gensmac a computational marker and cell method for free surface flows in general domains abstract a computer program for solving two dimensional incompressible viscous fluid flow in general domains is described this is based on the simplified marker and cell technique but it has a number of novel features a user supplied data file of coordinates prescribes the fluid domain which can be quite general and needs only to be connected with a view to parallelisation the momentum equations are solved explicitly but an automatic step changing routine optimises the stability restriction a conjugate gradient solver is used to invert the discrete poisson equation an accurate approximation to the stress conditions on the free surface is adopted the code is written in structured fortran with features from fortran 90 the efficacy of the code is illustrated by applying it to some industrial problems

model selection criteria in multivariate models with multiple structural changes abstract this paper considers the issue of selecting the number of regressors and the number of structural breaks in multivariate regression models in the possible presence of multiple structural changes we develop a modified akaike information criterion aic a modified mallows c p criterion and a modified bayesian information criterion bic the penalty terms in these criteria are shown to be different from the usual terms we prove that the modified bic consistently selects the regressors and the number of breaks whereas the modified aic and the modified c p criterion tend to overfit with positive probability the finite sample performance of these criteria is investigated through monte carlo simulations and it turns out that our modification is successful in comparison to the classical model selection criteria and the sequential testing procedure robust to heteroskedasticity and autocorrelation

on strong invariance principles under dependence assumptions on obtient des principes d invariance forts avec un ordre d approximation o t 1 2 k pour des suites de variables aleatoires dependantes

estimating and testing structural changes in multivariate regressions this paper considers issues related to estimation inference and computation with multiple structural changes that occur at unknown dates in a system of equations changes can occur in the regression coefficients and or the covariance matrix of the errors we also allow arbitrary restrictions on these parameters which permits the analysis of partial structural change models common breaks that occur in all equations breaks that occur in a subset of equations and so forth the method of estimation is quasi maximum likelihood based on normal errors the limiting distributions are obtained under more general assumptions than previous studies for testing we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present for computation an algorithm for an efficient procedure is proposed to construct the estimates and test statistics we also introduce a novel locally ordered breaks model which allows the breaks in different equations to be related yet not occurring at the same dates

inference on the quantile regression process tests based on the quantile regression process can be formulated like the classical kolmogorov smirnov and cramer von mises tests of goodness of fit employing the theory of bessel processes as in kiefer 1959 however it is frequently desirable to formulate hypotheses involving unknown nuisance parameters thereby jeopardizing the distribution free character of these tests we characterize this situation as the durbin problem since it was posed in durbin 1973 for parametric empirical processes in this paper we consider an approach to the durbin problem involving a martingale transformation of the parametric empirical process suggested by khmaladze 1981 and show that it can be adapted to a wide variety of inference problems involving the quantile regression process in particular we suggest new tests of the location shift and location scale shift models that underlie much of classical econometric inference the methods are illustrated with a reanalysis of data on unemployment durations from the pennsylvania reemployment bonus experiments the pennsylvania experiments conducted in 1988 89 were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells

testing for factor loading structural change under common breaks abstract this paper proposes a new test for factor loading structural change in dynamic factor models we first show that the leading test proposed by breitung and eickmeier 2011 exhibits nonmonotonic power essentially because the breaks are considered as spurious factors with stable factor loadings the proposed test eliminates the effects of the spurious factors by maximizing the test statistic over possible numbers of the original factors monte carlo simulations and an empirical example using u s treasury yield curve data clearly illustrate the usefulness of the proposed test

numerical simulation of axisymmetric free surface flows this paper describes an extension of the gensmac code for solving two dimen sional free surface flows to axisymmetric flows like gensmac the technique is finite difference based and embodies but considerably extends the smac simplified marker and cell ideas it incorporates adaptive time stepping and an accurate representation of the free surfaces while at the same time only uses surface particles to define the free surfaces greatly increasing the computational speed in addition it employs a graphic interface with solid modeling techniques to provide enhanced three dimensional visualization various simulations are undertaken to illustrate and validate typical flows both g i taylor s viscous jet plunging into a fluid and a liquid drop splashing onto a fluid are simulated also the important industrial application of container filling is illustrated finally a comparison is made with the linear theory of standing waves and the code is validated by a numerical convergence study

testing for structural stability of factor augmented forecasting models abstract mild factor loading instability particularly if sufficiently independent across the different constituent variables does not affect the estimation of the number of factors nor subsequent estimation of the factors themselves see e g stock and watson 2009 this result does not hold in the presence of large common breaks in the factor loadings however in this case information criteria overestimate the number of breaks additionally estimated factors are no longer consistent estimators of true factors hence various recent research papers in the diffusion index literature focus on testing the constancy of factor loadings however forecast failure of factor augmented models can be due to either factor loading instability regression coefficient instability or both to address this issue we develop a test for the joint hypothesis of structural stability of both factor loadings and factor augmented forecasting model regression coefficients our proposed test statistic has a chi squared limiting distribution and we are able to establish the first order validity of block bootstrap critical values empirical evidence is also presented for 11 us macroeconomic indicators

a front tracking front capturing method for the simulation of 3d multi fluid flows with free surfaces a method for simulating incompressible imiscible unsteady newtonian multi fluid flows with free surfaces is described a sharp interface separates fluids of different density and viscosity surface and interfacial tensions are also considered and the required curvature is geometrically approximated at the fronts by a least squares quadratic fitting to remove small undulations at the fronts a mass conserving filter is employed the numerical method employed to solve the navier stokes equations is based on the gensmac 3d front tracking method the velocity field is computed using a finite difference scheme on an eulerian grid the free surface and the interfaces are represented by an unstructured lagrangian grid moving through an eulerian grid the method was validated by comparing the numerical results with analytical results for a number of simple problems complex numerical simulations show the capability and emphasize the robustness of this new method

unstructured mel modelling of nonlinear unsteady ship waves an unstructured mixed eulerian lagrangian model mel is described for the simulation of the nonlinear wave body interaction as opposed to the structured model used widely in this field in present model the free surface is interpolated accurately using a polynomial scheme coupled with the moving least squares method and is triangulated with a local interrogation method coupled with the advancing front method to provide a high quality mesh a new method is devised to update the free surface intersection with the body based on the desingularized boundary integral method double desingularized point sources are used for a control point at the intersection with one inside the body and the other above the free surface to satisfy both the body and free surface boundary conditions over there the desingularized point sources are positioned in terms of the element sizes as well as solid angles of the boundary surface so as to avoid possible overcrowding of the sources at the corners of the surface solid angles on the surface are computed analytically using the spherical triangle theory as an illustration the algorithm is used to simulate the wave generation for a wigley hull which impulsively starts to move at a constant speed on a calm water surface the anticipated kelvin ship wave pattern is well simulated the wave profiles along the hull agree well with the measured results of nobeless and mccarthy proceedings of the 2nd dtnsrdc workshop maryland 1983 pp 5 35 as compared to a structured approach the unstructured model reduces the cpu time and memory requirements and being robust in handling complex geometries is more versatile in practical applications

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

model selection and the principle of minimum description length this article reviews the principle of minimum description length mdl for problems of model selection by viewing statistical modeling as a means of generating descriptions of observed data the mdl framework discriminates between competing models based on the complexity of each description this approach began with kolmogorov s theory of algorithmic complexity matured in the literature on information theory and has recently received renewed attention within the statistics community here we review both the practical and the theoretical aspects of mdl as a tool for model selection emphasizing the rich connections between information theory and statistics at the boundary between these two disciplines we find many interesting interpretations of popular frequentist and bayesian procedures as we show mdl provides an objective umbrella under which rather disparate approaches to statistical modeling can coexist and be compared we illustrate the mdl principle by considering problems in regression nonpar

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

modeling of electromagnetic absorption scattering problems using hp adaptive finite elements a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for affine elements is presented the proposed method is illustrated and verified with a series of 2d experiments including elements with curved boundaries and nonhomogeneous media

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

consistency of data driven histogram methods for density estimation and classification we present general sufficient conditions for the almost surel1 consistency of histogram density estimates based on data dependent partitions analogous conditions guarantee the almost sure risk consistency of histogram classification schemes based on data dependent partitions multivariate data is considered throughout in each case the desired consistency requires shrinking cells subexponential growth of a combinatorial complexity measure and sub linear growth of the number of cells it is not required that the cells of every partition be rectangles with sides paralles to the coordinate axis or that each cell contain a minimum number of points no assumptions are made concerning the common distribution of the training vectors we apply the results to establish the consistency of several known partitioning estimates including the kn spacing density estimate classifiers based on statistically equivalent blocks and classifiers based on multivariate clustering schemes

front tracking with moving least squares surfaces the representation of interfaces by means of the algebraic moving least squares amls technique is addressed this technique in which the interface is represented by an unconnected set of points is interesting for evolving fluid interfaces since there is no surface connectivity the position of the surface points can thus be updated without concerns about the quality of any surface triangulation we introduce a novel amls technique especially designed for evolving interfaces applications that we denote ramls for robust amls the main advantages with respect to previous amls techniques are increased robustness computational efficiency and being free of user tuned parameters further we propose a new front tracking method based on the lagrangian advection of the unconnected point set that defines the ramls surface we assume that a background eulerian grid is defined with some grid spacing h the advection of the point set makes the surface evolve in time the point cloud can be regenerated at any time in particular we regenerate it each time step by intersecting the gridlines with the evolved surface which guarantees that the density of points on the surface is always well balanced the intersection algorithm is essentially a ray tracing algorithm well studied in computer graphics in which a line ray is traced so as to detect all intersections with a surface also the tracing of each gridline is independent and can thus be performed in parallel several tests are reported assessing first the accuracy of the proposed ramls technique and then of the front tracking method based on it comparison with previous eulerian lagrangian and hybrid techniques encourage further development of the proposed method for fluid mechanics applications

a finite difference technique for solving a time strain separable k bkz constitutive equation for two dimensional moving free surface flows this work is concerned with the numerical solution of the k bkz integral constitutive equation for two dimensional time dependent free surface flows the numerical method proposed herein is a finite difference technique for simulating flows possessing moving surfaces that can interact with solid walls the main characteristics of the methodology employed are the momentum and mass conservation equations are solved by an implicit method the pressure boundary condition on the free surface is implicitly coupled with the poisson equation for obtaining the pressure field from mass conservation a novel scheme for defining the past times t is employed the finger tensor is calculated by the deformation fields method and is advanced in time by a second order runge kutta method this new technique is verified by solving shear and uniaxial elongational flows furthermore an analytic solution for fully developed channel flow is obtained that is employed in the verification and assessment of convergence with mesh refinement of the numerical solution for free surface flows the assessment of convergence with mesh refinement relies on a jet impinging on a rigid surface and a comparison of the simulation of a extrudate swell problem studied by mitsoulis 2010 44 was performed finally the new code is used to investigate in detail the jet buckling phenomenon of k bkz fluids

quantile regression in reproducing kernel hilbert spaces in this article we consider quantile regression in reproducing kernel hilbert spaces which we call kernel quantile regression kqr we make three contributions 1 we propose an efficient algorithm that computes the entire solution path of the kqr with essentially the same computational cost as fitting one kqr model 2 we derive a simple formula for the effective dimension of the kqr model which allows convenient selection of the regularization parameter and 3 we develop an asymptotic theory for the kqr model

a posteriori finite element bounds for linear functional outputs of elliptic partial differential equations we present a domain decomposition finite element technique for efficiently generating lower and upper bounds to outputs which are linear functionals of the solutions to symmetric or nonsymmetric second order coercive linear partial differential equations in two space dimensions the method is based upon the construction of an augmented lagrangian in which the objective is a quadratic energy reformulation of the desired output and the constraints are the finite element equilibrium equations and intersubdomain continuity requirements the bounds on the output for a suitably fine truth mesh discretization are then derived by appealing to a dual max min relaxation evaluated for optimally chosen adjoint and hybrid flux candidate lagrange multipliers generated by a k element coarser working mesh approximation independent of the form of the original partial differential equation the computation on the truth mesh is reduced to k decoupled subdomain local symmetric neumann problems the technique is illustrated for the convection diffusion and linear elasticity equations

a three dimensional self adaptive hp finite element method for the characterization of waveguide discontinuities abstract we propose the use of a highly accurate three dimensional 3d fully automatic hp adaptive finite element method fem for the characterization of rectangular waveguide discontinuities these discontinuities are either the unavoidable result of mechanical electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems the proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi analytical methods it supports anisotropic refinements on irregular meshes with hanging nodes and isoparametric elements it makes use of hexahedral elements compatible with high order h curl discretizations the 3d hp adaptive fem is applied for the first time to solve a wide range of 3d waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed

a stabilized finite element method using a discontinuous level set approach for the computation of bubble dynamics a novel numerical method for solving three dimensional two phase flow problems is presented this method combines a quadrature free discontinuous galerkin method for the level set equation with a pressure stabilized finite element method for the navier stokes equations the main challenge in the computation of such flows is the accurate evaluation of surface tension forces this involves the computation of the curvature of the fluid interface in the context of the discontinuous galerkin method we show that the use of a curvature computed by means of a direct derivation of the level set function leads to inaccurate and oscillatory results a more robust second order least squares computation of the curvature that filters out the high frequencies and produces converged results is presented this whole numerical technology allows to simulate a wide range of flow regimes with large density ratios to accurately capture the shape of the deforming interface of the bubble and to maintain good mass conservation

consistent estimation for partition wise regression and classification models partition wise models offer a flexible approach for modeling complex and multidimensional data and are capable of producing interpretable results they are based on partitioning the observed data into regions each of which is modeled with a simple submodel the success of this approach highly depends on the quality of the partition as too large a region could lead to a nonsimple submodel while too small a region could inflate estimation variance this paper proposes an automatic procedure for choosing the partition i e the number of regions and the boundaries between regions as well as the submodels for the regions it is shown that under the assumption of the existence of a true partition as well as a set of known significant predictors the proposed partition estimator is statistically consistent features of the proposed methodology are highlighted for both regression and classification problems on synthetic and real data

estimating structural changes in regression quantiles this paper considers the estimation of multiple structural changes occurring at unknown dates in one or multiple conditional quantile functions the analysis covers time series models as well as models with repeated cross sections we estimate the break dates and other parameters jointly by minimizing the check function over all permissible break dates the limiting distribution of the estimator is derived and the coverage property of the resulting confidence interval is assessed via simulations a procedure to determine the number of breaks is also discussed empirical applications to the quarterly us real gdp growth rate and the underage drunk driving data suggest that the method can deliver more informative results than the analysis of the conditional mean function alone

structural break estimation for nonstationary time series models this article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive ar processes the number and locations of the piecewise ar segments as well as the orders of the respective ar processes are assumed unknown the minimum description length principle is applied to compare various segmented ar fits to the data the goal is to find the best combination of the number of segments the lengths of the segments and the orders of the piecewise ar processes such a best combination is implicitly defined as the optimizer of an objective function and a genetic algorithm is implemented to solve this difficult optimization problem numerical results from simulation experiments and real data analyses show that the procedure has excellent empirical properties the segmentation of multivariate time series is also considered assuming that the true underlying model is a segmented autoregression this procedure is shown to be consistent for estimating the location of

a hybrid variational front tracking level set mesh generator for problems exhibiting large deformations and topological changes we present a method for generating 2 d unstructured triangular meshes that undergo large deformations and topological changes in an automatic way we employ a method for detecting when topological changes are imminent via distance functions and shape skeletons when a change occurs we use a level set method to guide the change of topology of the domain mesh this is followed by an optimization procedure using a variational formulation of active contours that seeks to improve boundary mesh conformity to the zero level contour of the level set function our method is advantageous for arbitrary lagrangian eulerian ale type methods and directly allows for using a variational formulation of the physics being modeled and simulated including the ability to account for important geometric information in the model such as for surface tension driven flow furthermore the meshing procedure is not required at every time step and the level set update is only needed during a topological change hence our method does not significantly affect computational cost

an infinite element for maxwell s equations a new infinite element ie approximation for steady state maxwell s equations is proposed the ie is compatible with a new class of hp finite element fe discretizations presented in 13 32 following 12 a convergence analysis for the proposed coupled fe ie approximations is presented

application of the fem with adaptivity for electromagnetic inverse medium scattering problems abstract the paper presents a study of solution of inverse medium scattering problems for 3d time harmonic electromagnetics the solution is based on minimization of the misfit function between the observed scattered fields and trial solutions of direct problems for the sought approximate distribution of electric permittivity the sources of illuminating waves and the observation points of the scattered fields are located in the nearfield the scatterer the simulations of the direct problems are performed with the finite element method application of adaptive mesh refinement to improve accuracy of solutions is illustrated tests with real and complex valued distributions of electric permittivity and with complete and incomplete measurement data are presented

segmented model selection in quantile regression using the minimum description length principle this article proposes new model fitting techniques for quantiles of an observed data sequence including methods for data segmentation and variable selection the main contribution however is in providing a means to perform these two tasks simultaneously this is achieved by matching the data with the best fitting piecewise quantile regression model where the fit is determined by a penalization derived from the minimum description length principle the resulting optimization problem is solved with the use of genetic algorithms the proposed fully automatic procedures are unlike traditional break point procedures not based on repeated hypothesis tests and do not require unlike most variable selection procedures the specification of a tuning parameter theoretical large sample properties are derived empirical comparisons with existing break point and variable selection methods for quantiles indicate that the new procedures work well in practice

transient adaptivity applied to two phase incompressible flows an anisotropic adaptation process is applied to a three dimensional incompressible two phase flow solver the solver uses a level set finite element method on unstructured tetrahedral meshes we show how the level set function can be used to build an anisotropic mesh with good properties some computations with a strong transient character and large densities ratios 1 1000 are presented we show that the efficiency of the computations can be deeply enhanced by mesh adaptations

an interface reconstruction method based on an analytical formula for 3d arbitrary convex cells in this paper we are interested in an interface reconstruction method for 3d arbitrary convex cells that could be used in multi material flow simulations for instance we assume that the interface is represented by a plane whose normal vector is known and we focus on the volume matching step that consists in finding the plane constant so that it splits the cell according to a given volume fraction we follow the same approach as in the recent authors publication for 2d arbitrary convex cells in planar and axisymmetrical geometries namely we derive an analytical formula for the volume of the specific prismatoids obtained when decomposing the cell using the planes that are parallel to the interface and passing through all the cell nodes this formula is used to bracket the interface plane constant such that the volume matching problem is rewritten in a single prismatoid in which the same formula is used to find the final solution the proposed method is tested against an important number of reproducible configurations and shown to be at least five times faster

an improved finite element space for discontinuous pressures abstract we consider incompressible stokes flow with an internal interface at which the pressure is discontinuous as happens for example in problems involving surface tension we assume that the mesh does not follow the interface which makes classical interpolation spaces to yield suboptimal convergence rates typically the interpolation error in the l 2 norm is of order h 1 2 we propose a modification of the p 1 conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system the unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element so that the implementation of the proposed space into existing codes is straightforward with this modification numerical tests show that the interpolation order improves to o h 3 2 the new pressure space is implemented for the stable p 1 p 1 mini element discretization and for the stabilized equal order p 1 p 1 discretization assessment is carried out for poiseuille flow with a forcing surface and for a static bubble in all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard p 1 space in addition two navier stokes simulations with moving interfaces rayleigh taylor instability and merging bubbles are reported to show that the proposed space is robust enough to carry out realistic simulations

a non local perspective on the power properties of the cusum and cusum of squares tests for structural change abstract we consider the power properties of the cusum and cusum of squares cusq tests in the presence of a one time change in the parameters of a linear regression model a result due to ploberger and kramer 1990 the local power of the cusum and cusum of squares tests econometric theory 6 335 347 is that the cusq test has only trivial asymptotic local power in this case while the cusum test has non trivial local asymptotic power unless the change is orthogonal to the mean regressor the main theme of the paper is that such conclusions obtained from a local asymptotic framework are not reliable guides to what happens in finite samples the approach we take is to derive expansions of the test statistics that retain terms related to the magnitude of the change under the alternative hypothesis this enables us to analyze what happens for non local to zero breaks our theoretical results are able to explain how the power function of the tests can be drastically different depending on whether one deals with a static regression with uncorrelated errors a static regression with correlated errors a dynamic regression with lagged dependent variables or whether a correction for non normality is applied in the case of the cusq we discuss in which cases the tests are subject to a non monotonic power function that goes to zero as the magnitude of the change increases and uncover some curious properties all theoretical results are verified to yield good guides to the finite sample power through simulation experiments we finally highlight the practical importance of our results

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

an hp adaptive finite element method for electromagnetics part 3 a three dimensional infinite element for maxwell s equations this paper is a continuation of reference 26 cecot demkowicz and rachowicz computer methods in applied mechanics and engineering 2000 188 625 643 and describes an implementation of the infinite element for three dimensional time harmonic maxwell s equations proposed in reference 15 demkowicz and pal computer methods in applied mechanics and engineering 1998 164 77 94 the element is compatible with the hp finite element discretizations for maxwell s equations in bounded domains reported in references 16 18 computer methods in applied mechanics and engineering 1998 152 103 124 1999 169 331 344 2000 187 307 337 copyright 2003 john wiley sons ltd

connectivity free front tracking method for multiphase flows with free surfaces in this study a connectivity free front tracking method is developed to simulate multiphase flows with free surfaces this method is based on the point set method which does not require any connectivities between interfacial points to represent the interface the main advantage of the connectivity free approach is the easiness in re constructing the interface when large topology change occurs it requires an indicator field to be constructed first based on the existing interface and the surface curvature and normal are then computed using the indicator field here we adopt the reproducing kernel particle method rkpm interpolation function that provides the ability to deal with free surface flows and the flexibility of using non uniform meshes when local fine resolution is needed a points regeneration scheme is developed to construct smooth interfaces and to automatically handle topology changes the mass conservation is verified by performing a single vortex advection test several 2 d and 3 d numerical tests including an oscillating droplet dam breaking two droplet impacting and multi bubble merging are presented to show the accuracy and the robustness of the method

shrinkage estimation of the varying coefficient model the varying coefficient model is a useful extension of the linear regression model nevertheless how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood to solve the problem we propose here a novel method which combines the ideas of the local polynomial smoothing and the least absolute shrinkage and selection operator lasso the new method can do nonparametric estimation and variable selection simultaneously with a local constant estimator and the adaptive lasso penalty the new method can identify the true model consistently and that the resulting estimator can be as efficient as the oracle estimator numerical studies clearly confirm our theories extension to other shrinkage methods e g the scad i e the smoothly clipped absolute deviation and other smoothing methods is straightforward

a goal oriented adaptive finite element method for 3d scattered airborne electromagnetic method modeling abstractwe have developed a goal oriented adaptive unstructured finite element method based on the scattered field for 3d frequency domain airborne electromagnetic aem modeling to guarantee the em field divergence free within each element and the continuity conditions at electrical material interfaces we have used the edge based shape functions to approximate the electrical field the posterior error for finite element adaptive meshing procedure is estimated from the continuity of the normal component of the current density whereas the influence functions are estimated by solving a dual forward problem because the imaginary part of the scattered current is discontinuous and the real part is continuous we use the latter to estimate the posterior error for the multisources and multifrequencies problem in aem we calculate the weighted posterior error for each element by considering only those transmitter receiver pairs that do not adhere to our convergence criteria finally we add a minimum volume

a goal oriented hp adaptive finite element approach to radar scattering problems abstract the paper presents application of an hp adaptive finite element method for scattering of electromagnetic waves the main objective of the numerical analysis is to determine the characteristics of the scattered waves indicating the power being scattered at a given direction i e the radar cross section rcs this is achieved considering the scattered far field which defines rcs and which is expressed as a linear functional of the solution techniques of error estimation for the far field are considered and an h adaptive strategy leading to the fast reduction of the error of the far field is presented the simulations are performed with a three dimensional version of an hp adaptive finite element method for electromagnetics based on the hexahedral edge elements combined with infinite elements for modeling the unbounded space surrounding the scattering object

free surface flows under impacting droplets a numerical method which fulfils the free surface boundary conditions and extrapolates the fluid velocity into empty grid cells outside the fluid region on a fixed cartesian grid system is presented the complex three dimensional vortex structures formed via surface vortex interaction and induction between vortices have been computed using the proposed technique implemented within a level set method for both vertical and oblique droplet impacts in incompressible fluids the present results have been validated through numerical tests which confirm zero tangential shear at the free surface and comparisons with experimental observations of cavity and vortex ring formation underneath the impact location in some cases transitions from a concentric vortex ring to a fully three dimensional vortex structure has been confirmed whilst the primary vortex ring is initiated at the highly curved contact surface between the droplet and receiving surface azimuthal instabilities are manifested in the shear layer around the cavity crater developing after the vertical impact resulting in axial counter rotating vorticity between the cavity and descending vortex ring underlying mechanisms which induce local deformation of the free surface creating a so called scar due to the sub surface vortices at the oblique impacts are also discussed

an implicit technique for solving 3d low reynolds number moving free surface flows this paper describes the development of an implicit finite difference method for solving transient three dimensional incompressible free surface flows to reduce the cpu time of explicit low reynolds number calculations we have combined a projection method with an implicit technique for treating the pressure on the free surface the projection method is employed to uncouple the velocity and the pressure fields allowing each variable to be solved separately we employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly in addition we show that the proposed method can be applied to viscoelastic fluids numerical results include the simulation of jet buckling and extrudate swell for reynolds numbers in the range 0 01 0 5

testing for common breaks in a multiple equations system abstract the issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system our framework is very general and allows integrated regressors and trends as well as stationary regressors the null hypothesis is that breaks in different parameters occur at common locations and are separated by some positive fraction of the sample size unless they occur across different equations under the alternative hypothesis the break dates across parameters are not the same and also need not be separated by a positive fraction of the sample size whether within or across equations the test considered is the quasi likelihood ratio test assuming normal errors though as usual the limit distribution of the test remains valid with non normal errors of independent interest we provide results about the rate of convergence of the estimates when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as some positive fraction of the sample size allowing break dates not separated by a positive fraction of the sample size across equations simulations show that the test has good finite sample properties we also provide an application to issues related to level shifts and persistence for various measures of inflation to illustrate its usefulness

a minimum description length based image segmentation procedure and its comparison with a cross validation based segmentation procedure abstract image segmentation is a very important problem in image analysis as quite often it is a key component of a good practical solution to a real life imaging problem it aims to partition a digital image into a set of nonoverlapping homogeneous regions one approach to segmenting an image is to fit a piecewise constant function to the image and define the segmentation by the discontinuity points of the fitted function the article s first contribution is to present a new and automatic segmentation procedure which follows this piecewise constant function fitting approach this procedure is based on rissanen s minimum description length mdl principle and consists of two components a an mdl based criterion in which the best segmentation i e the best fitted piecewise constant function is defined as its minimizer and b a fast merging algorithm that attempts to locate this minimizer as a second contribution the new mdl based procedure is compared with a cross validation based segmentation

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

assessing the relative power of structural break tests using a framework based on the approximate bahadur slope abstract we compare the asymptotic relative efficiency of the exp mean and sup functionals of the wald lm and lr tests for structural change analyzed by andrews andrews d w k 1993 tests for parameter instability and structural change with unknown change point econometrica 61 821 856 and andrews and ploberger andrews d w k ploberger w 1994 optimal tests when a nuisance parameter is present only under the alternative econometrica 62 1383 1414 we derive the approximate bahadur slopes of these tests using large deviations techniques these show that tests based on the mean functional are inferior to those based on the sup and exp when using the same base statistic also for a given functional the wald based test dominates the lr based test which dominates the lm based one we show that the sup and mean type tests satisfy wieand s wieand h s 1976 a condition under which the pitman and bahadur approaches to efficiency coincide annals of statistics 4 1003 1011 condition so that their slopes yield the limiting as the size tends to zero asymptotic relative pitman efficiency whether this holds for the exp type tests still remains a conjecture using this measure of efficiency the mean type tests are also inferior to the sup we also compare tests based on the wald and lm statistics modified with a hac estimator in this case the inferiority of the lm based tests is especially pronounced the relevance of our theoretical results in finite samples is assessed via simulations our results are in contrast to those obtained by the authors in the second reference cited above based on a local asymptotic framework and our analysis thereby reveals its potential weaknesses in the context of structural change problems

common breaks in means and variances for panel data this paper establishes the consistency of the estimated common break point in panel data consistency is obtainable even when a regime contains a single observation making it possible to quickly identify the onset of a new regime we also propose a new framework for developing the limiting distribution for the estimated break point and show how to construct confidence intervals the least squares method is used for estimating breaks in means and the quasi maximum likelihood qml method is used to estimate breaks in means and in variances qml is shown to be more efficient than the least squares even if there is no change in the variances

testing for structural breaks in dynamic factor models in this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks it is shown that structural breaks severely inflate the number of factors identified by the usual information criteria the hypothesis of a structural break is tested by using lr lm and wald statistics the lm test which performs best in our monte carlo simulations is generalized to test for structural breaks in factor models where the break date is unknown and the common factors and idiosyncratic components are serially correlated the proposed test procedures are applied to datasets from the us and the euro area

an efficient front tracking method for fully nonlinear interfacial waves a fully nonlinear and dispersive model within the framework of potential theory is developed for interfacial 2 layer waves to circumvent the difficulties arisen from the moving boundary problem a viable technique based on the mixed eulerian and lagrangian concept is proposed the computing area is partitioned by a moving mesh system which adjusts its location vertically to conform to the shape of the moving boundaries but keeps frozen in the horizontal direction accordingly a modified dynamic condition is required to properly compute the boundary potentials to demonstrate the effectiveness of the current method two important problems for the interfacial wave dynamics the generation and evolution processes are investigated firstly analytical solutions for the interfacial wave generations by the interaction between the barotropic tide and topography are derived and compared favorably with the numerical results furthermore simulations are performed for the nonlinear interfacial wave evolutions at various water depth ratios and satisfactory agreement is achieved with the existing asymptotical theories

inference regarding multiple structural changes in linear models with endogenous regressors this paper considers the linear model with endogenous regressors and multiple changes in the parameters at unknown times it is shown that minimization of a generalized method of moments criterion yields inconsistent estimators of the break fractions but minimization of the two stage least squares 2sls criterion yields consistent estimators of these parameters we develop a methodology for estimation and inference of the parameters of the model based on 2sls the analysis covers the cases where the reduced form is either stable or unstable the methodology is illustrated via an application to the new keynesian phillips curve for the us

bent line quantile regression with application to an allometric study of land mammals speed and mass summary quantile regression which models the conditional quantiles of the response variable given covariates usually assumes a linear model however this kind of linearity is often unrealistic in real life one situation where linear quantile regression is not appropriate is when the response variable is piecewise linear but still continuous in covariates to analyze such data we propose a bent line quantile regression model we derive its parameter estimates prove that they are asymptotically valid given the existence of a change point and discuss several methods for testing the existence of a change point in bent line quantile regression together with a power comparison by simulation an example of land mammal maximal running speeds is given to illustrate an application of bent line quantile regression in which this model is theoretically justified and its parameters are of direct biological interests

estimating restricted structural change models abstract this paper considers issues related to multiple structural changes occurring at unknown dates in the linear regression model when restrictions are imposed on the parameters this includes for example the important special case where different nonadjacent regimes are the same the estimates are constructed as global minimizers of the restricted sum of squared residuals and we provide an extension of the algorithm discussed in bai and perron 2003b computation and analysis of multiple structural change models journal of applied econometrics 18 1 22 to efficiently compute them we show that the estimates of the break dates have the same asymptotic properties with or without the restrictions imposed that is in large samples there is no efficiency gain from imposing valid restrictions as far as the estimates of the break dates are concerned of course efficiency gains occur for the other parameters of the model simulations show that in small samples all parameters are more efficiently estimated using the restrictions we also consider tests of the null hypothesis of no structural change these are also more powerful when the restrictions are imposed a gauss code for all the procedures discussed in this paper is available from the authors

on image segmentation using information theoretic criteria image segmentation is a long studied and important problem in image processing different solutions have been proposed many of which follow the information theoretic paradigm while these information theoretic segmentation methods often produce excellent empirical results their theoretical properties are still largely unknown the main goal of this paper is to conduct a rigorous theoretical study into the statistical consistency properties of such methods to be more specific this paper investigates if these methods can accurately recover the true number of segments together with their true boundaries in the image as the number of pixels tends to infinity our theoretical results show that both the bayesian information criterion bic and the minimum description length mdl principle can be applied to derive statistically consistent segmentation methods while the same is not true for the akaike information criterion aic numerical experiments were conducted to illustrate and support our theoretical findings

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

estimating a common deterministic time trend break in large panels with cross sectional dependence abstract this paper develops an estimation procedure for a common deterministic time trend break in large panels the dependent variable in each equation consists of a deterministic trend and an error term the deterministic trend is subject to a change in the intercept slope or both and the break date is common for all equations the estimation method is simply minimizing the sum of squared residuals for all possible break dates both serial and cross sectional correlations are important factors that decide the rate of convergence and the limiting distribution of the break date estimate the rate of convergence is faster when the errors are stationary than when they have a unit root when there is no cross sectional dependence among the errors the rate of convergence depends on the number of equations and thus is faster than the univariate case when the errors have a common factor structure with factor loadings correlated with the intercept and slope change parameters the rate of convergence does not depend on the number of equations and thus reduces to the univariate case the limiting distribution of the break date estimate is also provided some monte carlo experiments are performed to assess the adequacy of the asymptotic results a brief empirical example using the us gdp price index is offered

a second order boundary fitted projection method for free surface flow computations this paper describes a new approach to the high fidelity simulation of axisymmetric free surface flows a boundary fitted grid is coupled with a new projection method for the solution of the navier stokes equations with second order accuracy in space and time two variants of this new method are developed by adapting two existing algorithms suitable for prescribed velocity boundary conditions to the case of prescribed normal and tangential stresses at the free boundary a normal mode analysis for a fixed boundary problem confirms the second order accuracy of the algorithms the approach is validated by comparison with a rayleigh plesset solution for an oscillating spherical bubble with an analysis of shape oscillations and with existing results for the buoyant rise of a deforming bubble for reynolds numbers up to 200 and weber numbers up to 12 in addition to the simulation of axisymmetric free surface flows of intrinsic interest the present approach is suitable for the validation of genuinely three dimensional calculations

shrinkage estimation of common breaks in panel data models via adaptive group fused lasso abstract in this paper we consider estimation and inference of common breaks in panel data models via adaptive group fused lasso we consider two approaches penalized least squares pls for first differenced models without endogenous regressors and penalized gmm pgmm for first differenced models with endogeneity we show that with probability tending to one both methods can correctly determine the unknown number of breaks and estimate the common break dates consistently we establish the asymptotic distributions of the lasso estimators of the regression coefficients and their post lasso versions we also propose and validate a data driven method to determine the tuning parameter used in the lasso procedure monte carlo simulations demonstrate that both the pls and pgmm estimation methods work well in finite samples we apply our pgmm method to study the effect of foreign direct investment fdi on economic growth using a panel of 88 countries and regions from 1973 to 2012 and find multiple breaks in the model

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

the p and h p versions of the finite element method basic principles and properties in the classical form of the finite element method called the hversion piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy in this paper we discuss the fundamental theoretical ideas behind the relatively recent p version and h p version in the p version a fixed mesh is used and p is allowed to increase the h p version combines both approaches the authors describe and explain the basic properties and characteristics of these newer versions especially in areas where their behavior is significantly different from that of the h version simplified proofs of key concepts are included and computational illustrations of several results are provided a benchmark comparison between the various versions in included

the limit distribution of the estimates in cointegrated regression models with multiple structural changes abstract we study estimation and inference in cointegrated regression models with multiple structural changes allowing both stationary and integrated regressors both pure and partial structural change models are analyzed we derive the consistency rate of convergence and the limit distribution of the estimated break fractions our technical conditions are considerably less restrictive than those in bai et al bai j lumsdaine r l stock j h 1998 testing for and dating breaks in multivariate time series review of economic studies 65 395 432 who considered the single break case in a multi equations system and permit a wide class of practically relevant models our analysis is however restricted to a single equation framework we show that if the coefficients of the integrated regressors are allowed to change the estimated break fractions are asymptotically dependent so that confidence intervals need to be constructed jointly if however only the intercept and or the coefficients of the stationary regressors are allowed to change the estimates of the break dates are asymptotically independent as in the stationary case analyzed by bai and perron bai j perron p 1998 estimating and testing linear models with multiple structural changes econometrica 66 47 78 we also show that our results remain valid under very weak conditions when the potential endogeneity of the non stationary regressors is accounted for via an increasing sequence of leads and lags of their first differences as additional regressors simulation evidence is presented to assess the adequacy of the asymptotic approximations in finite samples

fast and robust solvers for pressure correction in bubbly flow problems we consider the numerical simulation of two phase fluid flow where bubbles or droplets of one phase move against a background of the other phase such flows are governed by the navier stokes equations the solution of which may be approximated using a pressure correction approach within such an approach the computational cost is often dominated by the solution of a linear system corresponding to a discrete poisson equation with discontinuous coefficients in this paper we explore the efficient solution of these linear systems using robust multilevel solvers such as deflated variants of the preconditioned conjugate gradient method or robust multigrid techniques we consider these families of methods in more detail and compare their performance in the simulation of bubbly flows some of these methods turn out to be very effective and reduce the amount of work to solve the pressure correction system substantially resulting in efficient calculations for two phase flows on highly resolved grids

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

numerical simulation of viscoelastic flows using integral constitutive equations a finite difference approach this work presents a numerical technique for simulating incompressible isothermal viscoelastic flows of fluids governed by the upper convected maxwell ucm and k bkz kaye bernstein kearsley and zapas integral models the numerical technique described herein is an extension of the gensmac method to the solution of the momentum and mass conservation equations to include integral constitutive equations the governing equations are solved by the finite difference method on a staggered grid using a marker and cell approach the finger tensor b t t is computed in an eulerian framework using the ideas of the deformation fields method however improvements to the deformation fields method are introduced the finger tensor b t x t is obtained by a second order accurate method and the stress tensor t x t is computed by a second order quadrature formula the numerical method presented in this work is validated by comparing the predictions of velocity and stress fields in two dimensional fully developed channel flow of a maxwell fluid with the corresponding analytic solutions furthermore the flow through a planar 4 1 contraction is investigated and the numerical results were compared with the corresponding experimental data finally the ucm and the k bkz models were used to simulate the planar 4 1 contraction flow over a wide range of reynolds and weissenberg numbers and the numerical results obtained are in agreement with published data

model based classification trees the construction of classification trees is nearly always top down locally optimal and data driven such recursive designs are often globally inefficient for instance in terms of the mean depth necessary to reach a given classification rate we consider statistical models for which exact global optimization is feasible and thereby demonstrate that recursive and global procedures may result in very different tree graphs and overall performance

testing for structural change in regression quantiles abstract most studies in the structural change literature focus solely on the conditional mean while under various circumstances structural change in the conditional distribution or in conditional quantiles is of key importance this paper proposes several tests for structural change in regression quantiles two types of statistics are considered namely a fluctuation type statistic based on the subgradient and a wald type statistic based on comparing parameter estimates obtained from different subsamples the former requires estimating the model under the null hypothesis and the latter involves estimation under the alternative hypothesis the tests proposed can be used to test for structural change occurring in a pre specified quantile or across quantiles which can be viewed as testing for change in the conditional distribution with a linear specification of the conditional quantile function both single and multiple structural changes are considered we derive the limiting distributions under the null hypothesis and show they are nuisance parameter free and can be easily simulated a simulation study is conducted to assess the size and power in finite samples

a discontinuous galerkin based immersed boundary method a numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced the proposed method is conceptually simple and free of user defined parameters starting with a conforming finite element mesh the key ingredient is to switch those elements intersected by the dirichlet boundary to a discontinuous galerkin approximation and impose the dirichlet boundary conditions strongly by virtue of relaxing the continuity constraint at those elements boundary locking is avoided and optimal order convergence is achieved this is shown through numerical experiments in reaction diffusion problems copyright 2008 john wiley sons ltd

three dimensional adaptive cartesian grid method with conservative interface restructuring and reconstruction multiphase flows associated with interfacial dynamics steep jumps in fluid properties and moving boundaries between different phases pose substantial computational challenges in terms of both modeling as well as computational efficiency the present work extends a marker based immersed boundary or front tracking technique to model the three dimensional interfacial dynamics it tracks the moving boundary using triangulated surface grids and solves the flow governing equations on a stationary cartesian grid a locally adaptive grid is employed to help meet the resolution requirements based on the interface location and solution features the interface resolution is controlled via a conservative restructuring technique satisfying mass continuity an improved level contour reconstruction algorithm for topology change preserving the interface connectivity information is presented highlighting various algorithmic difficulties and implemented remedies the outlines of a finite volume staggered grid navier stokes solution using the projection method are discussed the impact of conservative interface restructuring and reconstruction has been assessed against mass conservation and spurious velocity errors the overall capabilities of the developed algorithms have been demonstrated for large density ratios o 1000 interfacial flows using various rising bubbles and drop collision coalescence computations involving coalescence and break up dynamics

detecting differential expressions in genechip microarray studies a quantile approach in this article we consider testing for differentially expressed genes in genechip studies by modeling and analyzing the quantiles of gene expression through probe level measurements by developing a robust rank score test for linear quantile models with a random effect we propose a reliable test for detecting differences in certain quantiles of the intensity distributions by using a genomewide adjustment to the test statistic to account for within array correlation we demonstrate that the proposed rank score test is highly effective even when the number of arrays is small our empirical studies with real experimental data show that detecting differences in the quartiles for the probe level data is a valuable complement to the usual mixed model analysis based on gaussian likelihood the methodology proposed in this article is a first attempt to develop inferential tools for quantile regression in mixed models

convergence analysis of canonical genetic algorithms this paper analyzes the convergence properties of the canonical genetic algorithm cga with mutation crossover and proportional reproduction applied to static optimization problems it is proved by means of homogeneous finite markov chain analysis that a cga will never converge to the global optimum regardless of the initialization crossover operator and objective function but variants of cga s that always maintain the best solution in the population either before or after selection are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent cga these results are discussed with respect to the schema theorem