generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

finite size scaling analysis of the φ 4 field theory on the square lattice monte carlo calculations are performed for the model hamiltonian i r 2 2 i u 4 gf4 i c 2 i j 2 for various values of the parametersr u c in the crossover region from the ising limit r u to the displacive limit r 0 the variable i is a scalar continuous spin variable which can lie in the range i for each lattice site i i is a priori selected proportional to the single site probability in our monte carlo algorithm the critical line is obtained in very good agreement with other previous approaches a decrease of apparent critical exponents deduced from a finite size scaling analysis is attributed to a crossover toward mean field values at the displacive limit the relation of this model to the coarse grained landau ginzburg wilson free energy functional of ising models is discussed in detail and by matching local moments 2 i 4 i to corresponding averages of subsystem blocks of ising systems with linear dimensionsl 5 tol 15 an explicit construction of this coarse grained free energy is attempted self consistency checks applied to this matching procedure show qualitatively reasonable behavior but quantitative difficulties remain indicating that higher order terms are needed for a quantitatively satisfactory description

compact quantum ergodic systems we develop theory of multiplicity maps for compact quantum groups as an application we obtain a complete classification of right coideal c algebras of c suq 2 for q 1 1 0 they are labeled with dynkin diagrams but classification results for positive and negative cases of q are different many of the coideals are quantum spheres or quotient spaces by quantum subgroups but we do have other ones in our classification list

critical adsorption and critical casimir forces in the canonical ensemble critical properties of a liquid film between two planar walls are investigated in the canonical ensemble within which the total number of fluid particles rather than their chemical potential is kept constant the effect of this constraint is analyzed within mean field theory mft based on a ginzburg landau free energy functional as well as via monte carlo simulations of the three dimensional ising model with fixed total magnetization within mft and for finite adsorption strengths at the walls the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the lagrange multiplier associated with the constraint however due to a nonintegrable divergence of the mean field order parameter profile near a wall the limit of infinitely strong adsorption turns out to be not well defined within mft because it would necessarily violate the constraint the critical casimir force ccf acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles for instance the canonical ccf in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart we derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case but with the chemical potential playing the role of the lagrange multiplier associated with the constraint the different behavior of the ccf in the two ensembles is rationalized within mft by showing that for a prescribed value of the thermodynamic control parameter of the film i e density or chemical potential the film pressures are identical in the two ensembles while the corresponding bulk pressures are not

simple and prime crossed products of c algebras by compact quantum group coactions let g a be a compact quantum group and a coaction of g on a c algebra b we give necessary and sufficient conditions for the simplicity and primeness of the crossed product b g in terms of certain fixed point algebras

locally compact group actions on c algebras and compact subgroups be a compact subgroup in this paper we shall give necessary and sufficient conditions in order that the crossed product g x a be simple or prime our conditions are in terms of the dual 2 of the com pact subgroup k the paper is organized as follows in the second section we summarize some preliminary definitions and results about continuous banach representations of compact groups the same section contains the definitions of the subspaces of spherical functions sn nl l 7 n e e those of the algebras s i and the relations between these subspaces section 3 contains a study of saturated actions of g on a in terms of the ideals s s we mention that for compact groups the notion of saturated action has been defined by rieffel see 19 chap 73 the same section contains conditions in order that the crossed product be simple for compact abelian groups g our result reduces to the following g x

spectra for compact quantum group coactions and crossed products we present definitions of both connes spectrum and strong connes spectrum for actions of compact quantum groups on c algebras and obtain necessary and sufficient conditions for a crossed product to be a prime or a simple c algebra our results extend to the case of compact quantum ac tions the results in 8 which in turn generalize results by connes olesen and pedersen and kishimoto for abelian group actions we prove in addition that the connes spectra are closed under tensor products these results are new for compact nonabelian groups as well

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

controlling variable selection by the addition of pseudovariables we propose a new approach to variable selection designed to control the false selection rate fsr defined as the proportion of uninformative variables included in selected models the method works by adding a known number of pseudovariables to the real dataset running a variable selection procedure and monitoring the proportion of pseudovariables falsely selected information obtained from bootstrap like replications of this process is used to estimate the proportion of falsely selected real variables and to tune the selection procedure to control the fsr

critical dynamics in thin films critical dynamics in film geometry is analyzed within the field theoretical approach in particular we consider the case of purely relaxational dynamics model a and dirichlet boundary conditions corresponding to the so called ordinary surface universality class on both confining boundaries the general scaling properties for the linear response and correlation functions and for dynamic casimir forces are discussed within the gaussian approximation we determine the analytic expressions for the associated universal scaling functions and study quantitatively in detail their qualitative features as well as their various limiting behaviors close to the bulk critical point in addition we consider the effects of time dependent fields on the fluctuation induced dynamic casimir force and determine analytically the corresponding universal scaling functions and their asymptotic behaviors for two specific instances of instantaneous perturbations the universal aspects of nonlinear relaxation from an initially ordered state are also discussed emphasizing the different crossovers occurring during this evolution the model considered is relevant to the critical dynamics of actual uniaxial ferromagnetic films with symmetry preserving conditions at the confining surfaces and for monte carlo simulations of spin system with glauber dynamics and free boundary conditions

field theory of finite size effects for systems with a one component order parameter the field theoretic renormalization group approach is used to describe finite size effects near the critical point of the 4 model with a one component order parameter problems of previous perturbation approaches for t tc are discussed and an improved perturbation theory is employed that is applicable both above and below tc the susceptibility order parameter specific heat and a cumulant ratio are calculated for fixed d 4 in one loop order for the case of a cube with periodic boundary conditions finite size scaling functions are evaluated in three dimensions without using the e 4 d expansion quantitative agreement with monte carlo mc data of the three dimensional ising model is found in most cases additional mc data of larger systems would be desirable in order to test the detailed predictions of the finite size field theory more conclusively in the asymptotic region

simulation of static critical phenomena in nonideal fluids with the lattice boltzmann method a fluctuating nonideal fluid at its critical point is simulated with the lattice boltzmann method it is demonstrated that the method employing a ginzburg landau free energy functional correctly reproduces the static critical behavior associated with the ising universality class a finite size scaling analysis is applied to determine the critical exponents related to the order parameter compressibility and specific heat a particular focus is put on finite size effects and issues related to the global conservation of the order parameter

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

on almost linearity of low dimensional projections from high dimensional data this paper studies the shapes of low dimensional projections from high dimensional data after standardization let mathbf x be a p dimensional random variable with mean zero and identity covariance for a projection beta mathbf x beta 1 find another direction b so that the regression curve of b mathbf x against beta mathbf x is as nonlinear as possible we show that when the dimension of mathbf x is large for most directions beta even the most nonlinear regression is still nearly linear our method depends on the construction of a pair of p dimensional random variables mathbf w 1 mathbf w 2 called the rotational twin and its density function with respect to the standard normal density with this we are able to obtain closed form expressions for measuring deviation from normality and deviation from linearity in a suitable sense of average as an interesting by product from a given set of data we can find simple unbiased estimates of e f beta mathbf x t phi 1 t 1 2 and e lbrack e mathbf x mid beta beta mathbf x t 2 t 2 f 2 beta mathbf x t phi 2 1 t rbrack where phi 1 is the standard normal density f beta mathbf x is the density for beta mathbf x and the e is taken with respect to the uniformly distributed beta this is achieved without any smoothing and without resorting to any laborious projection procedures such as grand tours our result is related to the work of diaconis and freedman the impact of our result on several fronts of data analysis is discussed for example it helps establish the validity of regression analysis when the link function of the regression model may be grossly wrong a further generalization which replaces beta mathbf x by b mathbf x with b beta 1 ldots beta k for k randomly selected orthonormal vectors beta i i 1 ldots k helps broaden the scope of application of sliced inverse regression sir

universality in the two dimensional continuous spin model monte carlo methods have been used to analyse the critical behaviour of the d 2 border phi 4 model which according to a recent series expansion study violates expectations based upon universality the results suggest that the model does in fact fall into the ising universality class at least as regards those parameters which characterise the critical point configurations of the ordering variable

lattice boltzmann langevin simulations of binary mixtures we report a hybrid numerical method for the solution of the model h fluctuating hydrodynamic equations for binary mixtures the momentum conservation equations with landau lifshitz stresses are solved using the fluctuating lattice boltzmann equation while the order parameter conservation equation with langevin fluxes is solved using stochastic method of lines two methods based on finite difference and finite volume are proposed for spatial discretization of the order parameter equation special care is taken to ensure that the fluctuation dissipation theorem is maintained at the lattice level in both cases the methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results the galilean invariance of the model is tested and found to be satisfactory thermally induced capillary fluctuations of the interface are captured accurately indicating that the model can be used to study nonlinear fluctuations

tuning variable selection procedures by adding noise many variable selection methods for linear regression depend critically on tuning parameters that control the performance of the method for example entry and stay significance levels in forward and backward selection however most methods do not adapt the tuning parameters to particular datasets we propose a general strategy for adapting variable selection tuning parameters that effectively estimates the tuning parameters so that the selection method avoids overfitting and underfitting the strategy is based on the principle that overfitting and underfitting can be directly observed in estimates of the error variance after adding controlled amounts of additional independent noise to the response variable then running a variable selection method it is related to the simulation technique simex found in the measurement error literature we focus on forward selection because of its simplicity and ability to handle large numbers of explanatory variables monte carlo studies show that the new method c

critical dynamics a field theoretical approach we review the progress made in dynamic bulk critical behaviour in equilibrium in the last 25 years since the review of halperin and hohenberg we unify the presentation of the theoretical background by restricting ourselves to the field theoretic renormalization group method the main results obtained in the different universality classes are presented this contains the critical dynamics near the gas liquid transition in pure fluids model h the plait point and consolute point in mixtures model h the superfluid transition in 4 he model f and 4 he 3 he mixtures model f the curie point model j and neel point model g in heisenberg magnets and the superconducting transition in comparison with experimental results it became clear that in most cases one has to consider apart from the universal asymptotic critical behaviour also the non universal effective behaviour either because it turned out to be inevitable due to a small dynamical transient exponent inhibiting the system to reach the asymptotics e g at the superfluid transition or because one is interested in the region further away from the phase transition like in pure fluids and mixtures at their gas liquid or demixing transition the calculation of the critical dynamics is adequate in most cases only in two loop order we review these results and present the solution to unreasonable features found for some models thus we consider model c where relaxational and diffusive dynamics are coupled and the scaling properties and the limit to a purely relaxational model model a have not been understood in general for models where the order parameter couples to other conserved densities time scale ratios between the kinetic coefficients of the order parameter and the conserved densities play an important role their fixed point values and the approach to the fixed point are changed considerably in two loop order compared to their values in one loop order these considerations are relevant for the explanation of the dynamical critical shape functions of systems such as superfluid helium model f and the isotropic antiferromagnet model g as far as possible the comparison of results obtained by the renormalization group theory with numerical simulations has been made

critical phenomena at perfect and non perfect surfaces the effect of imperfections on surface critical properties is studied for ising models with nearest neighbour ferromagnetic couplings on simple cubic lattices in particular results of monte carlo simulations for flat perfect surfaces are compared to those for flat surfaces with random weak or strong interactions between neighbouring spins in the surface layer and for surfaces with steps of monoatomic height surface critical exponents at the ordinary transition in particular are found to be robust against these perturbations

coarse grained properties of three dimensional ising systems the universal coarse grained properties of three dimensional ising systems are investigated with the aid of wilson s recursion formula 1971 the helmholtz function is obtained in the critical regions both above and below the critical point the coarse grained free energy functional believed to control spinodal decomposition is also determined the crossover from non gaussian critical to gaussian central limit behaviour in the coarse grained coordinate distribution is investigated in both high and low temperature phases

nonlinear models using dirichlet process mixtures we introduce a new nonlinear model for classification in which we model the joint distribution of response variable y and covariates x non parametrically using dirichlet process mixtures we keep the relationship between y and x linear within each component of the mixture the overall relationship becomes nonlinear if the mixture contains more than one component with different regression coefficients we use simulated data to compare the performance of this new approach to alternative methods such as multinomial logit mnl models decision trees and support vector machines we also evaluate our approach on two classification problems identifying the folding class of protein sequences and detecting parkinson s disease our model can sometimes improve predictive accuracy moreover by grouping observations into sub populations i e mixture components our model can sometimes provide insight into hidden structure in the data

regular article calculation of two phase navier stokes flows using phase field modeling phase field models provide a way to model fluid interfaces as having finite thickness this can allow the computation of interface movement and deformation on fixed grids this paper applies phase field modeling to the computation of two phase incompressible navier stokes flows the navier stokes equations are modified by the addition of the continuum forcing email protected f where c is the composition variable and f is c s chemical potential the equation for interface advection is replaced by a continuum advective diffusion equation with diffusion driven by c s chemical potential gradients the paper discusses how solutions to these equations approach those of the original sharp interface navier stokes equations as the interface thickness e and the diffusivity both go to zero the basic flow physics of phase field interfaces is discussed straining flows can thin or thicken an interface and this must be resisted by a high enough diffusion on the other hand too large a diffusion will overly damp the flow these two constraints result in an upper bound for the diffusivity of o e and a lower bound of o e 2 within these two bounds the phase field navier stokes equations appear to generate an o e error relative to the exact sharp interface equations an o h 2 e 2 numerical method is introduced that is energy conserving in the sense that creation of interface energy by convection is always balanced by an equal decrease in kinetic energy caused by surface tension forcing an o h 4 e 4 compact scheme is introduced that takes advantage of the asymptotic comparatively smooth behavior of the chemical potential for o e accurate phase field models the optimum path to convergence for this scheme appears to be email protected 4 5 the asymptotic rate of convergence corresponding to this is o h 4 5 but results at practical resolutions show that the practical convergence of the method is generally considerably faster than linear extensive analysis and computations show that this scheme is very effective and accurate it allows the accurate calculation of two phase flows with interfaces only two cells wide computational results are given for linear capillary waves and for rayleigh taylor instabilities the first set of computations is compared to exact solutions of the diffuse interface equations and of the original sharp interface equations the rayleigh taylor computations test the ability of the method to compute highly deforming flows these flows include near singular phenomena such as interface coalescences and breakups contact line movement and the formation and breakup of thin wall films grid refinement studies are made and rapid convergence is found for macroscopic flow features such as instability growth rate and propagation speed wavelength and the general physical characteristics of the instability and mass transfer rates

comparison between finite size field theory and monte carlo simulations for the three dimensional ising model abstract recent field theoretic predictions of finite size effects for various thermodynamic quantities near the critical point are compared with new accurate monte carlo mc data for the l l l ising model obtained from a cluster algorithm special purpose computer owing to the large size l 32 64 128 256 of the ising models these mc data permit to test the finite size field theory in the asymptotic scaling region above and below t c the results constitute the most accurate confirmation of finite size scaling in three dimensions obtained to date in a wide range of temperatures agreement with the predicted shape of the finite size scaling functions is found on a quantitative level

ergodic actions of universal quantum groups on operator algebras we construct ergodic actions of compact quantum groups on c algebras and von neumann algebras and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups

are critical finite size scaling functions calculable from knowledge of an appropriate critical exponent critical finite size scaling functions for the order parameter distribution of the two and three dimensional ising model are investigated within a recently introduced classification theory of phase transitions the universal part of critical finite size scaling functions has been derived by employing a scaling limit which differs from the traditional finite size scaling limit in this paper the analytical predictions are compared with monte carlo simulation results we find good agreement between the analytical expression and the simulation results the agreement is consistent with the possibility that the functional form of the critical finite size scaling function for the order parameter distribution is determined uniquely by only a few universal parameters most notably the equation of state exponent

ageing properties of critical systems in the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest ageing phenomena are observed during this everlasting non equilibrium evolution a simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high temperature phase to the critical point the aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case particular emphasis is put on the field theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities fluctuation dissipation relations are discussed and in particular the concept of fluctuation dissipation ratio fdr is reviewed emphasizing its connection with the definition of a possible effective temperature the renormalization group approach to critical dynamics is summarized and the scaling forms of the time dependent non equilibrium correlation and response functions of a generic observable are discussed from them the universality of the associated fdr follows as an amplitude ratio it is then possible to provide predictions for ageing quantities in a variety of different models in particular the results for models a b and c dynamics of the o n ginzburg landau hamiltonian and model a dynamics of the weakly dilute ising magnet and of the 3 theory are reviewed and compared with the available numerical results and exact solutions the effect of a planar surface on the ageing behaviour of model a dynamics is also addressed within the mean field approximation

eliminating spurious velocities in the free energy lattice boltzmann method spurious velocities are unphysical currents that appear close to curved interfaces in diffuse interface methods we analyze the causes of these spurious velocities in the free energy lattice boltzmann algorithm by making a suitable choice of the equilibrium distribution and by finding the best way to numerically calculate derivatives we show that these velocities may be decreased by an order of magnitude compared to previous models furthermore we propose a momentum conserving forcing method that reduces spurious velocities by another factor of approximately 5 in three dimensions we find that 19 velocity vectors is the minimum number necessary

model free feature screening for ultrahigh dimensional data with the recent explosion of scientific data of unprecedented size and complexity feature ranking and screening are playing an increasingly important role in many scientific studies in this article we propose a novel feature screening procedure under a unified model framework which covers a wide variety of commonly used parametric and semiparametric models the new method does not require imposing a specific model structure on regression functions and thus is particularly appealing to ultrahigh dimensional regressions where there are a huge number of candidate predictors but little information about the actual model forms we demonstrate that with the number of predictors growing at an exponential rate of the sample size the proposed procedure possesses consistency in ranking which is both useful in its own right and can lead to consistency in selection the new procedure is computationally efficient and simple and exhibits a competent empirical performance in our intensive simulations and real