determination of the algebraic relations among special γ values in positive characteristic we devise a new criterion for linear independence over function fields using this tool in the setting of dual t motives we find that all algebraic relations among special values of the geometric r function over f q t are explained by the standard functional equations

propagation on networks an exact alternative perspective by generating the specifics of a network structure only when needed on the fly we derive a simple stochastic process that exactly models the time evolution of susceptible infectious dynamics on finite size networks the small number of dynamical variables of this birth death markov process greatly simplifies analytical calculations we show how a dual analytical description treating large scale epidemics with a gaussian approximation and small outbreaks with a branching process provides an accurate approximation of the distribution even for rather small networks the approach also offers important computational advantages and generalizes to a vast class of systems

on the formulation and application of design rules abstract design rules are stated in the form of a predictor of failure initiation and its allowable value in the context of design of mechanical and structural components subjected to cyclic loading calibration and validation procedures are described and illustrated for the predictors with the aid of published experimental data it is noted that mathematical models cannot be validated with respect to the allowable value of predictors

small but slow world how network topology and burstiness slow down spreading while communication networks show the small world property of short paths the spreading dynamics in them turns out slow here the time evolution of information propagation is followed through communication networks by using empirical data on contact sequences and the susceptible infected model introducing null models where event sequences are appropriately shuffled we are able to distinguish between the contributions of different impeding effects the slowing down of spreading is found to be caused mainly by weight topology correlations and the bursty activity patterns of individuals

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

dynamics of rumor propagation on small world networks we study the dynamics of an epidemiclike model for the spread of a rumor on a small world network it has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network randomness here by numerical means we perform a quantitative characterization of the evolution in the two regimes the variant of dynamic small worlds where the quenched disorder of small world networks is replaced by randomly changing connections between individuals is also analyzed in detail and compared with a mean field approximation

anderson s double complex and gamma monomials for rational function fields we investigate algebraic monomials of thakur s positive characteristic r function by using anderson and das double complex method of computing the sign cohomology of the universal ordinary distribution we prove that the monomial associated to an element of the second sign cohomology of the universal ordinary distribution of f q t generates a kummer extension of some carlitz cyclotomic function field which is also a galois extension of the base field f q t these results are characteristic p analogues of those of deligne on classical r monomials proofs of which were given by das using the double complex method in this paper we also obtain some results on e monomials of carlitz s exponential function

kronecker weber plus epsilon we say that a group is almost abelian if every commutator is central and squares to the identity now let g be the galois group of the algebraic closure of the field q of rational numbers in the field of complex numbers let gab be the quotient of g universal for continuous homomorphisms to almost abelian profinite groups and let qab q be the corresponding galois extension we prove that qab is generated by the roots of unity the fourth roots of the rational primes and the square roots of certain algebraic sine monomials the inspiration for the paper came from recent studies of algebraic monomials by p das and by s seo

estimating fatigue curves with the random fatigue limit model in a fatigue limit model units tested below the fatigue limit also known as the threshold stress theoretically will never fail this article uses a random fatigue limit model to describe a the dependence of fatigue life on the stress level b the variation in fatigue life and c the unit tounit variation in the fatigue limit we fit the model to actual fatigue datasets by maximum likelihood methods and study the fits under different distributional assumptions small quantiles of the life distribution are often of interest to designers lower confidence bounds based on likelihood ratio methods are obtained for such quantiles to assess the fits of the model we construct diagnostic plots and perform goodness of fit tests and residual analyses

random graphs containing arbitrary distributions of subgraphs traditional random graph models of networks generate networks that are locally treelike meaning that all local neighborhoods take the form of trees in this respect such models are highly unrealistic most real networks having strongly nontreelike neighborhoods that contain short loops cliques or other biconnected subgraphs in this paper we propose and analyze a class of random graph models that incorporates general subgraphs allowing for nontreelike neighborhoods while still remaining solvable for many fundamental network properties among other things we give solutions for the size of the giant component the position of the phase transition at which the giant component appears and percolation properties for both site and bond percolation on networks generated by the model

the stabilized probability plot summary the stabilized probability plot is introduced an attractive feature of the plot that enhances its interpretability is that the variances of the plotted points are approximately equal this prompts the definition of a new and powerful goodness of fit statistic dsp which analogous to the standard kolmogorov smirnov statistic d is defined to be the maximum deviation of the plotted points from their theoretical values using either d or dsp it is shown how to construct acceptance regions for qq pp and the new plots acceptance regions can help remove much of the subjectivity from the interpretation of these probability plots

bayesian inference and model comparison for metallic fatigue data abstract in this work we present a statistical treatment of stress life s n data drawn from a collection of records of fatigue experiments that were performed on 75s t6 aluminum alloys our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration model selection and model ranking with reference to s n data to this purpose we consider fatigue limit models and random fatigue limit models that are specially designed to allow the treatment of the run outs right censored data we first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen to assess the robustness of the estimation of the quantile functions we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio we then compare and rank the models by classical measures of fit based on information criteria we also consider a bayesian approach that provides under the prior distribution of the model parameters selected by the user their simulation based posterior distributions we implement and apply bayesian model comparison methods such as bayes factor ranking and predictive information criteria based on cross validation techniques under various a priori scenarios

dynamics of epidemics on random networks this paper examines how diseases on random networks spread in time the disease is described by a probability distribution function for the number of infected and recovered individuals and the probability distribution is described by a generating function the time development of the disease is obtained by iterating the generating function in cases where the disease can expand to an epidemic the probability distribution function is the sum of two parts one that is static at long times and another whose mean grows exponentially the time development of the mean number of infected individuals is obtained analytically when epidemics occur the probability distributions are very broad and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals

group cohomology of the universal ordinary distribution for any odd squarefree integer r we obtain a complete description of the gra galqom r u q group cohomology of the universal ordinary distribution ur in this paper moreover for m a fixed integer dividing l 1 for all prime factors l of r we study the cohomology group hogr ur muru in particular we explain the construction of the elements kr0 for r 0 jr in rubin 9 which come exactly from a certain z mz basis of the cohomology group h 0 ogr ur muru through an evaluation map

the unramified brauer group of norm one tori let k be a number field and k k galois we transform the construction of the unramified brauer group of the norm one torus rk k1 gm into the construction of a special abelian extension over k if k q and k q biquadratic we explicitly construct the unramified brauer group of rk q1 gm

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

all double coverings of cyclotomic fields a double covering of a galois extension k f in the sense of 3 is an extension open image in new window k of degree 2 such that open image in new window f is galois in this paper we determine explicitly all double coverings of any cyclotomic extension over the rational number field in the complex number field we get the results mainly by galois theory and by using and modifying the results and the methods in 2 and 3

theory for optimal test plans for the random fatigue limit model this article presents methodology for planning life tests based on the random fatigue limit model rflm the rflm describes the relationship between fatigue life and the applied load in the presence of fatigue limits a standardization of the rflm is presented and corresponding expressions for the elements of the fisher information matrix are given different test plan criteria that express various objectives that the practitioner may have in conducting experiments under the rflm are discussed these criteria include estimation of life quantiles estimation of stress strain levels that yield a specific life quantile estimation of fatigue limit quantiles and d and ds optimality equivalence theorems used to verify optimality of test plans are also presented the methods are sufficiently general so they can be applied to criteria based on any function of the model parameters they are demonstrated using a nickel base superalloy experiment

confidence bands for survival functions with censored data a comparative study consider the problem of obtaining simultaneous confidence bands for the survival function s x when the data are arbitrarily right censored the usual pointwise confidence intervals based on greenwood s variance formula can be adapted to yield a large sample confidence band this band has in a certain sense equal precision at each point of s x it is compared with the censored versions of the kolmogorov band and the renyi band the comparisons are made in terms of the widths and the adequacy of large sample approximations and are carried out under various censoring models and degrees of censoring the bands are illustrated by applying them to data from a mechanical switch life test

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

validation of a predictor of fatigue failure in the high cycle range abstract a predictor of failure initiation in high cycle fatigue was calibrated on the basis of uniaxial experimental data and its predictive performance tested against biaxial data the procedures of solution verification calibration ranking validation and uncertainty quantification were employed a condition that defines the domain of the predictor is inferred from the results of validation experiments

exact solution of a stochastic susceptible infectious recovered model the susceptible infectious recovered sir model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism a susceptible s can become infectious with an infection rate beta by an infectious i type provided that both are in contact the i type may recover with a rate gamma and from then on stay immune due to the coupling between the different individuals the model is nonlinear and out of equilibrium we adopt a stochastic individual based description where individuals are represented by nodes of a graph and contact is defined by the links of the graph mapping the underlying master equation onto a quantum formulation in terms of spin operators the hierarchy of evolution equations can be solved exactly for arbitrary initial conditions on a linear chain in the case of uncorrelated random initial conditions the exact time evolution for all three individuals of the sir model is given analytically depending on the initial conditions and reaction rates beta and gamma the i population may increase initially before decaying to zero due to fluctuations isolated regions of susceptible individuals evolve and unlike in the standard mean field sir model one observes a finite stationary distribution of the s type even for large population size the exact results for the ensemble averaged population size are compared with simulations for single realizations of the process and also with standard mean field theory which is expected to be valid on large fully connected graphs