rotational degeneracy of hyperbolic systems of conservation laws the purpose of the paper is to study wave patterns of hyperbolic systems in which rotational symmetry creates a specific kind of degeneracy in this situation hyperbolicity is necessarily non strict so that the elementary waves have interesting patterns the discussion is centered around a theorem on existence and uniqueness of solutions of the riemann problem we give a unified presentation of examples from continuum mechanics

a time series ddp for functional proteomics profiles using a new type of array technology the reverse phase protein array rppa we measure time course protein expression for a set of selected markers that are known to co regulate biological functions in a pathway structure to accommodate the complex dependent nature of the data including temporal correlation and pathway dependence for the protein markers we propose a mixed effects model with temporal and protein specific components we develop a sequence of random probability measures rpm to account for the dependence in time of the protein expression measurements marginally for each rpm we assume a dirichlet process dp model the dependence is introduced by defining multivariate beta distributions for the unnormalized weights of the stick breaking representation we also acknowledge the pathway dependence among proteins via a conditionally autoregressive car model applying our model to the rppa data we reveal a pathway dependent functional profile for the set of proteins as well as marginal expression profiles over time for individual markers

order based dependent dirichlet processes in this article we propose a new framework for bayesian nonparametric modeling with continuous covariates in particular we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick breaking representation we focus mostly on the class of random distributions that induces a dirichlet process at each covariate value we derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering two main constructions with analytically known correlation structures are proposed practical and efficient computational methods are introduced we apply our framework through mixtures of these processes to regression modeling the modeling of stochastic volatility in time series data and spatial geostatistical modeling

modeling for dynamic ordinal regression relationships an application to estimating maturity of rockfish in california abstractwe develop a bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time the motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age length and maturity the latter recorded on an ordinal scale the methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses this approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models that arise from estimation of cut off points relating the latent continuous and ordinal responses a novel dependent dirichlet process prior for time dependent mixing distributions extends the model to the dynamic setting the methodology is used for a detailed study of relationships between maturity age and length for chilipepper rockfish using data collected over 15 years along th

rotationally invariant hyperbolic waves we use weakly nonlinear asymptotics to derive a canonical asymptotic equation for rotationally invariant hyperbolic waves the equation can include weak dissipative dispersive or diffractive effects we give applications to equations from magnetohydrodynamics elasticity and viscoelasticity

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

cr invariants of weight five in the bergman kernel abstract fefferman s program 1979 c fefferman adv math 31 131 262 of getting a biholomorphically invariant asymptotic expansion of the bergman kernel for smoothly bounded strictly pseudoconvex domains is realized in dimension 2 with the identification of universal constants according to the program the expansion is in terms of an approximately invariant smooth defining function of the domain which we refer to as fefferman s defining function and the coefficients are functions in the domain constructed by using derivatives of fefferman s defining function consequently the invariant expansion is necessarily a finite sum with a remainder term and the ambiguity estimate is crucial in the problem we get an expansion such that the boundary values of the coefficients are cr invariants of weight 5 this refines earlier results of c r graham 1987 in lecture notes in math vol 1276 pp 108 135 springer verlag new york berlin and the authors 1993 k hirachi g komatsu and n nakazawa in lecture notes in pure and appl math vol 143 pp 77 96 dekker new york the refinement becomes possible by appropriate extensions inside the domain of the cr invariants of weight 4 due to the ambiguity estimate of these extensions our expansion is optimal as far as fefferman s defining function is used a similar result for the szego kernel is also obtained

on a nonstrictly hyperbolic system of conservation laws a system of quasi linear hyperbolic conservation laws which is hyperbolic but not strictly hyperbolic is studied the system was derived as a model for the elastic string b keyfitz and kranzer arch rational mech anal 72 1980 210 241 and is assumed to be diagonizable interest is mainly in the large time behavior of the solution due to the nonlinearity of the system and the entropy condition solutions converge to very simple elementary waves nonstrict hyperbolicity of the system may cause stronger nonlinear interactions between waves pertaining to different families in particular such interactions may regularize linear waves in the solution the solutions are constructed using the random choice method

integral kahler invariants and the bergman kernel asymptotics for line bundles abstract on a compact kahler manifold one can define global invariants by integrating local invariants of the metric assume that a global invariant thus obtained depends only on the kahler class then we show that the integrand can be decomposed into a chern polynomial the integrand of a chern number and divergences of one forms which do not contribute to the integral we apply this decomposition formula to describe the asymptotic expansion of the bergman kernel for positive line bundles and to show that the cr q curvature on a sasakian manifold is a divergence

toeplitz operators and weighted bergman kernels abstract for a smoothly bounded strictly pseudoconvex domain we describe the boundary singularity of weighted bergman kernels with respect to weights behaving like a power possibly fractional of a defining function and more generally of the reproducing kernels of sobolev spaces of holomorphic functions of any real order this generalizes the classical result of fefferman for the unweighted bergman kernel finally we also exhibit a holomorphic continuation of the kernels with respect to the sobolev parameter to the entire complex plane our main tool are the generalized toeplitz operators of boutet de monvel and guillemin

nonlinear stability of an undercompressive shock for complex burgers equation though there is strong numerical evidence for the stability of undercompressive shocks their stability has not been verified analytically in particular the energy methods used to analyze stability of standard shocks do not apply here we present the first proof of stability for a particular undercompresive shock the real burgers shock considered as a solution of the complex burgers equation our analysis is by direct calculation of the green s function for the linearized equations combined with pointwise estimates of nonlinear effects a benefit of this method is to obtain fairly detailed information about the solution includingl1 behavior and rates of decay in different regions of space

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

existence and stability of viscoelastic shock profiles we investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by antman and malek madani we establish that the resulting equations fall into the class of symmetrizable hyperbolic parabolic systems hence spectral stability implies linearized and nonlinear stability with sharp rates of decay the new contributions are treatment of the compressible case formulation of a rigorous nonlinear stability theory including verification of stability of small amplitude lax shocks and the systematic incorporation in our investigations of numerical evans function computations determining stability of large amplitude and nonclassical type shock profiles

theory and numerical analysis for exact distributions of functionals of a dirichlet process the distribution of a mean or more generally of a vector of means of a dirichlet process is considered some characterizing aspects of this paper are i a review of a few basic results providing new formulations free from many of the extra assumptions considered to date in the literature and giving essentially new simpler and more direct proofs ii new numerical evaluations with any prescribed error of approximation of the distribution at issue iii a new form for the law of a vector of means moreover as applications of these results we give iv the sharpest condition sufficient for the distribution of a mean to be symmetric v forms for the probability distribution of the variance of the dirichlet random measure vi some hints for determining the finite dimensional distributions of a random function connected with bayesian methods for queuing models

on the lower order terms of the asymptotic expansion of tian yau zelditch we compute the first three coefficients of the asymptotic expansion of tian yau zelditch we also prove that in general the fcth coefficient is a polynomial of the curvature and its derivative of weight k

on nonlinear stability of general undercompressive viscous shock waves we study the nonlinear stability of general undercompressive viscous shock waves previously the authors showed stability in a special case when the shock phase shift can be determined a priori from the total mass of the perturbation using new pointwise methods by examining time invariants associated with the linearized equations we can now overcome a new difficulty in the general case namely nonlinear movement of the shock we introduce a coordinate transformation suitable to treat this new aspect and demonstrate our method by analyzing a model system of generic type we obtain sharp pointwise bounds andlp behavior of the solution for allp 1 p

nonuniqueness for the vanishing viscosity solution with fixed initial condition in a nonstrictly hyperbolic system of conservation laws we consider the riemann problem for a system of two decoupled nonstrictly hyperbolic burgers like conservation equations with added artificial viscosity we analytically establish two different vanishing viscosity limits for the solution of this system which correspond to the two cases where one of the viscosities vanishes much faster than the other this is done without altering the initial condition as is necessary with travelling wave methods numerical evidence is then provided to show that when the two viscosities vanish at the same rate the solution converges to a limit that lies strictly between the two previously established limits finally we use control theory to explain the mechanism behind this nonuniqueness behavior which indicates other systems of nonstrictly hyperbolic conservation laws where nonuniqueness will occur

an anova model for dependent random measures we consider dependent nonparametric models for related random probability distributions for example the random distributions might be indexed by a categorical covariate indicating the treatment levels in a clinical trial and might represent random effects distributions under the respective treatment combinations we propose a model that describes dependence across random distributions in an analysis of variance anova type fashion we define a probability model in such a way that marginally each random measure follows a dirichlet process dp and use the dependent dirichlet process to define the desired dependence across the related random measures the resulting probability model can alternatively be described as a mixture of anova models with a dp prior on the unknown mixing measure the main features of the proposed approach are ease of interpretation and computational simplicity because the model follows the standard anovastructure interpretation and inference parallels conventions for anova mode

marginal likelihood and bayes factors for dirichlet process mixture models we present a method for comparing semiparametric bayesian models constructed under the dirichlet process mixture dpm framework with alternative semiparameteric or parameteric bayesian models a distinctive feature of the method is that it can be applied to semiparametric models containing covariates and hierarchical prior structures and is apparently the first method of its kind formally the method is based on the marginal likelihood estimation approach of chib 1995 and requires estimation of the likelihood and posterior ordinates of the dpm model at a single high density point an interesting computation is involved in the estimation of the likelihood ordinate which is devised via collapsed sequential importance sampling extensive experiments with synthetic and real data involving semiparametric binary data regression models and hierarchical longitudinal mixed effects models are used to illustrate the implementation performance and applicability of the method

a stability index for detonation waves in majda s model for reacting flow abstract using evans function techniques we develop a stability index for weak and strong detonation waves analogous to that developed for shock waves in siam j math anal 32 2001 929 commun pure appl math 51 7 1998 797 yielding useful necessary conditions for stability here we carry out the analysis in the context of the majda model a simplified model for reacting flow the method is extended to the full navier stokes equations of reacting flow in g lyng one dimensional stability of detonation waves doctoral thesis indiana university 2002 g lyng k zumbrun stability of detonation waves preprint 2003 the resulting stability condition is satisfied for all nondegenerate i e spatially exponentially decaying weak and strong detonations of the majda model in agreement with numerical experiments of siam j sci statist comput 7u 1986 1059 and analytical results of commun math phys 204 3 1999 551 commun math phys 202 3 1999 547 for a related model of majda and rosales we discuss also the role in the znd limit of degenerate subalgebraically decaying weak detonation and for a modified bump type ignition function deflagration profiles as discussed in siam j math anal 24 1993 968 siam j appl math 55 1995 175 for the full equations

a numerical study of a rotationally degenerate hyperbolic system part i the riemann problem abstract we study numerically the riemann problem for a 2 x 2 system of conservation laws with a cubic flux function a particular case of the class of models introduced by keyfitz and kranzer the system is not strictly hyperbolic and the classical lax theory for hyperbolic systems is not directly applicable correspondingly some numerical schemes which are accurate for strictly hyperbolic systems are not well behaved for this example when they do work different schemes yield markedly different results for certain data we explain this effect by observing that near these data viscous regularization is non uniform as the viscosity tends to zero this fact does not contradict the well posedness of the hyperbolic model it does imply that precise control of the viscosity introduced into a computational method is crucial for generating the correct numerical solutions we examine all of these issues and comment on their implications for similar systems which arise in continuum mechanics

construction of boundary invariants and the logarithmic singularity of the bergman kernel in which case the coefficients aj are expressed by the weyl invariant theory in terms of the riemannian curvature tensor and its covariant derivatives the bergman kernel s counterpart of the time variable t is a defining function r of the domain by f1 and bs the formal singularity of k at a boundary point p is uniquely determined by the taylor expansion of r at p thus one has hope of expressing modulo on 1 r and modulo o r in terms of local biholomorphic invariants of the boundary provided r is appropriately chosen in f3 fefferman proposed to find such expressions by reducing the problem to an algebraic one in invariant theory associated with cr geometry and indeed expressed modulo on 19 r invariantly by solving the reduced problem partially the solution in f3 was then completed in beg to give a full invariant expression of modulo on 1 r but the reduction is still

bayesian nonparametric spatial modeling with dirichlet process mixing customary modeling for continuous point referenced data assumes a gaussian process that is often taken to be stationary when such models are fitted within a bayesian framework the unknown parameters of the process are assumed to be random so a random gaussian process results here we propose a novel spatial dirichlet process mixture model to produce a random spatial process that is neither gaussian nor stationary we first develop a spatial dirichlet process model for spatial data and discuss its properties because of familiar limitations associated with direct use of dirichlet process models we introduce mixing by convolving this process with a pure error process we then examine properties of models created through such dirichlet process mixing in the bayesian framework we implement posterior inference using gibbs sampling spatial prediction raises interesting questions but these can be handled finally we illustrate the approach using simulated data as well as a dataset involving precipitati

nonclassical multidimensional viscous and inviscid shocks extending our earlier work on lax type shocks of systems of conservation laws we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general lax or undercompressive type shock waves of nonconservative hyperbolic systems with parabolic regularization the hyperbolic equations may be of variable multiplicity and the parabolic regularization may be of real or partially parabolic type we prove an existence result for inviscid nonconservative shocks that extends to multidimensional shocks a one dimensional result of x lin proved by quite different methods in addition we construct families of smooth viscous shocks converging to a given inviscid shock as viscosity goes to zero thereby justifying the small viscosity limit for multidimensional nonconservative shocks in our previous work on shocks we made use of conservative form especially in parts of the low frequency analysis thus most of the new analysis of this paper is concentrated in this area by adopting the more general nonconservative viewpoint we are able to shed new light on both the viscous and inviscid theory for example we can now provide a clearer geometric motivation for the low frequency analysis in the viscous case also we show that one may in the treatment of inviscid stability of nonclassical and or nonconservative shocks remove an apparently restrictive technical assumption made by mokrane and coulombel in their work on respectively shocktype nonconservative boundary problems and conservative undercompressive shocks another advantage of the nonconservative perspective is that lax and undercompressive shocks can be treated by exactly the same analysis

stable viscosity matrices for systems of conservation laws abstract a natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension u 1 f u x 0 u r m is studied these matrices are admissible in the sense that small amplitude shock wave solutions of the hyperbolic system are shown to be limits of smooth traveling wave solutions of the parabolic system u t f u x v du x x as ifv 0 if d is in this class the class is determined by a linearized stability requirement the cauchy problem for the equation u 1 f u 0 u x vdu xx should be well posed in l 2 uniformly in v as v 0 previous examples of inadmissible viscosity matrices are accounted for through violation of the stability criterion

autoregressive mixture models for dynamic spatial poisson processes application to tracking intensity of violent crime this article develops a set of tools for smoothing and prediction with dependent point event patterns the methodology is motivated by the problem of tracking weekly maps of violent crime events but is designed to be straightforward to adapt to a wide variety of alternative settings in particular a bayesian semiparametric framework is introduced for modeling correlated time series of marked spatial poisson processes the likelihood is factored into two independent components the set of total integrated intensities and a series of process densities for the former it is assumed that poisson intensities are realizations from a dynamic linear model in the latter case a novel class of dependent stick breaking mixture models are proposed to allow nonparametric density estimates to evolve in discrete time this a simple and flexible new model for dependent random distributions is based on autoregressive time series of marginally beta random variables applied as correlated stick breaking proportions the

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

nonparametric bayesian bioassay including ordered polytomous response abstract previous attempts at implementing fully bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties we show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features a useful extension is presented which treats the case of ordered polytomous response illustrative examples are provided

retrospective markov chain monte carlo methods for dirichlet process hierarchical models inference for dirichlet process hierarchical models is typically performed using markov chain monte carlo methods which can be roughly categorized into marginal and conditional methods the former integrate out analytically the infinite dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the gibbs sampler conditional methods impute the dirichlet process and update it as a component of the gibbs sampler since this requires imputation of an infinite dimensional process implementation of the conditional method has relied on finite approximations in this paper we show how to avoid such approximations by designing two novel markov chain monte carlo algorithms which sample from the exact posterior distribution of quantities of interest the approximations are avoided by the new technique of retrospective sampling we also show how the algorithms can obtain samples from functionals of the dirichlet process the marginal and the conditional methods are compared and a careful simulation study is included which involves a non conjugate model different datasets and prior specifications

stick breaking autoregressive processes this paper considers the problem of defining a time dependent nonparametric prior for use in bayesian nonparametric modelling of time series a recursive construction allows the definition of priors whose marginals have a general stick breaking form the processes with poisson dirichlet and dirichlet process marginals are investigated in some detail we develop a general conditional markov chain monte carlo mcmc method for inference in the wide subclass of these models where the parameters of the marginal stick breaking process are nondecreasing sequences we derive a generalised polya urn scheme type representation of the dirichlet process construction which allows us to develop a marginal mcmc method for this case we apply the proposed methods to financial data to develop a semi parametric stochastic volatility model with a time varying nonparametric returns distribution finally we present two examples concerning the analysis of regional gdp and its growth

bifurcation of nonclassical viscous shock profiles from the constant state we determine the bifurcation from the constant solution of nonclassical transitional and overcompressive viscous shock profiles in regions of strict hyperbolicity whereas classical shock waves in systems of conservation laws involve a single characteristic field nonclassical waves involve two fields in an essential way this feature is reflected in the viscous profile differential equation which undergoes codimension three bifurcation of the kind studied by dumortier et al as opposed to the codimension one bifurcation occurring in the classical case we carry out a complete bifurcation analysis for systems of two quadratic conservation laws with constant strictly parabolic viscosity matrices by reducing to a canonical form introduced by fiddelaers we show that all such systems except possibly those on a codimension one variety in parameter space give rise to nonclassical shock waves and we classify the number and types of their bifurcation points one consequence of our analysis is that weak transitional waves arise in pairs with profiles forming a 2 cycle configuration previously shown to lead to nonuniqueness of riemann solutions and to nontrivial asymptotic dynamics of the conservation laws another consequence is that appearance of weak nonclassical waves is necessarily associated with change of stability in constant solutions of the parabolic system of conservation laws rather than with change of type in the associated hyperbolic system