robust models in probability sampling in the estimation of a population mean or total from a random sample certain methods based on linear models are known to be automatically design consistent regardless of how well the underlying model describes the population a sufficient condition is identified for this type of robustness to model failure the condition which we call internal bias calibration relates to the combination of a model and the method used to fit it included among the internally bias calibrated models in addition to the aforementioned linear models are certain canonical link generalized linear models and nonparametric regressions constructed from them by a particular style of local likelihood fitting other models can often be made robust by using a suboptimal fitting method thus the class of model based but design consistent analyses is enlarged to include more realistic models for certain types of survey variable such as binary indicators and counts particular applications discussed are the estimation of the size of a population subdomain as arises in tax auditing for example and the estimation of a bootstrap tail probability

evaluation of eeg localization methods using realistic simulations of interictal spikes performing an accurate localization of sources of interictal spikes from eeg scalp measurements is of particular interest during the presurgical investigation of epilepsy the purpose of this paper is to study the ability of six distributed source localization methods to recover extended sources of activated cortex due to the frequent lack of a gold standard to evaluate source localization methods our evaluation was performed in a controlled environment using realistic simulations of eeg interictal spikes involving several anatomical locations with several spatial extents simulated data were corrupted by physiological eeg noise simulations involving pairs of sources with the same amplitude were also studied in addition to standard validation criteria e g geodesic distance or mean square error we proposed an original criterion dedicated to assess detection accuracy based on receiver operating characteristic roc analysis six source localization methods were evaluated the minimum norm the minimum norm weighted by multivariate source prelocalization msp cortical loreta with or without additional minimum norm regularization and two derivations of the maximum entropy on the mean mem approach results showed that loreta based and mem based methods were able to accurately recover sources of different spatial extents with the exception of sources in temporo mesial and fronto mesial regions several spurious sources were generated by those methods however whereas methods using the msp always located very accurately the maximum of activity but not its spatial extent these findings suggest that one should always take into account the results from different localization methods when analyzing real interictal spikes

marginal longitudinal nonparametric regression locality and efficiency of spline and kernel methods we consider nonparametric regression in a longitudinal marginal model of generalized estimating equation gee type with a time varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large in such models the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations two methods of estimating the nonparametric function can be considered kernel methods and spline methods recently surprising evidence has emerged suggesting that for kernel methods previously proposed in the literature it is generally asymptotically preferable to ignore the correlation structure in our marginal model and instead assume that the data are independent that is working independence in the gee jargon as seen through equivalent kernel results in univariate independent data problems splines and kernels have similar behavior smoothing splines are equivalent to kernel regression with a s

partial orders of similarity differences invariant between eeg recorded brain and perceptual representations of language the idea of a hierarchical structure of language constituents of phonemes syllables words and sentences is robust and widely accepted empirical similarity differences at every level of this hierarchy have been analyzed in the form of confusion matrices for many years by normalizing such data so that differences are represented by conditional probabilities semiorders of similarity differences can be constructed the intersection of two such orderings is an invariant partial ordering with respect to the two given orders these invariant partial orderings especially between perceptual and brain representations but also for comparison of brain images of words generated by auditory or visual presentations are the focus of this letter data from four experiments are analyzed with some success in finding conceptually significant invariants

discontinuous galerkin finite element approximation of the cahn hilliard equation with convection the paper is concerned with the construction and convergence analysis of a discontinuous galerkin finite element method for the cahn hilliard equation with convection using discontinuous piecewise polynomials of degree p geq1 and backward euler discretization in time we show that the order parameter c is approximated in the broken rm l infty rm h 1 norm with optimal order cal o h p tau the associated chemical potential w phi c gamma 2 delta c is shown to be approximated with optimal order cal o h p tau in the broken rm l 2 rm h 1 norm here phi c frac 1 4 1 c 2 2 is a quartic free energy function and gamma 0 is an interface parameter numerical results are presented with polynomials of degree p 1 2 3

self replicating spots in reaction diffusion systems in this article we discuss the self replicating spot a particlelike phenomenon that occurs in reaction diffusion rd systems 1 the spots consist of localized regions in which the concentrations of the reactants differ from the surrounding concentration fields they grow reaching a critical size at which time they divide in two the two resulting spots again grow and divide this process which is visually similar to cell division continues indefinitely the long time behavior depends on the precise values of the external control parameters but typically consists of a chaotic soup in which many spots compete for resources as illustrated in fig 1 those spots that find adequate resources continue to grow and divide those that are unable to find adequate resources decay into the background the spots observed in 1 were found during an attempt to model labyrinthine patterns in the ferrocyanide iodate sulfate fis reaction 2 since then replicating spot patterns have been observed both numerically and experimentally in the fis reaction 3 4 there are obvious differences in the gaspar showalter model of the fis reaction 5 and of the models discussed by us and others this fact suggests that replication is a generic feature characterizing a broad class of reaction diffusion systems in 6 we presented some arguments in support of this proposition these arguments included both a heuristic description of the process of replication and demonstrations of analytic features common to several related model rd systems it turns out that replication is more general than our analysis accounts for nevertheless we think it worthwhile to spell out the details of the theory presented in 6 we remark here that various aspects of the replication phenomenon have been discussed by other authors 7 8 kerner and osipov have a large body of work on largeamplitude dissipative structures including an analysis of the static division of one dimensional pulses as the system size is changed gurevich and mints have a body of work on replication of thermal hot spots in composite superconductors in the article by petrov scott and showalter replication

slowly modulated two pulse solutions in the gray scott model i asymptotic construction and stability two pulse solutions play a central role in the phenomena of self replicating pulses in the one dimensional 1 d gray scott model in the present work part i of two parts we carry out an existence study for solutions consisting of two symmetric pulses moving apart from each other with slowly varying velocities this corresponds to a mildly strong pulse interaction problem in which the inhibitor concentration varies on long spatial length scales critical maximum wave speeds are identified and odes are derived for the wave speed and for the separation distance between the pulses in addition the formal linear stability of these two pulse solutions is determined good agreement is found between these theoretical predictions and the results from numerical simulations the main methods used in this paper are analytical singular perturbation theory for the existence demonstration and the nonlocal eigenvalue problem nlep method developed in our earlier work for the stability analysis the analysis of

an adaptive finite element moreau yosida based solver for a coupled cahn hilliard navier stokes system an adaptive a posteriori error estimator based finite element method for the numerical solution of a coupled cahn hilliard navier stokes system with a double obstacle homogenous free interfacial energy density is proposed a semi implicit euler scheme for the time integration is applied which results in a system coupling a quasi stokes or oseen type problem for the fluid flow to a variational inequality for the concentration and the chemical potential according to the cahn hilliard model 16 a moreau yosida regularization is employed which relaxes the constraints contained in the variational inequality and thus enables semi smooth newton solvers with locally superlinear convergence in function space moreover upon discretization this yields a mesh independent method for a fixed relaxation parameter for the finite dimensional approximation of the concentration and the chemical potential piecewise linear and globally continuous finite elements are used and for the numerical approximation of the fluid velocity taylor hood finite elements are employed the paper ends by a report on numerical examples showing the efficiency of the new method

a wavelet or lifting scheme based imputation method summary the paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis our method incorporates a bayesian mixture prior for these wavelet coefficients into a gibbs sampler to generate a complete posterior distribution for the variable of interest intuitively the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites we demonstrate the strong performance of our estimator in both one and two dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines

existence and stability of multiple spot solutions for the gray scott model in r2 abstract in this paper we rigorously prove the existence and stability of multiple spot patterns for the gray scott system in a two dimensional domain which are far from spatial homogeneity the green s function and its derivatives together with two nonlocal eigenvalue problems both play a major role in the analysis we establish a threshold behavior for stability if a certain inequality for the parameters holds then we get stability otherwise we get instability of multiple spot solutions the exact asymptotics of the critical thresholds are obtained

an overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies relative survival provides a measure of the proportion of patients dying from the disease under study without requiring the knowledge of the cause of death we propose an overall strategy based on regression models to estimate the relative survival and model the effects of potential prognostic factors the baseline hazard was modelled until 10 years follow up using parametric continuous functions six models including cubic regression splines were considered and the akaike information criterion was used to select the final model this approach yielded smooth and reliable estimates of mortality hazard and allowed us to deal with sparse data taking into account all the available information splines were also used to model simultaneously non linear effects of continuous covariates and time dependent hazard ratios this led to a graphical representation of the hazard ratio that can be useful for clinical interpretation estimates of these models were obtained by likelihood maximization we showed that these estimates could be also obtained using standard algorithms for poisson regression

stationary patterns caused by cross diffusion for a three species prey predator model we study a system arising from a three component prey predator model with prey dependent and ratio dependent functional responses where cross diffusion is included in such a way that predator chases the prey and the prey runs away from the predator we prove that the cross diffusion can generate the stationary patterns nonconstant positive steady states

dynamics of two compartment gray scott equations abstract in this work the existence of a global attractor is proved for the solution semiflow of the coupled two compartment gray scott equations with the homogeneous neumann boundary condition on a bounded domain of space dimension n 3 the grouping estimation method combined with a new decomposition approach is introduced to overcome the difficulties in proving the absorbing property and the asymptotic compactness of this four component reaction diffusion systems with cubic autocatalytic nonlinearity and linear coupling the finite dimensionality of the global attractor is also proved

estimation of global temperature fields from scattered observations by a spherical wavelet based spatially adaptive method summary the paper considers the problem of estimating the entire temperature field for every location on the globe from scattered surface air temperatures observed by a network of weatherstations classical methods such as spherical harmonics and spherical smoothing splines are not efficient in representing data that have inherent multiscale structures the paper presents an estimation method that can adapt to the multiscale characteristics of the data the method is based on a spherical wavelet approach that has recently been developed for a multiscale representation and analysis of scattered data spatially adaptive estimators are obtained by coupling the spherical wavelets with different thresholding selective reconstruction techniques these estimators are compared for their spatial adaptability and extrapolation performance by using the surface air temperature data

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

a practically unconditionally gradient stable scheme for the n component cahn hilliard system we present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the n component cahn hilliard system modeling the phase separation of an n component mixture the scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method and the scheme allows us to convert the n component cahn hilliard system into a system of n 1 binary cahn hilliard equations and significantly reduces the required computer memory and cpu time we observe that our numerical solutions are consistent with the linear stability analysis results we also demonstrate the efficiency of the proposed scheme with various numerical experiments

a novel consistent and well balanced algorithm for simulations of multiphase flows on unstructured grids abstract we discuss the development and assessment of a robust numerical algorithm for simulating multiphase flows with complex interfaces and high density ratios on arbitrary polygonal meshes the algorithm combines the volume of fluid method with an incremental projection approach for incompressible multiphase flows in a novel hybrid staggered non staggered framework the key principles that characterise the algorithm are the consistent treatment of discrete mass and momentum transport and the similar discretisation of force terms appearing in the momentum equation the former is achieved by invoking identical schemes for convective transport of volume fraction and momentum in the respective discrete equations while the latter is realised by representing the gravity and surface tension terms as gradients of suitable scalars which are then discretised in identical fashion resulting in a balanced formulation the hybrid staggered non staggered framework employed herein solves for the scalar normal momentum at the cell faces while the volume fraction is computed at the cell centroids this is shown to naturally lead to similar terms for pressure and its correction in the momentum and pressure correction equations respectively which are again treated discretely in a similar manner we show that spurious currents that corrupt the solution may arise both from an unbalanced formulation where forces gravity and surface tension are discretised in dissimilar manner and from an inconsistent approach where different schemes are used to convect the mass and momentum with the latter prominent in flows which are convection dominant with high density ratios interestingly the inconsistent approach is shown to perform as well as the consistent approach even for high density ratio flows in some cases while it exhibits anomalous behaviour for other scenarios even at low density ratios using a plethora of test problems of increasing complexity we conclusively demonstrate that the consistent transport and balanced force treatment results in a numerically stable solution procedure and physically consistent results the algorithm proposed in this study qualifies as a robust approach to simulate multiphase flows with high density ratios on unstructured meshes and may be realised in existing flow solvers with relative ease

a numerical method for the incompressible navier stokes equations based on an approximate projection in this method we present a fractional step discretization of the time dependent incompressible navier stokes equations the method is based on a projection formulation in which we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields our treatment of the diffusion convection step uses a specialized second order upwind method for differencing the nonlinear convective terms that provides a robust treatment of these terms at a high reynolds number in contrast to conventional projection type discretizations that impose a discrete form of the divergence free constraint we only approximately impose the constraint i e the velocity field we compute is not exactly divergence free the approximate projection is computed using a conventional discretization of the laplacian and the resulting linear system is solved using conventional multigrid methods numerical examples are presented to validate the second order convergence of the method for euler finite reynolds number and stokes flow a second example illustrating the behavior of the algorithm on an unstable shear layer is also presented

brain wave representation of words by superposition of a few sine waves data from three previous experiments were analyzed to test the hypothesis that brain waves of spoken or written words can be represented by the superposition of a few sine waves first we averaged the data over trials and a set of subjects and in one case over experimental conditions as well next we applied a fourier transform to the averaged data and selected those frequencies with high energy in no case more than nine in number the superpositions of these selected sine waves were taken as prototypes the averaged unfiltered data were the test samples the prototypes were used to classify the test samples according to a least squares criterion of fit the results were seven of seven correct classifications for the first experiment using only three frequencies six of eight for the second experiment using nine frequencies and eight of eight for the third experiment using five frequencies

additive cubic spline regression with dirichlet process mixture errors abstract the goal of this article is to develop a flexible bayesian analysis of regression models for continuous and categorical outcomes in the models we study covariate or regression effects are modeled additively by cubic splines and the error distribution that of the latent outcomes in the case of categorical data is modeled as a dirichlet process mixture we employ a relatively unexplored but attractive basis in which the spline coefficients are the unknown function ordinates at the knots we exploit this feature to develop a proper prior distribution on the coefficients that involves the first and second differences of the ordinates quantities about which one may have prior knowledge we also discuss the problem of comparing models with different numbers of knots or different error distributions through marginal likelihoods and bayes factors which are computed within the framework of chib 1995 as extended to dpm models by basu and chib 2003 the techniques are illustrated with simulated and real data

a skeleton structure of self replicating dynamics abstract self replicating patterns srp have been observed in several chemical reaction models such as the gray scott gs model as well as in physical experiments watching these experiments computational and physical is like watching the more familiar coarsening processes but in reverse the number of unit localized patterns increases until they fill the domain completely self replicating dynamics then can be regarded as a transient process from a localized trigger to a stable stationery or oscillating turing pattern since it is a transient process it is very difficult to give a suitable definition to characterize srp it cannot be described in terms of well studied structures such as the attractor or a singular saddle orbit for a dynamical system in this paper we present a new point of view to describe the transient dynamics of srp over a finite interval of time we focus our attention on the basic mechanism causing srp from a global bifurcational point of view and take our clues from two model systems including the gs model a careful analysis of the anatomy of the global bifurcation diagram suggests that the dynamics of srp is related to a hierarchical structure of limit points of folding bifurcation branches in parameter regions where the branches have ceased to exist thus the skeleton structure mentioned in the title refers to the remains of bifurcation branches the aftereffects of which are manifest in the dynamics of srp one of the natural and important problems is about the existence of an organizing center from which the whole hierarchical structure of limit points emerges in our setting the numerics suggests a strong candidate for that i e bogdanov takens turing btt singularity together with the presence of a stable critical point and so this indicates a universality of the above structure in the class of equations sharing this characteristic

a stochastic daily weather generator for skewed data 1 to simulate multivariate daily time series minimum and maximum temperatures global radiation wind speed and precipitation intensity we propose a weather state approach with a multivariate closed skew normal generator wacs gen that is able to accurately reproduce the statistical properties of these five variables our weather generator construction takes advantage of two elements we first extend the classical wet and dry days dichotomy used in most past weather generators to the definition of multiple weather states using clustering techniques the transitions among weather states are modeled by a first order markov chain second the vector of our five daily variables of interest is sampled conditionally on these weather states from a closed skew normal distribution this class of distribution allows us to handle nonsymmetric behaviors our method is applied to the 20 years of daily weather measurements from colmar france this example illustrates the advantages of our approach especially improving the simulation of radiation and wind distributions

fast l p solution of large sparse linear systems application to seismic travel time tomography least squares inversion tends to be sensitive to small changes in the assumptions in the statistical lexicon it is not robust least squares solutions of noisy ill conditioned systems often exhibit unphysical high frequency oscillations which have to be damped or smoothed in some fashion the iteratively reweighted least squares irls algorithm provides a means of computing approximate lp solutions 1 p we will show that irls can be combined with the preconditioned conjugate gradient algorithm in order to solve large sparse rectangular systems of linear algebraic equations very efficiently further for p 1 the resulting algorithm is extremely stable it seems to give reasonably smooth solutions without minute adjustment of the parameters and does not become unstable if an overly optimistic error estimate is used it also has the ability to reject or at least significantly diminish the influence of outliers in the data and does not require the use of damping in addition we will show how to efficiently include diagonal weighting of the observations and parameters in order to incorporate a priori information into the inversion this combined inversion algorithm has wide applicability in real world inverse theory parameter estimation filtering etc where data are noisy and not uniformly reliable numerical examples of the l1 inversion of noisy seismic travel time data will be shown

optimal spline smoothing of fmri time series by generalized cross validation linear parametric regression models of fmri time series have correlated residuals one approach to address this problem is to condition the autocorrelation structure by temporal smoothing smoothing splines with the degree of smoothing selected by generalized cross validation gcv spline provide a method to find an optimal smoother for an fmri time series the purpose of this study was to determine if gcv spline of fmri time series yields unbiased variance estimates of linear regression model parameters gcv spline was evaluated with a real fmri data set and bias of the variance estimator was computed for simulated time series with autocorrelation structures derived from fmri data this study only considered fmri experimental designs of boxcar type the results from the real data suggest that gcv spline determines appropriate amounts of smoothing the simulations show that the variance estimates are on average unbiased the unbiased variance estimates come at some cost to signal detection efficiency this study demonstrates that gcv spline is an appropriate method for smoothing fmri time series

asymptotic confidence regions for kernel smoothing of a varying coefficient model with longitudinal data abstract we consider the estimation of the k 1 dimensional nonparametric component t of the varying coefficient model y t x t t t e t based on longitudinal observations yij x i tij tij i 1 n j 1 ni where tij is the jth observed design time point t of the ith subject and yij and x i tij are the real valued outcome and r k 1 valued covariate vectors of the ith subject at tij the subjects are independently selected but the repeated measurements within subject are possibly correlated asymptotic distributions are established for a kernel estimate of t that minimizes a local least squares criterion these asymptotic distributions are used to construct a class of approximate pointwise and simultaneous confidence regions for t applying these methods to an epidemiological study we show that our procedures are useful for predicting cd4 t helper lymphocytes cell changes among hiv human immunodeficiency virus infected persons the finite sample properties of o

quasi incompressible cahn hilliard fluids and topological transitions one of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect it is well known that classical methods involving sharp interfaces fail to describe this type of phenomena following some previous work in this area we suggest a physically motivated regularization of the euler equations which allows topological transitions to occur smoothly in this model the sharp interface is replaced by a narrow transition layer across which the fluids may mix the model describes a flow of a binary mixture and the internal structure of the interface is determined by both diffusion and motion an advantage of our regularization is that it automatically yields a continuous description of surface tension which can play an important role in topological transitions an additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the euler or navier stokes and the cahn hilliard equations the model takes into account weak non locality dispersion associated with an internal length scale and localized dissipation due to mixing the non locality introduces a dimensional surface energy dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes in particular we study a non trivial limit when both components are incompressible the pressure is kinematic but the velocity field is non solenoidal quasi incompressibility to demonstrate the effects of quasi incompressibility we analyse the linear stage of spinodal decomposition in one dimension we show that when the densities of the fluids are not perfectly matched the evolution of the concentration field causes fluid motion even if the fluids are inviscid in the limit of infinitely thin and well separated interfacial layers an appropriately scaled quasi incompressible euler cahn hilliard system converges to the classical sharp interface model in order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity

quantile regression methods for reference growth charts estimation of reference growth curves for children s height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population age specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods non parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions we compare estimated reference curves for height using the penalized likelihood approach of cole and green statistics in medicine 1992 11 1305 1319 with quantile regression curves based on data used for modern finnish reference charts an advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated copyright 2005 john wiley sons ltd

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

global dynamics and robustness of reversible autocatalytic reaction diffusion systems abstract global asymptotic dynamics of a representative cubic autocatalytic reaction diffusion system the reversible selkov equations are investigated this system features two pairs of oppositely signed nonlinear terms so that the asymptotic dissipative condition is not satisfied which causes substantial difficulties in an attempt to attest that the longtime dynamics are asymptotically dissipative an l 2 to h 1 global attractor of finite fractal dimension is shown to exist for the semiflow of the weak solutions of the reversible selkov equations with the dirichlet boundary condition on a bounded domain of dimension n 3 a new method of rescaling and grouping estimation is used to prove the absorbing property and the asymptotical compactness importantly the upper semicontinuity robustness in the h 1 product space of the global attractors for the family of solution semiflows with respect to the reverse reaction rate as it tends to zero is proved through a new approach of transformative decomposition to overcome the barrier of the perturbed singularity between the reversible and non reversible systems by showing the uniform dissipativity and the uniformly bounded evolution of the union of global attractors under the bundle of reversible and non reversible semiflows

solving the meg inverse problem a robust two way regularization method magnetoencephalography meg is a common noninvasive imaging modality for instantly measuring whole brain activities one challenge in meg data analysis is how to minimize the impact of the outliers that commonly exist in the images in this article we propose a robust two way regularization approach to solve the important meg inverse problem that is reconstructing neuronal activities using the measured meg signals the proposed method is based on the distributed source model and produces a spatio temporal solution for all the dipoles simultaneously unlike the traditional methods that use the squared error loss function our proposal uses a robust loss function which improves the robustness of the results against outliers to impose desirable spatial focality and temporal smoothness we then penalize the robust loss through appropriate spatial temporal two way regularization furthermore an alternating reweighted least squares algorithm is developed to optimize the penalized model fitting criterion

stability of multivariable fractional polynomial models with selection of variables and transformations a bootstrap investigation sauerbrei and royston have recently described an algorithm based on fractional polynomials for the simultaneous selection of variables and of suitable transformations for continuous predictors in a multivariable regression setting they illustrated the approach by analyses of two breast cancer data sets here we extend their work by considering how to assess possible instability in such multivariable fractional polynomial models we first apply the algorithm repeatedly in many bootstrap replicates we then use log linear models to investigate dependencies among the inclusion fractions for each predictor and among the simplified classes of fractional polynomial function chosen in the bootstrap samples to further evaluate the results we define measures of instability based on a decomposition of the variability of the bootstrap selected functions in relation to a reference function from the original model for each data set we are able to identify large reasonably stable subsets of the bootstrap replications in which the functional forms of the predictors appear fairly stable despite the considerable flexibility of the family of fractional polynomials and the consequent risk of overfitting when several variables are considered we conclude that the multivariable selection algorithm can find stable models

a comparison of random field theory and permutation methods for the statistical analysis of meg data we describe the use of random field and permutation methods to detect activation in cortically constrained maps of current density computed from meg data the methods are applicable to any inverse imaging method that maps event related meg to a coregistered cortical surface these approaches also extend directly to images computed from event related eeg data we determine statistical thresholds that control the familywise error rate fwer across space or across both space and time both random field and permutation methods use the distribution of the maximum statistic under the null hypothesis to find fwer thresholds the former methods make assumptions on the distribution and smoothness of the data and use approximate analytical solutions the latter resample the data and rely on empirical distributions both methods account for spatial and temporal correlation in the cortical maps unlike previous nonparametric work in neuroimaging we address the problem of nonuniform specificity that can arise without a gaussianity assumption we compare and evaluate the methods on simulated data and experimental data from a somatosensory evoked response study we find that the random field methods are conservative with or without smoothing though with a 5 vertex fwhm smoothness they are close to exact our permutation methods demonstrated exact specificity in simulation studies in real data the permutation method was not as sensitive as the rf method although this could be due to violations of the random field theory assumptions

comparing the shapes of regression functions summary does a regression function follow a specified shape do two regression functions have the same shape how can regression functions be grouped based on shape these questions can occur when investigating monotonicity when counting local maxima or when studying variation in families of curves one can address these questions by considering the rank correlation coefficient between two functions this correlation is a generalisation of the rank correlation between two finite sets of numbers and is equal to one if and only if the two functions have the same shape a sample rank correlation based on smoothed estimates of the regression functions consistently estimates the true correlation this sample rank correlation can be used as a measure of similarity between functions in cluster analysis and as a measure of monotonicity or modality

goodness of fit tests for parametric regression models several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives these tests formally check if the bias vector of residuals from parametric fits is negligible by using the adaptive neyman test and other methods the testing procedures formalize the traditional model diagnostic tools based on residual plots we examine the rates of contiguous alternatives that can be detected consistently by the adaptive neyman test applications of the procedures to the partially linear models are thoroughly discussed our simulation studies show that the new testing procedures are indeed powerful and omnibus the power of the proposed tests is comparable to the f test statistic even in the situations where the f test is known to be suitable and can be far more powerful than the f test statistic in other situations an application to testing linear models versus additive models is also discussed

comparison of the spatial resolution of source imaging techniques in high density eeg and meg abstract background the present study aims at evaluating and comparing electrical and magnetic distributed source imaging methods applied to high density electroencephalography hdeeg and magnetoencephalography meg data we used resolution matrices to characterize spatial resolution properties of minimum norm estimate mne dynamic statistical parametric mapping dspm standardized low resolution electromagnetic tomography sloreta and coherent maximum entropy on the mean cmem an entropy based technique the resolution matrix provides information of the point spread functions psf and of the crosstalk functions ct this latter being also called source leakage as it reflects the influence of a source on its neighbors methods the spatial resolution of the inverse operators was first evaluated theoretically and then with real data acquired using electrical median nerve stimulation on five healthy participants we evaluated the dipole localization error dle and the spatial dispersion sd of each psf and ct map results cmem showed the smallest spatial spread sd for both psf and ct maps whereas localization errors dle were similar for all methods whereas cmem sd values were lower in meg compared to hdeeg the other methods slightly favored hdeeg over meg in real data cmem provided similar localization error and significantly less spatial spread than other methods for both meg and hdeeg whereas both meg and hdeeg provided very accurate localizations all the source imaging methods actually performed better in meg compared to hdeeg according to all evaluation metrics probably due to the higher signal to noise ratio of the data in meg conclusion our overall results show that all investigated methods provide similar localization errors suggesting very accurate localization for both meg and hdeeg when similar number of sensors are considered for both modalities intrinsic properties of source imaging methods as well as their behavior for well controlled tasks suggest an overall better performance of cmem in regards to spatial resolution and spatial leakage for both hdeeg and meg this indicates that cmem would be a good candidate for studying source localization of focal and extended generators as well as functional connectivity studies

functional linear discriminant analysis for irregularly sampled curves we introduce a technique for extending the classical method of linear discriminant analysis lda to data sets where the predictor variables are curves or functions this procedure which we call functional linear discriminant analysis flda is particularly useful when only fragments of the curves are observed all the techniques associated with lda can be extended for use with flda in particular flda can be used to produce classifications on new test curves give an estimate of the discriminant function between classes and provide a one or two dimensional pictorial representation of a set of curves we also extend this procedure to provide generalizations of quadratic and regularized discriminant analysis

analysis of oldest old mortality lifetables revisited ing the hazard function we provide rigorous asymptotic results for the smoothing of lifetables and show that the transformation approach is supported by both asymptotic and simulation results we also demonstrate how the information contained in many samples of lifetables as typically obtained in aging experiments can be summarized in a twodimensional hazard surface

source localization using recursively applied and projected rap music a new method for source localization is described that is based on a modification of the well known music algorithm in classical music the array manifold vector is projected onto an estimate of the signal subspace errors in the estimate of the signal subspace can make localization of multiple sources difficult recursively applied and projected rap music uses each successively located source to form an intermediate array gain matrix and projects both the array manifold and the signal subspace estimate into its orthogonal complement the music projection to find the next source is then performed in this reduced subspace special assumptions about the array manifold structure such as vandermonde or shift invariance are not required using the metric of principal angles we describe a general form of the rap music algorithm for the case of diversely polarized sources through a uniform linear array simulation with two highly correlated sources we demonstrate the improved monte carlo error performance of rap music relative to music and two other sequential subspace methods s and ies music we then demonstrate the more general utility of this algorithm for multidimensional array manifolds in a magnetoencephalography meg source localization simulation

characterization of a family of algorithms for generalized discriminant analysis on undersampled problems a generalized discriminant analysis based on a new optimization criterion is presented the criterion extends the optimization criteria of the classical linear discriminant analysis lda when the scatter matrices are singular an efficient algorithm for the new optimization problem is presented the solutions to the proposed criterion form a family of algorithms for generalized lda which can be characterized in a closed form we study two specific algorithms namely uncorrelated lda ulda and orthogonal lda olda ulda was previously proposed for feature extraction and dimension reduction whereas olda is a novel algorithm proposed in this paper the features in the reduced space of ulda are uncorrelated while the discriminant vectors of olda are orthogonal to each other we have conducted a comparative study on a variety of real world data sets to evaluate ulda and olda in terms of classification accuracy

brain wave recognition of words electrical and magnetic brain waves of seven subjects under three experimental conditions were recorded for the purpose of recognizing which one of seven words was processed the analysis consisted of averaging over trials to create prototypes and test samples to both of which fourier transforms were applied followed by filtering and an inverse transformation to the time domain the filters used were optimal predictive filters selected for each subject and condition recognition rates based on a least squares criterion varied widely but all but one of 24 were significantly different from chance the two best were above 90 these results show that brain waves carry substantial information about the word being processed under experimental conditions of conscious awareness

slowly modulated two pulse solutions in the gray scott model ii geometric theory bifurcations and splitting dynamics with great sadness we note the passing away of our mentor and colleague wiktor abstract in this second paper we develop a geometrical method to systematically study the singular perturbed problem associated to slowly modulated two pulse solutions it enables one to see that the characteristics of these solutions are strongly determined by the flow on a slow manifold and hence also to identify the saddle node bifurcations and bifurcations to classical traveling waves in which the solutions constructed in part i are created and annihilated moreover we determine the geometric origin of the critical maximum wave speeds discovered in part i in this paper we also study the central role of the slowly varying inhibitor component of the two pulse solutions in the pulse splitting bifurcations finally the validity of the quasi stationary approximation is established here and we relate the results of both parts of this work to the literature on self replication

a spline framework for estimating the eeg surface laplacian using the euclidean metric this letter develops a framework for eeg analysis and similar applications based on polyharmonic splines this development overcomes a basic problem with the method of splines in the euclidean setting that it does not work on low degree algebraic surfaces such as spherical and ellipsoidal scalp models the method s capability is illustrated through simulations on the three sphere model and using empirical data

stability analysis of singular patterns in the 1d gray scott model a matched asymptotics approach abstract in this work we analyze the linear stability of singular homoclinic stationary solutions and spatially periodic stationary solutions in the one dimensional gray scott model this stability analysis has several implications for understanding the recently discovered phenomena of self replicating pulses for each solution constructed in a doelman et al nonlinearity 10 1997 523 563 we analytically find a large open region in the space of the two scaled parameters in which it is stable specifically for each value of the scaled inhibitor feed rate there exists an interval whose length and location depend on the solution type of values of the activator autocatalyst decay rate for which the solution is stable the upper boundary of each interval corresponds to a subcritical hopf bifurcation point and the lower boundary is explicitly determined by finding the parameter value where the solution disappears i e below which it no longer exists as a solution of the steady state system explicit asymptotic formulae show that the one pulse homoclinic solution gains stability first as the second parameter is decreased and then successively the spatially periodic solutions with decreasing period become stable moreover the stability intervals for different solutions overlap these stability results are derived via the reduction of a fourth order slow fast eigenvalue problem to a second order nonlocal eigenvalue problem nlep explicit determination of these stability intervals plays a central role in understanding pulse self replication numerical simulations confirm that the spatially periodic stationary solutions are attractors in the pulse splitting regime and moreover whenever for a given solution the value of the activator decay rate was taken to lie in the regime below that solution s stability interval initial data close to that solution were observed to evolve toward a different spatially periodic stationary solution one whose stability interval inclucded the parameter value the main analytical technique used is that of matched asymptotic expansions

axisymmetric ring solutions of the 2d gray scott model and their destabilization into spots this article concerns annular ring solutions of the gray scott model in the monostable regime annular rings are far fromequilibrium patterns supported on annuli inside of which the activator is concentrated the diffusive flux of inhibitor over long length scales toward such an annulus feeds the production of activator there and the interaction is semi strong numerical and experimental observations show that annular rings often split into spots and the main result presented in this article is a method to predict the number of spots that an annular ring unstable to angular disturbances will split into this method is an extension to 2d circular geometries of the nonlocal eigenvalue problem nlep method developed for pulse solutions of the 1d gray scott problem in which the full eigenvalue problem a pair of second order nonautonomous coupled equations is recast as a single second order equation with a nonlocal term we also continue the results for the monostable regime into the bistable regime of the gray scott model where target patterns exist and their rings are observed to destabilize into rings of spots as may be shown using a classical turing ginzburg landau analysis thus for these 2d circular geometries the nlep method is to the instability of annular rings in the monostable regime what the turing analysis is to the instability of target patterns in the bistable regime near criticality 2004 elsevier b v all rights reserved

exact homoclinic and heteroclinic solutions of the gray scott model for autocatalysis in this paper we obtain explicit nontrivial stationary patterns in the one dimensional gray scott model for cubic autocatalysis involved in the reaction are two chemicals a and b whose diffusion coefficients are denoted by da and db respectively the chemical a is fed into the system at a rate kf reacts with the catalyst b at a rate k1 and the catalyst decays at a rate k2 if these parameters obey the relation kf da k2 db then for appropriate values of the rate constants we present explicit expressions for two families of pulses and one kink we also show that if is only satisfied approximately these families of pulses are preserved and there exists a smooth branch of kinks leading from the explicit one obtained when is satisfied we determine the local behavior of this branch near the explicit kink

an efficient interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow in sussman smereka and osher j comp phys 94 1994 pp 146 159 a numerical scheme was presented for computing incompressible air water flows using the level set method crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set in this paper we implement a constraint along with higher order difference schemes in order to make the iteration method more accurate and efficient accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set we apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost we validate our results with experiment and theory we show that our distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface we perform basic accuracy checks and more stringent tests involving complicated interfacial structures as with all level set schemes our method is easy to implement

the impact of meg source reconstruction method on source space connectivity estimation a comparison between minimum norm solution and beamforming despite numerous important contributions the investigation of brain connectivity with magnetoencephalography meg still faces multiple challenges one critical aspect of source level connectivity largely overlooked in the literature is the putative effect of the choice of the inverse method on the subsequent cortico cortical coupling analysis we set out to investigate the impact of three inverse methods on source coherence detection using simulated meg data to this end thousands of randomly located pairs of sources were created several parameters were manipulated including inter and intra source correlation strength source size and spatial configuration the simulated pairs of sources were then used to generate sensor level meg measurements at varying signal to noise ratios snr next the source level power and coherence maps were calculated using three methods a l2 minimum norm estimate mne b linearly constrained minimum variance lcmv beamforming and c dynamic imaging of coherent sources dics beamforming the performances of the methods were evaluated using receiver operating characteristic roc curves the results indicate that beamformers perform better than mne for coherence reconstructions if the interacting cortical sources consist of point like sources on the other hand mne provides better connectivity estimation than beamformers if the interacting sources are simulated as extended cortical patches where each patch consists of dipoles with identical time series high intra patch coherence however the performance of the beamformers for interacting patches improves substantially if each patch of active cortex is simulated with only partly coherent time series partial intra patch coherence these results demonstrate that the choice of the inverse method impacts the results of meg source space coherence analysis and that the optimal choice of the inverse solution depends on the spatial and synchronization profile of the interacting cortical sources the insights revealed here can guide method selection and help improve data interpretation regarding meg connectivity estimation

statistical inferences for functional data with modem technology development functional data are being observed frequently in many scientific fields a popular method for analyzing such functional data is smoothing first then estimation that is statistical inference such as estimation and hypothesis testing about functional data is conducted based on the substitution of the underlying individual functions by their reconstructions obtained by one smoothing technique or another however little is known about this substitution effect on functional data analysis in this paper this problem is investigated when the local polynomial kernel lpk smoothing technique is used for individual function reconstructions we find that under some mild conditions the substitution effect can be ignored asymptotically based on this we construct lpk reconstruction based estimators for the mean covariance and noise variance functions of a functional data set and derive their asymptotics we also propose a gcv rule for selecting good bandwidths for the lpk reconstructions when the mean function also depends on some time independent covariates we consider a functional linear model where the mean function is linearly related to the covariates but the covariate effects are functions of time the lpk reconstruction based estimators for the covariate effects and the covariance function are also constructed and their asymptotics are derived moreover we propose a l 2 norm based global test statistic for a general hypothesis testing problem about the covariate effects and derive its asymptotic random expression the effect of the bandwidths selected by the proposed gcv rule on the accuracy of the lpk reconstructions and the mean function estimator is investigated via a simulation study the proposed methodologies are illustrated via an application to a real functional data set collected in climatology

semiparametric modeling of longitudinal measurements and time to event data a two stage regression calibration approach summary in this article we investigate regression calibration methods to jointly model longitudinal and survival data using a semiparametric longitudinal model and a proportional hazards model in the longi tudinal model a biomarker is assumed to followa semiparametric mixed model where covariate effects are modeled parametrically and subject specific time profiles are modeled nonparametrially using a population smoothing spline and subject specific random stochastic processes the cox model is assumed for survival data by including both the current measure and the rate of change of the underlying longitudinal trajectories as covariates as motivated by a prostate cancer study application we develop a two stage semiparametric regression calibration rc method two variations of the rc method are considered risk set regression calibration and a computationally simpler ordinary regression calibration simulation results showthat the two stage rc approach performs well in practice and effectively corrects the bias from the naive method we apply the proposed methods to the analysis of a dataset for evaluating the effects of the longitudinal biomarker psa on the recurrence of prostate cancer

extending the scope of wavelet regression methods by coefficient dependent thresholding abstract various aspects of the wavelet approach to nonparametric regression are considered with the overall aim of extending the scope of wavelet techniques to irregularly spaced data to regularly spaced datasets of arbitrary size to heteroscedastic and correlated data and to data that contain outliers the core of the methodology is an algorithm for finding ail of the variances and within level covariances in the wavelet table of a sequence with given covariance structure if the original covariance matrix is band limited then the algorithm is linear in the length of the sequence the variance calculation algorithm allows data on any set of independent variable values to be treated by first interpolating to a fine regular grid of suitable length and then constructing a wavelet expansion of the gridded data various thresholding methods are discussed and investigated exact risk formulas for the mean square error of the methodology for given design are derived good performance is obtained by nois

mapping human brain function with meg and eeg methods and validation we survey the field of magnetoencephalography meg and electroencephalography eeg source estimation these modalities offer the potential for functional brain mapping with temporal resolution in the millisecond range however the limited number of spatial measurements and the ill posedness of the inverse problem present significant limits to our ability to produce accurate spatial maps from these data without imposing major restrictions on the form of the inverse solution here we describe approaches to solving the forward problem of computing the mapping from putative inverse solutions into the data space we then describe the inverse problem in terms of low dimensional solutions based on the equivalent current dipole ecd and high dimensional solutions in which images of neural activation are constrained to the cerebral cortex we also address the issue of objective assessment of the relative performance of inverse procedures by the free response receiver operating characteristic froc curve we conclude with a discussion of methods for assessing statistical significance of experimental results through use of the bootstrap for determining confidence regions in dipole fitting methods and random field rf and permutation methods for detecting significant activation in cortically constrained imaging studies

stationary patterns for a prey predator model with prey dependent and ratio dependent functional responses and diffusion abstract we study a reaction diffusion system arising from a three species prey predator model with prey dependent and ratio dependent functional responses the main aim of this paper is to study the global existence and bifurcation of non constant positive steady states in particular we will show that even though the unique positive constant steady state is stable for the ode dynamics non constant positive steady states exist for the reaction diffusion system this demonstrates that stationary patterns arise as a result of diffusion

posterior probability intervals for wavelet thresholding summary we use cumulants to derive bayesian credible intervals for wavelet regression estimates the first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions these powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale hence a suitable modification of the discrete wavelet transform allows the posterior cumulants to be found efficiently for any given data set johnson transformations then yield the credible intervals themselves simulations show that these intervals have good coverage rates even when the underlying function is inhomogeneous where standard methods fail in the case where the curve is smooth the performance of our intervals remains competitive with established nonparametric regression methods

a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

bayesian smoothing and regression splines for measurement error problems in the presence of covariate measurement error estimating a regression function nonparametrically is extremely difficult the problem being related to deconvolution various frequentist approaches exist for this problem but to date there has been no bayesian treatment in this article we describe bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error the regression function is modeled with smoothing splines and regression p splines two methods are described for exploration of the posterior the first called the iterative conditional modes icm is only partially bayesian icm uses a componentwise maximization routine to find the mode of the posterior it also serves to create starting values for the second method which is fully bayesian and uses markov chain monte carlo mcmc techniques to generate observations from the joint posterior distribution use of the mcmc approach has the advantage that interval estimates that directly model and

a diffuse interface model for axisymmetric immiscible two phase flow a diffuse interface model is considered for solving axisymmetric immiscible two phase flow with surface tension the navier stokes ns equations are modified by the addition of a continuum forcing the interface between the two fluids is considered as the half level set of a mass concentration c which is governed by the cahn hilliard ch equation a fourth order degenerate nonlinear parabolic diffusion equation in this work we develop a nonlinear multigrid method to solve the ch equation with degenerate mobility and couple this to a projection method for the incompressible ns equations the diffuse interface method can deal with topological transitions such as breakup and coalescence smoothly without ad hoc cut and connect or other artificial procedures we present results for rayleigh s capillary instability up to forming satellite drops the results agree well with the linear stability theory

principal differential analysis data reduction by differential operators functional data are observations that are either themselves functions or are naturally representable as functions when these functions can be considered smooth it is natural to use their derivatives in exploring their variation principal differential analysis pda identifies a linear differential operator l w 0 i w 1 d w m 1 d m 1 d m that comes as close as possible to annihilating a sample of functions convenient procedures for estimating the m weighting functions w j are developed the estimated differential operator l is analogous to the projection operator used as the data annihilator in principal components analysis and thus can be viewed as a type of data reduction or exploration tool the corresponding linear differential equation may also have a useful substantive interpretation modelling and regularization features can also be incorporated into pda

bivariate quantile smoothing splines it has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample we introduce bivariate quantile smoothing splines which belong to the space of bilinear tensor product splines as nonparametric estimators for the conditional quantile functions in a two dimensional design space the estimators can be computed by using standard linear programming techniques and can further be used as building blocks for conditional quantile estimations in higher dimensions for moderately large data sets we recommend penalized bivariate b splines as approximate solutions we use real and simulated data to illustrate the methodology proposed

miscellanea on the optimal amount of smoothing in penalised spline regression summary the optimal amount of smoothing in penalised spline regression is investigated in particular a simple closed form approximation to the optimal smoothing parameter is derived comparisons with its exact counterpart show it to be a useful starting point for measuring the optimal amount of smoothing in penalised spline regression it also lends itself to the development of quick and simple rules for automatic smoothing parameter selection

smoothing parameter selection for a class of semiparametric linear models summary spline based approaches to non parametric and semiparametric regression as well as to regression of scalar outcomes on functional predictors entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized we demonstrate that the equations determining two popular methods for smoothing parameter selection generalized cross validation and restricted maximum likelihood share a similar form that allows us to prove several results which are common to both and to derive a condition under which they yield identical values these ideas are illustrated by application of functional principal component regression a method for regressing scalars on functions to two chemometric data sets

linear model selection by cross validation abstract we consider the problem of selecting a model having the best predictive ability among a class of linear models the popular leave one out cross validation method which is asymptotically equivalent to many other model selection methods such as the akaike information criterion aic the c p and the bootstrap is asymptotically inconsistent in the sense that the probability of selecting the model with the best predictive ability does not converge to 1 as the total number of observations n we show that the inconsistency of the leave one out cross validation can be rectified by using a leave n v out cross validation with n v the number of observations reserved for validation satisfying n v n 1 as n this is a somewhat shocking discovery because nv n 1 is totally opposite to the popular leave one out recipe in cross validation motivations justifications and discussions of some practical aspects of the use of the leave n v out cross validation method are provided and results