convergence analysis of the least squares identification algorithm with a variable forgetting factor the time varying linear systems abstract this paper studies the convergence of the least squares identification algorithm with a variable forgetting factor the evolution of the parameter estimator with respect to initial conditions actual parameter changes and stochastic perturbations is analysed bounds on the deterministic and stochastic parts of their estimator error are found and their relation to a persistent excitation condition is discussed this relation explains the possibility of having bursting phenomena during the identification process special attention is paid to the consistency of these results with the classical ones obtained for the ordinary least squares algorithm when the forgetting factor tends to unity

spectral flow and the unbounded kasparov product abstract we present a fairly general construction of unbounded representatives for the interior kasparov product as a main tool we develop a theory of c 1 connections on operator modules we do not require any smoothness assumptions our unitality assumptions are minimal furthermore we use work of kucerovsky and our recent local global principle for regular operators in hilbert c modules as an application we show that the spectral flow theorem and more generally the index theory of dirac schrodinger operators can be nicely explained in terms of the interior kasparov product

brief interval excitation through impulse sequences a technical lemma we present a technical lemma that establishes in a general framework an interval excitation property using a specific class of impulse sequences according to such an interval excitation property an impulse applied within a time interval generates excitation within the same interval this property does not hold for arbitrary exciting sequences the lemma is a unified statement of previous results corresponding to particular choices of the exciting sequence

unbounded bivariant k theory and correspondences in noncommutative geometry by adapting the algebraic notion of universal connection to the setting of unbounded kk cycles we show that the kasparov product of such cycles can be defined directly by an algebraic formula in order to achieve this it is necessary to develop a framework of smooth algebras and a notion of differentiable c module the theory of operator spaces provides the required tools finally the above mentioned kk cycles with connection can be viewed as the morphisms in a category whose objects are spectral triples

nonunital spectral triples and metric completeness in unbounded kk theory abstract we consider the general properties of bounded approximate units in non self adjoint operator algebras such algebras arise naturally from the differential structure of spectral triples and unbounded kasparov modules our results allow us to present a unified approach to characterising completeness of spectral metric spaces existence of connections on modules self adjointness and regularity of induced operators on tensor product c modules and the lifting of kasparov products to the unbounded category in particular we prove novel existence results for quasicentral approximate units in non self adjoint operator algebras allowing us to strengthen kasparov s technical theorem and extend it to this realm finally we show that given any two composable kk classes we can find unbounded representatives whose product can be constructed to yield an unbounded representative of the kasparov product

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

global adaptive pole positioning adaptive pole positioning for linear time invariant discrete time systems is considered under the constraint that the controller consists of an identifier the gains in which do not go to zero an observer and a state feedback law the latter two elements being viewed in transfer function form a globally convergent algorithm is presented for achieving a prescribed set of closed loop poles persistency of excitation of an external input is required together with an underbound on the magnitude of the sylvester resultant of the plant numerator and denominator polynomials this in effect being an underbound on the product of a measure of pole zero separation and a generalized gain

experimental evaluation of iterative reconstruction versus filtered back projection for 3d 15o water pet activation studies using statistical parametric mapping analysis iterative reconstructions are increasingly used for clinical pet studies owing to the better noise properties compared with filtered backprojection fbp the purpose of the present study was to compare ordered subsets expectation maximization osem iterative reconstruction with fbp as input for statistical parametric mapping spm analysis of pet activation studies two phantom studies were performed simulating both motor and cognitive tasks and acquiring data with both high and low statistics in contrast to clinical studies where no a priori information is known phantom studies allow for an accurate and detailed comparison between different reconstruction techniques the significance of activations during tasks was determined using spm99 software using region of interest analysis of spm results it was found that the maximum and average t values within each hot spot of the phantom were higher for osem than for fbp in addition osem4 x 16 4 iterations 16 subsets produced fewer false positive voxels than fbp osem1 x 16 and osem2 x 16 in conclusion for pet activation studies use of osem4 x 16 seems to give the best tradeoff between signal detection and noise reduction

a characterization of operator algebras abstract an operator algebra is a uniformly closed algebra of bounded operators on a hilbert space in this paper we give a characterization of unital operator algebras in terms of their matricial norm structure more precisely if a is an l matricially normed space and also an algebra with a completely contractive multiplication and an identity of norm 1 then there is a completely isometric isomorphism of a onto a unital operator algebra indeed the multiplication on a need not be assumed to be associative for this conclusion to follow examples are given to show that the condition on the identity is necessary it follows from the above that the quotient of an operator algebra by a closed two sided ideal with the natural matricial structure is again an operator algebra up to complete isometric isomorphism

adaptive control of nonminimum phase systems recent papers have established global convergence for a class of adaptive control algorithms for discrete time linear dynamic systems however in most cases studied to date it has been assumed that the system is stably invertible this assumption plays a major role in the proofs of convergence in this paper we consider the more general case in which it is not assumed that the system is either stable or stably invertible we establish local convergence for a class of adaptive control algorithms applied to general discrete deterministic linear time invariant systems by convergence in this context we mean that the system inputs and outputs remain bounded for all time and the closed loop poles are effectively assigned in the limit for a given desired trajectory

asymptotically convergent modified recursive least squares with data dependent updating and forgetting factor for systems with bounded noise continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances an algorithm which eliminates these difficulties is investigated based on a set theoretic assumption the algorithm yields modified least squares estimates with a forgetting factor it updates the estimates selectively depending on whether the observed data contain sufficient information the information evaluation required at each step involves very simple computations in addition the parameter estimates are shown to converge asymptotically at an exponential rate to a region around the true parameter

a serre swan theorem for bundles of bounded geometry abstract the serre swan theorem in differential geometry establishes an equivalence between the category of smooth vector bundles over a smooth compact manifold and the category of finitely generated projective modules over the unital ring of smooth functions this theorem is here generalized to manifolds of bounded geometry in this context it states that the category of hilbert bundles of bounded geometry is equivalent to the category of operator modules over the operator algebra of continuously differentiable functions which vanish at infinity operator modules are generalizations of hilbert c modules where the category of c algebras has been replaced by a more flexible category of involutive algebras of bounded operators the operator algebras operator modules play an important role in the study of the unbounded kasparov product

uniform k theory and poincare duality for uniform k homology abstract we revisit spakula s uniform k homology construct the external product for it and use this to deduce homotopy invariance of uniform k homology we define uniform k theory and on manifolds of bounded geometry we give an interpretation of it via vector bundles of bounded geometry we further construct a cap product with uniform k homology and prove poincare duality between uniform k theory and uniform k homology on spinc manifolds of bounded geometry

exponential convergence of recursive least squares with exponential forgetting factor adaptive control in this paper we demonstrate that provided the setpoint sequence is persistently exciting and the plant is linear finite dimensional time invariant and possesses a stable inverse a trajectory following adaptive control algorithm with exponential forgetting recursive least squares is exponentially stable

an index theorem on open manifolds ii on decrit et on applique un nouveau theoreme d indice pour des operateurs elliptiques sur certaines varietes non compactes on calcule un indice a valeur reelle pour des operateurs de type dirac sur des varietes non compactes de geometrie bornee

subspaces of c algebras abstract basic properties of matricially normed spaces are considered and a simple matrix norm characterization of the subspaces of c algebras is given the latter result is used to study the haagerup tensor products and quotients of such subspaces