spatio temporal covariance and cross covariance functions of the great circle distance on a sphere abstractin this article we propose stationary covariance functions for processes that evolve temporally over a sphere as well as cross covariance functions for multivariate random fields defined over a sphere for such processes the great circle distance is the natural metric that should be used to describe spatial dependence given the mathematical difficulties for the construction of covariance functions for processes defined over spheres cross time approximations of the state of nature have been proposed in the literature by using the euclidean based on map projections and the chordal distances we present several methods of construction based on the great circle distance and provide closed form expressions for both spatio temporal and multivariate cases a simulation study assesses the discrepancy between the great circle distance chordal distance and euclidean distance based on a map projection both in terms of estimation and prediction in a space time and a bivariate spatial setting where t

testing the covariance structure of multivariate random fields there is an increasing wealth of multivariate spatial and multivariate spatio temporal data appearing for such data an important part of model building is an assessment of the properties of the underlying covariance function describing variable spatial and temporal correlations in this paper we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio temporal context the methodology is based on the asymptotic joint normality of the sample space time cross covariance estimators specifically we address the assumptions of symmetry separability and linear models of coregionalization we conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio temporal dataset of pollutants over california

necessary conditions for stability and attractivity of continuous systems considered in this paper are control systems of the form f x u for such systems a number of related necessary conditions for various forms of stability and attractivity are presented the paper starts by showing that brockett s necessary condition for stabilizability via smooth feedback still persists if is continuous and the class of allowable u increased to include continuous feedbacks using similar ideas to those used to prove the continuous brockett result again only assuming continuity of f and u necessary conditions are then derived for global attractivity and for ultimate boundedness

on brockett s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback the necessity of brockett s condition for stabilizability of nonlinear systems by smooth feedback is shown by an argument based on properties of a degree for set valued maps to persist when the class of controls is enlarged to include discontinuous feedback

classes of nonseparable spatio temporal stationary covariance functions abstract suppose that a random process z s t indexed in space and time has spatio temporal stationary covariance c h u where h d d 1 is a spatial lag and u is a temporal lag separable spatio temporal covariances have the property that they can be written as a product of a purely spatial covariance and a purely temporal covariance their ease of definition is counterbalanced by the rather limited class of random processes to which they correspond in this article we derive a new approach that allows one to obtain many classes of nonseparable spatio temporal stationary covariance functions and fit several such classes to spatio temporal data on wind speed over a region in the tropical western pacific ocean

non gaussian spatiotemporal modelling through scale mixing we construct non gaussian processes that vary continuously in space and time with nonseparable covariance functions starting from a general and flexible way of constructing valid nonseparable covariance functions through mixing over separable covariance functions the resulting models are generalized by allowing for outliers as well as regions with larger variances we induce this through scale mixing with separate positive valued processes smooth mixing processes are applied to the underlying correlated processes in space and in time thus leading to regions in space and time of increased spread an uncorrelated mixing process on the nugget effect accommodates outliers posterior and predictive bayesian inference with these models is implemented through a markov chain monte carlo sampler an application to temperature data in the basque country illustrates the potential of this model in the identification of outliers and regions with inflated variance and shows that this improves the predictive performance

modeling non stationary processes through dimension expansion in this article we propose a novel approach to modeling nonstationary spatial fields the proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces transforming and clarifying complex patterns in the physical plane by combining aspects of multidimensional scaling group lasso and latent variable models a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity following a comparison with existing methods in a simulated environment dimension expansion is studied on a classic test bed dataset historically used to study nonstationary models following this we explore the use of dimension expansion in modeling air pollution in the united kingdom a process known to be strongly influenced by rural urban effects amongst others which gives rise to a nonstationary field

nonseparable stationary covariance functions for space time data geostatistical approaches to spatiotemporal prediction in environmental science climatology meteorology and related fields rely on appropriate covariance models this article proposes general classes of nonseparable stationary covariance functions for spatiotemporal random processes the constructions are directly in the space time domain and do not depend on closed form fourier inversions the model parameters can be associated with the data s spatial and temporal structures respectively and a covariance model with a readily interpretable space time interaction parameter is fitted to wind data from ireland

matern cross covariance functions for multivariate random fields we introduce a flexible parametric family of matrix valued covariance functions for multivariate spatial random fields where each constituent component is a matern process the model parameters are interpretable in terms of process variance smoothness correlation length and colocated correlation coefficients which can be positive or negative both the marginal and the cross covariance functions are of the matern type in a data example on error fields for numerical predictions of surface pressure and temperature over the north american pacific northwest we compare the bivariate matern model to the traditional linear model of coregionalization

lagrange stabilisation for uncertain phase controlled systems in this article we are concerned with the lagrange stabilisation problem for phase controlled systems with parameter uncertainties by using the kalman yakubovich popov lemma the frequency domain conditions for lagrange stability of nominal phase controlled systems are converted into linear matrix inequality lmi conditions the allowable parameter uncertainty bounds for controllability and observability as well as lmi conditions for lagrange stability of uncertain phase controlled systems are presented a controller design strategy based on the lmi method is proposed such that the uncertain phase controlled systems are lagrange stabilised a numerical example is provided to demonstrate the effectiveness of the proposed results

statistical methods for regular monitoring data summary meteorological and environmental data that are collected at regular time intervals on a fixed monitoring network can be usefully studied combining ideas from multiple time series and spatial statistics particularly when there are little or no missing data this work investigates methods for modelling such data and ways of approximating the associated likelihood functions models for processes on the sphere crossed with time are emphasized especially models that are not fully symmetric in space time two approaches to obtaining such models are described the first is to consider a rotated version of fully symmetric models for which we have explicit expressions for the covariance function the second is based on a representation of space time covariance functions that is spectral in just the time domain and is shown to lead to natural partially nonparametric asymmetric models on the sphere crossed with time various models are applied to a data set of daily winds at 11 sites in ireland over 18 years spectral and space time domain diagnostic procedures are used to assess the quality of the fits the spectral in time modelling approach is shown to yield a good fit to many properties of the data and can be applied in a routine fashion relative to finding elaborate parametric models that describe the space time dependences of the data about as well

a valid matern class of cross covariance functions for multivariate random fields with any number of components we introduce a valid parametric family of cross covariance functions for multivariate spatial random fields where each component has a covariance function from a well celebrated matern class unlike previous attempts our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components we present the conditions on the parameter space that result in valid models with varying degrees of complexity we discuss practical implementations including reparameterizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency we perform various monte carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging the application of the proposed multivariate matern model is illustrated on two meteorological datasets temperature pressure over the pacific northwest bivariate and wind temperature pressure in oklahoma trivariate in the latter case our flexi

aberrant crypt foci and semiparametric modeling of correlated binary data motivated by the spatial modeling of aberrant crypt foci acf in colon carcinogenesis we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent gaussian spatial process that accounts for short range dependencies the mean is modeled in a general way using regression splines the mean function can be viewed as a fixed effect and is estimated with a penalty for regularization with the latent process viewed as another random effect the model becomes a generalized linear mixed model in our motivating data set and other applications the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation reml so pairwise likelihood a special case of composite likelihood is used instead we develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications including but not limited to the problem that motivated this work the splines have penalty parameters that must converge to zero asymptotically we derive theory for this along with a data driven method for selecting the penalty parameter a method that is shown in simulations to improve greatly upon standard devices such as likelihood crossvalidation finally we apply the methods to the data from our experiment acf we discover an unexpected location for peak formation of acf

multivariate max stable spatial processes summary max stable processes allow the spatial dependence of extremes to be modelled and quantified so they are widely adopted in applications for a better understanding of extremes it may be useful to study several variables simultaneously to this end we study the maxima of independent replicates of multivariate processes both in the gaussian and student t cases we define a poisson process construction and introduce multivariate versions of the smith gaussian extreme value the schlather extremal gaussian and extremal t and the brown resnick models we develop inference for the models based on composite likelihoods we present results of monte carlo simulations and an application to daily maximum wind speed and wind gust

conjecture de type de serre et formes compagnons pour gsp4 we present a serre type conjecture on the modularity of four dimensional symplectic mod p galois representations we assume that the galois representation is irreducible and odd in the symplectic sense the modularity condition is formulated using the etale and the algebraic de rham cohomology of siegel modular varieties of level prime to p we concentrate on the case when the galois representation is ordinary at p and we give a corresponding list of serre weights when the representation is moreover tamely ramified at p we conjecture that all weights of this list are modular otherwise we describe a subset of weights on the list that should be modular we propose a construction of de rham cohomology classes using the dual bgg complex which should realise some of these weights partiellement soutenu par la nsf grant dms 0902044 et accord dms 0635607 partiellement soutenu par le projet blanc anr 10 blan 0114

a nonparametric assessment of properties of space time covariance functions we propose a unified framework for testing various assumptions commonly made for covariance functions of stationary spatio temporal random fields the methodology is based on the asymptotic normality of space time covariance estimators we focus on tests for full symmetry and separability in this article but our framework naturally covers testing for isotropy and taylor s hypothesis our test successfully detects the asymmetric and nonseparable features in two sets of wind speed data we perform simulation experiments to evaluate our test and conclude that our method is reliable and powerful for assessing common assumptions on space time covariance functions

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

on geodetic distance computations in spatial modeling summary statisticians analyzing spatial data often need to detect and model associations based upon distances on the earth s surface accurate computation of distances are sought for exploratory and interpretation purposes as well as for developing numerically stable estimation algorithms when the data come from locations on the spherical earth application of euclidean or planar metrics for computing distances is not straightforward yet planar metrics are desirable because of their easier interpretability easy availability in software packages and well established theoretical properties while distance computations are indispensable in spatial modeling their importance and impact upon statistical estimation and prediction have gone largely unaddressed this article explores the different options in using planar metrics and investigates their impact upon spatial modeling

dichotomy property and lagrange stability for uncertain pendulum like feedback systems abstract in this note property of dichotomy and lagrange stability of the uncertain pendulum like systems with additional multiplicative and h uncertainty are considered respectively by using some results of h theory the property of dichotomy and lagrange stability of uncertain pendulum like systems with multiple equilibria are transformed into l or h norm condition of some transfer functions the convergence problem of all bounded solutions for some uncertain pendulum like systems can be converted into the internal stability of another system under unstructured perturbations

daily spatiotemporal precipitation simulation using latent and transformed gaussian processes 1 a daily stochastic spatiotemporal precipitation generator that yields spatially consistent gridded quantitative precipitation realizations is described the methodology relies on a latent gaussian process to drive precipitation occurrence and a probability integral transformed gaussian process for intensity at individual locations the model reduces to a markov chain for precipitation occurrence and a gamma distribution for precipitation intensity allowing statistical parameters to be included in a generalized linear model framework statistical parameters are modeled as spatial gaussian processes which allows for interpolation to locations where there are no direct observations via kriging one advantage of such a model for the statistical parameters is that stochastic generator parameters are immediately available at any location with the ability to adapt to spatially varying precipitation characteristics a second advantage is that parameter uncertainty generally unavailable with deterministic interpolators can be immediately quantified at all locations the methodology is illustrated on two data sets the first in iowa and the second over the pampas region of argentina in both examples the method is able to capture the local and domain aggregated precipitation behavior fairly well at a wide range of time scales including daily monthly and annually

cross covariance functions for multivariate random fields based on latent dimensions summary the problem of constructing valid parametric cross covariance functions is challenging we propose a simple methodology based on latent dimensions and existing covariance models for univariate random fields to develop flexible interpretable and computationally feasible classes of cross covariance functions in closed form we focus on spatio temporal cross covariance functions that can be nonseparable asymmetric and can have different covariance structures for instance different smoothness parameters in each component we discuss estimation of these models and perform a small simulation study to demonstrate our approach we illustrate our methodology on a trivariate spatio temporal pollution dataset from california and demonstrate that our cross covariance performs better than other competing models

full scale multi output gaussian process emulator with nonseparable auto covariance functions gaussian process emulator with separable covariance function has been utilized extensively in modeling large computer model outputs the assumption of separability imposes constraints on the emulator and may negatively affect its performance in some applications where separability may not hold we propose a multi output gaussian process emulator with a nonseparable auto covariance function to avoid limitations of using separable emulators in addition to facilitate the computation of nonseparable emulator we introduce a new computational method referred to as the full scale approximation method with block modulating function fsa block approach the fsa block is an effective and accurate covariance approximation method to reduce computations for gaussian process models which applies to both nonseparable and partially separable covariance models we illustrate the effectiveness of our method through simulation studies and compare it with emulators with separable covariances we also apply our method to a real computer code of the carbon capture system

spatially varying cross correlation coefficients in the presence of nugget effects summary we derive sufficient conditions for the cross correlation coefficient of a multivariate spatial process to vary with location when the spatial model is augmented with nugget effects the derived class is valid for anychoiceofcovariancefunctions andyieldssubstantialflexibilitybetweenmultipleprocesses thekeyis to identify the cross correlation coefficient matrix with a contraction matrix which can be either diagonal implying a parsimonious formulation or a fully general contraction matrix yielding greater flexibility but added model complexity we illustrate the approach with a bivariate minimum and maximum temperature dataset in colorado allowing the two variables to be positively correlated at low elevations and nearly independent at high elevations while still yielding a positive definite covariance matrix

kernel based methods for vector valued data with correlated components this paper concerns kernel based interpolation methods for vector data with correlated components it gives conditions for a matrix kernel to be conditionally positive definite in an appropriate sense the conditions allow construction of matrix kernels from nonsymmetric mixtures and scalings of scalar kernels in particular the kernel used to model the influence of component i on component j can be different from that used to model the influence of component j on component i the vector modeling techniques considered are particularly appropriate when there are relatively few measurements of one quantity and relatively many of another correlated quantity the paper concludes with some numerical tests on model problems

decentralized dynamic output feedback for globally asymptotic stabilization of a class of dynamic networks the objective of this paper is to propose an approach to stabilization of a class of dynamic networks with each node being a non linear system with multiple equilibria the proposed algorithms which are developed within the convex optimization framework employ a decentralized dynamic output feedback structure furthermore an interesting conclusion is reached in which the stabilization problem for the whole nn dimensional dynamic networks can be converted into the simple n dimensional space in terms of only three lmis an application of output stabilization of mutually coupled phase locked loop networks is used to verify the effectiveness of the proposed methods

multivariate spatial covariance models a conditional approach multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain multivariate spatial covariance models need to be built with care since any covariance matrix that is derived from such a model must be nonnegative definite in this article we develop a conditional approach for spatial model construction whose validity conditions are easy to check we start with bivariate spatial covariance models and go on to demonstrate the approach s connection to multivariate models defined by networks of spatial variables in some circumstances such as modelling respiratory illness conditional on air pollution the direction of conditional dependence is clear when it is not the two directional models can be compared more generally the graph structure of the network reduces the number of possible models to compare model selection then amounts to finding possible causative links in the network we demonstrate our conditional approach on surface temperature and pressure data where the role of the two variables is seen to be asymmetric

aggregation cokriging for highly multivariate spatial data best linear unbiased prediction of spatially correlated multivariate random processes often called cokriging in geostatistics requires the solution of a large linear system based on the covariance and cross covariance matrix of the observations for many problems of practical interest it is impossible to solve the linear system with direct methods we propose an efficient linear unbiased predictor based on a linear aggregation of the covariables the primary variable together with this single meta covariable is used to perform cokriging we discuss the optimality of the approach under different covariance structures and use it to create reanalysis type high resolution historical temperature fields