frequency domain blind mimo system identification based on second and higher order statistics we present a novel frequency domain framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs the system frequency response is obtained based on singular value decomposition svd of a matrix constructed based on the power spectrum and slices of polyspectra of the system output by appropriately selecting the polyspectra slices we can create a set of such matrices each of which could independently yield the solution of they could all be combined in a joint diagonalization scheme to yield a solution with improved statistical performance the freedom to select the polyspectra slices allows us to bypass the frequency dependent permutation ambiguity that is usually associated with frequency domain svd while at the same time allows us compute and cancel the phase ambiguity an asymptotic consistency analysis of the system magnitude response estimate is performed

hermitian k theory of the integers rognes and weibel used voevodsky s work on the milnor conjecture to deduce the strong dwyer friedlander form of the lichtenbaum quillen conjecture at the prime 2 in consequence the 2 completion of the classifying space for algebraic k theory of the integers z 1 2 can be expressed as a fiber product of well understood spaces bo and bgl f3 over bu similar results are now obtained for hermitian k theory and the classifying spaces of the integral symplectic and orthogonal groups for the integers z 1 2 this leads to computations of the 2 primary hermitian k groups and affirmation of the lichtenbaum quillen conjecture in the framework of hermitian k theory

subspace methods for blind estimation of time varying fir channels novel linear algorithms are proposed in this paper for estimating time varying fir systems without resorting to higher order statistics the proposed methods are applicable to systems where each time varying tap coefficient can be described with respect to time as a linear combination of a finite number of basis functions examples of such channels include almost periodically varying ones fourier series description or channels locally modeled by a truncated taylor series or by a wavelet expansion it is shown that the estimation of the expansion parameters is equivalent to estimating the second order parameters of an unobservable fir single input many output simo process which are directly computed under some assumptions from the observation data by exploiting this equivalence a number of different blind subspace methods are applicable which have been originally developed in the context of time invariant simo systems identifiability issues are investigated and some illustrative simulations are presented

linear prediction error method for blind identification of periodically time varying channels blind channel estimation for single input multiple output simo periodically time varying channels is considered using only the second order statistics of the data the time varying channel is assumed to be described by a complex exponential basis expansion model ce bem the linear prediction error method for blind identification of time invariant channels is extended to time varying channels represented by a ce bem sufficient conditions for identifiability are investigated the cyclostationary nature of the received signal is exploited to consistently estimate the time varying correlation function of the data from a single observation record the proposed method requires the knowledge of the active basis functions but not the channel length an upper bound suffices several existing methods require precise knowledge of the channel length equalization of the time varying channel given the estimated channel is investigated computer simulation examples are presented to illustrate the approach and to compare it with two existing approaches

the homotopy type of the cobordism category the embedded cobordism category under study in this paper generalizes the category of conformal surfaces introduced by g segal in s2 in order to formalize the concept of field theories our main result identifies the homotopy type of the classifying space of the embedded d dimensional cobordism category for all d for d 2 our results lead to a new proof of the generalized mumford conjecture somewhat different in spirit from the original one presented in mw

blind mimo identification using the second characteristic function we propose a new approach for the blind identification of a multi input multi output mimo system as a substitute to using classical high order statistics hos in the form of time lagged joint cumulants or polyspectra we use the estimated hessian matrices of the second joint generalized characteristic function of time lagged observations evaluated at several preselected processing points these matrices admit straightforward consistent estimates whose statistical stability can be finely tuned by proper selection of the processing points in contrast to classical hos transforming the obtained matrix sequence into the frequency domain we obtain and solve a sequence of frequency dependent joint diagonalization problems this yields a set of estimated frequency response matrices which are transformed back into the time domain after resolving frequency dependent phase and permutation ambiguities the performance of the proposed algorithm depends on the choice of processing points yet compares favorably with other algorithms especially at moderate signal to noise ratio conditions as we demonstrate in simulation results

homological stability for the mapping class groups of non orientable surfaces we prove that the homology of the mapping class groups of non orientable surfaces stabilizes with the genus of the surface combining our result with recent work of madsen and weiss we obtain that the classifying space of the stable mapping class group of non orientable surfaces up to homology isomorphism is the infinite loop space of a thom spectrum built from the canonical bundle over the grassmannians of 2 planes in n 2 in particular we show that the stable rational cohomology is a polynomial algebra on generators in degrees 4i this is the non oriented analogue of the mumford conjecture

the structure of 2d semi simple field theories i classify the cohomological 2d field theories based on a semi simple complex frobenius algebra a they are controlled by a linear combination of classes and by an extension datum to the deligne mumford boundary their effect on the gromov witten potential is described by givental s fock space formulae this leads to the reconstruction of gromov witten ancestor invariants from the quantum cup product at a single semi simple point and the first chern class of the manifold confirming givental s higher genus reconstruction conjecture this in turn implies the virasoro conjecture for manifolds with semi simple quantum cohomology the classification uses the mumford conjecture proved by madsen and weiss european congress of mathematics pp 283 303 2005

universal moduli spaces of surfaces with flat bundles and cobordism theory for a compact connected lie group g we study the moduli of pairs e w here is a genus g riemann surface and e is a flat g bundle varying both the riemann surface and the flat bundle leads to a moduli space m g parametrizing families riemann surfaces with flat g bundles we show that there is a stable range in which the homology of m g is independent of g the stable range depends on the genus of the surface we then identify the homology of this moduli space in the stable range in terms of the homology of an explicit infinite loop space rationally the stable cohomology of this moduli space is generated by the mumford morita miller classes and the ring of characteristic classes of principal g bundles h bg equivalently our theorem calculates the homology of the moduli space of semi stable holomorphic bundles on riemann surfaces we then identify the homotopy type of the category of one manifolds and surface cobordisms each equipped with a flat g bundle our methods combine the classical techniques of atiyah and bott with the new techniques coming out of madsen and weiss s proof of mumford s conjecture on the stable cohomology of the moduli space of riemann surfaces

an efficient subspace method for the blind identification of multichannel fir systems we present a novel method for the blind identification of linear single input multiple output simo finite impulse response fir systems based on second order statistics our approach called the truncated transfer matrix method ttm proceeds in two major steps first the svd analysis of the lagged covariance matrix gives the subspace of the clipped system transfer matrix and second the block toeplitz structure of the transfer matrix gives extra constraints that allow us to reconstruct the matrix through the solution of a linear system of equations the proposed ttm method is analytical no optimization procedure involved and it is robust to noise we find that the method comes with an increased computational cost but it significantly outperforms state of the art second order methods in low signal to noise ratio snr situations

prediction error method for second order blind identification blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest in this paper we introduce a second order blind identification technique based on a linear prediction approach in contrast to eigenstructure based methods it will be shown that the linear prediction error method is robust to order overdetermination an asymptotic performance analysis of the proposed estimation method is carried out consistency and asymptotic normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are finally presented to demonstrate the potential and the robustness of the proposed method

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

precoder design and blind identification of mimo channels in this paper blind identification problem based on second order statistics sos of received signals is investigated for multiple input multiple output mimo channels it is shown that precoders introduced in transmitters can provide certain extra information for blind identification problem and commonly used identifiability conditions on mimo channels can be relaxed a design criterion for the precoders in frequency domain is proposed two blind identification algorithms based on the knowledge of the precoders and sos of the received signals are then developed in these algorithms due to particular structure of the precoders the blind identification problem for a mimo channel is decomposed into several independent single input multiple output simo channel identification problems the presented algorithms are robust to an overestimated channel order and not sensitive to signal to noise ratio snr compared with the existing results a larger class of mimo finite impulse response fir channels can be identified by the new methods

fourth order cumulant based blind identification of underdetermined mixtures in this paper we study two fourth order cumulant based techniques for the estimation of the mixing matrix in underdetermined independent component analysis the first method is based on a simultaneous matrix diagonalization the second is based on a simultaneous off diagonalization the number of sources that can be allowed is roughly quadratic in the number of observations for both methods explicit expressions for the maximum number of sources are given simulations illustrate the performance of the techniques

spaces of graphs and surfaces on the work of soren galatius galatius most striking result is easy enough to state let n be the symmetric group on n letters and fn be the free non abelian group with n generators the symmetric group n acts naturally by permutation on the n generators of fn and every permutation gives thus rise to an automorphism of the free group galatius proves that the map n autfn in homology induces an isomorphism in degrees less than n 1 2 the homology of the symmetric groups in these ranges is well understood in particular in common with all finite groups it has no non trivial rational homology by galatius theorem in low degrees this then is also true for autfn h autfn q 0 for 0 2n 3

blind mimo channel identification from second order statistics using rank deficient channel convolution matrix for multiuser systems several direct blind identification algorithms require that the linear multiple input multiple output mimo system have a full rank convolution matrix this condition requires that the system transfer function be irreducible and column reduced we show that this restrictive identification condition can be relaxed for some direct blind identification methods to accommodate more practical scenarios algorithms such as the outer product decomposition algorithm only require minor length adjustment to its processing window without the column reduced condition this result allows direct blind identification methods to be applicable to mimo without requiring a full rank channel convolution matrix

cumulant based blind identification of linear multi input multi output systems driven by colored inputs the blind identification problem of a linear multi input multi output mimo system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation however such a problem is ill posed and has no unique solution therefore we can only find a solution of the problem within an equivalence class we address the blind identification problem of the linear mimo system driven by unobservable colored inputs using higher order statistics hos particularly the fourth order cumulants of the outputs where the unobservable inputs are mutually independent but temporally colored linear processes we first define the set which is denoted by s of stable scalar transfer functions and then define the notion of a generalized permutation matrix which is abbreviated by a g matrix over s then it is shown that the transfer function matrix of an unknown system is identified only up to post multiplication by a g matrix this result is applied to identifying fir systems for blind signal separation

blind system identification using precise and quantized observations this paper studies the blind identification of multi channel fir systems using precise and quantized observations first a new deterministic blind identification dbi algorithm is presented for multi channel fir systems using precise observations in which the system parameters can be consistently estimated and the common source signal can be stably recovered when the observed samples are quantized by a static finite level quantizer an iterative deterministic blind identification idbi method is then provided the asymptotic characters of the proposed idbi method are discussed and the quantization effect on the identification performance is analyzed numerical simulations are given to support the developed dbi method and idbi method

blind identification of multi channel arma models based on second order statistics this correspondence presents a new second order statistical approach to blind identification of single input multiple output simo autoregressive and moving average arma system models the proposed approach exploits the dynamical autoregressive information of the model contained in the autocorrelation matrices of the system outputs but does not require the block toeplitz structure of the channel convolution matrix used by classical subspace methods for the multi channel model with the same autoregressive ar polynomial sufficient conditions and an efficient identification algorithm are given such that the multi channel model can be uniquely identified up to a constant scaling factor furthermore an extension of the result to blind identification of multi channel models with different ar polynomials is presented simulation results are given to show the effectiveness of the proposed approach

blind identification of digital communication channels with correlated noise blind identification consists of estimating the impulse response of a linear time invariant channel used for transmission of digital data by observing the channel output without knowledge of the transmitted symbol sequence we show how a previously proposed algorithm moulines et al 1995 based on second order statistics of the received signal can be modified to account for correlated noise

stable moduli spaces of high dimensional manifolds we prove an analogue of the madsen weiss theorem for high dimensional manifolds in particular we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of sn sn in the limit g to infty rationally it is a polynomial ring in certain explicit generators giving a high dimensional analogue of mumford s conjecture

the stable moduli space of riemann surfaces mumford s conjecture d mumford conjectured in 30 that the rational cohomology of the stable moduli space of riemann surfaces is a polynomial algebra generated by certain classes i of di mension 2i for the purpose of calculating rational cohomology one may replace the stable moduli space of riemann surfaces by b 1 where 1 is the group of isotopy classes of automorphisms of a smooth oriented connected surface of large genus tillmann s insight 41 that the plus construction makes b 1 into an infinite loop space led to a stable homo topy version of mumford s conjecture stronger than the original 22 we prove the stronger version relying on harer s stability theorem 15 vassiliev s theorem concerning spaces of functions with moderate singularities 43 42 and methods from homotopy theory

pontrjagin thom maps and the homology of the moduli stack of stable curves we study the singular homology with field coefficients of the moduli stack overline mathfrak m g n of stable n pointed complex curves of genus g each irreducible boundary component of overline mathfrak m g n determines via the pontrjagin thom construction a map from overline mathfrak m g n to a certain infinite loop space whose homology is well understood we show that these maps are surjective on homology in a range of degrees proportional to the genus this detects many new torsion classes in the homology of overline mathfrak m g n

the stable mapping class group and q ℂp in t2 it was shown that the classifying space of the stable mapping class groups after plus construction b has an infinite loop space structure this result and the tools developed in bm to analyse transfer maps are used here to show the following splitting theorem let p p e 0 e p 2 be the adams splitting of the p completed suspension spectrum of p then for some infinite loop space w p b p e 0 e p 3 w p where e i denotes the infinite loop space associated to the spectrum e i the homology of e i is known and as a corollary one obtains large families of torsion classes in the homology of the stable mapping class group this splitting also detects all the miller morita mumford classes our results suggest a homotopy theoretic refinement of the mumford conjecture the above p adic splitting uses a certain infinite loop map b p 1 that induces an isomorphims in rational cohomology precisely if the mumford conjecture is true we suggest that might be a homotopy equivalence

a sequential subspace method for blind identification of general fir mimo channels this correspondence addresses the problem of blindly identifying multiple input multiple output mimo finite impulse response fir channels without the conventional assumption of identical column degrees a subspace based algorithm is developed that identifies the channel s columns sequentially from the lowest degree columns to the highest degree ones compared with the previous generalized subspace method by gorokhov and loubaton 1997 the new method is simpler and more accurate

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

index theory in spaces of manifolds we formulate and prove a generalization of the atiyah singer family index theorem in the context of the theory of spaces of manifolds a la madsen tillmann weiss galatius and randal williams our results are for dirac type operators linear over arbitrary c algebras

braids mapping class groups and categorical delooping dehn twists around simple closed curves in oriented surfaces satisfy the braid relations this gives rise to a group theoretic map phi beta 2g to gamma g 1 from the braid group to the mapping class group we prove here that this map is trivial in homology with any trivial coefficients in degrees less than g 2 in particular this proves an old conjecture of j harer the main tool is categorical delooping in the spirit of tillmann in invent math 130 257 175 1997 by extending the homomorphism to a functor of monoidal 2 categories phi is seen to induce a map of double loop spaces on the plus construction of the classifying spaces any such map is null homotopic in an appendix we show that geometrically defined homomorphisms from the braid group to the mapping class group behave similarly in stable homology

optimal ripple free deadbeat controllers a ripple free deadbeat controller for a system exists if and only if there are no transmission zeros coinciding with the poles of the reference signal approaches to this problem often use the diophantine equation solution however solutions provided by the diophantine equation often exhibit extremely bad transient responses this approach gives a new affine parametrization of solutions of the diophantine equation based on this parametrization lmi conditions are used to provide optimal or constrained controllers for design quantities such as overshoot undershoot control amplitude slew rate as well as for norm bounds such as l1 l2 and l infinity