New approach to statistical description of fluctuating particle fluxes

The probability density functions (PDFs) of the increments of fluctuating particle fluxes are investigated. It is found that the PDFs have heavy power-law tails decreasing as x ^{?α ? 1} at x → ∞. This makes it possible to describe these PDFs in terms of fractionally stable distributions (FSDs) q(x; α, β, θ, λ). The parameters α, β, γ, and λ were estimated statistically using as an example the time samples of fluctuating particle fluxes measured in the edge plasma of the L-2M stellarator. Two series of fluctuating fluxes measured before and after boronization of the vacuum chamber were processed. It is shown that the increments of fluctuating fluxes are well described by DSDs. The effect of boronization on the parameters of FSDs is analyzed. An algorithm for statistically estimating the FSD parameters and a procedure for processing experimental data are described.     

New possibilities for the mathematical modeling of turbulent transport processes in plasma

A new mathematical model is proposed for the probability distributions of the characteristics of the processes observed in turbulent plasmas. The model is based on formal theoretical considerations related to probabilistic limit theorems for a nonhomogeneous random walk and has the form of a finite mixture of Gaussian distributions. The reliability of the model is confirmed by the results of a statistical analysis of the experimental data on density fluctuations in high-temperature plasmas of the L-2M, LHD, and TJ-II stellarators and the local fluctuating flux in the TAU-1 linear device and in the edge plasma of the L-2M stellarator with the use of the estimation-maximization algorithm. It is shown that low-frequency structural turbulence in a magnetized plasma is related to non-Brownian transport, which is determined by the characteristic temporal and spatial scales of the ensembles of stochastic plasma structures. Mechanisms that could be responsible for the random nature of time samples of the local turbulent flux in TAU-1 are indicated. A new physical concept of the intermittence of plasma turbulent pulsations is developed on the basis of the statistical separation of mixtures in terms of the model proposed. The intermittence of plasma pulsations is shown to be associated with the generation of plasma structures (solitons and vortices) and their nonlinear interaction, as well as with their damping and drift.     

Biochemical networks with uncertain parameters

The modelling of biochemical networks becomes delicate if kinetic parameters are varying, uncertain or unknown. Facing this situation, we quantify uncertain knowledge or beliefs about parameters by probability distributions. We show how parameter distributions can be used to infer probabilistic statements about dynamic network properties, such as steady-state fluxes and concentrations, signal characteristics or control coefficients. The parameter distributions can also serve as priors in Bayesian statistical analysis. We propose a graphical scheme, the 'dependence graph', to bring out known dependencies between parameters, for instance, due to the equilibrium constants. If a parameter distribution is narrow, the resulting distribution of the variables can be computed by expanding them around a set of mean parameter values. We compute the distributions of concentrations, fluxes and probabilities for qualitative variables such as flux directions. The probabilistic framework allows the study of metabolic correlations, and it provides simple measures of variability and stochastic sensitivity. It also shows clearly how the variability of biological systems is related to the metabolic response coefficients.     

Harmonic and anharmonic aspects in the dynamics of BPTI: a normal mode analysis and principal component analysis.

A comparison is made between a 200-ps molecular dynamics simulation in vacuum and a normal mode analysis on the protein bovine pancreatic trypsin inhibitor (BPTI) in order to elucidate the dual aspects of harmonicity and anharmonicity in the dynamics of proteins. The molecular dynamics trajectory is analyzed using principal component analysis, an effective harmonic analysis suited for comparison with the results from the normal mode analysis. The results suggest that the first principal component shows qualitatively different behavior from higher principal components and is associated with apparent barrier crossing events on an anharmonic conformational energy surface. The higher principal components appear to have probability distributions that are well approximated by Gaussians, indicating harmonicity. Eliminating the contribution from the first principal component reveals a great deal of correspondence between the 2 methods. This correspondence, however, involves a factor of 2, as the variances of the distribution of the higher principal components are, on average, roughly twice those found from the normal mode analysis. A model is proposed to reconcile these results with those from previous analyses.     

Numerical modeling of the formation of steady-state nonequilibrium distributions of particles interacting through a power-law potential

The formation of a steady-state nonequilibrium distribution function of particles interacting through the repulsive potential U ~ α/r ^β(1≤β≤4), which operates at an infinite range, is studied numerically. The collisional particle dynamics in such a system is investigated using a spatially homogeneous nonlinear collision integral in the Landau-Fokker-Planck form, which is a model Boltzmann collision integral for arbitrary potentials of interaction accompanied by little momentum transfer between particles in collisions. Numerical modeling is based on completely conservative difference schemes. It is shown that the principal condition for the existence of steady-state nonequilibrium distributions is the presence of a particle or an energy flux oriented in the proper manner in momentum space. A steady-state local distribution exists inside the momentum interval between the energy source and sink and has the form of a gradually decreasing function. Since a radical change in the distribution function under nonequilibrium conditions leads to an anomalous enhancement of the conduction of a medium and its emission characteristics, the results obtained can be used, e.g., to predict the behavior of semiconductors with an intrinsic or extrinsic conductivity under the action of particle fluxes or electromagnetic radiation.     

Establishment Probability in Fluctuating Environments: A Branching Process Model

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.     

On the origin of skewed distributions of spontaneous synaptic potentials in autonomic ganglia.

The histograms of spontaneous synaptic potentials at synapses in autonomic ganglia are described by distributions consisting of mixtures of Gaussians, rather than by single Gaussian distributions. The possible origin of these mixed distributions is investigated, using Monte-Carlo simulations of the action of spontaneously released units of transmitter. A single unit of acetylcholine of fixed size, released from an active zone with receptor patches both beneath and adjacent to the zone, does not give rise to the observed histograms. But if the unit is of variable size, consisting of integer multiples of smaller units, and release is from an active zone onto either the receptor patch beneath, or in addition onto adjacent patches, then the histogram is well described by a mixture of Gaussians. However, this explanation is unlikely to be correct as present evidence suggests that in most cases the released unit of transmitter saturates the postsynaptic receptor patch beneath the active zone. The final case considered is where a unit of transmitter is spontaneously released from an active zone, simultaneously with a unit in an adjacent zone less than one micron away. The histogram of potentials then conforms to those observed even when there are differences in the sizes of the receptor patches. It is suggested that this kind of release could provide an explanation for distributions of spontaneous potentials that are mixtures of Gaussians.     

A simulation approach to understanding the masticatory process

An analysis of the reduction of food particle sizes during human mastication is presented in terms of the probability of a particle being broken (selection function) and the distribution of fragment sizes produced when it fails (breakage function). Both selection and breakage functions are defined and a general equation produced. Several feasible behaviours for these two variables that have been suggested in the literature are modelled by computer simulation and the results are compared to published breakdown patterns. The conclusions are that selection and breakage functions probably behave very simply with respect to particle size, and that these behaviours could be deduced from an analysis of food particle size distributions and the rate at which particle sizes are reduced per chew.     

Peripheral fluctuations and particle transport during an L-H transition in the FT-2 tokamak

Experimental data on the processes in edge plasma that accompany the transition to an improved confinement regime during lower hybrid heating in the FT-2 tokamak are presented. The poloidal and radial distributions of the plasma parameters and drift particle fluxes were measured with the use of mobile mulitielectrode Langmuir probes and were found to be substantially nonuniform in the poloidal direction. The evolution of the plasma parameters in the course of heating and during an L-H transition is investigated. It is shown that, in FT-2 experiments, the drift of plasma particles in a slowly varying (quasi-steady) electric field and the fluctuation-induced particle fluxes make comparable contributions to the radial particle transport, whereas the contribution of fluctuations to poloidal plasma fluxes is negligibly small. The effective coefficient of radial diffusion is determined. The measurement results show that the L-H transition is accompanied by a substantial decrease in this coefficient.     

The question of fluctuating asymmetry in the blacklegged tick Ixodes scapularis (Acari: Ixodidae)

An analysis of fluctuating asymmetry was conducted on populations of the blacklegged tick Ixodes scapularis. The eight groups used in this study consisted of larvae and nymphs and males and females from the states of Minnesota, Massachusetts, Maryland, Missouri, North Carolina and Georgia and the F1 progenies of reciprocal crosses between ticks from Massachusetts and Georgia. Measurements included 16 larval, 19 nymphal, ten female and 12 male bilateral characters. Only five differences between the right and left bilateral characters had normal distributions with means of zero and differences in variances between the groups. These five characters included three setal lengths of the larvae, the spiracular plate length of females and the coxa I internal spur widths of males. Bivariate plots of character size ((R+L)/2) and asymmetry (R-L) showed no correlation. In the spiracular plate lengths of females and one of the setal lengths, ticks from Massachusetts had significantly less within-group variance than all the other groups. The only character in which fluctuating asymmetry was observed was the coxa I internal spur width of males, in which ticks from Minnesota, Missouri and North Carolina had significantly greater variance than the remaining groups; fluctuating asymmetry in this character may be explained by sexual selection. The cross progeny did not demonstrate any fluctuating asymmetry, as would be expected if the northern and southern forms of I. scapularis were true species. The virtual lack of fluctuating asymmetry in the characters used in this study further supports the conclusions of other studies which concluded that I. scapularis is a species with clinal variation and a broad geographic distribution.     

NEE观测误差分布类型对陆地生态系统机理模型参数估计的影响——以长白山温带阔叶红松林为例

基于观测数据的陆地生态系统模型参数估计有助于提高模型的模拟和预测能力,降低模拟不确定性.在已有参数估计研究中,涡度相关技术测定的净生态系统碳交换量(NEE)数据的随机误差通常被假设为服从零均值的正态分布.然而近年来已有研究表明NEE数据的随机误差更服从双指数分布.为探讨NEE观测误差分布类型的不同选择对陆地生态系统机理模型参数估计以及碳通量模拟结果造成的差异,以长白山温带阔叶红松林为研究区域,采用马尔可夫链-蒙特卡罗方法,利用2003～2005年测定的NEE数据对陆地生态系统机理模型CEVSA2的敏感参数进行估计,对比分析了两种误差分布类型(正态分布和双指数分布)的参数估计结果以及碳通量模拟的差异.结果表明,基于正态观测误差模拟的总初级生产力和生态系统呼吸的年总量分别比基于双指数观测误差的模拟结果高61～86 g C m-2 a-1和107～116 g C m-2 a-1,导致前者模拟的NEE年总量较后者低29～47 g C m-2 a-1,特别在生长旺季期间有明显低估.在参数估计研究中,不能忽略观测误差的分布类型以及相应的目标函数的选择,它们的不合理设置可能对参数估计以及模拟结果产生较大影响.     

河南省旬日照时数的标度不变性分析

利用河南省107个气象观测站1961-2012年逐旬日照时数资料,分析河南省旬日照时数的时空变化特征,并利用去趋势波动分析方法探讨了河南省旬日照时数的标度不变性.结果表明： 研究期间,河南省逐旬日照时数及其站间均方差的平均值分别为57.90和9.18h,其概率分布均不服从正态分布.河南省逐旬日照时数累积离差具有显著上升趋势,而逐旬日照时数站间均方差的累积离差具有阶段性变化特征,在阶段内均具有显著的线性变化趋势.河南省逐站旬日照时数的标度指数均在0.5以上,表明时间序列具有持久性.河南省旬日照时数标度指数空间变异性较小,具有正态分布的特征.     

Nonequilibrium electron distribution functions in a semiconductor plasma irradiated with fast ions

A kinetic equation for the electrons scattered by acoustic phonons in a solid is derived, and relationships between power-law asymptotic solutions and the particle and energy fluxes in phase space are established. The dependence of the nonextensivity parameter on the intensity of the particle flow in phase space is determined for a nonequilibrium solid-state plasma with sources and sinks. The formation of a steady-state nonequilibrium electron distribution function in a semiconductor with a source and a sink in phase space is numerically simulated using the Landau and Fokker-Planck collision integrals. The nonequilibrium electron distributions formed in the solid-state plasmas of semiconductors and of a Sb/Cs cathode are studied experimentally. It is shown that, within the electron energy range of 5–100 eV, the electron distribution functions decrease with energy according to a power law.     

Signed-Rank Tests in the Presence of Ties (with extended tables)

We begin with a review of the areas of application of the signed-rank tests (SRTs) and we conclude that the results are exact only if no ties of non-null differences exist. In order to apply the SRTs according to WILCOXON and according to PRATT also in the presence of ties, by assigning midranks, we derive their null distributions. As special cases the null distributions for the problem without ties are obtained. In order to save the practising statistician the time-consuming calculations of the distribution functions, we compute tables of critical values (for reasons of volume they will be published as part of the reprints only). For N₀ = 0 (1) 5 null differences and M = = 1(1) 10 non-null differences the critical values of all distributions with all possible tie vectors are calculated. Instructions are provided and an example serves to illustrate the use of the table. The extension of the tables are obtained by means of counting formulas given in the text. Approximations are provided in order to make the application of tests possible for larger samples as well. It is shown that the approximation of the null distribution in the presence of ties by the null distributions under the assumption of no ties in some cases overstates and sometimes understates the exact rejection probability. For N₀ = 0 (1) 10 and M = 1 (1) 10 all distributions with all possible tie vectors for the SRTs with WILCOXON and PRATT ranking are examined with respect to the lattice type of the test statistic. The result is given in table 6. It is evident that the portion of PRATT -distributions with lattice character decreases as the number of null differences increases. Continuity corrections are obtained for the asymptotic normal distribution which take into account the lattice character of the distribution of the test statistic.     

A simple method to fit geometric series and broken stick models in community ecology and island biogeography

Species abundance distributions are widely used in explaining natural communities, their natural evolution and the impacts of environmental disturbance. A commonly used approach is that of rank-abundance distributions. Favored, biologically founded models are the geometric series (GS) and the broken stick (BS) model. Comparing observed abundance distributions with those predicted by models is an extremely time-consuming task. Also, using goodness-of-fit tests for frequency distributions (like Chi-square or Kolmogorov–Smirnov tests) to compare observed with expected frequencies is problematic because the best way to calculate expected frequencies may be controversial. More important, the Chi-square test may prove if an observed distribution statistically differs from a model, but does not allow the investigator to choose among competing models from which the observed distribution does not differ. Both models can be easily tested by regression analysis. In GS, if a log scale is used for abundance, the species exactly fall along a straight line. The BS distribution shows up as nearly linear when a log scale is used for the rank axis. Regression analysis is proposed here as a simpler and more efficient method to fit the GS and BS models. Also, regression analysis (1) does not suffer from assumptions related to Chi-square tests; (2) obviates the need to establish expected frequencies, and (3) offers the possibility to choose the best fit among competing models. A possible extension of abundance-rank analysis to species richness on islands is also proposed as a method to discriminate between relict and equilibrial models. Examples of application to field data are also presented.     

A simple method to fit geometric series and broken stick models in community ecology and island biogeography

Species abundance distributions are widely used in explaining natural communities, their natural evolution and the impacts of environmental disturbance. A commonly used approach is that of rank-abundance distributions. Favored, biologically founded models are the geometric series (GS) and the broken stick (BS) model. Comparing observed abundance distributions with those predicted by models is an extremely time-consuming task. Also, using goodness-of-fit tests for frequency distributions (like Chi-square or Kolmogorov–Smirnov tests) to compare observed with expected frequencies is problematic because the best way to calculate expected frequencies may be controversial. More important, the Chi-square test may prove if an observed distribution statistically differs from a model, but does not allow the investigator to choose among competing models from which the observed distribution does not differ. Both models can be easily tested by regression analysis. In GS, if a log scale is used for abundance, the species exactly fall along a straight line. The BS distribution shows up as nearly linear when a log scale is used for the rank axis. Regression analysis is proposed here as a simpler and more efficient method to fit the GS and BS models. Also, regression analysis (1) does not suffer from assumptions related to Chi-square tests; (2) obviates the need to establish expected frequencies, and (3) offers the possibility to choose the best fit among competing models. A possible extension of abundance-rank analysis to species richness on islands is also proposed as a method to discriminate between relict and equilibrial models. Examples of application to field data are also presented.     

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

A novel analysis of ion current time series is proposed. It is shown that higher (second, third and fourth) statistical moments of the ion current probability distribution function (PDF) can yield new information about ion channel properties. The method is illustrated on a two-state model where the PDF of the compound states are given by normal distributions. The proposed method was applied to the analysis of the SV cation channels of vacuolar membrane of Beta vulgaris and the influence of trimethyllead chloride (Met₃PbCl) on the ion current probability distribution. Ion currents were measured by patch-clamp technique. It was shown that Met₃PbCl influences the variance of the open-state ion current but does not alter the PDF of the closed-state ion current. Incorporation of higher statistical moments into the standard investigation of ion channel properties is proposed.     

Apoptotic cell death and related gene expression in metastatic tumors of AKR lymphomas of varying malignancy

Resistance to apoptosis may be related to tumor progression, due to the implications it might have on both tumor mass and genetic instability. We compared the tendency to spontaneous apoptosis and the proliferative capacity of metastatic growths of several AKR lymphoma variants (TAU-45, TAU-47, TAU-44, TAU-33, TAU-42 and TAU-46, in the order of increasing metastatic potential). We further compared the expression of several apoptosis-related genes. Cell proliferative capacity did not appear to determine malignant behavior since, on the whole, a decrease in S + G2M fraction was observed with increasing malignancy. Sensitivity to apoptotic cell death decreased with increasing malignancy when comparing the TAU-45, TAU-47, TAU-44 and TAU-33 variants, suggesting a role of reduced apoptosis in this T-cell lymphoma. An increase in Bcl-2 content with increasing aggressiveness among these variants, implicates this protein in this tumor progression-related resistance to apoptosis. However, the two variants of highest malignancy, TAU-42 and TAU-46, did not follow the same trend, since they displayed a relatively high content in apoptotic cells and a low Bcl-2 content. Fas receptor expression did not correlate with tendency to apoptosis, indicating that malignant behavior in the AKR lymphoma does not depend on CD95/Fas/APO1 downregulation. Overexpression of p53 was observed only in one of the variants of lowest malignancy.