uniform decision problems for automatic semigroups we consider various decision problems for automatic semigroups which involve the provision of an automatic structure as part of the problem instance with mild restrictions on the automatic structure which are necessary to make the problem well defined the uniform word problem for semigroups described by automatic structures is decidable under the same conditions we show that one can also decide whether the semigroup is completely simple or completely zero simple in the case that it is one can compute a rees matrix representation for the semigroup in the form of a rees matrix together with an automatic structure for its maximal subgroup on the other hand we show that it is undecidable in general whether a given element of a given automatic monoid has a right inverse

dirichlet laplace priors for optimal shrinkage penalized regression methods such as l1 regularization are routinely used in high dimensional applications and there is a rich literature on optimality properties under sparsity assumptions in the bayesian paradigm sparsity is routinely induced through two component mixture priors having a probability mass at zero but such priors encounter daunting computational problems in high dimensions this has motivated continuous shrinkage priors which can be expressed as global local scale mixtures of gaussians facilitating computation in contrast to the frequentist literature little is known about the properties of such priors and the convergence and concentration of the corresponding posterior distribution in this article we propose a new class of dirichlet laplace priors which possess optimal posterior concentration and lead to efficient posterior computation finite sample performance of dirichlet laplace priors relative to alternatives is assessed in simulated and real data examples

second order boltzmann schemes for compressible euler equations in one and two space dimensions a class of second order numerical schemes for the compressible euler equations is described and their l 1 stability i e rho geqq 0 t geqq 0 is proved following van leer s approach the solution rho u sqrt t here is represented as piecewise linear functions the necessity of a slope limitation appears naturally in the derivation of the schemes but it can be less strict than the slope reconstructions usually used these schemes are written in terms of explicit flux splitting formula and are naturally multidimensional in space the upwinding is obtained through a very generalized notion of characteristics the kinetic one

weak entropy boundary conditions for isentropic gas dynamics via kinetic relaxation abstract we consider a kinetic bgk model relaxing to isentropic gas dynamics previously introduced by the authors but with dirichlet boundary condition on the incoming velocities we pass to the limit as the relaxation parameter tends to zero by compensated compactness inside the domain and obtain that the limit satisfies entropy inequalities on the boundary involving weak traces of entropy fluxes our method is very general and could be applied to any entropy satisfying bgk model as soon as we have strong compactness of the macroscopic variables inside the domain

an entropic solver for ideal lagrangian magnetohydrodynamics in this paper we adapt to the ideal 1d lagrangian mhd equations a class of numerical schemes of order one in time and space presented in an earlier paper and applied to the gas dynamics system they use some properties of systems of conservation laws with zero entropy flux which describe fluid models invariant by galilean transformation and reversible for regular solutions these numerical schemes satisfy an entropy inequality under cfl conditions in the last section we describe a particular scheme for the mhd equations and show with some numerical applications its robustness and accuracy the generalization to full eulerian multidimensional mhd will be the subject of a forthcoming paper

efficient solution algorithms for the riemann problem for real gases a procedure for constructing solutions to the riemann problem for gas dynamics with a general convex equation of state is given approximate procedures involving a local parametrization of the equation of state are introduced in order to calculate numerical fluxes in conservative finite difference schemes this leads to difference schemes which are as accurate and almost as fast as the analogous schemes for polytropic gases numerical results in one and two space variables are presented

effect of the numerical scheme resolution on quasi 2d simulation of an automotive radial turbine under highly pulsating flow automotive turbocharger turbines usually work under pulsating flow because of the sequential nature of engine breathing however existing turbine models are typically based on quasi steady assumptions in this paper a model where the volute is calculated in a quasi 2d scheme is presented the objective of this work is to quantify and analyse the effect of the numerical resolution scheme used in the volute model the conditions imposed upstream are isentropic pressure pulsations with different amplitude and frequency the volute is computed using a finite volume approach considering the tangential and radial velocity components the stator and rotor are assumed to be quasi steady in this paper different integration and spatial reconstruction schemes are explored the spatial reconstruction is based on the muscl method with different slope limiters fulfilling the tvd criterion the model results are assessed against 3d u rans calculations the results show that under low frequency pressure pulses all the schemes lead to similar solutions but for high frequency pulsation the results can be very different depending upon the selected scheme this may have an impact in noise emission predictions

a subgrid scale deconvolution approach for shock capturing we develop a method for the modeling of flow discontinuities which can arise as weak solutions of inviscid conservation laws due to its similarity with recently proposed approximate deconvolution models for large eddy simulation the method potentially allows for a unified treatment of flow discontinuities and turbulent subgrid scales a filtering approach is employed since for the filtered evolution equations the solution is smooth and can be solved for by standard central finite difference schemes without special consideration of discontinuities a sufficiently accurate representation of the filtered nonlinear combination of discontinuous solution components which arise from the convection term can be obtained by a regularized deconvolution applied to the filtered solution for stable integration the evolution equations are supplemented by a relaxation regularization based on a secondary filter operation and a relaxation parameter an estimate for the relaxation parameter is provided the method is related to the spectral vanishing viscosity method and the regularized chapman enskog expansion method for conservation laws we detail the approach and demonstrate its efficiency with the inviscid and viscous burgers equations the isothermal shock problem and the one dimensional euler equations

entropy satisfying relaxation method with large time steps for euler ibvps this paper could have been given the title how to positively and implicitly solve euler equations using only linear scalar advections the new relaxation method we propose is able to solve euler like systems as well as initial and boundary value problems with real state laws at very low cost using a hybrid explicit implicit time integration associated with the arbitrary lagrangian eulerian formalism furthermore it possesses many attractive properties such as i the preservation of positivity for densities ii the guarantee of min max principle for mass fractions iii the satisfaction of entropy inequality under an expressible bound on the cfl ratio the main feature that will be emphasized is the design of this optimal time step which takes into account data not only from the inner domain but also from the boundary conditions

extensions and submonoids of automatic monoids in this paper submonoids and extensions of automatic and p automatic monoids are studied the concept of a p automatic monoid is a variant on the usual concept of an automatic monoid designed to allow a geometric characterization analogous to the group case in the case of right cancellative monoids the two concepts coincide here we study rational submonoids of p automatic monoids being able to show in many cases that p automaticity is inherited our sharpest results concern rational subgroups also closure properties are established for various notions of extensions of p automatic monoids including different types of products ideal extensions and rees matrix constructions

etude variationnelle du probleme de riemann abstract we study the riemann problem for a system of conservation laws with a strongly convex entropy in arbitrary dimensions we show that the resolution of this problem can be reduced to solving an infinite number of entropy inequalities after this transformation we consider various applications maximum principles uniqueness of the solution of the trivial riemann problem etc these inequalities are also used for a study of the wave curves in connection with the ibvp as considered in a benabdallah et d serre problemes aux limites pour des systemes hyperboliques non lineaires de deux equations a une dimension d espace c r acad sci paris ser i math 305 1987 677 680 f dubois and p le floch boundary conditions for nonlinear hyperbolic system of conservation laws j differential equations71 1988 93 122 at last we propose a numerical scheme based on the discretization of the entropy inequalities for the solution of the monodimensional riemann problem wave curves are not involved thus multi dimensional extensions can be expected

numerical approximations of the 10 moment gaussian closure we propose a numerical scheme to approximate the weak solutions of the 10 moment gaussian closure the moment gaussian closure for gas dynamics is governed by a conservative hyperbolic system supplemented by entropy inequalities whose solutions satisfy positiveness of density and tensorial pressure we consider a suliciu type relaxation numerical scheme to approximate the solutions these methods are proved to satisfy all the expected positiveness properties and all the discrete entropy inequalities the scheme is illustrated by several numerical experiments

bayesian variable selection in linear regression abstract this article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable it is based on a bayesian approach intended to be as objective as possible a probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model the method is not fully bayesian however because the ultimate choice of prior distribution from this family is affected by the data it is assumed that the predictors represent distinct observables the corresponding regression coefficients are assigned independent prior distributions for each regression coefficient subject to deletion from the model the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere that is a spike and slab distribution the random error component is assigned a normal distribution with mean 0 and standard deviation

the numerical viscosity of entropy stable schemes for systems of conservation laws i discrete approximations to hyperbolic systems of conservation laws are studied the amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison to this end conservative schemes which are also entropy conservative are constructed these entropy conservative schemes enjoy second order accuracy moreover they can be interpreted as piecewise linear finite element methods and hence can be formulated on various mesh configurations it is then shown that conservative schemes are entropy stable if and for three point schemes only they contain more viscosity than that present in the above mentioned entropy conservative ones

entropy flux splittings for hyperbolic conservation laws part i general framework a general framework is proposed for the derivation and analysis of flux splittings and the corresponding flux splitting schemes for systems of conservation laws endowed with a strictly convex entropy the approach leads to several new properties of the existing flux splittings and to a method for the construction of entropy flux splittings for general situations a large family of genuine entropy flux splittings is derived for several significant examples the scalar conservation laws the p system and the euler system of isentropic gas dynamics in particular for the isentropic euler system we obtain a family of splittings that satisfy the entropy inequality associated with the mechanical energy for this system it is proved that there exists a unique genuine entropy flux splitting that satisfies all of the entropy inequalities which is also the unique diagonalizable splitting this splitting can be also derived by the so called kinetic formulation simple and useful difference schemes are derived from the flux splittings for hyperbolic systems such entropy flux splitting schemes are shown to satisfy a discrete cell entropy inequality for the diagonalizable splitting schemes an a priori l estimate is provided by applying the principle of bounded invariant regions the convergence of entropy flux splitting schemes is proved for the 2 2 systems of conservation laws and the isentropic euler system 1995 john wiley sons inc

variational inference a review for statisticians abstractone of the core problems of modern statistics is to approximate difficult to compute probability densities this problem is especially important in bayesian statistics which frames all inference about unknown quantities as a calculation involving the posterior density in this article we review variational inference vi a method from machine learning that approximates probability densities through optimization vi has been used in many applications and tends to be faster than classical methods such as markov chain monte carlo sampling the idea behind vi is to first posit a family of densities and then to find a member of that family which is close to the target density closeness is measured by kullback leibler divergence we review the ideas behind mean field variational inference discuss the special case of vi applied to exponential family models present a full example with a bayesian mixture of gaussians and derive a variant that uses stochastic optimization to scale up to massive data

construction of bgk models with a family of kinetic entropies for a given system of conservation laws we introduce a general framework for kinetic bgk models we assume to be given a system of hyperbolic conservation laws with a family of lax entropies and we characterize the bgk models that lead to this system in the hydrodynamic limit and that are compatible with the whole family of entropies this is obtained by a new characterization of maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family of entropies we deduce a general procedure to construct such bgk models and we show how classical examples enter the framework we apply our theory to isentropic gas dynamics and full gas dynamics and in both cases we obtain new bgk models satisfying all entropy inequalities

maximum principle on the entropy and second order kinetic schemes we consider kinetic schemes for the multidimensional inviscid gas dynamics equations compressible euler equations we prove that the discrete maximum principle holds for the specific entropy this fixes the choice of the equilibrium functions necessary for kinetic schemes we use this property to perform a second order oscillation free scheme where only one slope limitation for three conserved quantities in 1d is necessary numerical results exhibit stability and strong convergence of the scheme introduction we consider the gas dynamics equations in one or two space dimensions atp div pu 0 1 atpu div puju a p 0 j 1 2 9 e div e p u 0 where x xl x2 u ul u2 and the total energy e piu12 2 pt y 1 is related to the pressure by the relation p pt 1 oh and in 11d godunov and lax friedrichs schemes preserve this property at the discretized level because they solve exactly the system 1 a reason why 4 should hold is that s satisfies the meaningless equation ats u vxs 0 received by the editor march 10 1992 and in revised form january 7 1993 1991 mathematics subject classification primary 35l65 76n10 65m06 76po5

entropy satisfying flux vector splittings and kinetic bgk models we establish forward and backward relations between entropy satisfying bgk relaxation models such as those introduced previously by the author and the first order flux vector splitting numerical methods for general systems of conservation laws classically to a kinetic bgk model that is compatible with some family of entropies we can associate an entropy flux vector splitting we prove that the converse is true any entropy flux vector splitting can be interpreted by a kinetic model and we obtain an explicit characterization of entropy satisfying flux vector splitting schemes we deduce a new proof of discrete entropy inequalities under a sharp cfl condition that generalizes the monotonicity criterion in the scalar case in particular this gives a stability condition for numerical kinetic methods with noncompact velocity support a new interpretation of general kinetic schemes is also provided via approximate riemann solvers we deduce the construction of finite velocity relaxation systems for gas dynamics and obtain a hllc scheme for which we are able to prove positiveness of density and internal energy and discrete entropy inequalities

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

sharp cfl discrete kinetic formulation and entropic schemes for scalar conservation laws we consider semidiscrete and fully discrete conservative finite volume schemes approximating the solution to one dimensional scalar conservation law we show that all e schemes are associated with a discrete kinetic formulation with a nonnegative kinetic defect measure this construction provides an alternative proof of the discrete local entropy inequalities with simple expressions of the discrete entropy fluxes in contrast to the known results which are restricted to cfl of the form lambda q leq 1 2 our proof holds under sharp cfl conditions

a discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws abstract we present a new relaxation approximation to scalar conservation laws in several space variables by means of semilinear hyperbolic systems of equations with a finite number of velocities under a suitable multidimensional generalization of the whitham relaxation subcharacteristic condition we show the convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

large eddy simulation of high reynolds number free and wall bounded flows the ability to simulate complex unsteady flows is limited by the current state of the art of subgrid scale sgs modeling which invariably relies on the use of smagorinsky type isotropic eddy viscosity models turbulent flows of practical importance involve inherently three dimensional unsteady features often subjected to strong inhomogeneous effects and rapid deformation which cannot be captured by isotropic models although some available improved sgs models can outperform the isotropic eddy viscosity models their practical use is typically limited because of their complexity development of more sophisticated sgs models is actively pursued and it is desirable to also investigate alternative nonconventional approaches in ordinary large eddy simulation les approaches models are introduced for closure of the low pass filtered navier strokes equations nse a promising les approach is the monotonically integrated les miles which involves solving the unfiltered nse using high resolution monotone algorithms in this approach implicit sgs models provided by intrinsic nonlinear high frequeacy filters built into the convection discretization are coupled naturally to the resolvable scales of the flow formal properties of the effective sgs modeling using miles are documented using databases of simulated free and wall bounded inhomogeneous flows including isotropic decaying turbulence transitional jets and channel flows mathematical and physical aspects of implicit sgs modeling through the use of nonlinear flux limiters are addressed using a formalism based on the modified les equations

navier stokes equations with several independent pressure laws and explicit predictor corrector schemes this work is concerned with the numerical capture of stiff viscous shock solutions of navier stokes equations for complex compressible materials in the regime of large reynolds numbers after 2 and 6 a relevant numerical capture is known to require the satisfaction of an extended set of non classical rankine hugoniot conditions due to the non conservation form of the governing pde model here we show how to enforce their validity at the discrete level without the need for solving local non linear algebraic problems non linearities are bypassed when introducing new averaging techniques which are proved to satisfy all the desirable stability properties when invoking suitable approximate riemann solutions a relaxation procedure is proposed to that purpose with the benefit of a fairly simple overall numerical method

discrete kinetic schemes for multidimensional systems of conservation laws we present here some numerical schemes for general multidimensional systems of conservation laws based on a class of discrete kinetic approximations which includes the relaxation schemes by s jin and z xin these schemes have a simple formulation even in the multidimensional case and do not need the solution of the local riemann problems for these approximations we give a suitable multidimensional generalization of the whitham s stability subcharacteristic condition in the scalar multidimensional case we establish the rigorous convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

lagrangian systems of conservation laws we study the mathematical structure of 1d systems of conservation laws written in the lagrange variable modifying the symmetrization proof of systems of conservation laws with three hypothesis we prove that these models have a canonical formalism these hypothesis are i the entropy flux is zero ii galilean invariance iii reversibility for smooth solutions then we study a family of numerical schemes for the solution of these systems we prove that they are entropy consistent we also prove from general considerations the symmetry of the spectrum of the jacobian matrix

on the asymptotic efficiency of approximate bayesian computation estimators many statistical applications involve models for which it is difficult to evaluate the likelihood but from which it is relatively easy to sample approximate bayesian computation is a likelihood free method for implementing bayesian inference in such cases we present results on the asymptotic variance of estimators obtained using approximate bayesian computation in a large data limit our key assumption is that the data is summarized by a fixed dimensional summary statistic that obeys a central limit theorem we prove asymptotic normality of the mean of the approximate bayesian computation posterior this result also shows that in terms of asymptotic variance we should use a summary statistic that is the same dimension as the parameter vector p and that any summary statistic of higher dimension can be reduced through a linear transformation to dimension p in a way that can only reduce the asymptotic variance of the posterior mean we look at how the monte carlo error of an importance sampling algorithm that samples from the approximate bayesian computation posterior affects the accuracy of estimators we give conditions on the importance sampling proposal distribution such that the variance of the estimator will be the same order as that of the maximum likelihood estimator based on the summary statistics used this suggests an iterative importance sampling algorithm which we evaluate empirically on a stochastic volatility model

semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation we investigate totally linearly degenerate hyperbolic systems with relaxation we aim to study their semilinear behavior which means that the local smooth solutions cannot develop shocks and the global existence is controlled by the supremum bound of the solution in this paper we study two specific examples the it suliciu type and the it kerr debye type models for the suliciu model which arises from the numerical approximation of isentropic flows the semilinear behavior is obtained using pointwise estimates of the gradient for the kerr debye systems which arise in nonlinear optics we show the semilinear behavior via energy methods for the original kerr debye model thanks to the special form of the interaction terms we can show the global existence of smooth solutions

boundary conditions for nonlinear hyperbolic systems of conservation laws we propose two formulations of the boundary conditions for nonlinear hyperbolic systems of conservation laws a first approach is based on the vanishing viscosity method and a second one is related to the riemann problem the equivalence between these two conditions is studied the latter formulation is extended to treat numerically physically relevant boundary conditions monodimensional experiments are presented

geophysical astrophysical spectral element adaptive refinement gaspar object oriented h adaptive fluid dynamics simulation an object oriented geophysical and astrophysical spectral element adaptive refinement gaspar code is introduced like most spectral element codes gaspar combines finite element efficiency with spectral method accuracy it is also designed to be flexible enough for a range of geophysics and astrophysics applications where turbulence or other complex multiscale problems arise the formalism accommodates both conforming and non conforming elements several aspects of this code derive from existing methods but here are synthesized into a new formulation of dynamic adaptive refinement dare of non conforming h type as a demonstration of the code several new 2d test cases are introduced that have time dependent analytic solutions and exhibit localized flow features including the 2d burgers equation with straight curved radial and oblique colliding fronts these are proposed as standard test problems for comparable dare codes quantitative errors are reported for 2d spatial and temporal convergence of dare

convergence of relaxation schemes to the equations of elastodynamics we study the effect of approximation matrices to semi discrete relaxation schemes for the equations of one dimensional elastodynamics we consider a semi discrete relaxation scheme and establish convergence using the l p theory of compensated compactness then we study the convergence of an associated relaxation diffusion system inspired by the scheme numerical comparisons of fully discrete schemes are carried out

adaptive approximate bayesian computation sequential techniques can be adapted to the abc algorithm to enhance its efficiency for instance when sisson et al 2007 introduced the abc prc algorithm the goal was to improve upon existing abc mcmc algorithms marjoram et al 2003 while the abc prc method is based upon the theoretical developments of del moral et al 2006 the application to the setting of approximate bayesian computation induces a bias in the approximation to the posterior distribution of interest as we demonstrate in this paper via both theoretical reasoning and experimental results it is however possible to devise an alternative version based on genuine importance sampling arguments that we call abc pmc in connection with the population monte carlo method introduced in cappe et al 2004 furthermore the abc pmc algorithm is simpler than the abc prc algorithm in that it does not require any backward transition kernel and proposes an automatic scaling of the forward kernel in this paper we demonstrate the applicability of abc pmc and compare its performances with abc prc

measures of intermittency in driven supersonic flows scaling exponents for structure functions of the velocity density and entropy are computed for driven supersonic flows for rms mach numbers of order unity with numerical simulations using the piecewise parabolic method algorithm on grids of up to 512 3 points the driving is made up of either one or three orthogonal shear waves in all cases studied the compressible component of the velocity in the statistically steady regime is weaker than its solenoidal counterpart by roughly a factor of 6 exponents for the longitudinal component of the velocity are comparable to what is found in the incompressible case and appear insensitive to the presence of numerous shocks scaling exponents of the transverse components of the velocity are comparable to those for the longitudinal component density and entropy structure functions display strong departures from linear scaling finally the scaling of structure functions of the energy transfer is also given and compared with the kolmogorov refined similarity hypothesis

foundations for envelope models and methods envelopes were recently proposed by cook li and chiaromonte as a method for reducing estimative and predictive variations in multivariate linear regression we extend their formulation proposing a general definition of an envelope and a general framework for adapting envelope methods to any estimation procedure we apply the new envelope methods to weighted least squares generalized linear models and cox regression simulations and illustrative data analysis show the potential for envelope methods to significantly improve standard methods in linear discriminant analysis logistic regression and poisson regression supplementary materials for this article are available online

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems we design numerical schemes for nonlinear degenerate parabolic systems with possibly dominant convection these schemes are based on discrete bgk models where both characteristic velocities and the source term depend singularly on the relaxation parameter general stability conditions are derived and convergence is proved to the entropy solutions for scalar equations

convergence tests for the piecewise parabolic method and navier stokes solutions for homogeneous compressible turbulence the need to simulate fully developed turbulence with wide range of scales led us to use the piecewise parabolic method ppm to solve the euler equations of motions to obtain data for 3 d homogeneous compressible decaying turbulence numerical simulations were performed on computational meshes of up to 10243 zones these data were compared with data obtained by solving the navier stokes ns equations results of studying the kinetic energy enstrophy and the energy power spectra with different resolutions are presented for both the ppm and ns data the results of the comparison show convergence of the ppm and ns solutions to the same limit

resolution d equations d evolution quasilineaires en dimension n d espace a l aide d equations lineaires en dimension n 1 on montre que l on peut calculer les solutions de l equation d evolution quasi lineaire dans r n d t u div b u a u 0 u x t r x r n t 0 et en particulier de l equation d ordre 1 d t u div b u 0 u x t r x r n t 0 a l aide d une equation d evolution lineaire dans r n r

on positivity preserving finite volume schemes for euler equations we consider the positivity preserving property of first and higher order finite volume schemes for one and two dimensional euler equations of gas dynamics a general framework is established which shows the positivity of density and pressure whenever the underlying one dimensional first order building block based on an exact or approximate riemann solver and the reconstruction are both positivity preserving appropriate limitation to achieve a high order positivity preserving reconstruction is described

bayesian analysis of constrained parameter and truncated data problems using gibbs sampling abstract constrained parameter problems arise in a wide variety of applications including bioassay actuarial graduation ordinal categorical data response surfaces reliability development testing and variance component models truncated data problems arise naturally in survival and failure time studies ordinal data models and categorical data studies aimed at uncovering underlying continuous distributions in many applications both parameter constraints and data truncation are present the statistical literature on such problems is very extensive reflecting both the problems widespread occurrence in applications and the methodological challenges that they pose however it is striking that so little of this applied and theoretical literature involves a parametric bayesian perspective from a technical viewpoint this perhaps is not difficult to understand the fundamental tool for bayesian calculations in typical realistic models is multidimensional numerical integration which often is problem

a kinetic construction of global solutions of first order quasilinear equations on considere le probleme de cauchy pour des equations quasilineaires d ordre 1 de type conservation dans la region t 0 u t i 1 u a i u x i 0 u x o u o x ou x x 1 x n u u x t et a i i 1 n sont des fonctions continument differentiables a valeurs reelles d une seule variable reelle

kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas we consider a time discrete kinetic scheme known as transport collapse method for the inviscid burgers equation partial t u partial x frac u 2 2 0 we prove the convergence of the scheme by using averaging lemmas without bounded variation estimate then the extension of this result to the kinetic model of brenier and corrias is discussed

flux corrected transport this paper describes a class of explicit eulerian finite difference algorithms for solving the continuity equation which are built around a technique called flux correction these flux corrected transport fct algorithms are of indeterminate order but yield realistic accurate results in addition to the mass conserving property of most conventional algorithms the fct algorithms strictly maintain the positivity of actual mass densities so steep gradients and inviscid shocks are handled particularly well this first paper concentrates on a simple one dimensional version of fct utilizing shasta a new transport algorithm for the continuity equation which is described in detail

kinetic formulation for systems of two conservation laws and elastodynamics for scalar conservation laws the kinetic formulation makes it possible to generate all the entropies from a simple kernel we show how this concept replaces and simplifies greatly the concept of young measures avoiding the difficulties encountered when working in lp the general construction of the two kinetic functions that generate the entropies of 2 2 strictly hyperbolic systems is also developed here we show that it amounts to building a universal entropy i e one that can be truncated by a kinetic value along riemann invariants for elastodynamics this construction can be completed and specialized using the additional galilean invariance this allows a full characterization of convex entropies it yields a kinetic formulation consisting of two semi kinetic equations which as usual are equivalent to the infinite family of all the entropy inequalities

numerical comparison of riemann solvers for astrophysical hydrodynamics the idea of this work is to compare a new positive and entropy stable approximate riemann solver by francois bouchut with a state of the art algorithm for astrophysical fluid dynamics we implemented the new riemann solver into an astrophysical ppm code the prometheus code and also made a version with a different more theoretically grounded higher order algorithm than ppm we present shock tube tests two dimensional instability tests and forced turbulence simulations in three dimensions we find subtle differences between the codes in the shock tube tests and in the statistics of the turbulence simulations the new riemann solver increases the computational speed without significant loss of accuracy

automatic semigroup acts to give a general framework for the theory of automatic groups and semigroups we introduce the notion of automaticity for semigroup acts we investigate their basic properties and discuss how the property of being automatic behaves under changing the generators of the acting semigroup and under changing the generators of the semigroup act in particular we prove that under some conditions on the acting semigroup the automaticity of the act is invariant under changing the generators since automatic semigroups can be seen as a special case of automatic semigroup acts our result generalizes and extends the corresponding result on automatic semigroups where the semigroup s satisfies s sss ss we also give a geometric approach in terms of the fellow traveller property and discuss the solvability of the equality problem in automatic semigroup acts our notion gives rise to a variety of definitions of automaticity depending on the set chosen as a semigroup act and we discuss future research directions

high order positivity preserving kinetic schemes for the compressible euler equations we present a new class of high order kinetic flux splitting schemes for the compressible euler equations and we prove that these schemes are positivity preserving i e rho and t remain geq 0 the first order kinetic scheme is based on the maxwellian equilibrium function and was initially proposed by pullin j comput phys 34 1980 pp 231 244 our higher order extension can be seen as a variant of the corrected antidiffusive flux approach the necessity of a limitation on the antidiffusive correction appears naturally in order to satisfy the constraint of positivity

a robust low diffusive kinetic scheme for the navier stokes euler equations a new kinetic scheme based on the equilibrium flux method efm and modified using osher intermediate states is proposed this new scheme called efmo combines the robustness of the equilibrium flux method and the accuracy of flux difference splitting schemes the original efm scheme is expressed in terms of simple wave decomposition in which only the linearly degenerate subpath is calculated from osher numerical flux while nonlinear waves are still evaluated from the regular efm splitting owing to its capability of withstanding intense nonlinear waves and yet exactly resolving contact discontinuities efmo is particularly well suited for the resolution of the navier stokes equations as demonstrated by a series of severe test cases including the high speed viscous flow around a cone a shock boundary layer interaction problem a vacuum apparition problem the hypersonic flow around a circular cylinder at mach 100 and the forward facing step at mach 3

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

the horseshoe estimator for sparse signals this paper proposes a new approach to sparsity called the horseshoe estimator the horseshoe is a close cousin of other widely used bayes rules arising from for example double exponential and cauchy priors in that it is a member of the same family of multivariate scale mixtures of normals but the horseshoe enjoys a number of advantages over existing approaches including its robustness its adaptivity to dierent sparsity patterns and its analytical tractability we prove two theorems that formally characterize both the horseshoe s adeptness at large outlying signals and its super ecient rate of convergence to the correct estimate of the sampling density in sparse situations finally using a combination of real and simulated data we show that the horseshoe estimator corresponds quite closely to the answers one would get by pursuing a full bayesian model averaging approach using a discrete mixture prior to model signals and noise

a kinetic equation with kinetic entropy functions for scalar conservation laws we construct a nonlinear kinetic equation and prove that it is welladapted to describe general multidimensional scalar conservation laws in particular we prove that it is well posed uniformly in e the microscopic scale we also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions analogous to boltzmann s microscopich function such that they recover krushkov type entropy inequality on the macroscopic scale finally we prove by both bv compactness arguments in the multidimensional case and by compensated compactness arguments in the one dimensional case that the local density of kinetic particles admits a continuum limit as it converges strongly with e 0 to the unique entropy solution of the corresponding conservation law

boltzmann type schemes for gas dynamics and the entropy property let h be a convex function a boltzmann equation is built following the b g k model for which h is an entropy in the fluid limit the compressible euler equations are obtained with a convex entropy naturally associated to h the motivation is to define numerical boltzmann schemes with finite speed of propagation corresponding to an equilibrium density function with bounded support the classical scheme obtained with h f f log f is based on the equilibrium density function exp v 2 2 which has infinite support

materials with internal variables and relaxation to conservation laws the theory of materials with internal state variables of coleman gurtin cg provides a natural framework to investigate the structure of relaxation approximations of conservation laws from the viewpoint of continuum thermomechanics after reviewing the requirements imposed on constitutive theories by the principle of consistency with the clausius duhem inequality we pursue two specific theories pertaining to stress relaxation and relaxation of internal energy they each lead to a relaxation framework for the theory of thermoelastic non conductors of heat equipped with globally defined entropy functions for the associated relaxation process next we consider a semilinear model problem of stress relaxation we discuss uniform stability and compactness for solutions of the relaxation system in the zero relaxation limit and establish convergence to the system of isothermal elastodynamics by using compensated compactness finally we prove a strong dissipation estimate for the relaxation approximations proposed in jin xin jx when the limit system is equipped with a strictly convex entropy

bayesian constraint relaxation prior information often takes the form of parameter constraints bayesian methods include such information through prior distributions having constrained support by using posterior sampling algorithms one can quantify uncertainty without relying on asymptotic approximations however sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally we propose to replace the sharp indicator function of the constraint with an exponential kernel thereby creating a close to constrained neighbourhood within the euclidean space in which the constrained subspace is embedded this kernel decays with distance from the constrained space at a rate depending on a relaxation hyperparameter by avoiding the sharp constraint we enable use of off the shelf posterior sampling algorithms such as hamiltonian monte carlo facilitating automatic computation in a broad range of models we study the constrained and relaxed distributions under multiple settings and theoretically quantify their differences application of the method is illustrated through several novel modelling examples