on existence of positive solutions of sturm liouville boundary value problems for a nonlinear singular differential system abstract by employing the fixed point theorem of cone expansion and compression of norm type we investigate the existence of positive solutions of sturm liouville boundary value problems for a nonlinear singular differential system some well known results in the literature are generalized and improved an example is presented to illustrate the application of our main result

nonlinear scattering theory at low energy abstract we study the scattering theory of a conservative nonlinear one parameter group of operators on a hilbert space x relative to a group of linear unitary operators under certain hypotheses the scattering operator carries a neighborhood of 0 in x into x the theory is designed to apply to the semilinear schrodinger and klein gordon equations

positive solutions for systems of a nonlinear fourth order singular semipositone boundary value problems in this paper we study the existence of positive solutions of a two point boundary value problem for a system of fourth order nonlinear singular semipositone differential equations by the fixed point index theorem some new existence results are established and an example is given to demonstrate the application of our main results

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

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

existence of positive solutions for a system of generalized lidstone problems in this paper we study the existence of positive solutions for the system of generalized lidstone problems for ordinary differential equations 1 mu 2 m f 1 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 1 nv 2 n f 2 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 a 0u 2 i 0 b 0u 2 i 1 0 a 1u 2 i 1 b 1u 2 i 1 1 0 i 0 1 m 1 a 0v 2 j 0 b 0v 2 j 1 0 a 1v 2 j 1 b 1v 2 j 1 1 0 j 0 1 n 1 here f 1 f 2 c 0 1 xr m n r r 0 our hypotheses imposed on the nonlinearities f 1 and f 2 are formulated in terms of nonnegative matrices we use fixed point index theory to establish our main results based on a priori estimates of positive solutions

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

local superlinearity for elliptic systems involving parameters abstract we study the existence non existence and multiplicity of positive solutions for a class of systems of second order ordinary differential equations using the fixed point theorem of cone expansion compression type the upper lower solutions method and degree arguments we apply our abstract results to study semilinear elliptic systems in bounded annular domains with non homogeneous boundary conditions here the nonlinearities satisfy local superlinear assumptions

weighted strichartz estimates and global existence for semilinear wave equations in this paper we prove a sharp global existence theorem in all dimensions for nonlinear wave equations with power type nonlinearities the proof is based on a weighted strichartz estimate involving powers of the lorentz distance

a nonparametric bayesian modeling approach for cytogenetic dosimetry summary in cytogenetic dosimetry samples of cell cultures are exposed to a range of doses of a given agent in each sample at each dose level some measure of cell disability is recorded the objective is to develop models that explain cell response to dose such models can be used to predict response at unobserved doses more important such models can provide inference for unknown exposure doses given the observed responses typically cell disability is viewed as a poisson count but in the present work a more appropriate response is a categorical classification in the literature modeling in this case is very limited what exists is purely parametric we propose a fully bayesian nonparametric approach to this problem we offer comparison with a parametric model through a simulation study and the analysis of a real dataset modeling blood cultures exposed to radiation where classification is with regard to number of micronuclei per cell

linear bayes estimators of the potency curve in bioassay abstract the bayesian nonparametric approach to estimating the tolerance distribution in quantal bioassay has received some attention the computational difficulty in evaluating these bayes estimators has hindered their applications this paper explores the linear bayes approach to the bioassay problem these linear bayes estimators can be computed easily by using statistical software which has the capability of inverting a matrix let us state the quantal bioassay problem as follows the experimenter intends to test the potency of a stimulus by giving subjects injections of the stimulus at different levels namely he chooses l dosage levels t sub 1 t sub l and treats n sub 1 n sub l subjects at these levels respectively each subject possesses a fixed tolerance level if a stimulus exceeds a subject s tolerance level the subject responds positively if not there is no response therefore we observe the number of positive responses at each level these numbers are denoted by k sub 1 k sub l the potency curve f is the distribution of tolerance levels i e f is defined by the probability f t of getting a positive response to a dosage at level t for all t the objective of this article is to make inferences about the potency curve f keywords ferguson s dirichlet process

local energy decay for linear wave equations with variable coefficients abstract a uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients we deal with this equation in an exterior domain with a star shaped complement our advantage is that we do not assume any compactness of the support on the initial data and its proof is quite simple this generalizes a previous famous result due to morawetz the decay of solutions of the exterior initial boundary value problem for the wave equation comm pure appl math 14 1961 561 568 in order to prove local energy decay we mainly apply two types of ideas due to ikehata matsuyama l 2 behaviour of solutions to the linear heat and wave equations in exterior domains sci math japon 55 2002 33 42 and todorova yordanov critical exponent for a nonlinear wave equation with damping j differential equations 174 2001 464 489

on existence of positive solutions of a two point boundary value problem for a nonlinear singular semipositone system by employing the well known fixed point index theorem and making a substitution the existence of positive solutions of a two point boundary value problem for a nonlinear singular semipositone system is investigated some new existence results are established and an example is presented to demonstrate the application of our main results

bayesian nonparametric estimation of continuous monotone functions with applications to dose response analysis in this article we consider monotone nonparametric regression in a bayesian framework the monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions and a general random probability measure is assumed as the prior for the mixing distribution we investigate the choice of the underlying parametric distribution function and find that the two sided power distribution function is well suited both from a computational and mathematical point of view the model is motivated by traditional nonlinear models for dose response analysis and provides possibilities to elicitate informative prior distributions on different aspects of the curve the method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose response analysis

bayesian nonparametric inference on the dose level with specified response rate the richness of nonparametric bayesian models has attracted many different applications its application in dose finding studies has been hindered due to lack of methodologies on the nonparametric bayesian inference on percentiles the primary interest in dose finding studies focuses inference on the unknown toxicity or efficacy dose level corresponding to a prespecified rate this paper shows how this problem may generally be handled by deriving inference on percentiles of a distribution following a dirichlet process prior in particular theoretical results are derived to obtain the nonparametric bayesian inference of the unknown dose level this is followed by a description of the numerical implementation of that theory the method also allows efficient estimation of the entire potency curve finally the usefulness of the approach is demonstrated via an experimental data example

positive solutions of second order systems of boundary value problems abstract the existence of nonnegative solutions of boundary value problems of the form x t a t x t y t 0 y t b t g x t y t 0 x 0 x 1 y 0 y 1 0 is investigated where and g are functions from r p r q into r p and r q respectively and a b are functions defined on 0 1 with values in the spaces of diagonal matrices of order p and q respectively all functions are assumed to be continuous and nonnegativity as well as monotonicity and growth conditions are imposed on and g the existence results hold for a bounded interval of values of if and g are assumed to grow fast and have only nonzero values while if 0 0 0 g 0 0 0 it is shown that under reasonable conditions there exists a nontrivial nonnegative solution for every 0

a bayesian analysis of quantal bioassay experiments incorporating historical controls via bayes factors this paper addresses model based bayesian inference in the analysis of data arising from bioassay experiments in such experiments increasing doses of a chemical substance are given to treatment groups usually rats or mice for a fixed period of time usually 2 years the goal of such an experiment is to determine whether an increased dosage of the chemical is associated with increased probability of an adverse effect usually presence of adenoma or carcinoma the data consists of dosage survival time and the occurrence of the adverse event for each unit in the study to determine whether such relationship exists this paper proposes using bayes factors to compare two probit models the model that assumes increasing dose effects and the model that assumes no dose effect these models account for the survival time of each unit through a poly k type correction in order to increase statistical power the proposed approach allows the incorporation of information from control groups from previous studies the proposed method is able to handle data with very few occurrences of the adverse event the proposed method is compared with a variation of the peddada test via simulation and is shown to have higher power we demonstrate the method by applying it to the two bioassay experiment datasets previously analyzed by other authors copyright 2017 john wiley sons ltd

nonexistence of global solutions to semilinear wave equations in high dimensions on considere le probleme de cauchy pour l equation d onde semi lineaire 2 t 2 u x t u x t p p 1 u x o f x u t x o g x avec f g c o r n

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

posterior distribution of a dirichlet process from quantal response data the posterior distribution of a dirichlet process from n quantal responses at r dosage levels has been recognized by antoniak as a mixture of dirichlet processes the purpose of this paper is to develop a systematic procedure for computing finite dimensional distributions of such mixtures which can be equivalently expressed as multivariate beta distributions with random parameter vectors it is shown that the sequence of random parameter vectors of the updated beta posteriors from observations at increasing dosage levels evolves in a manner which is described by r separate markov chains this description is then used to derive the asymptotic posterior distribution the weak limits of the relevant markov chains are shown to be solutions of certain stochastic differential equations and the random parameter vector of the posterior beta distribution is shown to be asymptotically normal the mean vector and covariance matrix of which are given by recursion formulas

probits of mixtures the tolerances of individuals insects parasites in a population have a frequency or probability distribution called a tolerance distribution many tolerance distributions in bioassay studies can be the result of a rather heterogeneous population of individuals and can often be modelled as a mixture of a number of standard unimodal distributions a probit analysis can be generalized to the case where the tolerance distribution is a mixture of location and scale parameter distributions in this article the existence and determination of the maximum likelihood estimates are investigated an expectation maximization em algorithm for probits of mixtures is developed and it is shown that by application of the em algorithm the problem of probits of mixtures can be separated into a series of probits of individual component tolerance distributions

markov chain monte carlo in approximate dirichlet and beta two parameter process hierarchical models summary we present some easy to construct random probability measures which approximate the dirichlet process and an extension which we will call the beta two parameter process the nature of these constructions makes it simple to implement markov chain monte carlo algorithms for fitting nonparametric hierarchical models and mixtures of nonparametric hierarchical models for the dirichlet process we consider a truncation approximation as well as a weak limit approximation based on a mixture of dirichlet processes the same type of truncation approximation can also be applied to the beta two parameter process both methods lead to posteriors which can be fitted using markov chain monte carlo algorithms that take advantage of blocked coordinate updates these algorithms promote rapid mixing of the markov chain and can be readily applied to normal mean mixture models and to density estimation problems we prefer the truncation approximations since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the gibbs sampler furthermore for the dirichlet process the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort we also find that a certain beta two parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution

decay estimates for wave equations with variable coefficients we establish weighted l 2 estimates for dissipative wave equations with variable coefficients that exhibit a dissipative term with a space dependent potential these results yield decay estimates for the energy and the l 2 norm of solutions the proof is based on the multiplier method where multipliers are specially engineered from asymptotic profiles of related parabolic equations

bayesian nonparametric inference for effective doses in a quantal response experiment ramsey 1972 biometrics 28 841 858 developed a prior distribution for a single response curve arising from an indirect biological assay based upon quantal responses this paper presents the derivation of the exact prior and posterior distributions of an effective dose which follow from ramsey s prior since the posterior distribution of an effective dose is numerically difficult to compute in a large experiment methods for approximating this distribution are given numerical examples are presented to show the accuracy of the approximate methods finally the usefulness of the present results in assessing ramsey s prior is illustrated

a bayesian approach to the analysis of quantal bioassay studies using nonparametric mixture models we develop a bayesian nonparametric mixture modeling framework for quantal bioassay settings the approach is built upon modeling dose dependent response distributions we adopt a structured nonparametric prior mixture model which induces a monotonicity restriction for the dose response curve particular emphasis is placed on the key risk assessment goal of calibration for the dose level that corresponds to a specified response the proposed methodology yields flexible inference for the dose response relationship as well as for other inferential objectives as illustrated with two data sets from the literature

strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation the aim of this article is twofold first we consider the wave equation in the hyperbolic space hi and obtain the counterparts of the strichartz type estimates in this context next we examine the relationship between semilinear hyperbolic equations in the minkowski space and in the hyperbolic space this leads to a simple proof of the recent result of georgiev lindblad and sogge on global existence for solutions to semilinear hyperbolic problems with small data shifting the space time strichartz estimates from the hyperbolic space to the minkowski space yields weighted strichartz estimates in rn x 1r which extend the ones of georgiev lindblad and sogge

positive solutions of a system of second order boundary value problems involving first order derivatives via r n monotone matrices abstract in this paper we study the existence and multiplicity of positive solutions for the system of second order boundary value problems for nonlinear ordinary differential equations depending on first order derivatives u i f i t u 1 u 1 u n u n u i 0 u i 1 0 i 1 n here n 2 f i c 0 1 r 2 n r r 0 based on a priori estimates achieved by using integral inequalities and r n monotone matrices we use fixed point index theory to establish our main results for the above problem

positive solutions of a singular boundary value problem for systems of second order differential equations abstract in this paper we establish the conditions for the existence of positive solutions of a singular boundary value problem with two second order differential equations the development is based on a new maximum principle for the operator l 2 u u 2 au a 2 b 2 u under periodic boundary conditions and a fixed point theorem in cones when the eigenvalue lies in certain range the boundary value problem in question has at least one positive solution our results include extend and improve some previous results

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