bayesian inference in models based on equilibrium search theory the equilibrium search model represents a substantial advance over previous models of job search but its empirical performance fails in some crucial ways hence flexible extensions are called for in this paper we consider three such extensions in areas where bayesian methods can be used to great advantage these are i a specification where bayesian priors are used to center a model over the restrictions implied by economic theory ii a model involving a nonlinear production function where a closed form expression for the likelihood function does not exist and iii a model which allows for unobserved heterogeneity we show how posterior simulation methods can be used for empirical analysis for all three models the paper includes an empirical exercise involving the school to work transitions of canadian and us school leavers

the algebraic theory of quasicrystals with five fold symmetries an algebraic binary operation is introduced into quasicrystals admitting five fold symmetry in terms of this many quasicrystals displaying full pentagonal or icosahedral symmetry are seen to be finitely generated examples are given in dimensions 1 2 3 and 4 the operation of left quasicrystal addition is affine linear the monoid generated by these operators is discussed and a presentation for it given in the generic case

importance of convection and damping on rates of convergence for the lax wendroff method it is well known that in solving steady state problems using hyperbolic time stepping methods the intent is to drive the transients to zero as quickly as possible in this paper the convergence to steady state of the lax wendroff method applied to solving the equations of gas dynamics is analyzed for the laval nozzle problem by comparing the relative rates of damping and convection using a linearized eigenmode analysis this analysis is developed for the simpler isenthalpic system and then extended to the full euler equations finally this allows a comparison between these systems for both models useful analytical information can be gleaned about the transient behavior of these systems especially in regard to quantifying the competitive factors affecting the removal of unsteady waves

finite volume solutions of convection diffusion test problems the cell vertex formulation of the finite volume method has been developed and widely used to model inviscid flows in aerodynamics more recently one of us has proposed an extension for viscous flows the purpose of the present paper is two fold first we have applied this scheme to a well known convection diffusion model problem involving flow round a 180 degrees bend which highlights some of the issues concerning the application of the boundary conditions in such cell based schemes the results are remarkably good when the boundary conditions are applied in an appropriate manner in our efforts to explain the high quality of the results we were led to a detailed analysis of the corresponding one dimensional problem our second purpose is thus to gather together various approaches to the analysis of this problem and to draw attention to the supra convergence phenomena enjoyed by the proposed methods 25 refs 9 figs 1 tab

substitution rules for aperiodic sequences of the cut and project type we consider one dimensional aperiodic sequences arising from a cut and project scheme with quadratic unitary pisot numbers a construction of the substitution rule is described under rather general assumptions it allows one to build a given cut and project sequence starting from its arbitrary point for a sequence with a convex acceptance window interval we prove that a substitution rule exists precisely if the boundary points of are in the corresponding quadratic field typically such a substitution has a reducible characteristic polynomial our main result is an algorithm for construction of such a substitution rule some examples are shown

on the affine self similarities of the three dimensional penrose pattern we prove that the vertex set of the usual three dimensional penrose tiling admits an infinite number of independent scaling factors and an infinite number of inflation centres more exactly we prove that there exist an infinite number of real numbers and an infinite number of points such that

computing bayes factors using a generalization of the savage dickey density ratio abstract we present a simple method for computing bayes factors the method derives from observing that in general a bayes factor can be written as the product of a quantity called the savage dickey density ratio and a correction factor both terms are easily estimated from posterior simulation in some cases it is possible to do these computations without ever evaluating the likelihood

the accuracy of cell vertex finite volume methods on quadrilateral meshes for linear first order hyperbolic equations in two dimensions we restate the cell vertex finite volume scheme as a finite element method on structured meshes consisting of distorted quadrilaterals the global error is shown to be of second order in various mesh dependent norms provided that the quadrilaterals are close to parallelograms in the sense that the distance between the midpoints of the diagonals is of the same order as the measure of the guadrilateral on tensor product nonuniform meshes the cell vertex scheme coincides with the familiar box scheme in this case second order accuracy is shown without any additional assumption on the regularity of the mesh which explains the insensitivity of the cell vertex scheme to mesh stretching in the coordinate directions observed in practice 17 refs

minimal distances in quasicrystals a general expression is derived for the minimal distance between points of a cut and project quasicrystal in with a convex acceptance window the study of minimal distances amounts to the study of one dimensional quasicrystals and their rescalings which occur in for an n dimensional ball as the exact value of is calculated for any radius for close to a ball a simple formula is given for all upper and lower bounds for are found the latter are easy to use even when is of a complicated shape

posterior predictive p values extending work of rubin this paper explores a bayesian counterpart of the classical p value namely a tail area probability of a test statistic under a null hypothesis the bayesian formulation using posterior predictive replications of the data allows a test statistic to depend on both data and unknown nuisance parameters and thus permits a direct measure of the discrepancy between sample and population quantities the tail area probability for a test statistic is then found under the joint posterior distribution of replicate data and the nuisance parameters both conditional on the null hypothesis this posterior predictive p value can also be viewed as the posterior mean of a classical p value averaging over the posterior distribution of nuisance parameters under the null hypothesis and thus it provides one general method for dealing with nuisance parameters two classical examples including the behrens fisher problem are used to illustrate the posterior predictive p value and some of its interesting properties which also reveal a new bayesian interpretation for some classical p values an application to multiple imputation inference is also presented a frequency evaluation shows that in general if the replication is defined by new nuisance parameters and new data then the type i frequentist error of an level posterior predictive test is often close to but less than and will never exceed 2

tau wavelets in the plane first an iterative process is described for subdivision and for scaling up of the penrose robinson tiles then we build the wavelets of haar i e suitably normalized characteristic functions on the tiles so that the orthogonality and multiresolution conditions are satisfied here 12 1 5

convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions we prove convergence of a class of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions the result is applied to the discontinuous galerkin method due to cockburn hou and shu

large sample significance levels from multiply imputed data using moment based statistics and an f reference distribution abstract we present a procedure for computing significance levels from data sets whose missing values have been multiply imputed data this procedure uses moment based statistics m 3 repeated imputations and an f reference distribution when m we show first that our procedure is essentially the same as the ideal procedure in cases of practical importance and second that its deviations from the ideal are basically a function of the coefficient of variation of the canonical ratios of complete to observed information for small m our procedure s performance is largely governed by this coefficient of variation and the mean of these ratios using simulation techniques with small m we compare our procedure s actual and nominal large sample significance levels and conclude that it is essentially calibrated and thus represents a definite improvement over previously available procedures furthermore we compare the large sample power of the procedure as a function of m and other factors such as the di

numerical study for differential constitutive equations with polymer melts by using a hybrid finite element volume method this paper covers the numerical investigation of complex flow tube tooling cable coating using the single equation representation of the pom pom sxpp model here the hybrid scheme consists of a taylor galerkin finite element discretisation and a cell vertex fluctuation distribution finite volume approach is employed for this method the momentum continuity equations have been solved by a fractional staged taylor galerkin pressure correction procedure and invoke a cell vertex fluctuation distribution finite volume scheme for the constitutive law stress response and pressure drop across the flow are investigated with respect to variation in weissenberg number and solvent fraction investigation of complex flow tube tooling cable coating using the single equation representation of the pom pom sxpp model influence of variation in weissenberg number on stress response and pressure drop across the flow evaluate free surface movement by using the time dependent prediction method which is termed phan thien dh dt scheme

fresh look at floating shock fitting a fast implicit upwind procedure for the two dimensional euler equations is described that allows accurate computations of shocked flows on nonadapted meshes away from shocks the second order accurate upwinding is based on the split coefficient matrix scm method in the presence of shocks the difference stencils are modified using a floating shock fitting technique rapid convergence to steady state solutions is attained with a diagonalized approximate factorization af algorithm results are presented for riemann s problem for a regular shock reflection at an inviscid wall for supersonic flow past a cylinder and for a transonic airfoil all computed shocks are ideally sharp and in excellent agreement with other numerical results or exact solutions most importantly this has been accomplished on unusually crude meshes without any attempt to align grid lines with shock fronts or to cluster grid lines around shocks

the efficient generation of simple two dimensional adaptive grids we present an efficient adaptive procedure for solving steady partial differential equations based on the simple two dimensional quadrilateral grid generator of huang and sloan siam j sci comput 15 1994 pp 776 797 the mesh equations are derived using an equidistribution principle and are discretized in the physical domain this allows the application of the adaptive grid generator to finite element and finite volume methods to efficiently solve the nonlinear algebraic equations describing the adapted grid we propose an alternating line gauss seidel relaxation procedure the beneficial effect of adaptive grids is demonstrated by coupling the grid generator to finite volume and finite difference approximations of advection and advection diffusion test problems for some examples the proposed method is shown to be 50 times more efficient than previously used solution procedures

tau wavelets of haar in this paper we construct a new type of haar wavelets called wavelets of haar using the arithmetics of the solutions and of the algebraic equation

quasicrystals and icosians a family of quasicrystals of dimensions 1 2 3 4 governed by the root lattice e8 is constructed the use of the icosian ring found in the quaternions with coefficients in q square root 5 allows simultaneous interpretation of the construction both in physical space and as a result of the standard cut and projection method in double dimension icosians are seen to provide a natural co ordination scheme for these quasicrystals nested sequences of quasicrystals form systems whose symmetries are all derivable from inflational and reflective symmetries directly related to the arithmetic of the icosians the use of coxeter diagrams clarifies the amazing relationship of e8 and quasicrystal symmetries and leads to the fundamental chain e8 contains implies d6 contains implies a4 contains implies a1 a1 that underlies five fold symmetry in quasicrystals decomposition of quasicrystals into concentric shells and a counting formula for the cardinalities of these shells is discussed

g model sets and their self similarities the model sets also called cut and project sets first defined by yves meyer in harmonic analysis play a central role in quasicrystal modelling each of them is defined by using a cut and project scheme containing two projectors and a lattice we present a method which can be used to study the self similarities of a model set based on the matrices of these projectors in a basis of the lattice this method also allows one to study the self similarities of the diffraction spectrum of a model set because generally the bragg peaks with intensity above a given threshold also form a model set the diffraction pattern corresponding to a quasicrystal is invariant under a finite group g and the local structure of the quasicrystal can be described by using a finite union of orbits of g called a g cluster the neighbours of each atom belong to some orbits of g and the quasicrystal can be regarded as a union of interpenetrating partially occupied translations of the corresponding g cluster we present a method to obtain a model set called the g model set by starting from a g cluster the experimental diffraction patterns allow one to determine the symmetry group g and high resolution electron microscopy images enable one to choose a g cluster describing the local structure the existing computer programs for the cut and project method allow one to pass directly from the local structure of the quasicrystal to a mathematical model to compute the theoretical diffraction spectrum and to compare it with the experimental data

a fast algorithm for direct simulation of particulate flows using conforming grids this paper presents a development of the direction splitting algorithm for flows in complex geometries proposed in 2 to the case of flows containing rigid particles the main novelty of this method is that the grid is fit to the time dependent domain at each time step which allows for an optimal spatial approximation of the navier stokes equations in general this is a very hard task for multidimensional problems however it is significantly simplified if the momentum equations are discretized by a direction splitting scheme such a scheme requires only solving a set of one dimensional problems and the grid can be easily fit to the boundary in the direction of each of these problems here we use a mac discretization stencil but the same idea can be applied to other discretizations the equations of motion of each particle are discretized explicitly and the computed particle velocities are imposed as dirichlet boundary conditions for the navier stokes equations on the adapted grid the pressure is extended within the particles in a fictitious domain fashion but the divergence stencil is fit to the particle boundaries in this paper the direction splitting algorithm with boundary fitting is compared to pure fictitious domain methods

generalized p values in significance testing of hypotheses in the presence of nuisance parameters abstract this article examines some problems of significance testing for one sided hypotheses of the form h 0 0 versus h 1 0 where is the parameter of interest in the usual setting let x be the observed data and let t x be a test statistic such that the family of distributions of t x is stochastically increasing in define cx as x t x t x 0 the p value is p x sup 0 pr x cx in the presence of a nuisance parameter there may not exist a nontrivial cx with a p value independent of we consider tests based on generalized extreme regions of the form cx x t x x t x x and conditions on t x x are given such that the p value p x sup 0 pr x cx is free of the nuisance parameter where t is stochastically increasing in we provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions a problem for which the fixed level testing approach

on the self similarities of a model set we present a method to determine certain self similarities of model sets the collection of spaces and mappings r n 1 r n r k n 2 r k n

upwind iteration methods for the cell vertex scheme in one dimension this paper describes and analyses a series of methods for solving the algebraic equations obtained from the cell vertex finite volume discretisation in one dimension the objective is to explore the possibilities for improved iteration methods that may be applied to cell vertex discretisations of the navier stokes equations in higher dimensions in general there is no natural one to one correspondence between cellbased residuals and nodal unknowns for this system in order to devise iteration schemes it is therefore necessary to provide a mapping between cells and nodes the family of methods introduced here is based on the application of standard iterative techniques to a nodal residual formed of a combination of neighbouring cell based residuals it includes the familiar lax wendroff iteration upwind iteration schemes and marching schemes capable of attaining convergence rates independent of the number of algebraic equations the aim in each case is to set to zero the residual for each cell apart from exceptional cells such as those containing shocks the final results show that matrix based upwind iteration methods using cell residuals modified to take account of critical points and applying several local iterations converge in around 15 iterations

inflation centres of the cut and project quasicrystals a rather general form of the conventional cut and project scheme is used to define quasicrystals as point sets in real n dimensional euclidean space the inflation or equivalently the self similarity properties of such quasicrystals are studied here assuming only the convexity of the acceptance window our result is a description of inflation centres of all types in a quasicrystal and a proof that our description is complete there are no other inflation centres for any chosen quasicrystal point internal inflation centre u its inflation properties are given as a set of scaling factors it turns out that the scaling factors form a one dimensional quasicrystal with a u dependent acceptance window scaling window the intersection of the scaling windows associated with all points of a quasicrystal is the one dimensional quasicrystal of universal internal scaling symmetries its acceptance window is the interval external inflation centres of a cut and project quasicrystal are those which are not among quasicrystal points their complete description is given analogically to the description of the internal ones imposing some additional requirements on the scaling factors between any two adjacent quasicrystal points one finds a countable infinity of external inflation centres the scaling factors belonging to any such centre u form an infinite u dependent subset of points of the quasicrystal with acceptance window containing

hyperbolicity and optimal coordinates for the three dimensional supersonic euler equations the two dimensional 2 d steady euler equations for supersonic flow in cartesian coordinates x y is hyperbolic except on the singular line u a where a is the speed of sound and u is the x component of velocity however the cauchy problem for x x circ with initial data prescribed at x x circ is well posed only when u a for the 2 d case the optimal coordinates have been found w h hui and d l chu comput fluid dynamics 4 1996 pp 403 426 to be the orthogonal system consisting of streamlines and their orthogonal lines this gives the most robust and accurate computation for supersonic flow it is commonly thought e g c y loh and m s liou j comput phys 113 1994 pp 224 248 that the system of three dimensional 3 d steady euler equations for supersonic flow is hyperbolic the present paper shows that it is hyperbolic only when the velocity in the marching direction is supersonic in which case it also simultaneously guarantees the well posedness of the cau

affine extension of noncrystallographic coxeter groups and quasicrystals unique affine extensions haff2 haff3 and haff4 are determined for the noncrystallographic coxeter groups h2 h3 and h4 they are used for the construction of new mathematical models for quasicrystal fragments with tenfold symmetry the case of haff2 corresponding to planar point sets is discussed in detail in contrast to the cut and project scheme we obtain by construction finite point sets which grow with a model specific growth parameter

the torus parametrization of quasiperiodic li classes the torus parametrization of quasiperiodic local isomorphism classes is introduced and used to determine the number of elements in such a class with special symmetries or inflation properties the method is explained in an illustrative fashion for some widely used tiling classes with golden mean rescaling namely for the fibonacci chain one dimensional the triangle and penrose patterns two dimensional and for kramer s and danzer s icosahedral tilings three dimensional we obtain a rather complete picture of the orbit structure within these classes and also discuss various general results

bayesianly justifiable and relevant frequency calculations for the applied statistician a common reaction among applied statisticians is that the bayesian statistician s energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying bayes s theorem to calculate conditional distributions of unknowns given knowns i feel however that the applied bayesian statistician s tool kit should be more extensive and include tools that may be usefully labeled frequency calculations three types of bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician

truncation error analysis of the finite volume method for a model steady convective equation abstract a fundamental error relation inherent in the gauss divergence theorem provided the basis for studying the truncation error of the finite volume method with cell center formulation for a model steady convective equation the consistency of the classical first and second order upwind schemes are proved to be seriously dependent on the grid distribution if the simple nature of the finite volume method is retained it is found that a consistent scheme for convective terms can not avoid the dissipation due to grid nonuniformity the geometrical interpretation of the diffusive terms such as vzo are undertaken classical finite volume methods which average an undefined 0 from its neighbouring nodes are shown to introduce false fluxes whenever grid nonuniformity is present a simple modification is proposed to cancel the false fluxes two test cases for the laplace equation illustrate the applicability of the proposed scheme however even with this modified scheme the consistency problem of the diffusion term is found to be seriously dependent on the grid uniformity

self similar delone sets and quasicrystals in this paper we answer the question whether any delone set invariant under quasiaddition of berman and moody can be identified with a cut and project quasicrystal for any such set we find an acceptance window which is bounded but has only convex interior the cut and project quasicrystal is then identified with an affine image of constructive methods used in the paper allow one in principle to put bounds on from a given fragment of a delone set

a finite volume scheme with shock fitting for the steady euler equations abstract analysis of two alternative finite volume formulations in respect of accuracy on non uniform meshes and number of spurious modes leads to a preference for the more compact cell vertex scheme over the cell centre scheme the resulting equations are solved iteratively by using a lax wendroff procedure as a smoother for a multigrid algorithm then application of boundary conditions in a natural way leads rapidly to all individual residuals being driven close to zero except at shocks at shocks the residuals should not be zero and a shock fitting procedure is introduced to avoid this inconsistency sharp accurate solutions on a relatively coarse mesh are obtained for a channel low problem in which the zierep singularity is displayed and for the naca 0012 aerofoil

the bayes non bayes compromise a brief review abstract various compromises that have occurred between bayesian and non bayesian methods are reviewed a citation is provided that discusses the inevitability of compromises within the bayesian approach one example deals with the masses of elementary particles but no knowledge of physics will be assumed

densities minimal distances and coverings of quasicrystals quasicrystals are generalizaions of lattices in this spirit we consider here three kinds of geometric properties of mathematical models of quasicrystals minimal distances between quasicrystal points covering radii of quasicrystals and the densities of quasicrystal points

performing likelihood ratio tests with multiply imputed data sets summary existing procedures for obtaining significance levels from multiply imputed data either i require access to the completed data point estimates and variance covariance matrices which may not be available in practice when the dimensionality of the estimand is high or ii directly combine p values with less satisfactory results taking advantage of the well known relationship between the wald and log likelihood ratio test statistics we propose a complete data log likelihood ratio based procedure it is shown that for any number of multiple imputations the proposed procedure is equivalent in large samples to the existing procedure based on the point estimates and the variance covariance matrices yet it only requires the point estimates and evaluations of the complete data log likelihood ratio statistic as a function of these estimates and the completed data the proposed procedure therefore is especially attractive with highly multiparameter incomplete data problems since it does not involve the computation of any matrices