further results on least squares based adaptive minimum variance control based on the recently established results on self tuning regulators originally proposed by astrom and wittenmark this paper presents various novel and extended results on least squares based adaptive minimum variance control for linear stochastic systems these results establish self optimality self tuning property and the best possible convergence rate of the control law in a variety of situations of interest

adaptive control of parametric nonlinear autoregressive models via a new martingale approach the purpose of this note is to investigate the stability and the optimality of the adaptive tracking for a wide class of parametric nonlinear autoregressive models via a new martingale approach several asymptotic results for the standard least squares estimator of the unknown model parameter such as a central limit theorem a law of iterated logarithm and strong laws of large numbers are also provided

stability and convergence of a finite element method for reactive transport in ground water an explicit finite element method is used to solve the linear convection diffusion reaction equations governing contaminant transport in ground water flowing through an adsorbing porous medium the use of discontinuous finite elements for the convective part of the equations combined with mixed finite elements for the diffusive part renders the method for the concentration solution which displays strong gradients trivially conservative and fully parallelizable we carry out a stability and convergence analysis in particular the method is proven to satisfy a maximum principle to be total variation bounded and to converge to the unique weak solution of the equations special attention is paid to the convective part of the equations numerical simulations are presented and discussed

on the implementation of mixed methods as nonconforming methods for second order elliptic problems in this paper we show that mixed finite element methods for a fairly general second order elliptic problem with variable coefficients can be given a nonmixed formulation lower order terms are treated so our results apply also to parabolic equations we define an approximation method by incorporating some projection operators within a standard galerkin method which we call a projection finite element method it is shown that for a given mixed method if the projection method s finite element space m h satisfies three conditions then the two approximation methods are equivalent these three conditions can be simplified for a single element in the case of mixed spaces possessing the usual vector projection operator we then construct appropriate nonconforming spaces m h for the known triangular and rectangular elements the lowest order raviart thomas mixed solution on rectangular finite elements in r 2 and r 3 on simplices or on prisms is then implemented as a nonconforming method modified in a simple and computationally trivial manner this new nonconforming solution is actually equivalent to a postprocessed version of the mixed solution a rearrangement of the computation of the mixed method solution through this equivalence allows us to design simple and optimal order multigrid methods for the solution of the linear system

convergence rates in stochastic adaptive tracking abstract for stochastic control systems described by the armax model with unknown matrix coefficients the stochastic adaptive control is designed so that the parameter estimates converge to the true values with a rate of convergence o log n log log n c n a with a 0 c 1 and the tracking error tends to its minimum value at a speed of o n 1 2e with e 0

hierarchical image segmentation part i detection of regular curves in a vector graph the problem of edge detection is viewed as a hierarchy of detection problems where the geometric objects to be detected e g edge points curves regions have increasing complexity and spatial extent an early stage of the proposed hierarchy consists in detecting the regular portions of the visible edges the input to this stage is given by a graph whose vertices are tangent vectors representing local and uncertain information about the edges a model relating the input vector graph to the curves to be detected is proposed an algorithm with linear time complexity is described which solves the corresponding detection problem in a worst case scenario the stability of curve reconstruction in the presence of uncertain information and multiple responses to the same edge is analyzed and addressed explicitly by the proposed algorithm

an in depth study of graph partitioning measures for perceptual organization in recent years one of the effective engines for perceptual organization of low level image features is based on the partitioning of a graph representation that captures gestalt inspired local structures such as similarity proximity continuity parallelism and perpendicularity over the low level image features mainly motivated by computational efficiency considerations this graph partitioning process is usually implemented as a recursive bipartitioning process where at each step the graph is broken into two parts based on a partitioning measure we focus on three such measures namely the minimum average and normalized cuts the minimum cut partition seeks to minimize the total link weights cut the average cut measure is proportional to the total link weight cut normalized by the sizes of the partitions the normalized cut measure is normalized by the product of the total connectivity valencies of the nodes in each partition we provide theoretical and empirical insight into the nature of the three partitioning measures in terms of the underlying image statistics in particular we consider for what kinds of image statistics would optimizing a measure irrespective of the particular algorithm used result in correct partitioning are the quality of the groups significantly different for each cut measure are there classes of images for which grouping by partitioning does not work well also can the recursive bipartitioning strategy separate out groups corresponding to k objects from each other in the analysis we draw from probability theory and the rich body of work on stochastic ordering of random variables our major conclusion is that optimization of none of the three measures is guaranteed to result in the correct partitioning of k objects in the strict stochastic order sense for all image statistics

nonparametric density estimation prediction and regression for markov sequences abstract let xi be a stationary markov sequence having a transition probability density function f y x giving the pdf of x i 1 xi x in this study nonparametric density and regression techniques are employed to infer f y x and m x e x i 1 xi x it is seen that under certain regularity and markovian assumptions the asymptotic convergence rate of the nonparametric estimator mn x to the predictor m x is the same as it would have been had the xi s been independently and identically distributed and this rate is optimal in a certain sense consistency can be maintained after differentiability and even the markovian assumptions are abandoned computational and modeling ramifications are explored i claim that my methodology offers an interesting alternative to the popular arma approach

nonlinearity estimation in hammerstein systems based on ordered observations the nonlinear subsystem of a hammerstein system is identified i e its characteristic is recovered from input output ohservations of the whole system the input and disturbance are white stochastic processes the identified characteristic satisfies a piecewise lipschitz condition only algorithms presented in the paper are calculated from ordered input output observations i e from pairs of observations arranged in a sequence in which input measurements increase in value the mean integrated square error converges to zero as the number of observations tends to infinity convergence rates are insensitive to the shape of the probability density of the input signal results of numerical simulation are also shown

central limit theorem and law of iterated logarithm for least squares algorithms in adaptive tracking in autoregressive adaptive tracking we prove that the least squares and the weighted least squares algorithms possess the same asymptotic properties sharing the same central limit theorem and the same law of iterated logarithm we also obtain the same asymptotic behavior and show the limitations of these results in the autoregressive with moving average framework

discrete time model reference adaptive control of nonlinear dynamical systems using neural networks a multilayer discrete time neural net nn controller is presented for the direct model reference adaptive control of a class of multi input multi output mim0 nonlinear dynamical systems the nonlinear dynamical system is assumed to be controllable and its state vector is available for measurement the nn controller exhibits learning while functioning features instead of learning then control so that control is immediate with no explicit learning phase needed the tracking error between the output of a nonlinear plant and an ideal linear model converges within a very short time persistence of excitation pe is not needed linearity in the parameters is not required and certainty equivalence is not used this overcomes several limitations of standard adaptive control the novel weight tuning paradigm for the nn controller is based on the well known delta rule but includes a modification to the learning rate parameter plus a correction term it guarantees tracking as well as bounded nn weights in non i

space and time bounds on indexing 3d models from 2d images model based visual recognition systems often match groups of image features to groups of model features to form initial hypotheses which are then verified in order to accelerate recognition considerably the model groups can be arranged in an index space hashed offline such that feasible matches are found by indexing into this space for the case of 2d images and 3d models consisting of point features bounds on the space required for indexing and on the speedup that such indexing can achieve are demonstrated it is proved that even in the absence of image error each model must be represented by a 2d surface in the index space this places an unexpected lower bound on the space required to implement indexing and proves that no quantity is invariant for all projections of a model into the image theoretical bounds on the speedup achieved by indexing in the presence of image error are also determined and an implementation of indexing for measuring this speedup empirically is presented it is found that indexing can produce only a minimal speedup on its own however when accompanied by a grouping operation indexing can provide significant speedups that grow exponentially with the number of features in the groups

stochastic adaptive prediction and model reference control guo and chen 1991 have recently shown how to establish the self optimality and mean square stability of a self tuning regulator the idea allows us to proceed with the development of a more comprehensive theory of stochastic adaptive filtering control and identification in adaptive filtering we examine both indirect and noninterlaced direct schemes for prediction using both least squares and gradient parameter estimation algorithms in addition to analyzing similar direct adaptive control algorithms we propose new generalized certainty equivalence adaptive model reference control laws with simultaneous disturbance rejection we also establish that the parameters converge to the null space of a certain matrix from this one may deduce the convergence of several adaptive controllers

almost sure rate of convergence of the parameter estimates in stochastic approximation algorithm this paper presents novel results on the almost sure convergence of the parameter estimates in stochastic approximation algorithm it is proved that this rate has the same order as the best one established for the least squares algorithm although we consider the case of self tuning controllers the presented results can easily be extended to some other adaptive processes

nonparametric estimation and adaptive control of functional autoregressive models this paper deals with nonparametric estimation and adaptive control of nonlinear systems of the form x n 1 f x n u n xi n 1 n in bkn where the state x n is observed f is an unknown function and the control un is chosen in order to track a given reference trajectory we estimate the function f using a nonparametric estimator and study two adaptive control laws built from this nonparametric estimator and derived from the self tuning control the first one can be used for open loop stable systems and requires an additional exciting noise the second one needs some a priori knowledge on function f but allows us to control open loop unstable systems we establish some general results on the nonparametric estimator of f like the uniform almost sure convergence over dilating sets and then prove that both adaptive control laws are asymptotically optimal in quadratic mean in addition we give a strongly consistent estimator of the covariance matrix of the unobservable white noise xi n

on feedback capability in a class of nonlinearly parameterized uncertain systems in this technical note we will investigate the maximum capability and limitations of the feedback mechanism in globally stabilizing a basic class of discrete time nonlinearly parameterized dynamical systems with multiple unknown parameters both possibility and impossibility theorems together with a fairly complete characterization on the capability of feedback will be presented it will be seen that to characterize the feedback capability the growth rates of the sensitivity functions of the nonlinear dynamics with respect to the uncertain parameters play a crucial role and a suitable decomposition of the family of the nonlinearly parameterized functions in question turns out to be necessary

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

self convergence of weighted least squares with applications to stochastic adaptive control a recursive least squares algorithm with slowly decreasing weights for linear stochastic systems is found to have self convergence property i e it converges to a certain random vector almost surely irrespective of the control law design such algorithms enjoy almost the same nice asymptotic properties as the standard least squares this universal convergence result combined with a method of random regularization then easily can be applied to construct a self convergent and uniformly controllable estimated model and thus may enable us to form a general framework for adaptive control of possibly nonminimum phase autoregressive moving average with exogenous input armax systems as an application we give a simple solution to the well known stochastic adaptive pole placement and linear quadratic gaussian lqg control problems in the paper

uniform consistency of kernel estimators of a regression function under generalized conditions abstract in this article we prove uniform consistency of kernel estimators of a multivariate regression function under various assumptions on the distribution of the data in addition to the usual assumptions that the data are iid and that the distribution of the regressors is absolutely continuous we consider the cases that some regressors are discrete and the data are either stationary mixing themselves or generated by a class of functions of one sided infinite stationary mixing sequences moreover we demonstrate the performance of the kernel estimation method under these generalized conditions by a numerical example

proprietes de convergence presque complete du predicteur a noyau let z n be a mixing process which is valued in mathbb e subset mathbb r q g be a real measurable function defined on mathbb e s and k be two positive integers we suppose the existence of a function r satisfying r e g z n s z n k 1 z n n n k and estimate the function r from a sequence z i i 1 n by r n with r n u frac sum limits i k n s g z i s k u z i k 1 cdots z i h n 1 sum limits i k n s k u z i k 1 cdots z i h n 1 forall u in mathbb e k where k is a kernel of kq and h n h n 0 we give various conditions on both the sequences h n and the sequence n which is associated with z n for the two following properties uniform complete convergence to r for the functional estimator r n and complete convergence to 0 for the real random variable r n z n k 1 z n r zn k 1 z n this last result concerns the predictor r n z n k 1 z n of g z n s from z i i 1 n when the process z n is stationary and markovian of order k

a comparison of measures for detecting natural shapes in cluttered backgrounds we propose a new measure of perceptual saliency and quantitatively compare its ability to detect natural shapes in cluttered backgrounds to five previously proposed measures as defined in the new measure the saliency of an edge is the fraction of closed random walks which contain that edge the transition probability matrix defining the random walk between edges is based on a distribution of natural shapes modeled by a stochastic motion each of the saliency measures in our comparison is a function of a set of affinity values assigned to pairs of edges although the authors of each measure define the affinity between a pair of edges somewhat differently all incorporate the gestalt principles of good continuation and proximity in some form in order to make the comparison meaningful we use a single definition of affinity and focus instead on the performance of the different functions for combining affinity values the primary performance criterion is accuracy we compute false positive rates in classifying edges as signal or noise for a large set of test figures in almost every case the new measure significantly outperforms previous measures

testing and estimation of thresholds based on wavelets in heteroscedastic threshold autoregressive models summary we consider the testing and estimation of thresholds in heteroscedastic threshold autoregressive models with an unknown number of thresholds a test statistic based on empirical wavelet coefficients is proposed the asymptotic distribution of the test statistic is established and consistent estimators of the thresholds and the number of thresholds are given a monte carlo study and a real example are used to assess the performance of our method

the aastrom wittenmark self tuning regulator revisited and els based adaptive trackers although considerable progress has been made in stochastic adaptive control the problem concerning the convergence of the original self tuning regulator proposed by k j aastrom and b wittenmark 1973 is still open since it is attractive in theory and important in applications this problem is examined and a rigorous proof of its stability and optimality is given related problems such as convergence of the extended least squares els based adaptive tracker are also considered

robust and efficient detection of salient convex groups this paper describes an algorithm that robustly locates salient convex collections of line segments in an image the algorithm is guaranteed to find all convex sets of line segments in which the length of the gaps between segments is smaller than some fixed proportion of the total length of the lines this enables the algorithm to find convex groups whose contours are partially occluded or missing due to noise we give an expected case analysis of the algorithm performance this demonstrates that salient convexity is unlikely to occur at random and hence is a strong clue that grouped line segments reflect underlying structure in the scene we also show that our algorithm run time is o n sup 2 log n nm when we wish to find the m most salient groups in an image with n line segments we support this analysis with experiments on real data and demonstrate the grouping system as part of a complete recognition system

semi smooth newton methods for nonlinear complementarity formulation of compositional two phase flow in porous media abstract simulating compositional multiphase flow in porous media is a challenging task especially when phase transition is taken into account the main problem with phase transition stems from the inconsistency of the primary variables such as phase pressure and phase saturation i e they become ill defined when a phase appears or disappears recently a new approach for handling phase transition has been developed whereby the system is formulated as a nonlinear complementarity problem ncp unlike the widely used primary variable switching pvs method which requires a drastic reduction of the time step size when a phase appears or disappears this approach is more robust and allows for larger time steps one way to solve an ncp system is to reformulate the inequality constraints as a non smooth equation using a complementary function c function because of the non smoothness of the constraint equations a semi smooth newton method needs to be developed in this work we consider two methods for solving ncp systems used to model multiphase flow 1 a semi smooth newton method for two c functions the minimum and the fischer burmeister functions and 2 a new inexact newton method based on the jacobian smoothing method for a smooth version of the fischer burmeister function we show that the new method is robust and efficient for standard benchmark problems as well as for realistic examples with highly heterogeneous media such as the spe10 benchmark

on the usefulness of persistent excitation in arx adaptive tracking the usefulness of persistent excitation is well known in the control community thanks to a persistently excited adaptive tracking control we show that it is possible to avoid the strong controllability assumption recently proposed in the multidimensional arx framework we establish the almost sure convergence for both least squares and weighted least squares estimators of the unknown parameters a central limit theorem and a law of iterated logarithm are also provided all this asymptotical analysis is related to the schur complement of a suitable limiting matrix

finding k cuts within twice the optimal two simple approximation algorithms for the minimum k cut problem are presented each algorithm finds a k cut having weight within a factor of 2 2 k of the optimal one of our algorithms is particularly efficient it requires a total of only n 1 maximum flow computations for finding a set of near optimal k cuts one for each value of k between 2 and n

identification of iir nonlinear systems without prior structural information in this paper we propose a kernel method for identification of infinite impulse response iir nonlinear systems without prior structural information the main result of the paper is to establish the conditions for asymptotic convergence in terms of the input to output exponential stability the performance of the method is tested on real world applications and computer simulations the results obtained show the efficacy of the method

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

weighted estimation and tracking for branching processes with immigration for branching processes with immigration we propose an approach which allows us to consistently estimate the means m spl lambda and the variances spl sigma sup 2 b sup 2 of the offspring and immigration distributions respectively generally statistical results for branching processes are established under the well known trichotomy m 1 for example no parameters of the immigration distribution can be consistently estimated if m 1 the purpose of the paper is to obtain through the introduction of a suitable adaptive control strongly consistent estimators for all the parameters m spl lambda spl sigma sup 2 and b sup 2 without any restriction on the range of m central limit theorems and laws of iterated logarithm are also provided

fully discrete finite element analysis of multiphase flow in groundwater hydrology this paper deals with the development and analysis of a fully discrete finite element method for a nonlinear differential system for describing an air water system in groundwater hydrology the nonlinear system is written in a fractional flow formulation i e in terms of a saturation and a global pressure the saturation equation is approximated by a finite element method while the pressure equation is treated by a mixed finite element method the analysis is carried out first for the case where the capillary diffusion coefficient is assumed to be uniformly positive and is then extended to a degenerate case where the diffusion coefficient can be zero it is shown that error estimates of optimal order in the l 2 norm and almost optimal order in the l infty norm can be obtained in the nondegenerate case in the degenerate case we consider a regularization of the saturation equation by perturbing the diffusion coefficient the norm of error estimates depends on the severity of the degeneracy in diffusivity with almost optimal order convergence for nonsevere degeneracy implementation of the fractional flow formulation with various nonhomogeneous boundary conditions is also discussed results of numerical experiments using the present approach for modeling groundwater flow in porous media are reported

convergence and logarithm laws of self tuning regulators abstract this paper starts with a survey of some recent results on least squares ls and ls based self tuning regulators str several long standing problems concerning the basic properties of ls based str such as stability optimality consistency and the best convergence rate are solved within a unified framework some previously related results are also subsumed and extended various new techniques for analysing ls based adaptive tracking systems are presented which may also be useful for analysing other adaptive control problems

on critical stability of discrete time adaptive nonlinear control in this paper we examine the global stability and instability problems for a class of discrete time adaptive nonlinear stochastic control the systems to be controlled may exhibit chaotic behavior and are assumed to be linear in unknown parameters but nonlinear in output dynamics which are characterized by a nonlinear function say f x it is found and proved that in the scalar parameter case there is a critical stability phenomenon for least squares ls based adaptive control systems to be specific let the growth rate of f x be f x o spl par x spl par sup 6 with b spl ges 0 then it is found that b 4 is a critical value for global stability i e the closed loop adaptive system is globally stable if b 4 and is unstable in general if b spl ges 4 as a consequence we find an interesting phenomenon that the linear case does not have for some ls based certainty equivalence adaptive controls even if the ls parameter estimates are strongly consistent the closed loop systems may still be unstable this paper also indicates that adaptive nonlinear stochastic control that is designed based on e g taylor expansion or weierstrass approximation for nonlinear models may not be feasible in general

asymptotically efficient self tuning regulators this paper studies the problem of adaptive regulation of linear systems with white noise disturbances the apparent dilemma between the control objective and the need of information for parameter estimation is resolved by occasional use of white noise probing inputs and by a reparametrization of the model insights into the question concerning how often and when such probing inputs should be introduced are provided by the concept of asymptotic efficiency which quantifies the asymptotically minimal cost due to parameter ignorance or equivalently due to the infeasibility of using the optimal regulator that assumes knowledge of the system parameters asymptotically efficient adaptive regulators are constructed by making use of certain basic properties of adaptive predictors involving recursive least squares for the reparametrized model

an optimal graph theoretic approach to data clustering theory and its application to image segmentation a novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated the data to be clustered are represented by an undirected adjacency graph g with arc capacities assigned to reflect the similarity between the linked vertices clustering is achieved by removing arcs of g to form mutually exclusive subgraphs such that the largest inter subgraph maximum flow is minimized for graphs of moderate size approximately 2000 vertices the optimal solution is obtained through partitioning a flow and cut equivalent tree of g which can be efficiently constructed using the gomory hu algorithm 1961 however for larger graphs this approach is impractical new theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size this algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices the new clustering algorithm is applied to the image segmentation problem the segmentation is achieved by effectively searching for closed contours of edge elements equivalent to minimum cuts in g which consist mostly of strong edges while rejecting contours containing isolated strong edges this method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

weighted estimation and tracking for armax models for complex multivariate armax models the author studies the weighted least squares algorithm which offers by the choice of suitable weightings the advantages of both the extended least squares and the stochastic gradient algorithms concerning adaptive tracking problems the strong consistency of the estimator and control optimality are both ensured almost sure rates of convergence are also provided

adaptive tracking control of linear systems with binary valued observations and periodic target this technical note studies the adaptive control for linear systems with set valued observations to track a given periodic target based on the system parameters accessorial parameters with the same order as that of the tracking targets are introduced and estimated considering the system parameters are unknown and set valued observations can supply only limited information each time a two scale adaptive control algorithm is designed each control input is designed at the large time scale and lasts for a holding time small scale during which the parameter estimation algorithm is constructed from the estimate of accessorial parameters the control signal is updated at the large time scale by the certainty equivalence principle as the holding time goes to infinity the algorithm can be proved to be asymptotically efficient in a certain sense meanwhile the adaptive tracking algorithm is shown to be asymptotically optimal a numerical example is given to demonstrate the effectiveness of the algorithms and the main results obtained

analysis of the inexact uzawa algorithm for saddle point problems in this paper we consider the so called inexact uzawa algorithm for iteratively solving linear block saddle point problems such saddle point problems arise for example in finite element and finite difference discretizations of stokes equations the equations of elasticity and mixed finite element discretization of second order problems we consider both the linear and nonlinear variants of the inexact uzawa iteration we show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left hand block in the case of nonlinear iteration the inexact uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left hand block is of sufficient accuracy bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear uzawa algorithm applications to the stokes equations and mixed finite element discretization of second order elliptic problems are discussed and finally the results of numerical experiments involving the algorithms are presented

brief paper a new concept of strong controllability via the schur complement for arx models in adaptive tracking we propose a new concept of strong controllability related to the schur complement of a suitable limiting matrix this new notion allows us to extend the previous convergence results associated with multidimensional arx models in stochastic adaptive tracking on the one hand we carry out a sharp analysis of the almost sure convergence for both least squares and weighted least squares algorithms on the other hand we also provide a central limit theorem and a law of iterated logarithm for these two algorithms

globally optimal regions and boundaries as minimum ratio weight cycles we describe a new form of energy functional for the modeling and identification of regions in images the energy is defined on the space of boundaries in the image domain and can incorporate very general combinations of modeling information both from the boundary intensity gradients etc and from the interior of the region texture homogeneity etc we describe two polynomial time digraph algorithms for finding the global minima of this energy one of the algorithms is completely general minimizing the functional for any choice of modeling information it runs in a few seconds on a 256 spl times 256 image the other algorithm applies to a subclass of functionals but has the advantage of being extremely parallelizable neither algorithm requires initialization

search for additive nonlinear time series causal models pointwise consistent feasible procedures for estimating contemporaneous linear causal structure from time series data have been developed using multiple conditional independence tests but no such procedures are available for non linear systems we describe a feasible procedure for learning a class of non linear time series structures which we call additive non linear time series we show that for data generated from stationary models of this type two classes of conditional independence relations among time series variables and their lags can be tested efficiently and consistently using tests based on additive model regression combining results of statistical tests for these two classes of conditional independence relations and the temporal structure of time series data a new consistent model specification procedure is able to extract relatively detailed causal information we investigate the finite sample behavior of the procedure through simulation and illustrate the application of this method through analysis of the possible causal connections among four ocean indices several variants of the procedure are also discussed

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extended least squares and their applications to adaptive control and prediction in linear systems herein strong consistency of recursive extended least squares is established under considerably weaker assumptions than previously assumed in the literature the argument used to establish consistency also leads to certain basic properties of adaptive predictors based on these recursive estimators making use of these properties of the adaptive predictors simple modifications of the astrom wittenmark self tuning regulator are proposed and shown to be asymptotically optimal

nonlinear adaptive tracking using kernel estimators estimation and test for linearity we present some statistical results on nonlinear adaptive control using kernel estimators we are concerned with a nonlinear autoregressive model of the form x n 1 f x n u n xi n 1 hskip 0 4cm n in mathbb n controlled using a nonparametric estimator of the unknown function f and derived from a tracking control policy we prove an almost sure convergence result for the noise density estimator a pointwise central limit theorem for f and a test for linearity of the driving function f

inferring global perceptual contours from local features we address the problem of contour inference from partial data as obtained from state of the art edge detectors we argue that in order to obtain more pereeptually salient contours it is necessary to impose generic constraints such as continuity and co curvilinearity the implementation is in the form of a convolution with a mask which encodes both the orientation and the strength of the possible continuations we first show how the mask called the extension field is derived then how the contributions from different sites are collected to produce a saliency map we show that the scheme can handle a variety of input data from dot patterns to oriented edgels in a unified manner and demonstrate results on a variety of input stimuli we also present a similar approach to the problem of inferring contours formed by end points in both cases the scheme is non linear non iterative and unified in the sense that all types of input tokens are handled in the same manner

adaptive control with the stochastic approximation algorithm geometry and convergence new geometric properties possessed by the sequence of parameter estimates are exhibited which yield valuable insight into the behavior of the stochastic approximation based algorithm as it is used in minimum variance adaptive control in particular these geometric properties together with certain probabilistic arguments prove that if the system does not have a reduced order minimum variance controller then the parameter estimates converge to a random multiple of the true parameter an explicit expression for the limiting parameter estimate is also available with strictly positive probability the limiting parameter estimate is not the true parameter and in some cases differs from the true parameter with probability one if the system possesses reduced order minimum variance controllers then convergence to a minimum variance controller in a cesaro sense is shown the geometry of the limit set is described sufficient conditions are also given for some of these results to hold for parameter estimation schemes other than stochastic approximation

comparison of various formulations of three phase flow in porous media various formulations of the governing equations that describe three phase e g water oil and gas flow in porous media including phase global and pseudo global pressure saturation formulations are discussed in this paper comparisons of these differential formulations are theoretically and numerically presented for the first time it is shown that the global pressure saturation formulation is the most efficient one from the computational point of view in the case where the three phase relative permeability and capillary pressure curves satisfy a so called total differential condition the pseudo global formulation is useful when the fractional flow functions of the water and gas phases are close to their respective mean values and the phase formulation can be applied generally

nonparametric function estimation involving time series consider a stationary time series mathbf x t y t t 0 pm 1 ldots with mathbf x t being mathbb r d valued and y t real valued the conditional mean function is given by theta mathbf x 0 e y 0 mid mathbf x 0 under appropriate regularity conditions a local average estimator of this function based on a finite realization mathbf x 1 y 1 ldots mathbf x n y n can be chosen to achieve the optimal rate of convergence n 1 2 d both pointwise and in l 2 norms restricted to a compact and it can also be chosen to achieve the optimal rate of convergence n 1 log n 1 2 d in l infty norm restricted to a compact similar results hold for local median estimators of the conditional median function which is given by theta mathbf x 0 operatorname med y 0 mid mathbf x 0

kernel density estimation and goodness of fit test in adaptive tracking we investigate the asymptotic properties of a recursive kernel density estimator of the driven noise of multivariate armax models in adaptive tracking we provide an almost sure pointwise and uniform strong law of large numbers as well as a pointwise and multivariate central limit theorem we also carry out a goodness of fit test together with some simulation experiments

salient closed boundary extraction with ratio contour we present ratio contour a novel graph based method for extracting salient closed boundaries from noisy images this method operates on a set of boundary fragments that are produced by edge detection boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency we encode the gestalt laws of proximity and continuity in a novel boundary saliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary this new measure attempts to remove a possible bias toward short boundaries we present a polynomial time algorithm for finding the most salient closed boundary we also present supplementary preprocessing steps that facilitate the application of ratio contour to real images we compare ratio contour to two closely related methods for extracting closed boundaries elder and zucker s method based on the shortest path algorithm and williams and thornber s method based on spectral analysis and a strongly connected components algorithm this comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images

three phase compressible flow in porous media we describe the construction of total differential td three phase data for the implementation of the exact global pressure formulation for the modeling of three phase compressible flow in porous media this global formulation is preferred since it reduces the coupling between the pressure and saturation equations compared to phase or weighted formulations it simplifies the numerical analysis of the problem and boosts its computational efficiency however this global pressure approach exists only for three phase data relative permeabilities capillary pressures which satisfy a td condition such td three phase data are determined by the choice of a global capillary pressure function and a global mobility function which take both saturations and global pressure level as argument boundary conditions for global capillary pressure and global mobility are given such that the corresponding three phase data are consistent with a given set of three two phase data the numerical construction of global capillary pressure and global mobility functions by c 1 and c 0 finite element is then performed using bi laplacian and laplacian interpolation examples of the corresponding td three phase data are given for a compressible and an incompressible case

robust streamline tracing for the simulation of porous media flow on general triangular and quadrilateral grids streamline methods for subsurface flow simulation have received renewed attention as fast alternatives to traditional finite volume or finite element methods key aspects of streamline simulation are the accurate tracing of streamlines and the computation of travel time along individual streamlines in this paper we propose a new streamline tracing framework that enables the extension of streamline methods to unstructured grids composed of triangular or quadrilateral elements and populated with heterogeneous full tensor coefficients the proposed method is based on the mathematical framework of mixed finite element methods which provides approximations of the velocity field that are especially suitable for streamline tracing we identify and implement two classes of velocity spaces the lowest order raviart thomas space low order tracing and the brezzi douglas marini space of order one high order tracing both on triangles and quadrilaterals we discuss the implementation of the streamline tracing method in detail and we investigate the performance of the proposed tracing strategy by means of carefully designed test cases we conclude that for the same computational cost high order tracing is more accurate smaller error in the time of flight and robust less sensitive to grid distortion than low order tracing

graph partitioning active contours gpac for image segmentation in this paper we introduce new types of variational segmentation cost functions and associated active contour methods that are based on pairwise similarities or dissimilarities of the pixels as a solution to a minimization problem we introduce a new curve evolution framework the graph partitioning active contours gpac using global features our curve evolution is able to produce results close to the ideal minimization of such cost functions new and efficient implementation techniques are also introduced in this paper our experiments show that gpac solution is effective on natural images and computationally efficient experiments on gray scale color and texture images show promising segmentation results