local knowledge of degree for existing pages. A qualitatively similar phase transition is found between linkage and semantic distance, with an exponential decay tail. Both relationships suggest that efficient paths can be discovered by decentralized Web navigation algorithms based on textual and/or categorical cues.

Growing and navigating the small world Web by local content.

PubMed

Menczer, Filippo

2002-10-29

Can we model the scale-free distribution of Web hypertext degree under realistic assumptions about the behavior of page authors? Can a Web crawler efficiently locate an unknown relevant page? These questions are receiving much attention due to their potential impact for understanding the structure of the Web and for building better search engines. Here I investigate the connection between the linkage and content topology of Web pages. The relationship between a text-induced distance metric and a link-based neighborhood probability distribution displays a phase transition between a region where linkage is not determined by content and one where linkage decays according to a power law. This relationship is used to propose a Web growth model that is shown to accurately predict the distribution of Web page degree, based on textual content and assuming only local knowledge of degree for existing pages. A qualitatively similar phase transition is found between linkage and semantic distance, with an exponential decay tail. Both relationships suggest that efficient paths can be discovered by decentralized Web navigation algorithms based on textual and/or categorical cues.

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.

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

Public Transport Systems in Poland: From Bialystok to Zielona Góra by Bus and Tram Using Universal Statistics of Complex Networks

NASA Astrophysics Data System (ADS)

Sienkiewicz, J.; Holyst, J. A.

2005-05-01

We have examined a topology of 21 public transport networks in Poland. Our data exhibit several universal features in considered systems when they are analyzed from the point of view of evolving networks. Depending on the assumed definition of a network topology the degree distribution can follow a power law p(k) ˜ k-γ or can be described by an exponential function p(k) ˜ exp (-α k). In the first case one observes that mean distances between two nodes are a linear function of logarithms of their degrees product.

Network topology of an experimental futures exchange

NASA Astrophysics Data System (ADS)

Wang, S. C.; Tseng, J. J.; Tai, C. C.; Lai, K. H.; Wu, W. S.; Chen, S. H.; Li, S. P.

2008-03-01

Many systems of different nature exhibit scale free behaviors. Economic systems with power law distribution in the wealth are one of the examples. To better understand the working behind the complexity, we undertook an experiment recording the interactions between market participants. A Web server was setup to administer the exchange of futures contracts whose liquidation prices were coupled to event outcomes. After free registration, participants started trading to compete for the money prizes upon maturity of the futures contracts at the end of the experiment. The evolving `cash' flow network was reconstructed from the transactions between players. We show that the network topology is hierarchical, disassortative and small-world with a power law exponent of 1.02±0.09 in the degree distribution after an exponential decay correction. The small-world property emerged early in the experiment while the number of participants was still small. We also show power law-like distributions of the net incomes and inter-transaction time intervals. Big winners and losers are associated with high degree, high betweenness centrality, low clustering coefficient and low degree-correlation. We identify communities in the network as groups of the like-minded. The distribution of the community sizes is shown to be power-law distributed with an exponent of 1.19±0.16.

Interspecific competition underlying mutualistic networks.

PubMed

Maeng, Seong Eun; Lee, Jae Woo; Lee, Deok-Sun

2012-03-09

Multiple classes of interactions may exist affecting one another in a given system. For the mutualistic networks of plants and pollinating animals, it has been known that the degree distribution is broad but often deviates from power-law form more significantly for plants than animals. To illuminate the origin of such asymmetry, we study a model network in which links are assigned under generalized preferential-selection rules between two groups of nodes and find the sensitive dependence of the resulting connectivity pattern on the model parameters. The nonlinearity of preferential selection can come from interspecific interactions among animals and among plants. The model-based analysis of real-world mutualistic networks suggests that a new animal determines its partners not only by their abundance but also under the competition with existing animal species, which leads to the stretched-exponential degree distributions of plants.

Interspecific Competition Underlying Mutualistic Networks

NASA Astrophysics Data System (ADS)

Maeng, Seong Eun; Lee, Jae Woo; Lee, Deok-Sun

2012-03-01

Multiple classes of interactions may exist affecting one another in a given system. For the mutualistic networks of plants and pollinating animals, it has been known that the degree distribution is broad but often deviates from power-law form more significantly for plants than animals. To illuminate the origin of such asymmetry, we study a model network in which links are assigned under generalized preferential-selection rules between two groups of nodes and find the sensitive dependence of the resulting connectivity pattern on the model parameters. The nonlinearity of preferential selection can come from interspecific interactions among animals and among plants. The model-based analysis of real-world mutualistic networks suggests that a new animal determines its partners not only by their abundance but also under the competition with existing animal species, which leads to the stretched-exponential degree distributions of plants.

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

PubMed

Rochon, Justine; Kieser, Meinhard

2011-11-01

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

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.

Modeling the germination kinetics of clostridium botulinum 56A spores as affected by temperature, pH, and sodium chloride.

PubMed

Chea, F P; Chen, Y; Montville, T J; Schaffner, D W

2000-08-01

The germination kinetics of proteolytic Clostridium botulinum 56A spores were modeled as a function of temperature (15, 22, 30 degrees C), pH (5.5, 6.0, 6.5), and sodium chloride (0.5, 2.0, 4.0%). Germination in brain heart infusion (BHI) broth was followed with phase-contrast microscopy. Data collected were used to develop the mathematical models. The germination kinetics expressed as cumulated fraction of germinated spores over time at each environmental condition were best described by an exponential distribution. Quadratic polynomial models were developed by regression analysis to describe the exponential parameter (time to 63% germination) (r2 = 0.982) and the germination extent (r2 = 0.867) as a function of temperature, pH, and sodium chloride. Validation experiments in BHI broth (pH: 5.75, 6.25; NaCl: 1.0, 3.0%; temperature: 18, 26 degrees C) confirmed that the model's predictions were within an acceptable range compared to the experimental results and were fail-safe in most cases.

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.

A Comparison of Two Algorithms for the Simulation of Non-Homogeneous Poisson Processes with Degree-Two Exponential Polynomial Intensity Function.

DTIC Science & Technology

1977-09-01

process with an event streaa intensity (rate) function that is of degree-two exponential pclyncaial foru. (The use of exponential pclynoaials is...4 \\v 01 ^3 C \\ \\ •r- S_ \\ \\ O \\ \\ a \\ \\ V IA C 4-> \\ \\ •«- c \\ 1 <— 3 • o \\ \\ Ol (J \\ \\ O U —1 <o \\ I...would serve as a good initial approxiaation t* , f-r the Newton-Raphson aethod. However, for the purpose of this implementation, the end point which

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.

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.

Evolution of Linux operating system network

NASA Astrophysics Data System (ADS)

Xiao, Guanping; Zheng, Zheng; Wang, Haoqin

2017-01-01

Linux operating system (LOS) is a sophisticated man-made system and one of the most ubiquitous operating systems. However, there is little research on the structure and functionality evolution of LOS from the prospective of networks. In this paper, we investigate the evolution of the LOS network. 62 major releases of LOS ranging from versions 1.0 to 4.1 are modeled as directed networks in which functions are denoted by nodes and function calls are denoted by edges. It is found that the size of the LOS network grows almost linearly, while clustering coefficient monotonically decays. The degree distributions are almost the same: the out-degree follows an exponential distribution while both in-degree and undirected degree follow power-law distributions. We further explore the functionality evolution of the LOS network. It is observed that the evolution of functional modules is shown as a sequence of seven events (changes) succeeding each other, including continuing, growth, contraction, birth, splitting, death and merging events. By means of a statistical analysis of these events in the top 4 largest components (i.e., arch, drivers, fs and net), it is shown that continuing, growth and contraction events occupy more than 95% events. Our work exemplifies a better understanding and describing of the dynamics of LOS evolution.

[Spatial structure analysis and distribution simulation of Therioaphis trifolii population based on geostatistics and GIS].

PubMed

Zhang, Rong; Leng, Yun-fa; Zhu, Meng-meng; Wang, Fang

2007-11-01

Based on geographic information system and geostatistics, the spatial structure of Therioaphis trifolii population of different periods in Yuanzhou district of Guyuan City, the southern Ningxia Province, was analyzed. The spatial distribution of Therioaphis trifolii population was also simulated by ordinary Kriging interpretation. The results showed that Therioaphis trifolii population of different periods was correlated spatially in the study area. The semivariograms of Therioaphis trifolii could be described by exponential model, indicating an aggregated spatial arrangement. The spatial variance varied from 34.13%-48.77%, and the range varied from 8.751-12.049 km. The degree and direction of aggregation showed that the trend was increased gradually from southwest to northeast. The dynamic change of Therioaphis trifolii population in different periods could be analyzed intuitively on the simulated maps of the spatial distribution from the two aspects of time and space, The occurrence position and degree of Therioaphis trifolii to a state of certain time could be determined easily.

Empirical study on human acupuncture point network

NASA Astrophysics Data System (ADS)

Li, Jian; Shen, Dan; Chang, Hui; He, Da-Ren

2007-03-01

Chinese medical theory is ancient and profound, however is confined by qualitative and faint understanding. The effect of Chinese acupuncture in clinical practice is unique and effective, and the human acupuncture points play a mysterious and special role, however there is no modern scientific understanding on human acupuncture points until today. For this reason, we attend to use complex network theory, one of the frontiers in the statistical physics, for describing the human acupuncture points and their connections. In the network nodes are defined as the acupuncture points, two nodes are connected by an edge when they are used for a medical treatment of a common disease. A disease is defined as an act. Some statistical properties have been obtained. The results certify that the degree distribution, act degree distribution, and the dependence of the clustering coefficient on both of them obey SPL distribution function, which show a function interpolating between a power law and an exponential decay. The results may be helpful for understanding Chinese medical theory.

Topological evolution of the internet public opinion

NASA Astrophysics Data System (ADS)

Lian, Ying; Dong, Xuefan; Liu, Yijun

2017-11-01

The Internet forms a platform featured with high liquidity, accessibility and concealment for the public to express their respective views on certain events, thus leading to a large network graph. Due to such environmental features, the public opinions formed on the Internet are different from those on traditional media. Studies focusing on the former area are relatively fewer. In addition, the majority of existing methods proposed for constructing the Internet public opinion topological structure are based on the classic BA model, thus resulting in drawbacks in the range of simplicity and a lack of strict deduction. Therefore, based on the complex networks theory, a model applied to describe the topology of the Internet public opinion is deduced with rigorous derivation in the present paper. Results show that the proposed expression could well reflect the degree distribution of Internet public opinion which follows an analogous power law distribution, and that the peak value and the degree distribution are not correlative to each other. Moreover, it has been also proved that compared to the classic BA model, the proposed model has better accuracy performance in the description of the degree distribution of the Internet public opinion, which contributes to future studies focusing on this area. Thus, an attempt has been made to give the first theoretical description of the Internet public opinion topology in the present paper. In addition, it is also the first paper focusing on the solution of networks degree distribution with an exponential growth form.

A UNIVERSAL NEUTRAL GAS PROFILE FOR NEARBY DISK GALAXIES

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

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

2012-09-10

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

The generalized truncated exponential distribution as a model for earthquake magnitudes

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2015-04-01

The random distribution of small, medium and large earthquake magnitudes follows an exponential distribution (ED) according to the Gutenberg-Richter relation. But a magnitude distribution is truncated in the range of very large magnitudes because the earthquake energy is finite and the upper tail of the exponential distribution does not fit well observations. Hence the truncated exponential distribution (TED) is frequently applied for the modelling of the magnitude distributions in the seismic hazard and risk analysis. The TED 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. It also applies to alternative distribution models. The presented generalized truncated exponential distribution (GTED) overcomes this weakness. The ED and the TED are special cases of the GTED. Different issues of the statistical inference are also discussed and an example of empirical data is presented in the current contribution.

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

PubMed Central

Zheng, Xiliang; Wang, Jin

2015-01-01

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

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.

Distributions of Autocorrelated First-Order Kinetic Outcomes: Illness Severity

PubMed Central

Englehardt, James D.

2015-01-01

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

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.

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

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 Mass Distribution of Stellar-mass Black Holes

NASA Astrophysics Data System (ADS)

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

2011-11-01

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

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.

The Oscillating Circular Airfoil on the Basis of Potential Theory

NASA Technical Reports Server (NTRS)

Schade, T.; Krienes, K.

1947-01-01

Proceeding from the thesis by W. Kinner the present report treats the problem of the circular airfoil in uniform airflow executing small oscillations, the amplitudes of which correspond to whole functions of the second degree in x and y. The pressure distribution is secured by means of Prandtl's acceleration potential. It results in a system of linear equations the coefficients of which can be calculated exactly with the aid of exponential functions and Hankel's functions. The equations necessary are derived in part I; the numerical calculation follows in part II.

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.

Complex network approach to fractional time series

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

Manshour, Pouya

In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacencymore » matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.« less

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.

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

PubMed

Currie, L A

2001-07-01

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

Directed networks' different link formation mechanisms causing degree distribution distinction

NASA Astrophysics Data System (ADS)

Behfar, Stefan Kambiz; Turkina, Ekaterina; Cohendet, Patrick; Burger-Helmchen, Thierry

2016-11-01

Within undirected networks, scientists have shown much interest in presenting power-law features. For instance, Barabási and Albert (1999) claimed that a common property of many large networks is that vertex connectivity follows scale-free power-law distribution, and in another study Barabási et al. (2002) showed power law evolution in the social network of scientific collaboration. At the same time, Jiang et al. (2011) discussed deviation from power-law distribution; others indicated that size effect (Bagrow et al., 2008), information filtering mechanism (Mossa et al., 2002), and birth and death process (Shi et al., 2005) could account for this deviation. Within directed networks, many authors have considered that outlinks follow a similar mechanism of creation as inlinks' (Faloutsos et al., 1999; Krapivsky et al., 2001; Tanimoto, 2009) with link creation rate being the linear function of node degree, resulting in a power-law shape for both indegree and outdegree distribution. Some other authors have made an assumption that directed networks, such as scientific collaboration or citation, behave as undirected, resulting in a power-law degree distribution accordingly (Barabási et al., 2002). At the same time, we claim (1) Outlinks feature different degree distributions than inlinks; where different link formation mechanisms cause the distribution distinctions, (2) in/outdegree distribution distinction holds for different levels of system decomposition; therefore this distribution distinction is a property of directed networks. First, we emphasize in/outlink formation mechanisms as causal factors for distinction between indegree and outdegree distributions (where this distinction has already been noticed in Barker et al. (2010) and Baxter et al. (2006)) within a sample network of OSS projects as well as Java software corpus as a network. Second, we analyze whether this distribution distinction holds for different levels of system decomposition: open-source-software (OSS) project-project dependency within a cluster, package-package dependency within a project and class-class dependency within a package. We conclude that indegree and outdegree dependencies do not lead to similar type of degree distributions, implying that indegree dependencies follow overall power-law distribution (or power-law with flat-top or exponential cut-off in some cases), while outdegree dependencies do not follow heavy-tailed distribution.

Empirical research on complex networks modeling of combat SoS based on data from real war-game, Part I: Statistical characteristics

NASA Astrophysics Data System (ADS)

Chen, Lei; Kou, Yingxin; Li, Zhanwu; Xu, An; Wu, Cheng

2018-01-01

We build a complex networks model of combat System-of-Systems (SoS) based on empirical data from a real war-game, this model is a combination of command & control (C2) subnetwork, sensors subnetwork, influencers subnetwork and logistical support subnetwork, each subnetwork has idiographic components and statistical characteristics. The C2 subnetwork is the core of whole combat SoS, it has a hierarchical structure with no modularity, of which robustness is strong enough to maintain normal operation after any two nodes is destroyed; the sensors subnetwork and influencers subnetwork are like sense organ and limbs of whole combat SoS, they are both flat modular networks of which degree distribution obey GEV distribution and power-law distribution respectively. The communication network is the combination of all subnetworks, it is an assortative Small-World network with core-periphery structure, the Intelligence & Communication Stations/Command Center integrated with C2 nodes in the first three level act as the hub nodes in communication network, and all the fourth-level C2 nodes, sensors, influencers and logistical support nodes have communication capability, they act as the periphery nodes in communication network, its degree distribution obeys exponential distribution in the beginning, Gaussian distribution in the middle, and power-law distribution in the end, and its path length obeys GEV distribution. The betweenness centrality distribution, closeness centrality distribution and eigenvector centrality are also been analyzed to measure the vulnerability of nodes.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Worldwide Marine Transportation Network: Efficiency and Container Throughput

NASA Astrophysics Data System (ADS)

Deng, Wei-Bing; Guo, Long; Li, Wei; Cai, Xu

2009-11-01

Through empirical analysis of the global structure of the Worldwide Marine Transportation Network (WMTN), we find that the WMTN, a small-world network, exhibits an exponential-like degree distribution. We hereby investigate the efficiency of the WMTN by employing a simple definition. Compared with many other transportation networks, the WMTN possesses relatively low efficiency. Furthermore, by exploring the relationship between the topological structure and the container throughput, we find that strong correlations exist among the container throughout the degree and the clustering coefficient. Also, considering the navigational process that a ship travels in a real shipping line, we obtain that the weight of a seaport is proportional to the total probability contributed by all the passing shipping lines.

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.

Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing

NASA Astrophysics Data System (ADS)

Zhang, Fode; Shi, Yimin; Wang, Ruibing

2017-02-01

In the information geometry suggested by Amari (1985) and Amari et al. (1987), a parametric statistical model can be regarded as a differentiable manifold with the parameter space as a coordinate system. Note that the q-exponential distribution plays an important role in Tsallis statistics (see Tsallis, 2009), this paper investigates the geometry of the q-exponential distribution with dependent competing risks and accelerated life testing (ALT). A copula function based on the q-exponential function, which can be considered as the generalized Gumbel copula, is discussed to illustrate the structure of the dependent random variable. Employing two iterative algorithms, simulation results are given to compare the performance of estimations and levels of association under different hybrid progressively censoring schemes (HPCSs).

Plasmodial vein networks of the slime mold Physarum polycephalum form regular graphs

NASA Astrophysics Data System (ADS)

Baumgarten, Werner; Ueda, Tetsuo; Hauser, Marcus J. B.

2010-10-01

The morphology of a typical developing biological transportation network, the vein network of the plasmodium of the myxomycete Physarum polycephalum is analyzed during its free extension. The network forms a classical, regular graph, and has exclusively nodes of degree 3. This contrasts to most real-world transportation networks which show small-world or scale-free properties. The complexity of the vein network arises from the weighting of the lengths, widths, and areas of the vein segments. The lengths and areas follow exponential distributions, while the widths are distributed log-normally. These functional dependencies are robust during the entire evolution of the network, even though the exponents change with time due to the coarsening of the vein network.

Plasmodial vein networks of the slime mold Physarum polycephalum form regular graphs.

PubMed

Baumgarten, Werner; Ueda, Tetsuo; Hauser, Marcus J B

2010-10-01

The morphology of a typical developing biological transportation network, the vein network of the plasmodium of the myxomycete Physarum polycephalum is analyzed during its free extension. The network forms a classical, regular graph, and has exclusively nodes of degree 3. This contrasts to most real-world transportation networks which show small-world or scale-free properties. The complexity of the vein network arises from the weighting of the lengths, widths, and areas of the vein segments. The lengths and areas follow exponential distributions, while the widths are distributed log-normally. These functional dependencies are robust during the entire evolution of the network, even though the exponents change with time due to the coarsening of the vein network.

Beyond the power law: Uncovering stylized facts in interbank networks

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

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.

Memory behaviors of entropy production rates in heat conduction

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2018-02-01

Based on the relaxation time approximation and first-order expansion, memory behaviors in heat conduction are found between the macroscopic and Boltzmann-Gibbs-Shannon (BGS) entropy production rates with exponentially decaying memory kernels. In the frameworks of classical irreversible thermodynamics (CIT) and BGS statistical mechanics, the memory dependency on the integrated history is unidirectional, while for the extended irreversible thermodynamics (EIT) and BGS entropy production rates, the memory dependences are bidirectional and coexist with the linear terms. When macroscopic and microscopic relaxation times satisfy a specific relationship, the entropic memory dependences will be eliminated. There also exist initial effects in entropic memory behaviors, which decay exponentially. The second-order term are also discussed, which can be understood as the global non-equilibrium degree. The effects of the second-order term are consisted of three parts: memory dependency, initial value and linear term. The corresponding memory kernels are still exponential and the initial effects of the global non-equilibrium degree also decay exponentially.

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.

Quark mixing and exponential form of the Cabibbo-Kobayashi-Maskawa matrix

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

Zhukovsky, K. V., E-mail: zhukovsk@phys.msu.ru; Dattoli, D., E-mail: dattoli@frascati.enea.i

2008-10-15

Various forms of representation of the mixing matrix are discussed. An exponential parametrization e{sup A} of the Cabibbo-Kobayashi-Maskawa matrix is considered in the context of the unitarity requirement, this parametrization being the most general form of the mixing matrix. An explicit representation for the exponential mixing matrix in terms of the first and second degrees of the matrix A exclusively is obtained. This representation makes it possible to calculate this exponential mixing matrix readily in any order of the expansion in the small parameter {lambda}. The generation of new unitary parametric representations of the mixing matrix with the aid ofmore » the exponential matrix is demonstrated.« less

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

PubMed

Lysyk, T J; Danyk, T

2007-09-01

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

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.

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.

Enhancement of large fluctuations to extinction in adaptive networks

NASA Astrophysics Data System (ADS)

Hindes, Jason; Schwartz, Ira B.; Shaw, Leah B.

2018-01-01

During an epidemic, individual nodes in a network may adapt their connections to reduce the chance of infection. A common form of adaption is avoidance rewiring, where a noninfected node breaks a connection to an infected neighbor and forms a new connection to another noninfected node. Here we explore the effects of such adaptivity on stochastic fluctuations in the susceptible-infected-susceptible model, focusing on the largest fluctuations that result in extinction of infection. Using techniques from large-deviation theory, combined with a measurement of heterogeneity in the susceptible degree distribution at the endemic state, we are able to predict and analyze large fluctuations and extinction in adaptive networks. We find that in the limit of small rewiring there is a sharp exponential reduction in mean extinction times compared to the case of zero adaption. Furthermore, we find an exponential enhancement in the probability of large fluctuations with increased rewiring rate, even when holding the average number of infected nodes constant.

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

Treesearch

Jeffrey H. Gove

2016-01-01

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

Exponentiated power Lindley distribution.

PubMed

Ashour, Samir K; Eltehiwy, Mahmoud A

2015-11-01

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

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

NASA Astrophysics Data System (ADS)

Nerantzaki, Sofia; Papalexiou, Simon Michael

2017-04-01

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

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

DTIC Science & Technology

2010-06-01

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

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

PubMed

Zhang, Guodong; Zeng, Zhigang; Hu, Junhao

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

He, Xiaozhou; Wang, Yin; Tong, Penger

2018-05-01

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

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

PubMed Central

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

2010-01-01

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

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

PubMed Central

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

2016-01-01

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

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.

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

The matrix exponential in transient structural analysis

NASA Technical Reports Server (NTRS)

Minnetyan, Levon

1987-01-01

The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.

Adsorption of nicotine from aqueous solution onto hydrophobic zeolite type USY

NASA Astrophysics Data System (ADS)

Lazarevic, Natasa; Adnadjevic, Borivoj; Jovanovic, Jelena

2011-07-01

The isothermal adsorption of nicotine from an aqueous solution onto zeolite type USY was investigated. The adsorption isotherms of nicotine onto the zeolite at different temperatures ranging from 298 to 322 K were determined. It was found that the adsorption isotherms can be described by the model of Freundlich adsorption isotherm. Based on the adsorption isotherms the changes of adsorption heat, free energy and entropy with adsorption degree were determined. The determined decrease of adsorption heat with adsorption degree can be explained by the presence of the adsorption centers of different energy and concentration on interface of zeolite-nicotine solution. It was found that the probability function of density distribution of the heat of adsorption (DDF) has exponential form. It was concluded that the possibility of fitting the adsorption isotherms of nicotine onto the zeolite by Freundlich adsorption isotherm was a direct consequence of that. The determined increase in entropy with the increase in adsorption degree can be explained with the change of phase state of adsorbed nicotine.

Visibility graph network analysis of natural gas price: The case of North American market

NASA Astrophysics Data System (ADS)

Sun, Mei; Wang, Yaqi; Gao, Cuixia

2016-11-01

Fluctuations in prices of natural gas significantly affect global economy. Therefore, the research on the characteristics of natural gas price fluctuations, turning points and its influencing cycle on the subsequent price series is of great significance. Global natural gas trade concentrates on three regional markets: the North American market, the European market and the Asia-Pacific market, with North America having the most developed natural gas financial market. In addition, perfect legal supervision and coordinated regulations make the North American market more open and more competitive. This paper focuses on the North American natural gas market specifically. The Henry Hub natural gas spot price time series is converted to a visibility graph network which provides a new direction for macro analysis of time series, and several indicators are investigated: degree and degree distribution, the average shortest path length and community structure. The internal mechanisms underlying price fluctuations are explored through the indicators. The results show that the natural gas prices visibility graph network (NGP-VGN) is of small-world and scale-free properties simultaneously. After random rearrangement of original price time series, the degree distribution of network becomes exponential distribution, different from the original ones. This means that, the original price time series is of long-range negative correlation fractal characteristic. In addition, nodes with large degree correspond to significant geopolitical or economic events. Communities correspond to time cycles in visibility graph network. The cycles of time series and the impact scope of hubs can be found by community structure partition.

A novel LTE scheduling algorithm for green technology in smart grid.

PubMed

Hindia, Mohammad Nour; Reza, Ahmed Wasif; Noordin, Kamarul Ariffin; Chayon, Muhammad Hasibur Rashid

2015-01-01

Smart grid (SG) application is being used nowadays to meet the demand of increasing power consumption. SG application is considered as a perfect solution for combining renewable energy resources and electrical grid by means of creating a bidirectional communication channel between the two systems. In this paper, three SG applications applicable to renewable energy system, namely, distribution automation (DA), distributed energy system-storage (DER) and electrical vehicle (EV), are investigated in order to study their suitability in Long Term Evolution (LTE) network. To compensate the weakness in the existing scheduling algorithms, a novel bandwidth estimation and allocation technique and a new scheduling algorithm are proposed. The technique allocates available network resources based on application's priority, whereas the algorithm makes scheduling decision based on dynamic weighting factors of multi-criteria to satisfy the demands (delay, past average throughput and instantaneous transmission rate) of quality of service. Finally, the simulation results demonstrate that the proposed mechanism achieves higher throughput, lower delay and lower packet loss rate for DA and DER as well as provide a degree of service for EV. In terms of fairness, the proposed algorithm shows 3%, 7 % and 9% better performance compared to exponential rule (EXP-Rule), modified-largest weighted delay first (M-LWDF) and exponential/PF (EXP/PF), respectively.

A Novel LTE Scheduling Algorithm for Green Technology in Smart Grid

PubMed Central

Hindia, Mohammad Nour; Reza, Ahmed Wasif; Noordin, Kamarul Ariffin; Chayon, Muhammad Hasibur Rashid

2015-01-01

Smart grid (SG) application is being used nowadays to meet the demand of increasing power consumption. SG application is considered as a perfect solution for combining renewable energy resources and electrical grid by means of creating a bidirectional communication channel between the two systems. In this paper, three SG applications applicable to renewable energy system, namely, distribution automation (DA), distributed energy system-storage (DER) and electrical vehicle (EV), are investigated in order to study their suitability in Long Term Evolution (LTE) network. To compensate the weakness in the existing scheduling algorithms, a novel bandwidth estimation and allocation technique and a new scheduling algorithm are proposed. The technique allocates available network resources based on application’s priority, whereas the algorithm makes scheduling decision based on dynamic weighting factors of multi-criteria to satisfy the demands (delay, past average throughput and instantaneous transmission rate) of quality of service. Finally, the simulation results demonstrate that the proposed mechanism achieves higher throughput, lower delay and lower packet loss rate for DA and DER as well as provide a degree of service for EV. In terms of fairness, the proposed algorithm shows 3%, 7 % and 9% better performance compared to exponential rule (EXP-Rule), modified-largest weighted delay first (M-LWDF) and exponential/PF (EXP/PF), respectively. PMID:25830703

Statistical analysis of passenger-crowding in bus transport network of Harbin

NASA Astrophysics Data System (ADS)

Hu, Baoyu; Feng, Shumin; Li, Jinyang; Zhao, Hu

2018-01-01

Passenger flow data is indispensable but rare in the study of public transport networks. In this study, we focus on the passenger-crowding characteristics of the bus transport network of Harbin (BTN-H) based on passenger flow investigation. The three frequency histograms for all the uplinks and downlinks in Harbin are presented, including passengers on the bus at each section, crowding coefficients, and position parameters of crowded sections. The differences in crowding position are analyzed on each route. The distributions of degree and crowding degree (in directed space L) follow an exponential law. The new finding indicates that there are many stations with few crowded sections and a few stations with many crowded sections. The distributions of path length and crowded length (in directed space P) are presented based on the minimum transfer times, and it is found that they can be fitted by a composite Gaussian function and a Gaussian function, respectively. The stations and paths can be divided into three crowd levels. We conclude that BTN-H is crowded from a network-based perspective.

The Significance of Interactions: Understanding Gender, Ethnicity/Race, and Socioeconomic Status as Related to the Likelihood of Bachelor's Degree Completion

ERIC Educational Resources Information Center

Lundy, Valerie Cyrina

2010-01-01

Although access to a postsecondary education has increased exponentially since 1970, access to a bachelor's degree has not grown as swiftly. Moreover, while national longitudinal trend data highlight improvements in bachelor's degree completion in the aggregate, they disguise important disparities in bachelor's degree completion across groups.…

Anomalous yet Brownian.

PubMed

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

2009-09-08

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

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

PubMed Central

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

2017-01-01

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

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2016-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking*

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059

Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth.

PubMed

Yan, Wanfeng; van Tuyll van Serooskerken, Edgar

2015-01-01

Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator.

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.

Investigation of non-Gaussian effects in the Brazilian option market

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Modeling the survival of Salmonella spp. in chorizos.

PubMed

Hajmeer, M; Basheer, I; Hew, C; Cliver, D O

2006-03-01

The survival of Salmonella spp. in chorizos has been studied under the effect of storage conditions; namely temperature (T=6, 25, 30 degrees C), air inflow velocity (F=0, 28.4 m/min), and initial water activity (a(w0)=0.85, 0.90, 0.93, 0.95, 0.97). The pH was held at 5.0. A total of 20 survival curves were experimentally obtained at various combinations of operating conditions. The chorizos were stored under four conditions: in the refrigerator (Ref: T=6 degrees C, F=0 m/min), at room temperature (RT: T=25 degrees C, F=0 m/min), in the hood (Hd: T=25 degrees C, F=28.4 m/min), and in the incubator (Inc: T=30 degrees C, F=0 m/min). Semi-logarithmic plots of counts vs. time revealed nonlinear trends for all the survival curves, indicating that the first-order kinetics model (exponential distribution function) was not suitable. The Weibull cumulative distribution function, for which the exponential function is only a special case, was selected and used to model the survival curves. The Weibull model was fitted to the 20 curves and the model parameters (alpha and beta) were determined. The fitted survival curves agreed with the experimental data with R(2)=0.951, 0.969, 0.908, and 0.871 for the Ref, RT, Hd, and Inc curves, respectively. Regression models relating alpha and beta to T, F, and a(w0) resulted in R(2) values of 0.975 for alpha and 0.988 for beta. The alpha and beta models can be used to generate a survival curve for Salmonella in chorizos for a given set of operating conditions. Additionally, alpha and beta can be used to determine the times needed to reduce the count by 1 or 2 logs t(1D) and t(2D). It is concluded that the Weibull cumulative distribution function offers a powerful model for describing microbial survival data. A comparison with the pathogen modeling program (PMP) revealed that the survival kinetics of Salmonella spp. in chorizos could not be adequately predicted using PMP which underestimated the t(1D) and t(2D). The mean of the Weibull probability density function correlated strongly with t(1D) and t(2D), and can serve as an alternative to the D-values normally used with first-order kinetic models. Parametric studies were conducted and sensitivity of survival to operating conditions was evaluated and discussed in the paper. The models derived herein provide a means for the development of a reliable risk assessment system for controlling Salmonella spp. in chorizos.

Scaling in the distribution of intertrade durations of Chinese stocks

NASA Astrophysics Data System (ADS)

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

2008-10-01

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

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

DTIC Science & Technology

2012-09-01

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

The size distribution of Pacific Seamounts

NASA Astrophysics Data System (ADS)

Smith, Deborah K.; Jordan, Thomas H.

1987-11-01

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

A mechanism producing power law etc. distributions

NASA Astrophysics Data System (ADS)

Li, Heling; Shen, Hongjun; Yang, Bin

2017-07-01

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

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

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2015-05-01

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

Hydrodynamics-based functional forms of activity metabolism: a case for the power-law polynomial function in animal swimming energetics.

PubMed

Papadopoulos, Anthony

2009-01-01

The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined.

Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation.

PubMed Central

Irvine, L A; Jafri, M S; Winslow, R L

1999-01-01

A Markov model of the cardiac sodium channel is presented. The model is similar to the CA1 hippocampal neuron sodium channel model developed by Kuo and Bean (1994. Neuron. 12:819-829) with the following modifications: 1) an additional open state is added; 2) open-inactivated transitions are made voltage-dependent; and 3) channel rate constants are exponential functions of enthalpy, entropy, and voltage and have explicit temperature dependence. Model parameters are determined using a simulated annealing algorithm to minimize the error between model responses and various experimental data sets. The model reproduces a wide range of experimental data including ionic currents, gating currents, tail currents, steady-state inactivation, recovery from inactivation, and open time distributions over a temperature range of 10 degrees C to 25 degrees C. The model also predicts measures of single channel activity such as first latency, probability of a null sweep, and probability of reopening. PMID:10096885

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation. Part 1; Analysis

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Nemeth, Noel N.; Gyekenyesi, John P.

2002-01-01

Extensive slow-crack-growth (SCG) analysis was made using a primary exponential crack-velocity formulation under three widely used load configurations: constant stress rate, constant stress, and cyclic stress. Although the use of the exponential formulation in determining SCG parameters of a material requires somewhat inconvenient numerical procedures, the resulting solutions presented gave almost the same degree of simplicity in both data analysis and experiments as did the power-law formulation. However, the fact that the inert strength of a material should be known in advance to determine the corresponding SCG parameters was a major drawback of the exponential formulation as compared with the power-law formulation.

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).

Betweenness centrality in a weighted network

NASA Astrophysics Data System (ADS)

Wang, Huijuan; Hernandez, Javier Martin; van Mieghem, Piet

2008-04-01

When transport in networks follows the shortest paths, the union of all shortest path trees G∪SPT can be regarded as the “transport overlay network.” Overlay networks such as peer-to-peer networks or virtual private networks can be considered as a subgraph of G∪SPT . The traffic through the network is examined by the betweenness Bl of links in the overlay G∪SPT . The strength of disorder can be controlled by, e.g., tuning the extreme value index α of the independent and identically distributed polynomial link weights. In the strong disorder limit (α→0) , all transport flows over a critical backbone, the minimum spanning tree (MST). We investigate the betweenness distributions of wide classes of trees, such as the MST of those well-known network models and of various real-world complex networks. All these trees with different degree distributions (e.g., uniform, exponential, or power law) are found to possess a power law betweenness distribution Pr[Bl=j]˜j-c . The exponent c seems to be positively correlated with the degree variance of the tree and to be insensitive of the size N of a network. In the weak disorder regime, transport in the network traverses many links. We show that a link with smaller link weight tends to carry more traffic. This negative correlation between link weight and betweenness depends on α and the structure of the underlying topology.

How people make friends in social networking sites—A microscopic perspective

NASA Astrophysics Data System (ADS)

Hu, Haibo; Wang, Xiaofan

2012-02-01

We study the detailed growth of a social networking site with full temporal information by examining the creation process of each friendship relation that can collectively lead to the macroscopic properties of the network. We first study the reciprocal behavior of users, and find that link requests are quickly responded to and that the distribution of reciprocation intervals decays in an exponential form. The degrees of inviters/accepters are slightly negatively correlative with reciprocation time. In addition, the temporal feature of the online community shows that the distributions of intervals of user behaviors, such as sending or accepting link requests, follow a power law with a universal exponent, and peaks emerge for intervals of an integral day. We finally study the preferential selection and linking phenomena of the social networking site and find that, for the former, a linear preference holds for preferential sending and reception, and for the latter, a linear preference also holds for preferential acceptance, creation, and attachment. Based on the linearly preferential linking, we put forward an analyzable network model which can reproduce the degree distribution of the network. The research framework presented in the paper could provide a potential insight into how the micro-motives of users lead to the global structure of online social networks.

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

PubMed Central

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

2016-01-01

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

Universality in stochastic exponential growth.

PubMed

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

2014-07-11

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

Universality in Stochastic Exponential Growth

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

Conditional optimal spacing in exponential distribution.

PubMed

Park, Sangun

2006-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2007-07-01

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

Normal Mode Analysis on the Relaxation of AN Excited Nitromethane Molecule in Argon Bath

NASA Astrophysics Data System (ADS)

Rivera-Rivera, Luis A.; Wagner, Albert F.

2017-06-01

In our previous work [Rivera-Rivera et al. J. Chem. Phys. 142, 014303 (2015).] classical molecular dynamics simulations followed, in an Ar bath, the relaxation of nitromethane (CH_3NO_2) instantaneously excited by statistically distributing 50 kcal/mol among all its internal degrees of freedom. The 300 K Ar bath was at pressures of 10 to 400 atm. Both rotational and vibrational energies exhibited multi-exponential decay. This study explores mode-specific mechanisms at work in the decay process. With the separation of rotation and vibration developed by Rhee and Kim [J. Chem. Phys. 107, 1394 (1997).], one can show that the vibrational kinetic energy decomposes only into vibrational normal modes while the rotational and Coriolis energies decompose into both vibrational and rotational normal modes. Then the saved CH_3NO_2 positions and momenta can be converted into mode-specific energies whose decay over 1000 ps can be monitored. The results identify vibrational and rotational modes that promote/resist energy lost and drive multi-exponential behavior. In addition to mode-specificity, the results show disruption of IVR with increasing pressure.

Effects of proliferation on the decay of thermotolerance in Chinese hamster cells.

PubMed

Armour, E P; Li, G C; Hahn, G M

1985-09-01

Development and decay of thermotolerance were observed in Chinese hamster HA-1 cells. The thermotolerance kinetics of exponentially growing and fed plateau-phase cells were compared. Following a 10-min heat exposure at 45 degrees C, cells in both growth states had similar rates of development of tolerance to a subsequent 45-min exposure at 45 degrees C. This thermotolerant state started to decay between 12 and 24 hr after the initial heat exposure. The decay appeared to initiate slightly sooner in the exponentially growing cells when compared to the fed plateau-phase cells. During the decay phase, the rate of thermotolerance decay was similar in the two growth conditions. In other experiments, cells were induced to divide at a slower rate by chronic growth (3 months) in a low concentration of fetal calf serum. Under these low serum conditions cells became more sensitive to heat and the rate of decay of thermotolerance remained the same for exponentially growing cells. Plateau-phase cells were also more sensitive, but thermotolerance decayed more rapidly in these cells. Although dramatic cell cycle perturbations were seen in the exponentially growing cells, these changes appeared not to be related to thermotolerance kinetics.

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.

Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods.

PubMed

Ye, Jun

2016-01-01

An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems. As a supplement, this paper firstly introduces new exponential operational laws of INSs, where the bases are crisp values or interval numbers and the exponents are interval neutrosophic numbers (INNs), which are basic elements in INSs. Then, we propose an interval neutrosophic weighted exponential aggregation (INWEA) operator and a dual interval neutrosophic weighted exponential aggregation (DINWEA) operator based on these exponential operational laws and introduce comparative methods based on cosine measure functions for INNs and dual INNs. Further, we develop decision-making methods based on the INWEA and DINWEA operators. Finally, a practical example on the selecting problem of global suppliers is provided to illustrate the applicability and rationality of the proposed methods.

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.

Universality in survivor distributions: Characterizing the winners of competitive dynamics

NASA Astrophysics Data System (ADS)

Luck, J. M.; Mehta, A.

2015-11-01

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and nonsurvivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterization is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept—the dynamical fugacity. Remarkably, in the large-mass limit, the survivor probability of a node becomes independent of network geometry and assumes a simple form which depends only on its mass and degree.

The shock waves in decaying supersonic turbulence

NASA Astrophysics Data System (ADS)

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

2000-04-01

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

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

USGS Publications Warehouse

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

2012-01-01

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

Universal patterns of inequality

NASA Astrophysics Data System (ADS)

Banerjee, Anand; Yakovenko, Victor M.

2010-07-01

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

Study on probability distributions for evolution in modified extremal optimization

NASA Astrophysics Data System (ADS)

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

2010-05-01

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

Spatio-temporal analysis of aftershock sequences in terms of Non Extensive Statistical Physics.

NASA Astrophysics Data System (ADS)

Chochlaki, Kalliopi; Vallianatos, Filippos

2017-04-01

Earth's seismicity is considered as an extremely complicated process where long-range interactions and fracturing exist (Vallianatos et al., 2016). For this reason, in order to analyze it, we use an innovative methodological approach, introduced by Tsallis (Tsallis, 1988; 2009), named Non Extensive Statistical Physics. This approach introduce a generalization of the Boltzmann-Gibbs statistical mechanics and it is based on the definition of Tsallis entropy Sq, which maximized leads the the so-called q-exponential function that expresses the probability distribution function that maximizes the Sq. In the present work, we utilize the concept of Non Extensive Statistical Physics in order to analyze the spatiotemporal properties of several aftershock series. Marekova (Marekova, 2014) suggested that the probability densities of the inter-event distances between successive aftershocks follow a beta distribution. Using the same data set we analyze the inter-event distance distribution of several aftershocks sequences in different geographic regions by calculating non extensive parameters that determine the behavior of the system and by fitting the q-exponential function, which expresses the degree of non-extentivity of the investigated system. Furthermore, the inter-event times distribution of the aftershocks as well as the frequency-magnitude distribution has been analyzed. The results supports the applicability of Non Extensive Statistical Physics ideas in aftershock sequences where a strong correlation exists along with memory effects. References C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1988) 479-487. doi:10.1007/BF01016429 C. Tsallis, Introduction to nonextensive statistical mechanics: Approaching a complex world, 2009. doi:10.1007/978-0-387-85359-8. E. Marekova, Analysis of the spatial distribution between successive earthquakes in aftershocks series, Annals of Geophysics, 57, 5, doi:10.4401/ag-6556, 2014 F. Vallianatos, G. Papadakis, G. Michas, Generalized statistical mechanics approaches to earthquakes and tectonics. Proc. R. Soc. A, 472, 20160497, 2016.

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.

A molecular dynamics study of the relaxation of an excited molecule in crystalline nitromethane

NASA Astrophysics Data System (ADS)

Rivera-Rivera, Luis A.; Siavosh-Haghighi, Ali; Sewell, Thomas D.; Thompson, Donald L.

2014-07-01

Classical molecular dynamics simulations were used to study the relaxation of an excited nitromethane molecule in perfect crystalline nitromethane at 250 K and 1 atm pressure. The molecule was instantaneously excited by statistically distributing energy E∗ between 25.0 kcal/mol and 125.0 kcal/mol among the 21 degrees of freedom of the molecule. The relaxation occurs exponentially with time constants between 11.58 ps and 13.57 ps. Energy transfer from the excited molecule to surrounding quasi-spherical shells of molecules occurs concurrently to both the nearest and next-nearest neighbor shells, but with more energy per molecule transferred more rapidly to the first shell.

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

Bennink, Ryan S.; Ferragut, Erik M.; Humble, Travis S.

Modeling and simulation are essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. In this paper, we present a method of simulating noisy Clifford circuits that is both accurate and practical in experimentally relevant regimes. In particular, the cost is weakly exponential in the size and the degree of non-Cliffordness of the circuit. Our approach is based on the construction of exact representations of quantum channels as quasiprobability distributions over stabilizer operations, which are then sampled, simulated, and weighted to yield unbiasedmore » statistical estimates of circuit outputs and other observables. As a demonstration of these techniques, we simulate a Steane [[7,1,3

Molar mass fractionation in aqueous two-phase polymer solutions of dextran and poly(ethylene glycol).

PubMed

Zhao, Ziliang; Li, Qi; Ji, Xiangling; Dimova, Rumiana; Lipowsky, Reinhard; Liu, Yonggang

2016-06-24

Dextran and poly(ethylene glycol) (PEG) in phase separated aqueous two-phase systems (ATPSs) of these two polymers, with a broad molar mass distribution for dextran and a narrow molar mass distribution for PEG, were separated and quantified by gel permeation chromatography (GPC). Tie lines constructed by GPC method are in excellent agreement with those established by the previously reported approach based on density measurements of the phases. The fractionation of dextran during phase separation of ATPS leads to the redistribution of dextran of different chain lengths between the two phases. The degree of fractionation for dextran decays exponentially as a function of chain length. The average separation parameters, for both dextran and PEG, show a crossover from mean field behavior to Ising model behavior, as the critical point is approached. Copyright © 2016 Elsevier B.V. All rights reserved.

Weblog patterns and human dynamics with decreasing interest

NASA Astrophysics Data System (ADS)

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

2011-06-01

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

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2005-08-05

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

Exponential order statistic models of software reliability growth

NASA Technical Reports Server (NTRS)

Miller, D. R.

1985-01-01

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

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

PubMed

Bhatt, Vijaya; Tiwari, Neeraj

2014-05-20

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

gamma-Glutamyltranspeptidase from Escherichia coli K-12: formation and localization.

PubMed

Suzuki, H; Kumagai, H; Tochikura, T

1986-12-01

Escherichia coli cells showed maximum activity of gamma-glutamyltranspeptidase (EC 2.3.2.2) when they were grown at 20 degrees C, 14% of maximum activity at 37 degrees C, and none at 43 degrees C. The enzyme activity of intact cells grown at 20 degrees C was stably maintained after the temperature was changed to 45 degrees C. The activity increased during the exponential phase, and maximum activity was found at stationary phase. Its intracellular localization in the periplasmic space was confirmed.

Initial conditions and degrees of freedom of non-local gravity

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe

2018-05-01

We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the dynamics of renormalizable non-local gravity with exponential operators into a higher-dimensional system local in spacetime coordinates. This method, first illustrated with a scalar field theory and then applied to gravity, allows one to solve the Cauchy problem and count the number of initial conditions and of non-perturbative degrees of freedom, which is finite. In particular, the non-local scalar and gravitational theories with exponential operators are both characterized by four initial conditions in any dimension and, respectively, by one and eight degrees of freedom in four dimensions. The fully covariant equations of motion are written in a form convenient to find analytic non-perturbative solutions.

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

PubMed Central

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-01-01

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

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

PubMed

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-10-01

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

Discrete Deterministic and Stochastic Petri Nets

NASA Technical Reports Server (NTRS)

Zijal, Robert; Ciardo, Gianfranco

1996-01-01

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

Exponential blocking-temperature distribution in ferritin extracted from magnetization measurements

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

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

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

Sharma, Sanjib; Bland-Hawthorn, Joss

2013-08-20

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

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

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

PubMed

McGee, Monnie; Chen, Zhongxue

2006-01-01

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

Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2005-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

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

DTIC Science & Technology

1981-06-01

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

Complex network study of Brazilian soccer players

NASA Astrophysics Data System (ADS)

Onody, Roberto N.; de Castro, Paulo A.

2004-09-01

Although being a very popular sport in many countries, soccer has not received much attention from the scientific community. In this paper, we study soccer from a complex network point of view. First, we consider a bipartite network with two kinds of vertices or nodes: the soccer players and the clubs. Real data were gathered from the 32 editions of the Brazilian soccer championship, in a total of 13411 soccer players and 127 clubs. We find a lot of interesting and perhaps unsuspected results. The probability that a Brazilian soccer player has worked at N clubs or played M games shows an exponential decay while the probability that he has scored G goals is power law. Now, if two soccer players who have worked at the same club at the same time are connected by an edge, then a new type of network arises (composed exclusively by soccer player nodes). Our analysis shows that for this network the degree distribution decays exponentially. We determine the exact values of the clustering coefficient, the assortativity coefficient and the average shortest path length and compare them with those of the Erdös-Rényi and configuration model. The time evolution of these quantities are calculated and the corresponding results discussed.

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.

A Narrative Study of Perspectives of Puerto Rican Doctoral Graduates

ERIC Educational Resources Information Center

Rapp, Doreen Rivera

2010-01-01

A review of the literature indicates that Latinos lag behind Whites and Blacks in college degree attainment. This educational disparity is of concern because Latinos are currently the largest minority group in the United States, and the Latino population is expected to increase exponentially in the future. College degree attainment for Latinos is…

Unbiased simulation of near-Clifford quantum circuits

DOE PAGES

Bennink, Ryan S.; Ferragut, Erik M.; Humble, Travis S.; ...

2017-06-28

Modeling and simulation are essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. In this paper, we present a method of simulating noisy Clifford circuits that is both accurate and practical in experimentally relevant regimes. In particular, the cost is weakly exponential in the size and the degree of non-Cliffordness of the circuit. Our approach is based on the construction of exact representations of quantum channels as quasiprobability distributions over stabilizer operations, which are then sampled, simulated, and weighted to yield unbiasedmore » statistical estimates of circuit outputs and other observables. As a demonstration of these techniques, we simulate a Steane [[7,1,3

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

PubMed

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

2003-10-01

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

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

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

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

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

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

NASA Astrophysics Data System (ADS)

Song, Qiankun; Cao, Jinde

2007-05-01

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

Self-narrowing of size distributions of nanostructures by nucleation antibunching

NASA Astrophysics Data System (ADS)

Glas, Frank; Dubrovskii, Vladimir G.

2017-08-01

We study theoretically the size distributions of ensembles of nanostructures fed from a nanosize mother phase or a nanocatalyst that contains a limited number of the growth species that form each nanostructure. In such systems, the nucleation probability decreases exponentially after each nucleation event, leading to the so-called nucleation antibunching. Specifically, this effect has been observed in individual nanowires grown in the vapor-liquid-solid mode and greatly affects their properties. By performing numerical simulations over large ensembles of nanostructures as well as developing two different analytical schemes (a discrete and a continuum approach), we show that nucleation antibunching completely suppresses fluctuation-induced broadening of the size distribution. As a result, the variance of the distribution saturates to a time-independent value instead of growing infinitely with time. The size distribution widths and shapes primarily depend on the two parameters describing the degree of antibunching and the nucleation delay required to initiate the growth. The resulting sub-Poissonian distributions are highly desirable for improving size homogeneity of nanowires. On a more general level, this unique self-narrowing effect is expected whenever the growth rate is regulated by a nanophase which is able to nucleate an island much faster than it is refilled from a surrounding macroscopic phase.

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.

The Structure of the Proton

DOE R&D Accomplishments Database

Chambers, E. E.; Hofstadter, R.

1956-04-01

The structure and size of the proton have been studied by means of the methods of high-energy electron scattering. The elastic scattering of electrons from protons in polyethylene has been investigated at the following energies in the laboratory system: 200, 300, 400, 500, 550 Mev. The range of laboratory angles examined has been 30 degrees to 135 degrees. At the largest angles and the highest energy, the cross section for scattering shows a deviation below that expected from a point proton by a factor of about nine. The magnitude and variation with angle of the deviations determine a structure factor for the proton, and thereby determine the size and shape of the charge and magnetic-moment distributions within the proton. An interpretation, consistent at all energies and angles and agreeing with earlier results from this laboratory, fixes the rms radius at 0.77 {plus or minus} 0.10 x 10{sup -13} cm for each of the charge and moment distributions. The shape of the density function is not far from a Gaussian with rms radius 0.70 x 10{sup -13} cm or an exponential with rms radius 0.80 x 10 {sup -13} cm. An equivalent interpretation of the experiments would ascribe the apparent size to a breakdown of the Coulomb law and the conventional theory of electromagnetism.

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.

Modulation of lens cell adhesion molecules by particle beams

NASA Technical Reports Server (NTRS)

McNamara, M. P.; Bjornstad, K. A.; Chang, P. Y.; Chou, W.; Lockett, S. J.; Blakely, E. A.

2001-01-01

Cell adhesion molecules (CAMs) are proteins which anchor cells to each other and to the extracellular matrix (ECM), but whose functions also include signal transduction, differentiation, and apoptosis. We are testing a hypothesis that particle radiations modulate CAM expression and this contributes to radiation-induced lens opacification. We observed dose-dependent changes in the expression of beta 1-integrin and ICAM-1 in exponentially-growing and confluent cells of a differentiating human lens epithelial cell model after exposure to particle beams. Human lens epithelial (HLE) cells, less than 10 passages after their initial culture from fetal tissue, were grown on bovine corneal endothelial cell-derived ECM in medium containing 15% fetal bovine serum and supplemented with 5 ng/ml basic fibroblast growth factor (FGF-2). Multiple cell populations at three different stages of differentiation were prepared for experiment: cells in exponential growth, and cells at 5 and 10 days post-confluence. The differentiation status of cells was characterized morphologically by digital image analysis, and biochemically by Western blotting using lens epithelial and fiber cell-specific markers. Cultures were irradiated with single doses (4, 8 or 12 Gy) of 55 MeV protons and, along with unirradiated control samples, were fixed using -20 degrees C methanol at 6 hours after exposure. Replicate experiments and similar experiments with helium ions are in progress. The intracellular localization of beta 1-integrin and ICAM-1 was detected by immunofluorescence using monoclonal antibodies specific for each CAM. Cells known to express each CAM were also processed as positive controls. Both exponentially-growing and confluent, differentiating cells demonstrated a dramatic proton-dose-dependent modulation (upregulation for exponential cells, downregulation for confluent cells) and a change in the intracellular distribution of the beta 1-integrin, compared to unirradiated controls. In contrast, there was a dose-dependent increase in ICAM-1 immunofluorescence in confluent, but not exponentially-growing cells. These results suggest that proton irradiation downregulates beta 1-integrin and upregulates ICAM-1, potentially contributing to cell death or to aberrant differentiation via modulation of anchorage and/or signal transduction functions. Quantification of the expression levels of the CAMs by Western analysis is in progress.

Freezing and melting water in lamellar structures.

PubMed Central

Gleeson, J T; Erramilli, S; Gruner, S M

1994-01-01

The manner in which ice forms in lamellar suspensions of dielaidoylphosphatidylethanolamine, dielaidoylphosphatidylcholine, and dioleoylphosphatidylcholine in water depends strongly on the water fraction. For weight fractions between 15 and 9%, the freezing and melting temperatures are significantly depressed below 0 degree C. The ice exhibits a continuous melting transition spanning as much as 20 degrees C. When the water weight fraction is below 9%, ice never forms at temperatures as low as -40 degrees C. We show that when water contained in a lamellar lipid suspension freezes, the ice is not found between the bilayers; it exists as pools of crystalline ice in equilibrium with the bound water associated with the polar lipid headgroups. We have used this effect, together with the known chemical potential of ice, to measure hydration forces between lipid bilayers. We find exponentially decaying hydration repulsion when the bilayers are less than about 7 A apart. For larger separations, we find significant deviations from single exponential decay. PMID:7948683

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

PubMed

Patel, Mainak; Rangan, Aaditya

2017-08-07

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

Statistical mechanics of money and income

NASA Astrophysics Data System (ADS)

Dragulescu, Adrian; Yakovenko, Victor

2001-03-01

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

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

NASA Astrophysics Data System (ADS)

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

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

Redshift data and statistical inference

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Human mobility in space from three modes of public transportation

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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.

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

PubMed

Zhao, Kaihong

2018-12-01

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

Probability distribution functions for intermittent scrape-off layer plasma fluctuations

NASA Astrophysics Data System (ADS)

Theodorsen, A.; Garcia, O. E.

2018-03-01

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

A mathematical model for evolution and SETI.

PubMed

Maccone, Claudio

2011-12-01

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

Modelling Evolution and SETI Mathematically

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2012-05-01

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

A Mathematical Model for Evolution and SETI

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2011-12-01

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

Accounting for inherent variability of growth in microbial risk assessment.

PubMed

Marks, H M; Coleman, M E

2005-04-15

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

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

NASA Astrophysics Data System (ADS)

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

2005-10-01

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

All-Optical Photoacoustic Sensors for Steel Rebar Corrosion Monitoring.

PubMed

Du, Cong; Owusu Twumasi, Jones; Tang, Qixiang; Guo, Xu; Zhou, Jingcheng; Yu, Tzuyang; Wang, Xingwei

2018-04-27

This article presents an application of an active all-optical photoacoustic sensing system with four elements for steel rebar corrosion monitoring. The sensor utilized a photoacoustic mechanism of gold nanocomposites to generate 8 MHz broadband ultrasound pulses in 0.4 mm compact space. A nanosecond 532 nm pulsed laser and 400 μm multimode fiber were employed to incite an ultrasound reaction. The fiber Bragg gratings were used as distributed ultrasound detectors. Accelerated corrosion testing was applied to four sections of a single steel rebar with four different corrosion degrees. Our results demonstrated that the mass loss of steel rebar displayed an exponential growth with ultrasound frequency shifts. The sensitivity of the sensing system was such that 0.175 MHz central frequency reduction corresponded to 0.02 g mass loss of steel rebar corrosion. It was proved that the all-optical photoacoustic sensing system can actively evaluate the corrosion of steel rebar via ultrasound spectrum. This multipoint all-optical photoacoustic method is promising for embedment into a concrete structure for distributed corrosion monitoring.

Water Dynamics in Egg White Peptide, Asp-His-Thr-Lys-Glu, Powder Monitored by Dynamic Vapor Sorption and LF-NMR.

PubMed

Yang, Shuailing; Liu, Xuye; Jin, Yan; Li, Xingfang; Chen, Feng; Zhang, Mingdi; Lin, Songyi

2016-03-16

Water absorbed into the bulk amorphous structure of peptides can have profound effects on their properties. Here, we elucidated water dynamics in Asp-His-Thr-Lys-Glu (DHTKE), an antioxidant peptide derived from egg white ovalbumin, using water dynamic vapor sorption (DVS) and low-field nuclear magnetic resonance (LF-NMR). The DVS results indicated that parallel exponential kinetics model fitted well to the data of sorption kinetics behavior of DHTKE. Four different proton fractions with different mobilities were identified based on the degree of interaction between peptide and water. The water could significantly change the proton distribution and structure of the sample. The different phases of moisture absorption were reflected in the T2 parameters. In addition, the combined water content was dominant in the hygroscopicity of DHTKE. This study provides an effective real-time monitoring method for water mobility and distribution in synthetic peptides, and this method may have applications in promoting peptide quality assurance.

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

USGS Publications Warehouse

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

2007-01-01

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

Min and Max Exponential Extreme Interval Values and Statistics

ERIC Educational Resources Information Center

Jance, Marsha; Thomopoulos, Nick

2009-01-01

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

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Heterogeneous characters modeling of instant message services users’ online behavior

PubMed Central

Fang, Yajun; Horn, Berthold

2018-01-01

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

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

PubMed

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Quantum Neural Nets

NASA Technical Reports Server (NTRS)

Zak, Michail; Williams, Colin P.

1997-01-01

The capacity of classical neurocomputers is limited by the number of classical degrees of freedom which is roughly proportional to the size of the computer. By Contrast, a Hypothetical quantum neurocomputer can implement an exponentially large number of the degrees of freedom within the same size. In this paper an attempt is made to reconcile linear reversible structure of quantum evolution with nonlinear irreversible dynamics for neural nets.

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.

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.

Scale dependence of entrainment-mixing mechanisms in cumulus clouds

DOE PAGES

Lu, Chunsong; Liu, Yangang; Niu, Shengjie; ...

2014-12-17

This work empirically examines the dependence of entrainment-mixing mechanisms on the averaging scale in cumulus clouds using in situ aircraft observations during the Routine Atmospheric Radiation Measurement Aerial Facility Clouds with Low Optical Water Depths Optical Radiative Observations (RACORO) field campaign. A new measure of homogeneous mixing degree is defined that can encompass all types of mixing mechanisms. Analysis of the dependence of the homogenous mixing degree on the averaging scale shows that, on average, the homogenous mixing degree decreases with increasing averaging scales, suggesting that apparent mixing mechanisms gradually approach from homogeneous mixing to extreme inhomogeneous mixing with increasingmore » scales. The scale dependence can be well quantified by an exponential function, providing first attempt at developing a scale-dependent parameterization for the entrainment-mixing mechanism. The influences of three factors on the scale dependence are further examined: droplet-free filament properties (size and fraction), microphysical properties (mean volume radius and liquid water content of cloud droplet size distributions adjacent to droplet-free filaments), and relative humidity of entrained dry air. It is found that the decreasing rate of homogeneous mixing degree with increasing averaging scales becomes larger with larger droplet-free filament size and fraction, larger mean volume radius and liquid water content, or higher relative humidity. The results underscore the necessity and possibility of considering averaging scale in representation of entrainment-mixing processes in atmospheric models.« less

Prediction of microbial growth in fresh-cut vegetables treated with acidic electrolyzed water during storage under various temperature conditions.

PubMed

Koseki, S; Itoh, K

2001-12-01

Effects of storage temperature (1, 5, and 10 degrees C) on growth of microbial populations (total aerobic bacteria, coliform bacteria, Bacillus cereus, and psychrotrophic bacteria) on acidic electrolyzed water (AcEW)-treated fresh-cut lettuce and cabbage were determined. A modified Gompertz function was used to describe the kinetics of microbial growth. Growth data were analyzed using regression analysis to generate "best-fit" modified Gompertz equations, which were subsequently used to calculate lag time, exponential growth rate, and generation time. The data indicated that the growth kinetics of each bacterium were dependent on storage temperature, except at 1 degrees C storage. At 1 degrees C storage, no increases were observed in bacterial populations. Treatment of vegetables with AcEW produced a decrease in initial microbial populations. However, subsequent growth rates were higher than on nontreated vegetables. The recovery time required by the reduced microbial population to reach the initial (treated with tap water [TW]) population was also determined in this study, with the recovery time of the microbial population at 10 degrees C being <3 days. The benefits of reducing the initial microbial populations on fresh-cut vegetables were greatly affected by storage temperature. Results from this study could be used to predict microbial quality of fresh-cut lettuce and cabbage throughout their distribution.

Normal mode analysis on the relaxation of an excited nitromethane molecule in argon bath

NASA Astrophysics Data System (ADS)

Rivera-Rivera, Luis; Wagner, Albert

In our previous work [J. Chem. Phys. 142, 014303 (2015)] classical molecular dynamics simulations followed in an Ar bath the relaxation of nitromethane (CH3NO2) instantaneously excited by statistically distributing 50 kcal/mol among all its internal degrees of freedom. The 300 K Ar bath was at pressures of 10 to 400 atm, a range spanning the breakdown of the isolated binary collision approximation. Both rotational and vibrational energies exhibit multi-exponential decay. This study explores mode-specific mechanisms at work in the decay process. With the separation of rotation and vibration developed by Rhee and Kim [J. Chem. Phys. 107, 1394 (1997)], one can show that the vibrational kinetic energy decomposes only into vibrational normal modes while the rotational and Coriolis energies decompose into both vibrational and rotational normal modes. Then the saved CH3NO2 positions and momenta can be converted into mode-specific energies whose decay over 1000 ps can be monitored. The results identify vibrational and rotational modes that promote/resist energy lost and drive multi-exponential behavior. Increasing pressure can be shown to increasingly interfere with post-collision IVR. The work was supported by the U.S. Department of Energy, Office of Science, Chemical Sciences, Geosciences, and Biosciences Division.

Linear prediction and single-channel recording.

PubMed

Carter, A A; Oswald, R E

1995-08-01

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

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

PubMed

Guo, Zhenyuan; Yang, Shaofu; Wang, Jun

2016-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-02-01

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

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation. Part 3; Constant Stress and Cyclic Stress Experiments

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Nemeth, Noel N.; Gyekenyesi, John P.

2002-01-01

The previously determined life prediction analysis based on an exponential crack-velocity formulation was examined using a variety of experimental data on advanced structural ceramics tested under constant stress and cyclic stress loading at ambient and elevated temperatures. The data fit to the relation between the time to failure and applied stress (or maximum applied stress in cyclic loading) was very reasonable for most of the materials studied. It was also found that life prediction for cyclic stress loading from data of constant stress loading in the exponential formulation was in good agreement with the experimental data, resulting in a similar degree of accuracy as compared with the power-law formulation. The major limitation in the exponential crack-velocity formulation, however, was that the inert strength of a material must be known a priori to evaluate the important slow-crack-growth (SCG) parameter n, a significant drawback as compared with the conventional power-law crack-velocity formulation.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

Exponential model for option prices: Application to the Brazilian market

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

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

PubMed

Plancade, Sandra; Rozenholc, Yves; Lund, Eiliv

2012-12-11

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

Influence of curing mode with a LED unit on polymerization contraction kinetics and degree of conversion of dental resin-based materials.

PubMed

Mortier, Eric; Simon, Yorick; Dahoun, Abdelsellam; Gerdolle, David

2009-01-01

The purpose of this study was to evaluate the influence of photopolymerization mode with a light emitting diode (LED) lamp on the curing contraction kinetics and degree of conversion of 3 resin-based restorative materials. The curing contraction kinetics of Admira (ADM), Filtek P60 (P60), and Filtek Flow (FLO) were measured by the glass slide method. The materials were exposed to light from a 1,000 mW/cm-(2) power LED lamp (Elipar Freelight 2) in 3 modes: 2 continuous modes of 20 and 40 seconds (C20 and C40), and 1 exponential mode (E20; 5 seconds of exponential power increase followed by 15 seconds of maximum intensity). The degree of conversion (DC) was measured for each of the materials, and each of the modes by Fourier transformed infra-red spectrometry. P60 had the significantly lowest final contraction and FLO the highest among all light exposure modes. The C20 and C40 modes did not produce any difference in contraction or degree of conversion. The E20 mode led to a significant slowing of contraction speed combined with greater final contraction. Use of a LED lamp (1,000 mW/cm2) in continuous mode reduces the exposure time by half for identical curing shrinkage and degree of conversion.

Mechanisms for Enhanced Supercurrent Across Meandered Grain Boundaries in High-Temperature Superconductors

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

Feldmann, D. M.; Holesinger, T. G.; Feenstra, Roeland

2007-01-01

It has been well established that the critical current density J{sub c} across grain boundaries (GBs) in high-temperature superconductors decreases exponentially with misorientation angle {theta} beyond {approx}2-3 degrees. This rapid decrease is due to a suppression of the superconducting order parameter at the grain boundary, giving rise to weakly pinned Abrikosov-Josephson (AJ) vortices. Here we show that if the GB plane meanders, this exponential dependence no longer holds, permitting greatly enhanced J{sub c} values: up to six times at 0 T and four times at 1 T at {theta}{approx}4-6 degrees. This enhancement is due to an increase in the current-carryingmore » cross section of the GBs and the appearance of short AJ vortex segments in the GB plane, confined by the interaction with strongly pinned Abrikosov (A) vortices in the grains.« less

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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

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

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

2013-06-15

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

Statistical analyses support power law distributions found in neuronal avalanches.

PubMed

Klaus, Andreas; Yu, Shan; Plenz, Dietmar

2011-01-01

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

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

PubMed

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

2013-01-01

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

Non-extensive quantum statistics with particle-hole symmetry

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Zhao, Yufeng; Xu, Chi; Shi, Liang

2018-04-01

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

How extreme are extremes?

NASA Astrophysics Data System (ADS)

Cucchi, Marco; Petitta, Marcello; Calmanti, Sandro

2016-04-01

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

Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Turbulence hierarchy in a random fibre laser

PubMed Central

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

2017-01-01

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

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

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

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

An analog neural hardware implementation using charge-injection multipliers and neutron-specific gain control.

PubMed

Massengill, L W; Mundie, D B

1992-01-01

A neural network IC based on a dynamic charge injection is described. The hardware design is space and power efficient, and achieves massive parallelism of analog inner products via charge-based multipliers and spatially distributed summing buses. Basic synaptic cells are constructed of exponential pulse-decay modulation (EPDM) dynamic injection multipliers operating sequentially on propagating signal vectors and locally stored analog weights. Individually adjustable gain controls on each neutron reduce the effects of limited weight dynamic range. A hardware simulator/trainer has been developed which incorporates the physical (nonideal) characteristics of actual circuit components into the training process, thus absorbing nonlinearities and parametric deviations into the macroscopic performance of the network. Results show that charge-based techniques may achieve a high degree of neural density and throughput using standard CMOS processes.

On the minimum of independent geometrically distributed random variables

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

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

NASA Astrophysics Data System (ADS)

Bakoban, Rana A.

2017-08-01

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

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

PubMed

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

2013-02-01

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

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

PubMed Central

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Shaikh, Anwar; Papanikolaou, Nikolaos; Wiener, Noe

2014-12-01

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

Diversity of individual mobility patterns and emergence of aggregated scaling laws

PubMed Central

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

2013-01-01

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

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

PubMed

Porto, Markus; Roman, H Eduardo

2002-04-01

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

Statistical modeling of storm-level Kp occurrences

USGS Publications Warehouse

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

2006-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Energy distributions of an ion in a radio-frequency trap immersed in a buffer gas under the influence of additional external forces

NASA Astrophysics Data System (ADS)

Rouse, I.; Willitsch, S.

2018-04-01

An ion held in a radio-frequency trap interacting with a uniform buffer gas of neutral atoms develops a steady-state energy distribution characterized by a power-law tail at high energies instead of the exponential decay characteristic of thermal equilibrium. We have previously shown that the Tsallis statistics frequently used as an empirical model for this distribution is a good approximation when the ion is heated due to a combination of micromotion interruption and exchange of kinetic energy with the buffer gas [Rouse and Willitsch, Phys. Rev. Lett. 118, 143401 (2017), 10.1103/PhysRevLett.118.143401]. Here, we extend our treatment to include the heating due to additional motion of the ion caused by external forces, including the "excess micromotion" induced by uniform electric fields and rf phase offsets. We show that this also leads to a Tsallis distribution with a potentially different power-law exponent from that observed in the absence of this additional forced motion, with the difference increasing as the ratio of the mass of the neutral atoms to that of the ion decreases. Our results indicate that unless the excess micromotion is minimized to a very high degree, then even a system with very light neutrals and a heavy ion does not exhibit a thermal distribution.

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.

The topology and dynamics of complex networks

NASA Astrophysics Data System (ADS)

Dezso, Zoltan

We start with a brief introduction about the topological properties of real networks. Most real networks are scale-free, being characterized by a power-law degree distribution. The scale-free nature of real networks leads to unexpected properties such as the vanishing epidemic threshold. Traditional methods aiming to reduce the spreading rate of viruses cannot succeed on eradicating the epidemic on a scale-free network. We demonstrate that policies that discriminate between the nodes, curing mostly the highly connected nodes, can restore a finite epidemic threshold and potentially eradicate the virus. We find that the more biased a policy is towards the hubs, the more chance it has to bring the epidemic threshold above the virus' spreading rate. We continue by studying a large Web portal as a model system for a rapidly evolving network. We find that the visitation pattern of a news document decays as a power law, in contrast with the exponential prediction provided by simple models of site visitation. This is rooted in the inhomogeneous nature of the browsing pattern characterizing individual users: the time interval between consecutive visits by the same user to the site follows a power law distribution, in contrast with the exponential expected for Poisson processes. We show that the exponent characterizing the individual user's browsing patterns determines the power-law decay in a document's visitation. Finally, we turn our attention to biological networks and demonstrate quantitatively that protein complexes in the yeast, Saccharomyces cerevisiae, are comprised of a core in which subunits are highly coexpressed, display the same deletion phenotype (essential or non-essential) and share identical functional classification and cellular localization. The results allow us to define the deletion phenotype and cellular task of most known complexes, and to identify with high confidence the biochemical role of hundreds of proteins with yet unassigned functionality.

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.

Analysis of nanopore arrangement of porous alumina layers formed by anodizing in oxalic acid at relatively high temperatures

NASA Astrophysics Data System (ADS)

Zaraska, Leszek; Stępniowski, Wojciech J.; Jaskuła, Marian; Sulka, Grzegorz D.

2014-06-01

Anodic aluminum oxide (AAO) layers were formed by a simple two-step anodization in 0.3 M oxalic acid at relatively high temperatures (20-30 °C) and various anodizing potentials (30-65 V). The effect of anodizing conditions on structural features of as-obtained oxides was carefully investigated. A linear and exponential relationships between cell diameter, pore density and anodizing potential were confirmed, respectively. On the other hand, no effect of temperature and duration of anodization on pore spacing and pore density was found. Detailed quantitative and qualitative analyses of hexagonal arrangement of nanopore arrays were performed for all studied samples. The nanopore arrangement was evaluated using various methods based on the fast Fourier transform (FFT) images, Delaunay triangulations (defect maps), pair distribution functions (PDF), and angular distribution functions (ADF). It was found that for short anodizations performed at relatively high temperatures, the optimal anodizing potential that results in formation of nanostructures with the highest degree of pore order is 45 V. No direct effect of temperature and time of anodization on the nanopore arrangement was observed.

All-Optical Photoacoustic Sensors for Steel Rebar Corrosion Monitoring

PubMed Central

Du, Cong; Owusu Twumasi, Jones; Tang, Qixiang; Guo, Xu; Zhou, Jingcheng; Yu, Tzuyang; Wang, Xingwei

2018-01-01

This article presents an application of an active all-optical photoacoustic sensing system with four elements for steel rebar corrosion monitoring. The sensor utilized a photoacoustic mechanism of gold nanocomposites to generate 8 MHz broadband ultrasound pulses in 0.4 mm compact space. A nanosecond 532 nm pulsed laser and 400 μm multimode fiber were employed to incite an ultrasound reaction. The fiber Bragg gratings were used as distributed ultrasound detectors. Accelerated corrosion testing was applied to four sections of a single steel rebar with four different corrosion degrees. Our results demonstrated that the mass loss of steel rebar displayed an exponential growth with ultrasound frequency shifts. The sensitivity of the sensing system was such that 0.175 MHz central frequency reduction corresponded to 0.02 g mass loss of steel rebar corrosion. It was proved that the all-optical photoacoustic sensing system can actively evaluate the corrosion of steel rebar via ultrasound spectrum. This multipoint all-optical photoacoustic method is promising for embedment into a concrete structure for distributed corrosion monitoring. PMID:29702554

Competition for popularity in bipartite networks.

PubMed

Díaz, Mariano Beguerisse; Porter, Mason A; Onnela, Jukka-Pekka

2010-12-01

We present a dynamical model for rewiring and attachment in bipartite networks. Edges are placed between nodes that belong to catalogs that can either be fixed in size or growing in size. The model is motivated by an empirical study of data from the video rental service Netflix, which invites its users to give ratings to the videos available in its catalog. We find that the distribution of the number of ratings given by users and that of the number of ratings received by videos both follow a power law with an exponential cutoff. We also examine the activity patterns of Netflix users and find bursts of intense video-rating activity followed by long periods of inactivity. We derive ordinary differential equations to model the acquisition of edges by the nodes over time and obtain the corresponding time-dependent degree distributions. We then compare our results with the Netflix data and find good agreement. We conclude with a discussion of how catalog models can be used to study systems in which agents are forced to choose, rate, or prioritize their interactions from a large set of options. © 2010 American Institute of Physics.

Remarkable features in lattice-parameter ratios of crystals. II. Monoclinic and triclinic crystals.

PubMed

de Gelder, R; Janner, A

2005-06-01

The frequency distributions of monoclinic crystals as a function of the lattice-parameter ratios resemble the corresponding ones of orthorhombic crystals: an exponential component, with more or less pronounced sharp peaks, with in general the most important peak at the ratio value 1. In addition, the distribution as a function of the monoclinic angle beta has a sharp peak at 90 degrees and decreases sensibly at larger angles. Similar behavior is observed for the three triclinic angular parameters alpha, beta and gamma, with characteristic differences between the organic and metal-organic, bio-macromolecular and inorganic crystals, respectively. The general behavior observed for the hexagonal, tetragonal, orthorhombic, monoclinic and triclinic crystals {in the first part of this series [de Gelder & Janner (2005). Acta Cryst. B61, 287-295] and in the present case} is summarized and commented. The data involved represent 366 800 crystals, with lattice parameters taken from the Cambridge Structural Database, CSD (294 400 entries), the Protein Data Bank, PDB (18 800 entries), and the Inorganic Crystal Structure Database, ICSD (53 600 entries). A new general structural principle is suggested.

Competition for popularity in bipartite networks

NASA Astrophysics Data System (ADS)

Beguerisse Díaz, Mariano; Porter, Mason A.; Onnela, Jukka-Pekka

2010-12-01

We present a dynamical model for rewiring and attachment in bipartite networks. Edges are placed between nodes that belong to catalogs that can either be fixed in size or growing in size. The model is motivated by an empirical study of data from the video rental service Netflix, which invites its users to give ratings to the videos available in its catalog. We find that the distribution of the number of ratings given by users and that of the number of ratings received by videos both follow a power law with an exponential cutoff. We also examine the activity patterns of Netflix users and find bursts of intense video-rating activity followed by long periods of inactivity. We derive ordinary differential equations to model the acquisition of edges by the nodes over time and obtain the corresponding time-dependent degree distributions. We then compare our results with the Netflix data and find good agreement. We conclude with a discussion of how catalog models can be used to study systems in which agents are forced to choose, rate, or prioritize their interactions from a large set of options.

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…

Responses to vertical vestibular stimulation of neurons in the nucleus reticularis gigantocellularis in rabbits.

PubMed

Fagerson, M H; Barmack, N H

1995-06-01

1. Because the nucleus reticularis gigantocellularis (NRGc) receives a substantial descending projection from the caudal vestibular nuclei, we used extracellular single-unit recording combined with natural vestibular stimulation to examine the possible peripheral origins of the vestibularly modulated activity of caudal NRGc neurons located within 500 microns of the midline. Chloralose-urethan anesthetized rabbits were stimulated with an exponential "step" and/or static head-tilt stimulus, as well as sinusoidal rotation about the longitudinal or interaural axes providing various combinations of roll or pitch, respectively. Recording sites were reconstructed from electrolytic lesions confirmed histologically. 2. More than 85% of the 151 neurons, in the medial aspect of the caudal NRGc, responded to vertical vestibular stimulation. Ninety-six percent of these responded to rotation onto the contralateral side (beta responses). Only a few also responded to horizontal stimulation. Seventy-eight percent of the neurons that responded to vestibular stimulation responded during static roll-tilt. One-half of these neurons also responded transiently to the change in head position during exponential "step" stimulation, suggesting input mediated by otolith and semicircular canal receptors or tonic-phasic otolith neurons. 3. Seventy-five percent of the responsive neurons had a "null plane." The planes of stimulation resulting in maximal responses, for cells that responded to static stimulation, were distributed throughout 150 degrees in both roll and pitch quadrants. Five of these cells responded only transiently during exponential "step" stimulation and responded maximally when stimulated in the plane of one of the vertical semicircular canals. 4. The phase of the response of the 25% of medial NRGc neurons that lacked "null planes" gradually shifted approximately 180 degrees during sinusoidal vestibular stimulation as the plane of stimulation was shifted about the vertical axis. These neurons likely received convergent input with differing spatial and temporal properties. 5. The activity of neurons in the medial aspect of the caudal NRGc of rabbits was modulated by both otolithic macular and vertical semicircular canal receptor stimulation. This vestibular information may be important for controlling the intensity of the muscle activity in muscles such as neck muscles where the load on the muscle is affected by the position of the head with respect to gravity. Some of these neurons may also shift muscle function from an agonist to an antagonist as the direction of head tilt changes.

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.

Single impacts of keV fullerene ions on free standing graphene: Emission of ions and electrons from confined volume

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

Verkhoturov, Stanislav V.; Geng, Sheng; Schweikert, Emile A., E-mail: schweikert@chem.tamu.edu

We present the first data from individual C{sub 60} impacting one to four layer graphene at 25 and 50 keV. Negative secondary ions and electrons emitted in transmission were recorded separately from each impact. The yields for C{sub n}{sup −} clusters are above 10% for n ≤ 4, they oscillate with electron affinities and decrease exponentially with n. The result can be explained with the aid of MD simulation as a post-collision process where sufficient vibrational energy is accumulated around the rim of the impact hole for sputtering of carbon clusters. The ionization probability can be estimated by comparing experimentalmore » yields of C{sub n}{sup −} with those of C{sub n}{sup 0} from MD simulation, where it increases exponentially with n. The ionization probability can be approximated with ejecta from a thermally excited (3700 K) rim damped by cluster fragmentation and electron detachment. The experimental electron probability distributions are Poisson-like. On average, three electrons of thermal energies are emitted per impact. The thermal excitation model invoked for C{sub n}{sup −} emission can also explain the emission of electrons. The interaction of C{sub 60} with graphene is fundamentally different from impacts on 3D targets. A key characteristic is the high degree of ionization of the ejecta.« less

Weighted Scaling in Non-growth Random Networks

NASA Astrophysics Data System (ADS)

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

2012-09-01

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

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

NASA Astrophysics Data System (ADS)

Zhao, Chen; Sichitiu, Mihail L.

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

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

PubMed

McNair, James N; Newbold, J Denis

2012-05-07

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

Evolution and mass extinctions as lognormal stochastic processes

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2014-10-01

In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time. (2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such b-lognormals is then seen to represent the `degree of progress' reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller `chaos'), and have their peaks on the increasing GBM exponential. This exponential is thus the `trend of progress' in human history. (4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics). (5) But the most striking new result is that the well-known `Molecular Clock of Evolution', namely the `constant rate of Evolution at the molecular level' as shown by Kimura's Neutral Theory of Molecular Evolution, identifies with growth rate of the entropy of our Evo-SETI model, because they both grew linearly in time since the origin of life. (6) Furthermore, we apply our Evo-SETI model to lognormal stochastic processes other than GBMs. For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on a parabolic mean value capable of covering both the extinction and the subsequent recovery of life forms. (7) Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is a cubic function of the time. In conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based upon b-lognormals and lognormal stochastic processes with arbitrary mean, of which the GBMs are the particular case of exponential growth.

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.

Attractors of three-dimensional fast-rotating Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Trahe, Markus

The three-dimensional (3-D) rotating Navier-Stokes equations describe the dynamics of rotating, incompressible, viscous fluids. In this work, they are considered with smooth, time-independent forces and the original statements implied by the classical "Taylor-Proudman Theorem" of geophysics are rigorously proved. It is shown that fully developed turbulence of 3-D fast-rotating fluids is essentially characterized by turbulence of two-dimensional (2-D) fluids in terms of numbers of degrees of freedom. In this context, the 3-D nonlinear "resonant limit equations", which arise in a non-linear averaging process as the rotation frequency O → infinity, are studied and optimal (2-D-type) upper bounds for fractal box and Hausdorff dimensions of the global attractor as well as upper bounds for box dimensions of exponential attractors are determined. Then, the convergence of exponential attractors for the full 3-D rotating Navier-Stokes equations to exponential attractors for the resonant limit equations as O → infinity in the sense of full Hausdorff-metric distances is established. This provides upper and lower semi-continuity of exponential attractors with respect to the rotation frequency and implies that the number of degrees of freedom (attractor dimension) of 3-D fast-rotating fluids is close to that of 2-D fluids. Finally, the algebraic-geometric structure of the Poincare curves, which control the resonances and small divisor estimates for partial differential equations, is further investigated; the 3-D nonlinear limit resonant operators are characterized by three-wave interactions governed by these curves. A new canonical transformation between those curves is constructed; with far-reaching consequences on the density of the latter.

TracerLPM (Version 1): An Excel® workbook for interpreting groundwater age distributions from environmental tracer data

USGS Publications Warehouse

Jurgens, Bryant C.; Böhlke, J.K.; Eberts, Sandra M.

2012-01-01

TracerLPM is an interactive Excel® (2007 or later) workbook program for evaluating groundwater age distributions from environmental tracer data by using lumped parameter models (LPMs). Lumped parameter models are mathematical models of transport based on simplified aquifer geometry and flow configurations that account for effects of hydrodynamic dispersion or mixing within the aquifer, well bore, or discharge area. Five primary LPMs are included in the workbook: piston-flow model (PFM), exponential mixing model (EMM), exponential piston-flow model (EPM), partial exponential model (PEM), and dispersion model (DM). Binary mixing models (BMM) can be created by combining primary LPMs in various combinations. Travel time through the unsaturated zone can be included as an additional parameter. TracerLPM also allows users to enter age distributions determined from other methods, such as particle tracking results from numerical groundwater-flow models or from other LPMs not included in this program. Tracers of both young groundwater (anthropogenic atmospheric gases and isotopic substances indicating post-1940s recharge) and much older groundwater (carbon-14 and helium-4) can be interpreted simultaneously so that estimates of the groundwater age distribution for samples with a wide range of ages can be constrained. TracerLPM is organized to permit a comprehensive interpretive approach consisting of hydrogeologic conceptualization, visual examination of data and models, and best-fit parameter estimation. Groundwater age distributions can be evaluated by comparing measured and modeled tracer concentrations in two ways: (1) multiple tracers analyzed simultaneously can be evaluated against each other for concordance with modeled concentrations (tracer-tracer application) or (2) tracer time-series data can be evaluated for concordance with modeled trends (tracer-time application). Groundwater-age estimates can also be obtained for samples with a single tracer measurement at one point in time; however, prior knowledge of an appropriate LPM is required because the mean age is often non-unique. LPM output concentrations depend on model parameters and sample date. All of the LPMs have a parameter for mean age. The EPM, PEM, and DM have an additional parameter that characterizes the degree of age mixing in the sample. BMMs have a parameter for the fraction of the first component in the mixture. An LPM, together with its parameter values, provides a description of the age distribution or the fractional contribution of water for every age of recharge contained within a sample. For the PFM, the age distribution is a unit pulse at one distinct age. For the other LPMs, the age distribution can be much broader and span decades, centuries, millennia, or more. For a sample with a mixture of groundwater ages, the reported interpretation of tracer data includes the LPM name, the mean age, and the values of any other independent model parameters. TracerLPM also can be used for simulating the responses of wells, springs, streams, or other groundwater discharge receptors to nonpoint-source contaminants that are introduced in recharge, such as nitrate. This is done by combining an LPM or user-defined age distribution with information on contaminant loading at the water table. Information on historic contaminant loading can be used to help evaluate a model's ability to match real world conditions and understand observed contaminant trends, while information on future contaminant loading scenarios can be used to forecast potential contaminant trends.

Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions.

ERIC Educational Resources Information Center

Holland, Paul W.; Thayer, Dorothy T.

2000-01-01

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

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

PubMed

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

2017-06-01

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

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

PubMed

Déjardin, P

2013-08-30

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

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

NASA Astrophysics Data System (ADS)

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

2015-01-01

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

Plume characteristics of MPD thrusters: A preliminary examination

NASA Technical Reports Server (NTRS)

Myers, Roger M.

1989-01-01

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

Magnetic pattern at supergranulation scale: the void size distribution

NASA Astrophysics Data System (ADS)

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

2014-08-01

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

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

PubMed

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

2006-01-01

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

A stochastic evolutionary model generating a mixture of exponential distributions

NASA Astrophysics Data System (ADS)

Fenner, Trevor; Levene, Mark; Loizou, George

2016-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

PubMed

Steinhauser, Marco; Hübner, Ronald

2009-10-01

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

What can graph theory tell us about word learning and lexical retrieval?

PubMed

Vitevitch, Michael S

2008-04-01

Graph theory and the new science of networks provide a mathematically rigorous approach to examine the development and organization of complex systems. These tools were applied to the mental lexicon to examine the organization of words in the lexicon and to explore how that structure might influence the acquisition and retrieval of phonological word-forms. Pajek, a program for large network analysis and visualization (V. Batagelj & A. Mvrar, 1998), was used to examine several characteristics of a network derived from a computerized database of the adult lexicon. Nodes in the network represented words, and a link connected two nodes if the words were phonological neighbors. The average path length and clustering coefficient suggest that the phonological network exhibits small-world characteristics. The degree distribution was fit better by an exponential rather than a power-law function. Finally, the network exhibited assortative mixing by degree. Some of these structural characteristics were also found in graphs that were formed by 2 simple stochastic processes suggesting that similar processes might influence the development of the lexicon. The graph theoretic perspective may provide novel insights about the mental lexicon and lead to future studies that help us better understand language development and processing.

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.

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.

Coevolutionary dynamics with clustering behaviors on cyclic competition

NASA Astrophysics Data System (ADS)

Dong, Linrong; Yang, Guangcan

2012-05-01

We propose a dynamic model for describing clustering behaviors on a cyclic game, in which the same species form a cluster to compete. The rates of consuming the prey depend not only on the individual competing ability v, but also on the two interacting cluster’s sizes. The fragmentation and coagulation rates of the clusters are related to the cohesive strength among the individuals. A new parameter u is introduced to indicate the uniting degree. We find that the probability distribution of the clustering sizes is almost a power law in a large regime specified by the two parameters, which reflects the scale-free behavior in complex systems. In addition, the exponential magnitudes are mostly in the range of real social systems. Our simulation shows that clustering promotes biodiversity. At steady state, the amounts about the three species evolve tempestuously with asymmetric period; the aggregations about big size’s clusters to compete are obvious and on-off intermittence.

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.

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

Non-parametric model selection for subject-specific topological organization of resting-state functional connectivity.

PubMed

Ferrarini, Luca; Veer, Ilya M; van Lew, Baldur; Oei, Nicole Y L; van Buchem, Mark A; Reiber, Johan H C; Rombouts, Serge A R B; Milles, J

2011-06-01

In recent years, graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain. Most of these networks have shown small-world topological characteristics: high efficiency in long distance communication between nodes, combined with highly interconnected local clusters of nodes. Moreover, functional studies performed at high resolutions have presented convincing evidence that resting-state functional connectivity networks exhibits (exponentially truncated) scale-free behavior. Such evidence, however, was mostly presented qualitatively, in terms of linear regressions of the degree distributions on log-log plots. Even when quantitative measures were given, these were usually limited to the r(2) correlation coefficient. However, the r(2) statistic is not an optimal estimator of explained variance, when dealing with (truncated) power-law models. Recent developments in statistics have introduced new non-parametric approaches, based on the Kolmogorov-Smirnov test, for the problem of model selection. In this work, we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest. The analysis, performed at voxel level and in a subject-specific fashion, confirmed the superiority of a truncated power-law model, showing high consistency across subjects. Moreover, the most highly connected voxels were found to be consistently part of the default mode network. Our results provide statistically sound support to the evidence previously presented in literature for a truncated power-law model of resting-state functional connectivity. Copyright © 2010 Elsevier Inc. All rights reserved.

An Exponential Teaching Model for Educational Cablevision with Implications for an Advanced Degree Program in Applied Learning Systems

ERIC Educational Resources Information Center

Zink, J.

1976-01-01

The design and implementation of a cablevision delivered course on Grand Opera is described. The unique aspect of this project is that both the viewers and the production teams experienced active learning situations. (Author)

Temporal effects in trend prediction: identifying the most popular nodes in the future.

PubMed

Zhou, Yanbo; Zeng, An; Wang, Wei-Hong

2015-01-01

Prediction is an important problem in different science domains. In this paper, we focus on trend prediction in complex networks, i.e. to identify the most popular nodes in the future. Due to the preferential attachment mechanism in real systems, nodes' recent degree and cumulative degree have been successfully applied to design trend prediction methods. Here we took into account more detailed information about the network evolution and proposed a temporal-based predictor (TBP). The TBP predicts the future trend by the node strength in the weighted network with the link weight equal to its exponential aging. Three data sets with time information are used to test the performance of the new method. We find that TBP have high general accuracy in predicting the future most popular nodes. More importantly, it can identify many potential objects with low popularity in the past but high popularity in the future. The effect of the decay speed in the exponential aging on the results is discussed in detail.

Temporal Effects in Trend Prediction: Identifying the Most Popular Nodes in the Future

PubMed Central

Zhou, Yanbo; Zeng, An; Wang, Wei-Hong

2015-01-01

Prediction is an important problem in different science domains. In this paper, we focus on trend prediction in complex networks, i.e. to identify the most popular nodes in the future. Due to the preferential attachment mechanism in real systems, nodes’ recent degree and cumulative degree have been successfully applied to design trend prediction methods. Here we took into account more detailed information about the network evolution and proposed a temporal-based predictor (TBP). The TBP predicts the future trend by the node strength in the weighted network with the link weight equal to its exponential aging. Three data sets with time information are used to test the performance of the new method. We find that TBP have high general accuracy in predicting the future most popular nodes. More importantly, it can identify many potential objects with low popularity in the past but high popularity in the future. The effect of the decay speed in the exponential aging on the results is discussed in detail. PMID:25806810

Flash spectroscopy of purple membrane.

PubMed Central

Xie, A H; Nagle, J F; Lozier, R H

1987-01-01

Flash spectroscopy data were obtained for purple membrane fragments at pH 5, 7, and 9 for seven temperatures from 5 degrees to 35 degrees C, at the magic angle for actinic versus measuring beam polarizations, at fifteen wavelengths from 380 to 700 nm, and for about five decades of time from 1 microsecond to completion of the photocycle. Signal-to-noise ratios are as high as 500. Systematic errors involving beam geometries, light scattering, absorption flattening, photoselection, temperature fluctuations, partial dark adaptation of the sample, unwanted actinic effects, and cooperativity were eliminated, compensated for, or are shown to be irrelevant for the conclusions. Using nonlinear least squares techniques, all data at one temperature and one pH were fitted to sums of exponential decays, which is the form required if the system obeys conventional first-order kinetics. The rate constants obtained have well behaved Arrhenius plots. Analysis of the residual errors of the fitting shows that seven exponentials are required to fit the data to the accuracy of the noise level. PMID:3580488

Flash spectroscopy of purple membrane.

PubMed

Xie, A H; Nagle, J F; Lozier, R H

1987-04-01

Flash spectroscopy data were obtained for purple membrane fragments at pH 5, 7, and 9 for seven temperatures from 5 degrees to 35 degrees C, at the magic angle for actinic versus measuring beam polarizations, at fifteen wavelengths from 380 to 700 nm, and for about five decades of time from 1 microsecond to completion of the photocycle. Signal-to-noise ratios are as high as 500. Systematic errors involving beam geometries, light scattering, absorption flattening, photoselection, temperature fluctuations, partial dark adaptation of the sample, unwanted actinic effects, and cooperativity were eliminated, compensated for, or are shown to be irrelevant for the conclusions. Using nonlinear least squares techniques, all data at one temperature and one pH were fitted to sums of exponential decays, which is the form required if the system obeys conventional first-order kinetics. The rate constants obtained have well behaved Arrhenius plots. Analysis of the residual errors of the fitting shows that seven exponentials are required to fit the data to the accuracy of the noise level.

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.

Behavioral and Network Origins of Wealth Inequality: Insights from a Virtual World

PubMed Central

Fuchs, Benedikt; Thurner, Stefan

2014-01-01

Almost universally, wealth is not distributed uniformly within societies or economies. Even though wealth data have been collected in various forms for centuries, the origins for the observed wealth-disparity and social inequality are not yet fully understood. Especially the impact and connections of human behavior on wealth could so far not be inferred from data. Here we study wealth data from the virtual economy of the massive multiplayer online game (MMOG) Pardus. This data not only contains every player's wealth at every point in time, but also all actions over a timespan of almost a decade. We find that wealth distributions in the virtual world are very similar to those in Western countries. In particular we find an approximate exponential distribution for low wealth levels and a power-law tail for high levels. The Gini index is found to be , which is close to the indices of many Western countries. We find that wealth-increase rates depend on the time when players entered the game. Players that entered the game early on tend to have remarkably higher wealth-increase rates than those who joined later. Studying the players' positions within their social networks, we find that the local position in the trade network is most relevant for wealth. Wealthy people have high in- and out-degrees in the trade network, relatively low nearest-neighbor degrees, and low clustering coefficients. Wealthy players have many mutual friendships and are socially well respected by others, but spend more time on business than on socializing. Wealthy players have few personal enemies, but show animosity towards players that behave as public enemies. We find that players that are not organized within social groups are significantly poorer on average. We observe that “political” status and wealth go hand in hand. PMID:25153072

Behavioral and network origins of wealth inequality: insights from a virtual world.

PubMed

Fuchs, Benedikt; Thurner, Stefan

2014-01-01

Almost universally, wealth is not distributed uniformly within societies or economies. Even though wealth data have been collected in various forms for centuries, the origins for the observed wealth-disparity and social inequality are not yet fully understood. Especially the impact and connections of human behavior on wealth could so far not be inferred from data. Here we study wealth data from the virtual economy of the massive multiplayer online game (MMOG) Pardus. This data not only contains every player's wealth at every point in time, but also all actions over a timespan of almost a decade. We find that wealth distributions in the virtual world are very similar to those in Western countries. In particular we find an approximate exponential distribution for low wealth levels and a power-law tail for high levels. The Gini index is found to be g = 0.65, which is close to the indices of many Western countries. We find that wealth-increase rates depend on the time when players entered the game. Players that entered the game early on tend to have remarkably higher wealth-increase rates than those who joined later. Studying the players' positions within their social networks, we find that the local position in the trade network is most relevant for wealth. Wealthy people have high in- and out-degrees in the trade network, relatively low nearest-neighbor degrees, and low clustering coefficients. Wealthy players have many mutual friendships and are socially well respected by others, but spend more time on business than on socializing. Wealthy players have few personal enemies, but show animosity towards players that behave as public enemies. We find that players that are not organized within social groups are significantly poorer on average. We observe that "political" status and wealth go hand in hand.

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.

Testing the mutual information expansion of entropy with multivariate Gaussian distributions.

PubMed

Goethe, Martin; Fita, Ignacio; Rubi, J Miguel

2017-12-14

The mutual information expansion (MIE) represents an approximation of the configurational entropy in terms of low-dimensional integrals. It is frequently employed to compute entropies from simulation data of large systems, such as macromolecules, for which brute-force evaluation of the full configurational integral is intractable. Here, we test the validity of MIE for systems consisting of more than m = 100 degrees of freedom (dofs). The dofs are distributed according to multivariate Gaussian distributions which were generated from protein structures using a variant of the anisotropic network model. For the Gaussian distributions, we have semi-analytical access to the configurational entropy as well as to all contributions of MIE. This allows us to accurately assess the validity of MIE for different situations. We find that MIE diverges for systems containing long-range correlations which means that the error of consecutive MIE approximations grows with the truncation order n for all tractable n ≪ m. This fact implies severe limitations on the applicability of MIE, which are discussed in the article. For systems with correlations that decay exponentially with distance, MIE represents an asymptotic expansion of entropy, where the first successive MIE approximations approach the exact entropy, while MIE also diverges for larger orders. In this case, MIE serves as a useful entropy expansion when truncated up to a specific truncation order which depends on the correlation length of the 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.

Reaching and Teaching Autistic Kids

ERIC Educational Resources Information Center

Boutelle, Marsha

2008-01-01

Autism is called a "spectrum" of disorders because a variety of symptoms and degrees of disability are involved, with autism spectrum disorders (ASD) defined by the severity of impairment. Since the 1940s, the incidence of autism has exploded exponentially. Researchers are scrambling to find effective strategies for helping autistic…

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.

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.

Quantum mechanical generalized phase-shift approach to atom-surface scattering: a Feshbach projection approach to dealing with closed channel effects.

PubMed

Maji, Kaushik; Kouri, Donald J

2011-03-28

We have developed a new method for solving quantum dynamical scattering problems, using the time-independent Schrödinger equation (TISE), based on a novel method to generalize a "one-way" quantum mechanical wave equation, impose correct boundary conditions, and eliminate exponentially growing closed channel solutions. The approach is readily parallelized to achieve approximate N(2) scaling, where N is the number of coupled equations. The full two-way nature of the TISE is included while propagating the wave function in the scattering variable and the full S-matrix is obtained. The new algorithm is based on a "Modified Cayley" operator splitting approach, generalizing earlier work where the method was applied to the time-dependent Schrödinger equation. All scattering variable propagation approaches to solving the TISE involve solving a Helmholtz-type equation, and for more than one degree of freedom, these are notoriously ill-behaved, due to the unavoidable presence of exponentially growing contributions to the numerical solution. Traditionally, the method used to eliminate exponential growth has posed a major obstacle to the full parallelization of such propagation algorithms. We stabilize by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing closed channels, while retaining all of the propagating open channel components, as well as exponentially decaying closed channel components.

The Entropy of Non-Ergodic Complex Systems — a Derivation from First Principles

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Hanel, Rudolf

In information theory the 4 Shannon-Khinchin1,2 (SK) axioms determine Boltzmann Gibbs entropy, S -∑i pilog pi, as the unique entropy. Physics is different from information in the sense that physical systems can be non-ergodic or non-Markovian. To characterize such strongly interacting, statistical systems - complex systems in particular - within a thermodynamical framework it might be necessary to introduce generalized entropies. A series of such entropies have been proposed in the past decades. Until now the understanding of their fundamental origin and their deeper relations to complex systems remains unclear. To clarify the situation we note that non-ergodicity explicitly violates the fourth SK axiom. We show that by relaxing this axiom the entropy generalizes to, S ∑i Γ(d + 1, 1 - c log pi), where Γ is the incomplete Gamma function, and c and d are scaling exponents. All recently proposed entropies compatible with the first 3 SK axioms appear to be special cases. We prove that each statistical system is uniquely characterized by the pair of the two scaling exponents (c, d), which defines equivalence classes for all systems. The corresponding distribution functions are special forms of Lambert-W exponentials containing, as special cases, Boltzmann, stretched exponential and Tsallis distributions (power-laws) - all widely abundant in nature. This derivation is the first ab initio justification for generalized entropies. We next show how the phasespace volume of a system is related to its generalized entropy, and provide a concise criterion when it is not of Boltzmann-Gibbs type but assumes a generalized form. We show that generalized entropies only become relevant when the dynamically (statistically) relevant fraction of degrees of freedom in a system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen. Systems governed by generalized entropies are therefore systems whose phasespace volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for accelerating random walks, and a spin system on a constant-conectancy network. We argue that generalized entropies should be relevant for self-organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.

Improving Bed Management at Wright-Patterson Medical Center

DTIC Science & Technology

1989-09-01

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

Compact continuous-variable entanglement distillation.

PubMed

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

2012-02-10

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

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

PubMed

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

2018-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

A Hierarchical Bayesian Model for Calibrating Estimates of Species Divergence Times

PubMed Central

Heath, Tracy A.

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

The social architecture of capitalism

NASA Astrophysics Data System (ADS)

Wright, Ian

2005-02-01

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

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

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.

Calling patterns in human communication dynamics

PubMed Central

Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Podobnik, Boris; Zhou, Wei-Xing; Stanley, H. Eugene

2013-01-01

Modern technologies not only provide a variety of communication modes (e.g., texting, cell phone conversation, and online instant messaging), but also detailed electronic traces of these communications between individuals. These electronic traces indicate that the interactions occur in temporal bursts. Here, we study intercall duration of communications of the 100,000 most active cell phone users of a Chinese mobile phone operator. We confirm that the intercall durations follow a power-law distribution with an exponential cutoff at the population level but find differences when focusing on individual users. We apply statistical tests at the individual level and find that the intercall durations follow a power-law distribution for only 3,460 individuals (3.46%). The intercall durations for the majority (73.34%) follow a Weibull distribution. We quantify individual users using three measures: out-degree, percentage of outgoing calls, and communication diversity. We find that the cell phone users with a power-law duration distribution fall into three anomalous clusters: robot-based callers, telecom fraud, and telephone sales. This information is of interest to both academics and practitioners, mobile telecom operators in particular. In contrast, the individual users with a Weibull duration distribution form the fourth cluster of ordinary cell phone users. We also discover more information about the calling patterns of these four clusters (e.g., the probability that a user will call the cr-th most contact and the probability distribution of burst sizes). Our findings may enable a more detailed analysis of the huge body of data contained in the logs of massive users. PMID:23319645

Calling patterns in human communication dynamics.

PubMed

Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Podobnik, Boris; Zhou, Wei-Xing; Stanley, H Eugene

2013-01-29

Modern technologies not only provide a variety of communication modes (e.g., texting, cell phone conversation, and online instant messaging), but also detailed electronic traces of these communications between individuals. These electronic traces indicate that the interactions occur in temporal bursts. Here, we study intercall duration of communications of the 100,000 most active cell phone users of a Chinese mobile phone operator. We confirm that the intercall durations follow a power-law distribution with an exponential cutoff at the population level but find differences when focusing on individual users. We apply statistical tests at the individual level and find that the intercall durations follow a power-law distribution for only 3,460 individuals (3.46%). The intercall durations for the majority (73.34%) follow a Weibull distribution. We quantify individual users using three measures: out-degree, percentage of outgoing calls, and communication diversity. We find that the cell phone users with a power-law duration distribution fall into three anomalous clusters: robot-based callers, telecom fraud, and telephone sales. This information is of interest to both academics and practitioners, mobile telecom operators in particular. In contrast, the individual users with a Weibull duration distribution form the fourth cluster of ordinary cell phone users. We also discover more information about the calling patterns of these four clusters (e.g., the probability that a user will call the c(r)-th most contact and the probability distribution of burst sizes). Our findings may enable a more detailed analysis of the huge body of data contained in the logs of massive users.

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.

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

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

PubMed Central

1994-01-01

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

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

PubMed

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

2018-05-08

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

Parametric resonant triad interactions in a free shear layer

NASA Technical Reports Server (NTRS)

Mallier, R.; Maslowe, S. A.

1993-01-01

We investigate the weakly nonlinear evolution of a triad of nearly-neutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees to the mean flow direction. Because the evolution occurs on a relatively fast time scale, the critical layer dynamics dominate the process and the amplitude evolution of the oblique waves is governed by an integro-differential equation. The long-time solution of this equation predicts very rapid (exponential of an exponential) amplification and we discuss the pertinence of this result to vortex pairing phenomena in mixing layers.

Growing trees in internet news groups and forums

NASA Astrophysics Data System (ADS)

Kujawski, B.; Hołyst, J.; Rodgers, G. J.

2007-09-01

We present an empirical study of the networks created by users within internet news groups and forums and show that they organize themselves into scale-free trees. The structure of these trees depends on the topic under discussion; specialist topics have trees with a short shallow structure whereas more universal topics are discussed widely and have a deeper tree structure. For news groups we find that the distribution of the time intervals between when a message is posted and when it receives a response exhibits a composite power-law behavior. From our statistics we can see if the news group or forum is free or is overseen by a moderator. The correlation function of activity, the number of messages posted in a given time, shows long-range correlations connected with the users’ daily routines. The distribution of distances between each message and its root is exponential for most news groups and power law for the forums. For both formats we find that the relation between the supremacy (the total number of nodes that are under the node i , including node i ) and the degree is linear s(k)˜k , in contrast to the analytical relation for the Barabási-Albert network.

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

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

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

PubMed Central

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

PubMed

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

2018-02-01

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

The ATP hydrolysis and phosphate release steps control the time course of force development in rabbit skeletal muscle.

PubMed

Sleep, John; Irving, Malcolm; Burton, Kevin

2005-03-15

The time course of isometric force development following photolytic release of ATP in the presence of Ca(2+) was characterized in single skinned fibres from rabbit psoas muscle. Pre-photolysis force was minimized using apyrase to remove contaminating ATP and ADP. After the initial force rise induced by ATP release, a rapid shortening ramp terminated by a step stretch to the original length was imposed, and the time course of the subsequent force redevelopment was again characterized. Force development after ATP release was accurately described by a lag phase followed by one or two exponential components. At 20 degrees C, the lag was 5.6 +/- 0.4 ms (s.e.m., n = 11), and the force rise was well fitted by a single exponential with rate constant 71 +/- 4 s(-1). Force redevelopment after shortening-restretch began from about half the plateau force level, and its single-exponential rate constant was 68 +/- 3 s(-1), very similar to that following ATP release. When fibres were activated by the addition of Ca(2+) in ATP-containing solution, force developed more slowly, and the rate constant for force redevelopment following shortening-restretch reached a maximum value of 38 +/- 4 s(-1) (n = 6) after about 6 s of activation. This lower value may be associated with progressive sarcomere disorder at elevated temperature. Force development following ATP release was much slower at 5 degrees C than at 20 degrees C. The rate constant of a single-exponential fit to the force rise was 4.3 +/- 0.4 s(-1) (n = 22), and this was again similar to that after shortening-restretch in the same activation at this temperature, 3.8 +/- 0.2 s(-1). We conclude that force development after ATP release and shortening-restretch are controlled by the same steps in the actin-myosin ATPase cycle. The present results and much previous work on mechanical-chemical coupling in muscle can be explained by a kinetic scheme in which force is generated by a rapid conformational change bracketed by two biochemical steps with similar rate constants -- ATP hydrolysis and the release of inorganic phosphate -- both of which combine to control the rate of force development.

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

NASA Astrophysics Data System (ADS)

Fa, Kwok Sau

2012-09-01

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

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

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

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

2009-09-15

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

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

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

NASA Astrophysics Data System (ADS)

Lanchier, Nicolas

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

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

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

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

NASA Astrophysics Data System (ADS)

Clotet, Xavier; Santucci, Stéphane; Ortín, Jordi

2016-01-01

We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities μ and nearly identical oil-air surface tension, and forced them to slowly invade a model open fracture at very different flow rates v . In this second part of the study we have carried out a scale-dependent statistical analysis of the front dynamics. We have specifically analyzed the influence of μ and v on the statistical properties of the velocity Vℓ, the spatial average of the local front velocities over a window of lateral size ℓ . We have varied ℓ from the local scale defined by our spatial resolution up to the lateral system size L . Even though the imposed flow rate is constant, the signals Vℓ(t ) present very strong fluctuations which evolve systematically with the parameters μ , v , and ℓ . We have verified that the non-Gaussian fluctuations of the global velocity Vℓ(t ) are very well described by a generalized Gumbel statistics. The asymmetric shape and the exponential tail of those distributions are controlled by the number of effective degrees of freedom of the imbibition fronts, given by Neff=ℓ /ℓc (the ratio of the lateral size of the measuring window ℓ to the correlation length ℓc˜1 /√{μ v } ). The large correlated excursions of Vℓ(t ) correspond to global avalanches, which reflect extra displacements of the imbibition fronts. We show that global avalanches are power-law distributed, both in sizes and durations, with robustly defined exponents—independent of μ , v , and ℓ . Nevertheless, the exponential upper cutoffs of the distributions evolve systematically with those parameters. We have found, moreover, that maximum sizes ξS and maximum durations ξT of global avalanches are not controlled by the same mechanism. While ξS are also determined by ℓ /ℓc , like the amplitude fluctuations of Vℓ(t ) , ξT and the temporal correlations of Vℓ(t ) evolve much more strongly with imposed flow rate v than with fluid viscosity μ .

A Random Variable Transformation Process.

ERIC Educational Resources Information Center

Scheuermann, Larry

1989-01-01

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

[Abdominal obesity and coronary heart disease. Pathophysiology and clinical significance].

PubMed

Hauner, H

1995-02-01

The relationship between overweight and cardiovascular disease was a matter of debate for many years. Recent studies have demonstrated that obesity defined as body mass index of 30 kg/m2 or higher is associated with an exponential increase of cardiovascular complications. This effect is largely mediated by the induction of established risk factors such as dyslipidemia, hypertension and type 2 diabetes mellitus. Recently, there is growing evidence that the occurrence of most complications of obesity depends not only on the degree of overweight but also on the pattern of body fat distribution. Many data suggest that the anatomical localization of body fat is more important for the risk of developing complications than the adipose tissue mass per se. An abdominal, upper-body type of fat distribution, which can be easily determined by the measurement of waist and hip circumferences (waist/hip ratio = WHR), is also a confirmed risk factor for metabolic disturbances, hypertension and atherosclerosis, independent of body weight. However, the clinical appearance of these disturbances is frequently associated with the development of obesity. This network of metabolic disorders and their vascular complications is termed "metabolic syndrome" or "syndrome X" (Table 2). Abdominal obesity is now known to be closely associated with the metabolic syndrome and is regarded to represent its readily recognizable phenotypic feature. The components of the metabolic syndrome are characterized by varying forms and degrees of insulin resistance. It is assumed that insulin resistance, defined as diminished biological response to the action of insulin, represents the primary defect or at least the common pathogenetic link between these disturbances.(ABSTRACT TRUNCATED AT 250 WORDS)

Lamination and mixing in laminar flows driven by Lorentz body forces

NASA Astrophysics Data System (ADS)

Rossi, L.; Doorly, D.; Kustrin, D.

2012-01-01

We present a new approach to the design of mixers. This approach relies on a sequence of tailored flows coupled with a new procedure to quantify the local degree of striation, called lamination. Lamination translates to the distance over which the molecular diffusion needs to act to finalise mixing. A novel in situ mixing is achieved by the tailored sequence of flows. This sequence is shown with the property that material lines and lamination grow exponentially, according to processes akin to the well-known baker's map. The degree of mixing (stirring coefficient) likewise shows exponential growth before the saturation of the stirring rate. Such saturation happens when the typical striations' thickness is smaller than the diffusion's length scale. Moreover, without molecular diffusion, the predicted striations' thickness would be smaller than the size of an atom of hydrogen within 40 flow turnover times. In fact, we conclude that about 3 minutes, i.e. 15 turnover times, are sufficient to mix species with very low diffusivities, e.g. suspensions of virus, bacteria, human cells, and DNA.

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

ERIC Educational Resources Information Center

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

2013-01-01

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

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

PubMed

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

2016-01-01

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

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

PubMed Central

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

2016-01-01

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

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.

[Spatial variability and evaluation of soil heavy metal contamination in the urban-transect of Shanghai].

PubMed

Liu, Yun-Long; Zhang, Li-Jia; Han, Xiao-Fei; Zhuang, Teng-Fei; Shi, Zhen-Xiang; Lu, Xiao-Zhe

2012-02-01

Soil heavy metal concentrations along the typical urban-transect in Shanghai were analyzed to indicate the effect of urbanization and industrialization on soil environment quality. Spatial variation structure and distribution of 5 heavy metals (Cu, Cr, Mn, Pb and Zn) in the top soil of urban-transect were analyzed. The single pollution index and the composite pollution index were used to evaluate the soil heavy metal pollution. The results showed that the average concentrations of the Cu, Pb, Zn, Cr, Mn were 27.80, 28.86, 99.36, 87.72, 556.97 mg x kg(-1), respectively. Cu, Cr, Mn, Pb and Zn were medium in variability, Mn was distributed lognormally, while Cu, Cr, Pb and Zn were distributed normally. The results of semivariance analysis showed that Mn was fit for the exponential model, Cr, Pb, Cu and Zn were fit for the linear model. The spatial distribution maps of heavy metal content of the topsoil in this city-transect were produced by means of the universal kriging interpolation. Cu was spatially distributed in ribbon, Cr and Mn were distributed in island, while the spatial distribution of Pb and Zn showed the mixed characteristic of ribbon and island. With the result of soil pollution evaluation, it showed that the pollution of Cr, Zn and Pb was relatively severe. Cr, Zn, Pb, Mn and Cu were significantly correlated, and heavy metal co-contamination existed in soil. Difference of soil heavy metals pollution along "Urban-suburban-rural" was obvious, the special variation of heavy metal concentrations in the soil closely related to the degree of industrialization and urbanization of the city.

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.

What Can Graph Theory Tell Us About Word Learning and Lexical Retrieval?

PubMed Central

Vitevitch, Michael S.

2008-01-01

Purpose Graph theory and the new science of networks provide a mathematically rigorous approach to examine the development and organization of complex systems. These tools were applied to the mental lexicon to examine the organization of words in the lexicon and to explore how that structure might influence the acquisition and retrieval of phonological word-forms. Method Pajek, a program for large network analysis and visualization (V. Batagelj & A. Mvrar, 1998), was used to examine several characteristics of a network derived from a computerized database of the adult lexicon. Nodes in the network represented words, and a link connected two nodes if the words were phonological neighbors. Results The average path length and clustering coefficient suggest that the phonological network exhibits small-world characteristics. The degree distribution was fit better by an exponential rather than a power-law function. Finally, the network exhibited assortative mixing by degree. Some of these structural characteristics were also found in graphs that were formed by 2 simple stochastic processes suggesting that similar processes might influence the development of the lexicon. Conclusions The graph theoretic perspective may provide novel insights about the mental lexicon and lead to future studies that help us better understand language development and processing. PMID:18367686

Event-Triggered Distributed Average Consensus Over Directed Digital Networks With Limited Communication Bandwidth.

PubMed

Li, Huaqing; Chen, Guo; Huang, Tingwen; Dong, Zhaoyang; Zhu, Wei; Gao, Lan

2016-12-01

In this paper, we consider the event-triggered distributed average-consensus of discrete-time first-order multiagent systems with limited communication data rate and general directed network topology. In the framework of digital communication network, each agent has a real-valued state but can only exchange finite-bit binary symbolic data sequence with its neighborhood agents at each time step due to the digital communication channels with energy constraints. Novel event-triggered dynamic encoder and decoder for each agent are designed, based on which a distributed control algorithm is proposed. A scheme that selects the number of channel quantization level (number of bits) at each time step is developed, under which all the quantizers in the network are never saturated. The convergence rate of consensus is explicitly characterized, which is related to the scale of network, the maximum degree of nodes, the network structure, the scaling function, the quantization interval, the initial states of agents, the control gain and the event gain. It is also found that under the designed event-triggered protocol, by selecting suitable parameters, for any directed digital network containing a spanning tree, the distributed average consensus can be always achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. Two simulation examples are provided to illustrate the feasibility of presented protocol and the correctness of the theoretical results.

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

PubMed

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

2017-03-21

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

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

PubMed Central

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

2009-01-01

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

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

NASA Astrophysics Data System (ADS)

Himeoka, Yusuke; Kaneko, Kunihiko

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

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

Accumulated distribution of material gain at dislocation crystal growth

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

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

2016-05-15

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

New tools for characterizing swarming systems: A comparison of minimal models

NASA Astrophysics Data System (ADS)

Huepe, Cristián; Aldana, Maximino

2008-05-01

We compare three simple models that reproduce qualitatively the emergent swarming behavior of bird flocks, fish schools, and other groups of self-propelled agents by using a new set of diagnosis tools related to the agents’ spatial distribution. Two of these correspond in fact to different implementations of the same model, which had been previously confused in the literature. All models appear to undergo a very similar order-to-disorder phase transition as the noise level is increased if we only compare the standard order parameter, which measures the degree of agent alignment. When considering our novel quantities, however, their properties are clearly distinguished, unveiling previously unreported qualitative characteristics that help determine which model best captures the main features of realistic swarms. Additionally, we analyze the agent clustering in space, finding that the distribution of cluster sizes is typically exponential at high noise, and approaches a power-law as the noise level is reduced. This trend is sometimes reversed at noise levels close to the phase transition, suggesting a non-trivial critical behavior that could be verified experimentally. Finally, we study a bi-stable regime that develops under certain conditions in large systems. By computing the probability distributions of our new quantities, we distinguish the properties of each of the coexisting metastable states. Our study suggests new experimental analyses that could be carried out to characterize real biological swarms.

Connecting the invisible dots: reaching lesbian, gay, and bisexual adolescents and young adults at risk for suicide through online social networks.

PubMed

Silenzio, Vincent M B; Duberstein, Paul R; Tang, Wan; Lu, Naiji; Tu, Xin; Homan, Christopher M

2009-08-01

Young lesbian, gay, and bisexual (young LGB) individuals report higher rates of suicide ideation and attempts from their late teens through early twenties. Their high rate of Internet use suggests that online social networks offer a novel opportunity to reach them. This study explores online social networks as a venue for prevention research targeting young LGB. An automated data collection program was used to map the social connections between LGB self-identified individuals between 16 and 24 years old participating in an online social network. We then completed a descriptive analysis of the structural characteristics known to affect diffusion within such networks. Finally, we conducted Monte Carlo simulations of peer-driven diffusion of a hypothetical preventive intervention within the observed network under varying starting conditions. We mapped a network of 100,014 young LGB. The mean age was 20.4 years. The mean nodal degree was 137.5, representing an exponential degree distribution ranging from 1 through 4309. Monte Carlo simulations revealed that a peer-driven preventive intervention ultimately reached final sample sizes of up to 18,409 individuals. The network's structure is consistent with other social networks in terms of the underlying degree distribution. Such networks are typically formed dynamically through a process of preferential attachment. This implies that some individuals could be more important to target to facilitate the diffusion of interventions. However, in terms of determining the success of an intervention targeting this population, our simulation results suggest that varying the number of peers that can be recruited is more important than increasing the number of randomly-selected starting individuals. This has implications for intervention design. Given the potential to access this previously isolated population, this novel approach represents a promising new frontier in suicide prevention and other research areas.

Connecting the Invisible Dots: Network-Based Methods to Reach a Hidden Population at Risk for Suicide

PubMed Central

Duberstein, Paul R; Tu, Xin; Tang, Wan; Lu, Naiji; Homan, Christopher M

2009-01-01

Young lesbian, gay, and bisexual (young LGB) individuals report higher rates of suicide ideation and attempts from their late teens through early twenties. Their high rate of Internet use suggests that online social networks offer a novel opportunity to reach them. This study explores online social networks as a venue for prevention research targeting young LGB. An automated data collection program was used to map the social connections between LGB self-identified individuals between 16 and 24 years old participating in an online social network. We then completed a descriptive analysis of the structural characteristics known to affect diffusion within such networks. Finally, we conducted Monte Carlo simulations of peer-driven diffusion of a hypothetical preventive intervention within the observed network under varying starting conditions. We mapped a network of 100,014 young LGB. The mean age was 20.4 years. The mean nodal degree was 137.5, representing an exponential degree distribution ranging from 1 through 4,309. Monte Carlo simulations revealed that a peer-driven preventive intervention ultimately reached final sample sizes of up to 18,409 individuals. The network’s structure is consistent with other social networks in terms of the underlying degree distribution. Such networks are typically formed dynamically through a process of preferential attachment. This implies that some individuals could be more important to target to facilitate the diffusion of interventions. However, in terms of determining the success of an intervention targeting this population, our simulation results suggest that varying the number of peers that can be recruited is more important than increasing the number of randomly-selected starting individuals. This has implications for intervention design. Given the potential to access this previously isolated population, this novel approach represents a promising new frontier in suicide prevention and other research areas. PMID:19540641

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

The chaotic physician work world.

PubMed

Paterick, Timothy E

2014-01-01

Physicians are immersed in a work environment where daily challenges seem to represent a condition or place of increasing disorder and confusion. The degree of "entropy" in the physician workplace is increasing exponentially. Healthcare systems are in a state of chaos and are dynamic--meaning the behavior at one time influences its behavior in the future. The initial changes have future exponential fluctuations that have created a state of healthcare crisis. These systems are nonlinear; the metaphor to describe the unruly nature of the physician work world is that in which the flap of a butterfly wing in Brazil can set off a tornado in Texas. The tornado affecting physician work life must be understood to be rectified. Physicians must slow down and pay attention.

Nonlinear analogue of the May−Wigner instability transition

PubMed Central

Fyodorov, Yan V.; Khoruzhenko, Boris A.

2016-01-01

We study a system of N≫1 degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium with rate μ. We show that, while increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically nontrivial regime characterized by an exponential number of equilibria, the vast majority of which are expected to be unstable. It is suggested that this picture provides a global view on the nature of the May−Wigner instability transition originally discovered by local linear stability analysis. PMID:27274077

Beyond the usual mapping functions in GPS, VLBI and Deep Space tracking.

NASA Astrophysics Data System (ADS)

Barriot, Jean-Pierre; Serafini, Jonathan; Sichoix, Lydie

2014-05-01

We describe here a new algorithm to model the water contents of the atmosphere (including ZWD) from GPS slant wet delays relative to a single receiver. We first make the assumption that the water vapor contents are mainly governed by a scale height (exponential law), and secondly that the departures from this decaying exponential can be mapped as a set of low degree 3D Zernike functions (w.r.t. space) and Tchebyshev polynomials (w.r.t. time.) We compare this new algorithm with previous algorithms known as mapping functions in GPS, VLBI and Deep Space tracking and give an example with data acquired over a one day time span at the Geodesy Observatory of Tahiti.

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.

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

Inverse method to estimate kinetic degradation parameters of grape anthocyanins in wheat flour under simultaneously changing temperature and moisture.

PubMed

Lai, K P K; Dolan, K D; Ng, P K W

2009-06-01

Thermal and moisture effects on grape anthocyanin degradation were investigated using solid media to simulate processing at temperatures above 100 degrees C. Grape pomace (anthocyanin source) mixed with wheat pastry flour (1: 3, w/w dry basis) was used in both isothermal and nonisothermal experiments by heating the same mixture at 43% (db) initial moisture in steel cells in an oil bath at 80, 105, and 145 degrees C. To determine the effect of moisture on anthocyanin degradation, the grape pomace-wheat flour mixture was heated isothermally at 80 degrees C at constant moisture contents of 10%, 20%, and 43% (db). Anthocyanin degradation followed a pseudo first-order reaction with moisture. Anthocyanins degraded more rapidly with increasing temperature and moisture. The effects of temperature and moisture on the rate constant were modeled according to the Arrhenius and an exponential relationship, respectively. The nonisothermal reaction rate constant and activation energy (mean +/- standard error) were k(80 degrees C, 43% (db) moisture) = 2.81 x 10(-4)+/- 1.1 x 10(-6) s(-1) and DeltaE = 75273 +/- 197 J/g mol, respectively. The moisture parameter for the exponential model was 4.28 (dry basis moisture content)(-1). One possible application of this study is as a tool to predict the loss of anthocyanins in nutraceutical products containing grape pomace. For example, if the process temperature history and moisture history in an extruded snack fortified with grape pomace is known, the percentage anthocyanin loss can be predicted.

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.

Functional network inference of the suprachiasmatic nucleus

PubMed Central

Abel, John H.; Meeker, Kirsten; Granados-Fuentes, Daniel; St. John, Peter C.; Wang, Thomas J.; Bales, Benjamin B.; Doyle, Francis J.; Herzog, Erik D.; Petzold, Linda R.

2016-01-01

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data from individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure. PMID:27044085

Ultrasonic Study of Dislocation Dynamics in Lithium -

NASA Astrophysics Data System (ADS)

Han, Myeong-Deok

1987-09-01

Experimental studies of dislocation dynamics in LiF single crystals, using ultrasonic techniques combined with dynamic loading, were performed to investigate the time evolution of the plastic deformation process under a short stress pulse at room temperature, and the temperature dependence of the dislocation damping mechanism in the temperature range 25 - 300(DEGREES)K. From the former, the time dependence of the ultrasonic attenuation was understood as resulting from dislocation multiplication followed by the evolution of mobile dislocations to immobile ones under large stress. From the latter, the temperature dependence of the ultrasonic attenuation was interpreted as due to the motion of the dislocation loops overcoming the periodic Peierls potential barrier in a manner analogous to the motion of a thermalized sine-Gordon chain under a small stress. The Peierls stress obtained from the experimental results by application of Seeger's relaxation model with exponential dislocation length distribution was 4.26MPa, which is consistent with the lowest stress for the linear relation between the dislocation velocity and stress observed by Flinn and Tinder.

A Comparison of Engagement and Overall Institutional Satisfaction between Chinese International and Domestic Students in the United States

ERIC Educational Resources Information Center

Wang, Rong

2017-01-01

With the exponential growth in international students pursing postsecondary degrees in the U.S., an increasing number of faculty members and staff have raised questions and concerns about supporting international students' academic engagement. Although prior studies have explored the educational experiences of international students in the United…

From Research to Praxis: Empowering Trinidadian Primary School Teachers via Action Research

ERIC Educational Resources Information Center

Bissessar, Charmaine S.

2015-01-01

An exponential body of extant research illustrates the symbiotic dyad action research, andragogy, reflective praxis, and transformative learning share. This paper contains a narrative review of 83 action research papers submitted to the researcher as part of the fulfilment of the Bachelor of Education degree from April 2011 to May 2013.…

Decision Support System for hydrological extremes

NASA Astrophysics Data System (ADS)

Bobée, Bernard; El Adlouni, Salaheddine

2014-05-01

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

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

NASA Astrophysics Data System (ADS)

Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo

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

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

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

A mathematical model for the occurrence of historical events

NASA Astrophysics Data System (ADS)

Ohnishi, Teruaki

2017-12-01

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

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

PubMed Central

Han, Fang; Wang, Zhijie; Fan, Hong

2017-01-01

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

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

PubMed Central

Lieberman, David N; Mody, Istvan

1999-01-01

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

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

NASA Astrophysics Data System (ADS)

Klimenko, V. V.

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Fathima, Dowlath; Uduman, P. Sheik

2013-09-01

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

The Superstatistical Nature and Interoccurrence Time of Atmospheric Mercury Concentration Fluctuations

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

PubMed

Wang, Dongshu; Huang, Lihong

2014-03-01

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

Probability Distributions for Random Quantum Operations

NASA Astrophysics Data System (ADS)

Schultz, Kevin

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

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

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

PubMed

Vadeby, Anna; Forsman, Åsa

2017-06-01

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

Momentum distributions for the quantum delta-kicked rotor with decoherence

PubMed

Vant; Ball; Christensen

2000-05-01

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

Reliability Overhaul Model

DTIC Science & Technology

1989-08-01

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

Topics in the Sequential Design of Experiments

DTIC Science & Technology

1992-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-08-01

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

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

PubMed

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

2011-03-01

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

Analytic solutions to modelling exponential and harmonic functions using Chebyshev polynomials: fitting frequency-domain lifetime images with photobleaching.

PubMed

Malachowski, George C; Clegg, Robert M; Redford, Glen I

2007-12-01

A novel approach is introduced for modelling linear dynamic systems composed of exponentials and harmonics. The method improves the speed of current numerical techniques up to 1000-fold for problems that have solutions of multiple exponentials plus harmonics and decaying components. Such signals are common in fluorescence microscopy experiments. Selective constraints of the parameters being fitted are allowed. This method, using discrete Chebyshev transforms, will correctly fit large volumes of data using a noniterative, single-pass routine that is fast enough to analyse images in real time. The method is applied to fluorescence lifetime imaging data in the frequency domain with varying degrees of photobleaching over the time of total data acquisition. The accuracy of the Chebyshev method is compared to a simple rapid discrete Fourier transform (equivalent to least-squares fitting) that does not take the photobleaching into account. The method can be extended to other linear systems composed of different functions. Simulations are performed and applications are described showing the utility of the method, in particular in the area of fluorescence microscopy.

Relationships between Heavy Metal Concentrations in Roadside Topsoil and Distance to Road Edge Based on Field Observations in the Qinghai-Tibet Plateau, China

PubMed Central

Yan, Xuedong; Gao, Dan; Zhang, Fan; Zeng, Chen; Xiang, Wang; Zhang, Man

2013-01-01

This study investigated the spatial distribution of copper (Cu), zinc (Zn), cadmium (Cd), lead (Pb), chromium (Cr), cobalt (Co), nickel (Ni) and arsenic (As) in roadside topsoil in the Qinghai-Tibet Plateau and evaluated the potential environmental risks of these roadside heavy metals due to traffic emissions. A total of 120 topsoil samples were collected along five road segments in the Qinghai-Tibet Plateau. The nonlinear regression method was used to formulize the relationship between the metal concentrations in roadside soils and roadside distance. The Hakanson potential ecological risk index method was applied to assess the degrees of heavy metal contaminations. The regression results showed that both of the heavy metals’ concentrations and their ecological risk indices decreased exponentially with the increase of roadside distance. The large R square values of the regression models indicate that the exponential regression method can suitably describe the relationship between heavy metal accumulation and roadside distance. For the entire study region, there was a moderate level of potential ecological risk within a 10 m roadside distance. However, Cd was the only prominent heavy metal which posed potential hazard to the local soil ecosystem. Overall, the rank of risk contribution to the local environments among the eight heavy metals was Cd > As > Ni > Pb > Cu > Co > Zn > Cr. Considering that Cd is a more hazardous heavy metal than other elements for public health, the local government should pay special attention to this traffic-related environmental issue. PMID:23439515

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Recurrence time statistics for finite size intervals

NASA Astrophysics Data System (ADS)

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

2004-12-01

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

Fast self contained exponential random deviate algorithm

NASA Astrophysics Data System (ADS)

Fernández, Julio F.

1997-03-01

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

Rainbow net analysis of VAXcluster system availability

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Capitalizing on the Dynamic Features of Excel to Consider Growth Rates and Limits

ERIC Educational Resources Information Center

Taylor, Daniel; Moore-Russo, Deborah

2012-01-01

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

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

PubMed Central

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

2018-01-01

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

Quantitative ultrasound backscatter for pulsed cavitational ultrasound therapy- histotripsy.

PubMed

Wang, Tzu-yin; Xu, Zhen; Winterroth, Frank; Hall, Timothy L; Fowlkes, J Brian; Rothman, Edward D; Roberts, William W; Cain, Charles A

2009-05-01

Histotripsy is a well-controlled ultrasonic tissue ablation technology that mechanically and progressively fractionates tissue structures using cavitation. The fractionated tissue volume can be monitored with ultrasound imaging because a significant ultrasound backscatter reduction occurs.This paper correlates the ultrasound backscatter reduction with the degree of tissue fractionation characterized by the percentage of remaining normal-appearing cell nuclei on histology.Different degrees of tissue fractionation were generated in vitro in freshly excised porcine kidneys by varying the number of therapeutic ultrasound pulses from 100 to 2000 pulses per treatment location. All ultrasound pulses were 15 cycles at 1 MHz delivered at 100 Hz pulse repetition frequency and 19 MPa peak negative pressure. The results showed that the normalized backscatter intensity decreased exponentially with increasing number of pulses. Correspondingly, the percentage of normal appearing nuclei in the treated area decreased exponentially as well. A linear correlation existed between the normalized backscatter intensity and the percentage of normal appearing cell nuclei in the treated region. This suggests that the normalized backscatter intensity may be a potential quantitative real-time feedback parameter for histotripsy-induced tissue fractionation. This quantitative feedback may allow the prediction of local clinical outcomes, i.e., when a tissue volume has been sufficiently treated.

Separability of spatiotemporal spectra of image sequences. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Eckert, Michael P.; Buchsbaum, Gershon; Watson, Andrew B.

1992-01-01

The spatiotemporal power spectrum was calculated of 14 image sequences in order to determine the degree to which the spectra are separable in space and time, and to assess the validity of the commonly used exponential correlation model found in the literature. The spectrum was expanded by a Singular Value Decomposition into a sum of separable terms and an index was defined of spatiotemporal separability as the fraction of the signal energy that can be represented by the first (largest) separable term. All spectra were found to be highly separable with an index of separability above 0.98. The power spectra of the sequences were well fit by a separable model. The power spectrum model corresponds to a product of exponential autocorrelation functions separable in space and time.

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

NASA Astrophysics Data System (ADS)

Kjellander, Roland

2006-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

ERIC Educational Resources Information Center

Macek, Victor C.

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

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

ERIC Educational Resources Information Center

Steinhauser, Marco; Hubner, Ronald

2009-01-01

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

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

ERIC Educational Resources Information Center

Gwanyama, Philip Wagala

2005-01-01

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

Individual and group dynamics in purchasing activity

NASA Astrophysics Data System (ADS)

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

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

Yang, Jiefan; Lei, Hengchi

2016-02-01

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

The Lunar Rock Size Frequency Distribution from Diviner Infrared Measurements

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Hazard function analysis for flood planning under nonstationarity

NASA Astrophysics Data System (ADS)

Read, Laura K.; Vogel, Richard M.

2016-05-01

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

Numerical investigations of two-degree-of-freedom vortex-induced vibration in shear flow

NASA Astrophysics Data System (ADS)

Zhang, Hui; Liu, Mengke; Han, Yang; Li, Jian; Gui, Mingyue; Chen, Zhihua

2017-06-01

Exponential-polar coordinates attached to a moving cylinder are used to deduce the stream function-vorticity equations for two-degree-of-freedom vortex-induced vibration, the initial and boundary conditions, and the distribution of the hydrodynamic force, which consists of the vortex-induced force, inertial force, and viscous damping force. The fluid-structure interactions occurring from the motionless cylinder to the steady vibration are investigated numerically, and the variations of the flow field, pressure, lift/drag, and cylinder displacement are discussed. Both the dominant vortex and the cylinder shift, whose effects are opposite, affect the shear layer along the transverse direction and the secondary vortex along the streamwise direction. However, the effect of the cylinder shift is larger than that of the dominant vortices. Therefore, the former dominates the total effects of the flow field. Moreover, the symmetry of the flow field is broken with the increasing shear rate. With the effect of the background vortex, the upper vortices are strengthened, and the lower vortices are weakened; thus, the shear layer and the secondary vortices induced by the upper shedding vortices are strengthened, while the shear layer and the secondary vortices induced by the lower shedding vortices are weakened. Therefore, the amplitudes of the displacement and drag/lift dominated by the upper vortex are larger than those of the displacement and drag/lift dominated by the lower vortex.

The non-hydrostatic figures of the terrestrial planets

NASA Technical Reports Server (NTRS)

Runcorn, S. K.

1985-01-01

Solid state creep being exponentially dependent on temperature must dominate the mechanical behavior of the mantles of terrestrial planets beneath their lithospheres. General arguments suggest that the lithospheres of the Moon and Mars are about 200 km thick; the Earth, Venus and Mercury much less. Short wavelength gravity anomalies are explained by the finite strength of the lithosphere: the lunar mascons being an example. The good correlation of the Venus and Mars gravity anomalies with topography up to spherical harmonics of degrees 10-15 is in striking contrast to the lack of correlation between the long wavelength components of the geoid and the continent-ocean distribution or even the plates. Attempts have been made to explain the former correlations by isostatic models but the depths of compensation seem implausible. Low degree harmonics of the gravity fields of the terrestrial planets as is certainly the case in the Earth must arise from the density variations driving solid state convection. In the case of Venus the less dense differentiated materials of the highlands seems to be positioned over the singular points of the convection pattern. Thus the correlated gravity field does not arise from the highlands but from the density difference in the convecting interior. In the Earth lack of correlation seems to arise from the fact that the plates have moved relative to the convection pattern the last 100 M yr.

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

PubMed

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

2012-08-01

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

Markov Analysis of Sleep Dynamics

NASA Astrophysics Data System (ADS)

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

2009-05-01

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

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

PubMed Central

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Experience versus talent shapes the structure of the Web.

PubMed

Kong, Joseph S; Sarshar, Nima; Roychowdhury, Vwani P

2008-09-16

We use sequential large-scale crawl data to empirically investigate and validate the dynamics that underlie the evolution of the structure of the web. We find that the overall structure of the web is defined by an intricate interplay between experience or entitlement of the pages (as measured by the number of inbound hyperlinks a page already has), inherent talent or fitness of the pages (as measured by the likelihood that someone visiting the page would give a hyperlink to it), and the continual high rates of birth and death of pages on the web. We find that the web is conservative in judging talent and the overall fitness distribution is exponential, showing low variability. The small variance in talent, however, is enough to lead to experience distributions with high variance: The preferential attachment mechanism amplifies these small biases and leads to heavy-tailed power-law (PL) inbound degree distributions over all pages, as well as over pages that are of the same age. The balancing act between experience and talent on the web allows newly introduced pages with novel and interesting content to grow quickly and surpass older pages. In this regard, it is much like what we observe in high-mobility and meritocratic societies: People with entitlement continue to have access to the best resources, but there is just enough screening for fitness that allows for talented winners to emerge and join the ranks of the leaders. Finally, we show that the fitness estimates have potential practical applications in ranking query results.

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

NASA Technical Reports Server (NTRS)

Leybold, H. A.

1971-01-01

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

The decline and fall of Type II error rates

Treesearch

Steve Verrill; Mark Durst

2005-01-01

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

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

NASA Astrophysics Data System (ADS)

Silva, Antonio

2005-03-01

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

The competitiveness versus the wealth of a country.

PubMed

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

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

The competitiveness versus the wealth of a country

PubMed Central

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

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2016-07-01

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

The competitiveness versus the wealth of a country

NASA Astrophysics Data System (ADS)

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

2012-09-01

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

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

NASA Astrophysics Data System (ADS)

Kumagai, Yoshiaki

2010-04-01

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

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

NASA Technical Reports Server (NTRS)

Solakiewicz, Richard; Attele, Rohan; Koshak, William

2011-01-01

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

Degrees of Change: How New Kinds of Professional Doctorates Are Changing Higher Education Institutions. Research & Occasional Paper Series: CSHE.8.13

ERIC Educational Resources Information Center

Zusman, Ami

2013-01-01

Over the past fifteen years, new types of "professional practice" doctorates in fields ranging from nursing to bioethics have increased exponentially, from near zero to over 500 programs in at least a dozen fields in the U.S. today. This growth raises many policy questions. For example, do doctorate holders serve their clients and…

Enhancing the violation of the einstein-podolsky-rosen local realism by quantum hyperentanglement.

PubMed

Barbieri, Marco; De Martini, Francesco; Mataloni, Paolo; Vallone, Giuseppe; Cabello, Adán

2006-10-06

Mermin's observation [Phys. Rev. Lett. 65, 1838 (1990)] that the magnitude of the violation of local realism, defined as the ratio between the quantum prediction and the classical bound, can grow exponentially with the size of the system is demonstrated using two-photon hyperentangled states entangled in polarization and path degrees of freedom, and local measurements of polarization and path simultaneously.

Novel mechanism of dissipation in synthetic rotary motors

NASA Astrophysics Data System (ADS)

Barbu, Corina; Crespi, Vincent

2007-03-01

We study novel mechanisms of dissipation in nanoscale and molecular-scale motors. In traditional treatments of such systems, the background degrees of freedom are integrated out into a thermal bath, and the rotator is coupled directly to this bath via phenomenological terms such as viscous damping or Langevin forces. We have investigated a situation in which one degree of freedom is pulled out from the thermal bath and into the explicit equations of motion, interposed between the bath and the motor. We describe a regime in which the deceleration of an unpowered rotor follows a universal power law, rather than a standard exponential decay.

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

NASA Astrophysics Data System (ADS)

Sonam, Sonam; Jain, Vikrant

2017-04-01

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

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

PubMed

Minor, A V; Kaissling, K-E

2003-03-01

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

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

NASA Astrophysics Data System (ADS)

Tomaschitz, Roman

2016-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2010-10-01

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

A study of personal income distributions in Australia and Italy

NASA Astrophysics Data System (ADS)

Banerjee, Anand; Yakovenko, Victor

2006-03-01

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

Dynamical analysis for a scalar-tensor model with kinetic and nonminimal couplings

NASA Astrophysics Data System (ADS)

Granda, L. N.; Jimenez, D. F.

We study the autonomous system for a scalar-tensor model of dark energy with nonminimal coupling to curvature and nonminimal kinetic coupling to the Einstein tensor. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential were considered: power-law and exponential functions of the scalar field. For power-law couplings, the restrictions on stable quintessence and phantom solutions lead to asymptotic freedom regime for the gravitational interaction. For the exponential functions, the stable quintessence, phantom or de Sitter solutions allow asymptotic behaviors where the effective Newtonian coupling can reach either the asymptotic freedom regime or constant value. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation dominated phases can also be described.

Learning Search Control Knowledge for Deep Space Network Scheduling

NASA Technical Reports Server (NTRS)

Gratch, Jonathan; Chien, Steve; DeJong, Gerald

1993-01-01

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

Inland empire logistics GIS mapping project.

DOT National Transportation Integrated Search

2009-01-01

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

Anomalous Diffusion in a Trading Model

NASA Astrophysics Data System (ADS)

Khidzir, Sidiq Mohamad; Wan Abdullah, Wan Ahmad Tajuddin

2009-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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

DTIC Science & Technology

1977-12-01

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

Droplet size and velocity distributions for spray modelling

NASA Astrophysics Data System (ADS)

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

2012-01-01

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

The Steep Nekhoroshev's Theorem

NASA Astrophysics Data System (ADS)

Guzzo, M.; Chierchia, L.; Benettin, G.

2016-03-01

Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.

Quantitative Ultrasound Backscatter for Pulsed Cavitational Ultrasound Therapy—Histotripsy

PubMed Central

Wang, Tzu-Yin; Xu, Zhen; Winterroth, Frank; Hall, Timothy L.; Fowlkes, J. Brian; Rothman, Edward D.; Roberts, William W.; Cain, Charles A.

2011-01-01

Histotripsy is a well-controlled ultrasonic tissue ablation technology that mechanically and progressively fractionates tissue structures using cavitation. The fractionated tissue volume can be monitored with ultrasound imaging because a significant ultrasound backscatter reduction occurs. This paper correlates the ultrasound backscatter reduction with the degree of tissue fractionation characterized by the percentage of remaining normal-appearing cell nuclei on histology. Different degrees of tissue fractionation were generated in vitro in freshly excised porcine kidneys by varying the number of therapeutic ultrasound pulses from 100 to 2000 pulses per treatment location. All ultrasound pulses were 15 cycles at 1 MHz delivered at 100 Hz pulse repetition frequency and 19 MPa peak negative pressure. The results showed that the normalized backscatter intensity decreased exponentially with increasing number of pulses. Correspondingly, the percentage of normal appearing nuclei in the treated area decreased exponentially as well. A linear correlation existed between the normalized backscatter intensity and the percentage of normal appearing cell nuclei in the treated region. This suggests that the normalized backscatter intensity may be a potential quantitative real-time feedback parameter for histotripsy-induced tissue fractionation. This quantitative feedback may allow the prediction of local clinical outcomes, i.e., when a tissue volume has been sufficiently treated. PMID:19750596

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.

Relationship between frequency power spectra and intermittent, large-amplitude bursts in the Alcator C-Mod scrape-off layer

NASA Astrophysics Data System (ADS)

Theodorsen, A.; Garcia, O. E.; Kube, R.; LaBombard, B.; Terry, J. L.

2017-11-01

Fluctuations in the boundary region of the Alcator C-Mod tokamak have been analyzed using gas puff imaging data from a set of Ohmically heated plasma density scan experiments. It is found that the relative fluctuation amplitudes are modest and close to normally distributed at the separatrix but become increasingly larger and skewed towards the main chamber wall. The frequency power spectra are nevertheless similar for all radial positions and line-averaged densities. Predictions of a stochastic model, describing the plasma fluctuations as a super-position of uncorrelated pulses, are shown to be in excellent agreement with the measurements. This implies that the pulse duration is the same, while the degree of pulse overlap decreases radially outwards in the scrape-off layer. The universal frequency power spectral density is thus determined by the shape and duration of the large-amplitude bursts associated with blob-like structures. The model also describes the rate of threshold level crossings, for which the exponential tails underline the intermittency of the fluctuations in the far scarpe-off layer.

Widespread Nanoflare Variability Detected with Hinode/XRT in a Solar Active Region

NASA Technical Reports Server (NTRS)

Reale, Fabio; Terzo, Sergio; Miceli, Marco; Klimchuk, James A.; Kano, Ryouhei; Tsuneta, Saku

2011-01-01

It is generally agreed that small impulsive energy bursts called nanoflares are responsible for at least some of the Sun s hot corona, but whether they are the explanation for most of the multi-million degree plasma has been a matter of ongoing debate. We here present evidence that nanoflares are widespread in an active region observed by the X-Ray Telescope on-board the Hinode mission. The distributions of intensity fluctuations have small but important asymmetries, whether taken from individual pixels, multi-pixel subregions, or the entire active region. Negative fluctuations (corresponding to reduced intensity) are greater in number but weaker in amplitude, so that the median fluctuation is negative compared to a mean of zero. Using Monte Carlo simulations, we show that only part of this asymmetry can be explained by Poisson photon statistics. The remainder is explainable with a tendency for exponentially decreasing intensity, such as would be expected from a cooling plasma produced, e.g., from a nanoflare. We suggest that nanoflares are a universal heating process within active regions.

Functional network inference of the suprachiasmatic nucleus

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

Abel, John H.; Meeker, Kirsten; Granados-Fuentes, Daniel

2016-04-04

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data frommore » individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure.« less

Extended state observer based robust adaptive control on SE(3) for coupled spacecraft tracking maneuver with actuator saturation and misalignment

NASA Astrophysics Data System (ADS)

Zhang, Jianqiao; Ye, Dong; Sun, Zhaowei; Liu, Chuang

2018-02-01

This paper presents a robust adaptive controller integrated with an extended state observer (ESO) to solve coupled spacecraft tracking maneuver in the presence of model uncertainties, external disturbances, actuator uncertainties including magnitude deviation and misalignment, and even actuator saturation. More specifically, employing the exponential coordinates on the Lie group SE(3) to describe configuration tracking errors, the coupled six-degrees-of-freedom (6-DOF) dynamics are developed for spacecraft relative motion, in which a generic fully actuated thruster distribution is considered and the lumped disturbances are reconstructed by using anti-windup technique. Then, a novel ESO, developed via second order sliding mode (SOSM) technique and adding linear correction terms to improve the performance, is designed firstly to estimate the disturbances in finite time. Based on the estimated information, an adaptive fast terminal sliding mode (AFTSM) controller is developed to guarantee the almost global asymptotic stability of the resulting closed-loop system such that the trajectory can be tracked with all the aforementioned drawbacks addressed simultaneously. Finally, the effectiveness of the controller is illustrated through numerical examples.

Individual T1-weighted/T2-weighted ratio brain networks: Small-worldness, hubs and modular organization

NASA Astrophysics Data System (ADS)

Wu, Huijun; Wang, Hao; Lü, Linyuan

Applying network science to investigate the complex systems has become a hot topic. In neuroscience, understanding the architectures of complex brain networks was a vital issue. An enormous amount of evidence had supported the brain was cost/efficiency trade-off with small-worldness, hubness and modular organization through the functional MRI and structural MRI investigations. However, the T1-weighted/T2-weighted (T1w/T2w) ratio brain networks were mostly unexplored. Here, we utilized a KL divergence-based method to construct large-scale individual T1w/T2w ratio brain networks and investigated the underlying topological attributes of these networks. Our results supported that the T1w/T2w ratio brain networks were comprised of small-worldness, an exponentially truncated power-law degree distribution, frontal-parietal hubs and modular organization. Besides, there were significant positive correlations between the network metrics and fluid intelligence. Thus, the T1w/T2w ratio brain networks open a new avenue to understand the human brain and are a necessary supplement for future MRI studies.

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

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-08-01

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

Parabolic replicator dynamics and the principle of minimum Tsallis information gain

PubMed Central

2013-01-01

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

Temperature variation and distribution of living cells within tree stems: implications for stem respiration modeling and scale-up.

PubMed

Stockfors, J

2000-09-01

Few studies have examined variation in respiration rates within trees, and even fewer studies have focused on variation caused by within-stem temperature differences. In this study, stem temperatures at 40 positions in the stem of one 30-year-old Norway spruce (Picea abies (L.) Karst.) were measured during 40 days between July 1994 and June 1995. The temperature data were used to simulate variations in respiration rate within the stem. The simulations assumed that the temperature-respiration relationship was constant (Q10 = 2) for all days and all stem positions. Total respiration for the whole stem was calculated by interpolating the temperature between the thermocouples and integrating the respiration rates in three dimensions. Total respiration rate of the stem was then compared to respiration rate scaled up from horizontal planes at the thermocouple heights (40, 140, 240 and 340 cm) on a surface area and on a sapwood volume basis. Simulations were made for three distributions of living cells in the stems: one with a constant 5% fraction of living cells, disregarding depth into the stem; one with a living cell fraction decreasing linearly with depth into the stem; and one with an exponentially decreasing fraction of living cells. Mean temperature variation within the stem was 3.7 degrees C, and was more than 10 degrees C for 8% of the time. The maximum measured temperature difference was 21.5 degrees C. The corresponding mean variation in respiration was 35% and was more than 50% for 24% of the time. Scaling up respiration rates from different heights between 40 and 240 cm to the whole stem produced an error of 2 to 58% for the whole year. For a single sunny day, the error was between 2 and 72%. Thus, within-stem variations in temperature may significantly affect the accuracy of scaling respiration data obtained from small samples to whole trees. A careful choice of chamber position and basis for scaling is necessary to minimize errors from variation in temperature.

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

NASA Astrophysics Data System (ADS)

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

2006-03-01

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

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

NASA Astrophysics Data System (ADS)

Bandi, Mahesh M.; Connaughton, Colm

2008-03-01

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

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

PubMed Central

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

2012-01-01

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

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

PubMed

Bandi, Mahesh M; Connaughton, Colm

2008-03-01

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

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

PubMed Central

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

2011-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2011-06-01

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

Mathematical Aspects of Reliability-Centered Maintenance

DTIC Science & Technology

1977-01-01

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

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

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

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

2013-03-15

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

Fluctuations in Wikipedia access-rate and edit-event data

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

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

PubMed Central

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

2009-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

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

PubMed Central

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

2016-01-01

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

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

PubMed

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

2015-10-01

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

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

NASA Astrophysics Data System (ADS)

Jain, Rohit; Sebastian, K. L.

2017-03-01

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

Adsorption of finite semiflexible polymers and their loop and tail distributions

NASA Astrophysics Data System (ADS)

Kampmann, Tobias A.; Kierfeld, Jan

2017-07-01

We discuss the adsorption of semiflexible polymers to a planar attractive wall and focus on the questions of the adsorption threshold for polymers of finite length and their loop and tail distributions using both Monte Carlo simulations and analytical arguments. For the adsorption threshold, we find three regimes: (i) a flexible or Gaussian regime if the persistence length is smaller than the adsorption potential range, (ii) a semiflexible regime if the persistence length is larger than the potential range, and (iii) for finite polymers, a novel crossover to a rigid rod regime if the deflection length exceeds the contour length. In the flexible and semiflexible regimes, finite size corrections arise because the correlation length exceeds the contour length. In the rigid rod regime, however, it is essential how the global orientational or translational degrees of freedom are restricted by grafting or confinement. We discuss finite size corrections for polymers grafted to the adsorbing surface and for polymers confined by a second (parallel) hard wall. Based on these results, we obtain a method to analyze adsorption data for finite semiflexible polymers such as filamentous actin. For the loop and tail distributions, we find power laws with an exponential decay on length scales exceeding the correlation length. We derive and confirm the loop and tail power law exponents for flexible and semiflexible polymers. This allows us to explain that, close to the transition, semiflexible polymers have significantly smaller loops and both flexible and semiflexible polymers desorb by expanding their tail length. The tail distribution allows us to extract the free energy per length of adsorption for actin filaments from experimental data [D. Welch et al., Soft Matter 11, 7507 (2015)].

Geostatistical analysis of fault and joint measurements in Austin Chalk, Superconducting Super Collider Site, Texas

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

Mace, R.E.; Nance, H.S.; Laubach, S.E.

1995-06-01

Faults and joints are conduits for ground-water flow and targets for horizontal drilling in the petroleum industry. Spacing and size distribution are rarely predicted accurately by current structural models or documented adequately by conventional borehole or outcrop samples. Tunnel excavations present opportunities to measure fracture attributes in continuous subsurface exposures. These fracture measurements ran be used to improve structural models, guide interpretation of conventional borehole and outcrop data, and geostatistically quantify spatial and spacing characteristics for comparison to outcrop data or for generating distributions of fracture for numerical flow and transport modeling. Structure maps of over 9 mi of nearlymore » continuous tunnel excavations in Austin Chalk at the Superconducting Super Collider (SSC) site in Ellis County, Texas, provide a unique database of fault and joint populations for geostatistical analysis. Observationally, small faults (<10 ft. throw) occur in clusters or swarms that have as many as 24 faults, fault swarms are as much as 2,000 ft. wide and appear to be on average 1,000 ft. apart, and joints are in swarms spaced 500 to more than 2l,000 ft. apart. Semi-variograms show varying degrees of spatial correlation. These variograms have structured sills that correlate directly to highs and lows in fracture frequency observed in the tunnel. Semi-variograms generated with respect to fracture spacing and number also have structured sills, but tend to not show any near-field correlation. The distribution of fault spacing can be described with a negative exponential, which suggests a random distribution. However, there is clearly some structure and clustering in the spacing data as shown by running average and variograms, which implies that a number of different methods should be utilized to characterize fracture spacing.« less

Obstructive sleep apnea alters sleep stage transition dynamics.

PubMed

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

2010-06-28

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

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2017-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and [Formula: see text] robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Combining Orthogonal Chain-End Deprotections and Thiol-Maleimide Michael Coupling: Engineering Discrete Oligomers by an Iterative Growth Strategy.

PubMed

Huang, Zhihao; Zhao, Junfei; Wang, Zimu; Meng, Fanying; Ding, Kunshan; Pan, Xiangqiang; Zhou, Nianchen; Li, Xiaopeng; Zhang, Zhengbiao; Zhu, Xiulin

2017-10-23

Orthogonal maleimide and thiol deprotections were combined with thiol-maleimide coupling to synthesize discrete oligomers/macromolecules on a gram scale with molecular weights up to 27.4 kDa (128mer, 7.9 g) using an iterative exponential growth strategy with a degree of polymerization (DP) of 2 n -1. Using the same chemistry, a "readable" sequence-defined oligomer and a discrete cyclic topology were also created. Furthermore, uniform dendrons were fabricated using sequential growth (DP=2 n -1) or double exponential dendrimer growth approaches (DP=22n -1) with significantly accelerated growth rates. A versatile, efficient, and metal-free method for construction of discrete oligomers with tailored structures and a high growth rate would greatly facilitate research into the structure-property relationships of sophisticated polymeric materials. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and H2 robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:28959117

Human vertical eye movement responses to earth horizontal pitch

NASA Technical Reports Server (NTRS)

Wall, C. 3rd; Petropoulos, A. E.

1993-01-01

The vertical eye movements in humans produced in response to head-over-heels constant velocity pitch rotation about a horizontal axis resemble those from other species. At 60 degrees/s these are persistent and tend to have non-reversing slow components that are compensatory to the direction of rotation. In most, but not all subjects, the slow component velocity was well characterized by a rapid build-up followed by an exponential decay to a non-zero baseline. Super-imposed was a cyclic or modulation component whose frequency corresponded to the time for one revolution and whose maximum amplitude occurred during a specific head orientation. All response components (exponential decay, baseline and modulation) were larger during pitch backward compared to pitch forward runs. Decay time constants were shorter during the backward runs, thus, unlike left to right yaw axis rotation, pitch responses display significant asymmetries between paired forward and backward runs.

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

NASA Astrophysics Data System (ADS)

Romero, Natalia E.

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

Frequency Distribution of Seismic Intensity in Japan between 1950 and 2009

NASA Astrophysics Data System (ADS)

Kato, M.; Kohayakawa, Y.

2012-12-01

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

Wigner functions for evanescent waves.

PubMed

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

2012-09-01

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

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

PubMed Central

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

2012-01-01

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

Verification of the exponential model of body temperature decrease after death in pigs.

PubMed

Kaliszan, Michal; Hauser, Roman; Kaliszan, Roman; Wiczling, Paweł; Buczyñski, Janusz; Penkowski, Michal

2005-09-01

The authors have conducted a systematic study in pigs to verify the models of post-mortem body temperature decrease currently employed in forensic medicine. Twenty-four hour automatic temperature recordings were performed in four body sites starting 1.25 h after pig killing in an industrial slaughterhouse under typical environmental conditions (19.5-22.5 degrees C). The animals had been randomly selected under a regular manufacturing process. The temperature decrease time plots drawn starting 75 min after death for the eyeball, the orbit soft tissues, the rectum and muscle tissue were found to fit the single-exponential thermodynamic model originally proposed by H. Rainy in 1868. In view of the actual intersubject variability, the addition of a second exponential term to the model was demonstrated to be statistically insignificant. Therefore, the two-exponential model for death time estimation frequently recommended in the forensic medicine literature, even if theoretically substantiated for individual test cases, provides no advantage as regards the reliability of estimation in an actual case. The improvement of the precision of time of death estimation by the reconstruction of an individual curve on the basis of two dead body temperature measurements taken 1 h apart or taken continuously for a longer time (about 4 h), has also been proved incorrect. It was demonstrated that the reported increase of precision of time of death estimation due to use of a multiexponential model, with individual exponential terms to account for the cooling rate of the specific body sites separately, is artifactual. The results of this study support the use of the eyeball and/or the orbit soft tissues as temperature measuring sites at times shortly after death. A single-exponential model applied to the eyeball cooling has been shown to provide a very precise estimation of the time of death up to approximately 13 h after death. For the period thereafter, a better estimation of the time of death is obtained from temperature data collected from the muscles or the rectum.

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

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2016-02-01

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

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

PubMed

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

2013-07-21

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

Power laws in citation distributions: evidence from Scopus.

PubMed

Brzezinski, Michal

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

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

PubMed

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2013-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS

PubMed Central

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2015-01-01

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

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

PubMed Central

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

1998-01-01

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

None of the Above

ERIC Educational Resources Information Center

Ray, Mark

2013-01-01

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

Revealing the microstructure of the giant component in random graph ensembles

NASA Astrophysics Data System (ADS)

Tishby, Ido; Biham, Ofer; Katzav, Eytan; Kühn, Reimer

2018-04-01

The microstructure of the giant component of the Erdős-Rényi network and other configuration model networks is analyzed using generating function methods. While configuration model networks are uncorrelated, the giant component exhibits a degree distribution which is different from the overall degree distribution of the network and includes degree-degree correlations of all orders. We present exact analytical results for the degree distributions as well as higher-order degree-degree correlations on the giant components of configuration model networks. We show that the degree-degree correlations are essential for the integrity of the giant component, in the sense that the degree distribution alone cannot guarantee that it will consist of a single connected component. To demonstrate the importance and broad applicability of these results, we apply them to the study of the distribution of shortest path lengths on the giant component, percolation on the giant component, and spectra of sparse matrices defined on the giant component. We show that by using the degree distribution on the giant component one obtains high quality results for these properties, which can be further improved by taking the degree-degree correlations into account. This suggests that many existing methods, currently used for the analysis of the whole network, can be adapted in a straightforward fashion to yield results conditioned on the giant component.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

PubMed

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

2015-01-01

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

Traction forces during collective cell motion.

PubMed

Gov, N S

2009-08-01

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

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

NASA Astrophysics Data System (ADS)

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

1995-06-01

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

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

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

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

2004-06-01

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

Work fluctuations for Bose particles in grand canonical initial states.

PubMed

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

2012-05-01

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

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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