a class of superrigid group von neumann algebras we prove that for any group g in a fairly large class of generalized wreath product groups the associated von neumann algebra lg completely remembers the group g more precisely if lg is isomorphic to the von neumann algebra l of an arbitrary countable group then must be isomorphic to g this represents the rst superrigidity result pertaining to group von neumann algebras

a modified higher order godunov s scheme for stiff source conservative hydrodynamics we present an efficient second order accurate scheme to treat stiff source terms within the framework of higher order godunov s methods we employ duhamel s formula to devise a modified predictor step which accounts for the effects of stiff source terms on the conservative fluxes and recovers the correct isothermal behavior in the limit of an infinite cooling reaction rate source term effects on the conservative quantities are fully accounted for by means of a one step second order accurate semi implicit corrector scheme based on the deferred correction method of dutt et al we demonstrate the accurate stable and convergent results of the proposed method through a set of benchmark problems for a variety of stiffness conditions and source types

block structured adaptive mesh and time refinement for hybrid hyperbolic n body systems we present a new numerical algorithm for the solution of coupled collisional and collisionless systems based on the block structured adaptive mesh and time refinement strategy amr we describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels we implement a code based on a higher order conservative and directionally unsplit godunov s method for hydrodynamics a symmetric time centered modified symplectic scheme for collisionless component and a multilevel multigrid relaxation algorithm for the elliptic equation coupling the two components numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented

unconventional schemes for a class of ordinary differential equations with applications to the korteweg de vries equation an unconventional numerical method for solving a restrictive and yet often encountered class of ordinary differential equations is proposed the method has a crucial what we callreflexive property and requires solving one linear system per time step but is second order accurate a systematical and easily implementable scheme is proposed to enhance the computational efficiency of such methods whenever needed applications are reported on how the idea can be applied to solve the korteweg de vries equation discretized in space

w superrigidity for group von neumann algebras of left right wreath products we prove that for many nonamenable groups including all hyperbolic groups and all nontrivial free products the left right wreath product groupg z 2z o is w superrigid this means that the group von neumann algebra lg entirely remembers g more precisely if lg is isomorphic with l for an arbitrary countable group then must be isomorphic withg

functional adaptive model estimation in this article we are interested in modeling the relationship between a scalar y and a functional predictor x t we introduce a highly flexible approach called functional adaptive model estimation fame which extends generalized linear models glms generalized additive models gams and projection pursuit regression ppr to handle functional predictors the fame approach can model any of the standard exponential family of response distributions that are assumed for glm or gam while maintaining the flexibility of ppr for example standard linear or logistic regression with functional predictors as well as far more complicated models can easily be applied using this approach we use a functional principal components decomposition of the predictor functions to aid visualization of the relationship between x t and y we also show how the fame procedure can be extended to deal with multiple functional and standard finite dimensional predictors possibly with missing data we illustrate the fame

on the stability of godunov projection methods for incompressible flow an analysis of the stability of certain numerical methods for the linear advection diffusion equation in two dimensions is performed the advection diffusion equation is studied because it is a linearized version of the navier stokes equations the evolution equation for density in boussinesq flows and a simplified form of the equations for bulk thermodynamic temperature and mass fraction in reacting flows it is found that various methods currently in use which are based on a crank nicholson type temporal discretization utilizing second order godunov methods for explicitly calculating advective terms suffer from a time step restriction which depends on the coefficients of diffusive terms a simple modification in the computation of the advective derivatives results in a method with a stability condition that is independent of the magnitude of the coefficients of the diffusive terms

a conservative three dimensional eulerian method for coupled solid fluid shock capturing a new method is presented for the explicit eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions we solve separately for each phase the equations of fluid dynamics or solid mechanics using as interface boundary conditions artificially extended representations of the individual phases for fluids we use a new 3d spatially unsplit implementation of the piecewise parabolic ppm method of colella and woodward for solids we use the 3d spatially unsplit eulerian solid mechanics method of miller and colella vacuum and perfectly incompressible obstacles may also be employed as phases a separate problem is the time evolution of material interfaces which are represented by planar segments constructed with a volume of fluid method the volume fractions are advanced in time using a second order 3d spatially unsplit advection routine with a velocity field determined by solution of interface normal two phase riemann problems from the riemann problem solutions we also determine cross interface momentum and energy fluxes the volume fractions in mixed cells may be arbitrarily small which would ordinarily make the courant friedrichs lewy time step stability limit arbitrarily small as well we overcome this limitation using the mass redistribution formalism to conservatively redistribute generalized mass in the neighborhood of the split cells we present an application of this method to an explosion contained in a metal can a reactive fluid approximating pbx 9404 is encased within an elastic plastic solid approximating copper surrounded by vacuum our implementation is in parallel and with adaptive mesh refinement

c superrigidity of 2 step nilpotent groups abstract we show that torsion free finitely generated nilpotent groups are characterised by their group c algebras and we additionally recover their nilpotency class as well as the subquotients of the upper central series we then use a c bundle decomposition and apply k theoretic methods based on noncommutative tori to prove that every torsion free finitely generated 2 step nilpotent group can be recovered from its group c algebra

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

some unique group measure space decomposition results using an approach emerging from the theory of closable deriva tions on von neumann algebras we exhibit a class of groups cr satisfying the following property given any groups 1 2 2 cr then any free ergodic measure preserving action on a probability space 1 2 y x gives rise to a von neumann algebra with unique group measure space cartan subalgebra pairing this result with popa s orbit equivalence superrigidity theorem we obtain new examples of w superrigid actions

functional principal component regression and functional partial least squares regression of a scalar response on signal predictors such as near infrared nir spectra of chemical samples presents a major challenge when as is typically the case the dimension of the signals far exceeds their number most solutions to this problem reduce the dimension of the predictors either by regressing on components e g principal component regression pcr and partial least squares pls or by smoothing methods which restrict the coefficient function to the span of a spline basis this article introduces functional versions of pcr and pls which combine both of the foregoing dimension reduction approaches two versions of functional pcr are developed both using b splines and roughness penalties the regularized components version applies such a penalty to the construction of the principal components i e it uses functional principal components whereas the regularized regression version incorporates a penalty in the regression for the latter form of functional pcr the penalty parame

single and multiple index functional regression models with nonparametric link fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of high dimensional functions this difficulty has led to an emphasis on the so called functional linear model which is much more flexible than common linear models in finite dimension but nevertheless imposes structural constraints on the relationship between predictors and responses recent advances have extended the linear approach by using it in conjunction with link functions and by considering multiple indices but the flexibility of this technique is still limited for example the link may be modeled parametrically or on a grid only or may be constrained by an assumption such as monotonicity multiple indices have been modeled by making finite dimensional assumptions in this paper we introduce a new technique for estimating the link function nonparametrically and we suggest an approach to multi index modeling using adaptively defined linear projections of functional data we show that our methods enable prediction with polynomial convergence rates the finite sample performance of our methods is studied in simulations and is illustrated by an application to a functional regression problem

generalized linear regression on sampled signals and curves a p spline approach we consider generalized linear regression with many highly correlated regressors for instance digitized points of a curve on a spatial or temporal domain we refer to this setting as signal regression which requires severe regularization because the number of regressors is large often exceeding the number of observations we solve collinearity by forcing the coefficient vector to be smooth on the same domain dimension reduction is achieved by projecting the signal coefficient vector onto a moderate number of b splines a difference penalty between the b spline coefficients further increases smoothness the p spline framework of eilers and marx the procedure is regulated by a penalty parameter chosen using information criteria or cross validation

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

most predictive design points for functional data predictors we suggest a way of reducing the very high dimension of a functional predictor x to a low number of dimensions chosen so as to give the best predictive performance specifically if x is observed on a fine grid of design points t 1 t r we propose a method for choosing a small subset of these say t i1 t ik to optimize the prediction of a response variable y the values t ij are referred to as the most predictive design points or covariates for a given value of k and are computed using information contained in a set of independent observations x i y i of x y the algorithm is based on local linear regression and calculations can be accelerated using linear regression to preselect the design points boosting can be employed to further improve the predictive performance we illustrate the usefulness of our ideas through simulations and examples drawn from chemometrics and we develop theoretical arguments showing that the methodology can be applied successfully in a range of settings

some oe and w rigidity results for actions by wreath product groups we use deformation rigidity theory in the von neumann algebra framework to study probability measure preserving actions by wreath product groups in particular we single out large families of wreath product groups satisfying various types of orbit equivalence oe rigidity for instance we show that whenever h k are icc property t groups such that h and k admit stably orbit equivalent action and such that h and k are ergodic then automatically is stably orbit equivalent to and h is stably orbit equivalent to k rigidity results for von neumann algebras arising from certain actions of such groups i e w rigidity results are also obtained

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

logistic regression with brownian like predictors this article introduces a new type of logistic regression model involving functional predictors of binary responses and provides an extension of this approach to generalized linear models the predictors are trajectories that have certain sample path properties in common with brownian motion time points are treated as parameters of interest and confidence intervals are developed under prospective and retrospective case control sampling designs in an application to functional magnetic resonance imaging data signals from individual subjects are used to find the portion of the time course that is most predictive of the response this allows the identification of sensitive time points specific to a brain region and associated with a certain task which can be used to distinguish between responses a second application concerns gene expression data in a case control study involving breast cancer where the aim is to identify genetic loci along a chromosome that best discriminate between cases and controls

the fast adaptive composite grid fac method for elliptic equation the fast adaptive composite grid fag method is a systematic process for solving differential boundary value problems fac uses global and local uniform grids both to define the composite grid problem and to interact for its fast solution it can with little added cost substantially improve accuracy of the coarse grid solution and is very suitable for vector and parallel computation this paper develops both the theoretical and practical aspects of fac as it applies to elliptic problems 1 introduction the need for local resolution in physical models occurs frequently in practice special local features of the forcing function operator coefficients boundary and boundary conditions can demand resolution in restricted regions of the domain that is much finer than the required global resolution it is important that the discretization and solution processes account for this locally that is that the local phenomena do not precipitate a dramatic increase in the overall computation unfortunately this objective of efficiently adapting to local features is often in conflict with the solution process equation solvers can degrade or even fail to apply in the presence of varying discretization scales data structures that account for irregular grids can be cumbersome the computer architecture may not be able to effectively account for grid irregularity e g vectorizability may be inhibited etc in fact even the discretization process itself may find difficulty with this objective for finite differences it is problematic to develop accurate difference formulae for irregular grids for finite elements this objective is reflected in the substantial overhead costs needed to automate the discretization the fast adaptive composite grid method fac 11 is a discretization and solution method designed to achieve efficient local resolution by constructing the

functional generalized linear models with images as predictors functional principal component regression fpcr is a promising new method for regressing scalar outcomes on functional predictors in this article we present a theoretical justification for the use of principal components in functional regression fpcr is then extended in two directions from linear to the generalized linear modeling and from univariate signal predictors to high resolution image predictors we show how to implement the method efficiently by adapting generalized additive model technology to the functional regression context a technique is proposed for estimating simultaneous confidence bands for the coefficient function in the neuroimaging setting this yields a novel means to identify brain regions that are associated with a clinical outcome a new application of likelihood ratio testing is described for assessing the null hypothesis of a constant coefficient function the performance of the methodology is illustrated via simulations and real data analyses with positron emission tomography images as predictors

on the structural theory of ii1 factors of negatively curved groups ii actions by product groups abstract this paper contains a series of structural results for von neumann algebras arising from measure preserving actions by product groups on probability spaces expanding upon the methods used earlier by the first two authors we obtain new examples of strongly solid factors as well as von neumann algebras with unique or no cartan subalgebra for instance we show that every ii 1 factor associated with a weakly amenable group in the class s of ozawa is strongly solid there is also the following product version of this result any maximal abelian subalgebra of any ii 1 factor associated with a finite product of weakly amenable groups in the class s of ozawa has an amenable normalizing algebra finally pairing some of these results with a cocycle superrigidity result of ioana it follows that compact actions by finite products of lattices in s p n 1 n 2 are virtually w superrigid

w superrigidity for bernoulli actions of property t groups we consider group measure space 1 factors m l x arising from bernoulli actions of icc property t groups more generally of groups containing an infinite normal subgroup with the relative property t and prove a rigidity result for homomorphisms m overbar m we deduce that the action x is w superrigid i e if y is any free ergodic measure preserving action such that the factors m l x and m l y are isomorphic then the actions x and y must be conjugate moreover we show that if p m 1 is a projection then pmp does not admit a group measure space decomposition nor a group von neumann algebra decomposition the latter under the additional assumption that is torsion free we also prove a rigidity result for homomorphisms m m this time for in a larger class of groups than above now including products of non amenable groups for certain groups e g f 2 f 2 we deduce that m does not embed into pmp for any projection p m 1 and obtain a description of the endomorphism semigroup of m

compressions of free products of von neumann algebras a reduction formula for compressions of von neumann algebra ii 1 factors arising as free products is proved this shows that the fundamental group is bf r for some such algebras additionally by taking a sort of free product with an unbounded semicircular element continuous one parameter groups of trace scaling automorphisms on ii infty factors are constructed this produces type iii 1 factors with core mathcal m otimes b mathcal h where mathcal m can be a full ii 1 factor without the haagerup approximation property

partial least squares regression on smooth factors in this article we present a modification of partial least squares regression to account for inherent nonexchangeabilities of the columns of the design matrix in chemometrics applications it is common to write the matrix as a bilinear form of latent variables and loadings these loadings are often interpreted as sampled values of functions hence they should exhibit a degree of smoothness our method forces the partial least squares factors to be smooth by using a roughness penalty motivated by nonparametric regression we present a computational method to determine the loadings that guarantees a desired orthogonality at successive steps we propose a cross validatory choice of the smoothing parameter and the number of loadings we illustrate the algorithm by an example and describe our experience with real data

a projection method for locally refined grids a numerical method for the solution of the two dimensional euler equatons for incompressible flow on locally refined grids is presented the method is a second order godunov projection method adapted from bell colella and glaz second order accuracy of the numerical method in time and space is established through numerical experiments the main contributions of this work concern the formulation and implementation of a projection for refined grids a discussion of the adjointness relation between gradient and divergence operators for a refined grid mac projection is presented and a refined grid approximate projection is developed an efficient multigrid method which exactly solves the projection is developed and a method for casting certain approximate projections as mac projections on refined grids is presented

one cohomology and the uniqueness of the group measure space decomposition of a ii1 factor we provide a unified and self contained treatment of several of the recent uniqueness theorems for the group measure space decomposition of a ii1 factor we single out a large class of groups characterized by a one cohomology property and prove that for every free ergodic probability measure preserving action of the associated ii1 factor has a unique group measure space cartan subalgebra up to unitary conjugacy our methods follow closely a recent article of chifan peterson but we replace the usage of peterson s unbounded derivations by thomas sinclair s dilation into a malleable deformation by a one parameter group of automorphisms

l 2 rigidity in von neumann algebras we introduce the notion of l2 rigidity for von neumann algebras a generalization of property t which can be viewed as an analogue for the vanishing of 1 cohomology into the left regular representation of a group we show that l2 rigidity passes to normalizers and is satisfied by nonamenable ii1 factors which are non prime have property or are weakly rigid as a consequence we obtain that if m is a free product of diffuse von neumann algebras or if m l where is a finitely generated group with 1 2 0 then any nonamenable regular subfactor of m is prime and does not have properties or t in particular this gives a new approach for showing solidity for a free group factor thus recovering a well known recent result of n ozawa

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

restricted likelihood ratio tests for functional effects in the functional linear model the goal of our article is to provide a transparent robust and computationally feasible statistical approach for testing in the context of scalar on function linear regression models assuming linearity between response and predictors we are interested in testing for the necessity of functional effects our methods are motivated by and applied to a large longitudinal study involving diffusion tensor imaging of intracranial white matter tracts in a susceptible cohort in the context of this study we conduct hypothesis tests that are motivated by anatomical knowledge and support recent findings regarding the relationship between cognitive impairment and white matter demyelination r code and data are in the examples of refund rlrt pfr supplementary materials for this article are available online

a hybrid scheme for gas dust systems stiffly coupled via viscous drag we present a stable and convergent method for studying a system of gas and dust coupled through viscous drag in both non stiff and stiff regimes to account for the effects of dust drag in the update of the fluid quantities we employ a fluid description of the dust component and study the modified gas dust hyperbolic system following the approach in miniati and colella 19 in addition to two entropy waves for the gas and dust components respectively the extended system includes three waves driven partially by gas pressure and partially by dust drift which in the limit of vanishing coupling tend to the two original acoustic waves and the unhindered dust streaming based on this analysis we formulate a predictor step providing first order accurate reconstruction of the time averaged state variables at cell interfaces whence a second order accurate estimate of the conservative fluxes can be obtained through a suitable linearized riemann solver the final source term update is carried out using a one step second order accurate l stable predictor corrector asymptotic method the a qss method suggested by mott et al 21 this procedure completely defines a two fluid method for gas dust system using the updated fluid solution allows us to then advance the individual particle solutions including self consistently the time evolution of the gas velocity in the estimate of the drag force this is done with a suitable particle scheme also based on the a qss method a set of benchmark problems shows that our method is stable and convergent when dust is modeled as a fluid two fluid second order accuracy is achieved in both stiff and non stiff regimes whereas when dust is modeled with particles hybrid second order is achieved in the non stiff regime and first order otherwise

generalized functional linear models we propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function a linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function and the expected value of the response is related to this linear predictor via a link function if in addition a variance function is specified this leads to a functional estimating equation which corresponds to maximizing a functional quasi likelihood this general approach includes the special cases of the functional linear model as well as functional poisson regression and functional binomial regression the latter leads to procedures for classification and discrimination of stochastic processes and functional data we also consider the situation where the link and variance functions are unknown and are estimated nonparametrically from the data using a semiparametric quasi likelihood procedure an essential step in our proposal is dimension reduction by approximating the predictor processes with a truncated karhunen loeve expansion we develop asymptotic inference for the proposed class of generalized regression models in the proposed asymptotic approach the truncation parameter increases with sample size and a martingale central limit theorem is applied to establish the resulting increasing dimension asymptotics we establish asymptotic normality for a properly scaled distance between estimated and true functions that corresponds to a suitable l 2 metric and is defined through a generalized covariance operator as a consequence we obtain asymptotic tests and simultaneous confidence bands for the parameter function that determines the model the proposed estimation inference and classification procedures and variants with unknown link and variance functions are investigated in a simulation study we find that the practical selection of the number of components works well with the aic criterion and this finding is supported by theoretical considerations we include an application to the classification of medflies regarding their remaining longevity status based on the observed initial egg laying curve for each of 534 female medflies

w superrigidity of mixing gaussian actions of rigid groups abstract we generalize w superrigidity results about bernoulli actions of rigid groups to general mixing gaussian actions we thus obtain the following if is any icc group which is w rigid i e it contains an infinite normal subgroup with the relative property t then any mixing gaussian action x is w superrigid more precisely if y is another free ergodic action such that the crossed product von neumann algebras are isomorphic l x l y then the actions are conjugate we prove a similar statement whenever is a non amenable icc product of two infinite groups

w superrigidity for arbitrary actions of central quotients of braid groups for any n geqslant 4 let tilde b n b n z b n be the quotient of the braid group b n through its center we prove that any free ergodic probability measure preserving pmp action tilde b n curvearrowright x mu is virtually hbox w superrigid in the following sense if l infty x rtimes tilde b n cong l infty y rtimes lambda for an arbitrary free ergodic pmp action lambda curvearrowright y nu then the actions tilde b n curvearrowright x lambda curvearrowright y are virtually conjugate moreover we prove that the same holds if tilde b n is replaced with a finite index subgroup of the direct product tilde b n 1 times cdots times tilde b n k for some n 1 ldots n k geqslant 4 the proof uses the dichotomy theorem for normalizers inside crossed products by free groups from popa and vaes 212 141 198 2014 in combination with the oe superrigidity theorem for actions of mapping class groups from kida 131 99 109 2008 similar techniques allow us to prove that if a group gamma is hyperbolic relative to a finite family of proper finitely generated residually finite infinite subgroups then the hbox ii 1 factor l infty x rtimes gamma has a unique cartan subalgebra up to unitary conjugacy for any free ergodic pmp action gamma curvearrowright x mu

a class of ii1 factors with many non conjugate cartan subalgebras abstract we construct a class of ii 1 factors m that admit unclassifiably many cartan subalgebras in the sense that the equivalence relation of being conjugate by an automorphism of m is complete analytic in particular non borel we also construct a ii 1 factor that admits uncountably many non isomorphic group measure space decompositions all involving the same group g so g is a group that admits uncountably many non stably orbit equivalent actions whose crossed product ii 1 factors are all isomorphic

nonparametric regression analysis of longitudinal data abstract nonparametric methods are developed for estimating the dose effect when a response consists of correlated observations over time measured in a dose response experiment the methods can also be applied to data collected from a completely randomized design experiment methods are developed for the detection and description of the effects of dose time and their interaction the methods allow for individual variation in the timing and number of observations a generalization allowing baseline covariates to be incorporated is addressed these results may be used in an exploratory fashion in the process of building a random effects model for longitudinal data

rigidity results for wreath product ii1 factors abstract we consider ii 1 factors of the form m g b g where either i b is a non hyperfinite ii 1 factor and g is an icc amenable group or ii b is a weakly rigid ii 1 factor and g is icc group and where g acts on g b by bernoulli shifts we prove that isomorphism of two such factors implies cocycle conjugacy of the corresponding bernoulli shift actions in particular the groups acting must be isomorphic as a consequence we can distinguish between certain classes of group von neumann algebras associated to wreath product groups

unique cartan decomposition for ii1 factors arising from arbitrary actions of free groups we prove that for any free ergodic probability measure preserving action mathbb f n curvearrowright x mu of a free group on n generators mathbb f n 2 leq n leq infty the associated group measure space ii1 factor l infty x rtimes mathbb f n has l x as its unique cartan subalgebra up to unitary conjugacy we deduce that group measure space ii1 factors arising from actions of free groups with different number of generators are never isomorphic we actually prove unique cartan decomposition results for ii1 factors arising from arbitrary actions of a much larger family of groups including all free products of amenable groups and their direct products

strong rigidity of generalized bernoulli actions and computations of their symmetry groups abstract we study equivalence relations and ii 1 factors associated with quotients of generalized bernoulli actions of kazhdan groups specific families of these actions are entirely classified up to isomorphism of ii 1 factors this yields explicit computations of outer automorphism and fundamental groups in particular every finitely presented group is concretely realized as the outer automorphism group of a continuous family of non stably isomorphic ii 1 factors

a smoothing based goodness of fit test of covariance for functional data functional data methods are often applied to longitudinal data as they provide a more flexible way to capture dependence across repeated observations however there is no formal testing procedure to determine if functional methods are actually necessary we propose a goodness of fit test for comparing parametric covariance functions against general nonparametric alternatives for both irregularly observed longitudinal data and densely observed functional data we consider a smoothing based test statistic and approximate its null distribution using a bootstrap procedure we focus on testing a quadratic polynomial covariance induced by a linear mixed effects model and the method can be used to test any smooth parametric covariance function performance and versatility of the proposed test is illustrated through a simulation study and three data applications

hypothesis testing in functional linear models functional data arise frequently in biomedical studies where it is often of interest to investigate the association between functional predictors and a scalar response variable while functional linear models flm are widely used to address these questions hypothesis testing for the functional association in the flm framework remains challenging a popular approach to testing the functional effects is through dimension reduction by functional principal component pc analysis however its power performance depends on the choice of the number of pcs and is not systematically studied in this article we first investigate the power performance of the wald type test with varying thresholds in selecting the number of pcs for the functional covariates and show that the power is sensitive to the choice of thresholds to circumvent the issue we propose a new method of ordering and selecting principal components to construct test statistics the proposed method takes into account both the association with the response and the variation along each eigenfunction we establish its theoretical properties and assess the finite sample properties through simulations our simulation results show that the proposed test is more robust against the choice of threshold while being as powerful as and often more powerful than the existing method we then apply the proposed method to the cerebral white matter tracts data obtained from a diffusion tensor imaging tractography study

short note controlling self force errors at refinement boundaries for amr pic we analyze the source of the self force errors in the node centered adaptive mesh refinement particle in cell amr pic algorithm and propose a method for reducing those self forces our approach is based on a method of charge deposition due to mayo a mayo the fast solution of poisson s and the biharmonic equations on irregular regions siam journal of numerical analysis 21 2 1984 285 299 that can reduce the self force error to any specified degree of accuracy

a cell centered adaptive projection method for the incompressible euler equations we present an algorithm to compute adaptive solutions for incompressible flows using block structured local refinement in both space and time this method uses a projection formulation based on a cell centered approximate projection which allows the use of a single set of cell centered solvers because of refinement in time additional steps are taken to accurately discretize the advection and projection operators at grid refinement boundaries using composite operators which span the coarse and refined grids this ensures that the method is approximately freestream preserving and satisfies an appropriate form of the divergence constraint

an unsplit 3d upwind method for hyperbolic conservation laws abstract an unsplit upwind method for solving hyperbolic conservation laws in three dimensions is developed this paper derives the algorithm by generalizing a two dimensional advection algorithm of van leer and colella to three dimensions and then making appropriate modifications the method is implemented using the equations of gas dynamics several test problems are computed to both verify and display the behavior of the method these test problems include a 1d blast wave a 2d shock reflection off a 30 ramp and a 3d astrophysical jet

gerris a tree based adaptive solver for the incompressible euler equations in complex geometries an adaptive mesh projection method for the time dependent incompressible euler equations is presented the domain is spatially discretised using quad octrees and a multilevel poisson solver is used to obtain the pressure complex solid boundaries are represented using a volume of fluid approach second order convergence in space and time is demonstrated on regular statically and dynamically refined grids the quad octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features the source code of the method implementation is freely available

a cell centered adaptive projection method for the incompressible navier stokes equations in three dimensions we present a method for computing incompressible viscous flows in three dimensions using block structured local refinement in both space and time this method uses a projection formulation based on a cell centered approximate projection combined with the systematic use of multilevel elliptic solvers to compute increments in the solution generated at boundaries between refinement levels due to refinement in time we use an l0 stable second order semi implicit scheme to evaluate the viscous terms results are presented to demonstrate the accuracy and effectiveness of this approach

on p values for smooth components of an extended generalized additive model the problem of testing smooth components of an extended generalized additive model for equality to zero is considered confidence intervals for such components exhibit good across the function coverage probabilities if based on the approximate result hat f i n f i v f i i where f is the vector of evaluated values for the smooth component of interest and v f is the covariance matrix for f according to the bayesian view of the smoothing process based on this result a wald type test of f 0 is proposed it is shown that care must be taken in selecting the rank used in the test statistic the method complements previous work by extending applicability beyond the gaussian case while considering tests of zero effect rather than testing the parametric hypothesis given by the null space of the component s smoothing penalty the proposed p values are routine and efficient to compute from a fitted model without requiring extra model fits or null distribution simulation

on the superrigidity of malleable actions with spectral gap some of the most interesting aspects of the dynamics of measure preserving actions of countable groups on probability spaces v rx x are revealed by the study of group measure space von neumann algebras l x x t mvnl and the classification of actions up to orbit equivalence oe i e up to isomorphism of probability spaces carrying the orbits of actions onto each other although one is in von neumann algebras and the other in ergodic theory the two problems are closely related as an oe of actions v rx x a rxy has been shown to implement an algebra isomorphism l x x t l y x a taking l x onto l y and vice versa si dy fm in particular the isomorphism class of l x xi t only depends on the equivalence relation 7 r t gt 1t x g t thus von neumann equivalence vne of group actions requiring isomorphism of their group measure space algebras is weaker than oe since there are exam ples of non oe actions whose associated von neumann algebras are all isomorphic cj1 it is in general strictly weaker on the other hand oe is manifestly weaker than classical conjugacy which for free actions r rx x a rx y requires isomor phism of probability spaces a x p y v satisfying ar a 1 a so in particular r a how much weaker vne and oe can be with respect to conju gacy is best seen in the amenable case where by a celebrated theorem of connes all free ergodic actions of all infinite amenable groups give rise to the same hi factor cl and by dy ow cfw they are undistinguishable under oe as well also any embedding of algebras l x xi t c l y x a with a amenable forces t to be amenable but the non amenable case is extremely complex and for many years progress has been slow mvn2 dy me c2 cw sc even after the discovery of the first rigidity phenomena by connes in von neumann algebras c3 c4 and by zimmer in oe ergodic theory zi z2 this changed dramatically over the last 7 8 years with the advent of a variety of striking rigidity results ful gl g2 mosh h hk p1 p8 see p9 for a survey also sh for a survey on oe rigidity our aim in this paper is to investigate the most extreme such phenomena called strong rigidity which show that for certain classes of source group actions

oe and w superrigidity results for actions by surface braid groups we show that several important normal subgroups of the mapping class group of a surface satisfy the following property any free ergodic probability measure preserving action y x is stablyoe superrigid these include the central quotients of most surface braid groups and most torelli groups and johnson kernels in addition we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice embeddings using these results in combination with previous results from cik13 we deduce that any free ergodic probabilitymeasure preserving action of almost any surface braid group is stablyw superrigid i e it can be completely reconstructed from its vonneumann algebra

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

exact likelihood ratio tests for penalised splines summary penalised spline based additive models allow a simple mixed model representation where the variance components control departures from linear models the smoothing parameter is the ratio of the random coefficient and error variances and tests for linear regression reduce to tests for zero random coefficient variances we propose exact likelihood and restricted likelihood ratio tests for testing polynomial regression versus a general alternative modelled by penalised splines their spectral decompositions are used as the basis of fast simulation algorithms we derive the asymptotic local power properties of the tests under weak conditions in particular we characterise the local alternatives that are detected with asymptotic probability one confidence intervals for the smoothing parameter are obtained by inverting the tests for a fixed smoothing parameter versus a general alternative we discuss f and r tests and show that ignoring the variability in the smoothing parameter estimator can have a dramatic effect on their null distributions the powers of several known tests are investigated and a small set of tests with good power properties is identified the restricted likelihood ratio test is among the best in terms of power

compact actions and uniqueness of the group measure space decomposition of ii1 factors abstract we prove that any ii1 factor l x arising from a compact free ergodic probability measure preserving action of a countable group with positive first l 2 betti number 1 2 0 has a unique group measure space cartan subalgebra up to unitary conjugacy

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

a simple multigrid scheme for solving the poisson equation with arbitrary domain boundaries we present a new multigrid scheme for solving the poisson equation with dirichlet boundary conditions on a cartesian grid with irregular domain boundaries this scheme was developed in the context of the adaptive mesh refinement amr schemes based on a graded octree data structure the poisson equation is solved on a level by level basis using a one way interface scheme in which boundary conditions are interpolated from the previous coarser level solution such a scheme is particularly well suited for self gravitating astrophysical flows requiring an adaptive time stepping strategy by constructing a multigrid hierarchy covering the active cells of each amr level we have designed a memory efficient algorithm that can benefit fully from the multigrid acceleration we present a simple method for capturing the boundary conditions across the multigrid hierarchy based on a second order accurate reconstruction of the boundaries of the multigrid levels in case of very complex boundaries small scale features become smaller than the discretization cell size of coarse multigrid levels and convergence problems arise we propose a simple solution to address these issues using our scheme the convergence rate usually depends on the grid size for complex grids but good linear convergence is maintained the proposed method was successfully implemented on distributed memory architectures in the ramses code for which we present and discuss convergence and accuracy properties as well as timing performances

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

some rigidity results for non commutative bernoulli shifts abstract we introduce the outer conjugacy invariants s s s for cocycle actions of discrete groups g on type ii 1 factors n as the set of real numbers t 0 for which the amplification t of can be perturbed to an action respectively to a weakly mixing action we calculate explicitly s s s and the fundamental group of f in the case g has infinite normal subgroups with the relative property t e g when g itself has the property t of kazhdan and is an action of g on the hyperfinite ii 1 factor by connes stormer bernoulli shifts of weights t i i thus s s and f coincide with the multiplicative subgroup s of r generated by the ratios t i t j i j while s z if s 1 i e when all weights are equal and s r otherwise in fact we calculate all the 1 cohomology picture of t t 0 and classify the actions g in terms of their weights t i i in particular we show that any 1 cocycle for g vanishes modulo scalars and that two such actions are cocycle conjugate iff they are conjugate also any cocycle action obtained by reducing a bernoulli action of a group g as above on n g g m n n c tr g to the algebra pnp for p a projection in n p 0 1 cannot be perturbed to a genuine action

on solid ergodicity for gaussian actions we investigate gaussian actions through the study of their crossed product von neumann algebra the motivational result is chifan and ioana s ergodic decomposition theorem for bernoulli actions chifan and ioana 2010 4 that we generalize to gaussian actions theorem a we also give general structural results theorems 3 4 and 3 8 that allow us to get a more accurate result at the level of von neumann algebras more precisely for a large class of gaussian actions x we show that any subfactor n of l x containing l x is either hyperfinite or is non gamma and prime at the end of the article we show a similar result for bogoliubov actions

functional linear regression that s interpretable regression models to relate a scalar y to a functional predictor x t are becoming increasingly common work in this area has concentrated on estimating a coefficient function t with y related to x t through f t x t dt regions where t 0 correspond to places where there is a relationship between x t and y alternatively points where t 0 indicate no relationship hence for interpretation purposes it is desirable for a regression procedure to be capable of producing estimates of t that are exactly zero over regions with no apparent relationship and have simple structures over the remaining regions unfortunately most fitting procedures result in an estimate for t that is rarely exactly zero and has unnatural wiggles making the curve hard to interpret in this article we introduce a new approach which uses variable selection ideas applied to various derivatives of t to produce estimates that are both interpretable flexible and accurate we call our method functional linear regression that s interpretable flirti and demonstrate it on simulated and real world data sets in addition non asymptotic theoretical bounds on the estimation error are presented the bounds provide strong theoretical motivation for our approach

a remark on t valued cohomology groups of algebraic group actions we prove that for a weakly mixing algebraic action g x the nth cohomology group hn g x t after quotienting out the natural subgroup hn g t contains hn g x as a natural subgroup for n 1 if we further assume the diagonal actions 2 4 are t cocycle superrigid and h2 g x is torsion free as an abelian group then the above also holds true for n 2 applying it for principal algebraic actions when n 1 we show that h2 g zg is torsion free as an abelian group when g has property t as a direct corollary of sorin popa s cocycle superrigidity theorem we also use it when n 2 to answer negatively a question of sorin popa on the 2nd cohomology group of bernoulli shift actions of property t groups