local radial basis function based gridfree scheme for unsteady incompressible viscous flows a local radial basic function rbf based gridfree scheme has been developed to solve unsteady incompressible navier stokes equations in primitive variables the velocity pressure decoupling is obtained by making use of a fractional step algorithm the scheme is validated over a variety of benchmark problems and found a very good agreement with the existing results comparisons with the benchmark solutions show that the developed local rbf gridfree scheme is stable and produces accurate results on domains discretized even with non uniform distribution of nodal points

a rbf based differential quadrature method for solving two dimensional variable order time fractional advection diffusion equation abstract numerical simulation technique of two dimensional variable order time fractional advection diffusion equation is developed in this paper using radial basis function based differential quadrature method rbf dq to the best of the authors knowledge this is the first application of this method to variable order time fractional advection diffusion equations for the general case of irregular geometries the meshless local form of rbf dq is used and the multiquadric type of radial basis functions is selected for the computations this approach allows one to define a reconstruction of the local radial basis functions to treat accurately both the dirichlet and neumann boundary conditions on the irregular boundaries the method is validated by the well documented test examples involving variable order fractional modeling of air pollution the numerical results demonstrate that the proposed method provides accurate solutions for two dimensional variable order time fractional advection diffusion equations

a numerical study of some radial basis function based solution methods for elliptic pdes abstract during the last decade three main variations have been proposed for solving elliptic pdes by means of collocation with radial basis functions rbfs in this study we have implemented them for infinitely smooth rbfs and then compared them across the full range of values for the shape parameter of the rbfs this was made possible by a recently discovered numerical procedure that bypasses the ill conditioning which has previously limited the range that could be used for this parameter we find that the best values for it often fall outside the range that was previously available we have also looked at piecewise smooth versus infinitely smooth rbfs and found that for pde applications with smooth solutions the infinitely smooth rbfs are preferable mainly because they lead to higher accuracy in a comparison of rbf based methods against two standard techniques a second order finite difference method and a pseudospectral method the former gave a much superior accuracy

improved multiquadric method for elliptic partial differential equations via pde collocation on the boundary the multiquadric radial basis function mq method is a recent meshless collocation method with global basis functions it was introduced for discretizing partial differential equations pdes by kansa in the early 1990s the mq method was originally used for interpolation of scattered data and it was shown to have exponential convergence for interpolation problems in 1 we have extended the kansa mq method to numerical solution and detection of bifurcations in 1d and 2d parameterized nonlinear elliptic pdes we have found there that the modest size nonlinear systems resulting from the mq discretization can be efficiently continued by a standard continuation software such as auto we have observed high accuracy with a small number of unknowns as compared with most known results from the literature in this paper we formulate an improved kansa mq method with pde collocation on the boundary mq pdecb we add an additional set of nodes which can lie inside or outside of the domain adjacent to the boundary and correspondingly add an additional set of collocation equations obtained via collocation of the pde on the boundary numerical results are given that show a considerable improvement in accuracy of the mq pdecb method over the kansa mq method with both methods having exponential convergence with essentially the same rates

on properties of discrete r q and s t inventory systems abstract we consider single item r q and s t inventory systems with integer valued demand processes while most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space we show that these properties no longer hold in the discrete space in the sense of linear interpolation extension and l convexity this nonconvexity can lead to failure of optimization techniques based on local optimality to obtain the optimal inventory policies it can also make certain comparative properties established previously using continuous variables invalid we revise these properties in the discrete space

some stochastic inventory models with deterministic variable lead time in this paper we determine optimal reduction in the procurement lead time duration for some stochastic inventory models jointly with the optimal ordering decisions the models are developed with complete and partial information about the lead time demand distribution the stochastic models analyzed in this paper are the classical continuous and periodic review models with a mixture of backorders and lost sales and the base stock model for each of these models we provide sufficient conditions for the uniqueness of the optimal operating policy we also develop algorithms for solving these models and provide illustrative numerical examples

accelerated hazards regression model and its adequacy for censored survival data summary the accelerated hazards regression model is introduced to study the relationship between survival times and covariates through a scale change between hazard functions the model is also compared with several other popular classes of regression models for censored survival data in statistical literature test statistics are proposed and studied to assess the model s adequacy actual data from a randomized clinical trial of biodegradable carmustine polymer for treatment of brain cancer are analyzed to demonstrate the potential application of the regression model and the proposed test statistics

development and validation of a 3d rbf spectral model for coastal wave simulation abstract with the objective of simulating wave propagation in the nearshore zone for engineering scale applications a two dimensional 2dv model based on the euler zakharov equations 73 54 is extended to three dimensions 3d to maintain the flexibility of the approach with the goal of applying the model to irregularly shaped domains the horizontal plane is discretized with scattered nodes the horizontal derivatives are then estimated using the radial basis function finite difference rbf fd method while a spectral approach is used in the vertical dimension a sensitivity analysis examined the robustness of the rbf fd approach as a function of rbf parameters when estimating the derivatives of a representative function for a targeted stencil size between 20 and 30 nodes piecewise smooth ps polyharmonic spline phs functions are recommended avoiding the use of infinitely smooth is rbfs which are less appropriate for the desired applications because of their dependence on a shape parameter comparisons of simulation results to observations from two wave basin experiments show that nonlinear effects induced by complex bottom bathymetries are reproduced well by the model with the recommended rbf approach validating the use of this method for 3d simulations of wave propagation

two sample goodness of fit tests for additive risk models with censored observations summary the additive risk model assumes that the hazard function associated with a set of covariates is the sum of the baseline hazard function and the regression function of covariates we propose two different test procedures for checking the adequacy of two sample additive risk models for randomly censored observations one is based on the martingale residuals and the other on the difference between weighted estimators of the excess risk the test statistics are shown to be asymptotically normal under appropriate regularity conditions and consistent under any model misspecifications finally two real examples are provided along with results of a simulation study

semiparametric analysis of the additive risk model in contrast to the proportional hazards model the additive risk model specifies that the hazard function associated with a set of possibly time varying covariates is the sum of rather than the product of the baseline hazard function and the regression function of covariates this formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model and is more plausible than the latter for many applications in the present paper simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function

fast generation of 2 d node distributions for mesh free pde discretizations abstract many applications require that nodes be scattered locally quasi uniformly within 2 d regions or on curved surfaces in 3 d space while obeying some prescribed spatially varying density function this study focuses on creating variable density node layouts that are suitable for mesh free discretizations of pdes another application is dithering to simulate half tone images the method is an advancing front type scheme inspired by the physical process of dropping of variable sized grains into a bucket

checking the cox model with cumulative sums of martingale based residuals summary this paper presents a new class of graphical and numerical methods for checking the adequacy of the cox regression model the procedures are derived from cumulative sums of martingale based residuals over follow up time and or covariate values the distributions of these stochastic processes under the assumed model can be approximated by zero mean gaussian processes each observed process can then be compared both visually and analytically with a number of simulated realizations from the approximate null distribution these comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are special attention is given to checking the functional form of a covariate the form of the link function and the validity of the proportional hazards assumption an omnibus test consistent against any model misspecification is also studied the proposed techniques are illustrated with two real data sets

on the role of polynomials in rbf fd approximations iii behavior near domain boundaries abstract radial basis function generated finite difference rbf fd approximations generalize grid based regular finite differences to scattered node sets these become particularly effective when they are based on polyharmonic splines phs augmented with multi variate polynomials phs poly one key feature is that high orders of accuracy can be achieved without having to choose an optimal shape parameter and without having to deal with issues related to numerical ill conditioning the strengths of this approach were previously shown to be especially striking for approximations near domain boundaries where the stencils become highly one sided due to the polynomial runge phenomenon regular fd approximations of high accuracy will in such cases have very large weights well into the domain the inclusion of phs type rbfs in the process of generating weights makes it possible to avoid this adverse effect with that as motivation this study aims at gaining a better understanding of the behavior of phs poly generated rbf fd approximations near boundaries illustrating it in 1 d 2 d and 3 d

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

semiparametric analysis of general additive multiplicative hazard models for counting processes the additive multiplicative hazard model specifies that the hazard function for the counting process associated with a multidimensional covariate process z w t x t t takes the form of t z g 0 t w t 0 t h 0 t x t where 0 0 t 0 t t is a vector of unknown regression parameters g and h are known link functions and 0 is an unspecified baseline hazard function in this paper we develop a class of simple estimating functions for 0 which contains the partial likelihood score function in the special case of proportional hazards models the resulting estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions weak convergence of the aalen breslow type estimators for the cumulative baseline hazard function 0 t 0 t 0 u du is also established furthermore we construct adaptive estimators for 0 and o that achieve the semiparametric information bounds finally a real example is provided along with some simulation results

pseudomartingale estimating equations for modulated renewal process models summary we adapt martingale estimating equations based on gap time information to a gen eral intensity model for a single realization of a modulated renewal process the consistency and asymptotic normality of the estimators is proved under ergodicity conditions previous work has considered either parametric likelihood analysis or semiparametric multiplicative models using partial likelihood the framework is generally applicable to semiparametric and paramet ric models including additive and multiplicative specifications and periodic models it facilitates a semiparametric extension of a popular parametric earthquake model simulations and empir ical analyses of taiwanese earthquake sequences illustrate the methodology s practical utility

mean range based distribution free procedures to minimize overage and underage costs abstract we discuss several mean range based distribution free decision procedures to minimize several overage and underage cost functions for a general cost function we identify the most favorable distribution and the least favorable distribution associated with the random variable of interest and determine the upper and lower bounds for the cost function for the quadratic cost function we recommend the min max distribution free decision for the linear cost function we identify the range of potential optimal decisions and recommend a hybrid distribution free decision that has several desirable properties we provide several numerical examples to demonstrate the robustness of the proposed distribution free decisions

a pseudospectral fictitious point method for high order initial boundary value problems when pseudospectral approximations are used for space derivatives one often encounters spurious eigenvalues these can lead to severe time stepping difficulties for pdes this is especially the case for equations with high order derivatives in space requiring multiple conditions at one or both boundaries we note here that a very simple to implement fictitious point approach circumvents most of these difficulties the new approach is tested on the kuramoto sivashinsky equation and on a dispersive linear pde featuring a time space corner singularity

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

a least squares radial basis function partition of unity method for solving pdes recently collocation based radial basis function rbf partition of unity methods pums for solving partial differential equations have been formulated and investigated numerically and theoretically when combined with stable evaluation methods such as the rbf qr method high order convergence rates can be achieved and sustained under refinement however some numerical issues remain the method is sensitive to the node layout and condition numbers increase with the refinement level here we propose a modified formulation based on least squares approximation we show that the sensitivity to node layout is removed and that conditioning can be controlled through oversampling we derive theoretical error estimates both for the collocation and least squares rbf pums numerical experiments are performed for the poisson equation in two and three space dimensions for regular and irregular geometries the convergence experiments confirm the theoretical estimates and the least squares formulation is shown to

an insight into rbf fd approximations augmented with polynomials abstract radial basis function generated finite differences rbf fd based on the combination of polyharmonic splines phs with high degree polynomials have recently emerged as a powerful and robust numerical approach for the local interpolation and derivative approximation of functions over scattered node layouts among the key features i high orders of accuracy can be achieved without the need of selecting a shape parameter or the issues related to numerical ill conditioning and ii the harmful edge effects associated to the use of high order polynomials better known as runge s phenomenon can be overcome by simply increasing the stencil size for a fixed polynomial degree the present study complements our previous results providing an analytical insight into rbf fd approximations augmented with polynomials it is based on a closed form expression for the interpolant which reveals the mechanisms underlying these features including the role of polynomials and rbfs in the interpolant the approximation error and the behavior of the cardinal functions near boundaries numerical examples are included for illustration

time space domain mesh free finite difference based on least squares for 2d acoustic wave modeling abstractfinite difference fd methods approximate derivatives through a weighted summation of function values from neighboring nodes traditionally these neighboring nodes are assumed to be distributed regularly such as in square or rectangular lattices to improve geometric flexibility one option is to develop fd in a mesh free discretization in which scattered nodes can be placed suitably with respect to irregular boundaries or arbitrarily shaped anomalies without coordinate transformation or forming any triangles or tetrahedra etc these mesh free fds have had successful applications especially in computational geoscience however they are all space domain fd schemes in which fd coefficients are derived by approximating spatial derivatives individually in the space domain for acoustic wave modeling it has been proven that space domain fd methods normally have higher dispersion error than time space domain fd methods which determine fd coefficients by approximating the time space domain disp

on the role of polynomials in rbf fd approximations radial basis function generated finite difference rbf fd approximations generalize classical grid based finite differences fd from lattice based to scattered node layouts this greatly increases the geometric flexibility of the discretizations and makes it easier to carry out local refinement in critical areas many different types of radial functions have been considered in this rbf fd context in this study we find that i polyharmonic splines phs in conjunction with supplementary polynomials provide a very simple way to defeat stagnation also known as saturation error and ii give particularly good accuracy for the tasks of interpolation and derivative approximations without the hassle of determining a shape parameter in follow up studies we will focus on how to best use these hybrid rbf polynomial bases for fd approximations in the contexts of solving elliptic and hyperbolic type pdes

two algorithms for fast 2d node generation application to rbf meshless discretization of diffusion problems and image halftoning abstract mesh generation techniques for traditional mesh based numerical approaches such as fem and fvm have now reached a good degree of maturity there is no such an acknowledged background when dealing with node generation techniques for meshless numerical approaches despite their theoretical simplicity and efficiency furthermore node generation can be put in connection with some well known image approximation techniques two node generation algorithms are here proposed and employed in the numerical solution of 2d steady state diffusion problems by means of a local radial basis function rbf meshless method finally such algorithms are also tested for grayscale image approximation through stippling

rbf loi augmenting radial basis functions rbfs with least orthogonal interpolation loi for solving pdes on surfaces abstract we present a new method for the solution of pdes on manifolds m r d of co dimension one using stable scale free radial basis function rbf interpolation our method involves augmenting polyharmonic spline phs rbfs with polynomials to generate rbf finite difference rbf fd formulas these polynomial basis elements are obtained using the recently developed least orthogonal interpolation technique loi on each rbf fd stencil to obtain local restrictions of polynomials in r 3 to stencils on m the resulting rbf loi method uses cartesian coordinates does not require any intrinsic coordinate systems or projections of points onto tangent planes and our tests illustrate robustness to stagnation errors we show that our method produces high orders of convergence for pdes on the sphere and torus and present some applications to reaction diffusion pdes motivated by biology

mesh free semi lagrangian methods for transport on a sphere using radial basis functions abstract we present three new semi lagrangian methods based on radial basis function rbf interpolation for numerically simulating transport on a sphere the methods are mesh free and are formulated entirely in cartesian coordinates thus avoiding any irregular clustering of nodes at artificial boundaries on the sphere and naturally bypassing any apparent artificial singularities associated with surface based coordinate systems for problems involving tracer transport in a given velocity field the semi lagrangian framework allows these new methods to avoid the use of any stabilization terms such as hyperviscosity during time integration thus reducing the number of parameters that have to be tuned the three new methods are based on interpolation using 1 global rbfs 2 local rbf stencils and 3 rbf partition of unity for the latter two of these methods we find that it is crucial to include some low degree spherical harmonics in the interpolants standard test cases consisting of solid body rotation and deformational flow are used to compare and contrast the methods in terms of their accuracy efficiency conservation properties and dissipation dispersion errors for global rbfs spectral spatial convergence is observed for smooth solutions on quasi uniform nodes while high order accuracy is observed for the local rbf stencil and partition of unity approaches

goodness of fit analysis for the cox regression model based on a class of parameter estimators abstract in this article we propose a class of estimation functions for the vector of regression parameters in the cox proportional hazards model with possibly time dependent covariates by incorporating the weight functions commonly used in weighted log rank tests into the partial likelihood score function the resulting estimators behave much like the conventional maximum partial likelihood estimator in that they are consistent and asymptotically normal when the cox model is inappropriate however the estimators with different weight functions generally converge to nonidentical constant vectors for example the magnitude of the parameter estimator using the kaplan meier survival estimator as the weight function will be stochastically larger than that of the maximum partial likelihood estimator if covariate effects diminish over time such facts motivate us to develop goodness of fit methods for the cox regression model by comparing parameter estimators with different weight functions under the assume

transport schemes in spherical geometries using spline based rbf fd with polynomials abstract this work presents a numerical algorithm for using radial basis function generated finite differences rbf fd to solve partial differential equations pdes on s 2 using polyharmonic splines with added polynomials defined in a 2d plane phs poly we introduce a novel method for calculating rbf fd phs poly differentiation weights on s 2 using first a householder reflection and then a projection onto the tangent plane the new phs poly rbf fd method is implemented on two standard test cases 1 solid body rotation on s 2 and 2 3d tracer transport within earth s atmosphere compared to existing methods including those in the rbf literature at similar resolutions this approach requires fewer degrees of freedom and is algorithmically much simpler a matlab code to implement the method is included in the appendix

the impact of stochastic lead time reduction on inventory cost under order crossover we use exponential lead times to demonstrate that reducing mean lead time has a secondary reduction of the variance due to order crossover the net effect is that of reducing the inventory cost and if the reduction in inventory cost overrides the investment in lead time reduction then the lead time reduction strategy would be tenable we define lead time reduction as the process of decreasing lead time at an increased cost to date decreasing lead times has been confined to deterministic instances we examine the case where lead times are exponential for when lead times are stochastic deliveries are subject to order crossover so that we must consider effective lead times rather than the actual lead times the result is that the variance of these lead times is less than the variance of the original replenishment lead times here we present a two stage procedure for reducing the mean and variance for exponentially distributed lead times we assume that the lead time is made of one or several components and is the time between when the need of a replenishment order is determined to the time of receipt

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

block pseudospectral methods for maxwell s equations ii two dimensional discontinuous coefficient case block pseudospectral bps methods are examined for maxwell s equations in two dimensional inhomogeneous media for the case of a rectangular strip with a straight line interface blocks may be coupled via fictitious points or a generalization of characteristic outflow conditions the bps methods generalize to curvilinear strips described by a change of variables such strips can conform to interfaces while overlapping with a high order free space grid to form a composite grid method numerical experiments on strips with dielectrics lossy materials perfect conductors and absorbing layers indicate that the two coupling methods are comparable and accurate with just 3 4 points per wavelength full composite examples are included to demonstrate high accuracy and geometric flexibility

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

a stabilized radial basis finite difference rbf fd method with hybrid kernels abstract recent developments have made it possible to overcome grid based limitations of finite difference fd methods by adopting the kernel based meshless framework using radial basis functions rbfs such an approach provides a meshless implementation and is referred to as the radial basis generated finite difference rbf fd method in this paper we propose a stabilized rbf fd approach with a hybrid kernel generated through a hybridization of the gaussian and cubic rbf this hybrid kernel was found to improve the condition of the system matrix consequently the linear system can be solved with direct solvers which leads to a significant reduction in the computational cost as compared to standard rbf fd methods coupled with present stable algorithms unlike other rbf fd approaches the eigenvalue spectra of differentiation matrices were found to be stable irrespective of irregularity and the size of the stencils as an application we solve the frequency domain acoustic wave equation in a 2d half space in order to suppress spurious reflections from truncated computational boundaries absorbing boundary conditions have been effectively implemented

on the role of polynomials in rbf fd approximations ii numerical solution of elliptic pdes rbf generated finite differences rbf fd have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of pdes we find in the present study that combining polyharmonic splines phs with multivariate polynomials offers an outstanding combination of simplicity accuracy and geometric flexibility when solving elliptic equations in irregular or regular regions in particular the drawbacks on accuracy and stability due to runge s phenomenon are overcome once the rbf stencils exceed a certain size due to an underlying minimization property test problems include the classical 2 d driven cavity and also a 3 d global electric circuit problem with the earth s irregular topography as its bottom boundary the results we find are fully consistent with previous results for data interpolation

an improved gregory like method for 1 d quadrature the quadrature formulas described by james gregory 1638 1675 improve the accuracy of the trapezoidal rule by adjusting the weights near the ends of the integration interval in contrast to the newton cotes formulas their weights are constant across the main part of the interval however for both of these approaches the polynomial runge phenomenon limits the orders of accuracy that are practical for the algorithm presented here this limitation is greatly reduced in particular quadrature formulas on equispaced 1 d node sets can be of high order tested here up through order 20 without featuring any negative weights

hyperviscosity based stabilization for radial basis function finite difference rbf fd discretizations of advection diffusion equations abstract we present a novel hyperviscosity formulation for stabilizing rbf fd discretizations of the advection diffusion equation the amount of hyperviscosity is determined quasi analytically for commonly used explicit implicit and implicit explicit imex time integrators by using a simple 1d semi discrete von neumann analysis the analysis is applied to an analytical model of spurious growth in rbf fd solutions that uses auxiliary differential operators mimicking the undesirable properties of rbf fd differentiation matrices the resulting hyperviscosity formulation is a generalization of existing ones in the literature but is free of any tuning parameters and can be computed efficiently to further improve robustness we introduce a simple new scaling law for polynomial augmented rbf fd that relates the degree of polyharmonic spline phs rbfs to the degree of the appended polynomial when used in a novel ghost node formulation in conjunction with the recently developed overlapped rbf fd method the resulting method is robust and free of stagnation errors we validate the high order convergence rates of our method on 2d and 3d test cases over a wide range of peclet numbers 1 1000 we then use our method to solve a 3d coupled problem motivated by models of platelet aggregation and coagulation again demonstrating high order convergence rates

enhancing finite differences with radial basis functions polynomials are used together with polyharmonic spline phs radial basis functions rbfs to create local rbf finite difference rbf fd weights on different node layouts for spatial discretizations that can be viewed as enhancements of the classical finite differences fd the presented method replicates the convergence properties of fd but for arbitrary node layouts it is tested on the 2d compressible navier stokes equations at low mach number relevant to atmospheric flows test cases are taken from the numerical weather prediction community and solved on bounded domains thus attention is given on how to handle boundaries with the rbf fd method as well as a novel implementation for hyperviscosity comparisons are done on cartesian hexagonal and quasi uniform node layouts consideration and guidelines are given on phs order polynomial degree and stencil size the main advantages of the present method are 1 capturing the basic physics of the problem surprisingly well even at very coarse resolutions 2 high order accuracy without the need of tuning a shape parameter and 3 the inclusion of polynomials eliminates stagnation saturation errors a matlab code is given to calculate the differentiation weights for this novel approach

testing goodness of fit for proportional hazards model with censored observations abstract a numerical omnibus test of fit for the two sample proportional hazards model is proposed for randomly censored observations the test is derived from cox s partial likelihood and does not need a dummy time dependent covariate or any partition of the time axis consistency of the test is established examples are provided for illustration

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

the stochastic eoq model with random sales price abstract the article deals with a stochastic economic order quantity eoq model over a finite time horizon where uniform demand over the replenishment period is price dependent the selling price is assumed to be a random variable that follows a probability density function as demand is probabilistic stock out situation may occur based on the partial backlogging and lost sale cases during stock out period the author develops the criterion for the optimal solution for the replenishment size such that the integrated expected profit is maximized moreover the article suggests a new function regarding price dependent demand finally numerical examples and its sensitivity analysis of key parameters are given to illustrate the proposed model

weighted least squares estimation for aalen s additive risk model abstract cox s proportional hazards model has so far been the most popular model for the regression analysis of censored survival data however the additive risk model of aalen can provide a useful and biologically more plausible alternative aalen s model stipulates that the conditional hazard function for a subject whose covariates are y y 1 yp has the form h t y y t where 1 p is an unknown vector of hazard functions this article discusses inference for based on a weighted least squares wls estimator of the vector of cumulative hazard functions the asymptotic distribution of the wls estimator is derived and used to obtain confidence intervals and bands for the cumulative hazard functions both a grouped data and a continuous data version of the estimator are examined an extensive simulation study is carried out the method is applied to grouped data on the incidence of cancer mortality among japanese atomic bomb survivors

fast high dimensional node generation with variable density abstract we present an algorithm for producing discrete distributions with a prescribed nearest neighbor distance function our approach is a combination of quasi monte carlo q mc methods and weighted riesz energy minimization the initial distribution is a stratified q mc sequence with some modifications a suitable energy functional on the configuration space is then minimized to ensure local regularity the resulting node sets are good candidates for building meshless solvers and interpolants as well as for other purposes where a point cloud with a controlled separation covering ratio is required applications of a three dimensional implementation of the algorithm in particular to atmospheric modeling are also given