levels of knotting of spatial handlebodies if h is a spatial handlebody i e a handlebody embedded in the 3 sphere a spine of h is a graph s3 such that h is a regular neighbourhood of usually h is said to be unknotted if it admits a planar spine this suggests that a handlebody should be considered not very knotted if it admits spines that enjoy suitable special properties building on this remark we define several levels of knotting of spatial handlebodies and we provide a complete description of the relationships between these levels focusing our attention on the case of genus 2 we also relate the knotting level of a spatial handlebody h to classical topological properties of its complement m s3 h such as its cut number more precisely we show that if h is not highly knotted then m admits special cut systems for m and we discuss the extent to which the converse implication holds along the way we construct obstructions that allow us to determine the knotting level of several families of spatial handlebodies these obstructions are based on recent quandle coloring invariants for spatial handlebodies on the extension to the context of spatial handlebodies of tools coming from the theory of homology boundary links on the analysis of appropriate coverings of handlebody complements and on the study of the classical alexander elementary ideals of their fundamental groups

a two part joint model for the analysis of survival and longitudinal binary data with excess zeros many longitudinal studies generate both the time to some event of interest and repeated measures data this article is motivated by a study on patients with a renal allograft in which interest lies in the association between longitudinal proteinuria a dichotomous variable measurements and the time to renal graft failure an interesting feature of the sample at hand is that nearly half of the patients were never tested positive for proteinuria 1g day during follow up which introduces a degenerate part in the random effects density for the longitudinal process in this article we propose a two part shared parameter model framework that effectively takes this feature into account and we investigate sensitivity to the various dependence structures used to describe the association between the longitudinal measurements of proteinuria and the time to renal graft failure

modeling λ invariants by p adic random matrices how often is the p adic invariant of an imaginary quadratic field equal to m we model this by the statistics of random p adic matrices and test these predictions numerically 2011 wiley periodicals inc

a lower bound for the volume of hyperbolic 3 orbifolds toutes les 3 varietes d orbites orientables completes ont un volume au moins 0 0000013 toutes les 3 varietes d orbites hyperboliques orientables completes cuspides ont un volume au moins 3 1 2 24

covolumes of nonuniform lattices in pu n 1 this paper studies the covolumes of nonuniform arithmetic lattices in pu n 1 we determine the smallest covolume nonuniform arithmetic lattices for each n the number of minimal covolume lattices for each n and study the growth of the minimal covolume as n varies in particular there is a unique lattice up to isomorphism in pu 9 1 of smallest euler poincare characteristic amongst all nonuniform arithmetic lattices in pu n 1 we also show that for each even n there are arbitrarily large families of nonisomorphic maximal nonuniform lattices in pu n 1 of equal covolume

a score test for zero inflation in a poisson distribution when analyzing poisson count data sometimes a lot of zeros are observed when there are too many zeros a zero inflated poisson distribution can be used a score test is presented to test whether the number of zeros is too large for a poisson distribution to fit the data well

bootstrap tests for overdispersion in a zero inflated poisson regression model summaryridout hinde and demetrio 2001 biometrics57 219 223 derived a score test for testing a zero inflated poisson zip regression model against zero inflated negative binomial zinb alternatives they mentioned that the score test using the normal approximation might underestimate the nominal significance level possibly for small sample cases to remedy this problem a parametric bootstrap method is proposed it is shown that the bootstrap method keeps the significance level close to the nominal one and has greater power uniformly than the existing normal approximation for testing the hypothesis

a geometrical angle on feynman integrals a direct link between a one loop n point feynman diagram and a geometrical representation based on the n dimensional simplex is established by relating the feynman parametric representations to the integrals over contents of n 1 dimensional simplices in non euclidean geometry of constant curvature in particular the four point function in four dimensions is proportional to the volume of a three dimensional spherical or hyperbolic tetrahedron which can be calculated by splitting into birectangular ones it is also shown that the known formula of reduction of the n point function in n 1 dimensions corresponds to splitting the related n dimensional simplex into n rectangular ones

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

a variational principle for weighted delaunay triangulations and hyperideal polyhedra we use a variational principle to prove an existence and uniqueness theorem for planar weighted delaunay triangulations with non intersecting site circles with prescribed combinatorial type and circle intersection angles such weighted delaunay triangulations may be interpreted as images of hyperbolic polyhedra with one vertex on and the remaining vertices beyond the infinite boundary of hyperbolic space thus the main theorem states necessary and sufficient conditions for the existence and uniqueness of such polyhedra with prescribed combinatorial type and dihedral angles more generally we consider weighted delaunay triangulations in piecewise flat surfaces allowing cone singularities with prescribed cone angles in the vertices the material presented here extends work by rivin on delaunay triangulations and ideal polyhedra

tubular neighborhoods of totally geodesic hypersurfaces in hyperbolic manifolds we show that a closed embedded totally geodesic hypersurface in a hyperbolic manifold has a tubular neighborhood whose width only depends on the area of the hypersurface namely we construct a tubular neighborhood function and show that an embedded closed totally geodesic hypersurface in a hyperbolic manifold has a tubular neighborhood whose width only depends on the area of the hypersurface and hence not on the geometry of the ambient manifold the implications of this result for volumes of hyperbolic manifolds is discussed in particular we show that ifm is a hyperbolic 3 manifold containingn rank two cusps andk disjoint totally geodesic embedded closed surfaces then the volume ofm is bigger than tfrac sqrt 3 4 n 4 4 k we also derive a hyperbolic quantitative version of the klein maskit combination theorem in all dimensions for free products of fuchsian groups using this last result we construct examples to illustrate the qualitative sharpness of our tubular neighborhood function in dimension three as an application of our results we give an eigenvalue estimate

specification and testing of some modified count data models abstract this paper explores the specification and testing of some modified count data models these alternatives permit more flexible specification of the data generating process dgp than do familiar count data models e g the poisson and provide a natural means for modeling data that are over or underdispersed by the standards of the basic models in the cases considered the familiar forms of the distributions result as parameter restricted versions of the proposed modified distributions accordingly score tests of the restrictions that use only the easily computed ml estimates of the standard models are proposed the tests proposed by hausman 1978 and white 1982 are also considered the tests are then applied to count data models estimated using survey microdata on beverage consumption

a score test for testing a zero inflated poisson regression model against zero inflated negative binomial alternatives count data often show a higher incidence of zero counts than would be expected if the data were poisson distributed zero inflated poisson regression models are a useful class of models for such data but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the poisson distribution we therefore provide a score test for testing zero inflated poisson regression models against zero inflated negative binomial alternatives

modeling heaping in self reported cigarette counts in studies of smoking behavior some subjects report exact cigarette counts whereas others report rounded off counts particularly multiples of 20 10 or 5 this form of data reporting error known as heaping can bias the estimation of parameters of interest such as mean cigarette consumption we present a model to describe heaped count data from a randomized trial of bupropion treatment for smoking cessation the model posits that the reported cigarette count is a deterministic function of an underlying precise cigarette count variable and a heaping behavior variable both of which are at best partially observed to account for an excess of zeros as would likely occur in a smoking cessation study where some subjects successfully quit we model the underlying count variable with zero inflated count distributions we study the sensitivity of the inference on smoking cessation by fitting various models that either do or do not account for heaping and zero inflation comparing the models by means of bayes factors our results suggest that sufficiently rich models for both the underlying distribution and the heaping behavior are indispensable to obtaining a good fit with heaped smoking data the analyses moreover reveal that bupropion has a significant effect on the fraction abstinent but not on mean cigarette consumption among the non abstinent

computation of the zeros of p adic l functions ii the authors have carried out a computational study of the zeros of kubota leopoldt p adic l functions results of this study have appeared recently in a previous article the present paper is a sequel to that article dealing with the computation of the zeros under certain conditions that complicate the original situation

a score type test for heterogeneity in zero inflated models in a stratified population we propose a score type statistic to evaluate heterogeneity in zero inflated models for count data in a stratified population where heterogeneity is defined as instances in which the zero counts are generated from two sources evaluating heterogeneity in this class of models has attracted considerable attention in the literature but existing testing procedures have primarily relied on the constancy assumption under the alternative hypothesis in this paper we extend the literature by describing a score type test to evaluate homogeneity against general alternatives that do not neglect the stratification information under the alternative hypothesis the limiting null distribution of the proposed test statistic is a mixture of chi squared distributions which can be well approximated by a simple parametric bootstrap procedure our numerical simulation studies show that the proposed test can greatly improve efficiency over tests of heterogeneity that ignore the stratification information an empirical application to dental caries data in early childhood further shows the importance and practical utility of the methodology in using the stratification profile to detect heterogeneity in the population

a score test for overdispersion in zero inflated poisson mixed regression model count data with extra zeros are common in many medical applications the zero inflated poisson zip regression model is useful to analyse such data for hierarchical or correlated count data where the observations are either clustered or represent repeated outcomes from individual subjects a class of zip mixed regression models may be appropriate however the zip parameter estimates can be severely biased if the non zero counts are overdispersed in relation to the poisson distribution in this paper a score test is proposed for testing the zip mixed regression model against the zero inflated negative binomial alternative sampling distribution and power of the test statistic are evaluated by simulation studies the results show that the test statistic performs satisfactorily under a wide range of conditions the test procedure is applied to pancreas disorder length of stay that comprised mainly same day separations and simultaneous prolonged hospitalizations

sensitivity of score tests for zero inflation in count data in many biomedical applications count data have a large proportion of zeros and the zero inflated poisson regression zip model may be appropriate a popular score test for zero inflation comparing the zip model to a standard poisson regression model was given by van den broek similarly for count data that exhibit extra zeros and are simultaneously overdispersed a score test for testing the zip model against a zero inflated negative binomial alternative was proposed by ridout hinde and demetrio however these test statistics are sensitive to anomalous cases in the data and incorrect inferences concerning the choice of model may be drawn in this paper diagnostic measures are derived to assess the influence of observations on the score statistics two examples that motivated the application of zero inflated regression models are considered to illustrate the importance of sensitivity analysis of the zero inflation tests

explicit bounds for primality testing and related problems many number theoretic algorithms rely on a result of ankeny which states that if the extended riemann hypothesis erh is true any nontrivial multiplicative subgroup of the integers modulo m omits a number that is o log2 m this has been generalized by lagarias montgomery and odlyzko to give a similar bound for the least prime ideal that does not split completely in an abelian extension of number fields this paper gives a different proof of this theorem in which explicit constants are supplied the bounds imply that if the erh holds a composite number m has a witness for its compositeness in the sense of miller or solovay strassen that is at most 2 log2m

smooth tests for the zero inflated poisson distribution in this article we construct three smooth goodness of fit tests for testing for the zero inflated poisson zip distribution against general smooth alternatives in the sense of neyman we apply our tests to a data set previously claimed to be zip distributed and show that the zip is not a good model to describe the data at rejection of the null hypothesis of zip the individual components of the test statistic which are directly related to interpretable parameters in a smooth model may be used to gain insight into an alternative distribution

empirical fitting of discrete distributions summary short tailed observed frequency distributions are often well fitted by a number of different theoretical discrete distributions with little discriminatory power an example is used to suggest how this may be carried further in some situations

computing p adic l functions of totally real number fields we prove explicit formulas for the p adic l functions of totally real number fields and show how these formulas can be used to compute values and representations of p adic l functions

modeling daily and weekly moderate and vigorous physical activity using zero inflated mixture poisson distribution recently developed accelerometer devices have been used in large epidemiological studies for continuous and objective monitoring of physical activities typically physical movements are summarized as minutes in light moderate and vigorous physical activities in each wearing day because of preponderance of zeros zero inflated distributions have been used for modeling the daily moderate or higher levels of physical activity yet these models do not fully account for variations in daily physical activity and cannot be extended to model weekly physical activity explicitly while the weekly physical activity is considered as an indicator for a subject s average level of physical activity to overcome these limitations we propose to use a zero inflated poisson mixture distribution that can model daily and weekly physical activity in same family of mixture distributions under this method the likelihood of an inactive day and the amount of exercise in an active day are simultaneously modeled by a joint random effects model to incorporate heterogeneity across participants if needed the method has the flexibility to include an additional random effect to address extra variations in daily physical activity maximum likelihood estimation can be obtained through gaussian quadrature technique which is implemented conveniently in an r package glmmadaptive method performances are examined using simulation studies the method is applied to data from the hispanic community health study study of latinos to examine the relationship between physical activity and bmi groups and within a participant the difference in physical activity between weekends and weekdays

on the volume of hyperbolic polyhedra where v1k is the volume vol 2 sj of the apex sjk sj c s to wjk schl ifli proved this formula for spherical simplices in 1936 h kneser gave a second very skilful proof of l see i l l and 4 sect 5 1 for both the spherical and hyperbolic cases up to a change of sign in the latter case but even for a three dimensional non euclidean simplex the integration of this schl li differential is practically impossible in fact the most basic objects in polyhedral geometry are orthoschemes or orthogonal simplices first introduced by schl fli an n orthoscheme r is an n simplex with vertices po pn such that

on the efficiency of score tests for homogeneity in two component parametric models for discrete data in many applications of two component mixture models for discrete data such as zero inflated models it is often of interest to conduct inferences for the mixing weights score tests derived from the marginal model that allows for negative mixing weights have been particularly useful for this purpose but the existing testing procedures often rely on restrictive assumptions such as the constancy of the mixing weights and typically ignore the structural constraints of the marginal model in this article we develop a score test of homogeneity that overcomes the limitations of existing procedures the technique is based on a decomposition of the mixing weights into terms that have an obvious statistical interpretation we exploit this decomposition to lay the foundation of the test simulation results show that the proposed covariate adjusted test statistic can greatly improve the efficiency over test statistics based on constant mixing weights a real life example in dental caries research is used to illustrate the methodology

analyzing excessive no changes in clinical trials with clustered data this article considers clinical trials in which the efficacy measure is taken from several sites within each patient such as the alveolar bone height of the tooth sites or bone mineral densities of the lumbar spine sites since usually only a small portion of these sites will exhibit changes the conventional method using per patient average gives a diluted result due to excessive no changes in the data different methods have been proposed for this type of data in the case where the observations are mutually independent this includes the popular two part model lachenbruch 2001 statistics in medicine 20 1215 1234 2002 statistical methods in medical research 11 297 302 which is related to the composite approach for discrete and continuous data in shih and quan 1997 statistics in medicine16 1225 1239 2001 statistica sinica 11 53 62 in this article we model the data with excessive zeros no changes in clustered data using a mixture of distributions and taking into account possible measurement errors this mixture model includes the two part model as a special case when one component of the mixture degenerates

fake quadrics from irreducible lattices acting on the product of upper half planes in the present article we provide examples of fake quadrics that is minimal complex surfaces of general type with the same numerical invariants as the smooth quadric in mathbb p 3 which are quotients of the bidisc by an irreducible lattice of automorphisms moreover we list classes of arithmetic lattices over a real quadratic number field which define a fake quadric and give general results towards a classification of all such fake quadrics

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

assessing influence for pharmaceutical data in zero inflated generalized poisson mixed models for clustered count data with excess zeros where the observations are either over dispersed or under dispersed the zero inflated generalized poisson mixed zigpm regression model may be appropriate in which the baseline discrete distribution is a generalized poisson distribution which is a natural extension of standard poisson distribution motivated by one data set drawn from a pharmaceutical study influence diagnostics for zigpm models based on case deletion and local influence analysis are developed in this work the one step approximations of the estimates under case deletion model and some case deletion measures are given meanwhile local influence measures are obtained under various perturbations of the observed data or model assumptions results from a pharmaceutical study illustrate the usefulness of the diagnostic statistics

maximum penalized likelihood estimation for independent and markov dependent mixture models summary this paper concerns the use and implementation of maximum penalized likelihood procedures for choosing the number of mixing components and estimating the parameters in independent and markov dependent mixture models computation of the estimates is achieved via algorithms for the automatic generation of starting values for the em algorithm computation of the information matrix is also discussed poisson mixture models are applied to a sequence of counts of movements by a fetal lamb in utero obtained by ultrasound the resulting estimates are seen to provide plausible mechanisms for the physiological process the analysis of count data that are overdispersed relative to the poisson distribution i e variance mean has received considerable recent attention such data might arise in a clinical study in which overdispersion is caused by unexplained or random subject effects alternatively we might observe a time series of counts in which temporal patterns in the data suggest that a poisson model and its implied randomness are inappropriate this paper is motivated by analysis of a time series of overdispersed count data generated in a study of central nervous system development in fetal lambs our data set consists of observed movement counts in 240 consecutive 5 second intervals obtained from a single animal in analysing these data we focus on the use of poisson mixture models assuming independent observations and also markov dependent mixture models or hidden markov models these models assume that the counts follow independent poisson distributions conditional on the rates which are generated from a mixing distribution either independently or with markov dependence we believe finite mixture models are particularly attractive because they provide plausible explanations for variation in the data this paper will emphasize the following issues concerning estimation inference and application of mixture models i choosing the number of model components ii applying the em algorithm to obtain parameter estimates iii generating sufficiently many starting values to identify a global maximum of the likelihood iv avoiding numerical instability

a score test for zero inflation in correlated count data to account for the preponderance of zero counts and simultaneous correlation of observations a class of zero inflated poisson mixed regression models is applicable for accommodating the within cluster dependence in this paper a score test for zero inflation is developed for assessing correlated count data with excess zeros the sampling distribution and the power of the test statistic are evaluated by simulation studies the results show that the test statistic performs satisfactorily under a wide range of conditions the test procedure is further illustrated using a data set on recurrent urinary tract infections