brief paper explicit predictive control with non convex polyhedral constraints this paper proposes an explicit solution to the model predictive control of linear systems subject to non convex polyhedral constraints these constraints are modeled as the union of a finite number of convex polyhedra the algorithm is based on calculating the explicit solution to a modified problem with linear constraints defined as the convex hull of the original ones and classifying its regions by their relation with the regions of the explicit solution to the original problem some of the regions are divided and a procedure based on sum of squares programming is designed to determine which of the possible solutions are in fact optimal finally the online algorithm is shown to be better in terms of computational cost and memory requirements than an algorithm based on obtaining and comparing the solutions of the problem using as constraints the polyhedra whose union forms the non convex regions both theoretically and by the results of an example

brief equivalence of hybrid dynamical models this paper establishes equivalences among five classes of hybrid systems mixed logical dynamical mld systems linear complementarity lc systems extended linear complementarity elc systems piecewise affine pwa systems and max min plus scaling mmps systems some of the equivalences are established under rather mild additional assumptions these results are of paramount importance for transferring theoretical properties and tools from one class to another with the consequence that for the study of a particular hybrid system that belongs to any of these classes one can choose the most convenient hybrid modeling framework

functional clustering by bayesian wavelet methods summary we propose a nonparametric bayes wavelet model for clustering of functional data the wavelet based methodology is aimed at the resolution of generic global and local features during clustering and is suitable for clustering high dimensional data based on the dirichlet process the nonparametric bayes model extends the scope of traditional bayes wavelet methods to functional clustering and allows the elicitation of prior belief about the regularity of the functions and the number of clusters by suitably mixing the dirichlet processes posterior inference is carried out by gibbs sampling with conjugate priors which makes the computation straightforward we use simulated as well as real data sets to illustrate the suitability of the approach over other alternatives

modelling the distribution of white matter hyperintensities due to ageing on mri images using bayesian inference white matter hyperintensities wmh also known as white matter lesions are localised white matter areas that appear hyperintense on mri scans wmh commonly occur in the ageing population and are often associated with several factors such as cognitive disorders cardiovascular risk factors cerebrovascular and neurodegenerative diseases despite the fact that some links between lesion location and parametric factors such as age have already been established the relationship between voxel wise spatial distribution of lesions and these factors is not yet well understood hence it would be of clinical importance to model the distribution of lesions at the population level and quantitatively analyse the effect of various factors on the lesion distribution model in this work we compare various methods including our proposed method to generate voxel wise distributions of wmh within a population with respect to various factors our proposed bayesian spline method models the spatio temporal distribution of wmh with respect to a parametric factor of interest in this case age within a population our probabilistic model takes as input the lesion segmentation binary maps of subjects belonging to various age groups and provides a population level parametric lesion probability map as output we used a spline representation to ensure a degree of smoothness in space and the dimension associated with the parameter and formulated our model using a bayesian framework we tested our algorithm output on simulated data and compared our results with those obtained using various existing methods with different levels of algorithmic and computational complexity we then compared the better performing methods on a real dataset consisting of 1000 subjects of the uk biobank divided in two groups based on hypertension diagnosis finally we applied our method on a clinical dataset of patients with vascular disease on simulated dataset the results from our algorithm showed a mean square error mse value of 7 27 10 5 which was lower than the mse value reported in the literature with the advantage of being robust and computationally efficient in the uk biobank data we found that the lesion probabilities are higher for the hypertension group compared to the non hypertension group and further verified this finding using a statistical t test finally when applying our method on patients with vascular disease we observed that the overall probability of lesions is significantly higher in later age groups which is in line with the current literature

a nonparametric spatial model for periodontal data with nonrandom missingness periodontal disease pd progression is often quantified by clinical attachment level cal defined as the distance down a tooth s root that is detached from the surrounding bone measured at six locations per tooth throughout the mouth excluding the molars it gives rise to a dependent data setup these data are often reduced to a one number summary such as the whole mouth average or the number of observations greater than a threshold to be used as the response in a regression to identify important covariates related to the current state of a subject s periodontal health rather than a simple one number summary we set forward to analyze all available cal data for each subject exploiting the presence of spatial dependence nonstationarity and nonnormality also many subjects have a considerable proportion of missing teeth which cannot be considered missing at random because pd is the leading cause of adult tooth loss under a bayesian paradigm we propose a nonparametric flexible spatial joint

optimal complexity reduction of polyhedral piecewise affine systems this paper focuses on the np hard problem of reducing the complexity of piecewise polyhedral systems e g polyhedral piecewise affine pwa systems the results are fourfold firstly the paper presents two computationally attractive algorithms for optimal complexity reduction that under the assumption that the system is defined over the cells of a hyperplane arrangement derive an equivalent polyhedral piecewise system that is minimal in the number of polyhedra the algorithms are based on the cells and the markings of the hyperplane arrangement in particular the first algorithm yields a set of disjoint non overlapping merged polyhedra by executing a branch and bound search on the markings of the cells the second approach leads to non disjoint overlapping polyhedra by formulating and solving an equivalent and well studied logic minimization problem secondly the results are extended to systems defined on general polyhedral partitions and not on cells of hyperplane arrangements thirdly the paper proposes a technique to further reduce the complexity of piecewise polyhedral systems if the introduction of an adjustable degree of error is acceptable fourthly the paper shows that based on the notion of the hyperplane arrangement pwa state feedback control laws can be implemented efficiently three examples including a challenging industrial problem illustrate the algorithms and show their computational effectiveness in reducing the complexity by up to one order of magnitude

joint estimation of multiple graphical models from high dimensional time series in this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions we assume that the data are collected from n subjects each of which consists of t possibly dependent observations the graphical models of subjects vary but are assumed to change smoothly corresponding to a measure of closeness between subjects we propose a kernel based method for jointly estimating all graphical models theoretically under a double asymptotic framework where both t n and the dimension d can increase we provide the explicit rate of convergence in parameter estimation it characterizes the strength one can borrow across different individuals and the impact of data dependence on parameter estimation empirically experiments on both synthetic and real resting state functional magnetic resonance imaging rs fmri data illustrate the effectiveness of the proposed method

estimating the fractal dimension of a locally self similar gaussian process by using increments summary consider the problem of estimating the parameter ca of a stationary gaussian process with

complexity reduction of explicit model predictive control via separation the problem of reducing complexity of explicit mpc feedback laws for linear systems is considered we propose to simplify controllers defined by continuous piecewise affine pwa functions by employing separating functions if a state resides in a region where the optimal control action attains a saturated value the optimal control move is determined from the sign of the separator thus instead of storing all regions only the unconstrained regions and the separator are needed we propose several approaches to construct separators with different efficacy and properties

finite mixture varying coefficient models for analyzing longitudinal heterogenous data this paper aims to develop a mixture model to study heterogeneous longitudinal data on the treatment effect of heroin use from a california civil addict program each component of the mixture is characterized by a varying coefficient mixed effect model we use the bayesian p splines approach to approximate the varying coefficient functions we develop markov chain monte carlo algorithms to estimate the smooth functions unknown parameters and latent variables in the model we use modified deviance information criterion to determine the number of components in the mixture a simulation study demonstrates that the modified deviance information criterion selects the correct number of components and the estimation of unknown quantities is accurate we apply the proposed model to the heroin treatment study furthermore we identify heterogeneous longitudinal patterns copyright 2011 john wiley sons ltd

minimal conjunctive normal expression of continuous piecewise affine functions continuous piecewise affine pwa functions arise in many aspects of control for this kind of function we propose the minimal conjunctive normal expression cne the cne can be expressed as the minimum of a collection of terms each of which is the maximum of a set of affine functions the minimal cne is defined to contain the smallest number of parameters analogous to boolean algebra we propose implicants and prime implicants for continuous pwa functions after obtaining all prime implicants the problem of finding minimal cnes can then be cast as a binary programming problem a sharp bound on the number of boolean variables in the binary programming problem is given in two worked examples minimal cnes are derived for given continuous pwa functions

stabilizing polynomial approximation of explicit mpc a given explicit piecewise affine representation of an mpc feedback law is approximated by a single polynomial computed using linear programming this polynomial state feedback control law guarantees closed loop stability and constraint satisfaction the polynomial feedback can be implemented in real time even on very simple devices with severe limitations on memory storage

clipping based complexity reduction in explicit mpc the idea of explicit model predictive control mpc is to characterize optimal control inputs as an explicit piecewise affine pwa function of the initial conditions the function however is often too complex and either requires too much processing power to evaluate on line or consumes a prohibitive amount of memory the paper focuses on the memory issue and proposes a novel method of replacing a generic continuous pwa function by a different function of significantly lower complexity in such a way that the simple function guarantees the same properties as the original the idea is based on eliminating regions of the pwa function over which the function attains a saturated value an extensive case study is presented which confirms that a significant reduction of complexity is achieved in general

directional rates of change under spatial process models spatial process models are now widely used for inference in many areas of application in such contexts interest is often in the rate of change of a spatial surface at a given location in a given direction examples include temperature or rainfall gradients in meteorology pollution gradients for environmental data and surface roughness assessment for digital elevation models because the spatial surface is viewed as a random realization all such rates of change are random as well we formalize the notions of directional finite difference processes and directional derivative processes building upon the concept of mean square differentiability as developed by stein and banerjee and gelfand we obtain complete distribution theory results under the assumptions of a stationary gaussian process model either for the data or for spatial random effects we present inference under a bayesian framework which in this setting presents several advantages finally we illustrate our methodology with a simulated dat

mixture of regression models for large spatial datasets abstractwhen a spatial regression model that links a response variable to a set of explanatory variables is desired it is unlikely that the same regression model holds throughout the domain when t

on the cell probe complexity of polynomial evaluation abstract we consider the cell probe complexity of the polynomial evaluation problem with preprocessing of coefficients for polynomials of degree at most n over a finite field k we show that the trivial cell probe algorithm for the problem is optimal if k is sufficiently large compared to n as an application we give a new proof of the fact that p incr time o log n log log n

gaussian predictive process models for large spatial data sets with scientific data available at geocoded locations investigators are increasingly turning to spatial process models for carrying out statistical inference over the last decade hierarchical models implemented through markov chain monte carlo methods have become especially popular for spatial modelling given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics however fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations rendering such models infeasible for large spatial data sets this computational burden is exacerbated in multivariate settings with several spatially dependent response variables it is also aggravated when data are collected at frequent time points and spatiotemporal process models are used with regard to this challenge our contribution is to work with what we call predictive process models for spatial and spatiotemporal data every spatial or spatiotemporal process induces a predictive process model in fact arbitrarily many of them the latter models project process realizations of the former to a lower dimensional subspace thereby reducing the computational burden hence we achieve the flexibility to accommodate non stationary non gaussian possibly multivariate possibly spatiotemporal processes in the context of large data sets we discuss attractive theoretical properties of these predictive processes we also provide a computational template encompassing these diverse settings finally we illustrate the approach with simulated and real data sets

brief paper on a reachability problem for affine hypersurface systems on polytopes this paper studies the problem for an affine hypersurface system with n 1 inputs to reach a polytopic target set starting from inside a polytope in the state space we present a solution which begins with a characterization of solvability by open loop control and concludes with a procedure to synthesize a feedback control our emphasis is on methods of subdivision triangulation and covers which explicitly account for the capabilities of the control system in contrast with the previous literature the partition methods are guaranteed to yield a correct feedback synthesis assuming the problem is solvable by open loop control

efficient mode enumeration of compositional hybrid systems a hyperplane arrangement is a polyhedral cell complex where the relative position of each cell of the arrangement and the composing hyperplanes are summarised by a sign vector computable in polynomial time this tool from computational geometry enables the development of a fast and efficient algorithm to translate the composition of discrete time linear hybrid systems into an equivalent piecewise affine model and to determine if the composition is well posed the tool also provides information on the real combinatorial degree of the system which can be used to reduce the size of the search tree and the computation time of the optimisation algorithms underlying optimal and model predictive control examples are presented illustrating the algorithm and showing its computational effectiveness

spatial modeling with spatially varying coefficient processes in many applications the objective is to build regression models to explain a response variable over a region of interest under the assumption that the responses are spatially correlated in nearly all of this work the regression coefficients are assumed to be constant over the region however in some applications coefficients are expected to vary at the local or subregional level here we focus on the local case although parametric modeling of the spatial surface for the coefficient is possible here we argue that it is more natural and flexible to view the surface as a realization from a spatial process we show how such modeling can be formalized in the context of gaussian responses providing attractive interpretation in terms of both random effects and explaining residuals we also offer extensions to generalized linear models and to spatio temporal setting we illustrate both static and dynamic modeling with a dataset that attempts to explain log selling price of single family houses

continuity properties for random fields l auteur donne pour un champ aleatoire n dimensionnel donne une condition simple sur la fonction de covariance qui garantit l existence d une version du champ aleatoire dans laquelle les realisations sont partout continues la demonstration implique une approximation assez delicate du champ aleatoire par des polynomes d interpellation d ordre eleve

spatial homogeneity pursuit of regression coefficients for large datasets spatial regression models have been widely used to describe the relationship between a response variable and some explanatory variables over a region of interest taking into account the spatial de

dynamic programming for constrained optimal control of discrete time linear hybrid systems in this paper we study the solution to optimal control problems for constrained discrete time linear hybrid systems based on quadratic or linear performance criteria the aim of the paper is twofold first we give basic theoretical results on the structure of the optimal state feedback solution and of the value function second we describe how the state feedback optimal control law can be constructed by combining multiparametric programming and dynamic programming

complexity models for incremental computation def nrp hbox rm protect small nrp def poly hbox rm protect small p def nick hbox rm protect small nc def incrplt hbox rm it incr allowbreak protect small polylogtime def logsp hbox rm protect small logspace def incrls hbox rm it incr allowbreak protect small logspace def rincrls hbox rm it rincr allowbreak protect small logspace def incrpls hbox rm it incr allowbreak protect small polylogspace def nlgsp hbox rm protect small nlogspace we present a new complexity theoretic approach to incremental computation we define complexity classes that capture the intuitive notion of incremental efficiency and study their relation to existing complexity classes we show that problems that have small sequential space complexity also have small incremental time complexity we show that all common logsp complete problems for poly are also incrplt complete for poly we introduce a restricted notion of completeness called nrp completeness and show that problems which are nrp complete for poly are also incrplt complete for poly we also give incrementally complete problems for nlgsp logsp and non uniform nick 1 we show that under certain restrictions problems which have efficient dynamic solutions also have efficient parallel solutions we also consider a non uniform model of incremental computation and show that in this model most problems have almost linear complexity in addition we present some techniques for lower bounding the complexity of explicitly defined problems we also look at the time complexity of circuit value and network stability problems restricted to comparator gates we show that the comparator circuit value problem and the lex first maximal matching problem are in incrls while the comparator network stability and the man optimal stable marriage problem are in rincrls nlgsp this shows that the dynamic versions of these problems are solvable quickly in parallel even though there are no known nick algorithms to solve them from scratch

the cell probe complexity of succinct data structures we consider time space tradeoffs for static data structure problems in the cell probe model with word size 1 the bit probe model in this model the goal is to represent n bit data with s n r bits such that queries of a certain type about the data can be answered by reading at most t bits of the representation ideally we would like to keep both s and t small but there are tradeoffs between the values of s and t that limit the possibilities of keeping both parameters small in this paper we consider the case of succinct representations where s n r for some email protected n for a boolean version of the problem of polynomial evaluation with preprocessing of coefficients we show a lower bound on the redundancy query time tradeoff of the form r 1 t email protected n logn in particular for very small redundancies r we get an almost optimal lower bound stating that the query algorithm has to inspect almost the entire data structure up to a logarithmic factor we show similar lower bounds for problems satisfying a certain combinatorial properties of a coding theoretic flavor and obtain r 1 t email protected n for certain problems previously no w m lower bounds were known on t in the general model for explicit boolean problems even for very small redundancies by restricting our attention to systematic or index structures f satisfying f x email protected email protected x for some map f where denotes concatenation we show similar lower bounds on the redundancy query time tradeoff for the natural data structuring problems of prefix sum and substring search

studies in the history of probability and statistics xlix on the matern correlation family summary handcock stein 1993 introduced the matern family of spatial correlations into statistics as a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field we document the varied history of this family which includes contributions by eminent physical scientists and statisticians

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

convex partitions of polyhedra a lower bound and worst case optimal algorithm the problem of partitioning a polyhedron into a minimum number of convex pieces is known to be np hard we establish here a quadratic lower bound on the complexity of this problem and we describe an algorithm that produces a number of convex parts within a constant factor of optimal in the worst case the algorithm is linear in the size of the polyhedron and cubic in the number of reflex angles since in most applications areas the former quantity greatly exceeds the latter the algorithm is viable in practice

model choice a minimum posterior predictive loss approach summary model choice is a fundamental and much discussed activity in the analysis of datasets nonnested hierarchical models introducing random effects may not be handled by classical methods bayesian approaches using predictive distributions can be used though the formal solution which includes bayes factors as a special case can be criticised we propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values we obtain this criterion by minimising posterior loss for a given model and then for models under consideration selecting the one which minimises this criterion for a broad range of losses the criterion emerges as a form partitioned into a goodness of fit term and a penalty term we illustrate its performance with an application to a large dataset involving residential property transactions

technical communique evaluation of piecewise affine control via binary search tree we present an algorithm for generating a binary search tree that allows efficient computation of piecewise affine pwa functions defined on a polyhedral partition this is useful for pwa control approaches such as explicit model predictive control as it allows the controller to be implemented online with small computational effort the computation time is logarithmic in the number of regions in the pwa partition

penalized local polynomial regression for spatial data when performing spatial regression analysis in environmental data applications spatial heterogeneity in the regression coefficients is often observed spatially varying coefficient models including geographically weighted regression and spline models are standard tools for quantifying such heterogeneity in this paper we propose a spatially varying coefficient model that represents the spatially varying parameters as a mixture of local polynomials at selected locations the local polynomial parameters have attractive interpretations indicating various types of spatial heterogeneity instead of estimating the spatially varying regression coefficients directly we develop a penalized least squares regression procedure for the local polynomial parameter estimation which both shrinks the parameter estimation and penalizes the differences among parameters that are associated with neighboring locations we develop confidence intervals for the varying regression coefficients and prediction intervals for the response we apply the proposed method to characterize the spatially varying association between particulate matter concentrations pm2 5 and pollutant gases related to the secondary aerosol formulation in china the identified regression coefficients show distinct spatial patterns for nitrogen dioxide sulfur dioxide and carbon monoxide during different seasons

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

should tables be sorted we examine optimality questions in the following information retrieval problem given a set s of n keys store them so that queries of the form is x in s can be answered quickly it is shown that in a rather general model including al1 the commonly used schemes lceil lg n l rceil probes to the table are needed in the worst case provided the key space is sufficiently large the effects of smaller key space and arbitrary encoding are also explored

error correcting data structures we study data structures in the presence of adversarial noise we want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object even if the data structure has been corrupted by a constant fraction of errors we measure the efficiency of a data structure in terms of its length the number of bits in its representation and query answering time measured by the number of bit probes to the possibly corrupted representation the main issue is the trade off between these two this new model is the common generalization of static data structures and locally decodable error correcting codes ldcs we prove a number of upper and lower bounds on various natural error correcting data structure problems in particular we show that the optimal length of t probe error correcting data structures for the membership problem where we want to store subsets of size s from a universe of size n such that membership queries can be answered effic

a multiparametric quadratic programming algorithm with polyhedral computations based on nonnegative least squares model predictive control mpc is one of the most successful techniques adopted in industry to control multivariable systems under constraints on input and output variables to circumvent the main drawback of mpc i e the need to solve a quadratic program qp on line to compute the control action explicit mpc was proposed in the past to precompute the control law off line using multiparametric qp mpqp the resulting form of the mpc law is piecewise affine which is extremely easy to code can be computed online by simple arithmetic operations and requires a maximum number of iterations that can be exactly determined a priori on the other hand the offline computations to solve the mpqp problem require detecting emptiness full dimensionality and minimal hyperplane representations of polyhedra and other computational geometric operations while most of the existing methods solve such operations via linear programming the approach proposed in this paper relies on a nonnegative least squares nnls solver that is very simple to code and fast to execute in addition the new approach exploits qp duality to identify and construct critical regions and to handle degeneracy issues

bayesian nonparametric spatial modeling with dirichlet process mixing customary modeling for continuous point referenced data assumes a gaussian process that is often taken to be stationary when such models are fitted within a bayesian framework the unknown parameters of the process are assumed to be random so a random gaussian process results here we propose a novel spatial dirichlet process mixture model to produce a random spatial process that is neither gaussian nor stationary we first develop a spatial dirichlet process model for spatial data and discuss its properties because of familiar limitations associated with direct use of dirichlet process models we introduce mixing by convolving this process with a pure error process we then examine properties of models created through such dirichlet process mixing in the bayesian framework we implement posterior inference using gibbs sampling spatial prediction raises interesting questions but these can be handled finally we illustrate the approach using simulated data as well as a dataset involving precipitati

gmm estimation of 2d rca models with applications to texture image classification the 2d indexed random coefficients autoregressive 2d rca models are obtained by introducing appropriate random field coefficients to an ar model on mathrm z 2 the study of such models is motivated by their capability to capture the space varying behavior of the volatility a generalized method of moment approach is considered to estimate the 2d rca models consistency and asymptotic normality of the estimates are derived estimated parameters are used at a later stage as pixel features in texture image classification

hierarchical spatially varying coefficient process model the spatially varying coefficient process model is a nonstationary approach to explaining spatial heterogen eity by allowing coefficients to vary across space in this article we develop a methodo

model reduction of switched affine systems this paper addresses model reduction and extends balanced truncation to the class of switched affine systems with endogenous switching the switched affine system is rewritten as a switched linear one with state resets that account for the affine terms balanced truncation can then be applied to each mode dynamics independently as a result different reduced state vectors are associated with the different modes and reset maps are here appropriately redefined so as to account and compensate for this mismatch possibly preserving the continuity of the output the overall behavior of the reduced switched system is determined by both the selected reduction per mode and the adopted reset maps in this paper we consider a stochastic setting and propose a randomized method for the selection of the reduced order the performance of the proposed approach is illustrated through a multi room temperature control example

linear combinations of space time covariance functions and variograms the difference or a linear combination of two space time covariance functions or variograms is not necessarily a valid covariance function or variogram in general there seems no simple condition that makes a linear combination permissible unless its coefficients are non negative the permissibility is investigated in this paper for the linear combination of two spatial or spatio temporal covariance functions or variograms isotropic in space so that we obtain flexible classes of spatial or spatio temporal covariance functions with various properties such as long range dependence and having different signs

hybrid model reference adaptive control of piecewise affine systems this paper is concerned with the derivation of a model reference adaptive control mrac scheme for multimodal piecewise affine pwa and piecewise linear systems the control allows the plant to track asymptotically the states of a multimodal piecewise affine or smooth reference model the reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability

fast polynomial factorization and modular composition we obtain randomized algorithms for factoring degree n univariate polynomials over mathbb f q requiring o n 1 5 o 1 rm log 1 o 1 q n 1 o 1 rm log 2 o 1 q bit operations when rm log q n this is asymptotically faster than the best previous algorithms j von zur gathen and v shoup comput complexity 2 1992 pp 187 224 e kaltofen and v shoup math comp 67 1998 pp 1179 1197 for rm log q ge n it matches the asymptotic running time of the best known algorithms the improvements come from new algorithms for modular composition of degree n univariate polynomials which is the asymptotic bottleneck in fast algorithms for factoring polynomials over finite fields the best previous algorithms for modular composition use o n omega 1 2 field operations where omega is the exponent of matrix multiplication r p brent and h t kung j assoc comput mach 25 1978 pp 581 595 with a slight improvement in the exponent achieved by employing fast rectangular matrix multiplication x huang and v y pan j complexity 14 1998 pp 257 299 we show that modular composition and multipoint evaluation of multivariate polynomials are essentially equivalent in the sense that an algorithm for one achieving exponent alpha implies an algorithm for the other with exponent alpha o 1 and vice versa we then give two new algorithms that solve the problem near optimally an algebraic algorithm for fields of characteristic at most n o 1 and a nonalgebraic algorithm that works in arbitrary characteristic the latter algorithm works by lifting to characteristic 0 applying a small number of rounds of multimodular reduction and finishing with a small number of multidimensional ffts the final evaluations are reconstructed using the chinese remainder theorem as a bonus this algorithm produces a very efficient data structure supporting polynomial evaluation queries which is of independent interest our algorithms use techniques that are commonly employed in practice in contrast to all previous subquadratic algorithms for these problems which relied on fast matrix multiplication

efficient parametrisations for normal linear mixed models summary the generality and easy programmability of modern sampling based methods for maximisation of likelihoods and summarisation of posterior distributions have led to a tremendous increase in the complexity and dimensionality of the statistical models used in practice however these methods can often be extremely slow to converge due to high correlations between or weak identifiability of certain model parameters we present simple hierarchical centring reparametrisations that often give improved convergence for a broad class of normal linear mixed models in particular we study the two stage hierarchical normal linear model the laird ware model for longitudinal data and a general structure for hierarchically nested linear models using analytical arguments simulation studies and an example involving clinical markers of acquired immune deficiency syndrome aids we indicate when reparametrisation is likely to provide substantial gains in efficiency

a fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects on decrit un algorithme qui utilise des formules explicites pour l inverse et le determinant de la matrice de covariance donnee par la motte 1972 et evite l inversion des grandes matrices