a new method for adding a parameter to a family of distributions with application to the exponential and weibull families summary a new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two parameter extension of the exponential distribution which may serve as a competitor to such commonly used two parameter families of life distributions as the weibull gamma and lognormal distributions in addition the general method is applied to yield a new three parameter weibull distribution families expanded using the method introduced here have the property that the minimum of a geometric number of independent random variables with common distribution in the family has a distribution again in the family bivariate versions are also considered

elastic and sound orthonormal beams and localized fields in linear mediums i basic equations basic definitions and general relations for elastic and sound fields defined by a given set of orthonormal functions on a real manifold are presented the proposed mathematical formalism makes it possible to obtain families of orthonormal beams and localized fields in both isotropic and anisotropic linear elastic mediums as well as the similar sound fields in an ideal liquid all these fields are described as superpositions of plane waves whose intensities and phases are specified by a set of orthonormal scalar functions on a two or three dimensional manifold by way of illustration the fields defined by the spherical harmonics are considered

vector beams as the superposition of cylindrical partial waves in bianisotropic media the exact solutions for arbitrary electromagnetic beams in bianisotropic media are constructed the solutions are expressed using tensor fourier transform whose physical meaning is the superposition of partial waves we use cylindrical partial waves vector bessel beams and derive exact and paraxial solutions for cylindrically symmetric beams in isotropic bi isotropic and bianisotropic media the comparison of the spatial evolution of vector bessel gauss beams in different media is made

factorization of the dissipative wave equation and inverse scattering a decomposition of the solution of the dissipative wave equation into incoming and outgoing components across a smooth surface in a homogeneous region is presented the proof of the decomposition is given only for the plane surface this is then applied to the factorization of the dissipative wave equation into incoming and outgoing components in a planar stratified medium the ricatti integral differential equation for the reflection operator that relates the two components is obtained it is shown how the zeroth and second moments with respect to the transverse variable in a planar stratified medium of the reflection kernel can be used in the inverse problem to recover the velocity and dissipation coefficient from knowledge of the scattered field

multivariate elliptically contoured distributions for repeated measurements summary the multivariate power exponential distribution a member of the multivariate elliptically contoured family provides a useful generalization of the multivariate normal distribution for the modeling of repeated measurements both light and heavy tailed distributions are included the covariance matrix retains its interpretation so that it can easily be structured for serial dependence and several levels of variance components a crossover trial on insulin applied to rabbits with a series of repeated measurements within each period is analyzed by means of this distribution using autocorrelation and two levels of variance components

random effects cox models a poisson modelling approach summary we propose a poisson modelling approach to nested random effects cox proportional hazards models an important feature of this approach is that the principal results depend only on the first and second moments of the unobserved random effects the orthodox best linear unbiased predictor approach to random effects poisson modelling techniques enables us to justify appropriate consistency and optimality the explicit expressions for the random effects given by our approach facilitate incorporation of a relatively large number of random effects the use of the proposed methods is illustrated through the reanalysis of data from a large scale cohort study of particulate air pollution and mortality previously reported by pope et al 1995

inverse problems for nonabsorbing media with discontinuous material properties one dimensional electromagnetic and elastic inverse problems are formulated for media with discontinuous material properties in addition an impedence mismatch between source and medium is allowed the measured data for either problem is shown to generate a reflection kernel which is used in the solution of the inverse problem the solution algorithm itself is a time domain technique which is a special case of previously obtained results for absorbing media

the electromagnetic scattering problem in the time domain for a dissipative slab and a point source using invariant imbedding a vertical magnetic dipole source above an inhomogeneous slab is considered where the permittivity e e z and conductivity z vary with the depth z using the axial symmetry of the problem a hankel transform is introduced besides physical scattering kernels nonphysical scattering kernels are introduced and the direct and inverse transformed problem is solved by means of wave splitting in an invariant imbedding approach the imbedding equations for the nonphysical scattering kernels are simpler than the corresponding equations for the physical kernels and they are solved using existing techniques for the imbedding equations for normally incident plane waves the solution for the physical kernels is obtained by establishing relations between the two sets of kernels these relations are given by volterra equations of the second kind and thus are very easy to solve numerically some applications and extensions of the results derived in the paper are discussed

exact and operator rational approximate solutions of the helmholtz weyl composition equation in underwater acoustics the quadratic profile the application of phase space and path integral methods to both mathematical and computational direct and inverse wave propagation modeling at the level of the scalar one way helmholtz equation is briefly reviewed the role of operator symbols is stressed and their properties briefly discussed the construction of the operator symbol requires the exact or approximate solution of the helmholtz weyl composition equation in the weyl pseudodifferential operator calculus the exact symbols for several quadratic profiles are presented and briefly analyzed the symbols exactly corresponding to a family of operator rational approximations are also presented for the quadratic case these results are used to illustrate several points pertinent to wide angle propagation modeling and the refractive index profile reconstruction problem in underwater acoustics

on an approximation measure founded on the links between optimization and polynomial approximation theory in order to define a polynomial approximation theory linked to combinatorial optimization closer than the existing one we first formally define the notion of a combinatorial optimization problem and then based upon this notion we introduce a notion of equivalence among optimization problems this equivalence includes for example translation or affine transformation of the objective function or yet some aspects of equivalencies between maximization and minimization problems for example the equivalence between minimum vertex cover and maximum independent set next we adress the question of the adoption of an approximation ratio respecting the defined equivalence we prove that an approximation ratio defined as a two variable function cannot respect this equivalence we then adopt a three variable function as a new approximation ratio already used by a number of researchers which is coherent to the equivalence and under the choice of the variables the new ratio is introduced by an axiomatic approach finally using the new ratio we prove approximation results for a number of combinatorial problems

on some applications of the selective graph coloring problem in this paper we present the selective graph coloring problem a generalization of the standard graph coloring problem as well as several of its possible applications given a graph with a partition of its vertex set into several clusters we want to select one vertex per cluster such that the chromatic number of the subgraph induced by the selected vertices is minimum this problem appeared in the literature under different names for specific models and its complexity has recently been studied for different classes of graphs here we describe different models some already discussed in previous papers and some new ones in very different contexts under a unified framework based on this graph problem we point out similarities between these models offering a new approach to solve them and show some generic situations where the selective graph coloring problem may be used we focus on specific graph classes motivated by each model and we briefly discuss the complexity of the selective graph coloring problem in each one of these graph classes and point out interesting future research directions

wave splitting and the reflection operator for the wave equation in r3 the problem of wave splitting in a nonhomogeneous medium in r3 is considered previous results for wave splitting in a planar stratified medium can be generalized to a general nonhomogeneous medium with sufficiently smooth velocity the wave equation is factorized into an up and down going wave system using certain integral and integral differential operators the equation for the reflection operator which relates the up going wave to a down going wave is then obtained and certain properties of the reflection operator are deduced

an intrinsic tensor technique in minkowski space with applications to boundary value problems this article describes an intrinsic tensor technique for solving boundary value problems in electrodynamics of moving media which entails considerable notational simplification and calculational advantages on the basis of generalized impedance and characteristic matrix methods the reflection and transmission operators of a multilayer structure consisting of anisotropic media uniformly moving with different velocities are found a general solution to the problem of reflection and transmission at the interface between two moving isotropic media is obtained and explicit expressions for doppler shifts snell s laws critical and brewster angles reflection and transmission coefficients and the radiation pressure force are found the material tensor of a uniformly moving linear medium is expressed through its reflection and transmission operators

modelling irregularly sampled profiles of non negative dog triglyceride responses under different distributional assumptions general methodology for modelling series of non negative data observed at unequally spaced times is developed the parameterization enables both the importance of the serial association as well the order of this dependence to be expressed an example is given where the effects of three fibre based diets on dog triglyceride profiles are analysed and compared many different types of models based on common distributions such as the normal exponential gamma weibull and log normal observations are presented comparison of possibly non nested models fitted on the same data set is made using the akaike criterion

p k coloring problems in line graphs the p k coloring problems generalize the usual coloring problem by replacing stable sets by cliques and stable sets complexities of some variations of p k coloring problems split coloring and cocoloring are studied in line graphs polynomial algorithms or proofs of np completeness are given according to the complexity status we show that the most general p k coloring problems are more difficult than the cocoloring and the split coloring problems while there is no such relation between the last two problems we also give complexity results for the problem of finding a maximum p k colorable subgraph in line graphs finally upper bounds on the optimal values are derived in general graphs by sequential algorithms based on welsh powell and matula orderings

on the green functions technique and phase velocity approximation of axially symmetric fields in stratified media in this paper a numerical method is developed to solve a one dimensional inverse scattering problem associated with a pair of two coupled partial differential equations these equations are for the green functions that can be used for the optimization of electromagnetic energy within selected regions of a medium in which the propagation is taking place the method is based upon constructing the nth degree interpolation polynomial to approximate the green functions and the phase velocity function using legendre gauss lobatto collocation points an example is given to demonstrate the accuracy of the developed method

on an instance of the inverse shortest paths problem the inverse shortest paths problem in a graph is considered that is the problem of recovering the arc costs given some information about the shortest paths in the graph the problem is first motivated by some practical examples arising from applications an algorithm based on the goldfarb idnani method for convex quadratic programming is then proposed and analyzed for one of the instances of the problem preliminary numerical results are reported

signal restoration after transmission through an advective and diffusive medium this paper considers an inverse problem associated with mass transport in a pipe it illustrates how wave splitting techniques can be used for an inverse problem associated with one dimensional mass transport processes this is done by using a generalization of fick s law which introduces a relaxation parameter into the problem so converting the parabolic partial differential equation by a singular perturbation into a hyperbolic one this generalized law by ensuring finite mass flux propagation speeds enables a stable equation to be used to reconstruct the interior boundary condition so providing a regularized solution to the inverse problem theoretical results for the solution of the inverse problem are also developed

factorization of a dissipative wave equation and the green functions technique for axially symmetric fields in a stratified slab the time domain scattering problem for axially symmetric fields and a dissipative stratified slab is considered explicit representations are derived for the wave splitting operators that factorize the dissipative hankel transformed wave equation the green functions approach associated with this splitting is developed partial differential equations pdes for the green functions are derived and used to derive the imbedding equations for the reflection and transmission kernels numerical results for the internal fields are given in the direct problem and the phase velocity is reconstructed in the inverse problem

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

statistical analysis of repeated events forming renewal processes for each of several individuals a sequence of repeated events forming a renewal process is observed up to some censoring time the object is to estimate the average interevent time over the population of individuals as well as the variation of interevent times within and between individuals medical motivation comes from gastroenterology and concerns the occurrence of certain cyclic movements in the small bowel during the fasting state two statistical models are considered one is the standard variance component model adapted to censored data and the other is a recent intensity based model with a random proportionality factor representing interindividual variation these models are applied to the motility data and their advantages are discussed the intensity based model allows simple empirical bayes estimation of the expected interevent times for an individual in the presence of censoring

a tutorial on the use of graph coloring for some problems in robotics we study the problem where a robot has to pick up items of different sizes which are stored along a corridor a natural requirement is that the items have to be collected in decreasing order of their sizes we deal with various systems according to the location of the entry exit station where the robot unloads the collected items after each trip along the corridor the links of these systems with generalized coloring problems and other applications such that train shunting and pallet loading problems are discussed and related results are obtained we conclude with several open questions on the topic

the graph coloring problem a neuronal network approach solution of an optimization problem with linear constraints through the continuous hopfield network chn is based on an energy or lyapunov function that decreases as the system evolves until a local minimum value is attained this approach is extended in to optimization problems with quadratic constraints as a particular case the graph coloring problem gcp is analyzed the mapping procedure and an appropriate parameter setting procedure are detailed to test the theoretical results some computational experiments solving the gcp are shown

on the differential approximation of min set cover we present in this paper differential approximation results for min set cover and min weighted set cover we first show that the differential approximation ratio of the natural greedy algorithm for min set cover is bounded below by 1 365 and above by 4 1 where is the maximum set cardinality in the min set cover instance next we study another approximation algorithm for min set cover that computes 2 optimal solutions i e solutions that cannot be improved by removing two sets belonging to them and adding another set not belonging to them we prove that the differential approximation ratio of this second algorithm is bounded below by 2 1 and that this bound is tight finally we study an approximation algorithm for min weighted set cover and provide a tight lower bound of 1 our results identically hold for max hypergraph independent set in both the standard and the differential approximation paradigms

approximation algorithms for the maximum hamiltonian path problem with specified endpoint s abstract this paper deals with the problem of constructing hamiltonian paths of optimal weight called hpps t if the two endpoints are specified hpps if only one endpoint is specified we show that hpps t is 1 2 differential approximable and hpps is 2 3 differential approximable moreover we observe that these problems cannot be differential approximable better than 741 742 based upon these results we obtain new bounds for standard ratio a 1 2 standard approximation for m ax hpps t and a 2 3 for m ax hpps which can be improved to 2 3 for m ax hpps t a 2a all the edge weights are within an interval a 2a to 5 6 for m ax hpps a 2a and to 2 3 for m in hpps t a 2a to 3 4 for m in hpps a 2a

factorization of the wave equation in higher dimensions the factorization of the wave equation into a coupled system involving up and down going wave components is obtained for the case where the field quantities are multivariate functions of spatial variables but the velocity c is a function of the z variable only the form of the reflection operator is derived and the quadratic differential integral equation satisfied by its kernel is obtained

reductions completeness and the hardness of approximability in computability and in complexity theory reductions are widely used for mapping sets into sets in order to prove undecidability or hardness results in the study of the approximate solvability of hard discrete optimization problems suitable kinds of reductions called approximation preserving reductions can also be used to transfer from one problem to another either positive results solution techniques or negative results non approximability results in this paper various kinds of approximation preserving reductions are surveyed and their properties discussed the role of completeness under approximation preserving reductions is also analyzed and its relationship with hardness of approximability is explained

mixtures of multivariate power exponential distributions summary an expanded family of mixtures of multivariate power exponential distributions is introduced while fitting heavy tails and skewness have received much attention in the model based clustering literature recently we investigate the use of a distribution that can deal with both varying tail weight and peakedness of data a family of parsimonious models is proposed using an eigen decomposition of the scale matrix a generalized expectation maximization algorithm is presented that combines convex optimization via a minorization maximization approach and optimization based on accelerated line search algorithms on the stiefel manifold lastly the utility of this family of models is illustrated using both toy and benchmark data

a general family of distributions for longitudinal dependence with special reference to event histories event histories play an increasingly important role in medical studies examples include times between recurrences of tumours as with bladder cancer and between repeated infections as with chronic granulotomous disease a general method for generating new distributions is proposed by introducing an intensity function into a density this procedure yields as special cases several distributions already proposed in the literature the families of distributions based on the pareto distribution are of particular interest for event history analysis because of their relationship to the laplace transform of a gamma distribution they can yield multivariate distributions with longitudinal serial dependence by a procedure similar to updating in the kalman filter and with uniform dependence in a similar way to copulas for longitudinal dependence several such updating procedures are proposed

inverse chromatic number problems in interval and permutation graphs abstract given a graph g and a positive integer k the inverse chromatic number problem consists in modifying the graph as little as possible so that it admits a chromatic number not greater than k in this paper we focus on the inverse chromatic number problem for certain classes of graphs first we discuss diverse possible versions and then focus on two application frameworks which motivate this problem in interval and permutation graphs the inverse booking problem and the inverse track assignment problem the inverse booking problem is closely related to some previously known scheduling problems we propose new hardness results and polynomial cases the inverse track assignment problem motivates our study of the inverse chromatic number problem in permutation graphs we show how to solve in polynomial time a generalization of the problem with a bounded number of colors

the electromagnetic inverse problem in the time domain for a dissipative slab and a point source using invariant imbedding reconstruction of the permittivity and conductivity abstract he s and s strom the electromagnetic inverse problem in the time domain for a dissipative slab and a point source using invariant imbedding reconstruction of the permittivity and conductivity journal of computational and applied mathematics 42 1992 137 155 we consider the electromagnetic inverse problem for a point source above an inhomogeneous dissipative slab of permittivity z and conductivity z where z is the depth two inversion algorithms based on the invariant imbedding equations derived in previous work are used to reconstruct both the permittivity and the conductivity both algorithms use two sided reflection data and one of them also uses transmission data results are presented for clean and noisy data

nonlinear modeling of serial immunologic data a case study abstract this article concerns the analysis of serial immunologic data from a clinical trial of immunosuppressive chemotherapy in the treatment of multiple sclerosis the goal of the analysis is to relate levels of drug dose to levels of an immunologic outcome variable i propose a new nonlinear model for the analysis of such data the model assumes that the mean function is the solution of an ordinary differential equation in time parameters of which are related to the dose via a regression function the defining differential equation is that which gives rise to the generalized logistic function a flexible form that includes a number of popular growth models we fit the model which accounts for random effects and time series autocorrelation by maximum likelihood results suggest strong treatment effects in two active drug groups and a small but significant effect in a placebo group these findings agree well with previously reported analyses of clinical outcomes from the trial an empirical comparis

spatial evolution of cylindrical beams in complex media the spatial evolution of vector electromagnetic fields in bianisotropic cylindrically symmetric structures is studied we introduce evolution operators characteristic matrices impedance tensors reflection and transmission operators of cylindrical beams which are convenient for describing waves in layered media we predict the existence of fractional bessel beams with integer topological charge and cylindrically symmetric beams which can be presented as the product of the bessel function and the exponent we investigate energy and polarization characteristics of such beams

reflection and transmission of weakly inhomogeneous anisotropic and bianisotropic layers calculated by perturbation method with the use of perturbation theory the zero and higher order approximations are obtained for characteristic matrices reflection and transmission operators scalar reflectance and transmittance of monochromatic electromagnetic waves impinging on a transparent weakly inhomogeneous stratified bianisotropic medium the proposed procedure of perturbation series formation enables finding the corrections to the reflection and transmission factors in closed form for specified coordinate dependencies for the material tensors of the bianisotropic layers the general expressions obtained are applied to calculate the first order corrections for normal incident light on i a twisted uniaxial slab ii an isotropic medium with arbitrary inhomogeneity profile and iii a one dimensional photonic crystal with arbitrary number of layers exact and approximate solutions of the wave equations are numerically compared

maxwell s square roots from the metric tensors of wave surfaces and branches of solutions of the photon and phonon wave equations for the wave equations of optics and acoustics of isotropic media the infinite families of three dimensional plane wave cauchy operators are found by a direct tensor method these families form involutive lie groups their generators n can be found by taking square roots from the unit tensors of the wavefront subspaces with outer normal n in optics the basic structural elements of n are complex involutive operators reflection isometries described by pairs of complex vectors s and c which satisfy the metric condition and also by a pair of projective operators of the two dimensional space of a plane orthogonal to n in the acoustics of isotropic media in view of the inequality of the longitudinal and transverse wave velocities the generators n are represented as a linear combination of an involutive operator and a diad it is shown that the projection of the average energy flux of the wave is conserved in the general case the families of vectors being a part of n are indicated for these families the global operators acting on initial field vectors give states described by the right hand and left hand elliptical helices the wave normal n characterizes the direction of the angular momentum of the field and for the case turns out to be equivalent to the darboux vector known in geometry

efficient approximation of min set cover by moderately exponential algorithms we study the approximation of min set cover combining ideas and results from polynomial approximation and from exact computation with non trivial worst case complexity upper bounds for np hard problems we design approximation algorithms for min set cover achieving ratios that cannot be achieved in polynomial time unless problems in np could be solved by slightly super polynomial algorithms with worst case complexity much lower though super polynomial than those of an exact computation

double exponential families and their use in generalized linear regression abstract in one parameter exponential families such as the binomial and poisson the variance is a function of the mean double exponential families allow the introduction of a second parameter that controls variance independently of the mean double families are used as constituent distributions in generalized linear regressions in which both means and variances are allowed to depend on observed covariates the theory is applied to two examples a logistic regression and a large two way contingency table in such cases the binomial model of variance is often untrustworthy for example because genuine random sampling was infeasible the subjects may have been obtained in clumps so that the statistician should really be using smaller sample sizes clumped sampling is just one of many possible causes of overdispersion a habitual source of concern to users of binomial and poisson models this article concerns a class of regression families that allow the statistician to model overdispersion while carrying

on convexity of error rates in digital communications convexity properties of error rates of a class of decoders including the maximum likelihood min distance one as a special case are studied for arbitrary constellations bit mapping and coding earlier results obtained for the additive white gaussian noise channel are extended to a wide class of noise densities including unimodal and spherically invariant noise under these broad conditions symbol and bit error rates are shown to be convex functions of the signal to noise ratio snr in the high snr regime with an explicitly determined threshold which depends only on the constellation dimensionality and minimum distance thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way it is the decreasing nature of the noise power density around the decision region boundaries that ensures the convexity of symbol error rates in the general case the known high low snr bounds of the convexity concavity regions are tightened and no further improvement is shown to be possible in general the high snr bound fits closely into the channel coding theorem all codes including capacity achieving ones whose decision regions include the hardened noise spheres from the noise sphere hardening argument in the channel coding theorem satisfy this high snr requirement and thus has convex error rates in both snr and noise power we conjecture that all capacity achieving codes have convex error rates convexity properties in signal amplitude and noise power are also investigated some applications of the results are discussed in particular it is shown that fading is convexity preserving and is never good in low dimensions under spherically invariant noise which may also include any linear diversity combining

single machine scheduling of unit time jobs with earliness and tardiness penalties the problem of determining a schedule of jobs with unit time lengths on a single machine that minimizes the total weighted earliness and tardiness penalties with respect to arbitrary rational due dates is formulated as an integer programming problem we show that if the penalties meet a certain criterion called the dominance condition then there exists an extremal optimal solution to the lp relaxation that is integral leading to a polynomial time solution procedure the general weighted symmetric penalty structure is one cost structure that satisfies the dominance condition we point out other commonly found penalty structures that also fall into this category

analysis of the green s function approach to one dimensional inverse problems i one parameter reconstruction an analysis of a green s function approach based on wave splitting to the one dimensional electromagnetic inverse problem is given the green s functions refer to split components of the fundamental solution the linear system of equations for the green s functions is shown to be well posed for the inverse problem and stability estimates theorems on existence uniqueness local correctness and convergence are given

differential approximation results for the traveling salesman problem with distances 1 and 2 abstract we prove that both minimum and maximum traveling salesman problems on complete graphs with edge distances 1 and 2 denoted by min tsp12 and max tsp12 respectively are approximable within 3 4 based upon this result we improve the standard approximation ratio known for maximum traveling salesman with distances 1 and 2 from 3 4 to 7 8 finally we prove that for any 0 it is np hard to approximate both problems better than within 741 742 the same results hold when dealing with a generalization of min and max tsp12 where instead of 1 and 2 edges are valued by a and b

the reflection of electromagnetic waves from stratified anisotropic media a direct approach to the investigation of the reflection of electromagnetic waves from a plane interface separating a vacuum half space and a stratified anisotropic layer is presented the formulation involves the generation of a riccati differential equation for a certain 2 2 reflection matrix the approach is already well established for scalar problems but its implementation in cases which allow mode conversion is believed to be new the reflection matrix concerned is unitary when the anisotropic layer is nondissipative and an efficient numerical method to solve the equation is outlined sample results are presented to illustrate the theory

operator matrices for describing guiding propagation in circular bianisotropic fibres operator techniques are developed for describing electromagnetic waves in circular waveguides on the basis of which an evolution operator characteristic matrix and impedance tensors of a homogeneous circular bianisotropic layer are determined we investigate solutions of maxwell s equations depending on the dielectric permittivity and magnetic permeability tensors and the gyration pseudotensors we show that the solutions are expressed in terms of the bessel functions with a matrix argument for the media isotropic in the fibre cross section the method proposed is applied for an analytical derivation of dispersion equations of isotropic and bianisotropic waveguides

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

a compact green function approach to the time domain direct and inverse problems for a stratified dissipative slab a new type of green function approach is introduced for time domain scattering for a stratified dissipative slab the new green functions are defined as mappings from the transmitted field to the split fields i e the right moving and left moving fields at any point within the stratified slab unlike the usual green functions the present green functions have compact support in the time variable the new technique is illustrated for the case of normally incident electromagnetic waves on a stratified slab where the permittivity permeability and conductivity vary with the depth the linear and homogeneous partial differential equations pdes for these compact green functions are derived the pdes together with the initial and boundary conditions are well suited for a numerical treatment numerical results for the compact green functions are presented in the direct problem while in the inverse problem the permittivity and conductivity or the permeability and conductivity are reconstructed simult

exponential dispersion models on etudie les proprietes generales de la classe des modeles de dispersion exponentiels qui est la generalisation multivariable des modeles de distribution d erreur de nelder et wedderburn 1972

on the complexity of the selective graph coloring problem in some special classes of graphs in this paper we consider the selective graph coloring problem given an integer k 1k 1 and a graph g v e g v e with a partition v1 vpv1 vp of vv it consists in deciding whether there exists a set v v in gg such that v vi 1 v vi 1 for all i 1 p i 1 p and such that the graph induced by v v is kk colorable we investigate the complexity status of this problem in various classes of graphs

routing and wavelength assignment by partition colouring the problem of routing and wavelength assignment in all optical networks may be solved by a combined approach involving the computation of alternative routes for the lightpaths followed by the solution of a partition colouring problem in a conflict graph a new tabu search heuristic is also proposed for the partition colouring problem which may be viewed as an extension of the graph colouring problem computational experiments are reported showing that the tabu search heuristic outperforms the best heuristic for partition colouring by approximately 20 in the average and illustrating that the new approach for the problem of routing and wavelength assignment is more robust than a well established heuristic for this problem

linear growth curve analysis based on exponential dispersion models the paper introduces a class of linear growth curve models based on combinations of exponential dispersion models the models have three components namely a latent markov growth process with stationary and independent increments a noise component and a component describing variation between subjects the models allow a wide range of continuous discrete and mixed distributions estimation for the models is based on an estimating equation derived from an em like algorithm combined with kalman smoothing

the double travelling salesman problem with multiple stacks formulation and heuristic solution approaches this paper introduces the double travelling salesman problem with multiple stacks and presents four different metaheuristic approaches to its solution the double tsp with multiple stacks is concerned with determining the shortest route performing pickups and deliveries in two separated networks one for pickups and one for deliveries using only one container repacking is not allowed instead each item can be positioned in one of several rows in the container such that each row can be considered a lifo last in first out stack but no mutual constraints exist between the rows two different neighbourhood structures are developed for the problem and used with each of three local search metaheuristics additionally some simpler removal and reinsertion operators are used in a large neighbourhood search framework finally some computational results are given along with lower bounds on the objective value

generalized norton simon models of tumour growth this paper considers the analysis of serial data on the growth of tumours in laboratory rodents i propose a model a generalization of the tumour growth model of norton and simon that leads to a rich family of growth and decay curves the model assumes that unperturbed growth follows the generalized logistic form it accommodates time varying treatment effects through an effective dose function i fit two such models to data on a human prostate tumour growing in nude mice and compare the fitted curves and dose functions with a non parametric curve and dose function estimated from a cubic spline model all three models account for both random animal effects and autocorrelation monte carlo results suggest that a maximum likelihood estimates of growth parameters are biased although not severely and b standard errors are conservative in small samples but become increasingly accurate in larger samples

the complexity of path coloring and call scheduling abstract modern high performance communication networks pose a number of challenging problems concerning the efficient allocation of resources to connection requests in all optical networks with wavelength division multiplexing connection requests must be assigned paths and colors wavelengths such that intersecting paths receive different colors and the goal is to minimize the number of colors used this path coloring problem is proved np hard for undirected and bidirected ring networks path coloring in undirected tree networks is shown to be equivalent to edge coloring of multigraphs which implies a polynomial time optimal algorithm for trees of constant degree as well as np hardness and an approximation algorithm with absolute approximation ratio 4 3 and asymptotic approximation ratio 1 1 for trees of arbitrary degree for bidirected trees path coloring is shown to be np hard even in the binary case a polynomial time optimal algorithm is given for path coloring in undirected or bidirected trees with n nodes under the assumption that the number of paths touching every single node of the tree is o log n 1 e call scheduling is the problem of assigning paths and starting times to calls in a network with bandwidth reservation such that the maximum completion time is minimized in the case of unit bandwidth requirements unit edge capacities and unit call durations call scheduling is equivalent to path coloring if either the bandwidth requirements or the call durations can be arbitrary call scheduling is shown np hard for virtually every network topology

the robust coloring problem abstract some problems can be modeled as graph coloring ones for which the criterion of minimizing the number of used colors is replaced by another criterion maintaining the number of colors as a constraint some examples of these problem types are introduced it would be the case for instance of the problem of scheduling the courses at a university with a fixed number of time slots the colors and with the objective of minimizing the probability to include an edge to the graph with its endpoints equally colored based on this example the new coloring problem introduced in this paper will be denoted as the robust coloring problem rcp for short it is proved that this optimization problem is np hard and consequently only small size problems could be solved with exact algorithms based on mathematical programming models otherwise for large size problems some heuristics are needed in order to obtain appropriate solutions a genetic algorithm which solves the rcp is outlined

propagation of classical waves in nonperiodic media scaling properties of an optical cantor filter wave propagation through a subclass of deterministic nonperiodic media namely fractal cantor multilayer structures are investigated theoretically as well as experimentally transmission spectra of cantor structures are found to have two distinctive properties scalability and sequential splitting closely related to the geometrical peculiarities of the multilayers a systematic correlation between structural self similarity and spectral regularities of cantor multilayers is established

families of multivariate distributions abstract for many years there has been an interest in families of bivariate distributions with marginals as parameters genest and mackay 1986a b showed that several such families that appear in the literature can be derived by a unified method a similar conclusion is obtained in this article through the use of mixture models these models might be regarded as multivariate proportional hazards models with random constants of proportionality the mixture models are useful for two purposes first they make some properties of the derived distributions more transparent the positive dependency property of association is sometimes exposed and a method for simulation of data from the distributions is suggested but the mixture models also allow derivation of several new families of bivariate distributions with marginals as parameters and they indicate obvious multivariate extensions some of the new families of bivariate distributions given in this article extend known distributions by adding a parameter

one processor scheduling with symmetric earliness and tardiness penalties we consider one processor scheduling problems having the following form tasks t1 t2 tn are given with each ti having a specified length li and a preferred starting time ai or equivalently a preferred completion time bi the tasks are to be scheduled nonpreemptively i e a task cannot be split on a single processor to begin as close to their preferred starting times as possible we examine two different cost measures for such schedules the sum of the absolute discrepancies from the preferred starting times and the maximum such discrepancy for the first of these we show that the problem of finding minimum cost schedules is np complete however we give an efficient algorithm that finds minimum cost schedules whenever the tasks either all have the same length or are required to be executed in a given fixed sequence for the second cost measure we give an efficient algorithm that finds minimum cost schedules in general with no constraints on the ordering or lengths of the tasks

the np completeness of edge coloring we show that it is np complete to determine the chromatic index of an arbitrary graph the problem remains np complete even for cubic graphs

refractive index tensors in connection with problems of photon scattering in terms of the refractive index tensors n the operator solving a problem of reflection and refraction of electromagnetic waves on plane boundary between isotropic dielectrics is given separately the behaviour of beltrami fields on the boundary is considered they are described by infinite sets of branches of the traceless indefinite tensors n which are generators of involutive maxwell groups for photon antiphoton meeting pairs the connections of the traceless tensors n with fresnel reflection and transmission coefficients stokes relations beltrami fields and reflectional coxeter s groups are established

a better differential approximation ratio for symmetric tsp in this paper we study the approximability properties of symmetric tsp under an approximation measure called the differential ratio more precisely we improve up to 3 email protected for any e 0 the best differential ratio of 2 3 known so far given in hassin and khuller r hassin s khuller z approximations j algorithms 41 2 2001 429 442

differential approximation algorithms for some combinatorial optimization problems we use a new approximation measure the differential approximation ratio to derive polynomial time approximation algorithms for minimum set covering for both weighted and unweighted cases minimum graph coloring and bin packing we also propose differential approximation ratio preserving reductions linking minimum coloring minimum vertex covering by cliques minimum edge covering by cliques and minimum edge covering of a bipartite graph by complete bipartite graphs

frequency domain wave splitting techniques for plane stratified bianisotropic media a plane harmonic electromagnetic wave obliquely incident on a plane stratified bianisotropic medium with multiple discontinuities in the parameters is considered a covariant wave splitting approach based on the use of the formula of integration by parts for multiplicative integrals and the impedance concept is presented it encompasses various types of decomposition of the total internal field into two waves propagating in opposite directions including the physical and vacuum wave splittings treated earlier in the literature and provides a convenient means for both analytical investigation and numerical calculation of evolution operators green s functions and impedance tensors of split waves as well as characteristic matrices and reflection and transmission tensors of stratified bianisotropic media the potentialities of the approach are illustrated by its application to the problems of reflection transmission and guided propagation and by generalizing the method of multiple reflections to the case of stratified bianisotropic media

wave propagation through cantor set media chaos scaling and fractal structures propagation of waves through cantor set media is investigated by renormalization group analysis for specific values of wave numbers transmission coefficients are shown to be governed by the logistic map and in the chaotic region they show sensitive dependence on small changes in parameters of the system such as the index of refraction for other values of wave numbers our numerical results suggest that light transmits completely or reflects completely by the cantor set media text c ensuremath infty it is also shown that transmission coefficients exhibit a local scaling behavior near complete transmission if the complete transmission is achieved at a wave number ensuremath kappa ensuremath kappa ensuremath ast with a rational ensuremath kappa ensuremath ast ensuremath pi the scaling function is obtained analytically by using the euler totient function and the local scaling behavior is confirmed numerically

a mixture model with detection limits for regression analyses of antibody response to vaccine antibody concentration values as determined by quantitative assays often are left censored due to detection limits or limits established for purpose of specificity standard analyses which assume the data arise from a single lognormal response distribution may not be appropriate when more observations are censored than would be expected under such a model interference from maternal antibodies due to vaccination at an early age for example could result in a high proportion of nonresponders to vaccine a mixture model consisting of a censored lognormal distribution and a point distribution located below the detection limit is proposed for such situations antibody data from a study of measles vaccine are used to illustrate the utility of this approach and the interpretation of the model parameters

factorization of the wave equation in a nonplanar stratified medium the wave equation is considered for a stratified medium where the stratifications are in the form of a family of nested c2 surfaces along which the velocity c is constant c varying only in a direction normal to the surfaces on each surface c is constant the solution u of the wave equation is decomposed into an outgoing wave component u and an incoming wave component u the associated outgoing and incoming wave conditions are expressed in terms of integral operators kernels being time dependent single and double layer potential type terms operating on u and the normal derivative u n on each surface using the decomposition the scalar wave equation is split into a vector system involving the components u and u the vector system decoupling in a region where c is constant such a splitting is useful for the inverse problem where a reflection operator relating the outgoing wave to an incoming wave can be defined and this in turn can be used to determine c

a review of some extensions to generalized linear models although generalized linear models are reasonably well known they are not as widely used in medical statistics as might be appropriate with the exception of logistic log linear and some survival models at the same time the generalized linear modelling methodology is decidedly outdated in that more powerful methods involving wider classes of distributions non linear regression censoring and dependence among responses are required limitations of the generalized linear modelling approach include the need for the iterated weighted least squares iwls procedure for estimation and deviances for inferences these restrict the class of models that can be used and do not allow direct comparisons among models from different distributions powerful non linear optimization routines are now available and comparisons can more fruitfully be made using the complete likelihood function the link function is an artefact necessary for iwls to function with linear models but that disappears once the class is extended to truly non linear models restricting comparisons of responses under different treatments to differences in means can be extremely misleading if the shape of the distribution is changing this may involve changes in dispersion or of other shape related parameters such as the skewness in a stable distribution with the treatments or covariates any exact likelihood function defined as the probability of the observed data takes into account the fact that all observable data are interval censored thus directly encompassing the various types of censoring possible with duration type data in most situations this can now be as easily used as the traditional approximate likelihood based on densities finally methods are required for incorporating dependencies among responses in models including conditioning on previous history and on random effects one important procedure for constructing such likelihoods is based on kalman filtering

integer isotone optimization consider the following integer isotone optimization problem given an n vector x find an n vector y with integer components so as to minimize max w j x j y j 1 leq j leq n subject to y 1 leq y 2 leq cdots leq y n where each weight w j 0 in this article the dual of this problem is defined a strong duality theorem is established and the set of all optimal solutions is shown to be all monotonic integer vectors lying in a vector interval in addition algorithms are obtained for computation of optimal solutions having the worst case time complexity o n 2 when w j are arbitrary and o n when w j 1 for all j the problem considered is of isotonic regression type and has practical applications for example to estimation and curve fitting it is also of independent mathematical interest the problem and the results can be easily extended to a partially ordered set

mixed poisson regression models with covariate dependent rates this paper studies a class of poisson mixture models that includes covariates in rates this model contains poisson regression and independent poisson mixtures as special cases estimation methods based on the em and quasi newton algorithms properties of these estimates a model selection procedure residual analysis and goodness of fit test are discussed a monte carlo study investigates implementation and model choice issues this methodology is used to analyze seizure frequency and ames salmonella assay data

topological interference management with transmitter cooperation interference networks with no channel state information at the transmitter except for the knowledge of the connectivity graph have been recently studied under the topological interference management framework in this paper we consider a similar problem with topological knowledge but in a distributed broadcast channel setting i e a network where transmitter cooperation is enabled we show that the topological information can also be exploited in this case to strictly improve the degrees of freedom dof as long as the network is not fully connected which is a reasonable assumption in practice achievability schemes from graph theoretic and interference alignment perspectives are proposed together with outer bounds built upon generator sequence the concept of compound channel settings and the relation to index coding we characterize the symmetric dof for the so called regular networks with constant number of interfering links and identify the sufficient and or necessary conditions for the arbitrary network topologies to achieve a certain amount of symmetric dof

generalized nonlinear models for pharmacokinetic data summary phase i trials to study the pharmacokinetic properties of a new drug generally involve a restricted number of healthy volunteers because of the nature of the group involved in such studies the appropriate distributional assumptions are not always obvious these model assumptions include the actual distribution but also the ways in which the dispersion of responses is allowed to vary over time and the fact that small concentrations of a substance are not easily detectable and hence are left censored we propose that a reasonably wide class of generalized nonlinear models allowing for left censoring be considered now that this is feasible with current computer power and sophisticated statistical packages these modelling strategies are applied to a phase i study of the drug flosequinan and its metabolite this drug was developed for the treatment of heart failure because the metabolite also exhibits an active pharmacologic effect study of both the parent drug and the metabolite is of interest

fresnel s reflection and transmission operators for stratified gyroanisotropic media for the general case of an inhomogeneous anisotropic and gyrotropic medium a differential tensor equation expressing the evolution of the tangential component of the field vectors of an electromagnetic wave is obtained a fundamental solution of this equation is given by a multiplicative integral a plane stratified system of anisotropic and gyrotropic layers is considered by means of the characteristic matrix of such a medium fresnel s reflection and transmission operators are derived these operators have wide utility because they describe exactly the interaction of light with any plane stratified gyroanisotropic structure the conservation of the normal component of the poynting vector in such a structure allows the authors to find a correlation between the operators of reflection and transmission the operator dispersion equation of the multilayer gyroanisotropic waveguide is presented all the calculations in this paper are based on the direct manipulation of tensors and their invariants eliminating the use of coordinate systems this facilitates solutions and provides results of great generality which are suitable for computer use

derivation and application of extended parabolic wave theories i the factorized helmholtz equation the reduced scalar helmholtz equation for a transversely inhomogeneous half space supplemented with an outgoing radiation condition and an appropriate boundary condition on the initial value plane defines a direct acoustic propagation model this elliptic formulation admits a factorization and is subsequently equivalent to a first order weyl pseudodifferential equation which is recognized as an extended parabolic propagation model perturbation treatments of the appropriate weyl composition equation result in a systematic development of approximate wave theories which extend the narrow angle weak inhomogeneity and weak gradient ordinary parabolic schrodinger approximation the analysis further provides for the formulation and exact solution of a multidimensional nonlinear inverse problem appropriate for ocean acoustic and seismic studies the wave theories foreshadow computational algorithms the inclusion of range dependent effects and the extension to 1 the vector formulation appropriate for elas

differential approximation for optimal satisfiability and related problems abstract we study the differential approximability of several optimization satisfiability problems we prove that unless co rp np min sat is not differential 1 m 1 e approximable for any e 0 where m is the number of clauses we also prove that any differential approximation algorithm for max minimal vertex cover can be transformed into a differential approximation algorithm for min k sat achieving the same differential performance ratio this leads us to study the differential approximability of max minimal vertex cover and min independent dominating set both of them are equivalent for the differential approximation for these problems we prove a strong inapproximability result informally unless p np any approximation algorithm has worst case approximation ratio equal to 0

direct and inverse scattering in the time domain via invariant imbedding equations this paper examines the implementation of a new approach to direct and inverse scattering problems in the time domain which is applied here to the case of a one dimensional lossless medium the method is based on an integro differential equation which is satisfied by the reflection kernel and has been derived elsewhere using invariant imbedding techniques an example of an exact solution to this equation is given numerical schemes for solving the direct and inverse problems are derived by discretizing this equation the behavior of the resulting algorithms is then tested on several examples the results suggest that the inversion method is stable in the presence of additive noise

response surfaces for overdispersion in the study of the conditions for fish eggs hatching summary response surface methodology originally developed for determining optimal conditions in industrial experiments was early adapted to experiments in marine ecology however these involved studying the shape of the complete response surface not only detecting the optimum and often had counts or durations as the response variable thus nonlinear nonnormal response models were required for counts binomial and beta binomial models have been used the latter because of substantial over dispersion in closely controlled experiments over dispersion among units held under the same conditions might indicate that some mishap has occurred in conducting the study one possible check is to model the dispersion as a second response surface this procedure is used to show that over dispersion in fish egg hatching experiments has a biological explanation in that it occurs only under suboptimal hatching conditions

bayesian inference for stable distributions abstract very little work on stable distribution parameter estimation and inference appears in the literature due to the nonexistence of the probability density function this has led in particular to a dearth of bayesian work in this area but bayesian computation via markov chain monte carlo allows us to sample from the distribution of the parameters of the stable distributions by exploiting a particular mathematical representation involving the stable density

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial