super lie groups global topology and local structure a general mathematical framework for the super lie groups of supersymmetric theories is presented the definition of super lie group is given in terms of supermanifolds and two theorems analogous to theorems in classical lie group theory are proved the relationship of the super lie groups defined here to the formal groups of berezin and kac and the graded lie groups of kostant is analyzed

recursive identification of wiener hammerstein systems identification of the wiener hammerstein system consisting of a linear subsystem in a cascade with a static nonlinearity f cdot followed by another linear subsystem with internal noises is considered on the basis of input and noisy output the impulse responses of the two linear subsystems are estimated by stochastic approximation sa algorithms and the nonlinear function is also estimated by sa algorithms but with kernel functions the system input is taken to be a sequence of independent and identically distributed iid gaussian random variables u k in mathcal n 0 vartheta 2 with vartheta 0 for convergence of the proposed algorithms the properties of martingale difference sequences mds and alpha mixings play an important role the estimates for coefficients of the linear subsystems as well as for values of the nonlinear function are proved to converge to the true values with probability one three numerical examples with nonlinearities possessing different properties are give

identification of errors in variables systems with arma observation noises abstract the purpose of the paper is to give the recursive estimate for coefficients of the single input single output siso errors in variables eiv system and to prove its strong consistency the observation noises of the eiv system are assumed to be arma processes and the system input is taken to be an iid sequence the recursive estimation algorithm is given with the help of stochastic approximation sa method and the strong consistency is established under reasonable conditions the numerical simulation is consistent with the theoretical analysis

identifiability and persistent excitation in full matrix fraction parameter estimation this paper analyzes the identifiability of the full matrix fraction description of multivariable systems and provides a lower bound on the persistence of excitation of the input output pair in terms of the persistence of excitation of the input

a twistor approach to the regularization of divergences one object of the twistor programme as developed principally by r penrose is the production of a manifestly finite theory of scattering in quantum field theory earlier work has shown that progress towards this goal is obstructed even at the first order level by the appearance of an infrared divergence in the standard theory new studies in many dimensional contour integration now suggest a simple but very powerful modification to this branch of twistor theory in which the full as opposed to the projective twistor space plays an essential role in this modified theory there arise natural contour integral expressions with the effect of eliminating the infrared divergence previously noted and replacing it by a finite quantity this regularization can be specified by using a formalism of inhomogeneous twistor diagrams the interpretation of this new formalism is not yet wholly clear but the inhomogeneity can be seen as a means of relinquishing the concept of space time point while preserving light cone structure it therefore suggests a quite fresh approach to the divergences of quantum field theory

robust waveform design for mimo radars the problem of robust waveform design for multiple input multiple output radars equipped with widely spaced antennas is addressed here robust design is needed as a number of parameters may be unknown e g the target scattering covariance matrix and the disturbance covariance matrix following a min max approach the code matrix is designed to minimize the worst case cost over all possible target or target and disturbance covariance matrices the same min max solution applies to many commonly adopted performance measures such as the average signal to disturbance ratio the linear minimum mean square error in estimating the target response the mutual information between the received signal echoes and the target response and the approximation of the detection probability in the high and low signal regimes for a fixed probability of false alarm examples illustrating the behavior of the min max codes are provided

space time code design for mimo detection based on kullback leibler divergence the focus of the paper is on the design of space time codes for a general multiple input multiple output detection problem when multiple observations are available at the receiver the figure of merit used for optimization purposes is the convex combination of the kullback leibler divergences between the densities of the observations under the two hypotheses and different system constraints are considered this approach permits to control the average sample number i e the time for taking a decision in a sequential probability ratio test and to asymptotically minimize the probability of miss in a likelihood ratio test the solutions offer an interesting insight in the optimal transmit policies encapsulated in the rank of the code matrix which rules the amount of diversity to be generated as well as in the power allocation policy along the active eigenmodes a study of the region of achievable divergence pairs whose availability permits optimization of a wide range of merit figures is also undertaken a set of numerical results is finally given in order to analyze and discuss the performance and validate the theoretical results

recursive identification of multi input multi output errors in variables hammerstein systems the note considers the identification of multi input multi output errors in variables hammerstein systems in which both the input and output can be observed but with additive noises being arma processes with unknown coefficients with the help of stochastic approximation combined with the deconvolution kernel function the recursive algorithms are proposed for estimating coefficients of the linear subsystem and for the values of the nonlinear function under some reasonable conditions all the estimates are proved to converge to the true values with probability one these results include identification of the errors in variables linear systems as a special case a simulation example is given justifying the theoretical analysis

generalized yule walker equations and testing the orders of multivariate time series consistency condi ions are given for the estimates of ar parameters of multivariate arma models obtained by using generalized yule walker equations the related problem of selecting the model orders by testing the rank of the output covariance matrix is also discussed

super twistor realization of unitary super representations of u p q n this paper is concerned with demonstrating that the twistor realization of the ladder representation of u p q can be generalized to super representations of u p q n this is achieved by considering the generalization of twistor elementary states to a super algebraic category unitarity of these super representations follows from the positive definiteness of a super twistor scalar product constructed in this paper although generalizations of the ladder representations have been well studied by other means it will be shown that the super twistor generalization is especially natural and merits special investigation

unitary representations of non compact supergroups we give a general theory for the construction of oscillator like unitary irreducible representations uirs of non compact supergroups in a super fock space this construction applies to all non compact supergroupsg whose coset spaceg k with respect to their maximal compact subsupergroupk is hermitean supersymmetric we illustrate our method with the example of su m p n q by giving its oscillator like uirs in a particle state basis as well as supercoherent state basis the same class of uirs can also be realized over the super hilbert spaces of holomorphic functions of az variable labelling the coherent states

determination of basis for the irreducible representations of the unitary group for u p q u p u q a direct procedure is outlined for determining the basis spanning finite dimensional irreducible representations of u p q adapted to the subgroup u p u q using a tableau based analysis it is shown that the realization of the semimaximal states follows readily from a knowledge of the matrix elements of the generators ei 1 of u p u q u p q

hankel matrices for system identification abstract the coefficients of a linear system even if it is a part of a block oriented nonlinear system normally satisfy some linear algebraic equations via hankel matrices composed of impulse responses or correlation functions in order to determine or to estimate the coefficients of a linear system it is important to require the associated hankel matrix be of row full rank the paper first discusses the equivalent conditions for identifiability of the system then it is shown that the row full rank of the hankel matrix composed of impulse responses is equivalent to identifiability of the system finally for the row full rank of the hankel matrix composed of correlation functions the necessary and sufficient conditions are presented which appear slightly stronger than the identifiability condition in comparison with existing results here the minimum phase condition is no longer required for the case where the dimension of the system input and output is the same though the paper does not make such a dimensional restriction

on mimo detection under non gaussian target scattering in this paper we consider a multiple input multiple output mimo detection problem with m widely spaced transmit antennas and l widely spaced receive antennas and we study the problem of designing the signal waveforms transmitted by each source node under non gaussian target scattering and temporally correlated gaussian clutter two figures of merit are investigated for space time code stc optimization under a semidefinite rank constraint 1 the lower chernoff bound lcb to the detection probability for fixed probability of false alarm and 2 the mutual information mi between the observations available at the receive nodes and the channel response generated by a point like target assumed present tout court both receive and transmit power constraints are discussed if the scattering distribution possesses some suitably defined properties of unitary invariance see both mi optimal and lcb optimal stcs have a simple canonical structure the same set of clutter dependant temporal codewords are employed at the transmit nodes the only difference among the many solutions being the amount of power radiated by each antenna such a spatial power allocation critically depends upon the adopted figure of merit the specified power constraint and the underlying scattering model sufficient conditions to determine the optimal power allocation for all design criteria are provided asymptotic power distributions are also derived in the limit of vanishingly small and increasingly large signal to clutter ratios proving that assuming gaussian scattering at the design stage is a robust choice a case study of relevant practical interest is examined in depth so as to compare the proposed design criteria and to assess the impact of signal non gaussianity on the system performances

group representations arising from lorentz conformal geometry abstract it is shown that there exist conformally covariant differential operators d 2 l k of all even orders 2 l on differential forms of all orders k in the double cover n of the n dimensional compactified minkowski space n these act as intertwining differential operators for natural representations of o 2 n the conformal group of n for even n the resulting decompositions of differential form representations of o 2 n the orthochronous conformal group produce infinite families of unitary representations the most interesting of which are carried by positive mass squared positive frequency quotients for 2l n 2k physically these generalize unitary representations of the conformal group associated with the modified wave operator d 2 0 n 2 2 2 and the maxwell operator on vector potentials d 2 n 2 2 d all the representation spaces produced unitary and nonunitary may be viewed as infinite systems of harmonic oscillators as a by product of the spectral resolution of the d 2 l k one gets some striking wave propagative properties for all of the equations d 2 l k 0 including huygens principle in the curved spacetime n the operators d 2 l k have not been seen before except in the special cases k 0 or n and k n 2 2 l 1 the maxwell operator thus much new information is obtained even in the physical case n 4

new approach to recursive identification for armax systems for the multivariate armax system a z yk b z uk 1 c z wk recursive algorithms are proposed for estimating coefficients of a z b z and c z and the covariance matrix rw of wk assuming that the orders of a z b z and c z are known and the control uk can be arbitrarily chosen the new method consists in on line solving the algebraic equations associated with armax on the basis of observed data the algorithms are easily computable and the almost sure convergence of the algorithms is proved under reasonable conditions

mass eigenstates in twistor theory the introduction of inhomogeneity into twistor diagram theory provides a solution to the problem of defining massive states in a suitably finite way to produce states of finite norm however it is necessary to make a further change in the fundamental definitions of twistor diagram theory with the effect of introducing new inverse derivative operators

diversity integration tradeoffs in mimo detection in this paper a multiple input multiple output mimo detection problem is considered at first we derive the generalized likelihood ratio test glrt for arbitrary transmitted signals and arbitrary time correlation of the disturbance then we investigate design criteria for the transmitted waveforms in both power unlimited and power limited systems and we derive closed form formulas for the probability of false alarm and the detection probability finally we study the interplay among the rank of the optimized space time code i e the number of linearly independent transmitted waveforms the number of transmit diversity paths generated in the signal space and the amount of energy integrated along each path the results confirm that there is an inherent tradeoff between diversity and integration and that no uniformly optimum waveform design strategy exists

recursive identification of mimo wiener systems stochastic approximation sa algorithms are proposed to identify a multi input and multi output mimo wiener system in which the system input is taken to be a sequence of independent and identically distributed i i d gaussian random vectors uk n 0 i the algorithm for identifying the nonlinear part is designed with multi variable kernel functions under suitable conditions we show that the estimates of the coefficients of the linear subsystem and of the values of the nonlinear function converge to the respective true values with probability one

comparison of generalized q function algorithms corresp several methods have been proposed for calculating the generalized q function q m alpha beta but only isolated comparisons of the various techniques have been reported the accuracy range and execution time of prominent methods for computing the q function are compared and limitations of the algorithms are identified

conformally invariant differential operators on minkowski space and their curved analogues this article describes the construction of a natural family of conformally invariant differential operators on a four dimensional pseudo riemannian manifold included in this family are the usual massless field equations for arbitrary helicity but there are many more besides the article begins by classifying the invariant operators on flat space this is a fairly straightforward task in representation theory best solved through the theory of verma modules the method generates conformally invariant operators in the curved case by means of penrose s local twistor transport

properties of zero free spectral matrices in factor analysis which is used for example in econometrics by definition the number of latent variables has to exceed the number of factor variables the associated transfer function matrix has more rows than columns and when the factor variables are independent zero mean white noise sequences and the transfer function matrix is stable then the output spectrum is singular while a related paper focusses on the properties of such a nonsquare transfer function matrix in this paper we explore a number of properties of the spectral matrix and associated covariance sequence in particular a zero free minimum degree spectral factor can be computed with a finite number of rational calculations from the spectrum in contrast to typical spectral factor calculations assuming the spectrum fulfills a generic condition application of the result to kalman filtering is indicated and presentation of the results is also achieved using finite block toeplitz matrices with entries obtained from the covariance of the latent variable vector