relativistic gamow vectors the friedrichs model has often been used in order to obtain explicit formulas for eigenvectors associated to complex eigenvalues corresponding to lifetimes such eigenvectors are called gamow vectors and they acquire meaning in extensions of the conventional hilbert space of quantum theory to the so called rigged hilbert space in this paper gamow vectors are constructed for a solvable model of an unstable relativistic field as a result we obtain a time asymmetric relativistic extension of the fock space this extension leads to two distinct poincare semigroups the time reversal transformation maps one semigroup to the other as a result the usual pct invariance should be extended we show that irreversibility as expressed by dynamical semigroups is compatible with the requirements of relativity

an efficient algorithm for decomposing a polygon into star shaped polygons abstract in this paper we show how a theorem in plane geometry can be converted into a o n log n algorithm for decomposing a polygon into star shaped subsets the computational efficiency of this new decomposition contrasts with the heavy computational burden of existing methods

third order cumulants based methods for continuous time errors in variables model identification in this paper the problem of identifying stochastic linear continuous time systems from noisy input output data is addressed the input of the system is assumed to have a skewed probability density function whereas the noises contaminating the data are assumed to be symmetrically distributed the third order cumulants of the input output data are then asymptotically insensitive to the noises that can be coloured and or mutually correlated using this noise cancellation property two computationally simple estimators are proposed the usefulness of the proposed algorithms is assessed through a numerical simulation

quadric inclusion programs an lmi approach to mathcal h_ infty model identification practical application of mathcal h infty robust control relies on the system identification of a valid model set described by a linear system in feedback with a stable norm bounded uncertainty this model set should explain all possible or at least all previously measured behavior for the controlled plant such models can be viewed as norm bounded inclusions in the frequency domain this note introduces the quadric inclusion program that can identify inclusions from the input output data as a convex problem we prove several key properties of this algorithm and give a geometric interpretation for its behavior while we stress that the inclusion fitting is outlier sensitive by design we offer a method to mitigate the effect of measurement noise we apply this method to robustly approximate the simulated frequency domain data using orthonormal basis functions the result compares favorably with a least squares approach that satisfies the same data inclusion requirements

on some key issues in the windsurfer approach to adaptive robust control we examine a number of crucial questions that arise in the windsurfer approach to adaptive robust control considerations are limited to the case where the plant is stable and has no zeros on the imaginary axis the key conclusion is that given a strictly proper stable model of a strictly proper stable plant we can improve the performance robustness of the closed loop system through the windsurfer approach if the plant and the existing model have no unstable zeros within the designed closed loop bandwidth and if the deterioration in performance robustness caused by increasing the closed loop bandwidth results in a sufficiently high signal to noise ratio for a certain closed loop output error situations that may cause the iterative identification and control design process to terminate prematurely are identified a simulation example is used to illustrate the results discussed

network identifiability from intrinsic noise this paper considers the problem of inferring an unknown network of dynamical systems driven by unknown intrinsic noise inputs equivalently we seek to identify direct causal dependencies among manifest variables only from observations of these variables for linear time invariant systems of minimal order we characterise under what conditions this problem is well posed we first show that if the transfer matrix from the inputs to manifest states is minimum phase this problem has a unique solution irrespective of the network topology this is equivalent to there being only one valid spectral factor up to a choice of signs of the inputs of the output spectral density if the assumption of phase minimality is relaxed we show that the problem is characterised by a single algebraic riccati equation are of dimension determined by the number of latent states the number of solutions to this are is an upper bound on the number of solutions for the network we give necessary and sufficient conditions for any two dynamical networks to have equal output spectral density which can be used to construct all equivalent networks extensive simulations quantify the number of solutions for a range of problem sizes for a slightly simpler case we also provide an algorithm to construct all equivalent networks from the output spectral density

symmetry representations in the rigged hilbert space formulation of quantum mechanics we discuss some basic properties of lie group representations in rigged hilbert spaces in particular we show that a differentiable representation in a rigged hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of hilbert spaces we also construct a couple of examples illustrative of the key features of group representations in rigged hilbert spaces finally we establish a simple criterion for the integrability of an operator lie algebra in a rigged hilbert space

an exact approach to the oscillator radiation process in an arbitrarily large cavity starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius r we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the confined solution from a mathematical point of view we show that this way of addressing the problem is not equivalent to considering the system a priori embedded in infinite space in particular the matrix elements of the transformation turning the system to the principal axis do not tend to distributions in the limit of an arbitrarily large sphere as should be the case if the two procedures were mathematically equivalent also we introduce dressed coordinates which allow an exact description of the oscillator radiation process expanding in powers of the coupling constant we recover from our exact expressions the well known decay formulae from perturbation theory

new resultant inequalities and complex polynomial factorization the author deduces some new probabilistic estimates on the distances between the zeros of a polynomial p x by using some properties of the discriminant of p x and applies these estimates to improve the fastest deterministic algorithm for approximating polynomial factorization over the complex field namely given a natural n positive epsilon such that log 1 epsilon o n log n and the complex coefficients of a polynomial p x sum n i 0 p ix i such that p n ne 0 sum i p i le 1 a factorization of p x within the error norm epsilon is computed as a product of factors of degrees at most n 2 by using o log 2n time and n 3 processors under the pram arithmetic model of parallel computing or by using o n 2 log 2 n arithmetic operations the algorithm is randomized of las vegas type allowing a failure with a probability at most delta for any positive delta 1 such that log 1 delta o log n except for a narrow class of polynomials p x these results can be also obtained for epsilon such that log 1 epsilon o n 2 log n

solving a polynomial equation some history and recent progress the classical problem of solving an nth degree polynomial equation has substantially influenced the development of mathematics throughout the centuries and still has several important applications to the theory and practice of present day computing we briefly recall the history of the algorithmic approach to this problem and then review some successful solution algorithms we end by outlining some algorithms of 1995 that solve this problem at a surprisingly low computational cost

some np hard polygon decomposition problems the inherent computational complexity of polygon decomposition problems is of theoretical interest to researchers in the field of computational geometry and of practical interest to those working in syntactic pattern recognition three polygon decomposition problems are shown to be np hard and thus unlikely to admit efficient algorithms the problems are to find minimum decompositions of a polygonal region into perhaps overlapping convex star shaped or spiral subsets we permit the polygonal region to contain holes the proofs are by transformation from boolean three satisfiability a known np complete problem several open problems are discussed

bakamjian thomas construction for quasistable states as is evident from the multiple values listed in the particle data table for the mass and width of resonances such as z and defining these resonance parameters uniquely and unambiguously remains an open problem this problem is ultimately rooted in the absence of a state vector description of a resonance that has definite properties under spacetime transformations we show that there exist irreducible representations of the causal poincare semigroup that provide such a state vector description to resonances leading to well defined mass and width parameters generated by an interaction incorporating poincare algebra and characterized by the complex s matrix pole position and spin of the resonance these representations synthesize the bakamjian thomas construction of relativistic interactions and the s matrix description of resonances

closed loop subspace identification using the parity space it is known that many subspace algorithms give biased estimates for closed loop data due to the existence of feedback in this paper we present a new subspace identification method using the parity space employed in fault detection in the past the basic algorithm known as subspace identification method via principal component analysis simpca gives consistent estimation of the deterministic part and stochastic part of the system under closed loop column weighting for simpca is introduced which shows improved efficiency accuracy a simulation example is given to illustrate the performance of the proposed algorithm in closed loop identification and the effect of column weighting

algebraic complexity of computing polynomial zeros abstract using the power sum techniques of turan we evaluate all the complex zeros of an n th degree univariate polynomial with relative errors using o n 2 log n n log n log 1 arithmetic operations o n log n log 1 operations suffice to approximate with relative error a single complex zero using turan s method and all the zeros if they are real using graeffe s method in all cases n processors suffice for cn times parallel acceleration where c is a positive constant incorporating turan s techniques into another more recent algorithm gives a single complex zero with absolute error using o log 2 n log log 1 arithmetic parallel steps n 2 processors which places the problem in nc and also gives all the complex zeros in o n 2 log n log log 1 arithmetic operations where 1 is the absolutely largest zero computations with o log n 1 binary bits support the latter estimates for the arithmetic complexity which leads to a simple proof of the current best estimate for the boolean circuit complexity bit operation complexity of computing all the complex zeros of a polynomial announced by a schonhage in 1982 but not proven yet

kinetic time irreversible evolution of the unstable π meson abstract in liouville formalism the expression for density matrix determining the time evolution of unstable meson in the framework of unified formulation of quantum and kinetic dynamics is defined the eigenvalues problem is investigated in the framework of prigogine s principles of description of nonequilibrium processes at microscopic level the problem was solved on the basis of complex spectral representation it was shown that the approach leads to pauli master equation for the weakly interacting system

on covering orthogonal polygons with star shaped polygons abstract in this paper we present an o n time algorithm for covering a horizontally convex orthogonal polygon with the minimum number of orthogonal star shaped polygons finding minimum covers by star shaped polygons is equivalent to finding the minimum number of guards needed so that every point in the polygon is visible to at least one guard this problem has important applications in robotics and pattern recognition

on the worst case arithmetic complexity of approximating zeros of systems of polynomials let d 1 cdots d n be positive integers let mathcal p denote the set of systems of polynomials f mathbb c n to mathbb c n that have only finitely many zeros including those at infinity and that satisfy degree f i d i for all i let 0 varepsilon leqq r it is shown for fixed d 1 cdots d n that with respect to a certain model of computation the worst case computational complexity of obtaining varepsilon approximations to at least those zeros xi satisfying xi leqq r for arbitrary f in mathcal p is theta log log r varepsilon that is to say both upper and lower bounds are proved an algorithm for proving the upper bound is introduced the number of operations required by this algorithm is o left n mathcal d 4 log mathcal d log log r varepsilon n 2 mathcal d 4 left begin array 20 c 1 sigma d i n end array right 4 right quad text where mathcal d prod limits i 1

frequency response estimation for ncfs of an mimo plant from closed loop time domain experimental data frequency response estimation from closed loop time domain experimental data is investigated in this paper for normalized coprime factors ncf of a multiple input multiple output mimo plant based on a linear fractional transformation lft representation for all the ncfs of plants internally stabilizable by a known controller this estimation problem is converted into the open loop nonparametric estimation of an inner transfer function matrix tfm an estimate is derived through constrained data matching it is proved that when the probing signals are periodic and the ncfs of the auxiliary plant are appropriately selected the estimate is asymptotically unbiased and with a normal complex normal distribution it has been made clear that the estimation bias and the estimation variance are always finite computationally tractable procedures are suggested for choosing the desirable auxiliary tfms

quantum theory of non integrable systems in 1889 h poincare introduced a basic distinction between integrable and non integrable dynamical systems this distinction refers to the role of resonances which may lead to divergences a specially important class of non integrable systems are large poincare systems lps which have a continuous spectrum and present continuous sets of resonances as has been shown earlier lps play an essential role both in classical and quantum mechanics essentially all nontrivial problems of field theory as well as kinetic theory belong this class we consider here the well known friedrichs model in which an unstable discrete level is coupled to a continuum poincare s theorem prevents the existence of solutions of the eigenvalue problem associated to the hamiltonian which would be analytic in the coupling constant

resonances and the extension of dynamics to rigged hilbert space abstract we propose a unified operator theoretic formulation of resonances and resonance states in rigged hilbert space our approach shows how resonances are the basis for the extension of dynamics for unstable systems and in a synthesis and a generalization of the work of the brussels austin groups directed by prigogine with the work of bohm and gadella on gamow vectors and with the extension theory developed by the st petersburg group directed by pavlov we illustrate the approach for prototypes of resonances namely resonances of the power spectrum scattering resonances and resonances associated with the unstable bloch states

errors in variables identification in dynamic networks consistency results for an instrumental variable approach in this paper we consider the identification of a linear module that is embedded in a dynamic network using noisy measurements of the internal variables of the network this is an extension of the errors in variables eiv identification framework to the case of dynamic networks the consequence of measuring the variables with sensor noise is that some prediction error identification methods no longer result in consistent estimates the method developed in this paper is based on a combination of the instrumental variable philosophy and closed loop prediction error identification methods and leads to consistent estimates of modules in a dynamic network we consider a flexible choice of which internal variables need to be measured in order to identify the module of interest this allows for a flexible sensor placement scheme we also present a method that can be used to validate the identified model

a quantitative condition for the well posedness of interconnected dynamical systems a sufficient condition for the well posedness of interconnected dynamical systems is reported the condition is stated in terms of the uniform instantaneous gains of subsystems and interconnections and includes vidyasagar s condition 8 as a special case the result is useful for testing the validity of the dynamical model of a large scale system which is obtained by combining the models of subsystems

identification of systems with unknown inputs using indirect input measurements abstracta common issue with many system identification problems is that the true input to the system is unknown this paper extends a previously presented indirect modelling framework that deals with identification of systems where the input is partially or fully unknown in this framework unknown inputs are eliminated by using additional measurements that directly or indirectly contain information about the unknown inputs the resulting indirect predictor model is only dependent on known and measured signals and can be used to estimate the desired dynamics or properties since the input of the indirect model contains both known inputs and measurements that could all be correlated with the same disturbances as the output estimation of the indirect model has similar challenges as a closed loop estimation problem in fact due to the generality of the indirect modelling framework it unifies a number of already existing system identification problems that are contained as special cases for completeness

optimal and nearly optimal algorithms for approximating polynomial zeros abstract we substantially improve the known algorithms for approximating all the complex zeros of an n th degree polynomial p x our new algorithms save both boolean and arithmetic sequential time versus the previous best algorithms of schonhage 1 pan 2 and neff and reif 3 in parallel nc implementation we dramatically decrease the number of processors versus the parallel algorithm of neff 4 which was the only nc algorithm known for this problem so far specifically under the simple normalization assumption that the variable x has been scaled so as to confine the zeros of p x to the unit disc x x 1 our algorithms which promise to be practically effective approximate all the zeros of p x within the absolute error bound 2 b by using order of n arithmetic operations and order of b n n 2 boolean bitwise operations in both cases up to within polylogarithmic factors the algorithms allow their optimal work preserving nc parallelization so that they can be implemented by using polylogarithmic time and the orders of n arithmetic processors or b n n 2 boolean processors all the cited bounds on the computational complexity are within polylogarithmic factors from the optimum in terms of n and b under both arithmetic and boolean models of computation in the boolean case under the additional realistic assumption that n o b

an indirect method for transfer function estimation from closed loop data abstract an indirect method is introduced that is able to estimate consistently the transfer function of a linear plant on the basis of data obtained from closed loop experiments even in the situation where the model of the noise disturbance on the data is not accurate moreover the method allows approximate identification of the open loop plant with an explicit and tunable expression for the bias distribution of the resulting model

complexity of computations with matrices and polynomials this paper reviews the complexity of polynomial and matrix computations as well as their various correlations to each other and some major techniques for the design of algebraic and numerical algorithms

identification of dynamic models in complex networks with prediction error methods basic methods for consistent module estimates abstract the problem of identifying dynamical models on the basis of measurement data is usually considered in a classical open loop or closed loop setting in this paper this problem is generalized to dynamical systems that operate in a complex interconnection structure and the objective is to consistently identify the dynamics of a particular module in the network for a known interconnection structure it is shown that the classical prediction error methods for closed loop identification can be generalized to provide consistent model estimates under specified experimental circumstances two classes of methods considered in this paper are the direct method and the joint io method that rely on consistent noise models and indirect methods that rely on external excitation signals like two stage and iv methods graph theoretical tools are presented to verify the topological conditions under which the several methods lead to consistent module estimates

efficient algorithms for the evaluation of the eigenvalues of block banded toeplitz matrices on presente des algorithmes de calcul des valeurs propres des matrices bandes blocs de toeplitz

complexity of parallel matrix computations abstract we estimate parallel complexity of several matrix computations under both boolean and arithmetic machine models using deterministic and probabilistic approaches those computations include the evaluation of the inverse the determinant and the characteristic polynomial of a matrix recently processor efficiency of the previous parallel algorithms for numerical matrix inversion has been substantially improved in pan and reif 1987 reaching optimum estimates up to within a logarithmic factor that work however applies neither to the evaluation of the determinant and the characteristic polynomial nor to exact matrix inversion nor to the numerical inversion of ill conditioned matrices we present four new approaches to the solution of those latter problems having several applications to combinatorial computations in order to extend the suboptimum time and processor bounds of pan and reif 1987 to the case of computing the inverse determinant and characteristic polynomial of an arbitrary integer input matrix in addition processor efficient algorithms using polylogarithmic parallel time are devised for some other matrix computations such as triangular and qr factorizations of a matrix and its reduction to hessenberg form

partial wave decomposition in friedrichs model with self interacting continua we consider the nonrelativistic model of coupling bare discrete states with continuum states in which the continuum states can have interactions among themselves by partial wave decomposition and constraint to the conserved angular momentum eigenstates the model can be reduced to friedrichs like model with additional interactions between the continua if a kind of factorizable form factor is chosen the model can be exactly solvable that is the generalized discrete eigenstates including bound states virtual states and resonances can all be represented using the original bare states and so do the in state and out state the exact s matrix is thus obtained we then discuss the behaviors of the dynamically generated s wave and p wave discrete states as the coupling is varying when there is only one self interacting bare continuum state we find that even when the potential is repulsive there could also be resonances and virtual states in the p wave cases with attractive interaction we find that when

a general multirate approach for direct closed loop identification to the nyquist frequency and beyond without injecting any external persistently exciting signals a general multirate approach is proposed for direct closed loop identification first an extended least squares algorithm is designed to identify the mixed rate model after polynomial transformation next the identified mixed rate model is used to compute the fast rate model from which system dynamics to the nyquist frequency and beyond can be obtained identifiability is mathematically proven if the plant output sampling rate is non integer multiples of the controller sampling rate the effectiveness of the proposed approach is evaluated by both the simulation and experimental results in a hard disk drive

resonance poles and gamow vectors in the rigged hilbert space formulation of quantum mechanics after a summary of the rigged hilbert space formulation of quantum mechanics and a brief statement of its advantages over von neumann s formulation a mathematically correct definition of gamow s exponentially decaying vectors as generalized energy eigenvectors is suggested it is shown that exponentially decaying vectors are obtained from the s matrix poles in the lower half of the second sheet and exponentially growing vectors from the s matrix poles in the upper half of the second sheet decaying state vectors are defined as functionals over half of the space of physical states and growing state vectors are defined as functionals over the other half on functionals over these subspaces the dynamical group of time development splits into two semigroups one for t 0 and the other for t 0 the generalized basis system connected with the spectrum of the hamiltonian is transformed into a new basis system in which the exponentially decaying component of the density matrix is separated

the asymptotic crlb for the spectrum of arma processes this paper addresses the issue of quantifying the frequency domain accuracy of autoregressive moving average arma spectral estimates as dictated by the cramer rao lower bound crlb classical work in this area has led to expressions that are asymptotically exact as both data length and model order tend to infinity although they are commonly used in finite model order and finite data length settings as approximations more recent work has established quantifications that for ar models are exact for finite model order by employing new analysis methods based on rational orthonormal parameterizations together with the ideas of reproducing kernel hilbert spaces this paper develops quantifications that extend this previous work by being exact for finite model order in all of the ar ma and arma system cases these quantifications via their explicit dependence on poles and zeros of the underlying spectral factor reveal certain fundamental aspects of the accuracy achievable by spectral estimates of arma processes

an indirect prediction error method for system identification abstract a new form of prediction error method pem is developed it is applicable to the case where the model structure of interest can be imbedded in a larger model structure whose estimation is relatively easy an optimal way of reducing the larger model to the smaller model structure is presented and various interpretations of this reduction are given the proposed method will have the same asymptotic statistical properties as the standard pem but it can be implemented by a more efficient algorithm the properties of the method are illustrated by the means of some simulated examples

computational complexity on the geometry of polynomials and a theory of cost ii this paper deals with traditional algorithms newton s method and a higher order generalization due to euler these iterations schemes and their modifications have had a great success in solving nonlinear systems of equations we give some understanding of this phenomenon by giving estimates of efficiency the problem we focus on is that of finding a zero of a complex polynomial

optimum placement of guards abstract we consider the problem of placing guards in a polygon so that 1 a the area or 2 b the portion of the boundary visible to the guards is maximized we show that finding optimum placements for k guards is np hard if k is a variable we reduce the problem of optimally placing one guard to solving a high order equation and give a polynomial time approximation scheme for placing one guard in a simple polygon

instrumental variable methods for closed loop system identification in this paper several instrumental variable iv and instrumental variable related methods for closed loop system identification are considered and set in an extended iv framework extended iv methods require the appropriate choice of particular design variables as the number and type of instrumental signals data prefiltering and the choice of an appropriate norm of the extended iv criterion the optimal iv estimator achieves minimum variance but requires the exact knowledge of the noise model for the closed loop situation several iv methods are put in an extended iv framework and characterized by different choices of design variables their variance properties are considered and illustrated with a simulation example

deterministic improvement of complex polynomial factorization based on the properties of the associated resultant abstract we show an improvement of the known best deterministic approach to factorization of a univariate polynomial p x over the complex field previously such an improvement was achieved by means of a random perturbation of the coefficients of the input polynomial we now apply some new techniques which lead to a similar result without any randomization the approach is unusual in exploiting some properties of the resultant of p x and p x which is completely distinct from the techniques usually applied in order to compute complex polynomial factorization

solving matrix polynomial equations arising in queueing problems abstract the matrix equation i 0 n a i x i 0 where the a i s are m m matrices is encountered in the numerical solution of markov chains which model queueing problems we provide here a unifying framework in terms of mobius mapping to relate different resolution algorithms having a quadratic convergence this allows us to compare algorithms like logarithmic reduction lr and cyclic reduction cr which extend graeffe s iteration to matrix polynomials and the invariant subspace is approach which extends cardinal s algorithm we devise new iterative techniques having quadratic convergence and present numerical experiments

on boundaries of highly visible spaces and applications the purpose of this paper is to investigate the properties of a certain class of highly visible spaces for a given geometric space c containing obstacles specified by disjoint subsets of c the free space f is defined to be the portion of c not occupied by these obstacles the space is said to be highly visible if at each point in f a viewer can see at least an e fraction of the entire f this assumption has been used for robotic motion planning in the analysis of random sampling of points in the robot s configuration space as well as the upper bound of the minimum number of guards needed for art gallery problems however there is no prior result on the implication of this assumption to the geometry of the space under study for the two dimensional case with the additional assumptions that c is bounded within a rectangle of constant aspect ratio and that the volume ratio between f and c is a constant we use the proof technique of charging each obstacle boundary segment by a certain portion of c to show that the total length of all obstacle boundaries in c is o n f e if f contains polygonal obstacles with a total of n boundary edges or o n f e if c contains n convex obstacles that are piecewise smooth in both cases f is the volume of f for the polygonal case this bound is tight as we can construct a space whose boundary size is n f e these results can be partially extended to three dimensions we show that these results can be applied to the analysis of certain probabilistic roadmap planners as well as a variant of the art gallery problem we also propose a number of conjectures on the properties of these highly visible spaces

generalization of the coleman mandula theorem to higher dimension the coleman mandula theorem which states that space time and internal symmetries cannot be combined in any but a trivial way is generalized to an arbitrarily higher spacelike dimension prospects for further generalizations of the theorem spacelike representations larger timelike dimension infinite number of particle types are also discussed the original proof relied heavily on the dirac formalism which was not well defined mathematically at that time the proof given here is based on the rigorous version of the dirac formalism based on the theory of distributions this work also serves to demonstrate the suitability of this formalism for practical applications

computing matrix eigenvalues and polynomial zeros where the output is real surprisingly simple corollaries from the courant fischer minimax characterization theorem enable us to devise a very effective algorithm for the evaluation of a set s interleaving the set e of the eigenvalues of an n x n real symmetric tridiagonal rst matrix tn as well as a point that splits e into two subsets of comparable cardinalities furthermore we extend this algorithm so as to approximate all the n eigenvalues of tn at nearly optimal sequential and parallel cost that is at the cost of staying within polylogarithmic factors from the straightforward lower bounds the resulting improvement of the known processor bound in nc algorithms for the rst eigenproblem is roughly by factor n our approach extends the previous works m ben or and p tiwari j complexity 6 1990 pp 417 442 and m ben or et al siam j comput 17 1988 pp 1081 1092 for the approximation of the zeros of a polynomial having only real zeros and our algorithm leads to an alternative and simplified derivation of the known record parallel and sequential complexity estimates for the latter problem

the variation of non parametric estimates in closed loop it is known that non parametric transfer function estimates in closed loop often have infinite variance we characterise the probability density function of such estimates under the assumption that the corresponding closed loop system estimate has complex normal distribution in the frequency domain the probability density function can be described as a horseshoe encircling the inverse of the controller with a global maximum on the line between the true value and the inverse of the controller the expected value of the absolute value of such estimates is finite and we propose it as a measure of variation we also derive and discuss new expressions for the variance when an exclusion zone is introduced around the singularity

exact markovian kinetic equation for a quantum brownian oscillator we derive an exact markovian kinetic equation for an oscillator linearly coupled to a heat bath describing quantum brownian motion our work is based on the subdynamics formulation developed by prigogine and collaborators the space of distribution functions is decomposed into independent subspaces that remain invariant under liouville dynamics for integrable systems in poincar e s sense the invariant subspaces follow the dynamics of uncoupled renormalized particles in contrast for nonintegrable systems the invariant subspaces follow a dynamics with broken time symmetry involving generalized functions this result indicates that irreversibility and stochasticity are exact properties of dynamics in generalized function spaces we comment on the relation between our markovian kinetic equation and the hu paz zhang equation

technical communique asymptotic variance expressions for closed loop identification asymptotic variance expressions are analyzed for models that are identified on the basis of closed loop data the considered methods comprise the classical direct method as well as the more recently developed indirect methods employing coprime factorized models dual youla kucera parametrizations and the two stage approach the variance expressions are compared with the open loop situation and evaluated in terms of their relevance for subsequent model based control design

a new attempt towards the unification of space time and internal gauge symmetries the neat formulation that describes the gauge interactions associated with internal symmetries is extended to the case of a simple yet non trivial symmetry group structure which mixes gravity and electromagnetism by associating a gauge symmetry with a central extension of the poincare group

a projection method for closed loop identification a new method for closed loop identification that allows fitting the model to the data with arbitrary frequency weighting is described and analyzed just as the direct method this new method is applicable to systems with arbitrary feedback mechanisms this is in contrast to other methods such as the indirect method and the two stage method that assume linear feedback the finite sample behavior of the proposed method is illustrated in a simulation study

brief subspace identification of closed loop systems by the orthogonal decomposition method in this paper we consider a problem of identifying the deterministic part of a closed loop system by applying the stochastic realization technique of signal process 52 2 1996 145 in the framework of the joint input output approach using a preliminary orthogonal decomposition the problem is reduced to that of identifying the plant and controller based on the deterministic component of the joint input output process we discuss the role of input signals in closed loop identification and the realization method based on a finite data and then sketch a subspace method for identifying state space models of the plant and controller since the obtained models are of higher order a model reduction procedure should be applied for deriving lower order models some numerical results are included to show the applicability of the present technique

parametric identification using weighted null space fitting in identification of dynamical systems the prediction error method with a quadratic cost function provides asymptotically efficient estimates under gaussian noise but in general it requires solving a nonconvex optimization problem which may imply convergence to nonglobal minima an alternative class of methods uses a nonparametric model as intermediate step to obtain the model of interest weighted null space fitting wnsf belongs to this class starting with the estimate of a nonparametric arx model with least squares then the reduction to a parametric model is a multistep procedure where each step consists of the solution of a quadratic optimization problem which can be obtained with weighted least squares the method is suitable for both open and closed loop data and can be applied to many common parametric model structures including output error armax and box jenkins the price to pay is the increase of dimensionality in the nonparametric model which needs to tend to infinity as function of the sample size for certain asymptotic statistical properties to hold in this paper we conduct a rigorous analysis of these properties namely consistency and asymptotic efficiency also we perform a simulation study illustrating the performance of wnsf and identify scenarios where it can be particularly advantageous compared with state of the art methods

closed loop identification revisited identification of systems operating in closed loop has long been of prime interest in industrial applications the problem offers many possibilities and also some fallacies and a wide variety of approaches have been suggested many quite recently the purpose of the current contribution is to place most of these approaches in a coherent framework thereby showing their connections and display similarities and differences in the asymptotic properties of the resulting estimates the common framework is created by the basic prediction error method and it is shown that most of the common methods correspond to different parameterizations of the dynamics and noise models the so called indirect methods e g are indeed direct methods employing noise models that contain the regulator the asymptotic properties of the estimates then follow from the general theory and take different forms as they are translated to the particular parameterizations we also study a new projection approach to closed loop identification with the advantage of allowing approximation of the open loop dynamics in a given and user chosen frequency domain norm even in the case of an unknown nonlinear regulator

construction of a complete set of states in relativistic scattering theory the space of physical states in relativistic scattering theory is constructed using a rigorous version of the dirac formalism where the hilbert space structure is extended to a gel fand triple this extension enables the construction of a complete set of states the basic concept of the original dirac formalism also in the cases of unbounded operators and continuous spectra we construct explicitly the gel fand triple and a complete set of plane waves momentum eigenstates using the group of space time symmetries this construction is used in a separate article to prove a generalization of the coleman mandula theorem to higher dimension

sparse network identifiability via compressed sensing the problem of identifying sparse solutions for the link structure and dynamics of an unknown linear time invariant network is posed as finding sparse solutions x to a x b if the matrix a satisfies a rank condition this problem has a unique sparse solution here each row of a comprises one experiment consisting of input output measurements and cannot be freely chosen we show that if experiments are poorly designed the rank condition may never be satisfied resulting in multiple solutions we discuss strategies for designing experiments such that a has the desired properties and the problem is therefore well posed this formulation allows prior knowledge to be taken into account in the form of known nonzero entries of x requiring fewer experiments to be performed simulated examples are given to illustrate the approach which provides a useful strategy commensurate with the type of experiments and measurements available to biologists we also confirm suggested limitations on the use of convex relaxations for the efficient solution of this problem

identification and the information matrix how to get just sufficiently rich in prediction error identification the information matrix plays a central role specifically when the system is in the model set the covariance matrix of the parameter estimates converges asymptotically up to a scaling factor to the inverse of the information matrix the existence of a finite covariance matrix thus depends on the positive definiteness of the information matrix and the rate of convergence of the parameter estimate depends on its size the information matrix is also the key tool in the solution of optimal experiment design procedures which have become a focus of recent attention introducing a geometric framework we provide a complete analysis for arbitrary model structures of the minimum degree of richness required to guarantee the nonsingularity of the information matrix we then particularize these results to all commonly used model structures both in open loop and in closed loop in a closed loop setup our results provide an unexpected and precisely quantifiable trade off between controller degree and required degree of external excitation

a bias correction method for closed loop identification of linear parameter varying systems abstract due to safety constraints and unstable open loop dynamics system identification of many real world processes often requiresgathering data from closed loop experiments in this paper we present a bias correction scheme for closed loop identification of linear parameter varying input output lpv io models which aims at correcting the bias caused by the correlation between the input signal exciting the process and output noise the proposed identification algorithm provides a consistent estimate of the open loop model parameters when both the output signal and the scheduling variable are corrupted by measurement noise the effectiveness of the proposed methodology is tested in two simulation case studies

fast and efficient parallel evaluation of the zeros of a polynomial having only real zeros abstract given a polynomial p x of degree n with integer coefficients between 2 m and 2 m it suffices to use o log 2 n log b parallel arithmetic steps and n 2 processors in order to compute all the zeros of p x with absolute errors at most 2 h provided that all the zeros are real and b m h the algorithm combines the recent techniques and results of 1 3 in order to improve the previous record processor bound of 1 at least on the factor of n preserving its upper bound on parallel time

on the consistency between an lft described model set and frequency domain data the main objective of this technical note is to derive a simple necessary and sufficient condition for a linear fractional transformation lft perturbed model set being consistent with frequency domain plant input output data only discrete time models and unstructured modeling errors are dealt with compared with the available results in which the eigenvalues of a matrix are involved this condition is related only to the euclidean norms of two vectors moreover these vectors linearly depend on measurement errors some of its applications to model set validation have been briefly discussed based on this condition an almost analytic solution has been established for model set validation under a deterministic framework when the measurement errors are energy bounded numerical simulations show that this consistency condition can lead to a significant computation cost reduction

asymptotic variance expressions for identified black box transfer function models identification of black box transfer function models is considered it is assumed that the transfer function models possess a certain shift property which is satisfied for example by all polynomial type models expressions for the variances of the transfer function estimates are derived that are asymptotic both in the number of observed data and in the model orders the result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance respectively is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise the factor of proportionality is the ratio of model order to number of data this result is independent of the particular model structure used the result is applied to evaluate the performance degradation due to variance for a number of typical model uses some consequences for input design are also drawn

placing guards inside orthogonal polygons abstract we consider the problem of locating guards inside a polygon under standard visibility and orthogonal visibility given a polygon the maximum visibility problem maxvp asks for locating a point inside the polygon from which the visible area is maximized minimum visibility problem minvp is defined similarly under standard visibility we show that the boundary point solution for minvp can be obtained in o n 3 time for simple orthogonal polygons and in o n 3 log n time for orthogonal polygons with holes for class 3 polygons under stair case visibility we show that the solution for minvp lies on the boundary this leads to an o n 2 time algorithm to locate the solution

variance analysis of linear simo models with spatially correlated noise in this paper we address the identification of linear time invariant single input multi output simo systems in particular we assess the performance of the prediction error method by quantifying

necessary and sufficient conditions for dynamical structure reconstruction of lti networks this paper formulates and solves the network reconstruction problem for linear time invariant systems the problem is motivated from a variety of disciplines but it has recently received considerable attention from the systems biology community in the study of chemical reaction networks here we demonstrate that even when a transfer function can be identified perfectly from input output data not even boolean reconstruction is possible in general without more information about the system we then completely characterize this additional information that is essential for dynamical reconstruction without appeal to ad hoc assumptions about the network such as sparsity or minimality

sequential and parallel complexity of approximate evaluation of polynomial zeros our new sequential and parallel algorithms establish new record upper bounds on both arithmetic and boolean complexity of approximating to complex polynomial zeros o n2 log b log n arithmetic operations or o n log n log bn parallel steps and n log b log bn processors suffice in order to approximate with absolute errors 2m b to all the complex zeros of an nth degree polynomial p x whose coefficients have mod 2m if we only need such an approximation to a single zero of p x then o n log b log n arithmetic operations or o log2 n log bn steps and n log n log b log bn processors suffice which places the latter problem in nc that is in the class of problems that can be solved using polylogarithmic parallel time and a polynomial number of processors those estimates are reached in computations with o bn binary bits where the polynomial has integer coefficients we also reach the sequential boolean time bounds o bn3 log bn log log bn for approximating to all the zeros very minor improvement of the bound announced in 1982 by schonhage and o bn2log log n log bn log log bn for approximating to a single zero among further implications are the improvements of the known algorithms and complexity estimates for computing matrix eigenvalues for polynomial factorization over the field of complex numbers and for solving systems of polynomial equations the computations rely on recursive application of turan s proximity test of 1968 on its more recent extensions to root radii computations on contour integration via fast fourier transform fft within geometric constructions for search and exclusion and for the final minor improvements of the complexity bounds on the recursive factorization of p x over discs on the complex plane via numerical integration and newton s iterations

computational complexity of art gallery problems we study the computational complexity of the art gallery problem originally posed by klee and its variations specifically the problem of determining the minimum number of vertex guards that can see an n wall simply connected art gallery is shown to be np hard the proof can be modified to show that the problems of determining the minimum number of edge guards and the minimum number of point guards in a simply connected polygonal region are also np hard as a byproduct the problem of decomposing a simple polygon into a minimum number of star shaped polygons such that their union is the original polygon is also shown to be np hard

bounded error identification for closed loop systems this paper presents a scheme for the identification of a system which operates in closed loop and in the presence of bounded output disturbances two algorithms are proposed to solve this identification problem the first algorithm is an optimal bounding ellipsoid obe type algorithm this first algorithm is analyzed and sufficient conditions for stability and convergence are established relaxation of these conditions leads to a second identification algorithm the implementation of that second algorithm is realized in an iterative scheme a numerical example is provided to show the efficiency of the scheme

a rigged hilbert space for the free radiation field we here construct a rigged hilbert space suitable for the description of the free radiation field in a box and in the coulomb gauge we prove the continuity of the main observables on this structure

delay structure conditions for identifiability of closed loop systems abstract when identifying a linear system operating under a linear feedback law specific restrictions have to be imposed on the presence of delays in the plant and or the controller in order to obtain identifiability in this paper the delay structure conditions are investigated under which a least squares direct type prediction error identification method is able to consistently estimate the open loop plant it is shown that the commonly required condition of strictly properness of the loop transfer function can be relaxed to a condition that relates to the absence of algebraic loops in the closed loop plant models