spectral flow is the integral of one forms on the banach manifold of self adjoint fredholm operators abstract one may trace the idea that spectral flow should be given as the integral of a one form back to the 1974 vancouver icm address of i m singer our main theorem gives analytic formulae for the spectral flow along a norm differentiable path of self adjoint bounded breuer fredholm operators in a semifinite von neumann algebra these formulae have a geometric interpretation which derives from the proof namely we define a family of banach submanifolds of all bounded self adjoint breuer fredholm operators and on each submanifold define global one forms whose integral on a norm differentiable path contained in the submanifold calculates the spectral flow along this path we emphasise that our methods do not give a single globally defined one form on the self adjoint breuer fredholms whose integral along all paths is spectral flow rather as the choice of the plural forms in the title suggests we need a family of such one forms in order to confirm singer s idea the original context for this result concerned paths of unbounded self adjoint fredholm operators we therefore prove analogous formulae for spectral flow in the unbounded case as well the proof is a synthesis of key contributions by previous authors whom we acknowledge in detail in the introduction combined with an additional important recent advance in the differential calculus of functions of non commuting operators

parameter dependent lmis in robust analysis characterization of homogeneous polynomially parameter dependent solutions via lmi relaxations this note investigates the robust stability of uncertain linear time invariant systems in polytopic domains by means of parameter dependent linear matrix inequality pd lmi conditions exploiting some algebraic properties provided by the uncertainty representation a systematic procedure to construct a family of finite dimensional lmi relaxations is provided the robust stability is assessed by means of the existence of a lyapunov function more specifically a homogeneous polynomially parameter dependent lyapunov hppdl function of arbitrary degree for a given degree if an hppdl solution exists a sequence of relaxations based on real algebraic properties provides sufficient lmi conditions of increasing precision and constant number of decision variables for the existence of an hppdl function which tend to the necessity alternatively if an hppdl solution of degree exists a sequence of relaxations which increases the number of variables and the number of lmis will provide an hppdl solution of larger degree the method proposed can be applied to determine homogeneous parameter dependent matrix solutions to a wide variety of pd lmis by transforming the infinite dimensional lmi problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite dimensional lmi conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter dependent solution of arbitrary degree illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature

performance of blind and group blind multiuser detectors in blind or group blind linear multiuser detection the detector is estimated from the received signals with the prior knowledge of only the signature waveform of the desired user or the signature waveforms of some but not all users the performance of a number of such estimated linear detectors including the direct matrix inversion dmi blind linear minimum mean square error mmse detector the subspace blind linear mmse detector and the form i and form ii group blind linear hybrid detectors are analyzed asymptotic limit theorems for each of the estimates of these detectors when the signal sample size is large are established based on which approximate expressions for the average output signal to interference plus noise ratios sinrs and bit error rates bers are given to gain insights on these analytical results the performance of these detectors in an equicorrelated code division multiple acces cdma system is compared examples are provided to demonstrate the excellent match between the theory developed here and the simulation results

a subspace method for signature waveform estimation in synchronous cdma systems synchronous code division multiple access cdma techniques possess intrinsic protection against co channel interference due to orthogonal codes employed and thus offers higher capacity than existing frequency division multiple access fdma or time division multiple access tdma systems in the presence of multipath however each signal is subject to frequency selective fading and the orthogonality condition does not necessarily hold leading to increased cross correlation in these scenarios multiuser detection need to be performed to suppress interference and recover the message symbols to implement such a technique explicit knowledge of the nonorthogonal signature waveforms of all users is required we propose a blind estimation scheme that provides closed form estimates of the signature waveforms by exploiting the structure information of the data output in particular we show that the subspace of the data matrix contains sufficient information for unique determination of the signature waveforms based on this observation a multiple signal classification music like algorithm is derived performance analysis of the new approach is also presented

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

robust controller synthesis via non linear matrix inequalities over thelastseveralyears fixed structure multiplier versions of mixed structured singular value mssv theory have been developed and have led to the development of linear matrix inequalities lmis for the analysis of robust stability and performance these lmis have in turn led to the development of bilinear matrix inequalities bmis for the synthesis of robust controllers the bmi formulation in practice requires the multiplier to lie in the span of a stable basis potentially introducing significant conservatism this paper uses the lmi approach to mssv analysis to develop an approach to robust controller synthesis that is based on the stable factors of the multipliers and does not require the multipliers to be restricted to a basis it is shown that this approach requires the solution of non linear matrix inequalities nmis a continuation algorithm is presented for the solution of nmis this algorithm may be used to solve nmis in general and its usefulness is not limited to the robust controller synt

a dilated lmi approach to robust performance analysis of linear time invariant uncertain systems this paper studies robust performance analysis problems of linear time invariant systems affected by real parametric uncertainties in the case where the state space matrices of the system depend affinely on the uncertain parameters it is know that recently developed extended or dilated linear matrix inequalities lmis are effective to assess the robust performance in a less conservative fashion this paper further extends those preceding results and propose a unified way to obtain numerically verifiable dilated lmi conditions even in the case of rational parameter dependence in particular it turns out that the proposed dilated lmis enable us to assess the robust performance via multiaffine parameter dependent lyapunov variables so that less conservative analysis results can be achieved connections among the proposed conditions and existing results are also discussed concretely several existing results can be viewed as particular cases of the proposed conditions

weak type commutator and lipschitz estimates resolution of the nazarov peller conjecture let m be a semi finite von neumann algebra and let f r c be a lipschitz function if a b m are self adjoint operators such that a b l1 m then

instability analysis of uncertain systems via determinants and lmis this technical note investigates two instability measures in continuous time ct and discrete time dt uncertain systems the first given by the spectral abscissa ct case or radius dt case and the second given by the sum ct case or product dt case of the unstable eigenvalues it is supposed that the system depends polynomially on an uncertain vector constrained into a semi algebraic set the problem is to determine the largest instability measures over the admissible uncertainties it is shown that a sufficient condition for establishing an upper bound of the sought measures can be obtained in terms of linear matrix inequality lmi feasibility tests by exploiting the determinants of some specific matrices and that this condition is also necessary under some mild conditions on the semi algebraic set by using multipliers with degree sufficiently large moreover a condition is provided for establishing the tightness of the found best upper bounds lastly it is shown that in the special case where the semi algebraic set is an interval the degree of the multipliers is known a priori some numerical examples illustrate the proposed results

spectral flow and dixmier traces abstract we obtain general theorems which enable the calculation of the dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semi finite von neumann algebra our results have several applications we deduce a formula for the chern character of an odd l 1 summable breuer fredholm module in terms of a hochschild 1 cycle we explain how to derive a wodzicki residue for pseudo differential operators along the orbits of an ergodic r n action on a compact space x finally we give a short proof of an index theorem of lesch for generalised toeplitz operators

convex synthesis of robust controllers for linear systems with polytopic time varying uncertainty the design of robust controllers for linear systems with structured time varying uncertainty is a fundamental problem in control systems this problem is still open because the available methods for robust analysis lead to nonconvex optimization whenever design variables are present this paper proposes a novel approach that overcomes this difficulty specifically continuous time linear systems with polytopic time varying uncertainty are considered the basic problem consists of designing a robust static output feedback controller ensuring robust asymptotical stability a novel approach is proposed through the introduction of robust stabilizability functions rsfs i e functions able to establish whether a controller is robustly asymptotically stabilizing in particular rsfs based on homogeneous polynomial lyapunov functions hplfs are searched for the proposed approach requires the solution of two convex optimization problems with constraints expressed as linear matrix inequalities lmis for any size of the lmis the proposed approach provides a sufficient condition for the existence of a sought controller moreover this condition is also necessary when the size of the lmis is large enough several extensions of the proposed methodology are presented which deal with the synthesis of controllers ensuring desired decay rate fixed order dynamic output controllers and controllers with the minimum norm

inner approximations for polynomial matrix inequalities and robust stability regions following a polynomial approach many robust fixed order controller design problems can be formulated as optimization problems whose set of feasible solutions is modeled by parametrized polynomial matrix inequalities pmis these feasibility sets are typically nonconvex given a parametrized pmi set we provide a hierarchy of linear matrix inequality lmi problems whose optimal solutions generate inner approximations modeled by a single polynomial superlevel set those inner approximations converge in a well defined analytic sense to the nonconvex original feasible set with asymptotically vanishing conservatism one may also impose the hierarchy of inner approximations to be nested or convex in the latter case they do not converge any more to the feasible set but they can be used in a convex optimization framework at the price of some conservatism finally we show that the specific geometry of nonconvex polynomial stability regions can be exploited to improve convergence of the hierarchy of inner approximations

the dixmier trace and asymptotics of zeta functions abstract we obtain general theorems which enable the calculation of the dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup we prove our results in a general semi finite von neumann algebra we find for p 1 that the asymptotics of the zeta function determines an ideal strictly larger than l p on which the dixmier trace may be defined we also establish stronger versions of other results on dixmier traces and zeta functions

robust static output feedback controllers via robust stabilizability functions this technical note addresses the design of robust static output feedback controllers that minimize a polynomial cost and robustly stabilize a system with polynomial dependence on an uncertain vector constrained in a semialgebraic set the admissible controllers are those in a given hyper rectangle for which the system is well posed first the class of robust stabilizability functions is introduced i e the functions of the controller that are positive whenever the controller robustly stabilizes the system second the approximation of a robust stabilizability function with a controller dependent lower bound is proposed through a sums of squares sos program exploiting a technique developed in the estimation of the domain of attraction third the derivation of a robust stabilizing controller from the found controller dependent lower bound is addressed through a second sos program that provides an upper bound of the optimal cost the proposed method is asymptotically non conservative under mild assumptions

unified large system analysis of mmse and adaptive least squares receivers for a class of random matrix channels we present a unified large system analysis of linear receivers for a class of random matrix channels the technique unifies the analysis of both the minimum mean squared error mmse receiver and the adaptive least squares als receiver and also uses a common approach for both random independent identically distributed i i d and random orthogonal precoding we derive expressions for the asymptotic signal to interference plus noise ratio sinr of the mmse receiver and both the transient and steady state sinr of the als receiver trained using either i i d data sequences or orthogonal training sequences the results are in terms of key system parameters and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix in the case of the als receiver we allow a diagonal loading constant and an arbitrary data windowing function for i i d training sequences and no diagonal loading we give a fundamental relationship between the transient steady state sinr of the als and the mmse receivers we demonstrate that for a particular ratio of receive to transmit dimensions and window shape all channels which have the same mmse sinr have an identical transient als sinr response we demonstrate several applications of the results including an optimization of information throughput with respect to training sequence length in coded block transmission

open string theory and planar algebras in this paper we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with lagrangian boundary conditions which in the case of the projective line are described in terms of real rational functions these moduli spaces appear naturally in the formulation of open string theory on the projective line we also show two geometric ways to obtain planar algebras from real algebraic geometry one based on string topology and one on gromov witten theory in particular through the well known relation between planar algebras and subfactors these results establish a connection between open string theory real algebraic geometry and subfactors of von neumann algebras

spectral shift function of higher order this paper resolves affirmatively koplienko s sib mat zh 25 62 71 1984 conjecture on existence of higher order spectral shift measures moreover the paper establishes absolute continuity of these measures and thus existence of the higher order spectral shift functions a spectral shift function of order n is the function n n h v such that operatorname tr biggl f h v sum k 0 n 1 frac 1 k frac d k dt k bigl f h tv bigr bigg t 0 biggr int mathbb r f n t eta n t dt for every sufficiently smooth function f where h is a self adjoint operator defined in a separable hilbert space and v is a self adjoint operator in the n th schatten von neumann ideal sn existence and summability of 1 and 2 were established by krein mat sb 33 597 626 1953 and koplienko sib mat zh 25 62 71 1984 respectively whereas for n 2 the problem was unresolved we show that n h v exists integrable and vert eta n vert l 1 mathbb r leq c n vert v vert s n n for some constant cn depending only on n our results for n rely on estimates for multiple operator integrals obtained in this paper our method also applies to the general semi finite von neumann algebra setting of the perturbation theory

estimating the domain of attraction for uncertain polynomial systems estimating the domain of attraction da of equilibrium points is a problem of fundamental importance in systems engineering several approaches have been proposed for the case of known polynomial systems allowing one to find the largest estimate of the da leda for a given lyapunov function lf however the problem of estimating the robust da rda that is the da guaranteed for all possible uncertainties in an uncertain system it is still an unsolved problem in this paper lmi methods are proposed for estimating the rda in the case of systems depending polynomially in the state and in the uncertainty which is supposed to belong to a polytope specifically the issue of computing the robust leda rleda that is the intersection of all ledas is considered for common and parameter dependent lfs providing constant and parameter dependent lower bounds the computation of approximations with simple shape of the rleda in the case of parameter dependent lfs is also discussed

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

on the performance of semi blind subspace based channel estimation this paper is devoted to the analysis of a semi blind estimation framework in which the standard least squares estimator based on a known training sequence is enhanced by using the statistical structure of the observations more specifically we consider the case of a general time division multiple access tdma frame based receiver equipped with multiple sensors and restrict our attention to second order based subspace methods that are suitable for most standard communication applications due to their moderate computational cost the semi blind channel estimator is obtained as a regularized least squares solution where a blind subspace criterion plays the role of the regularization constraint the main contribution of the paper consists of showing by asymptotic analysis how to optimally tune the balance between the blind criterion and the least squares fit depending on the design parameters of the system simulations show that the proposed solutions are robust and significantly improve the efficiency of the equalization

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

asymptotic analysis of blind multiuser detection with blind channel estimation the analytical performance of the subspace based blind linear minimum mean square error mmse multiuser detection algorithm in general multipath multi antenna code division multiple access cdma systems is investigated in blind multiuser detection the linear mmse detector of a given user is estimated from the received signals based on the knowledge of only the spreading sequence of that user typically the channel of that user must be estimated first based on the orthogonality between the signal and noise subspaces an asymptotic limit theorem for the estimate of the blind linear detector when the received signal sample size is large is obtained based on which approximate expressions of the average output signal to inference plus noise ratios sinrs and bit error rates bers for both binary phase shift keying bpsk and quaternary phase shift keying qpsk modulations are given corresponding results for group blind multiuser detectors are also obtained examples are provided to demonstrate the excellent match between the theory developed in this paper and the simulation results

stabilisation of discrete time systems via schur stability region abstractin this paper we consider the stabilisation problem of discrete time systems by affine compensator using the known properties of the schur stability region of monic polynomials we give conditions under which stabilising controllers exist a necessary and sufficient condition is obtained when the difference of the order of the system and the number of stabilising parameters is one in the general case two solution algorithms division elimination and least square minimisation algorithms are suggested

type ii non commutative geometry i dixmier trace in von neumann algebras abstract we define the notion of connes von neumann spectral triple and consider the associated index problem we compute the analytic chern connes character of such a generalized spectral triple and prove the corresponding local formula for its hochschild class this formula involves the dixmier trace for ii von neumann algebras in the case of foliations we identify this dixmier trace with the corresponding measured wodzicki residue

integration on locally compact noncommutative spaces abstract we present an ab initio approach to integration theory for nonunital spectral triples this is done without reference to local units and in the full generality of semifinite noncommutative geometry the main result is an equality between the dixmier trace and generalised residue of the zeta function and heat kernel of suitable operators we also examine definitions for integrable bounded elements of a spectral triple based on zeta function heat kernel and dixmier trace techniques we show that zeta functions and heat kernels yield equivalent notions of integrability which imply dixmier traceability

parameter and controller dependent lyapunov functions for robust d stability and robust performance controller design this paper addresses the design of output controllers of chosen order in a given set for ensuring a number of desired properties such as robust d stability and robust performance it is shown that a sufficient condition for determining such controllers can be obtained by solving convex optimization problems with linear matrix inequality constraints through the introduction of a lyapunov function depending polynomially on both uncertainty and controller the proposed condition is also necessary for sufficiently large degrees of the polynomials involved under some assumptions

the index formula and the spectral shift function for relatively trace class perturbations we compute the fredholm index index da of the operator da d dt a on l2 r h associated with the operator path a t t where af t a t f t for a e t r and appropriate f l2 r h via the spectral shift function a a associated with the pair a a of asymptotic operators a a on the separable complex hilbert space h in the case when a t is generally an unbounded relatively trace class perturbation of the unbounded self adjoint operator a we derive a formula an extension of a formula due to pushnitski relating the spectral shift function a a for the pair a a and the corresponding spectral shift function h2 h1 for the pair of operators h2 h1 dada da da in this relative trace class context h2 h1 1 1 2 1 2 a a d 2 1 2for a e 0 this formula is then used to identify the fredholm index of da with 0 a a in addition we prove that index da coincides with the spectral flow spflow a t t of the family a t t r and also relate it to the fredholm perturbation determinant for the pair a a index da spflow a t t 0 a a 1lime 0im ln deth a iei a iei 1 0 h2 h1 with the choice of the branch of ln deth on c such that limim z ln deth a zi a zi 1 0 we also provide some applications in the context of supersymmetric quantum mechanics to zeta function and heat kernel regularized spectral asymmetries and the eta invariant

a convex approach to robust stability for linear systems with uncertain scalar parameters in this paper robust stability for linear systems with several uncertain complex and or real scalar parameters is studied a countable family of conditions sufficient for robust stability is given in terms of solvability of some simple linear matrix inequalities lmis these conditions are of increasing precision and it is shown conversely that robust stability implies solvability of these lmis from a certain rank and beyond this result constitutes an extension of the characterization by solvability of lyapunov inequality of the asymptotic stability for usual linear systems it is based on the search of parameter dependent quadratic lyapunov functions polynomial of increasing degree in the parameters

operator lipschitz functions in schatten von neumann classes this paper resolves a number of problems in the perturbation theory of linear operators linked with the 45 year old conjecure of m g kre n in particular we prove that every lipschitz function is operator lipschitz in the schatten von neumann ideals s 1 0 such that left f a f b right alpha leqslant c alpha left f right text lip 1 left a b right alpha where f is a lipschitz function with left f right text lip 1 mathop sup limits lambda ne mu lambda mu in mathbb r left frac f left lambda right f left mu right lambda mu right infty left cdot right alpha is the norm is s and a and b are self adjoint linear operators such that a b in s alpha

a complete set of numerical invariants for a subfactor abstract we show that certain numerical invariants associated naturally to a subfactor planar algebra constitute a complete family in the sense of determining the isomorphism class of the subfactor planar algebra in the course of the proof we show also that planar algebra isomorphisms of subfactor planar algebras can always be chosen to be preserving this latter statement generalises the fact that hopf algebra isomorphisms of finite dimensional kac algebras can be chosen to be preserving

perturbation analysis for subspace decomposition with applications in subspace based algorithms subspace decomposition has been exploited in different applications due to perturbations from various sources such as finite data samples and measurement noise perturbations arise in subspaces therefore some loss is introduced to performance of subspace based algorithms although first order perturbation results have been proposed in the literature and applied to various problems up to second order perturbation analysis can provide more accurate analytical results and is studied in this paper based on the orthogonality principle perturbations of subspaces and singular values or eigenvalues are derived explicitly as functions of a perturbation in the objective matrix up to the second order respectively all in closed forms it is shown that by keeping only the first order terms the derived results reduce to those from existing approaches examples to apply the proposed results to both matrix computation and subspace based channel estimation are provided to verify our analysis

double operator integrals this paper is concerned with perturbation formulae of the form f a f b lp m k a b lp m with k 0 being a constant depending on p and f only where f is a real valued lipschitz function and a b are self adjoint measurable operators affiliated with a semifinite von neumann algebra m such that the difference a b belongs to lp m 1 p in order to treat the situation where the von neumann algebra m is not necessarily hyperfinite we first develop an integration theory with respect to finitely additive spectral measures in a banach space applied to product measures this integration theory may be considered as an abstract version of the double operator integrals due to birman and solomyak to describe the class of integrable functions we employ our recent study of multiplier theory in umd spaces our perturbation formulae extend those of davies and birman solomyak for the case when m is a hyperfinite i factor i e for the schatten p classes we also discuss analogous perturbation results in the setting of symmetric operator spaces associated with m

blind multiuser detection a subspace approach a new multiuser detection scheme based on signal subspace estimation is proposed it is shown that under this scheme both the decorrelating detector and the linear minimum mean square error mmse detector can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest the consistency and asymptotic variance of the estimates of the two linear detectors are examined a blind adaptive implementation based on a signal subspace tracking algorithm is also developed it is seen that compared with the previous minimum output energy blind adaptive multiuser detector the proposed subspace based blind adaptive detector offers lower computational complexity better performance and robustness against signature waveform mismatch two extensions are made within the framework of signal subspace estimation first a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel secondly a multiuser detection scheme using spatial diversity in the form of an antenna array is considered a blind adaptive technique for estimating the array response for diversity combining is proposed it is seen that under the proposed subspace approach blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection with little attendant increase in complexity

lmi techniques for optimization over polynomials in control a survey numerous tasks in control systems involve optimization problems over polynomials and unfortunately these problems are in general nonconvex in order to cope with this difficulty linear matrix inequality lmi techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems this survey aims to provide the reader with a significant overview of the lmi techniques that are used in control systems for tackling optimization problems over polynomials describing approaches such as decomposition in sum of squares positivstellensatz theory of moments polya s theorem and matrix dilation moreover it aims to provide a collection of the essential problems in control systems where these lmi techniques are used such as stability and performance investigations in nonlinear systems uncertain systems time delay systems and genetic regulatory networks it is expected that this survey may be a concise useful reference for all readers

on the second order statistics of the eigenvectors of sample covariance matrices eigenvectors of sample covariance matrices are used in a variety of statistical signal processing problems the second order statistics of these eigenvectors are needed to compute the variance of estimates based on these eigenvectors formulas for the second order statistics of the eigenvectors have been derived in the statistical literature and are widely used we point out a discrepancy between the statistics observed in numerical simulations and the theoretical formulas due to the nonuniqueness of the definition of eigenvectors we present two ways to resolve this discrepancy the first involves modifying the theoretical formulas to match the computational results the second involved a simple modification of the computations to make them match existing formulas

noncommutative kothe duality using techniques drawn from the classical theory of rearrangement invariant banach function spaces we develop a duality theory in the sense of kothe for symmetric banach spaces of measurable operators affiliated with a semifinite von neumann algebra equipped with a distinguished trace a principal result of the paper is the identification of the kothe dual of a given banach space of measurable operators in terms of normality

frechet differentiability of sp norms abstract one of the long standing questions in the theory of schatten von neumann ideals of compact operators is whether their norms have the same differentiability properties as the norms of their commutative counterparts we answer this question in the affirmative a key technical observation underlying our proof is a discovery of connection between this question and recent affirmative resolution of l s koplienko s conjecture concerning existence of higher order spectral shift functions

classification of simple c algebras inductive limits of matrix algebras over one dimensional spaces abstract in this article we will give a complete classification of simple c algebras which can be written as inductive limits of algebras of the form a n i 1 k n m n i c x n i where x n i are arbitrary variable one dimensional compact metrizable spaces the results unify and generalize the previous results for the case x n i s 1 and for the case of x n i being trees we obtain our classification results by reducing the case of general one dimensional spaces to the case of circles the techniques in this paper play important roles in the study of the case of higher dimensional spaces

quantum differentiability of essentially bounded functions on euclidean space abstract we investigate the properties of the singular values of the quantised derivatives of essentially bounded functions on r d with d 1 the commutator i sgn d 1 m f of an essentially bounded function f on r d acting by pointwise multiplication on l 2 r d and the sign of the dirac operator d acting on c 2 d 2 l 2 r d is called the quantised derivative of f we prove the condition that the function x f x 2 d 1 f x 2 d f x 2 d 2 x r d being integrable is necessary and sufficient for the quantised derivative of f to belong to the weak schatten d class this problem has been previously studied by rochberg and semmes and is also explored in a paper of connes sullivan and telemann here we give new and complete proofs using the methods of double operator integrals furthermore we prove a formula for the dixmier trace of the d th power of the absolute value of the quantised derivative for real valued f when x f x 2 d is integrable there exists a constant c d 0 such that for every continuous normalised trace on the weak trace class l 1 we have sgn d 1 m f d c d r d f x 2 d d x

on unbounded p summable fredholm modules abstract we prove that odd unbounded p summable fredholm modules are also bounded p summable fredholm modules this is the odd counterpart of a result of a connes for the case of even fredholm modules the approach we use is via estimates of the form d d0 lp m c d d0 1 2 where t t 1 t2 1 2 d0 d 0 is an unbounded linear operator affiliated with a semifinite von neumann algebra m d d0 is a bounded self adjoint linear operator from m and 1 d20 1 2 lp m where lp m is a non commutative lp space associated with m it follows from our results that if p 1 then d d0 belongs to the space lp m

robust observed state feedback design for discrete time systems rational in the uncertainties design of controllers in the form of a state feedback coupled to a state observer is studied in the context of uncertain systems the classical approach by luenberger is revisited results provide a heuristic design procedure that mimics the independent state feedback observer gains design by minimizing the coupling of observation error dynamics on the ideal state feedback dynamics the proposed design and analysis conditions apply to linear systems rationally dependent on uncertainties defined in the cross product of polytopes convex linear matrix inequality results are given thanks to the combination of a new descriptor multi affine representations of systems and the s variable approach stability and h performances are assessed by multi affine parameter dependent lyapunov matrices for both cases of constant and time varying uncertainties or combinations of the two numerical complexity issues and ways to keep it as limited as possible are discussed and illustrated on an academic example

complexity reduction in subspace based blind channel identification for ds cdma systems direct sequence code division multiple access is emerging as a potential multiple access communication scheme for future digital wireless communications systems such wide band systems usually operate in a frequency selective fading channel that introduces intersymbol interference and thus potential performance degradation previously proposed subspace based blind channel identification algorithms which provide estimates of channel parameters for effective equalization suffer from high numerical complexity for systems with large spreading gains in this paper it is shown that through the use of matched filter outputs reduction in numerical complexity can be obtained the complexity reduction is considerable when the channel length is small and the system is moderately loaded the results show that the new algorithm suffers a slight performance loss although the employed matched filter outputs do not form a set of sufficient statistics for the unknown channels the difference between the matched filter outputs and the sufficient statistics becomes negligible for large observation lengths and the asymptotic normalized fisher information does not change performance is evaluated through simulations the derivation of a tight approximation of the mean squared channel estimation error and through comparisons to the cramer rao bound for the estimation error variance it is shown that the approximation of the mean squared error can be obtained in terms of the correlation of the spreading codes and the channels this representation of the error supplies a tool for investigating the relationship between performance and spreading sequence correlations

the hochschild class of the chern character for semifinite spectral triples abstract we provide a proof of connes formula for a representative of the hochschild class of the chern character for p summable spectral triples our proof is valid for all semifinite von neumann algebras and all integral p 1 we employ the minimum possible hypotheses on the spectral triples

non commutative banach function spaces in this paper we survey some aspects of the theory of non commutative banach function spaces that is spaces of measurable operators associated with a semi finite von neumann algebra these spaces are also known as non commutative symmetric spaces the theory of such spaces emerged as a common generalization of the theory of classical commutative rearrangement invariant banach function spaces in the sense of w a j luxemburg and a c zaanen and of the theory of symmetrically normed ideals of bounded linear operators in hilbert space in the sense of i c gohberg and m g krein these two cases may be considered as the two extremes of the theory in the first case the underlying von neumann algebra is the commutative algebra l on some measure space with integration as trace in the second case the underlying von neumann algebra is b the algebra of all bounded linear operators on a hilbert space with standard trace important special cases of these non commutative spaces are the non commutative l p spaces which correspond in the commutative case with the usual l p spaces on a measure space and in the setting of symmetrically normed operator ideals they correspond to the schatten p classes mathfrak s p