the fixed mesh ale approach for the numerical approximation of flows in moving domains in this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization and therefore the formulation to be presented falls within the category of fixed grid methods even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed grid method our approach can be applied together with any technique to impose approximately boundary conditions although we also describe the one we actually favor our main concern is to properly account for the advection of information as the domain boundary evolves to achieve this we use an arbitrary lagrangian eulerian framework the distinctive feature being that at each time step results are projected onto a fixed background mesh that is where the problem is actually solved

logarithmic transformations in anova a method is presented for choosing an additive constant c when transforming data x to y log x c the method preserves type i error probability and power in anova under the assumption that the x c for some c are log normally distributed the method has advantages similar to those of rank transformations namely it is easy to use and is resistant to extreme observations since the special case c infinity corresponds in anova to y x the method is a useful generalization of least squares

exploratory longitudinal factor analysis in multiple populations for multiple populatios a longtidinal factor analytic model which is entirely exploratory that is no explicit identification constraints is proposed factorial collapse and period practice effects are allowed an invariant and or stationary factor pattern is permitted this model is formulated stochastically to implement this model a stagewise em algorithm is developed finally a numerical illustration utilizing nesselroade and baltes data is presented

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

sequential estimation of log abundance i discuss the estimation of the abundance of a biological population its logarithm and the variances of these estimates from a sequential sampling scheme with minimum and maximum sample sizes observations are counts of organisms in randomly chosen packets such as cores branches bushes and so forth for preassigned values m ni and n2 samples are taken until a at least ni packets and b either m positive packets or a total of n2 packets have been observed abundance estimates are based on an estimate of the fraction of positive packets given by kremers 1987 technometrics 29 109 112 with a modification to avoid estimates of zero estimates of log abundance are given by log estimated abundance with an adjustment for bias due to the concavity of the log function two adjustments are considered one based on taylor series expansion the delta method and the other on the bootstrap these techniques are also used to estimate the variance of the estimate of log abundance simulations suggest that both methods are better than not adjusting though the gain is small compared to the standard deviation of the estimates the bootstrap estimates are less biased than the taylor series estimates but have larger variances so that the taylor series estimates have smaller mean squared errors the variances of the sequential estimates of log abundance tend to be only weakly dependent on the true abundance

weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes this is the accepted version of the following article codina r and baiges j 2015 weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes int j numer meth engng 104 624 654 doi 10 1002 nme 4815 which has been published in final form at http onlinelibrary wiley com doi 10 1002 nme 4815 abstract

domain imbedding methods for the stokes equations we study direct and iterative domain imbedding methods for the stokes equations on certain non rectangular domains in two space dimensions we analyze a continuous analog of numerical domain imbedding for bounded smooth domains and give an example of a simple numerical algorithm suggested by the continuous analysis this algorithms is applicable for simply connected domains which can be covered by rectangular grids with uniformly spaced grid lines in at least one coordinate direction we also discuss a related fft based fast solver for stokes problems with physical boundary conditions on rectangles and present some numerical results

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

power transformations to symmetry summary power transformations for achieving distributional symmetry are discussed estimates of the transformation power are based on general measures of symmetry they are shown to be consistent and asymptotically normal use of the skewness coefficient as a measure of symmetry is shown to be optimal in an important special case the methods are compared to the likelihood methods of box cox 1964 and alternative methods of hinkley 1975 1977 the box cox method or a robust adaptation of it carroll 1980 bickel doksum 1981 is found to be the generally most suitable method

on strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method we consider a problem stemming from recent models of phase transitions in stimulus responsive hydrogels wherein a sharp interface separates swelled and collapsed phases extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly fit the interface geometry are emphasized attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface we show that as the reciprocal interfacial mobility vanishes it plays the role of a penalty parameter enforcing a pure dirichlet constraint eventually triggering oscillations in the interfacial velocity we also examine alternative formulations employing a lagrange multiplier to enforce this constraint it is shown that the most convenient choice of basis for the lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms suggesting a lack of stability in the discrete formulation under such conditions neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux fortunately the adaptation and use of local domain integral methodologies considerably improves the flux evaluations several example problems are presented to compare and contrast the various techniques and methods

a family of association coefficients for metric scales four types of metric scales are distinguished the absolute scale the ratio scale the difference scale and the interval scale a general coefficient of association for two variables of the same metric scale type is developed some properties of this general coefficient are discussed it is shown that the matrix containing these coefficients between any number of variables is gramian the general coefficient reduces to specific coefficients of association for each of the four metric scales two of these coefficients are well known the product moment correlation and tucker s congruence coefficient applications of the new coefficients are discussed

simulation of elastic filaments interacting with a viscous pulsatile flow abstract motivated by the need to understand the motion of ruptured atherosclerosis plaque fragments in a flowing blood we simulated flexible elastic filaments interacting with a viscous pulsatile flow in two dimensions using the immersed boundary method our simulations show that 1 a flexible horizontal filament positioned perpendicularly to the flow is a stable configuration and 2 hydrodynamical forces prevent adhesion of filaments but mutual interaction of vortical fields yields clustering of filaments into groups that may be called aggregation

high breakdown inference for mixed linear models mixed linear models are used to analyze data in many settings these models have a multivariate normal formulation in most cases the maximum likelihood estimator mle or the residual mle reml is usually chosen to estimate the parameters however the latter are based on the strong assumption of exact multivariate normality welsh and richardson have shown that these estimators are not robust to small deviations from multivariate normality this means that in practice a small proportion of data even only one can drive the value of the estimates on their own because the model is multivariate we propose a high breakdown robust estimator for very general mixed linear models that include for example covariates this robust estimator belongs to the class of s estimators from which we can derive asymptotic properties for inference we also use it as a diagnostic tool to detect outlying subjects we discuss the advantages of this estimator compared with other robust estimators proposed previously and i

comparison of several independent population means when their samples contain log normal and possibly zero observations summary in this paper we consider the problem of testing the mean equality of several independent populations that contain log normal and possibly zero observations we first showed that the currently used methods in statistical practice including the nonparametric kruskal wallis test the standard anova f test and its two modified versions the welch test and the brown forsythe test could have poor type i error control then we propose a likelihood ratio test that is shown to have much better type i error control than the existing methods finally we analyze two real data sets that motivated our study using the proposed test

estimate of standard deviation for a log transformed variable using arithmetic means and standard deviations analyses of study variables are frequently based on log transformations to calculate the power for detecting the between treatment difference in the log scale we need an estimate of the standard deviation of the log transformed variable however in many situations a literature search only provides the arithmetic means and the corresponding standard deviations without individual log transformed data to directly calculate the sample standard deviation we need alternative methods to estimate it this paper presents methods for estimating and constructing confidence intervals for the standard deviation of a log transformed variable given the mean and standard deviation of the untransformed variable it also presents methods for estimating the standard deviation of change from baseline in the log scale given the means and standard deviations of the untransformed baseline value on treatment value and change from baseline simulations and examples are provided to assess the performance of these estimates

a fictitious domain method for dirichlet problem and applications abstract in this article we discuss the solution of the dirichlet problem for a class of elliptic operators by a lagrange multiplier fictitious domain method this approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries the resulting saddle point system can be solved by an uzawa conjugate gradient algorithm in the case of two dimensional problems a quasi optimal preconditioner has been found by fourier analysis and numerical experiments confirm its nice scaling properties the resulting methodology is applied to a nonlinear time dependent problem namely the flow of a viscous plastic medium in a cylindrical pipe showing the potential of this methodology for some classes of nonlinear problems

transformation to achieve a longitudinally stationary factor pattern matrix meredith s method of extracting a factorially invariant solution is adapted to longitudinal settings an explorational estimation procedure is presented which attempts to identify the longitudinal factor components of an across occasion variance covariance matrix this is effected by transforming an initial factor pattern matrix to stationarity the estimation is performed in two parts the first employing a stepwise algorithm to ascertain the dimensionality and existence of the longitudinal components and the second being the direct estimation of the existing factor pattern

some power considerations when deciding to use transformations conventional wisdom suggests that for small data sets having substantial skew one should attempt to determine the correct distributional form if possible and apply statistical methods appropriate for that distribution transformations such as the log or square root are often used if an appropriate distributional form cannot be determined a distribution free procedure such as a rank transformation or a randomization test procedure can be used to better appreciate the effect of such alternatives on both the type i error and power of detecting differences between treatment groups simulation studies were conducted for responses having specific gamma g r theta and log normal ln m v distributions the gamma and log normal distributions were selected so that they had the same first two moments a simple two group design was assumed the reference group always had an average disease level mu 3 0 mu r theta for gamma mu m for log normal and the treatment group always had means whose reductions ranged from 0 per cent to 50 per cent the effect of distributional type and the degree of skewness was investigated by varying the population parameter values six statistical test procedures were compared for the gamma distributions all test procedures were robust relative to the type i error the ump test based on a ratio of sample means produced the greatest power for all combinations of n r and rt the power losses associated with the randomization test the t test on original scale and the t test on the square root scale were very small 3 per cent to 6 per cent in absolute value for n 10 and 15 and less than 2 per cent for group sizes of 25 or more the power loss associated with the t test on the log scale was much larger ranging from 5 per cent to 10 per cent smaller power than the t test on original scale the wilcoxon rank test produced similar results to that of the log t test for small samples the power for the shifted log x c test increased monotonically to the asymptotic value of the orig t test the same five test procedures based on differences in sample means were then compared for the corresponding log normal distributions the ump test that is log x produced the highest power there was very little power lost for the sqrt t test the loss in power varied between 2 per cent and 5 per cent for the rank test abstract truncated at 400 words

a fictitious domain method for the simulation of thermoelastic deformations in nc milling processes summary this paper presents a higher order finite element approach for the simulation of heat diffusion and thermoelastic deformations in nc milling processes the inherent continuous material removal in the process of the simulation is taken into account via continuous removal dependent refinements of a paraxial hexahedron base mesh covering a given workpiece these refinements rely on isotropic bisections of these hexahedrons along with subdivisions of the latter into tetrahedrons and pyramids in correspondence to a milling surface triangulation obtained from the application of the marching cubes algorithm the resulting mesh is employed for an element wise defined characteristic function for the milling dependent workpiece within that paraxial hexahedron base mesh using this characteristic function a higher order fictitious domain method is used to compute the heat diffusion and thermoelastic deformations where the corresponding ansatz spaces are defined for some hexahedron based refinement of the base mesh numerical experiments compared to real physical experiments exhibit the applicability of the proposed approach to predict deviations of the milled workpiece from its designed shape due to thermoelastic deformations in the process this article is protected by copyright all rights reserved

an operator splitting scheme with a distributed lagrange multiplier based fictitious domain method for wave propagation problems we propose a novel fictitious domain method based on a distributed lagrange multiplier technique for the solution of the time dependent problem of scattering by an obstacle we study discretizations that include a fully conforming approach as well as mixed finite element formulations utilizing the lowest order nedelec edge elements in 2d on rectangular grids we also present a symmetrized operator splitting scheme for the scattering problem which decouples the operator that propagates the wave from the operator that enforces the dirichlet condition on the boundary of an obstacle a new perfectly matched layer pml model is developed to model the unbounded problem of interest this model is based on a formulation of the wave equation as a system of first order equations and uses a change of variables approach that has been developed to construct pml s for maxwell s equations we present an analysis of our fictitious domain approach for a one dimensional wave problem based on calculations of reflection coefficients we demonstrate the advantages of our fictitious domain approach over the staircase approximation of the finite difference method we also demonstrate some important properties of the distributed multiplier approach that are not shared by a boundary multiplier fictitious domain approach for the same problem numerical results for two dimensional wave problems that validate the effectiveness of the different methods are presented

a wald test comparing medical costs based on log normal distributions with zero valued costs medical cost data often exhibit strong skewness and sometimes contain large proportions of zero values such characteristics prevent the analysis of variance anova f test and other frequently used standard tests from providing the correct inferences when the comparison of means is of interest one solution to the problem is to introduce a parametric structure based on log normal distributions with zero values and then construct a likelihood ratio test while such a likelihood ratio test possesses excellent type i error control and power its implementation requires a rather complicated iterative optimization program in this paper we propose a wald test with simple computation we then conduct a monte carlo simulation to compare the type i error rates and powers of the proposed wald test with those of the likelihood ratio test our simulation study indicates that although the likelihood ratio test slightly outperforms the wald test the performance of the wald test is also satisfactory especially when the sample sizes are reasonably large finally we illustrate the use of the proposed wald test by analysing a clinical study assessing the effects of a computerized prospective drug utilization intervention on in patient charges

a cartesian grid nonconforming immersed finite element method for planar elasticity interface problems in this paper a new nonconforming immersed finite element ife method on triangular cartesian meshes is developed for solving planar elasticity interface problems the proposed ife method possesses optimal approximation property for both compressible and nearly incompressible problems its degree of freedom is much less than those of existing finite element methods for the same problem moreover the method is robust with respect to the shape of the interface and its location relative to the domain and the underlying mesh both theory and numerical experiments are presented to demonstrate the effectiveness of the new method theoretically the unisolvent property and the consistency of the ife space are proved experimentally extensive numerical examples are given to show that the approximation orders in l2 norm and semi h1 norm are optimal under various lam parameters settings and different interface geometry configurations

parallel computation of unsteady incompressible viscous flows around moving rigid bodies using an immersed object method with overlapping grids a novel immersed object method is developed for simulating two dimensional unsteady incompressible viscous flows around arbitrarily moving rigid bodies it has been implemented in a parallel unstructured finite volume incompressible navier stokes solver based on the artificial compressibility ac approach using a higher order characteristics based upwind scheme and matrix free implicit dual time stepping in the immersed object method an object is immersed in the flow field and it is supposed to contain frozen fluid which moves like a solid body this is realized by introducing source terms in the momentum equations during the ac sub iterations an internal mesh within the object is employed to search and locate all the eulerian nodes within the object in every time step for imposing the source terms unlike many existing methods this method does not require complex searching extrapolation and interpolation to find the intersections of the object boundary with the unstructured background mesh and assign flow condition onto the object boundary if it is necessary to capture the boundary layer accurately then a dense overlapping grid can then be constructed around the object for further refined calculation the immersed object method has been used to simulate steady and unsteady incompressible viscous flows over a stationary circular cylinder rotating square cylinder and moving disk in cavity the results agree well with published numerical solutions and experimental measurements

the effects of transformations and preliminary tests for non linearity in regression non linear relationships between two variables are often detected as a result of a preliminary statistical test for linearity common approaches to dealing with non linearity are to a make a linearizing transformation in the independent variable or b fit a relationship that is non linear in the independent variable such as including a quadratic term with either approach the resulting test for association between the two variables can have an inflated type i error we consider testing the significance of the quadratic term in a quadratic model as a preliminary test for non linearity using simulation experiments and asymptotic arguments we quantify the type i error inflation and suggest simple modifications of standard practice to protect the size of the type i error in the case of quadratic regression the type i error will be increased by roughly 50 per cent the simple strategy of appropriately correcting the alpha level is shown to have minimal loss of power if the relationship is truly linear in the case of a linearizing transformation the impact on the type i error will depend on the values of the independent variable and on the set of potential linearizing transformations considered simulation results suggest that a procedure which adjusts the test statistic according to the results of the preliminary test may offer adequate protection

the use of a mixture model in the analysis of count data a mixture model is presented for the analysis of data on premature ventricular contractions the analysis is shown to be straightforward and the conclusions relatively simple

the log transformation is special the logarithmic log transformation is a simple yet controversial step in the analysis of positive continuous data measured on an interval scale situations where a log transformation is indicated will be reviewed this paper contends that the log transformation should not be classed with other transformations as it has particular advantages problems with using the data themselves to decide whether or not to transform will be discussed it is recommended that log transformed analyses should frequently be preferred to untransformed analyses and that careful consideration should be given to use of a log transformation at the protocol design stage