topologies on measured groupoids abstract if an analytic borel group g has a quasiinvariant measure it is known that g is actually a locally compact group with the original borel structure being generated by the topology and the original measure being equivalent to haar measure in this paper a variation is given on the known proof which then extends to show that an analytic measured groupoid has a compact and also a locally compact inessential reduction which is a topological groupoid in the compact case it is proved that every almost homomorphism agrees a e with a strict homomorphism also the topology is used to show that every measured groupoid has a complete countable section 7 and that every locally compact equivalence relation has a complete transversal 3 these are further used to show that some results of feldman et al 7 apply in general and that a locally compact groupoid with continuous haar system has sufficiently many non singular borel g sets provided that the orbit measures are atom free 23

ergodic theory group representations and rigidity in these lectures we discuss some topics concerning the relationship of ergodic theory representation theory and the structure of lie groups and their discrete subgroups

cech de rham theory for leaf spaces of foliations we present a new cech de rham model for the cohomology of the classifying space of a foliated manifold this model enables us to lift the construction of known characteristic classes in the cohomology of the manifold to the cohomology of the classifying space by standard geometric methods and without making any reference to necessarily non hausdorff groupoids and their classifying spaces we also show how the cech de rham model can be used to prove some other known formulas as well as a version of poincare duality for foliations

unscented kalman filter over unreliable communication networks with markovian packet dropouts the paper investigates the stability of the discrete time modified unscented kalman filter mukf in transmitting measurement outputs to the filter via a network since the communication channel states do not always vary in time the arrival of the observations is modeled as a two state time homogeneous markov process k the stability of the estimation error covariance matrices at packet reception times is analyzed sufficient conditions related to hk and the initial conditions for the peak covariance stability and the usual covariance stability are given also the relationship between the different types of stability notions is illustrated for systems with i i d observation dropouts numerical example is given to illustrate the effectiveness of the techniques developed

stochastic stability of the extended kalman filter with intermittent observations in this technical note we analyze the error behavior of the discrete time extended kalman filter for nonlinear systems with intermittent observations modelling the arrival of the observations as a random process we show that given a certain regularity of the system the estimation error remains bounded if the noise covariance and the initial estimation error are small enough we also study the effect of different measurement models on the bounds for the error covariance matrices

ls category of compact hausdorff foliations the transverse saturated lusternik schnirelmann category of foliations introduced by the first author in 5 9 is an invariant of foliated homotopy type with values in 1 2 1 a foliation with all leaves compact and hausdorff leaf space m f is called compact hausdorff the transverse saturated category cat m of a compact hausdorff foliation is always finite in this paper we study the transverse category of compact hausdorff foliations our main result provides upper and lower bounds on the transverse category cat m in terms of the geometry of f and the epstein filtration of the exceptional set e the exceptional set is the closed saturated foliated space which is the union of the leaves with non trivial holonomy we prove that max cat m f cat e cat m cat e q we give examples to show that both the upper and lower bounds are realized so the estimate is sharp we also construct a family of examples for which the transverse category for a compact hausdorff foliation can be arbitrarily large though the category of the leaf spaces is constant

flat bundles and residues for foliations in this note we compute the residues for a vector field preserving a foliation we assume the vector field disappears only to first order along its singular set and that its singular set consists of closed separated leaves under these conditions the residue is completely determined by the characteristic classes of the flat bundle v o which is the normal bundle v of the foliation restricted to the singular set and the action of the vector field on v o for a foliation of even codimension q whose normal bundle has euler class zero we interpret the pontrjagin ring of the normal bundle in dimension 2q as an obstruction to the existence of such a vector field we show that if the euler class of the normal bundle of a foliation is zero and it admits such a vector field then many of its secondary characteristic classes must be also be zero this is one of the few results relating the geometry of a foliation to its characteristic classes we will make extensive use of the material in 6 it will be very helpful to the reader to be familiar with this paper

liaison classes of modules abstract we propose a concept of module liaison that extends gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative gorenstein ring analyzing the resulting equivalence classes we show that several results known for gorenstein liaison are still true in the more general case of module liaison in particular we construct two maps from the set of even liaison classes of modules of fixed codimension into stable equivalence classes of certain reflexive modules as a consequence we show that the intermediate cohomology modules and properties like being perfect cohen macaulay buchsbaum or surjective buchsbaum are preserved in even module liaison classes furthermore we prove that the module liaison class of a complete intersection of codimension one consists of precisely all perfect modules of codimension one

graph based transductive learning for robust visual tracking in object tracking problem most methods assume brightness constancy or subspace constancy which are violated in practice in this paper the object tracking problem is considered as a transductive learning problem and a robust tracking method is proposed under intrinsic and extrinsic varieties the object not only fits the object model but also has the same cluster with the previous objects which are the labeled data by constraining the global and local information the cost function is constructed firstly the solution for minimizing the cost function can be solved by a simple linear algebra with graph laplacian moreover a novel graph is constructed over the positive samples and candidate patches which can simultaneously learn the object s global appearance model and the local intrinsic geometric structure of all the patches furthermore a heuristic positive samples selection scheme is adopted to make the method more effective the proposed method is tested on different videos which undergo large pose expression illumination and partial occlusion and compared with state of the art algorithms experimental results and comparative studies are provided to demonstrate the efficiency of the proposed method

ensemble tracking we consider tracking as a binary classification problem where an ensemble of weak classifiers is trained online to distinguish between the object and the background the ensemble of weak classifiers is combined into a strong classifier using adaboost the strong classifier is then used to label pixels in the next frame as either belonging to the object or the background giving a confidence map the peak of the map and hence the new position of the object is found using mean shift temporal coherence is maintained by updating the ensemble with new weak classifiers that are trained online during tracking we show a realization of this method and demonstrate it on several video sequences

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

on the characteristic classes of actions of lattices in higher rank lie groups we show that under certain assumptions the measurable cohomology class of the linear holonomy cocycle of a foliation yields information about the characteristic classes of the foliation combined with the results of a previous paper this yields vanishing theorems for characteristic classes of certain actions of lattices in higher rank semisimple lie groups let f be a discrete group acting by diffeomorphisms on a smooth compact manifold m associated to this action are certain characteristic classes in h f r which are constructed as characteristic classes of a natural foliation associated to the group action the action of f on m induces an action of f on the principal frame bundle p m of m and the characteristic classes of the action can be interpreted as obstructions to the existence of invariant geometric structures on m i e principal subbundles of p m invariant by the f action if f is a lattice in a higher rank semisimple lie group then f has strong rigidity properties see e g m z1 in an earlier paper s we showed using techniques from ergodic theory that for a certain class of f actions there is always an invariant measurable reductive geometric structure i e a measurable principal subbundle with reductive structure group which is invariant by the f action moreover the noncompact semisimple part of this reductive group is locally isomorphic to a semisimple factor of the ambient lie group of f zi zimmer z3 recently proved this result for a large class of actions which does not a priori include the class of actions considered in s a natural question is whether these results remain true in the smooth category the purpose of this paper is to show that the characteristic classes which obstruct a smooth geometric structure vanish in the presence of a measurable geometric structure explicitly we have main theorem let m y be a codimension n c 2 foliated manifold and suppose that the linear holonomy cocycle is measurably equivalent to a locally tempered cocycle taking values in a subgroup h c gl n r which is stable under transpose then the weil homomorphism x h g n 0 n hc m yi received by the editors february 24 1989 1980 mathematics subject classification 1985 revision primary 57r32 secondary 57s20 research partially supported by an alfred p sloan dissertation fellowship 1991 american mathematical society 0002 9947 91 1 00 25 per page

technical communique stochastic stability of the unscented kalman filter with intermittent observations in this paper the stochastic stability of the discrete time unscented kalman filter for general nonlinear stochastic systems with intermittent observations is proposed it is shown that the estimation error remains bounded if the system satisfies some assumptions and the statistical convergence property of the estimation error covariance is studied showing the existence of a critical value for the arrival rate of the observations an upper bound on this expected state error covariance is given a numerical example is given to illustrate the effectiveness of the techniques developed

performance evaluation of ukf based nonlinear filtering the performance of the modified unscented kalman filter ukf for nonlinear stochastic discrete time system with linear measurement equation is investigated it is proved that under certain conditions the estimation error of the ukf remains bounded furthermore it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm error behavior of the ukf is then derived in terms of mean square error mse and the cramer rao lower bound crlb is introduced as a performance measure the modified ukf is found to approach the crlb if the difference between the real noise covariance matrix and the selected one is small enough these results are verified by using monte carlo simulations on two example systems

equicontinuous foliated spaces riemannian foliations are characterized as those foliations whose holonomy pseudogroup consists of local isometries of a riemannian manifold their main structural features are well understood since the work of molina in this paper we analyze the more general concept of equicontinuous pseudogroup of homeomorphisms which gives rise to the notion of equicontinuous foliated space we show that equicontinuous foliated spaces have structural properties similar to those known for riemannian foliations the universal covers of their leaves are in the same quasi isometry class leaf closures are homogeneous spaces and the holonomy pseudogroup is indeed given by local isometries

robust control on saturated markov jump systems with missing information in this paper a robust h controller is designed for saturated markov jump systems with uncertainties and time varying transition probabilities the time varying transition probability uncertainty is described as a polytope set stochastic stability is analyzed for the underlying systems by lyapunov function approach and a sufficient condition is derived to design controllers such that the resulting closed loop system is stochastically stable and a prescribed h performance is also achieved furthermore the attraction domain of this markov jump system is estimated and evaluated a simulation example is given to show the effectiveness of the developed techniques

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

robust discriminative tracking via landmark based label propagation the appearance of an object could be continuously changing during tracking thereby being not independent identically distributed a good discriminative tracker often needs a large number of training samples to fit the underlying data distribution which is impractical for visual tracking in this paper we present a new discriminative tracker via landmark based label propagation llp that is nonparametric and makes no specific assumption about the sample distribution with an undirected graph representation of samples the llp locally approximates the soft label of each sample by a linear combination of labels on its nearby landmarks it is able to effectively propagate a limited amount of initial labels to a large amount of unlabeled samples to this end we introduce a local landmarks approximation method to compute the cross similarity matrix between the whole data and landmarks moreover a soft label prediction function incorporating the graph laplacian regularizer is used to diffuse the known labels to all the unlabeled vertices in the graph which explicitly considers the local geometrical structure of all samples tracking is then carried out within a bayesian inference framework where the soft label prediction value is used to construct the observation model both qualitative and quantitative evaluations on the benchmark data set containing 51 challenging image sequences demonstrate that the proposed algorithm outperforms the state of the art methods

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

global invariants for measured foliations new exotic invariants for measured foliations are constructed which we call the u classes of a pair f u the dependence of the s classes on the geometry of the foliation gis examined and the dynamics of a foliation is shown to determine the u classes in many cases we use the u classes to study the classifying space bfsl of foliations with a transverse invariant volume form and we show the homotopy groups of bfsl are uncountably generated starting in degrees q 3 new invariants for groups of volume preserving diffeomorphisms also arise from the t classes these invariants are nontrivial and related to the geometric aspects of the group action relations between the tl classes and the secondary classes of a foliation are exhibited 0 introduction in this paper we construct new exotic characteristic classes for foliations which have a transverse invariant measure these invariants which we call the t classes are similar to the secondary classes and take values in the real cohomology h m of the foliated manifold m theorem 1 6 the values of the m classes are strongly related to the geometry of the foliation proposition 3 4 the u classes have applications to the study of foliations with a transverse invariant volume form theorems 5 1 and 5 2 to the computations of the homology groups of the discrete group of volume preserving diffeomorphisms of rw theorem 7 4 and to the problem of relating the secondary classes of a foliation with its global geometry 15 201 the a classes arose from an attempt to obtain general invariants of a foliation which are intermediate between the leaf and secondary classes they are a special case of a family of universal invariants associated to a c2 foliation the weil operators in codimension one the introduction of the weil operator is a decisive ingredient in duminy s elegant proof of the sullivan conjecture about the godbillon vey class 9 the properties of the weil operators in higher codimensions are given in 15 where they are used to study the residuable secondary classes we briefly describe the construction of the weil operators and their relations with the l classes and other foliation invariants in 2 for a foliation with all leaves compact we note that the weil operators are identically zero proposition 2 6 we denote by f a c2 foliation of codimension q on a paracompact manifold m and i denotes a transverse invariant measure for sf recall that ti assigns to each received by the editors june 28 1982 and in revised form november 9 1982 1980 mathematics subject classification primary 57r30 57r20 58f1 1 secondary 58h10 28d15

the harmonic measures of lucy garnett abstract this paper presents an improved approach to the theory of harmonic measures for foliated spaces introduced by garnett this approach is based on a method for solving elliptic equations on foliated spaces and on the hille yosida theory the diffusion semigroup of a general laplacian and its infinitesimal generator are made explicit applications of the path space to the dynamical study of a foliated space are described in particular the final section studies cocycles on foliated spaces a formula for their asymptotic limit and some analytic and geometric consequences

cocycles of ergodic group actions and vanishing of first cohomology for s arithmetic groups introduction in this paper we study cocycles of ergodic actions of s arithmetic subgroups of semisimple lie groups of higher rank we show that under suitable hypotheses the algebraic hull of the cocycle is reductive in the special case of the trivial action on a point this gives a new proof of the vanishing of first cohomology for s arithmetic nonarithmetic groups

improved cubature kalman filter for gnss ins based on transformation of posterior sigma points error tightly coupled gnss ins has been widely approved as a promising substitute for standalone gnss in urban areas navigation however due to the frequent gnss signal outages the filter used in gnss ins should be insensitive to the less informative observations in this paper a novel sigma points update method is proposed to enhance the robustness of cubature kalman filter ckf under the circumstance of unavailable observations first the problems of existing sampling based filters are analyzed then by transforming the posterior sigma points error matrix from prediction phase of filtering to the posterior domain of update the updated sigma points are expected to capture the covariance more precisely than traditional sigma points finally an improved ckf ickf is developed by embedding these points into the bayesian estimation framework and the upper bounds of error covariance matrices are analyzed theoretically signal outages with different durations are simulated and results demonstrate that ickf outperforms state of the art methods

secondary classes and transverse measure theory of a foliation 1 the purpose of this note is to announce several theorems showing how the secondary classes of a foliation j of a compact manifold x depend upon the measure theoretic properties of the equivalence relation determined by the foliation the relevant properties are i amenability 14 which is equivalent to hyperfiniteness by connesfeldman weiss 3 and ii the murray von neumann type a set b c x is saturated if it is the union of leaves of 7 the equivalence relation 7 has type i if there is a measurable subset of x which intersects almost every leaf exactly once type ii if it admits an invariant measure finite or infinite in the given measure class but does not have an essential saturated set of type i and type iii if it does not have any essential saturated sets of types i or ii every equivalence relation can be decomposed into parts of types i ii and iii these types correspond to certain algebraic properties of the von neumann algebra m x 7 associated with the equivalence relation 1 13 let x be a compact manifold without boundary and j a c 2 codimensionn foliation of x the secondary classes are given by a map a h won h x r with image spanned by the classes of the form a yicj here yi is a basis element for the relative cohomology if gln on and cj is a chern form of degree at most 2n if degree cj 2n we say the class is residual the godbillon vey classes are those of the form a yicj 2 n 1 x r with 2 1 g if gln on the normalized basis element the generalized godbillonvey classes are those of the form a yiy cj where yi 1 is permitted for a convenient reference see 11 the residual secondary classes have the unusual property that they localize to the measurable saturated subsets of x for each such b c x and residual yicj e p wo n the restriction a 2 cj g h x is well defined 5 the following theorems are stated for the secondary classes of 7 on x but corresponding theorems also hold for the localized classes a yicj b of the restriction 7 b

a strong tracking extended kalman observer for nonlinear discrete time systems the authors show how the extended kalman filter used as an observer for nonlinear discrete time systems or extended kalman observer eko becomes a useful state estimator when the arbitrary matrices namely r sub k and q sub k are adequately chosen as a first step we use the linearization technique given by boutayed et al 1997 which consists of introducing unknown diagonal matrices to take the approximation errors into account it is shown that the decreasing lyapunov function condition leads to a linear matrix inequality lmi problem which points out the connection between a good convergence behavior of the eko and the instrumental matrices r sub k and q sub k in order to satisfy the obtained lmi a particular design of q sub k is given high performances of the proposed technique are shown through numerical examples under the worst conditions

visual tracking via discriminative sparse similarity map in this paper we cast the tracking problem as finding the candidate that scores highest in the evaluation model based upon a matrix called discriminative sparse similarity map dss map this map demonstrates the relationship between all the candidates and the templates and it is constructed based on the solution to an innovative optimization formulation named multitask reverse sparse representation formulation which searches multiple subsets from the whole candidate set to simultaneously reconstruct multiple templates with minimum error a customized apg method is derived for getting the optimum solution in matrix form within several iterations this formulation allows the candidates to be evaluated accurately in parallel rather than one by one like most sparsity based trackers do and meanwhile considers the relationship between candidates therefore it is more superior in terms of cost performance ratio the discriminative information containing in this map comes from a large template set with multiple positive target templates and hundreds of negative templates a laplacian term is introduced to keep the coefficients similarity level in accordance with the candidates similarities thereby making our tracker more robust a pooling approach is proposed to extract the discriminative information in the dss map for easily yet effectively selecting good candidates from bad ones and finally get the optimum tracking results plenty experimental evaluations on challenging image sequences demonstrate that the proposed tracking algorithm performs favorably against the state of the art methods

a new continuous discrete particle filter for continuous discrete nonlinear systems abstract the continuous discrete version of particle filter cd pf for continuous discrete nonlinear systems is proposed in this paper firstly the continuous discrete extended kalman filter cd ekf and the cd pf are described in detail then some comparisons of these two methods are carried out the simulation results show that the performance of the cd pf is better than that of the cd ekf then higher order stochastic runge kutta schemes are proposed to improve the stability and precision of the filter furthermore the cd pf is applied to nonlinear systems with nongaussian noise finally some simulations are provided to illustrate the effectiveness of the proposed filter

state estimation incorporating infrequent delayed and integral measurements this paper investigates the problem of state estimation incorporating infrequent delayed and integral measurements in chemical process there often exist two types of measurements on one hand the measurements for process variables such as flow rates and pressures are sampled frequently and are available nearly instantaneously on the other hand the measurements for quality variables such as concentration are sampled infrequently and are available with a delay due to long analysis time involved moreover due to the interval time taken by chemical sample collection the measurements for some quality variables have another important characteristic it is a function of the states of the compositions over a period of time this paper formulates the process with infrequent delayed and integral measurements as an equivalent variable dimension system whose measurements are both delay and integration free based on the new model a variable dimension unscented kalman filter vd ukf is proposed to estimate the states furthermore the stability of the proposed vd ukf is analyzed compared with the existing results the proposed stability condition is significantly relaxed and the invertibility condition of jacobian matrices is no longer needed finally a simulation example demonstrates the effectiveness of the proposed method

rigidity of some abelian by cyclic solvable group actions on mathbb t n in this paper we study a natural class of groups that act as affine transformations of mathbb t n we investigate whether these solvable abelian by cyclic groups can act smoothly and nonaffinely on mathbb t n while remaining homotopic to the affine actions in the affine actions elliptic and hyperbolic dynamics coexist forcing a priori complicated dynamics in nonaffine perturbations we first show using the kam method that any small and sufficiently smooth perturbation of such an affine action can be conjugated smoothly to an affine action provided certain diophantine conditions on the action are met in dimension two under natural dynamical hypotheses we get a complete classification of such actions namely any such group action by c r diffeomorphisms can be conjugated to the affine action by c r varepsilon conjugacy next we show that in any dimension c 1 small perturbations can be conjugated to an affine action via c 1 varepsilon conjugacy the method is a generalization of the herman theory for circle diffeomorphisms to higher dimensions in the presence of a foliation structure provided by the hyperbolic dynamics

the dynamics of open foliated manifolds and a vanishing theorem for the godbillon vey class let m f be a c3 foliated n manifold with leaves of dimension n 1 let gv f e h3 m ir denote the characeristic class introduced by godbillon and vey in g v considerable effort has been made to discover the geometric significance of this invariant recall thurston s helical wobble th which can be interpreted via the formulas in r w in addition to celebrated examples of foliations for which gv f does not vanish g v th br the list of foliations for which it does has been growing steadily by work of herman her and wallet wi gv sr 0 for foliated circle bundles and interval bundles over t2 this result has interesting consequences that are far from being obvious thus morita and tsuboi have deduced the vanishing of gv x for closed foliated manifolds without holonomy m t and mizutani morita and tsuboi have extended this to foliations almost without holonomy m m t in all of the above vanishing theorems the leaves of the foliations have polynomial growth other classes of foliations with all leaves polynomial and gv f 0 were found by nishimori n sergiescu ser and tsuchiya ts in a preprint c c2 that became obsolete within a few months of its distribution the present authors proved the vanishing theorem for all closed foliated manifolds in which every leaf has polynomial growth indeed we proved that if every leaf is nonresilient l and if no leaf lies at infinite level then gv st 0