null surgery on knots in l spaces let k be a knot in an l space y with a dehn surgery to a surface bundle over s 1 we prove that k is rationally fibered that is the knot complement admits a fibration over s 1 as part of the proof we show that if k c y has a dehn surgery to s 1 x s 2 then k is rationally fibered in the case that k admits some s 1 x s 2 surgery k is floer simple that is the rank of hfk y k is equal to the order of h 1 y by combining the latter two facts we deduce that the induced contact structure on the ambient manifold y is tight in a different direction we show that if k is a knot in an l space y then any thurston norm minimizing rational seifert surface for k extends to a thurston norm minimizing surface in the manifold obtained by the null surgery on k i e the unique surgery on k with b 1 0

knot floer homology detects fibred knots ozsvath and szabo conjectured that knot floer homology detects fibred knots in s 3 we will prove this conjecture for null homologous knots in arbitrary closed 3 manifolds namely if k is a knot in a closed 3 manifold y y k is irreducible and hat hfk y k is monic then k is fibred the proof relies on previous works due to gabai ozsvath szabo ghiggini and the author a corollary is that if a knot in s 3 admits a lens space surgery then the knot is fibred

risk ratio and rate ratio estimation in case cohort designs hypertension and cardiovascular mortality multivariate analysis in case base designs depends on approximate methods in the present study new pseudo likelihood methods are developed for this design with these methods the case cohort risk ratio and rate ratio as well as their standard errors are easily estimated using logistic regression and poisson regression respectively this is illustrated by the association between hypertension and cardiovascular mortality in a cohort estimated by case cohort analysis using samples of several sizes the estimates are compared with those obtaining in full cohort and nested case control designs the results indicate that these methods which require nothing but widely available computer software are valid the case cohort design therefore is a good sometimes even advantageous alternative to the nested case control design in studying a disease that is not very rare application of the risk ratio method to the full cohort using a sample of 100 per cent follows logically whenever the true risk ratio is desired instead of the odds ratio a multivariate model for its estimation is therefore available

likelihood inference for exchangeable binary data with varying cluster sizes ce papier etudie l estimation au maximum de vraisemblance dans des modeles satures et insatures pour des donnees binaires correlees echangeables lorsqu on dispose d un echantillon de clusters independants de tailles variables nous discutons plusieurs parametrisations de ces modeles et nous proposons l utilisation de l algorithme em pour obtenir des estimations du maximum de vraisemblance la methodologie est illustree par des applications a une etude d agregation familiale de maladie et a la construction d un essai randomise par groupe pour la prevention du cancer

a flexible method to measure synchrony in neuronal firing neurons can transmit information about the characteristics of a stimulus through the spike rate of neurons and synchronization of the neurons various association measure can be used to describe how synchronous two spike trains are we propose a new measure of synchrony the conditional synchrony measure which is the probability of firing together given that at least one of the two neurons is active focus is on the specification of a flexible marginal model for multivariate correlated binary data together with a pseudolikelihood estimation approach to adequately and directly describe the measures of interest a joint model must allow different time and covariate dependent firing rates for each neuron and also must account for the association between them the association between neurons might depend on covariates as well

a simple frailty model for family studies with covariates a simple easily analysed frailty model based on logistic regression and employing only binary frailties is developed and analysed methods for testing for frailty and estimates of frailty parameters and covariate effects are presented the effects of ignoring or mis specifying frailty are examined in detail and shown to downwardly bias the estimates of covariate effects in a variety of situations even when frailty is overestimated when the true frailty is large it can be difficult to estimate accurately because of the flatness of the likelihood however it is shown that this does not have a large influence on the estimates of the effects of the observed covariates methods for dealing with multiple frailties for example sibships and spouse pairs are also developed the results are illustrated on a large data set examining the risk factors associated with palmar keratoses

foliations orders representations l spaces and graph manifolds abstract we show that the properties of admitting a co oriented taut foliation and having a left orderable fundamental group are equivalent for rational homology 3 sphere graph manifolds and relate them to the property of not being a heegaard floer l space this is accomplished in several steps first we show how to detect families of slopes on the boundary of a seifert fibred manifold in four different fashions using representations using left orders using foliations and using heegaard floer homology then we show that each method of detection determines the same family of detected slopes next we provide necessary and sufficient conditions for the existence of a co oriented taut foliation on a graph manifold rational homology 3 sphere respectively a left order on its fundamental group which depend solely on families of detected slopes on the boundaries of its pieces the fact that heegaard floer methods can be used to detect families of slopes on the boundary of a seifert fibred manifold combines with certain conjectures in the literature to suggest an l space gluing theorem for rational homology 3 sphere graph manifolds as well as other interesting problems in heegaard floer theory

statistical properties of aggregation with injection we study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice for one dimensional and mean field models we show that there exists a statistically invariant steady state when randomly charged particles are continuously injected the steady state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension the response of the system to a perturbation i e relaxation is characterized by either a power law decay t 1 or a compressed exponential decay exp t 1

separability of item and person parameters in response time models this paper discusses two forms of separability of item and person parameters in the context of response time rt models the first is separate sufficiency the existence of sufficient statistics for the item person parameters that do not depend on the person item parameters the second is ranking independence the likelihood of the item person ranking with respect to rts does not depend on the person item parameters for each form a theorem stating sufficient conditions is proved the two forms of separability are shown to include several special cases of models from psychometric and biometric literature ranking independence imposes no restrictions on the general distribution form but on its parametrization an estimation procedure based upon ranks and pseudolikelihood theory is discussed as well as the relation of ranking independence to the concept of double monotonicity

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

comparison of alternative regression models for paired binary data we used simulated data derived from real ophthalmologic examples to evaluate the performance of alternative logistic regression approaches for paired binary data approaches considered were standard logistic regression ignoring the correlation between fellow eyes treating individuals classified on the basis of their more impaired eye as the unit of analysis or considering only right eyes marginal logistic regression models fitted by the maximum likelihood approach of lipsitz laird and harrington or the estimating equation approach of liang and zeger and conditional logistic regression models fitted by the maximum likelihood approach of rosner or the estimating equation approach of connolly and liang taylor series approximations were used to compare conditional and marginal parameter estimates consideration of type i and ii error rates found application of standard logistic regression to be inferior to methods that treated the eye as the unit of analysis and accounted for the correlation between fellow eyes among these latter approaches none was uniformly superior to the others across the range of condition considered

functional association models for multivariate survival processes we consider multivariate temporal processes that are continuously observed within overlapping time windows the intended application is in censored multistate and multivariate survival settings where point processes are continuously observed these data differ from other functional data like longitudinal data which are discretely observed at irregular times existing functional approaches to survival processes use intensity models which require smoothing and depend critically on the choice of smoothing parameters similarly to discretely observed data in this article we study functional mean and association regression models for the point processes with unspecified time varying coefficients the continuous observation scheme is exploited the coefficients may be estimated nonparametrically by extending generalized estimating equations to continuously observed data the estimators automatically converge at the parametric rate without smoothing unlike with discretely observed data uniform consistenc

a class of logistic regression models for multivariate binary time series abstract a logistic model for multivariate binary time series is proposed first we establish the equivalence between a log linear model for the marginal distribution of a multivariate binary random vector and logistic models for the conditional distributions of each component given the others the logistic formulation is used to describe a markov chain for each series which implies a markov model for the vector of time series a pseudolikelihood estimation procedure is presented the methods are illustrated with data on psychosomatic and psychological diagnoses for families in a health maintenance plan

on floer homology and the berge conjecture on knots admitting lens space surgeries we complete the first step in a two part program proposed by baker grigsby and the author to prove that berge s construction of knots in the three sphere which admit lens space surgeries is complete the first step which we prove here is to show that a knot in a lens space with a threesphere surgery has simple in the sense of rank knot floer homology the second conjectured step involves showing that for a fixed lens space the only knots with simple floer homology belong to a simple finite family using results of baker we provide evidence for the conjectural part of the program by showing that it holds for a certain family of knots coupled with work of ni these knots provide the first infinite family of non trivial knots which are characterized by their knot floer homology as another application we provide a floer homology proof of a theorem of berge

on l spaces and left orderable fundamental groups examples suggest that there is a correspondence between l spaces and three manifolds whose fundamental groups cannot be left ordered in this paper we establish the equivalence of these conditions for several large classes of manifolds in particular we prove that they are equivalent for any closed connected orientable geometric three manifold that is non hyperbolic a family which includes all closed connected orientable seifert fibred spaces we also show that they are equivalent for the twofold branched covers of non split alternating links to do this we prove that the fundamental group of the twofold branched cover of an alternating link is left orderable if and only if it is a trivial link with two or more components we also show that this places strong restrictions on the representations of the fundamental group of an alternating knot complement with values in text homeo s 1

two random effects models for multivariate binary data we consider two regression models for multivariate binary data in the case that the marginal success probabilities are unequal the first model is based on an additive random effect operating on the probability scale the second model assumes a discrete random effect operates on the logit scale consequently the interpretation of the regression parameters differs for the two models their use is illustrated by application to some dental data

architecture of optimal transport networks we analyze the structure of networks minimizing the global resistance to flow or dissipative energy with respect to two different constraints fixed total channel volume and fixed total channel surface area first we show that channels must be straight and have uniform cross sectional areas in such optimal networks we then establish a relation between the cross sectional areas of adjoining channels at each junction indeed this relation is a generalization of murray s law originally established in the context of local optimization we establish a relation too between angles and cross sectional areas of adjoining channels at each junction which can be represented as a vectorial force balance equation where the force weight depends on the channel cross sectional area a scaling law between the minimal resistance value and the total volume or surface area value is also derived from the analysis furthermore we show that no more than three or four channels meet at each junction of optimal bidimensional networks depending on the flow profile e g poiseuille like or pluglike and the considered constraint fixed volume or surface area in particular we show that sources are directly connected to wells without intermediate junctions for minimal resistance networks preserving the total channel volume in case of plug flow regime finally all these results are compared with the structure of natural networks

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

marginal models for correlated binary responses with multiple classes and multiple levels of nesting a model for correlated binary data is presented marginal probabilities and odds ratios are allowed to have general regression structures that include multiple classes and multiple levels of nesting estimation is done through the generalized estimating equations approach of liang and zeger 1986 biometrika 73 13 22 they are contrasted with conditional models and recommendations for choosing between the two are given examples from genetic epidemiology are presented

multivariate methods for clustered binary data with more than one level of nesting abstract clustered data occur frequently in statistical practice in some areas of application such as ophthalmology clustered data are the rule rather than the exception in this setting standard multivariate methods such as logistic regression are invalid because of the lack of independence among outcomes for individual sample points within a cluster in rosner 1984 a polychotomous logistic regression model was presented to control for the effect of both cluster and individual specific covariates while accounting for the correlation among units within a cluster this model reduces to a beta binomial model in the absence of covariates and to an ordinary logistic model for clusters of size 1 and for larger clusters when no correlation is present a 1 level of nesting correlation structure is assumed as is typically found in ophthalmology where the person is the cluster and the individual eyes are the units within a cluster in this article this model is generalized to a 2 level of nesting struc

floer simple manifolds and l space intervals abstract an oriented three manifold with torus boundary admits either no l space dehn filling a unique l space filling or an interval of l space fillings in the latter case which we call floer simple we construct an invariant which computes the interval of l space filling slopes from the turaev torsion and a given slope from the interval s interior as applications we give a new proof of the classification of seifert fibered l spaces over s 2 and prove a special case of a conjecture of boyer and clay 6 about l spaces formed by gluing three manifolds along a torus

rotation numbers of products of circle homeomorphisms let h homeo s 1 be the group of orientation preserving homeomorphisms of the circle our main question is the following for given numbers 71 and y2 what are the possible rotation numbers of a product qlq2 of elements ql q2 of h with rotation numbers 71 y2 what if some or all of ql q2 qlq2 are required to be conjugate to rotations our original motivation was the question of which seifert fibered 3 manifolds admit transverse foliations which we discuss in sect 7 the answers turn out to be much more subtle than we originally expected we can make the question more precise by working in the universal covering group 7 of h this is the group of homeomorphisms of f which lift from an orientation preserving homeomorphism of s 1 r z that is 7 q r r i q monotonically increasing q r 1 q r 1 for all r r 7 is simply connected since it is a convex subset of ir for y define sh h by

analytical and numerical study of optimal channel networks we analyze the optimal channel network model for river networks using both analytical and numerical approaches this is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the optimal configurations the fractal character of river networks is reflected in the power law behavior of various quantities characterizing the morphology of the basin in the context of a finite size scaling ansatz the exponents describing the power law behavior are calculated exactly and show mean field behavior except for two limiting values of a parameter characterizing the dissipated energy for which the system belongs to different universality classes two modified versions of the model incorporating quenched disorder are considered the first simulates heterogeneities in the local properties of the soil and the second considers the effects of a nonuniform rainfall in the region of mean field behavior the model is shown to be robust for both kinds of perturbations in the two limiting cases the random rainfall is still irrelevant whereas the heterogeneity in the soil properties leads to different universality classes results of a numerical analysis of the model are reported that confirm and complement the theoretical analysis of the global minimum the statistics of the local minima are found to resemble more strongly observational data on real rivers

dehn surgery on knots in d dehn considered the following method for constructing 3 manifolds remove a solid torus neighborhood n k of some knot x in the 3 sphere s and sew it back differently in particular he showed that taking x to be the trefoil one could obtain infinitely many non simply connected homology spheres o in this way let mx s n k then the different resewings are parametrized by the isotopy class r of the simple closed curve on the torus omk that bounds a meridional disk in the re attached solid torus we denote the resulting closed oriented 3 manifold by mk and say that it is obtained by r dehn surgery on x more generally one can consider the manifolds ml obtained by r dehn surgery on a fc component link l xi u u kk in s where r r it turns out that every closed oriented 3 manifold can be constructed in this way wal lie thus a good understanding of dehn surgery might lead to progress on general questions about the structure of 3 manifolds starting with the case of knots it is natural to extend the context a little and consider the manifolds m r obtained by attaching a solid torus v to an arbitrary compact oriented irreducible every 2 sphere bounds a 3 ball 3 manifold m with dm an incompressible torus where r is the isotopy class slope on dm of the boundary of a meridional disk of v we say that m r is the result of r dehn filling on m an observed feature of this construction is that

on the set of l space surgeries for links abstract we study the qualitative structure of the set ls of integral l space surgery slopes for links with two components it is known that the set of l space surgery slopes for a nontrivial l space knot is always a positive half line however already for two component torus links the set ls has a very complicated structure e g in some cases it can be unbounded from below in order to probe the geometry of this set we ask if it is bounded from below for more general l space links with two components for algebraic two component links we provide three complete characterizations for the boundedness from below one in terms of the alexander polynomial one in terms of the embedded resolution graph and one in terms of the so called h function introduced by the authors in 9 it turns out that ls is bounded from below for most algebraic links if it is unbounded from below it must contain a negative half line parallel to one of the axes we also give a sufficient condition for boundedness for arbitrary l space links

a parametric model for cluster correlated categorical data summary a fully parametric copula model for symmetric dependent clustered categorical data is discussed the model accommodates any marginal regression models of interest and admits a broad range of within cluster association the form of the distribution is independent of cluster size and may be used to model data with varying cluster sizes the model contains an association parameter that is estimated from the data to give a measure of the strength of the within cluster association and also a test of independence two examples are given to illustrate the methods

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

some comments on rosner s multiple logistic model for clustered data rosner 1984 biometrics 41 1025 1035 proposed a binary regression model for analyzing binary response data gathered in clusters or groups this model is useful for understanding the degree of intracluster correlation among responses adjusted for the potential confounding effects of other covariates however estimates of the effects of covariates on the binary outcome obtained using rosner s model can be misleading for example we show that the covariate effects given by rosner s model do not correspond to those measured by either of the two standard approaches for correlated binary data we present an example that compares the regression coefficients arising from fits of rosner s model to other logistic models for clustered observations using data from a study of breast disease

multivariate methods for binary longitudinal data with heterogeneous correlation over time clustered binary data occur frequently in biostatistical work one particular application is in binary longitudinal data where several visits are available for the same individual several approaches have been proposed for the analysis of clustered binary data in rosner a polychotomous logistic regression model was proposed which is a generalization of the beta binomial distribution and allows for person and visit specific covariates while controlling for clustering effects one assumption of this model is that all pairs of visits within an individual are equally correlated which may be inappropriate if several visits are available over a long follow up period in this paper this approach is extended to allow for heterogeneous correlation over time the total time period is divided into subintervals and a beta binomial mixture model is introduced to estimate odds ratios relating outcomes for pairs of visits both within a subinterval as well as in different subintervals to include covariates an extension of the polychotomous logistic regression model is proposed which allows one to estimate effects of person subinterval and visit specific covariates while controlling for clustering using the beta binomial mixture model this model is applied to the analysis of respiratory symptom data in children collected over a 14 year period in east boston ma in relation to maternal and child smoking where the unit is the child and symptom history is divided into early adolescent and late adolescent symptom experience

scaling optimality and landscape evolution a nonlinear model is studied which describes the evolution of a landscape under the effects of erosion and regeneration by geologic uplift by mean of a simple differential equation the equation already in wide use among geomorphologists and in that context obtained phenomenologically is here derived by reparametrization invariance arguments and exactly solved in dimension d 1 results of numerical simulations in d 2 show that the model is able to reproduce the critical scaling characterizing landscapes associated with natural river basins we show that configurations minimizing the rate of energy dissipation optimal channel networks are stationary solutions of the equation describing the landscape evolution numerical simulations show that a careful annealing of the equation in the presence of additive noise leads to configurations very close to the global minimum of the dissipated energy characterized by mean field exponents we further show that if one considers generalized river network configurations in which splitting of the flow i e braiding and loops are allowed the minimization of the dissipated energy results in spanning loopless configurations under the constraints imposed by the continuity equations this is stated in the form of a general theorem applicable to generic networks suggesting that other branching structures occurring in nature may possibly arise as optimal structures minimizing a cost function

multivariate methods in ophthalmology with application to other paired data situations methods are presented for performing multiple regression analyses and multiple logistic regression analyses on ophthalmologic data with normally and binomially distributed outcome variables while accounting for the intraclass correlation between eyes these methods are extended to more general nested data structures where a variable number of subunits are available for each primary unit of analysis as in familial data these methods can also be applied to other types of paired data as in matched studies with a variable matching ratio where one has a continuous outcome variable and wishes to control for other confounding variables while maintaining the matching examples are given of these methods with a group of over 400 patients with retinitis pigmentosa in which spherical refractive error and visual acuity are related to genetic type after the effects of age sex and the presence of cataract have been controlled

minimum energy and fractal structures of drainage networks this paper explores the similarities of digital elevation maps dems of natural river basins and optimal channel network ocn configurations obtained minimizing the total rate of energy expenditure in the system as a whole and in its parts striking similarities are observed for natural and optimal networks in their fractal aggregation structure and in certain multifractal structures found to be characteristic of river basins our results suggest upon critical assessment of the reliability of the identification of the attractor of the underlying dynamics implied by our optimality concepts that fractal structures are indeed possibly a product of least energy dissipation power laws emerging in the description of the distribution of aggregated quantities from both dems and ocns suggest a link with the framework of self organized criticality in the dynamics of natural channel network formation also the geomorphological description of ocns reveals surprising analogies with well known empirical or experimental results a comparison of peano s basins with ocns suggests that nature seems to reject the type of strict self similarity exhibited by peano s construct in favor of different shapes implying statistical self similarity not only because of chance acting through random conditions but also because of necessity as reflected by least energy expenditure considerations

conditional logistic regression models for correlated binary data summary a class of conditional logistic regression models for clustered binary data is considered this includes the polychotomous logistic model of rosner 1984 as a special case properties such as the joint distribution and pairwise odds ratio are investigated a class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach an example on chronic obstructive pulmonary disease among sibs is presented for illustration

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

graphical methods for assessing logistic regression models abstract in ordinary linear regression graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data for logistic regression models the discreteness of binary data makes it difficult to interpret such displays modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models local mean deviance plots are useful for detecting overall lack of fit empirical probability plots help point out isolated departures from the fitted model partial residual plots when smoothed to show underlying structure help identify specific causes of lack of fit these methods are illustrated through the analyses of simulated and real data

the colored jones polynomials and the simplicial volume of a knot we show that the set of colored jones polynomials and the set of generalized alexander polynomials defined by akutsu deguchi and ohtsuki intersect non trivially moreover it is shown that the intersection is at least includes the set of kashaev s quantum dilogarithm invariants for links therefore kashaev s conjecture can be restated as follows the colored jones polynomials determine the hyperbolic volume for a hyperbolic knot modifying this we propose a stronger conjecture the colored jones polynomials determine the simplicial volume for any knot if our conjecture is true then we can prove that a knot is trivial if and only if all of its vassiliev invariants are trivial in 13 r m kashaev defined a family of complex valued link invariants indexed by integers n 2 using the quantum dilogarithm later he calculated the asymptotic behavior of his invariant and observed that for the three simplest hyperbolic knots it grows as exp vol k n 2 when n goes to the infinity where vol k is the hyperbolic volume of the complement of a knotk 14 this amazing result and his conjecture that the same also holds for any hyperbolic knot have been almost ignored by mathematicians since his definition of the invariant is too complicated though it uses only elementary tools the aim of this paper is to reveal his mysterious definition and to show that his invariant is nothing but a specialization of the colored jones polynomial the colored jones polynomial is defined for colored links each component is decorated with an irreducible representation of the lie algebra sl 2 c the original jones polynomial corresponds to the case that all the colors are identical to the 2 dimensional fundamental representation we show that kashaev s invariant with parameter n coincides with the colored jones polynomial in a certain normalization with every color the n dimensional representation evaluated at the primitive n th root of unity we have to normalize the colored jones polynomial so that the value for the trivial knot is one for otherwise it always vanishes on the other hand there are other colored polynomial invariants the generalized multivariable alexander polynomial defined by y akutsu t deguchi and t ohtsuki 1 they used the same lie algebra sl 2 c but a different hierarchy of representations their invariants are parameterized by c 1 parameters an integer date february 1 2008 1991 mathematics subject classification 57m25 57m50 17b37 81r50

quasipositivity as an obstruction to sliceness for an oriented link l s 3 d 4 let s l be the greatest euler characteristic f of an oriented 2 manifold f without closed components smoothly embedded in d 4 with boundary l a knot k is slice if s k 1 realize d 4 in c 2 as z w z 2 w 2 1 it has been conjectured that if v is a nonsingular complex plane curve transverse to s 3 then s v s 3 v d 4 kronheimer and mrowka have proved this conjecture in the case that v d 4 is the milnor fiber of a singularity i explain how this seemingly special case implies both the general case and the slice bennequin inequality for braids as applications i show that various knots are not slice e g pretzel knots like p 3 5 7 all knots obtained from a positive trefoil o 2 3 by iterated untwisted positive doubling

maximum likelihood estimation of order m for stationary stochastic processes sometimes the likelihood cannot be computed even introducing approximations whose effect is asymptotically negligible to overcome this problem for inference from a stochastic process we approximate the log likelihood by a sum whose generic term is the density function of the corresponding sample element conditional on the m most recent observations for some m s 0 general results on the asymptotic properties of the associated estimates are given and numerical comparisons with other estimators are carried out in special cases

multivariate methods for clustered binary data with multiple subclasses with application to binary longitudinal data clustered binary data occur frequently in biostatistical work several approaches have been proposed for the analysis of clustered binary data in rosner 1984 biometrics 40 1025 1035 a polychotomous logistic regression model was proposed that is a generalization of the beta binomial distribution and allows for unit and subunit specific covariates while controlling for clustering effects one assumption of this model is that all pairs of subunits within a cluster are equally correlated this is appropriate for ophthalmologic work where clusters are generally of size 2 but may be inappropriate for larger cluster sizes a beta binomial mixture model is introduced to allow for multiple subclasses within a cluster and to estimate odds ratios relating outcomes for pairs of subunits within a subclass as well as in different subclasses to include covariates an extension of the polychotomous logistic regression model is proposed which allows one to estimate effects of unit class and subunit specific covariates while controlling for clustering using the beta binomial mixture model this model is applied to the analysis of respiratory symptom data in children collected over a 14 year period in east boston massachusetts in relation to maternal and child smoking where the unit is the child and symptom history is divided into early adolescent and late adolescent symptom experience

khovanov homology and the slice genus we use lee s work on the khovanov homology to define a knot invariant s we show that s k is a concordance invariant and that it provides a lower bound for the smooth slice genus of k as a corollary we give a purely combinatorial proof of the milnor conjecture

constrained monte carlo maximum likelihood for dependent data maximum likelihood estimates mles in autologistic models and other exponential family models for dependent data can be calculated with markov chain monte carlo methods the metropolis algorithm or the gibbs sampler which simulate ergodic markov chains having equilibrium distributions in the model from one realization of such a markov chain a monte carlo approximant to the whole likelihood function can be constructed the parameter value if any maximizing this function approximates the mle

knot floer homology detects genus one fibred knots ozsv ath and szab o conjectured that knot floer homology detects fibred knots we propose a strategy to approach this conjecture based on contact topology and gabai s theory of sutured manifold decomposition we implement this strategy for genus one knots obtaining as a corollary that if rational surgery on a knot k gives the poincar e homology sphere sigma 2 3 5 then k is the left handed trefoil knot

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

relative risk risk difference and rate difference models for sparse stratified data a pseudo likelihood approach we consider a relative risk and a risk difference model for binomial data and a rate difference model for poisson person year data it is assumed that the data are stratified in a large number of small strata if each stratum has its own parameter in the model then due to the large number of parameters straightforward maximum likelihood leads to inconsistent estimates of the relevant parameters by contrast to the logistic model conditioning on the number of events per stratum does not help in eliminating the stratum nuisance parameters we propose a pseudo likelihood method to overcome these consistency problems the resulting pseudo maximum likelihood estimates can easily be computed with standard statistical software our approach gives a more general framework for the mantel haenszel type estimators proposed in the literature in the special case of a series of 2 x 2 tables for the risk and rate difference models our approach yields exactly these ad hoc mantel haenszel estimators while for the relative risk model it gives a close approximation of the mantel haenszel relative risk estimator for the regression models corresponding to the association measures relative risk risk difference and rate difference our method provides analogues of conditional logistic regression which were not previously available

universal scaling of optimal current distribution in transportation networks transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents we prove that optimal current distributions for a uniformly injected d dimensional network exhibit robust scale invariance properties independently of the particular cost function considered as long as it is convex we find that in the limit of large currents the distribution decays as a power law with an exponent equal to 2d 1 d 1 the current distribution can be exactly calculated in d 2 for all values of the current numerical simulations further suggest that the scaling properties remain unchanged for both random injections and by randomizing the convex cost functions