the discrete duality finite volume method for stokes equations on three dimensional polyhedral meshes we develop a discrete duality finite volume method for the three dimensional steady stokes problem with a variable viscosity coefficient on polyhedral meshes under very general assumptions on the mesh which may admit nonconforming polyhedrons we prove the stability and well posedness of the scheme we also prove the convergence of the numerical approximation to the velocity velocity gradient and pressure and derive a priori estimates for the corresponding approximation error final numerical experiments confirm the theoretical predictions

bootstrap for the case cohort design the case cohort design facilitates economical investigation of risk factors in a large survival study with covariate data collected only from the cases and a simple random subset of the full cohort methods that accommodate the design have been developed for various semiparametric models but most inference procedures are based on asymptotic distribution theory such inference can be cumbersome to derive and implement and does not permit confidence band construction while bootstrap is an obvious alternative how to resample is unclear because of complications from the two stage sampling design we establish an equivalent sampling scheme and propose a novel and versatile nonparametric bootstrap for robust inference with an appealingly simple single stage resampling theoretical justification and numerical assessment are provided for a number of procedures under the proportional hazards model

convergence analysis of the mimetic finite difference method for elliptic problems with staggered discretizations of diffusion coefficients we study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in k lipnikov g manzini j d moulton and m shashkov j comput phys 305 2016 pp 111 126 in contrast to the conventional approach the diffusion coefficient enters both the primary mimetic operator i e the discrete divergence and the inner product in the space of gradients the diffusion coefficient is therefore evaluated on different mesh locations i e inside mesh cells and on mesh faces such a staggered discretization may provide the flexibility necessary for future development of efficient numerical schemes for nonlinear problems especially for problems with degenerate coefficients these new mimetic schemes preserve symmetry and positive definiteness of the continuum problem which allow us to use efficient algebraic solvers such as the preconditioned conjugate gradient method we show that these schemes are inf sup stable and establish a priori error

more efficient estimators for case cohort studies the case cohort study design used to reduce costs in large cohort studies is a random sample of the entire cohort named the subcohort augmented with subjects having the disease of interest but not in the subcohort sample when several diseases are of interest several case cohort studies may be conducted using the same subcohort with each disease analyzed separately ignoring the additional exposure measurements collected on subjects with the other diseases this is not an efficient use of the data and in this paper we propose more efficient estimators we consider both joint and separate analyses for the multiple diseases we propose an estimating equation approach with a new weight function and we establish the consistency and asymptotic normality of the resulting estimator simulation studies show that the proposed methods using all available information gain efficiency we apply our proposed method to the data from the busselton health study

a unified approach to semiparametric transformation models under general biased sampling schemes we propose a unified estimation method for semiparametric linear transformation models under general biased sampling schemes the new estimator is obtained from a set of counting process based unbiased estimating equations developed through introducing a general weighting scheme that offsets the sampling bias the usual asymptotic properties including consistency and asymptotic normality are established under suitable regularity conditions a closed form formula is derived for the limiting variance and the plug in estimator is shown to be consistent we demonstrate the unified approach through the special cases of left truncation length bias the case cohort design and variants thereof simulation studies and applications to real datasets are presented

calibration weighted estimation of semiparametric transformation models for two phase sampling two phase designs are commonly used to subsample subjects from a cohort in order to study covariates that are too expensive to ascertain for everyone in the cohort this is particularly true for the study of immune response biomarkers in vaccine immunology where new elaborate assays are constantly being developed to improve our understanding of the human immune responses to vaccines and how the immune response may protect humans from virus infection it has long being recognized that if there exist variables that are correlated with expensive variables and can be measured for every subject in the cohort they can be leveraged to improve the estimation efficiency for the effects of the expensive variables in this research article we developed an improved inverse probability weighted estimation approach for semiparametric transformation models with a two phase study design semiparametric transformation models are a class of models that include the cox ph and proportional odds models they provide an attractive way to model the effects of immune response biomarkers as human immune responses generally wane over time our approach is based on weights calibration which has its origin in survey statistics and was used by breslow et al to improve inverse probability weighted estimation of the cox regression model we develop asymptotic theory for our estimator and examine its performance through simulation studies we illustrate the proposed method with application to two hiv 1 vaccine efficacy trials

the discrete duality finite volume method for convection diffusion problems in this paper we extend the discrete duality finite volume ddfv formulation to the steady convection diffusion equation the discrete gradients defined in ddfv are used to define a cell based gradient for the control volumes of both the primal and dual meshes in order to achieve a higher order accurate numerical flux for the convection term a priori analysis is carried out to show convergence of the approximation and a global first order convergence rate is derived the theoretical results are confirmed by some numerical experiments

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

action of truncated quantum groups on quasi quantum planes and a quasi associative differential geometry and calculus ifq is apth root of unity there exists a quasi coassociative truncated quantum group algebra whose indecomposable representations are the physical representations ofu q sl2 whose coproduct yields the truncated tensor product of physical representations ofu q sl2 and whoser matrix satisfies quasi yang baxter equations these truncated quantum group algebras are examples of weak quasitriangular quasi hopf algebras quasi quantum group algebras open image in new window we describe a space open image in new window of functions on the quasi quantum plane i e of polynomials in noncommuting complex coordinate functionsz a on which multiplication operatorsz a and the elements of open image in new window can act so thatz a will transform according to some representation f of open image in new window open image in new window can be made into a quasi associative graded algebra open image in new window on which elements of open image in new window act as generalized derivations in the special case of the truncatedu q sl2 algebra we show that the subspaces open image in new window of monomials inz a ofnth degree vanish forn p 1 and that open image in new window carries the 2j 1 dimensional irreducible representation of open image in new window ifn 2j j 0 1 2 1 2 p 2 assuming that the representation f of the quasi quantum group algebra gives rise to anr matrix with two eigenvalues we develop a quasi associative differential calculus on open image in new window this implies construction of an exterior differentiation a graded algebra open image in new window of forms and partial derivatives a quasi associative generalization of noncommutative differential geometry is introduced by defining a covariant exterior differentiation of forms it is covariant under open image in new window gauge transformations

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences we present an expanded mixed finite element approximation of second order elliptic problems containing a tensor coefficient the mixed method is expanded in the sense that three variables are explicitly approximated namely the scalar unknown the negative of its gradient and its flux the tensor coefficient times the negative gradient the resulting linear system is a saddle point problem in the case of the lowest order raviart thomas elements on rectangular parallelepipeds we approximate this expanded mixed method by incorporating certain quadrature rules this enables us to write the system as a simple cell centered finite difference method requiring the solution of a sparse positive semidefinite linear system for the scalar unknown for a general tensor coefficient the sparsity pattern for the scalar unknown is a 9 point stencil in two dimensions and 19 points in three dimensions existing theory shows that the expanded mixed method gives optimal order approximations in the l 2 and h s norms and superconvergence is obtained between the l 2 projection of the scalar variable and its approximation we show that these rates of convergence are retained for the finite difference method if h denotes the maximal mesh spacing then the optimal rate is o h the superconvergence rate o h 2 is obtained for the scalar unknown and rate o h 3 2 for its gradient and flux in certain discrete norms moreover the full o h 2 is obtained in the strict interior of the domain computational results illustrate these theoretical results

semiparametric inference for data with a continuous outcome from a two phase probability dependent sampling scheme multi phased designs and biased sampling designs are two of the well recognized approaches to enhance study efficiency in this paper we propose a new and cost effective sampling design the two phase probability dependent sampling design pds for studies with a continuous outcome this design will enable investigators to make efficient use of resources by targeting more informative subjects for sampling we develop a new semiparametric empirical likelihood inference method to take advantage of data obtained through a pds design simulation study results indicate that the proposed sampling scheme coupled with the proposed estimator is more efficient and more powerful than the existing outcome dependent sampling design and the simple random sampling design with the same sample size we illustrate the proposed method with a real data set from an environmental epidemiologic study

enhanced cell centered finite differences for elliptic equations on general geometry we present an expanded mixed finite element method for solving second order elliptic partial differential equations on geometrically general domains for the lowest order raviart thomas approximating spaces we use quadrature rules to reduce the method to cell centered finite differences possibly enhanced with some face centered pressures this substantially reduces the computational complexity of the problem to a symmetric positive definite system for essentially only as many unknowns as elements our new method handles general shape elements triangles quadrilaterals and hexahedra and full tensor coefficients while the standard mixed formulation reduces to finite differences only in special cases with rectangular elements as in other mixed methods we maintain the local approximation of the divergence i e local mass conservation in contrast galerkin finite element methods facilitate general element shapes at the cost of achieving only global mass conservation our method is shown to be as accurate as the standard mixed method for a large class of smooth meshes on nonsmooth meshes or with nonsmooth coefficients one can add lagrange multiplier pressure unknowns on certain element edges or faces this enhanced cell centered procedure recovers full accuracy with little additional cost if the coefficients or mesh geometry are piecewise smooth theoretical error estimates and numerical examples are given illustrating the accuracy and efficiency of the methods

on semiparametric transformation cure models a general class of semiparametric transformation cure models is studied for the analysis of survival data with long term survivors it combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence included as special cases are the proportional hazards cure model farewell 1982 kuk chen 1992 sy taylor 2000 peng dear 2000 and the proportional odds cure model generalised estimating equations are proposed for parameter estimation it is shown that the resulting estimators are asymptotically normal with variance covariance matrix that has a closed form and can be consistently estimated by the usual plug in method simulation studies show that the proposed approach is appropriate for practical use an application to data from a breast cancer study is given to illustrate the methodology

symmetric positive definite flux continuous full tensor finite volume schemes on unstructured cell centered triangular grids novel cell centered full tensor finite volume methods are presented for general unstructured grids in two spatial dimensions the numerical schemes are flux continuous and based on computing the transmissibilities in a local subcell transform space ensuring that local flux matrices are symmetric as a result the global discretization matrix is shown to be symmetric positive definite for any grid type a symmetric physical space method is also introduced and the symmetric methods are shown to be closely related discrete ellipticity conditions are derived for positive definiteness of the physical space and subcell space schemes computational examples are presented for unstructured triangular grids demonstrating good performance of the scheme the schemes are compared with the so called multipoint flux approximation mpfa o method i aavatsmark t barkve o boe and t mannseth siam j sci comput 19 1998 pp 1700 1716 good agreement between the methods is obtained but the new scheme shows improved behavior in challenging cases

monotone finite volume schemes for diffusion equations on unstructured triangular and shape regular polygonal meshes we consider a non linear finite volume fv scheme for stationary diffusion equation we prove that the scheme is monotone i e it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients the scheme is extended to regular star shaped polygonal meshes and isotropic heterogeneous coefficients

weighted estimating equations for semiparametric transformation models with censored data from a case cohort design summary in a case cohort design introduced by prentice 1986 covariates are assembled only for a subcohort randomly selected from the entire cohort and any additional cases outside the subcohort semiparametric transformation models are considered here for failure time data from the case cohort design weighted estimating equations are proposed for esti mation of the regression parameters the estimation procedure of survival probability at given covariate levels is also provided asymptotic properties are derived for the estimators using finite population sampling theory u statistics theory and martingale convergence results the finite sample properties of the proposed estimators as well as the efficiency relative to the full cohort estimators are assessed via simulation studies a case cohort dataset from the atherosclerosis risk in communities study is used to illustrate the estimating procedure

a discrete duality finite volume approach to hodge decomposition and div curl problems on almost arbitrary two dimensional meshes we define discrete differential operators such as gradient divergence and curl on general two dimensional nonorthogonal meshes these discrete operators verify discrete analogues of usual continuous theorems discrete green formulae discrete hodge decomposition of vector fields and vector curls have a vanishing divergence and gradients have a vanishing curl we apply these ideas to discretize div curl systems we give error estimates based on the reformulation of these systems into equivalent equations for the potentials numerical results illustrate the use of the method on several types of meshes some of which are degenerating triangular meshes and nonconforming locally refined meshes

semiparametric transformation models for the case cohort study a general class of semiparametric transformation models is studied for analysing survival data from the case cohort design which was introduced by prentice 1986 weighted estimating equations are proposed for simultaneous estimation of the regression parameters and the transformation function it is shown that the resulting regression estimators are asymptotically normal with variance covariance matrix that has a closed form and can be consistently estimated by the usual plug in method simulation studies show that the proposed approach is appropriate for practical use an application to a case cohort dataset from the atherosclerosis risk in communities study is also given to illustrate the methodology

a vertex centered and positivity preserving scheme for anisotropic diffusion problems on arbitrary polygonal grids abstract we suggest a new positivity preserving finite volume scheme for anisotropic diffusion problems on arbitrary polygonal grids the scheme has vertex centered edge midpoint and cell centered unknowns the vertex centered unknowns are primary and have finite volume equations associated with them the edge midpoint and cell centered unknowns are treated as auxiliary ones and are interpolated by the primary unknowns which makes the final scheme a pure vertex centered one unlike most existing positivity preserving schemes the construction of the scheme is based on a special nonlinear two point flux approximation that has a fixed stencil and does not require the convex decomposition of the co normal in order to solve efficiently the nonlinear systems resulting from the nonlinear scheme picard method and its anderson acceleration are discussed numerical experiments demonstrate the second order accuracy and well positivity of the solution for heterogeneous and anisotropic problems on severely distorted grids the high efficiency of the anderson acceleration is also shown on reduction of the number of nonlinear iterations moreover the proposed scheme does not have the so called numerical heat barrier issue suffered by most existing cell centered and hybrid schemes however further improvements have to be made if the solution is very close to the machine precision and the mesh distortion is very severe

monotone corrections for generic cell centered finite volume approximations of anisotropic diffusion equations we present a nonlinear technique to correct a general finite volume scheme for anisotropic diffusion problems which provides a discrete maximum principle we point out general properties satisfied by many finite volume schemes and prove the proposed corrections also preserve these properties we then study two specific corrections proving under numerical assumptions that the corresponding approximate solutions converge to the continuous one as the size of the mesh tends to zero finally we present numerical results showing that these corrections suppress local minima produced by the original finite volume scheme

enforcing positivity with conservation for nine point scheme of nonlinear diffusion equations abstract the nine point scheme nps is a finite volume scheme for solving nonlinear diffusion equations on quadrilateral grids it s well known that the solution of the scheme on distorted grids cannot preserve positivity when all given data are nonnegative here for the nps of nonlinear diffusion problems we propose a conservative enforcing positivity algorithm cepa which is posterior correction of the discrete solution and allows the new solution preserves positivity as well as local conservation at each step of nonlinear iteration numerical results are presented to demonstrate that the accuracy of our algorithm of enforcing positivity with conservation is higher than some common procedures of positivity correction

estimation and inference of quantile regression for survival data under biased sampling abstractbiased sampling occurs frequently in economics epidemiology and medical studies either by design or due to data collecting mechanism failing to take into account the sampling bias usually leads to incorrect inference we propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for quantile regression with survival data under general biased sampling schemes including but not limited to the length biased sampling the case cohort design and variants thereof we establish the uniform consistency and weak convergence of the proposed estimator as a process of the quantile level we also investigate more efficient estimation using the generalized method of moments and derive the asymptotic normality we further propose a new resampling method for inference which differs from alternative procedures in that it does not require to repeatedly solve estimating equations it is proved that the resampling method consistently estimates the asymptoti

monotone finite volume schemes for diffusion equations on polygonal meshes we construct a nonlinear finite volume fv scheme for diffusion equation on star shaped polygonal meshes and prove that the scheme is monotone i e it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients our scheme has only cell centered unknowns and it treats material discontinuities rigorously and offers an explicit expression for the normal flux numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes for both smooth and non smooth highly anisotropic solutions and numerical results show that our scheme appears to be approximate second order accuracy for the solution and first order accuracy for the flux

finite volume method for 2d linear and nonlinear elliptic problems with discontinuities in this paper we study the approximation of solutions to linear and nonlinear elliptic problems with discontinuous coefficients in the discrete duality finite volume ddfv framework this family of schemes allows very general meshes and inherits the main properties of the continuous problem in order to take into account the discontinuities and to prevent consistency defect in the scheme we propose to modify the definition of the numerical fluxes on the edges of the mesh where the discontinuity occurs we first illustrate our approach by the study of the 1d situation then we show how to design our new scheme called m ddfv and we propose its analysis we also describe an iterative solver whose convergence is proved which can be used to solve the nonlinear discrete equations defining the finite volume scheme finally we provide numerical results which confirm that the m ddfv scheme significantly improves the convergence rate of the usual ddfv method for both linear and nonlinear problems

a finite volume method for approximating 3d diffusion operators on general meshes a finite volume method is presented for discretizing 3d diffusion operators with variable full tensor coefficients this method handles anisotropic non symmetric or discontinuous variable tensor coefficients while distorted non matching or non convex n faced polyhedron meshes can be used for meshes of polyhedra whose faces have not more than four edges the associated matrix is positive definite and symmetric if the diffusion tensor is symmetric a second order resp first order accuracy is numerically observed for the solution resp gradient of the solution

a 3d discrete duality finite volume method for nonlinear elliptic equations discrete duality finite volume ddfv schemes have recently been developed in two dimensions to approximate nonlinear diffusion problems on general meshes in this paper a three dimensional extension of these schemes is proposed the construction of this extension is detailed and its main properties are proved a priori bounds well posedness and error estimates the practical implementation of this scheme is easy numerical experiments are presented to illustrate its good behavior

a finite volume method for the approximation of maxwell s equations in two space dimensions on arbitrary meshes a new finite volume method is presented for discretizing the two dimensional maxwell equations this method may be seen as an extension of the covolume type methods to arbitrary possibly non conforming or even non convex n sided polygonal meshes thanks to an appropriate choice of degrees of freedom an equivalent formulation of the scheme is given in terms of discrete differential operators obeying discrete duality principles the main properties of the scheme are its energy conservation its stability under a cfl like condition and the fact that it preserves gauss law and divergence free magnetic fields second order convergence is demonstrated numerically on non conforming and distorted meshes

interpolation based second order monotone finite volume schemes for anisotropic diffusion equations on general grids we propose two interpolation based monotone schemes for the anisotropic diffusion problems on unstructured polygonal meshes through the linearity preserving approach the new schemes are characterized by their nonlinear two point flux approximation which is different from the existing ones and has no constraint on the associated interpolation algorithm for auxiliary unknowns thanks to the new nonlinear two point flux formulation it is no longer required that the interpolation algorithm should be a positivity preserving one the first scheme employs vertex unknowns as the auxiliary ones and a second order but not positivity preserving interpolation algorithm is utilized the second scheme uses the so called harmonic averaging points located on cell edges to define the auxiliary unknowns and a second order positivity preserving interpolation method is employed both schemes have nearly the same convergence rates as compared with their related second order linear schemes numerical results demonstrate that the new schemes are monotone and have the second order accuracy for the solution and first order for its gradient on severely distorted meshes

anderson acceleration for nonlinear finite volume scheme for advection diffusion problems we consider the solution of systems of nonlinear algebraic equations that appear in a positivity preserving finite volume scheme for steady state advection diffusion equations we propose and analyze numerically an efficient strategy for accelerating the picard method when it is applied to these systems the strategy is based on the anderson acceleration and the adaptive inexact solution of linear systems we demonstrate its numerical robustness for three black box preconditioners

a decoupled and positivity preserving discrete duality finite volume scheme for anisotropic diffusion problems on general polygonal meshes abstract we suggest a new positivity preserving discrete duality finite volume ddfv scheme for anisotropic diffusion problems on general polygonal meshes like existing ddfv schemes this scheme is built on the primary and dual meshes and has finite volume fv equations for both vertex and cell centered unknowns the transpose of the coefficient matrix for the fv equations of the cell centered unknowns is an m matrix while that for the vertex unknowns is not an m matrix but a symmetric and positive definite matrix by employing a certain truncation technique for the vertex unknowns the positivity preserving property for both categories of unknowns is guaranteed local conservation is strictly maintained for the cell centered unknowns and conditionally maintained for the vertex unknowns since the fv equations of the vertex unknowns can be solved independently the two sets of fv equations are decoupled in contrast to existing nonlinear positivity preserving schemes the new scheme requires no nonlinear iterations for linear problems for nonlinear problems the positivity preserving mechanism of the new scheme is decoupled from its nonlinear iteration so that any nonlinear solver can be adopted moreover the positivity of the discrete solution is proved and the well posedness is analyzed rigorously for linear problems in numerical experiments the new scheme is examined extensively and compared with two positivity preserving cell centered schemes and a nonlinear ddfv scheme numerical results show that the present ddfv scheme achieves second order accuracy and preserves the positivity of the solution for heterogeneous and anisotropic problems on severely distorted grids the high efficiency of the scheme is also demonstrated by the comparison of computation time and number of nonlinear iterations

efficient estimation of semiparametric transformation models for two phase cohort studies under two phase cohort designs such as case cohort and nested case control sampling information on observed event times event indicators and inexpensive covariates is collected in the first phase and the first phase information is used to select subjects for measurements of expensive covariates in the second phase inexpensive covariates are also used in the data analysis to control for confounding and to evaluate interactions this article provides efficient estimation of semiparametric transformation models for such designs accommodating both discrete and continuous covariates and allowing inexpensive and expensive covariates to be correlated the estimation is based on the maximization of a modified nonparametric likelihood function through a generalization of the expectation maximization algorithm the resulting estimators are shown to be consistent asymptotically normal and asymptotically efficient with easily estimated variances simulation studies demonstrate that the asymptotic approximati

semiparametric analysis of transformation models with censored data summary a unified estimation procedure is proposed for the analysis of censored data using linear transformation models which include the proportional hazards model and the proportional odds model as special cases this procedure is easily implemented numerically and its validity does not rely on the assumption of independence between the covariates and the censoring variable the estimator is the same as the cox partial likelihood estimator in the case of the proportional hazards model moreover the asymptotic variance of the proposed estimator has a closed form and its variance estimator is easily obtained by plug in rules the method is illustrated by simulation and is applied to the veterans administration lung cancer data

on the linear transformation model for censored data recently cheng wei ying 1995 1997 proposed a class of estimation procedures for semi parametric linear transformation models with censored observations when the support of the censoring variable is shorter than that of the failure time the estimators are asymptotically biased in this paper we present a simple modification of cheng s estimation procedures for the regression parameters through extensive numerical studies with practical sample sizes we find that the new proposals perform well but the original interval estimators may not have correct coverage probabilities when censoring is heavy prediction procedures for the survival probabilities of future subjects are also modified accordingly

approximating second order vector differential operators on distorted meshes in two space dimensions a new finite volume method is presented for approximating second order vector differential operators in two space dimensions this method allows distorted triangle or quadrilateral meshes to be used without the numerical results being too much altered the matrices that need to be inverted are symmetric positive definite therefore the most powerful linear solvers can be applied the method has been tested on a few second order vector partial differential equations coming from elasticity and fluids mechanics areas these numerical experiments show that it is second order accurate and locking free copyright 2008 john wiley sons ltd

on the structure of unitary conformal field theory ii representation theoretic approach two dimensional unitary rational conformal field theory is studied from the point of view of the representation theory of chiral algebras chiral algebras are equipped with a family of co multiplications which serve to define tensor product representations chiral vertices arise as clebsch gordan operators from tensor product representations to irreducible subrepresentations of a chiral algebra the algebra of chiral vertices is studied and shown to give rise to representations of the braid groups determined by yang baxter braid matrices chiral fusion is analyzed it is shown that the braid and fusion matrices determine invariants of knots and links connections between the representation theories of chiral algebras and of quantum groups are sketched finally it is shown how the local fields of a conformal field theory can be reconstructed from the chiral vertices of two chiral algebras

relationship between the vertex centered linearity preserving scheme and the lowest order virtual element method for diffusion problems on star shaped polygons abstract as a generalization of the finite element method the virtual element method vem has made remarkable achievements in the algorithm and analysis of simulating various problems recently vertex centered linearity preserving scheme vlps wu et al 2016 is a linear finite volume scheme which is currently only applied to the numerical simulation of diffusion problems in this paper we study the relationship between vlps and the lowest order vem for diffusion problems on star shaped polygonal meshes from an algebraic point of view the global stiffness matrix of vlps with a special stabilization term coincides with that of the lowest order vem while the load terms are generally different specifically we find that the global stiffness matrices of the two methods can be split as the consistency parts and the stability parts and the consistency parts are the same while the stability parts coincide under some assumptions as a by product a new stability term is obtained for vlps besides a post processing procedure is suggested for the lowest order vem to preserve the positivity of the cell centered unknowns and maintain at the same time the local conservation on the primary meshes the positivity existence and uniqueness of the cell centered unknowns are studied numerical experiments confirm the theoretical findings and demonstrate the efficiency of the post processing procedure on various polygonal meshes

convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes abstract in the present work we deal with the convergence of cell centered nonlinear finite volume schemes for anisotropic and heterogeneous diffusion operators a general framework for the convergence study of finite volume methods is provided and used to establish the convergence of the new methods thorough assessment on a set of anisotropic heterogeneous problems as well as a comparison with linear finite volume schemes is provided

the mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient numerical schemes for nonlinear parabolic equations based on the harmonic averaging of cell centered diffusion coefficients break down when some of these coefficients go to zero or their ratio grows to tackle this problem we propose new mimetic finite difference schemes that use a staggered discretization of the diffusion coefficient the primary mimetic operator approximates div k the derived dual mimetic operator approximates the new mimetic schemes preserve symmetry and positive definiteness of the continuum problem which allows us to use algebraic solvers with optimal complexity we perform detailed numerical analysis of the new schemes for linear elliptic problems and a specially designed linear parabolic problem that has solution dynamics typical for nonlinear problems we show that the new schemes are competitive with the state of the art schemes for steady state problems but provide much more accurate solution dynamics for the transient problem

reconstruction of weak quasi hopf algebras abstract all rational semisimple braided tensor categories are representation categories of weak quasi hopf algebras to prove this result we construct for any given category of this kind a weak quasi tensor functor to the category of finite dimensional vector spaces this allows us to reconstruct a weak quasi hopf algebra with the given category as its representation category

numerical artifacts in the generalized porous medium equation why harmonic averaging itself is not to blame abstract the degenerate parabolic generalized porous medium equation gpme poses numerical challenges due to self sharpening and its sharp corner solutions for these problems we show results for two subclasses of the gpme with differentiable k p with respect to p namely the porous medium equation pme and the superslow diffusion equation spurious temporal oscillations and nonphysical locking and lagging have been reported in the literature these issues have been attributed to harmonic averaging of the coefficient k p for small p and arithmetic averaging has been suggested as an alternative we show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues here we investigate the causes of these numerical artifacts using modified equation analysis the modified equation framework can be used for any type of discretization we show results for the second order finite volume method the observed problems with harmonic averaging can be traced to two leading error terms in its modified equation this is also illustrated numerically through a modified harmonic method mhm that can locally modify the critical terms to remove the aforementioned numerical artifacts

discretisation and multigrid solution of elliptic equations with mixed derivative terms and strongly discontinuous coefficients this paper introduces a new conservative cell centred finite volume scheme for the accurate solution of elliptic diffusion equations with strongly varying coefficients the discretisation is designed to model a wide range of heterogeneities and anisotropies and in particular the case where the diffusivity is represented by a nondiagonal matrix which may occur if the medium is anisotropic in a general direction such problems arise for example in oil reservoir simulation when renormalisation techniques are used to model the reservoir geology it is in this context that the method is described although it is applicable to a far wider class of problems in heat conduction electrostatics and potential theory the paper also describes the application of a mulitigrid scheme for efficient numerical solution of the algebraic equations derived using the new discretisation

weighted semiparametric likelihood method for fitting a proportional odds regression model to data from the case cohort design the problem of fitting a proportional odds regression model to data from the case cohort design proposed by prentice is considered a weighted semiparametric likelihood method is proposed under the proportional odds model the maximum weighted semiparametric likelihood estimators of both the regression parameter and the transformation function are shown to be consistent and normally distributed the applicability of the weighted semiparametric likelihood method to the semiparametric transformation regression models is also discussed in particular when the proportional hazards regression model is fitted estimators proposed by chen and lo can be generated by the weighted semiparametric likelihood method under different weighting schemes a simulation study suggests that the case cohort design is also useful under the proportional odds regression model and the proposed method performs well with practical finite sample sizes

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f

global quantum gauge symmetry via reconstruction theorems in this paper we establish that every quantum field theory satisfying some basic axioms posseses a weak quasi hopf algebra as gauge symmetry we use a reconstruction theorem to find this symmetry algebra and show how it is used to build a gauge covariant field algebra we investigate the question of why this generality is necessary the non uniqueness of the reconstruction process is interpreted and a cohomological classification of possible global gauge symmetries is given

the cutoff method for the numerical computation of nonnegative solutions of parabolic pdes with application to anisotropic diffusion and lubrication type equations the cutoff method which cuts off the values of a function less than a given number is studied for the numerical computation of nonnegative solutions of parabolic partial differential equations a convergence analysis is given for a broad class of finite difference methods combined with cutoff for linear parabolic equations two applications are investigated linear anisotropic diffusion problems satisfying the setting of the convergence analysis and nonlinear lubrication type equations for which it is unclear if the convergence analysis applies the numerical results are shown to be consistent with the theory and in good agreement with existing results in the literature the convergence analysis and applications demonstrate that the cutoff method is an effective tool for use in the computation of nonnegative solutions cutoff can also be used with other discretization methods such as collocation finite volume finite element and spectral methods and for the computation of positive solutions