Effects of heterogeneous adoption thresholds on contact-limited social contagions

Limited contact capacity and heterogeneous adoption thresholds have been proven to be two essential characteristics of individuals in natural complex social systems, and their impacts on social contagions exhibit complex nature. With this in mind, a heterogeneous contact-limited threshold model is proposed, which adopts one of four threshold distributions, namely Gaussian distribution, log-normal distribution, exponential distribution and power-law distribution. The heterogeneous edge-based compartmental theory is developed for theoretical analysis, and the calculation methods of the final adoption size and outbreak threshold are given theoretically. Many numerical simulations are performed on the Erdös-Rényi and scale-free networks to study the impact of different forms of the threshold distribution on hierarchical spreading process, the final adoption size, the outbreak threshold and the phase transition in contact-limited propagation networks. We find that the spreading process of social contagions is divided into three distinct stages. Moreover, different threshold distributions cause different spreading processes, especially for some threshold distributions, there is a change from a discontinuous first-order phase transition to a continuous second-order phase transition. Further, we find that changing the standard deviation of different threshold distributions will cause the final adoption size and outbreak threshold to change, and finally tend to be stable with the increase of standard deviation.     

Lévy-statistics for partially equilibrated systems

We examine deviations from Boltzmann-Gibbs statistics for a certain class of partially equilibrated systems of finite size. We find that such systems are characterized by the Lévy distribution whose non-extensivity parameter is related to the number of internally equilibrated subsystems and to correlations among them. This concept is applicable to relativistic heavy ion collisions.     

Calculating statistics of complex networks through random walks with an application to the on-line social network Bebo

We develop a methodology with which to calculate typical network statistics by sampling a network through a random walk. By examining the statistics of degree and return times of walks which return to the same vertex, we can estimate characteristics of the giant component such as average clustering coefficient, degree distribution, degree correlations and network size. We confirm the validity of the methods using a variety of available network network data sets and then apply these methods to data collected by performing a random walk on the large on-line social networking website, Bebo. We find good agreement between our results and the results of previous studies of on-line social networks in which data collection was performed by a BFS (“snow-ball”) sampling algorithm. In particular, we find that the degree distribution exhibits a multi-scaling power-law tail and the network exhibits clustering and positive degree correlations.     

Statistics of narrow distributions

In expressing the results of particle size analysis from micrographs, i t is customary to report statistics of the distribution such as mean diameter and standard deviation, together with various weighted average diameters. Each of these values represents one or more moments of the distribution, as do the various average particle sizes which are determined by different experimental methods. An analogous situation prevails in the reporting of molecular weights of heterogeneous polymers. During recent extensive work in this laboratory on lattices of very narrow-size distributions, correlations among the various statistics became apparent; this led us to consider the narrow distribution as a special limiting case.     

Billion-atom synchronous parallel kinetic Monte Carlo simulations of critical 3D Ising systems

An extension of the synchronous parallel kinetic Monte Carlo (spkMC) algorithm developed by Martinez et al. [J. Comp. Phys. 227 (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors’ time clocks current in a global sense. Boundary conflicts are resolved by adopting a chessboard decomposition into non-interacting sublattices. We find that the bias introduced by the spatial correlations attendant to the sublattice decomposition is within the standard deviation of serial calculations, which confirms the statistical validity of our algorithm. We have analyzed the parallel efficiency of spkMC and find that it scales consistently with problem size and sublattice partition. We apply the method to the calculation of scale-dependent critical exponents in billion-atom 3D Ising systems, with very good agreement with state-of-the-art multispin simulations.     

基于贝叶斯方法的设备级电磁脉冲效应评估

在电磁脉冲效应试验中,由于所获得的效应数据量一般较少,利用经典的数理统计方法对效应阈值场强进行概率拟合非常困难。基于贝叶斯数理统计方法,对油气管道数据采集与监视控制系统的中心控制系统客户端的电磁脉冲效应数据拟合分析。选择了Weibull分布模型和正态分布模型作为假设模型,并依次求得这两种模型参数的先验分布、似然函数和后验分布。通过拟合优度检验,最后基于贝叶斯信息准则选择形状参数、尺度参数分别为8.87,21.11的Weibull模型作为更合理的阈值场强概率分布模型。     

Growth, percolation, and correlations in disordered fiber networks

This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameterp which controls the degree of clustering. Forp=1 the deposited network is uniformly random, while forp=0 only a single connected cluster can grow. Forp=0 we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. Forp>0 we carry out extensive simulations on fibers, and also needles and disks, to study the dependence of the percolation threshold onp. We also derive a mean-field theory for the threshold nearp=0 andp=1 and find good qualitative agreement with the simulations. The fiber networks produced by the model display nontrivial density correlations forp<1. We study these by deriving an approximate expression for the pair distribution function of the model that reduces to the exactly known case of a uniformly random network. We also show that the two-point mass density correlation function of the model has a nontrivial form, and discuss our results in view of recent experimental data on mss density correlations in paper sheets.     

Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets

We study the statistics of return intervals between events above a certain threshold in multifractal data sets without linear correlations. We find that nonlinear correlations in the record lead to a power-law (i) decay of the autocorrelation function of the return intervals, (ii) increase in the conditional return period, and (iii) decay in the probability density function of the return intervals. We show explicitly that all the observed quantities depend both on the threshold value and system size, and hence there is no simple scaling observed. We also demonstrate that this type of behavior can be observed in real economic records and can be used to improve considerably risk estimation.     

Statistics of count numbers from a photomultiplier tube and its implications for error estimation

We present investigations of counting statistics for five different luminescence-measuring systems. The dark current background and the counts obtained for a PM tube under constant illumination at various light intensities were measured. Where no divider is present in the counting system, the standard deviation of the number of counts exceeds the value predicted by a Poisson distribution but by different amounts in the different systems. This has implications for analysis of the uncertainties in the estimated equivalent doses and other quantitative analyses of luminescence measurements. We suggest how to account for the observed overdispersion of count numbers in uncertainty estimation.     

Recurrence time statistics for finite size intervals

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 Poincare recurrence time statistics.     

Tuning the intensity statistics of random speckle patterns

Speckle patterns are a fundamental tool in a variety of physical and optical applications. Here, we investigate a method of precisely tuning the intensity statistics of random speckle patterns into a desirable pattern that possesses the same spatial correlation length and similar statistics distribution. This tuning mechanism relies on the derivation of the transform function and transmission matrix, which achieves different contrasts while maintaining the same average value or energy level. The statistics properties of the generated speckle patterns are further investigated by analyzing the standard deviation under different fitting parameters. Precisely tuning the intensity statistics of random speckle patterns could be useful for both fundamental research and practical applications, such as microscopy, imaging, and optical manipulation.     

Bell-type inequalities to detect true n-body nonseparability

We analyze the structure of correlations among more than two quantum systems. We introduce a classification of correlations based on the concept of nonseparability, which is different a priori from the concept of entanglement. Generalizing a result of Svetlichny [Phys. Rev. D 35, 3066 (1987)] on three-particle correlations, we find an inequality for n-particle correlations that holds under the most general separability condition and that is violated by some quantum-mechanical states.     

Delocalization due to correlations in two-dimensional disordered systems

We study the spectral statistics of interacting spin-less fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle systems, we compute the low-energy many-body states numerically. While at weak disorder the interactions reduce spectral correlations and lead to localization, for the case of strong disorder we find that a moderate Coulomb interaction has a delocalizing effect. In addition, we observe a non-universal structure in the level-spacing distribution which we attribute to a mechanism reinforcing spectral correlations taking place in small systems at strong disorder.Received: 1 July 2004, Published online: 14 December 2004PACS: 71.27. + a Strongly correlated electron systems; heavy fermions - 73.20.Jc Delocalization processes - 72.15.Rn Localization effects (Anderson or weak localization)     

Finite-size effects on the statistics of extreme events in the BTW model

The BTW Abelian sandpile model is a prominent example of systems showing self-organised criticality (SOC) in the infinite size limit. We study finite-size effects with special focus on the statistics of extreme events, i.e., of particularly large avalanches. Not only the avalanche size probability distribution, but also the mutual independence of large avalanches in the critical state is affected by finite-size effects. Instead of a Poissonian recurrencetime distribution, in the finite system we find a repulsion of extreme events that depends on the avalanche size and not on the respective probability. The dependence of these effects on the system size is investigated and some data collapse is found. Our results imply that SOC is an unsuitable mechanism for the explanation of extreme events which occur in clusters.     

Different Avalanche Behaviors in Different Specific Areas of a System Based on Neural Networks

Based on the standard self-organizing map (SOM) neural network model and an integrate-and-fire mecha-nism, we introduce a kind of coupled map lattice system to investigate scale-invariance behavior in the activity of model neural populations. We find power-law distribution behavior of avalanche size in our model. But more importantly, we find there are different avalanche distribution behaviors in different specific areas of our system, which are formed by the topological learning process of the SOM net.     

Nonextensive formalism and continuous Hamiltonian systems

A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of “statistics from dynamics” in systems out of equilibrium. Among several possible analytical developments which have been proposed, the idea of nonextensive statistics introduced by Tsallis about 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium where the Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more general function Sq while maintaining the formalism of thermodynamics. From a phenomenological viewpoint, nonextensive statistics appeared to be of interest because maximization of the generalized entropy Sq yields the q-exponential distribution which has been successfully used to describe distributions observed in a large class of phenomena, in particular power law distributions for q>1. Here we re-examine the validity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider the q-ideal gas, a model system of quasi-particles where the effect of the interactions are included in the particle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restricted to the range q<1, which raises the question of its formal validity range for continuous Hamiltonian systems.     

A multichannel shot noise approach to describe synaptic background activity in neurons

Systems driven by Poisson-distributed quantal inputs can be described as “shot noise” stochastic processes. This formalism can apply to neurons which receive a large number of Poisson-distributed synaptic inputs of similar quantal size. However, the presence of temporal correlations between these inputs destroys their quantal nature, and such systems can no longer be described by classical shot noise processes. Here, we show that explicit expressions for various statistical properties, such as the amplitude distribution and the power spectral density, can be deduced and investigated as functions of the correlation between input channels. The monotonic behavior of these expressions allows an one-to-one relation between temporal correlations and the statistics of fluctuations. Multi-channel shot noise processes, therefore, open a way to deduce correlations in input patterns by analyzing fluctuations in experimental systems. We discuss applications such as detecting correlations in networks of neurons from intracellular recordings of single neurons.     

随机外磁场对一维Blume-Capel模型动力学性质的影响

近几十年来,量子自旋系统的动力学性质引起了人们的广泛关注,随着研究的不断深入,随机自旋系统的性质受到了人们的重视. 利用递推关系式方法研究了高温极限下随机外磁场中自旋s=1的一维Blume-Capel模型的动力学性质, 通过计算自旋自关联函数和相应的谱密度,探讨了外场对系统动力学行为的影响.研究表明,在无晶格场的情况下, 当外场满足双模分布时,系统的动力学性质存在从中心峰值行为到集体模行为的交跨效应.当外场满足Gauss分布, 标准偏差较小时,系统也存在交跨效应;标准偏差足够大时,系统只表现为无序行为. 另外还研究了晶格场对系统动力学性质的影响,发现晶格场的存在减弱了系统的集体模行为.     

Expressing the Entropy of Lattice Systems as Sums of Conditional Entropies

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively taken into account. Compared to the traditional approach for estimating the entropy density, in which successive approximations build on step-wise extensions of blocks of symbols, we show that one can take larger steps when collecting the statistics necessary to calculate the entropy density of the system. In one dimension this means that, instead of a single sweep over the system in which states are read sequentially, one take several sweeps with larger steps so that eventually the whole lattice is covered. This means that the information in correlations is captured in a different way, and in some situations this will lead to a considerably much faster convergence of the entropy density estimate as a function of the size of the configurations used in the estimate. The formalism is exemplified with both an example of a free energy minimisation scheme for the two-dimensional Ising model, and an example of increasingly complex spatial correlations generated by the time evolution of elementary cellular automaton rule 60.