generalized chapman kolmogorov equation a unifying approach to the description of anomalous transport in external fields the generalized chapman kolmogorov equation v m kenkre e w montroll and m f shlesinger j stat phys 9 45 1973 is discussed it is demonstrated that this equation unifies recently proposed kinetic equations of fractional order that describe anomalous transport in external fields as well as continuous time random walks the conditions under which the individual models can be established are discussed

the effect of two stage sampling on ordinary least squares methods abstract we look at the effect of intracluster correlation on standard procedures in linear regression the ordinary least squares estimator of the coefficient vector performs well in most cases but the usual estimator of cov and procedures based on this such as confidence intervals and hypothesis tests can be seriously misleading the size of the effect however tends to be smaller than the corresponding effect on the variance of an estimated mean in two stage sampling provided that the cluster sample sizes are approximately equal

general framework for dynamic substructuring history review and classification of techniques four decades after the development of the first dynamic substructuring techniques there is a necessity to classify the different methods in a general framework that outlines the relations between them in this paper a certain vision on substructuring methods is proposed by recalling important historical milestones that allow us to understand substructuring as a domain decomposition concept thereafter based on the dual and primal assembly of substructures a general framework for the classification of the methods is presented this framework allows us to indicate how the various classes of methods proposed along the years can be derived from a clear mathematical description of substructured problems current bottlenecks in experimental dynamic substructuring as well as solutions found in literature will also be briefly discussed

age representation of levy walks partial density waves relaxation and first passage time statistics l vy walks lws define a fundamental class of finite velocity stochastic processes that can be introduced as a special case of continuous time random walks alternatively there is a hyperbolic representation of them in terms of partial probability density waves using the latter framework we explore the impact of aging on lws which can be viewed as a specific initial preparation of the particle ensemble with respect to an age distribution we show that the hyperbolic age formulation is suitable for a simple integral representation in terms of linear volterra equations for any initial preparation on this basis relaxation properties i e the convergence towards equilibrium of a generic thermodynamic function dependent on the spatial particle distribution and first passage time statistics in bounded domains are studied by connecting the latter problem with solute release kinetics we find that even normal diffusive lws where the long term mean square displacement increases linearly with time may display anomalous relaxation properties such as stretched exponential decay we then discuss the impact of aging on the first passage time statistics of lws by developing the corresponding volterra integral representation as a further natural generalization the concept of lws with wearing is introduced to account for mobility losses

a second order difference scheme for the time fractional substantial diffusion equation abstract in this work a second order approximation of the fractional substantial derivative is presented by considering a modified shifted substantial grunwald formula and its asymptotic expansion moreover the proposed approximation is applied to a fractional diffusion equation with fractional substantial derivative in time with the use of the fourth order compact scheme in space we give a fully discrete grunwald letnikov formula based compact difference scheme and prove its stability and convergence by the energy method under smooth assumptions in addition the problem with nonsmooth solution is also discussed and an improved algorithm is proposed to deal with the singularity of the fractional substantial derivative numerical examples show the reliability and efficiency of the scheme

using sample survey weights in multiple regression analyses of stratified samples abstract the rationale for the use of sample survey weights in a least squares regression analysis is examined with respect to four increasingly general specifications of the population regression model the appropriateness of the weighted regression estimate depends on which model is chosen a proposal is made to use the difference between the weighted and unweighted estimates as an aid in choosing the appropriate model and hence the appropriate estimator when applied to an analysis of the familial and environmental determinants of the educational level attained by a sample of young adults the methods lead to a revision of the initial additive model in which interaction terms between county unemployment and race as well as between sex and mother s education are included

retarding subdiffusion and accelerating superdiffusion governed by distributed order fractional diffusion equations we propose diffusionlike equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena whose diffusion exponent varies with time and which correspondingly cannot be viewed as self affine random processes possessing a unique hurst exponent we prove the positivity of the solutions of the proposed equations and establish their relation to the continuous time random walk theory we show that the distributed order time fractional diffusion equation describes the subdiffusion random process that is subordinated to the wiener process and whose diffusion exponent decreases in time retarding subdiffusion this process may lead to superslow diffusion with the mean square displacement growing logarithmically in time we also demonstrate that the distributed order space fractional diffusion equation describes superdiffusion phenomena with the diffusion exponent increasing in time accelerating superdiffusion

towards deterministic equations for levy walks the fractional material derivative levy walks are random processes with an underlying spatiotemporal coupling this coupling penalizes long jumps and therefore levy walks give a proper stochastic description for a particle s motion with broad jump length distribution we derive a generalized dynamical formulation for levy walks in which the fractional equivalent of the material derivative occurs our approach is expected to be useful for the dynamical formulation of levy walks in an external force field or in phase space for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited

first passage and arrival time densities for levy flights and the failure of the method of images we discuss the first passage time problem in the semi infinite interval for homogeneous stochastic markov processes with levy stable jump length distributions x l x 1 x l namely levy flights lfs in particular we demonstrate that the method of images leads to a result which violates a theorem due to sparre andersen according to which an arbitrary continuous and symmetric jump length distribution produces a first passage time density fptd governed by the universal long time decay t 3 2 conversely we show that for lfs the direct definition known from gaussian processes in fact defines the probability density of first arrival which for lfs differs from the fptd our findings are corroborated by numerical results

scale invariant motion in intermittent chaotic systems we investigate the dynamics generated from iterated maps and analyze the motion in terms of the probabilistic continuous time random walk ctrw approach two different ctrw models are considered i particles jump between sites turning points or ii particles move at a constant velocity between sites and choose a new direction at random for both models we study the mean squared displacement mathit r 2 t and the propagator p r t the probability to be at location r at time t having started at the origin at t 0 iterated maps are used to generate both dispersive and enhanced diffusion and the results are analyzed using the ctrw framework and scaling arguments for the case of dispersive motion we discuss the problem of the stationary state and point out its relevance

inference from stratified samples properties of the linearization jackknife and balanced repeated replication methods the asymptotic normality of both linear and nonlinear statistics and the consistency of the variance estimators obtained using the linearization jackknife and balanced repeated replication brr methods in stratified samples are established the results are obtained as l oa within the context of a sequence of finite populations jil with l strata in ji l and are valid for any stratified multistage design in which the primary sampling units psu s are selected with replacement and in which independent subsamples are taken within those psu s selected more than once in addition some exact analytical results on the bias and stability of these alternative variance estimators in the case of ratio estimation are obtained for small l under a general linear regression model

testing hardy weinberg equilibrium and homogeneity of hardy weinberg disequilibrium using complex survey data summary for studies on population genetics the use of representative random samples of the target population can avoid ascertainment bias genetic variation data from over a hundred genes were collected in a u s nationally representative sample in the third national health and nutrition examination survey nhanes iii surveys such as the nhanes have complex stratified multistage cluster sample designs with sample weighting that can inflate variances and alter the expectations of test statistics thus classical statistical tests of hardy weinberg equilibrium hwe and homogeneity of hw disequilibrium hhwd for simple random samples are not suitable for data from complex samples we propose using wald tests for hwe and generalized score tests for hhwd that have been modified for complex samples monte carlo simulation studies are used to investigate the finite sample properties of the proposed tests rao scott corrections applied to the tests were found to improve their type i error properties our methods are applied to the nhanes iii genetic data for three loci involved in metabolizing lead in the body

the analysis of categorical data from complex sample surveys chi squared tests for goodness of fit and independence in two way tables abstract the effect of stratification and clustering on the asymptotic distributions of standard pearson chi squared test statistics for goodness of fit simple hypothesis and independence in a two way contingency table denoted as x 2 and xi 2 respectively is investigated it is shown that both x 2 and xi 2 are asymptotically distributed as weighted sums of independent 1 2 random variables the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 which requires only the knowledge of variance estimates or deffs for individual cells in the goodness of fit problem is proposed and empirical results on the performance of corrected x 2 provided empirical work on xi 2 indicated that the distortion of nominal significance level is substantially smaller with xi 2 than with x 2 some results under simple models for clustering are also given

non markovian noise the properties of non markovian noises with exponentially correlated memory are discussed considered are dichotomic noise white shot noise gaussian white noise and gaussian colored noise the stationary correlation functions of the non markovian versions of these noises are given by linear combinations of two or three exponential functions colored noises or of the delta function and exponential function white noises the non markovian white noises are well defined only when the kernel of the non markovian master equation contains a nonzero admixture of a markovian term approximate equations governing the probability densities for processes driven by such non markovian noises are derived including non markovian versions of the fokker planck equation and the telegrapher s equation as an example it is shown how the non markovian nature changes the behavior of the driven linear process

on chi squared tests for multiway contingency tables with cell proportions estimated from survey data the impact of survey design on standard multinomial based methods for a multiway contingency table is studied under nested loglinear models the asymptotic null distribution of the pearson chi squared test statistic x 2 or the likelihood ratio test statistic g 2 is obtained as a weighted sum of independent chi 2 1 random variables and the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 or g 2 is also obtained which requires the knowledge of only the cell deffs and the deffs for collapsed tables marginals whenever the model admits a direct solution of likelihood equations under multinomial sampling finally an example on the relative performance of x 2 and some corrected x 2 statistics in a three way table is given using some data from the canada health survey 1978 1979

explicit densities of multidimensional ballistic levy walks levy walks have proved to be useful models of stochastic dynamics with a number of applications in the modeling of real life phenomena in this paper we derive explicit formulas for densities of the two 2d and three dimensional 3d ballistic levy walks which are most important in applications it turns out that in the 3d case the densities are given by elementary functions the densities of the 2d levy walks are expressed in terms of hypergeometric functions and the right side riemann liouville fractional derivative which allows us to efficiently evaluate them numerically the theoretical results agree perfectly with monte carlo simulations

random walk model with waiting times depending on the preceding jump length in the present paper the generalized continuous time random walk model with a coupled transition kernel is considered the coupling occurs through the dependence of the waiting time probability distribution on the preceding jump length for the description of this model a method is suggested that includes the details of the microscopic distribution over the waiting times and arrival distances at a given point a close analogy to the problem of a random walk with finite velocity is demonstrated for the particular case of coupling when a waiting time is a simple function of a preceding jump length with its help an analytical solution for the generalized random walk model is found including both effects finite velocity and jump dependent waiting times simultaneously

a psychophysical model of decision making abstract herein we develop a psychophysical model of decision making based on the difference between objective clock time and the human brain s perception of time in this model the utility function is given by the survival probability which is shown to be a generalized hyperbolic distribution the parameters of the utility function are fit to intertemporal choice model experimental data and decision making is determined to be a 1 f noise process

extended preconditioners for the feti method applied to constrained problems an efficient and simple approach for handling linear multipoint constraints in a class of substructure based solvers namely the finite element tearing and interconnecting feti method is proposed previously it was argued that multipoint constraints should be handled in feti by adding a second level iteration on a coarse grid such that the feti iterates satisfy the multipoint constraints exactly the procedure presented here does not require an additional coarse grid but instead takes account of the multipoint constraints in the preconditioning step the preconditioning strategy is shown to be mechanically consistent and to incur only a small additional computational cost this strategy is simpler and computationally less expensive than the two level feti procedure its numerical scalability even for highly heterogeneous problems is demonstrated in several test examples

a jackknifed chi squared test for complex samples abstract complex sample designs typically invalidate the direct application of the familiar pearson or likelihood ratio chi squared statistics for testing the fit of a model to a cross classified table of counts this article discusses the adjustment of these statistics through a jackknifing approach the technique may generally be applied whenever a standard replication method such as the jackknife bootstrap or repeated half samples provides a consistent estimate of the covariance matrix of the sample estimates properties of the limiting distribution of new test statistics xj and gj are described the new statistics may be used to test goodness of fit and to compare nested models

hypothesis testing with complex survey data the use of classical quadratic test statistics with particular reference to regression problems abstract sample surveys often have complex sample designs with multistage cluster sampling stratification and differential selection probabilities this article is concerned with testing the null hypothesis h 0 where the p dimensional parameter g and is a q dimensional vector of means the asymptotic framework that consists of a sequence of increasing finite populations is used to define as the limit of finite population means as part of the inference we use replicated estimates of variances that take into account the complex sample design the wald statistic can be used to test h 0 but inference for based on the wald statistic can have low power thus an alternative to using a wald test is pursued in this article first define a classical quadratic test statistic that would be used if one had a simple random sample of the population second treating this quadratic form as a population parameter use design based methods to estimate it from the observed survey data last use

aging and rejuvenation with fractional derivatives we discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non poisson processes we find that two state fluctuations with an inverse power law distribution of waiting times finite first moment and divergent second moment namely with the power indexm in the interval 2 m 3 yield a generalized master equation equivalent to the sum of an ordinary markov contribution and a fractional derivative term we show that the order of the fractional derivative depends on the age of the process under study if the system is infinitely old the order of the fractional derivative o is given by o 3 m a brand new system is characterized by the degree o m 2 if the system is prepared at time ta 0 and the observation begins at time t 0 we derive the following scenario for times 0 t ta the system is satisfactorily described by the fractional derivative with o 3 m upon time increase the system undergoes a rejuvenation process that in the time limit t ta yields o m 2 the intermediate time regime is probably incompatible with a picture based on fractional derivatives or at least with a mono order fractional derivative

scaling breakdown a signature of aging we prove that the levy walk is characterized by bilinear scaling this effect mirrors the existence of a form of aging that does not require the adoption of nonstationary conditions

generalized master equation via aging continuous time random walks this article discusses the problem of the equivalence between continuous time random walk ctrw and generalized master equation gme

stability in a system subject to noise with regulated periodicity the stability of a simple dynamical system subject to multiplicative one side pulse noise with hidden periodicity is investigated both analytically and numerically the stability analysis is based on the exact result for the characteristic functional of the renewal pulse process the influence of the memory effects on the stability condition is analyzed for two cases i the dead time distorted poissonian process and ii the renewal process with pareto distribution we show that for fixed noise intensity the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity

small sample comparisons of level and power for simple goodness of fit statistics under cluster sampling abstract monte carlo methods were used to examine the type i error performance of a number of goodness of fit statistics under cluster sampling the study has reduced the comparison to four procedures a x 2 s the rao scott satterthwaite adjusted x 2 b xj fay s jackknifed x 2 c fw a modified wald statistic referred to an f distribution and d fx 2 c an f based version of the rao scott adjusted x 2 depending only on the cell design effects de unlike the others the statistic fx 2 c performs well provided that the coefficient of variation a of the eigenvalues i of the design effects matrix is small in general both x 2 s and xj perform well even when a is not small fw behaves reasonably well for tests of uniform probability 0 1 k 1 k where k is the number of categories and 1 k 1 k 1 1 k 1 but it is sensitive to skewness in 0 the power performance of procedures a d was also examined attention was focused on 0 1 k 1 k

resampling inference with complex survey data abstract methods for standard errors and confidence intervals for nonlinear statistics such as ratios regression and correlation coefficients have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement in particular the important special case of two sampled clusters per stratum these methods include the customary linearization or taylor method and resampling methods based on the jackknife and balanced repeated replication brr unlike the jackknife or the brr the linearization method is applicable to general sampling designs but it involves a separate variance formula for each nonlinear statistic thereby requiring additional programming efforts both the jackknife and the brr use a single variance formula for all nonlinear statistics but they are more computing intensive the resampling methods developed here retain these features of the jackknife and the brr yet permit extension to more complex designs involving sampling without replace

microscopic approach to random walks in the present paper the microscopic approach to random walk models is introduced for any particular model it provides a rigorous way to derive the transport equations for the macroscopic density of walking particles although it is not more complicated than the standard random walk framework it has virtually no limitations with respect to the initial distribution of particles as a consequence the transport equations derived with this method almost automatically give answers to such important problems as aging and two point probability distribution

aging properties of an anomalously diffusing particule we report new results about the two time dynamics of an anomalously diffusing classical particle as described by the generalized langevin equation with a frequency dependent noise and the associated friction the noise is defined by its spectral density proportional to 1 at low frequencies with 0 1 subdiffusion or 1 2 superdiffusion using laplace analysis we derive analytic expressions in terms of mittag leffler functions for the correlation functions of the velocity and of the displacement while the velocity thermalizes at large times slowly in contrast to the standard brownian motion case 1 the displacement never attains equilibrium it ages we thus show that this feature of normal diffusion is shared by a subdiffusive or superdiffusive motion we provide a closed form analytic expression for the fluctuation dissipation ratio characterizing aging

bifurcation bimodality and finite variance in confined levy flights we investigate the statistical behavior of levy flights confined in a symmetric quartic potential well u x proportional variant x 4 at stationarity the probability density function features a distinct bimodal shape and decays with power law tails which are steep enough to give rise to a finite variance in contrast to free levy flights from a delta initial condition a bifurcation of the unimodal state is observed at t c 0 the nonlinear oscillator with potential u x ax 2 2 bx 4 4 a b 0 shows a crossover from unimodal to bimodal behavior at stationarity depending on the ratio a b

cooperation in neural systems bridging complexity and periodicity inverse power law distributions are generally interpreted as a manifestation of complexity and waiting time distributions with power index 2 reflect the occurrence of ergodicity breaking renewal events in this paper we show how to combine these properties with the apparently foreign clocklike nature of biological processes we use a two dimensional regular network of leaky integrate and fire neurons each of which is linked to its four nearest neighbors to show that both complexity and periodicity are generated by locality breakdown links of increasing strength have the effect of turning local interactions into long range interactions thereby generating time complexity followed by time periodicity increasing the density of neuron firings reduces the influence of periodicity thus creating a cooperation induced renewal condition that is distinctly non poissonian

implicit time integration of a class of constrained hybrid formulations part i spectral stability theory abstract incomplete field formulations have recently been the subject of intense research because of their potential in coupled analysis of independently modeled substructures adaptive refinement domain decomposition and parallel processing this paper presents a spectral stability theory for the differential algebraic dynamic systems associated with these formulations discusses the design and analysis of suitable time integration algorithms and emphasizes the treatment of the inter subdomain linear constraint equations these constraints are shown to introduce a destabilizing effect in the dynamic system that can be analyzed by investigating the behavior of the time integration algorithm at infinite and zero frequencies three different approaches for constructing penalty free unconditionally stable second order accurate solution procedures for this class of hybrid formulations are presented analyzed and illustrated with numerical examples in particular the advantages of the hilber hughes taylor hht method and its generalized version generalized a are highlighted the family of problems discussed in this paper can also be viewed as model problems for the more general case of hybrid formulations with non linear constraints for example it is shown numerically in this paper that the theoretical results predicted by the spectral stability theory also apply to non linear multibody dynamics formulations therefore some of the algorithms outlined in this work are important alternatives to the popular technique consisting of transforming differential algebraic equations into ordinary differential equations via the introduction of a stabilization term that depends on arbitrary constants and that influences the computed solution

renewal modulation and superstatistics in times series we consider two different approaches to which we refer to as renewal and modulation to generate time series with a nonexponential distribution of waiting times we show that different time series with the same waiting time distribution are not necessarily statistically equivalent and might generate different physical properties renewal generates aging and anomalous scaling while modulation yields no significant aging and either ordinary or anomalous diffusion according to the dynamic prescription adopted we show in fact that the physical realization of modulation generates two classes of events the events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time and consequently are numerous the events of the second class are identified with the abrupt changes from one to another exponential prescription and consequently are rare the events of the second class although rare determine the scaling of the diffusion process and for this reason we term them as crucial events according to the prescription adopted to produce modulation the distribution density of the time distances between two consecutive crucial events might have or not a diverging second moment in the former case the resulting diffusion process although going through a transition regime very extended in time will eventually become anomalous in conclusion modulation rather than ruling out the action of renewal events produces crucial events hidden by clouds of exponential events thereby setting the challenge for their identification

an impulse based substructuring method for coupling impulse response functions and finite element models abstract in the field of dynamic substructuring ds large and complex structures are divided into several smaller and simpler components the linear substructures are subsequently described in their dominant dynamics and reassembled allowing one to compute the coupled dynamic behavior ds methods are often classified into two distinct families the frequency based substructuring fbs methods and component mode synthesis cms techniques in the former substructures are assembled whose dynamics are described in terms of frequency response functions frfs and the latter are used to reduce and assemble the substructure finite element fe models lately a new substructuring method has been proposed one that does not fit the framework of the fbs and cms methods the method named impulse based substructuring ibs was first used to obtain the coupled response of a system by assembling its component impulse response functions irfs in this paper the ibs method is extended thereby allowing one to determine the coupled behavior of structures that are composed of both substructure fe models and substructure irfs the method can be regarded as an extension to the normal time integration methods used for obtaining the time responses of fe models as the linear substructures described in their irfs are fully condensed on the interface of the fe model one can significantly reduce the computational cost required for time integrating otherwise large fe models however as the linear irf domains are exactly accounted for the ibs method can be seen as a dynamic condensation on the interface but not as a reduction method in the classical sense nonetheless one can regard irfs as a sort of superelements in time and the ibs method can therefore serve as an attractive alternative to cms methods in case these are not available in the applied fe modeling programs or if a high spectral bandwidth of the substructure is required the method proposed in this work is based on the generalized time integration scheme and it is analytically proven that it can be applied in such a way that the simulation results are identical to the responses obtained from a monolithic integration of the full system thereby guaranteeing its stability and accuracy the method is demonstrated using a numerical test case where a wind turbine fe model is coupled with a the irfs of a marine foundation

linear response to perturbation of nonexponential renewal processes we study the linear response of a two state stochastic process obeying the renewal condition by means of a stochastic rate equation equivalent to a master equation with infinite memory we show that the condition of perennial aging makes the response to coherent perturbation vanish in the long time limit

aging in mortal superdiffusive levy walkers a growing body of literature examines the effects of superdiffusive subballistic movement premeasurement aging or time lag on observations arising from single particle tracking a neglected aspect is the finite lifetime of these levy walkers be they proteins cells or larger structures we examine the effects of aging on the motility of mortal walkers and discuss the means by which permanent stopping of walkers may be categorized as arising from natural death or experimental artifacts such as low photostability or radiation damage this is done by comparison of the walkers mean squared displacement msd with the front velocity of propagation of a group of walkers which is found to be invariant under time lags for any running time distribution of a mortal random walker the msd is tempered by the stopping rate this provides a physical interpretation for truncated heavy tailed diffusion processes and serves as a tool by which to better classify the underlying running time distributions of random walkers tempering of aged msds raises the issue of misinterpreting superdiffusive motion which appears brownian or subdiffusive over certain time scales

novel generalized α methods for interfield parallel integration of heterogeneous structural dynamic systems a novel partitioned algorithm able to solve odes arising from transient structural dynamics is presented the spatial domain is partitioned into a set of disconnected subdomains owing to computational or physical considerations and continuity conditions of velocity at the interface are modelled using a dual schur formulation where lagrange multipliers represent reaction forces interface equations along with subdomain equations lead to a system of daes for which an interfield parallel procedure is developed the algorithm solves interface lagrange multipliers which are subsequently used to advance the solution in subdomains the proposed coupling algorithm that enables arbitrary email protected schemes to be coupled with different time steps in each subdomain is an extension of a method originally proposed by pegon and magonette thus subcycling permitting to deal also with stiff and nonstiff subsystems is allowed in detail the paper presents the convergence analysis of the novel interfield parallel scheme for linear single and two degrees of freedom systems because a multi degrees of freedom system is too difficult for a mathematical treatment however the insight gained from the analysis of these coupled problems and the consequent conclusions are confirmed by means of numerical experiments on a four degrees of freedom system

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

the effect of two stage sampling on the f statistic abstract the assumption of iid observations that underlies many statistical procedures is called into question when analyzing complex survey data the population structure particularly the existence of clusters in two stage samples that usually exhibit positive intracluster correlation invalidates the independence assumption kish and frankel 1974 investigated the impact of this fact on regression analysis by using the standard sample survey theory framework campbell 1977 and scott and holt 1982 used the linear model framework in general although ordinary least squares ols procedures are unbiased but not fully efficient for estimation of the regression coefficients serious difficulties can arise when using ols estimators for second order terms variances of the ols estimators for the regression coefficients can be larger sometimes much larger than the usual ols variance expression would indicate failure to consider this possibility leads to underestimation of variances with consequences fo

fractional langevin equation we investigate fractional brownian motion with a microscopic random matrix model and introduce a fractional langevin equation we use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath we further compare fractional brownian motion with the fractal time process the respective mean square displacements of these two forms of anomalous diffusion exhibit the same power law behavior here we show that their lowest moments are actually all identical except the second moment of the velocity this provides a simple criterion that enable us to distinguish these two non markovian processes

dynamically generated enhanced diffusion the stationary state case abstract we investigate the dynamics generated by iterated maps and analyze the motion in terms of the probabilistic continuous time levy walk approach we consider the case of particles which move randomly with a constant velocity between points of halt and study the mean squared displacement r 2 t and the propagator p r t the probability to be at location r at time t having started at the origin at t 0 we emphasize the importance of the stationary state and demonstrate it in the case of enhanced diffusion