a sampling based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory evidence theory provides an alternative to probability theory for the representation of epistemic uncertainty in model predictions that derives from epistemic uncertainty in model inputs where the descriptor epistemic is used to indicate uncertainty that derives from a lack of knowledge with respect to the appropriate values to use for various inputs to the model the potential benefit and hence appeal of evidence theory is that it allows a less restrictive specification of uncertainty than is possible within the axiomatic structure on which probability theory is based unfortunately the propagation of an evidence theory representation for uncertainty through a model is more computationally demanding than the propagation of a probabilistic representation for uncertainty with this difficulty constituting a serious obstacle to the use of evidence theory in the representation of uncertainty in predictions obtained from computationally intensive models this presentation describes and illustrates a sampling based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory preliminary trials indicate that the presented strategy can be used to propagate uncertainty representations based on evidence theory in analysis situations where naive sampling based i e unsophisticated monte carlo procedures are impracticable due to computational cost

computer model calibration using high dimensional output this work focuses on combining observations from field experiments with detailed computer simulations of a physical process to carry out statistical inference of particular interest here is determining uncertainty in resulting predictions this typically involves calibration of parameters in the computer simulator as well as accounting for inadequate physics in the simulator the problem is complicated by the fact that simulation code is sufficiently demanding that only a limited number of simulations can be carried out we consider applications in characterizing material properties for which the field data and the simulator output are highly multivariate for example the experimental data and simulation output may be an image or may describe the shape of a physical object we make use of the basic framework of kennedy and o hagan however the size and multivariate nature of the data lead to computational challenges in implementing the framework to overcome these challenges we make use of basis repre

multivariate gaussian process emulators with nonseparable covariance structures the gaussian process regression model is a popular type of emulator used as a fast surrogate for computationally expensive simulators deterministic computer models for simulators with multivariate output common practice is to specify a separable covariance structure for the gaussian process though computationally convenient this can be too restrictive leading to poor performance of the emulator particularly when the different simulator outputs represent different physical quantities also treating the simulator outputs as independent can lead to inappropriate representations of joint uncertainty we develop nonseparable covariance structures for gaussian process emulators based on the linear model of coregionalization and convolution methods using two case studies we compare the performance of these covariance structures both with standard separable covariance structures and with emulators that assume independence between the outputs in each case study we find that only emulators with nons

on the numerical approximation of finite speed diffusion problems lagrangian formulations for the cauchy problems for the generalized heat and porous media equations are introduced and equivalence and existence results discussed efficient interface tracking finite difference and finite element discretizations of the lagrangian formulation are discussed mixed euler lagrange formulations for mixed problems and the one phase stefan problem are presented numerical experiments are discussed

on the approximability of numerical taxonomy fitting distances by tree metrics we consider the problem of fitting an n n distance matrix d by a tree metric t let varepsilon be the distance to the closest tree metric under the l infty norm that is varepsilon min t parallel t d parallel infty first we present an o n2 algorithm for finding a tree metric t such that parallel t d parallel infty leq 3 varepsilon second we show that it is cal np hard to find a tree metric t such that parallel t d parallel infty frac 9 8 varepsilon this paper presents the first algorithm for this problem with a performance guarantee

bayesian calibration of inexact computer models bayesian calibration is used to study computer models in the presence of both a calibration parameter and model bias the parameter in the predominant methodology is left undefined this results in an issue where the posterior of the parameter is suboptimally broad there has been no generally accepted alternatives to date this article proposes using bayesian calibration where the prior distribution on the bias is orthogonal to the gradient of the computer model problems associated with bayesian calibration are shown to be mitigated through analytic results in addition to examples supplementary materials for this article are available online

interfaces with a corner point in one dimensional porous medium flow we prove that for a large class of initial distributions the solutions of the initial value problem for the one dimensional porous medium equation have interfaces which start to move abruptly after a positive waiting time this happens for example if the initial pressure is o x 2 as x 0 we also give sufficient conditions for the smoothness of the interface which improve previous results

on the hardness of inferring phylogenies from triplet dissimilarities this work considers the problem of reconstructing a phylogenetic tree from triplet dissimilarities which are dissimilarities defined over taxon triplets triplet dissimilarities are possibly the simplest generalization of pairwise dissimilarities and were used for phylogenetic reconstructions in the past few years we study the hardness of finding a tree best fitting a given triplet dissimilarity table under the norm we show that the corresponding decision problem is np hard and that the corresponding optimization problem cannot be approximated in polynomial time within a constant multiplicative factor smaller than 1 4 on the positive side we present a polynomial time constant rate approximation algorithm for this problem we also address the issue of best fit under maximal distortion which corresponds to the largest ratio between matching entries in two triplet dissimilarity tables we show that it is np hard to approximate the corresponding optimization problem within any constant multiplicative factor

a constructive algorithm for realizing a distance matrix the natural metric of a weighted graph is the length of the shortest paths between all pairs of vertices the investigated problem consists in a representation of a given metric by a graph such that the total length of the graph is minimized for that purpose we give a constructive algorithm based on a technique of reduction fusion and deletion we then show some results on a set of various distance matrices whose optimal realization is known

efficient algorithms for inverting evolution evolution can be mathematically modelled by a stochastic process that operates on the dna of species such models are based on the established theory that the dna sequences or genomes of all extant species have been derived from the genome of the common ancestor of all species by a process of random mutation and natural selection a stochastic model of evolution can be used to construct phylogenies or evolutionary trees for a set of species maximum likelihood estimation mle methods seek the evolutionary tree which is most likely to have produced the dna under consideration while these methods are intellectually satisfying they have not been widely accepted because of their computational intractability in this paper we address the intractability of mle methods as follows we introduce a metric on stochastic process models of evolution we show that this metric is meaningful by proving that in order for any algorithm to distinguish between two stochastic models that are close according to this metric it needs to be given many observations we complement this result with a simple and efficient algorithm for inverting the stochastic process of evolution that is for building a tree from observations on two state characters we will use the same techniques in a subsequent paper to solve the problem for multistate characters and hence for building a tree from dna sequence data the tree we build is provably close in our metric to the tree generating the data and gets closer as more observations become available though there have been many heuristics suggested for the problem of finding good approximations to the most likely tree our algorithm is the first one with a guaranteed convergence rate and further this rate is within a polynomial of the lower bound rate we establish ours is also the first polynomial time algorithm that is proven to converge at all to the correct tree

skeletal shape abstraction from examples learning a class prototype from a set of exemplars is an important challenge facing researchers in object categorization although the problem is receiving growing interest most approaches assume a one to one correspondence among local features restricting their ability to learn true abstractions of a shape in this paper we present a new technique for learning an abstract shape prototype from a set of exemplars whose features are in many to many correspondence focusing on the domain of 2d shape we represent a silhouette as a medial axis graph whose nodes correspond to partsrdquo defined by medial branches and whose edges connect adjacent parts given a pair of medial axis graphs we establish a many to many correspondence between their nodes to find correspondences among articulating parts based on these correspondences we recover the abstracted medial axis graph along with the positional and radial attributes associated with its nodes we evaluate the abstracted prototypes in the context of a recognition task

error bounds for finite difference approximations for a class of nonlinear parabolic systems in this paper we establish error bounds for a finite difference approximation to solutions of certain parabolic systems of the form t f po u we assume that the cauchy data is of class bv and we show that the sup norm of the error is bounded by o axiln axi at positive times

a necessary and sufficient condition for finite speed of propagation in the theory of doubly nonlinear degenerate parabolic equations a degenerate parabolic partial differential equation with a time derivative and first and second order derivatives with respect to one spatial variable is studied the coefficients in the equation depend nonlinearly on both the unknown and the first spatial derivative of a function of the unknown the equation is said to display finite speed of propagation if a non negative weak solution which has bounded support with respect to the spatial variable at some initial time also possesses this property at later times a criterion on the coefficients in the equation which is both necessary and sufficient for the occurrence of this phenomenon is established according to whether or not the criterion holds weak travelling wave solutions or weak travelling wave strict subsolutions of the equation are constructed and used to prove the main theorem via a comparison principle applications to special cases are provided

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

lagrangian non oscillatory and fem schemes for the porous media equation abstract interface tracking schemes derived from a lagrangian formulation of the equation are considered existence and equivalence results valid even for the non smooth interface case are given and non oscillatory schemes needed in this case are discussed mixed euler lagrange fem discretization for mixed problems and numerical experiments are presented

the l 1 global decay to discrete shocks for scalar monotone schemes given a family of discrete shocks of a monotone scheme we prove that the discrete shock profile with rational shock speed is asymptotically stable with respect to the l1 topology 1 if u0 l1 then un n 1 0 as n under no restriction conditions of the initial data to the interval inf sup the asymptotic wave profile is uniquely identified from the above family by a mass parameter

on lagrangian schemes for porous medium type generalized diffusion equations a discrete energetic variational approach abstract in this paper we present a systematic framework to derive a variational lagrangian scheme for porous medium type generalized diffusion equations by employing a discrete energetic variational approach such discrete energetic variational approaches are analogous to energetic variational approaches 39 25 in a semidiscrete level which provide a basis of deriving the semi discrete equations and can be applied to a large class of partial differential equations with energy dissipation laws and kinematic relations the numerical schemes derived by this framework can inherit the variational structure from the continuous energy dissipation law as an illustration we develop two variational lagrangian schemes for the multidimensional porous medium equations pme based on two different energy dissipation laws we focus on the numerical scheme based on the energy dissipation law with 1 2 u 2 d x as the dissipation functional several numerical experiments demonstrate the accuracy of this scheme as well as its ability in capturing the free boundary and estimating the waiting time for the pme in both 1d and 2d

on a doubly nonlinear diffusion equation in hydrology on considere l equation aux derivees partielles non lineaires u t d u u x x ou d et satisfont certaines hypotheses on etudie le probleme de neumann sur 1 1 avec les conditions aux limites naturelles d u u x 1 t 0 pour t 0 le probleme de cauchy et un probleme de cauchy dirichlet sur 0 avec les conditions aux limites u 0 t a pour t 0 a 0 1

object recognition as many to many feature matching object recognition can be formulated as matching image features to model features when recognition is exemplar based feature correspondence is one to one however segmentation errors articulation scale difference and within class deformation can yield image and model features which don t match one to one but rather many to many adopting a graph based representation of a set of features we present a matching algorithm that establishes many to many correspondences between the nodes of two noisy vertex labeled weighted graphs our approach reduces the problem of many to many matching of weighted graphs to that of many to many matching of weighted point sets in a normed vector space this is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure many to many vector correspondences established by the earth mover s distance framework are mapped back into many to many correspondences between graph nodes empirical evaluation of the algorithm on an extensive set of recognition trials including a comparison with two competing graph matching approaches demonstrates both the robustness and efficacy of the overall approach

water quality modeling a review of the analysis of uncertainty this paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction more specifically four problem areas are examined in detail uncertainty about model structure uncertainty in the estimated model parameter values the propagation of prediction errors and the design of experiments in order to reduce the critical uncertainties associated with a model the review is rather lengthy and it has therefore been prepared in effect as two papers there is a shorter largely nontechnical version which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling enclosed by this shorter discussion is the main body of the review dealing in turn with 1 identifiability and experimental design 2 the generation of preliminary model hypotheses under conditions of sparse grossly uncertain field data 3 the selection and evaluation of model structure 4 parameter estimation model calibration 5 checks and balances on the identified model i e model verification and model discrimination and 6 prediction error propagation much time is spent in discussing the algorithms of system identification in particular the methods of recursive estimation and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first order error analysis there are two obvious omissions from the review it is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty although clearly some reference must be made to these topics in brief the review concludes not surprisingly that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality and much remains to be done a lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior and there is ample evidence to show that the larger more comprehensive models are easily capable of generating highly uncertain predictions of future behavior for the future of the subject it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification a need for new questions to be posed in the problem of prediction and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence

a class of convergent finite difference schemes for certain nonlinear parabolic systems on considere le systeme des equations v t u x ev xx u t p v x u xx x t rxr avec les donnees initiales v u x 0 v 0 x u 0 x x r

blow up phenomena for polytropic equation with inhomogeneous density and source the subject of this investigation is the blow up phenomena of the positive solutions of the mixed problem for the one dimensional polytropic filtration equation with inhomogeneous density and source it is shown that under certain conditions on the nonlinearities and data blow up will occur at some finite time note that the technique applied for the proof does not use the zel dovich kompaneets barenblatt solutions since the construction of such type of function is more complicated in our case therefore we obtain a result by multiplying on a special factor which has convenient properties in particular by choosing the parameters of the factor and using the properties of the solution we obtain the inequality which allows us to show the blow up phenomena

computer model validation with functional output a key question in evaluation of computer models is does the computer model adequately represent reality a six step process for computer model validation is set out in bayarri et al technometrics 49 2007 138 154 and briefly summarized below based on comparison of computer model runs with field data of the process being modeled the methodology is particularly suited to treating the major issues associated with the validation process quantifying multiple sources of error and uncertainty in computer models combining multiple sources of information and being able to adapt to different but related scenarios two complications that frequently arise in practice are the need to deal with highly irregular functional data and the need to acknowledge and incorporate uncertainty in the inputs we develop methodology to deal with both complications a key part of the approach utilizes a wavelet representation of the functional data applies a hierarchical version of the scalar validation methodology to the wavelet coefficients and transforms back to ultimately compare computer model output with field output the generality of the methodology is only limited by the capability of a combination of computational tools and the appropriateness of decompositions of the sort wavelets employed here the methods and analyses we present are illustrated with a test bed dynamic stress analysis for a particular engineering system

clustering and variable selection in the presence of mixed variable types and missing data we consider the problem of model based clustering in the presence of many correlated mixed continuous and discrete variables some of which may have missing values discrete variables are treated with a latent continuous variable approach and the dirichlet process is used to construct a mixture model with an unknown number of components variable selection is also performed to identify the variables that are most influential for determining cluster membership the work is motivated by the need to cluster patients thought to potentially have autism spectrum disorder on the basis of many cognitive and or behavioral test scores there are a modest number of patients 486 in the data set along with many 55 test score variables many of which are discrete valued and or missing the goal of the work is to 1 cluster these patients into similar groups to help identify those with similar clinical presentation and 2 identify a sparse subset of tests that inform the clusters in order to eliminate unnecessary testing the proposed approach compares very favorably with other methods via simulation of problems of this type the results of the autism spectrum disorder analysis suggested 3 clusters to be most likely while only 4 test scores had high 0 5 posterior probability of being informative this will result in much more efficient and informative testing the need to cluster observations on the basis of many correlated continuous discrete variables with missing values is a common problem in the health sciences as well as in many other disciplines

systems of conservation laws with invariant submanifolds systems of conservation laws with coinciding shock and rarefaction curves arise in the study of oil reservoir simulation multicomponent chromatogra phy as well as in the study of nonlinear motion in elastic strings here we characterize this phenomenon by deriving necessary and sufficient conditions on the geometry of a wave curve in order that the shock wave curve coincide with its associated rarefaction wave curve for a system of conservation laws this coinci dence is the one dimensional case of a submanifold of the state variables being invariant for the system of equations and the necessary and sufficient conditions are derived for invariant submanifolds of arbitrary dimension in the case of 2 x 2 systems we derive explicit formulas for the class of flux functions that give rise to the coupled nonlinear conservation laws for which the shock and rarefaction wave curves coincide introduction systems of conservation laws which have coinciding shock and rarefaction curves arise in the study of oil reservoir simulation nonlinear wave motion in elastic strings as well as in multicomponent chromatography 1 4 5 6 9 11 12 these systems have many interesting features the riemann problem for these equations can be explicitly solved in the large and wave interactions have a simplified structure even in the presence of a nonconvex flux function for this reason these systems represent some of the few examples for which the cauchy problem has been solved for arbitrary data of bounded variation also hyperbolic degeneracies appear in each of these systems in the present paper we are concerned with characterizing the phenomenon of coinciding shock and rarefaction curves this phenomenon turns out to be a special case of the general phenomenon of a submanifold of r being invariant for weak solutions of a given system of n conservation laws invariant manifolds of higher dimension also appear in physical conservation equations in which the conserved quantities represent concentrations i e when the concentrations c of any of the species vanish the system must reduce to a lower order system that expresses the conservation of the remaining species thus c 0 defines a manifold which is invariant in the sense that solutions that start on the manifold remain there for all time moreover such an invariant manifold of dimension n 1 is the boundary of an dimensional invariant region in the sense of chueh conley and smoller 14 in the case of

periodic solutions of non newtonian polytropic filtration equations with nonlinear sources in this paper the authors first consider the dirichlet boundary value problem to the non newtonian polytropic filtration equation of the form u t div u m p 2 u m h x t u a in wxrwith strong nonlinear sources the existence of nontrivial periodic solutions is established based on topological degree theory the authors also studied the dirichlet boundary value problem to the equation in the form u t div u m 1u p 2 u m 1u b x t u f x t in wxrwith weak nonlinear sources the existence is treated with leray schauder fixed point theory

gaussian process models for computer experiments with qualitative and quantitative factors modeling experiments with qualitative and quantitative factors is an important issue in computer modeling we propose a framework for building gaussian process models that incorporate both types of factors the key to the development of these new models is an approach for constructing correlation functions with qualitative and quantitative factors an iterative estimation procedure is developed for the proposed models modern optimization techniques are used in the estimation to ensure the validity of the constructed correlation functions the proposed method is illustrated with an example involving a known function and a real example for modeling the thermal distribution of a data center

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

the error in spatial truncation for systems of parabolic conservation laws on etudie le comportement de la solution de u t du xx f u x u o x u 0 x l u t l u ou t 0 et x l l on obtient des resultats de decroissance relatifs aux normes de la difference entre la solution pour l infini et pour l fini

upscaling uncertainty with dynamic discrepancy for a multi scale carbon capture system abstractuncertainties from model parameters and model discrepancy from small scale models impact the accuracy and reliability of predictions of large scale systems inadequate representation of these uncertainties may result in inaccurate and overconfident predictions during scale up to larger systems hence multiscale modeling efforts must accurately quantify the effect of the propagation of uncertainties during upscaling using a bayesian approach we calibrate a small scale solid sorbent model to thermogravimetric tga data on a functional profile using chemistry based priors crucial to this effort is the representation of model discrepancy which uses a bayesian smoothing splines bss anova framework our uncertainty quantification uq approach could be considered intrusive as it includes the discrepancy function within the chemical rate expressions resulting in a set of stochastic differential equations such an approach allows for easily propagating uncertainty by propagating the joint model p

upgma and the normalized equidistant minimum evolution problem upgma unweighted pair group method with arithmetic mean is a widely used clustering method here we show that upgma is a greedy heuristic for the normalized equidistant minimum evolution neme problem that is finding a rooted tree that minimizes the minimum evolution score relative to the dissimilarity matrix among all rooted trees with the same leaf set in which all leaves have the same distance to the root we prove that the neme problem is np hard in addition we present some heuristic and approximation algorithms for solving the neme problem including a polynomial time algorithm that yields a binary rooted tree whose neme score is within o log2n of the optimum

homogeneous diffusion in ℝ with power like nonlinear diffusivity we study the nonnegative solutions of the initial value problem ut ur ux p 1ux x u x 0 l1 where p 0 r p 0 the local velocity of propagation of the solutions is identified as v vx vx p 1 where v cu with r p 1 p and c r p r p 1 is the nonlinear potential our main result is the a priori estimate vx vx p 1 x frac 1 2p r t

a finite difference scheme for a class of nonlinear parabolic systems in 3d space variables abstract in this paper we establish error bound analysis for a finite difference approximation to the solutions for a class of nonlinear parabolic systems in the form t v x f v y g v z h v d v we assume that the initial data is sufficiently smooth and of class bv the error is proved to be bounded by o x ln x for all positive time in an appropriate norm

separation of variables of a generalized porous medium equation with nonlinear source this paper considers a general form of the porous medium equation with nonlinear source term ut d u u n x f u n 1 the functional separation of variables of this equation is studied by using the generalized conditional symmetry approach we obtain a complete list of canonical forms for such equations which admit the functional separable solutions as a consequence some exact solutions to the resulting equations are constructed and their behavior are also investigated 2002 elsevier science usa all rights reserved

asymptotic preserving and well balanced schemes for the 1d cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes abstract the original well balanced wb framework of greenberg and leroux 1996 24 and gosse 2002 18 relying on non conservative nc products see lefoch and tzavaras 1999 41 is set up in order to efficiently treat the so called cattaneo model of chemotaxis in 1d see hillen and stevens 2000 29 it proceeds by concentrating the source terms onto dirac masses this allows to handle them by nc jump relations based on steady state equations which can be integrated explicitly a riemann solver is deduced and the corresponding wb godunov scheme completed with the standard hoff smoller theory see hillen and stevens 2000 29 for the diffusion reaction equation ruling the evolution of the chemoattractant concentration is studied in detail later following former results of gosse and toscani 2002 2003 21 22 a simple rewriting of the nc jump relations allows to generate another version of the same godunov scheme which is well adapted to the parabolic scaling involving a small parameter e the standard bv framework is used to study the uniform stability of this asymptotic preserving ap scheme with respect to e allows to pass to the limit and derive a simple centered discretization of the keller segel model finally results by filbet 2006 14 permit to pass to the complementary limit when the space step h is sent to zero numerical results are included to illustrate the feasibility and the efficiency of the method

the cauchy problem for ut δu m when 0 m 1 this paper deals with the cauchy problem for the nonlinear diffusion equation u t u u m 1 0 on 0 x rn u 0 u0 when 0 m 1 fast diffusion case we prove that there exists a global time solution for any locally integrable function u0 hence no growth condition at infinity for u0 is required moreover the solution is shown to be unique in that class behavior at infinity of the solution and l loc regularizing effects are also examined when m max n 2 n 0 1

the interfaces of one dimensional flows in porous media abstract a porous media equation pme has been used as a model for a number of physical phenomena heat diffusion at high temperatures boundary layer theory spread of a thin layer of viscous material and mainly the flow of gas in a porous medium the most distinctive characteristic of the solutions to pme as compared with the linear heat equation is the finite speed of propagation in this paper the properties of the interfaces are studied in terms of the initial data sometimes the interface is stationary for a certain time and then begins to move we characterize the existence of a positive waiting time and give bounds for it

probabilistic sensitivity analysis of complex models a bayesian approach summary in many areas of science and technology mathematical models are built to simulate complex real world phenomena such models are typically implemented in large computer programs and are also very complex such that the way that the model responds to changes in its inputs is not transparent sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs this may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application a broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model s output to variation in its inputs in practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs an approach which is known as probabilistic sensitivity analysis we present a bayesian framework which unifies the various tools of prob abilistic sensitivity analysis the bayesian approach is computationally highly efficient it allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard monte carlo methods furthermore all measures of interest may be computed from a single set of runs

blow up for the porous media equation with source term and positive initial energy abstract we study the cauchy dirichlet problem for the porous media equation with nonlinear source term in a bounded subset of r n the problem describes the propagation of thermal perturbations in a medium with a nonlinear heat conduction coefficient and a heat source depending on the temperature the aim of the paper is to extend the unstable set to a part of the positive energy region a phenomenon which was known only for linear conduction

propagation profile of support for evolution p laplacian with convection in half space abstract consider the cauchy dirichlet problem in half space for a one dimensional evolution p laplacian with convection for p 2 and pay attention to the interface t sup x u x t 0 it is well known that lim t t in the absence of the convection while the inclusion of the first order term may change the property of finite or infinite speed of propagation in this paper it will be shown that the nonlinear convection plays a very important role to the evolution of t for the convection with promoting diffusion the fast propagation phenomenon occurs i e u x t 0 whenever t 0 if the convection is strong enough otherwise t remains finite and non localized while under the convection with counteracting diffusion if the convection is strong enough localization even shrinking and extinction appears otherwise t keeps non localized in addition it is found that the time related boundary data are significant also to the behavior of solutions the decay or incremental rates of the boundary data affect not only the contraction or expansion of the supports but also the propagation speed of the interface

testing metric properties finite metric spaces and in particular tree metrics play an important role in various disciplines such as evolutionary biology and statistics a natural family of problems concerning metrics is deciding given a matrix m whether or not it is a distance metric of a certain predetermined type here we consider the following relaxed version of such decision problems for any given matrix m and parameter e we are interested in determining by probing m whether m has a particular metric property p or whether it is e far from having the property in e far we mean that at least an e fraction of the entries of m must be modified so that it obtains the property the algorithm may query the matrix on entries m i j of its choice and is allowed a constant probability of error we describe algorithms for testing euclidean metrics tree metrics and ultrametrics furthermore we present an algorithm that tests whether a matrix m is an approximate ultrametric in all cases the query complexity and running time are polynomial in 1 e and independent of the size of the matrix finally our algorithms can be used to solve relaxed versions of the corresponding search problems in time that is sub linear in the size of the matrix

operator spltting methods for systems of convection diffusion equations nonlinear error mechanisms and correction strategies abstract many numerical methods for systems of convection diffusion equations are based on an operator splitting formulation where convective and diffusive forces are accounted for in separate substeps we describe the nonlinear mechanism of the splitting error in such numerical methods in the one dimensional case a mechanism that is intimately linked to the local linearizations introduced implicitly in the hyperbolic convection steps by the use of an entropy condition for convection dominated flows we demonstrate that operator splitting methods typically generate a numerical widening of viscous fronts unless the splitting step is of the same magnitude as the diffusion scale to compensate for the potentially damaging splitting error we propose a corrected operator splitting cos method for general systems of convection diffusion equations with the ability of correctly resolving the nonlinear balance between the convective and diffusive forces in particular cos produces viscous shocks with a correct structure also when the splitting step is large a front tracking method for systems of conservation laws which in turn relies heavily on a riemann solver constitutes an important part of our cos strategy the proposed cos method is successfully applied to a system modeling two phase multicomponent flow in porous media and a triangular system modeling three phase flow

a simple approach to emulation for computer models with qualitative and quantitative factors we propose a flexible yet computationally efficient approach for building gaussian process models for computer experiments with both qualitative and quantitative factors this approach uses the hypersphere parameterization to model the correlations of the qualitative factors thus avoiding the need of directly solving optimization problems with positive definite constraints the effectiveness of the proposed method is successfully illustrated by several examples

provably fast and accurate recovery of evolutionary trees through harmonic greedy triplets we give a greedy learning algorithm for reconstructing an evolutionary tree based on a certain harmonic average on triplets of terminal taxa after the pairwise distances between terminal taxa are estimated from sequence data the algorithm runs in smallbigo numtaxa 2 time using smallbigo numtaxa work space where numtaxa is the number of terminal taxa these time and space complexities are optimal in the sense that the size of an input distance matrix is numtaxa 2 and the size of an output tree is numtaxa moreover in the jukes cantor model of evolution the algorithm recovers the correct tree topology with high probability using sample sequences of length polynomial in 1 numtaxa 2 the logarithm of the error probability and 3 the inverses of two small parameters

variable selection in bayesian smoothing spline anova models application to deterministic computer codes with many predictors choosing an appropriate subset of the covariates is a crucial and difficult step in nonparametric regression we propose a bayesian nonparametric regression model for curve fitting and variable selection we use the smoothing splines anova framework to decompose the regression function into interpretable main effect and interaction functions and use stochastic search variable selection through markov chain monte carlo sampling to search for models that fit the data well we also show that variable selection is highly sensitive to hyperparameter choice and develop a technique for selecting hyperparameters that control the long run false positive rate we use our method to build an emulator for a complex computer model for two phase fluid flow

the smoothing property for a class of doubly nonlinear parabolic equations we consider a class of doubly nonlinear parabolic equations used in modeling free boundaries with a finite speed of propagation we prove that nonnegative weak solutions satisfy a smoothing property this is a well known feature in some particular cases such as the porous medium equation or the parabolic p laplace equation the result is obtained via regularization and a comparison theorem

improving skeletal shape abstraction using multiple optimal solutions shape abstraction is an important problem faced by researchers in many fields such as pattern recognition computer vision and industrial design a recently developed previous shape abstraction framework demirci et al 20 generates an abstracted shape based on the correspondences between the features of the input shapes where the correspondences are obtained using the first optimal solution of a well known transportation problem as the size of the feature space grows the possibility of having more than one optimal solution for the same problem increases considering the case where multiple optimal solutions exist for the same transportation problem we first rank all optimal solutions based on how much they preserve the local neighborhood relations in this paper instead of creating the abstracted shape using the first optimal solution as done by the previous work we create the abstracted shape using the highest ranked optimal solution with this new property more effective abstracted shapes are generated experimental evaluation of the framework demonstrates that the proposed approach compares favorably with the previous technique in a set of shape retrieval experiments for different datasets highlightsskeletal shape abstraction is reformulated as the transportation problem a distortion free graph embedding is used for a better representation all optimal solutions for the transportation problem are considered the optimal solution which most resembles the neighborhood relations is used experiments demonstrate the improved performance

calibration of computational models with categorical parameters and correlated outputs via bayesian smoothing spline anova it has become commonplace to use complex computer models to predict outcomes in regions where data do not exist typically these models need to be calibrated and validated using some experimental data which often consists of multiple correlated outcomes in addition some of the model parameters may be categorical in nature such as a pointer variable to alternate models or submodels for some of the physics of the system here we present a general approach for calibration in such situations where an emulator of the computationally demanding models and a discrepancy term from the model to reality are represented within a bayesian smoothing spline bss anova framework the bss anova framework has several advantages over the traditional gaussian process including ease of handling categorical inputs and correlated outputs and improved computational efficiency finally this framework is then applied to the problem that motivated its design a calibration of a computational fluid dynamics cfd model of

a frequentist approach to computer model calibration summary the paper considers the computer model calibration problem and provides a general frequentist solution under the framework proposed the data model is semiparametric with a non parametric discrepancy function which accounts for any discrepancy between physical reality and the computer model in an attempt to solve a fundamentally important but often ignored identifiability issue between the computer model parameters and the discrepancy function the paper proposes a new and identifiable parameterization of the calibration problem it also develops a two step procedure for estimating all the relevant quantities under the new parameterization this estimation procedure is shown to enjoy excellent rates of convergence and can be straightforwardly implemented with existing software for uncertainty quantification bootstrapping is adopted to construct confidence regions for the quantities of interest the practical performance of the methodology is illustrated through simulation examples and an application to a computational fluid dynamics model

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise

invariant regions for systems of conservation laws on decrit des conditions necessaires et suffisantes pour qu une region dans r n soit invariante pour des solutions du systeme de n lois de conservations u t f u x o