fock space representations of affine lie algebras and integral representations in the wess zumino witten models fock space representations of affine lie algebras are studied explicit forms of correction terms adding to the currentsf i z are determined it is proved that the sugawara energy momentum tensor on the fock spaces is quadratic in free bosons furthermore screening operators are constructed this implies the existence of generalized hypergeometric integrals satisfying the knizhnik zamolodchikov equation

a q deformation of wakimoto modules primary fields and screening operators theq vertex operators of frenkel and reshetikhin are studied by means of aq deformation of the wakimoto module for the quantum affine algebrau q widehat mathfrak s mathfrak l 2 at an arbitrary levelk 0 2 a fock module version of theq deformed primary field of spinj is introduced as well as the screening operators which anti commute with the action ofu q widehat mathfrak s mathfrak l 2 up to a total difference of a field a proof of the intertwining property is given for theq vertex operators corresponding to the primary fields of spinj 1 2z 0 a sample calculation of the correlation function is also given

modelling extreme multivariate events summary the classical treatment of multivariate extreme values is through componentwise ordering though in practice most interest is in actual extreme events here the point process of observations which are extreme in at least one component is considered parametric models for the dependence between components must satisfy certain constraints two new techniques for generating such models are presented aspects of the statistical estimation of the resulting models are discussed and are illustrated with an application to oceanographic data

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

new method for deriving eigenvalue rate with respect to support location the authors present a new method to derive the formulas of eigenvalue rate with respect to in span support location using the generalized variational principle of the rayleigh quotient following the ideas of this note the eigenvalue rate with respect to such variables as location of discrete or continuous in span supports the location of concentrated mass location of elastic support and location of a substructure can be derived without any conceptual difficulties

on osp 2 2 conformal field theories we study the conformal field theories corresponding to current superalgebras osp 2 2 1 k and osp 2 2 2 k we construct the free field realizations screen currents and primary fields of these current superalgebras at general level k all the results for osp 2 2 2 k are new and the results for the primary fields of osp 2 2 1 k also seem to be new our results are expected to be useful in the supersymmetric approach to gaussian disordered systems such as the random bond ising model and the dirac model

fisher information for a bivariate extreme value distribution summary a representation of lee 1979 is used to give an explicit algebraic formula for the 5 x 5dimensional fisher information matrix for gumbel s 1960 bivariate type ii distribution of extreme values with weibull marginals numerical evaluations show that our parameterization makes the dependence parameter almost exactly orthogonal to the two marginal scale parameters

non weight modules over the affine virasoro algebra of type a1 in this paper we study a class of nonweight modules over the affine virasoro algebra of type a1 which are free modules of rank one when restricted to the universal enveloping algebra of the cartan subalgebra modulo center we give the classification of such modules moreover the simplicity and the isomorphism classes of these modules are determined in this paper we study a class of nonweight modules over the affine virasoro algebra of type a1 which are free modules of rank one when restricted to the universal enveloping algebra of the cartan subalgebra modulo center we give the classification of such modules moreover the simplicity and the isomorphism classes of these modules are determined

eigenvalue sensitivity analysis of planar frames with variable joint and support locations various sensitivity equations are developed in this study for eigenvalue sensitivity analysis of planar frames with variable joint and support locations the emphasis is placed on the derivation of the sensitivity equations by the continuum approach a variational form of an eigenvalue equation is first derived in which all of the quantities are expressed with respect to the local coordinate system the material derivative of this variational form is then sought to account for the changes in the member s length and orientation resulting from the perturbation of joint and support locations finally eigenvalue sensitivity equations are formulated in either domain quantities by the domain method or boundary quantities by the boundary method examples are presented to validate these derived sensitivity equations with analytical solutions as well as numerical results it is concluded that the sensitivity equation derived by the boundary method is computationally more efficient but less accurate than that of the domain method nevertheless both of them are superior to the conventional discrete analytical method in terms of computational efficiency nomenclature ait ei ij cross sectional area young s modulus and moment of inertia of member respectively b design variable j a line functional j and its total shape derivative k m global stiffness and mass matrices at m elementary stiffness and mass matrices dj pj length orientation angle and mass density of member respectively mit rij cosine and sine of member n total number of members n

markov chain models for threshold exceedances in recent research on extreme value statistics there has been an extensive development of threshold methods first in the univariate case and subsequently in the multivariate case as well in this paper an alternative methodology for extreme values of univariate time series is developed by assuming that the time series is markovian and using bivariate extreme value theory to suggest appropriate models for the transition distributions a new likelihood representation for threshold methods is presented which we apply to a markovian time series an important motivation for developing this kind of theory is the possibility of calculating probability distributions for functionals of extreme events we address this issue by showing how a theory of compound poisson limits for additive functionals can be combined with simulation to obtain numerical solutions for problems of practical interest the methods are illustrated by application to temperature data

pairwise dependence diagnostics for clustered failure time data frailty and copula models specify a parametric dependence structure for multivariate failure time data estimation of some joint quantities can be highly sensitive to the assumed parametric form and hence model fit is an important issue this paper lays out a general diagnostic framework for evaluating and selecting frailty and copula models the approach is based on the cumulative sum of residuals that are calculated in bivariate time the residuals reflect the difference between the observed and expected bivariate association structures the proposed model checking process is interpretable with a limiting distribution which can be approximated using the bootstrap simulations and a data example illustrate the practical application of the method

affine kac moody algebras and semi infinite flag manifolds we study representations of affine kac moody algebras from a geometric point of view it is shown that wakimoto modules introduced in 18 which are important in conformal field theory correspond to certain sheaves on a semi infinite flag manifold with support on its schhubert cells this manifold is equipped with a remarkable semi infinite structure which is discussed in particular the semi infinite homology of this manifold is computed the cousin grothendieck resolution of an invertible sheaf on a semi infinite flag manifold gives a two sided resolution of an irreducible representation of an affine algebras consisting of wakimoto modules this is just the brst complex as a byproduct we compute the homology of an algebra of currents on the real line with values in a nilpotent lie algebra

semiparametric regression analysis for recurrent event interval counts this paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation we consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow up at each visit the patient reports the number of events that occurred since the previous visit or an examination reveals the number of accumulated events such as skin cancers the exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow up times each patient s record thus consists of a sequence of clinic visit dates event counts corresponding to the successive time intervals between clinic visits and baseline covariates we propose a semiparametric regression model extending the fully parametric model of thall 1988 biometrics 44 197 209 to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time varying nature of the underlying event rate covariate effects enter the model parametrically while the underlying time varying event rate is modelled nonparametrically the method of severini and wong 1992 annals of statistics 20 1768 1802 is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution a simulation study and application to a data set are provided

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

bayesian modeling of air pollution extremes using nested multivariate max stable processes capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks in order to investigate the multivariate spatial dependence properties of air pollution extremes we introduce a new class of multivariate max stable processes our proposed model admits a hierarchical tree based formulation in which the data are conditionally independent given some latent nested positive stable random factors the hierarchical structure facilitates bayesian inference and offers a convenient and interpretable characterization we fit this nested multivariate max stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the los angeles area showing that the proposed model succeeds in capturing their complex tail dependence structure

bosonic fock representations of the affine virasoro algebra bosonic fock representations of the virasoro algebra and the affine lie algebras attached to classical lie algebras with non zero centres are explicitly presented based on these fock representations of the affine virasoro algebra are constructed an automorphism of the affine virasoro algebra is also given

two interpretations of the discrimination parameter in this paper we propose two interpretations for the discrimination parameter in the two parameter logistic model 2plm the interpretations are based on the relation between the 2plm and two stochastic models in the first interpretation the 2plm is linked to a diffusion model so that the probability of absorption equals the 2plm the discrimination parameter is the distance between the two absorbing boundaries and therefore the amount of information that has to be collected before a response to an item can be given for the second interpretation the 2plm is connected to a specific type of race model in the race model the discrimination parameter is inversely related to the dependency of the information used in the decision process extended versions of both models with person to person variability in the difficulty parameter are considered when fitted to a data set it is shown that a generalization of the race model that allows for dependency between choices and response times rts is the best fitting model

bivariate extreme value theory models and estimation summary bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima no natural parametric family exists for the dependence between the marginal distributions but there are considerable restrictions on the dependence structure we consider modelling the dependence function with parametric models for which two new models are presented tests for independence and discriminating between models are also given the estimation procedure and the flexibility of the new models are illustrated with an application to sea level data extreme value theory has recently been an area of much theoretical and practical work univariate theory is a well documented area whereas bivariate multivariate extreme value theory has until recently received surprisingly little attention in the multivariate case no natural parametric family exists for the dependence structure so this must be modelled in some way in the analysis of environmental extreme value data there is a need for models of dependence between extremes from different sources for example at various sea ports or at various points of a river in this paper we consider bivariate extreme value distributions we assume without loss of generality that we have exponential marginal distributions with unit means the class of bivariate exponential distributions in which we are interested satisfy a strong stability relation exponential variables x y satisfy the stability relation if and only if w min ax by is also exponentially distributed for all a b 0 pickands 1981 therefore the models we will consider have particular application in reliability and survival analysis one approach to modelling the dependence structure is via parametric models this requires a flexible family of models which satisfy certain constraints models are of two kinds either differentiable or nondifferentiable all nondifferentiable models give distri butions which are singular with nonzero probability concentrated on a certain subspace the differentiable models have densities but the existing models are symmetric which leads to the variables being exchangeable here we present two new asymmetric differenti able models which have increased flexibility properties of the differentiable models are examined estimation of the parametric models has previously been by ad hoc methods because there is a nonregular estimation problem when the margins are independent for the

fisher information for a multivariate extreme value distribution summary explicit algebraic formulae for the fisher information matrix of the multivariate extreme value distribution with generalised extreme value margins and logistic dependence structure are given

fock representations of the affine lie algebra a 1 1 the aim of this note is to show that the affine lie algebraa1 1 has a natural family v of fock representations on the spacec xi yj i andj parametrized by v c2 by corresponding the highest weight of to each the parameter spacec2 forms a double cover of the weight spacec 0 c 1 with singularities at linear forms of level 2 this number is 1 times the dual coxeter number our results contain explicit realizations of irreducible non integrable highest wieghta1 1 modules for generic v

failure time models with matched data summary holt prentice 1974 adapted the proportional hazards model to give failure time models for matched pairs in which a member of the ith pair with covariate z has hazard function aoi t exp bz with full data more efficient estimators of b can be obtained if a weibull specialization ai qt11 of the baseline hazard can be assumed but these estimators are unavailable for censored data estimates of formed by assuming the ai s are independent gamma variates are investigated the resulting estimators are found to be more efficient than those obtained by holt prentice when the ai s are in fact gamma to be available for censored data and to perform well under a number of very different unimodal alternatives to a gamma distribution for the ai s

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

eigenpair derivative with respect to boundary shape this work focuses on how changes of boundary shapes affect eigenvalues and eigenfunctions in continuous systems the governing equation plus its boundary conditions for the eigenpair derivatives is derived using the 6 function method which can facilitate the differentiation of boundary conditions with respect to boundary shapes even though the eigenproblem equation with its corresponding boundary conditions is homogeneous the governing equation with its boundary conditions for the eigenpair derivatives may be nonhomogeneous a transformation method is proposed to transform the differential equation with nonhomogeneous boundary conditions into a new problem with homogeneous boundary conditions so that the eigenfunctions form a complete set for this new problem the explicit results for the eigenpair derivatives are given and an example is presented to illustrate the method and its validity

determining the dependence structure of multivariate extremes in multivariate extreme value analysis the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models interest often lies in determining which subsets of variables can take their largest values simultaneously while the others are of smaller order our approach to this problem exploits hidden regular variation properties on a collection of nonstandard cones and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence we derive theoretical properties of these indices demonstrate their utility through a series of examples and develop methods of inference that also estimate the proportion of extremal mass associated with each cone we apply the methods to river flows in the u k estimating the probabilities of different subsets of sites being large simultaneously

regional modelling of extreme storms via max stable processes asymptotic models for extremes of random processes often form the basis for estimating the extremal behaviour of environmental phenomena most such phenomena have a spatial dimension and the aim of this paper is to develop a procedure for modelling in continuous space the spatial dependence within extreme events a principal objective in the analysis as with other current research on extremes is to base inference on as much of the available data as possible the modelling procedures are justified on simulated data and subsequently applied to a series of rainfall data

confluent primary fields in the conformal field theory for any complex simple lie algebra we generalize the primary fields in the wess zumino novikov witten conformal field theory for a case with irregular singularities we refer to these generalized primary fields as confluent primary fields we present the screening currents ward identity a recursion rule for computing the expectation values of the products of confluent primary fields in the case of the expectation values of the products of confluent primary fields are integral formulas of solutions to confluent knizhnik zamolodchikov kz equations given in jimbo et al 2008 j phys a math theor 41 175205 by computing the operator product expansion of the energy momentum tensor t z and the confluent primary fields we obtain new differential operators moreover in the case of these differential operators are the same as those of the confluent kz equations jimbo et al 2008

jackson integrals of jordan pochhammer type and quantum knizhnik zamolodchikov equations we show that theq difference systems satisfied by jackson integrals of jordan pochhammer type give a class of the quantum knizhnik zamolodchikov equation for u q widehat mathfrak s mathfrak l 2 in the sense of frenkel and reshetikhin

natural frequency sensitivity analysis with respect to lumped mass location the calculation of natural frequencies for beams and plates with attached lumped masses is considered when the lumped masses are moved from a reference location as such the objective is to determine the natural frequency sensitivity to a change in the lumped mass location the problem is solved using the rayleigh quotient of the system in conjunction with rayleigh s principle the developed approach is straightforward to implement and yet has the capability of providing accurate predictions to changes in natural frequency even with substantial movement of a lumped mass from its original position the formulation is developed for both distinct and repeated eigenvalues

quantum algebra structure of certain jackson integrals theq difference system satisfied by jackson integrals with a configuration ofa type root system is studied we explicitly construct some linear combination of jackson integrals which satisfies the quantum knizhnik zamolodchikov equation for the 2 point correlation function ofq vertex operators introduced by frenkel and reshetikhin for the quantum affine algebra u q widehat mathfrak s mathfrak l 2 the expression of integrands for then point case is conjectured and a set of linear relations for the corresponding jackson integrals is proved

on self similar lie algebras and virtual endomorphisms we introduce the notion of virtual endomorphisms of lie algebras and use it as an approach for constructing self similarity of lie algebras this is done in particular for a class of metabelian lie algebras having homological type fp n which are lie algebra analogues of lamplighter groups we establish several criteria when the existence of virtual endomorphism implies a self similar lie structure furthermore we prove that the classical lie algebra sl n k where char k does not divide n affords non trivial faithful self similarity

an application of aomoto gelfand hypergeometric functions to the su n knizhnik zamolodchikov equation solutions to the knizhnik zamolodchikov equation for verma modules of the lie algebra mathfrak s mathfrak l n 1 mathbb c are explicitly given by certain integrals called aomoto gelfand hypergeometric functions

exploiting occurrence times in likelihood inference for componentwise maxima multivariate extreme value distributions arise as the limiting distributions of normalised componentwise maxima they are often used to model multivariate data that can be regarded as the componentwise maxima of some unobserved underlying multivariate process in many applications we have extra information we often know the locations of the maxima within the underlying process if the process is temporal this knowledge is frequently available through the dates on which the maxima are recorded we show how to incorporate this extra information into maximum likelihood procedures asymptotic and small sample efficiency results are presented for the dependence parameter in the logistic parametric sub class of bivariate extreme value distributions we conclude with an application to sea levels

fock representations and brst cohomology insl 2 current algebra we investigate the structure of the fock modules overa 1 1 introduced by wakimoto we show that irreducible highest weight modules arise as degree zero cohomology groups in a brst like complex of fock modules chiral primary fields are constructed as brst invariant operators acting on fock modules as a result we obtain a free field representation of correlation functions of thesu 2 wzw model on the plane and on the torus we also consider representations of fractional level arising in polyakov s 2d quantum gravity finally we give a geometrical borel weil like interpretation of the wakimoto construction

the identifiability of the competing risks model summary this paper considers the consequences for identifiability of introducing regressors into the competing risks model of multistate duration analysis we establish conditions under which access to regressors overturns the nonidentification theorem of cox and tsiatis for both proportional and accelerated failure time models

modelling multivariate extreme value distributions summary multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima minima no parametric family exists for the depen dence between the margins this paper extends to more than two variables the models and results for the bivariate case obtained by tawn 1988 two new families of physically motivated parametric models for the dependence structure are presented and are illus trated with an application to trivariate extreme sea level data in the analysis of environmental extreme value data there is often need to study joint inter site extreme behaviour examples are joint flooding at various sea ports or at various rain gauges in this paper the class of multivariate extreme value distributions is considered the marginal distributions are all extreme value distributions without loss of generality we follow pickands s 1981 approach in transforming the margins to unit mean exponential distributions the resulting class of p variable multivariate exponential distributions satisfies a strong stability relation de haan resnick 1977 and pickands 1981 show that the resulting dependence structure is uniquely specified up to an arbitrary finite positive measure on p 1 variables therefore the bivariate dependence structure is univariate only when p 3 as considered here does the problem become really multivari ate in addition unlike in the multivariate normal distribution the multivariate depen dence structure is generally only restricted and not uniquely specified by the dependence structure of all possible pairs much has been written about the representations of multivariate extremes see resnick 1987 for a good review on the other hand models and estimation for such distributions have received little attention these aspects are considered here as no finite parametric family exists for the general dependence structure it must be modelled in some way thus true multivariate models are required using the most flexible bivariate model of tawn 1988 as a basis multivariate extensions are generated a model derived in the discrete choice literature will also be introduced and extended the resulting families of models are physically motivated flexible and possess hierarchical properties

twisted wess zumino witten models on elliptic curves investigated is a variant of the wess zumino witten model called a twisted wzw model which is associated to a certain lie group bundle on a family of elliptic curves the lie group bundle is a non trivial bundle with flat connection and related to the classical elliptic r matrix the usual non twisted wzw model is associated to a trivial group bundle with trivial connection on a family of compact riemann surfaces and a family of its principal bundles the twisted wzw model on a fixed elliptic curve at the critical level describes the xyz gaudin model the elliptic knizhnik zamolodchikov equations associated to the classical elliptic r matrix appear as flat connections on the sheaves of conformal blocks in the twisted wzw model

wakimoto realizations of current algebras an explicit construction a generalized wakimoto realization of can be associated with each parabolic subalgebra of a simple lie algebra according to an earlier proposal by feigin and frenkel in this paper the proposal is made explicit by developing the construction of wakimoto realizations from a simple but unconventional viewpoint an explicit formula is derived for the wakimoto current first at the poisson bracket level by hamiltonian symmetry reduction of the wznw model the quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate by means of commutators the affine sugawara stress energy tensor is verified to have the expected quadratic form in the constituents which are symplectic bosons belonging to and a current belonging to the quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold the effect of this choice is investigated in detail by constructing quantum coordinate transformations finally the explicit form of the screening charges for each generalized wakimoto realization is determined and some applications are briefly discussed

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

quantum group structure in the fock space resolutions of widehat sl n representations we describe a complex of wakimoto type fock space modules for the affine kac moody algebra widehat sl n the intertwining operators that build the complex are obtained from contour integrals of so called screening operators we show that a quantum group structure underlies the algebra of screening operators this observation greatly facilitates the explicit determination of the intertwiners we conjecture that the complex provides a resolution of an irreducible highest weight module in terms of fock spaces

on the occurrence times of componentwise maxima and bias in likelihood inference for multivariate max stable distributions full likelihood based inference for high dimensional multivariate extreme value distributions or max stable processes is feasible when incorporating occurrence times of the maxima without this information ddd dimensional likelihood inference is usually precluded due to the large number of terms in the likelihood however some studies have noted bias when performing high dimensional inference that incorporates such event information particularly when dependence is weak we elucidate this phenomenon showing that for unbiased inference in moderate dimensions dimension ddd should be of a magnitude smaller than the square root of the number of vectors over which one takes the componentwise maximum a bias reduction technique is suggested and illustrated on the extreme value logistic model

wess zumino witten model on elliptic curves at the critical level we construct a gaudin type lattice model as the wess zumino witten model on elliptic curves at the critical level bethe eigenvectors are obtained by the bosonization technique

a conditional approach for multivariate extreme values with discussion summary multivariate extreme value theory and methods concern the characterization estimation and extrapolation of the joint tail of the distribution of a d dimensional random variable existing approaches are based on limiting arguments in which all components of the variable become large at the same rate this limit approach is inappropriate when the extreme values of all the variables are unlikely to occur together or when interest is in regions of the support of the joint distribution where only a subset of components is extreme in practice this restricts existing methods to applications where d is typically 2 or 3 under an assumption about the asymptotic form of the joint distribution of a d dimensional random variable conditional on its having an extreme component we develop an entirely new semiparametric approach which overcomes these existing restrictions and can be applied to problems of any dimension we demonstrate the performance of our approach and its advantages over existing methods by using theoretical examples and simulation studies the approach is used to analyse air pollution data and reveals complex extremal dependence behaviour that is consistent with scientific understanding of the process we find that the dependence structure exhibits marked seasonality with ex tremal dependence between some pollutants being significantly greater than the dependence at non extreme levels

a multivariate distribution with weibull connections a simple form of multivariate distribution is defined which for certain parameter values has weibull marginals the distribution has a single parameter governing association between the variates which may be positive negative or zero the simple forms for marginal and conditional distributions hazard functions and densities make it attractive for practical application and interpretation

estimation of husler reiss distributions and brown resnick processes summary estimation of extreme value parameters from observations in the max domain of attraction of a multivariate max stable distribution commonly uses aggregated data such as block maxima multivariate peaks over threshold methods in contrast exploit additional information from the non aggregated large observations we introduce an approach based on peaks over thresholds that provides several new estimators for processes in the max domain of attraction of the frequently used husler reiss model and its spatial extension brown resnick processes the method relies on increments t0 conditional on t0 exceeding a high threshold where t0 is a fixed location when the marginals are standardized to the gumbel distribution these increments asymptotically form a gaussian process resulting in computationally simple estimates of the husler reiss parameter matrix and particularly enables parametric inference for brown resnick processes based on high dimensional multivariate densities this is a major advantage over composite likelihood methods that are commonly used in spatial extreme value statistics since they rely only on bivariate densities a simulation study compares the performance of the new estimators with other commonly used methods as an application we fit a non isotropic brown resnick process to the extremes of 12 year data of daily wind speed measurements

a dependence measure for multivariate and spatial extreme values properties and inference we present properties of a dependence measure that arises in the study of extreme values in multivariate and spatial problems for multivariate problems the dependence measure characterises dependence at the bivariate level for all pairs and all higher orders up to and including the dimension of the variable necessary and sufficient conditions are given for subsets of dependence measures to be self consistent that is to guarantee the existence of a distribution with such a subset of values for the dependence measure for pairwise dependence these conditions are given in terms of positive semidefinite matrices and non differentiable positive definite functions we construct new nonparametric estimators for the dependence measure which unlike all naive nonparametric estimators impose these self consistency properties as the new estimators provide an improvement on the naive methods both in terms of the inferential and interpretability properties their use in exploratory extreme value analyses should aid the identification of appropriate dependence models the methods are illustrated through an analysis of simulated multivariate data which shows that a lack of self consistency is frequently a problem with the existing estimators and by a spatial analysis of daily rainfall extremes in south west england which finds a smooth decay in extremal dependence with distance

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

efficient inference for spatial extreme value processes associated to log gaussian random functions max stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes and thus form an important class of models for the extreme values of spatial processes until recently inference for max stable processes has been restricted to the use of pairwise composite likelihoods due to intractability of higher dimensional distributions in this work we consider random fields that are in the domain of attraction of a widely used class of max stable processes namely those constructed via manipulation of log gaussian random functions for this class we exploit limiting d dimensional multivariate poisson process intensities of the underlying process for inference on all d vectors exceeding a high marginal threshold in at least one component employing a censoring scheme to incorporate information below the marginal threshold we also consider the d dimensional distributions for the equivalent max stable process and perform full likelihood inference by exploiting the methods of stephenson tawn 2005 where information on the occurrence times of extreme events is shown to dramatically simplify the likelihood the stephenson tawn likelihood is in fact simply a special case of the censored poisson process likelihood we assess the improvements in inference from both methods over pairwise likelihood methodology by simulation

realization of the space of conformal blocks in lie algebra modules abstract using integrable irreducible representations of generalized twisted affine lie algebra modules we give a realization of the space of conformal blocks of conformal field theory on a stable algebraic curve many basic properties of the conformal blocks such as finite dimensionality of the space invariance of the conformal blocks under suitable formal neighborhood changes and the property of propagation of vacua are discussed finally a relative local 1 form around a fixed point of the order two automorphism of the curve is given

modelling pairwise dependence of maxima in space we model pairwise dependence of temporal maxima such as annual maxima of precipitation that have been recorded in space either on a regular grid or at irregularly spaced locations the construction of our estimators stems from the variogram concept the asymptotic properties of our pairwise dependence estimators are established through properties of empirical processes the performance of our approach is illustrated by simulations and by the treatment of a real dataset in addition to bringing new results about the asymptotic behaviour of copula estimators the latter being linked to first order variograms one main advantage of our approach is to propose a simple connection between extreme value theory and geostatistics

bosonization and integral representation of solutions of the knizhnik zamolodchikov bernard equations we construct an integral representation of solutions of the knizhnik zamolodchikov bernard equations using the wakimoto modules