a pseudospectral method for time domain computation of electromagnetic scattering by bodies of revolution we present a multidomain pseudospectral method for the accurate and efficient time domain computation of scattering by body of revolution bor perfectly electrically conducting objects in the bor formulation of the maxwell equations the azimuthal dependence of the fields is accounted for analytically through a fourier series the numerical scheme in the r z plane is developed in general curvilinear coordinates and the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution a modified matched layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time domain boundary conditions along edges numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis symmetric objects including spheres cone spheres and finite cylinders is compared with results from the literature illustrating the accuracy and computational efficiency associated with the use of properly constructed spectral methods to emphasize the versatility of the presented framework we compute plane wave scattering by a missile and find satisfactory agreement with method of moment mom computations

the pod deim reduced order method for stochastic allen cahn equations with multiplicative noise abstract in this paper we propose a reduced order method rom based on the monte carlo finite difference method fdm or monte carlo finite element method fem for the stochastic allen cahn sac equation with multiplicative noise the reduction method is a combination of proper orthogonal decomposition pod and discrete empirical interpolation method deim in the theoretical part the error bounds of full order method fom and pod deim are provided as well as the computational complexity of fom and pod deim in the numerical experiments section several two dimensional sac examples with multiplicative noise are considered using the monte carlo fdm and monte carlo fem as the reference methods the pod deim has obvious advantage in the computational efficiency and with the encryption in the space or time direction this advantage is more prominent

breakdown points of t type regression estimators summary to bound the influence of a leverage point generalised m estimators have been suggested however the usual generalised m estimator of regression has a breakdown point that is less than the inverse of its dimension this paper shows that dimension independent positive breakdown points can be attained by a class of well defined generalised mestimators with redescending scores the solution can be determined through optimisation of t type likelihood applied to properly weighted residuals the highest breakdown point of is attained by cauchy score these bounded influence and high breakdown estimators can be viewed as a fully iterated version of the one step generalised m estimates of simpson ruppert carroll 1992 with the two advantages of easier interpretability and avoidance of undesirable roots to estimating equations given the design dependent weights they can be computed via em algorithms empirical investigations show that they are highly competitive with other robust estimators of regression

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

timely communication symmetry and the karhunen loeve analysis the karhunen loeve k l analysis is widely used to generate low dimensional dynamical systems which have the same low dimensional attractors as some large scale simulations of pdes if the pde is symmetric with respect to a symmetry group g the dynamical system has to be equivariant under g to capture the full phase space it is shown that symmetrizing the k l eigenmodes instead of symmetrizing the data leads to considerable computational savings if the k l analysis is done in the snapshot method the feasibility of the approach is demonstrated with an analysis of kolmogorov flow

a new look at proper orthogonal decomposition we investigate some basic properties of the proper orthogonal decomposition pod method as it is applied to data compression and model reduction of finite dimensional nonlinear systems first we provide an analysis of the errors involved in solving a nonlinear ode initial value problem using a pod reduced order model then we study the effects of small perturbations in the ensemble of data from which the pod reduced order model is constructed on the reduced order model we explain why in some applications this sensitivity is a concern while in others it is not we also provide an analysis of computational complexity of solving an ode initial value problem and study the computational savings obtained by using a pod reduced order model we provide several examples to illustrate our theoretical results

optimal control of the cylinder wake in the laminar regime by trust region methods and pod reduced order models in this paper optimal control theory is used to minimize the total mean drag for a circular cylinder wake flow in the laminar regime re 200 the control parameters are the amplitude and the frequency of the time harmonic cylinder rotation in order to reduce the size of the discretized optimality system a proper orthogonal decomposition pod reduced order model rom is derived to be used as state equation we then propose to employ the trust region proper orthogonal decomposition trpod approach originally introduced by fahl m fahl trust region methods for flow control based on reduced order modeling ph d thesis trier university 2000 to update the reduced order models during the optimization process a lot of computational work is saved because the optimization process is now based only on low fidelity models a particular care was taken to derive a pod rom for the pressure and velocity fields with an appropriate balance between model accuracy and robustness the key enablers are the extension of the pod basis functions to the pressure data the use of calibration methods for the pod rom and the addition in the pod expansion of several non equilibrium modes to describe various operating conditions when the trpod algorithm is applied to the wake flow configuration this approach converges to the minimum predicted by an open loop control approach and leads to a relative mean drag reduction of 30 at reduced cost

constrained centroidal voronoi tessellations for surfaces centroidal voronoi tessellations are useful for subdividing a region in euclidean space into voronoi regions whose generators are also the centers of mass with respect to a prescribed density function of the regions their extensions to general spaces and sets are also available for example tessellations of surfaces in a euclidean space may be considered in this paper a precise definition of such constrained centroidal voronoi tessellations ccvts is given and a number of their properties are derived including their characterization as minimizers of an energy deterministic and probabilistic algorithms for the construction of ccvts are presented and some analytical results for one of the algorithms are given computational examples are provided which serve to illustrate the high quality of ccvt point sets finally ccvt point sets are applied to polynomial interpolation and numerical integration on the sphere

dynamic iteration using reduced order models a method for simulation of large scale modular systems we describe a new iterative method dynamic iteration using reduced order models dirm for simulation of large scale modular systems using reduced order models that preserve the interconnection structure this method may be compared to the waveform relaxation technique however unlike dirm waveform relaxation does not take advantage of model reduction techniques the dirm method involves simulating in turn each subsystem connected to model reduced versions of the other subsystems the data from this simulation is then used to update the reduced model for that particular subsystem we provide analytical results on convergence and accuracy of the dirm method as well as numerical examples that demonstrate the success of dirm and verify the analysis

preserving symmetries in the proper orthogonal decomposition the proper orthogonal decomposition pod also called karhunen loeve expansion has been recently used in turbulence to derive optimally fast converging bases of spatial functions leading to efficient finite truncations whether a finite number of these modes can be used in numerical simulations to derive an accurate finite set of ordinary differential equations over a certain range of bifurcation parameter values still remains an open question it is shown here that a necessary condition for achieving this goal is that the truncated system inherit the symmetry properties of the original infinite dimensional system in most cases this leads to a systematic involvement of the symmetry group in deriving a new expansion basis called the symmetric pod basis the kuramoto sivashinsky equation with periodic boundary conditions is used as a paradigm to illustrate this point of view however the conclusion is general and can be applied to other equations such as the navier stokes equations the complex g

a new numerical method for the boundary optimal control problems of the heat conduction equation a new numerical method is developed for the boundary optimal control problems of the heat conduction equation in the present paper when the boundary optimal control problem is solved by minimizing the objective function employing a conjugate gradient method the most crucial step is the determination of the gradient of objective function usually employing either the direct differentiation method or the adjoint variable method the direct differentiation method is simple to implement and always yields accurate results but consumes a large amount of computational time although the adjoint variable method is computationally very efficient the adjoint variable does not have sufficient regularity at the boundary for the boundary optimal control problems as a result a large numerical error is incurred in the evaluation of the gradient function resulting in premature termination of the conjugate gradient iteration in the present investigation a new method is developed that circumvents this difficulty with the adjoint variable method by introducing a partial differential equation that describes the temporal and spatial dynamics of the control variable at the boundary the present method is applied to the neumann and dirichlet boundary optimal control problems respectively and is found to solve the problems efficiently with sufficient accuracy

comparison of approximate methods for handling hyperparameters i examine two approximate methods for computational implementation of bayesian hierarchical models that is models that include unknown hyperparameters such as regularization constants and noise levels in the evidence framework the model parameters are integrated over and the resulting evidence is maximized over the hyperparameters the optimized hyperparameters are used to define a gaussian approximation to the posterior distribution in the alternative map method the true posterior probability is found by integrating over the hyperparameters the true posterior is then maximized over the model parameters and a gaussian approximation is made the similarities of the two approaches and their relative merits are discussed and comparisons are made with the ideal hierarchical bayesian solution in moderately ill posed problems integration over hyperparameters yields a probability distribution with a skew peak which causes signifi cant biases to arise in the map method in contrast the evidence fram

mixed finite elements for numerical weather prediction we show how mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo uniform grids this family of mixed finite element methods can be thought of in the numerical weather prediction context as a generalisation of the popular polygonal c grid finite difference methods there are a few major advantages the mixed finite element methods do not require an orthogonal grid and they allow a degree of flexibility that can be exploited to ensure an appropriate ratio between the velocity and pressure degrees of freedom so as to avoid spurious mode branches in the numerical dispersion relation these methods preserve several properties of the c grid method when applied to linear barotropic wave propagation namely a energy conservation b mass conservation c no spurious pressure modes and d steady geostrophic modes on the f plane we explain how these properties are preserved and describe two examples that can be used on pseudo uniform grids the recently developed modified rtk q k 1 element pairs on quadrilaterals and the bdfm1 p 1 dg element pair on triangles all of these mixed finite element methods have an exact 2 1 ratio of velocity degrees of freedom to pressure degrees of freedom finally we illustrate the properties with some numerical examples

low dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition in formulating mathematical models for dynamical systems obtaining a high degree of qualitative correctness i e predictive capability may not be the only objective the model must be useful for its intended application and models of reduced complexity are attractive in many cases where time consuming numerical procedures are required this paper discusses the derivation of discrete low dimensional models for the nonlinear vibration analysis of thin cylindrical shells in order to understand the peculiarities inherent to this class of structural problems the nonlinear vibrations and dynamic stability of a circular cylindrical shell subjected to static and dynamic loads are analyzed this choice is based on the fact that cylindrical shells exhibit a highly nonlinear behavior under both static and dynamic loads geometric nonlinearities due to finite amplitude shell motions are considered by using donnell s nonlinear shallow shell theory a perturbation procedure validated in previous studies is used to derive a general expression for the nonlinear vibration modes and the discretized equations of motion are obtained by the galerkin method using modal expansions for the displacements that

voronoi based finite volume methods optimal voronoi meshes and pdes on the sphere we first develop and analyze a finite volume scheme for the discretization of partial differential equations pdes on the sphere the scheme uses voronoi tessellations of the sphere for a model convection diffusion problem the finite volume scheme is shown to produce first order accurate approximations with respect to a mesh dependent discrete firstderivative norm then we introduce the notion of constrained centroidal voronoi tessellations ccvts of the sphere these are special voronoi tessellation of the sphere for which the generators of the voronoi cells are also the constrained centers of mass with respect to a prescribed density function of the cells after discussing an algorithm for determining ccvt meshes on the sphere we discuss and illustrate several desirable properties possessed by these meshes in particular it is shown that ccvt meshes define very high quality uniform and non uniform meshes on the sphere finally we discuss through some computational experiments the performance of the ccvt meshes used in conjunction with the finite volume scheme for the solution of simple model pdes on the sphere the experiments show for example that the ccvt based finite volume approximations are second order accurate if errors are measured in

studentized dynamical system for robust object tracking this paper describes a studentized dynamical system sds for robust target tracking using a subspace representation dynamical systems ds provide a powerful framework for the probabilistic modeling of temporal sequences visual tracking problems are often cast as a sequential inference problem within the ds framework and a compact way to model the observation distributions i e object appearances is through probabilistic principal component analysis ppca ppca is a classic gaussian based subspace representation method and a popular tool for appearance modeling although gaussian density has theoretically nice properties resulting in models that are always tractable they are also severely limited in practical settings one of the central issues in the use of ppca for target appearance modeling is that it is very sensitive to outliers the gaussian density has a very light tail while real world data with outliers exhibit heavy tails recently more heavy tailed distributions e g student s t distribution have been introduced to increase the robustness of the original ppca we propose to augment the traditional target tracking ds by adding a set of auxiliary latent variables to adjust the shape of the observation distribution we show that by carefully choosing the probability density of these auxiliary latent variables a more robust observation distribution can be obtained with tails heavier than gaussian numerical experiments verify that the proposed sds has a better capability to handle considerable amount of outlier noise and an improved tracking performance over ds with a gaussian based observation model

evaluation of proper orthogonal decomposition based decomposition techniques applied to parameter dependent nonturbulent flows the proper orthogonal decomposition pod method as a systematic technique to analyze parameter dependent problems may be inappropriate as a practical tool for generating low dimensional models we propose a weighted pod w pod as an alternative to give higher priority to low energetic or important modes by simply weighting a predefined pod p pod is suggested where modes are selected not only on the basis of energy but also on some a priori knowledge of the system the techniques are tested on a flow problem undergoing steady or unsteady transition but may in general be applied to nonlinear systems of discretized pdes closed by additional linear algebraic equations various residual functions to measure the quality of the reduced models are introduced they provide lower limits of residual energy to ensure an adequate physical representation for a given modeling it is shown that modes extracted locally may generally not contain information regarding the global dynamics and the dynamics may not be correctly predicted over a longer range of model parameters it is demonstrated that by weighting and predefining base vectors it is possible to improve the pod technique s capability to generate low dimensional models

probabilistic tracking with exemplars in a metric space a new exemplar based probabilistic paradigm for visual tracking is presented probabilistic mechanisms are attractive because they handle fusion of information especially temporal fusion in a principled manner exemplars are selected representatives of raw training data used here to represent probabilistic mixture distributions of object configurations their use avoids tedious hand construction of object models and problems with changes of topology using exemplars in place of a parameterized model poses several challenges addressed here with what we call the metric mixture m2 approach which has a number of attractions principally it provides alternatives to standard learning algorithms by allowing the use of metrics that are not embedded in a vector space secondly it uses a noise model that is learned from training data lastly it eliminates any need for an assumption of probabilistic pixelwise independence experiments demonstrate the effectiveness of the m2 model in two domains tracking walking people using chamfer distances on binary edge images and tracking mouth movements by means of a shuffle distance

stabilized reduced order models for the advection diffusion reaction equation using operator splitting reduced order modeling rom coupled with finite element methods has been used effectively in many disciplines to efficiently solve complex problems however for advection dominated flows numerical simulations often contain spurious nonphysical oscillations which will also be apparent in the rom simulations in this work we consider stabilization methods for rom for the advection diffusion reaction adr equation when it is solved both with and without operator splitting specifically we consider the streamline upwind petrov galerkin supg stabilization method and the spurious oscillations at layers diminishing sold stabilization method we build on these methods by constructing a coherent framework which successfully integrates these model reduction stabilization and operator splitting approaches and we provide numerical examples detailing the application of this framework in the adr setting the stabilized rom results are compared numerically with their corresponding full finite element simulations

linearized reduced order models for subsurface flow simulation a trajectory piecewise linearization tpwl procedure for the reduced order modeling of two phase flow in subsurface formations is developed and applied the method represents new pressure and saturation states using linear expansions around states previously simulated and saved during a series of preprocessing training runs the linearized representation is projected into a low dimensional space with the projection matrix constructed through proper orthogonal decomposition of the states determined during the training runs the tpwl model is applied to two example problems containing 24 000 and 79 200 grid blocks which are characterized by heterogeneous permeability descriptions extensive test simulations are performed for both models it is shown that the tpwl model provides accurate results when the controls bottom hole pressures of the production wells in this case applied in test simulations are within the general range of the controls applied in the training runs even though the well pressure schedules for the test runs can differ significantly from those of the training runs this indicates that the tpwl model displays a reasonable degree of robustness runtime speedups using the procedure are very significant a factor of 100 2000 depending on model size and whether or not mass balance error is computed at every time step for the cases considered the preprocessing overhead required by the tpwl procedure is the equivalent of about four high fidelity simulations finally the tpwl procedure is applied to a computationally demanding multiobjective optimization problem for which the pareto front is determined limited high fidelity simulations demonstrate the accuracy and applicability of tpwl for this optimization future work should focus on error estimation and on stabilizing the method for large models with significant density differences between phases

low dimensional dynamics for the complex ginzburg landau equation abstract a method is presented which results in low dimensional dynamical systems for situations in which low dimensional attractors are known to exist the method is based on the use of the karhunen loeve procedure for the determination of an optimal basis and the subsequent use of the galerkin procedure to generate the dynamical system the method is applied to two problems for the ginzburg landau equation for which large databases have been obtained in each instance a dynamical system is generated which has roughly twice the number of degrees of freedom as the hausdorff dimension of the exact case it is also demonstrated that the approximations are robust in that they are accurate over a wide range of parameter space

galerkin proper orthogonal decomposition methods for parabolic problems in this work error estimates for galerkin proper orthogonal decomposition pod methods for linear and certain non linear parabolic systems are proved the resulting error bounds depend on the number of pod basis functions and on the time discretization numerical examples are included

centroidal voronoi tessellation based reduced order modeling of complex systems noindent a reduced order modeling methodology based on centroidal voronoi tessellations cvts is introduced cvts are special voronoi tessellations for which the generators of the voronoi diagram are also the centers of mass means of the corresponding voronoi cells for discrete data sets cvts are closely related to the h means and k means clustering techniques a discussion of reduced order modeling for complex systems such as fluid flows is given to provide a context for the application of reduced order bases then detailed descriptions of cvt based reduced order bases and how they can be constructed from snapshot sets and how they can be applied to the low cost simulation of complex systems are given subsequently some concrete incompressible flow examples are used to illustrate the construction and use of cvt based reduced order bases the cvt based reduced order modeling methodology is shown to be effective for these examples

grid generation and optimization based on centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding voronoi regions such tessellations are of use in very diverse applications including data compression clustering analysis cell biology territorial behavior of animals and optimal allocation of resources in this paper we explore the use of cvts in grid generation in connection with finite element approximations of partial differential equations we being by describing these tessellations and methods for their determination we then discuss their application to mesh generation and finish with some examples of their use for the solution of partial differential equations

a priori space time separated representation for the reduced order modeling of low reynolds number flows abstract reduced order models roms in fluid dynamics are nowadays mostly developed by performing a projection of the navier stokes equations onto a low dimensional space basis this basis is usually obtained through proper orthogonal decomposition pod which remains one the most efficient techniques to compress precomputed data the main drawback of a posteriori pod based roms is however their lacks of reliability as their parameters are varied preventing their direct uses within optimization algorithms the goal of the present article is to obtain an a priori low dimensional space time separated representation of the fluid fields without precomputed data the approach is based on the use of space time proper generalized decomposition pgd definitions which are successfully applied in several fields but whose uses in fluid dynamics remain scarce their applications to the navier stokes equations are indeed not straightforward due to the pressure velocity coupling the divergence free constraint and the non linear convective term the roms are built here from a space time weak formulation of the chorin temam prediction correction scheme more particularly a priori space time separated representations are obtained by applying the galerkin based progressive pgd definition the minimax pgd definition is moreover experimented on a linear stokes simplified case the related algorithms are explicitly given and illustrated on a transient lid driven cavity flow it is shown that the a priori space time separated representations converge to the full model solution as the decomposition order increases the ability of the resulting rom to learn iteratively from its own error is highlighted the progressive pgd algorithm can be used to effectively enrich incomplete pod and pgd precomputed space bases such as those obtained with different parameter values this may allow to ensure the accuracy of a rom as the parameter is varied which is of crucial interest for optimization problems

reduced order modeling of time dependent pdes with multiple parameters in the boundary data abstract the computational approximation of solutions to nonlinear partial differential equations pdes such as the navier stokes equations is often a formidable task for this reason there is significant interest in the development of very low dimensional models that can be used to determine reasonably accurate approximations in simulation and control problems for pdes many concrete tests have been reported on in the literature that show that several classes of reduced order models roms are effective i e an accurate approximate solution can be obtained using very low dimensional roms most of these tests involved problems for which the solution depends on only a single parameter appearing in the boundary data the extension of the techniques used in those tests to the case of multiple parameters is not a straightforward matter here we present test and compare two methods for treating within the context of a class of roms inhomogeneous dirichlet type boundary conditions that contain multiple parameters in this study we focus on the proper orthogonal decomposition pod approach to rom however the issues and results discussed here in the pod context apply equally well to other rom approaches

an extension of dg methods for hyperbolic problems to one dimensional semi infinite domains abstract we consider spectral discretizations of hyperbolic problems on unbounded domains using laguerre basis functions taking as model problem the scalar advection equation we perform a comprehensive stability analysis that includes strong collocation formulations nodal and modal weak formulations with either inflow or outflow boundary conditions using either gauss laguerre or gauss laguerre radau quadrature and based on either scaled laguerre functions or scaled laguerre polynomials we show that some of these combinations give rise to intrinsically unstable discretizations while the combination of scaled laguerre functions with gauss laguerre radau quadrature appears to be stable for both strong and weak formulations we then show how a modal discretization approach for hyperbolic systems on an unbounded domain can be naturally and seamlessly coupled to a discontinuous finite element discretization on a finite domain an example of one dimensional hyperbolic system is solved with the proposed domain decomposition technique the errors obtained with the proposed approach are found to be small enabling the use of the coupled scheme for the simulation of rayleigh damping layers in the semi infinite part energy errors and reflection ratios of the scheme in absorbing wavetrains and single gaussian signals show that a small number of modes in the semi infinite domain are sufficient to damp the waves the theoretical insight and numerical results corroborate previous findings by the authors and establish the scaled laguerre functions based discretization as a flexible and efficient tool for absorbing layers as well as for the accurate simulation of waves in unbounded regions

stable and efficient spectral methods in unbounded domains using laguerre functions stable and efficient spectral methods using laguerre functions are proposed and analyzed for model elliptic equations on regular unbounded domains it is shown that spectral galerkin approximations based on laguerre functions are stable and convergent with spectral accuracy in the usual not weighted sobolev spaces efficient accurate and well conditioned algorithms using laguerre functions are developed and implemented numerical results indicating the spectral convergence rate and effectiveness of these algorithms are presented

an efficient method of solving the navier stokes equations for flow control a new method of solving the navier stokes equations efficiently by reducing their number of modes is proposed in the present paper it is based on the karhunen loeve decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system employing these empirical eigenfunctions as basis functions of a galerkin procedure one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena and consequently reduce the navier stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom the present algorithm is well suited for the problems of flow control or optimization where one has to compute the flow field repeatedly using the navier stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables the low dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the navier stokes equation 1998 john wiley sons ltd

convergence of the lloyd algorithm for computing centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids mass centers of the corresponding voronoi regions with respect to a given density function centroidal voronoi tessellations may also be defined in more abstract and more general settings due to the natural optimization properties enjoyed by cvts they have many applications in diverse fields the lloyd algorithm is one of the most popular iterative schemes for computing the cvts but its theoretical analysis is far from complete in this paper some new analytical results on the local and global convergence of the lloyd algorithm are presented these results are derived through careful utilization of the optimization properties shared by cvts numerical experiments are also provided to substantiate the theoretical analysis

eigentracking robust matching and tracking of articulated objects using a view based representation this paper describes an approach for tracking rigid and articulated objects using a view based representation the approach builds on and extends work on eigenspace representations robust estimation techniques and parameterized optical flow estimation first we note that the least squares image reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation second we define a subspace constancy assumption that allows us to exploit techniques for parameterized optical flow estimation to simultaneously solve for the view of an object and the affine transformation between the eigenspace and the image to account for large affine transformations between the eigenspace and the image we define a multi scale eigenspace representation and a coarse to fine matching strategy finally we use these techniques to track objects over long image sequences in which the objects simultaneously undergo both affine image motions and changes of view in particular we use this eigentracking technique to track and recognize the gestures of a moving hand

enablers for robust pod models this paper focuses on improving the stability as well as the approximation properties of reduced order models rom based on proper orthogonal decomposition pod the rom is obtained by seeking a solution belonging to the pod subspace and that at the same time minimizes the navier stokes residuals we propose a modified rom that directly incorporates the pressure term in the model the rom is then stabilized making use of a method based on the fine scale equations an improvement of the pod solution subspace is performed thanks to an hybrid method that couples direct numerical simulations and reduced order model simulations the methods proposed are tested on the two dimensional confined square cylinder wake flow in laminar regime

probabilistic principal component analysis principal component analysis pca is a ubiquitous technique for data analysis and processing but one which is not based upon a probability model in this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model closely related to factor analysis we consider the properties of the associated likelihood function giving an em algorithm for estimating the principal subspace iteratively and discuss the advantages conveyed by the definition of a probability density function for pca

a variational bayesian approach to robust sensor fusion based on student t distribution in this paper a robust sensor fusion method is proposed where the measurement noise is modeled by a student t distribution the student t distribution has a heavy tail compared to the gaussian distribution and is robust to outliers we formulate sensor fusion as a state space estimation problem in the bayesian framework both batch and recursive variational bayesian vb algorithms are developed to perform this non gaussian state space estimation problem to obtain the fusion results computer simulations show that the proposed approach has an improved fusion performance and a lower computation cost compared to methods based on gaussian and finite gaussian mixture models

meshfree probabilistic determination of point sets and support regions for meshless computing new algorithms are presented for the determination of point sets and associated support regions that can then be used in meshless computing methods the algorithms are probabilistic in nature so that they are totally meshfree i e they do not require at any stage the use of any coarse or fine boundary conforming or superimposed meshes computational examples are provided that show for both uniform and non uniform point distributions that the algorithms result in high quality point sets and high quality support regions furthermore the algorithms lend themselves well to parallelization

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments