graph grammars with neighbourhood controlled embedding abstract a central feature that distinguishes graph grammars we consider grammars generating sets of node labelled undirected graphs only from string grammars is that in the former one has to provide a mechanism by which a daughter graph the right hand side of a production can be embedded in the rest of the mother graph while in the latter this embedding is provided automatically by the structure that all strings possess left to right orientation in this paper we consider a possible classification of embedding mechanisms for node rewriting graph grammars this classification originates from the basic ideas of 9 on the one hand it allows one to fit a number of existing notions of a graph grammar into a common framework and on the other hand it points out new natural possibilities for defining the embedding mechanism in a graph grammar the relationship between the graph language generating power of graph grammars using various embedding mechanisms is established

a discrete formulation of the theory of sojourn times in a two state system abstract most theoretical analyses of single molecule spectroscopy sms are formulated in terms of a first order isomerization process the mathematical problem to which the analysis reduces requires one to find the probability density for the total residence time in one of the states at a given observation time t in this paper we develop a slightly more rigorous theory in which account is taken of the discrete pulsing of the laser it is shown how to pass to the continuum limit we develop analogous results to analyze experiments in which the quantum yield is less than 1

subspace fitting approaches for frequency estimation using real valued data a novel data covariance model has recently been proposed for the subspace based estimation of multiple real valued sine wave frequencies in this paper we develop weighted subspace fitting approaches using this new data model a new parameterization of the noise subspace is proposed this parameterization is used to solve the subspace fitting problem analytically an expression for the residual covariance matrix is derived this covariance matrix is further used to obtain an optimally weighted gauss markov estimator a computationally efficient suboptimal weighting is also proposed and the associated estimator is close to the gauss markov estimator in performance the suboptimal weighting strategy is quite general and can be used in other related applications the performance of the algorithms are illustrated using numerical simulations the proposed subspace fitting approach shows improved resolution performance it is also robust to additive noise

subspace identification of circulant systems this article concerns the identification of a class of large scale systems called circulant systems circulant systems have a special property that allows them to be decomposed into simpler subsystems through a state transformation this property has been used in literature for control design and here we show how it can be used for system identification the approach that is proposed here will both reduce the complexity of the problem as well as provide models which have a circulant structure that can be exploited for control design a novel identification algorithm for circulant systems based on subspace identification is presented the algorithm is then tested in simulation on an academic example of circulant system and on a realistic finite element model of a vibrating plate

a bayesian approach to sparse dynamic network identification modeling and identification of high dimensional systems involving signals with many components poses severe challenges to off the shelf techniques for system identification this is particularly so when relatively small data sets as compared to the number signal components have to be used it is often the case that each component of the measured signal can be described in terms of a few other measured variables and these dependences can be encoded in a graphical way via so called dynamic bayesian networks the problem of finding the interconnection structure as well as estimating the dynamic models can be posed as a system identification problem which involves variable selection while this variable selection could be performed via standard selection techniques computational complexity may however be a critical issue being combinatorial in the number of inputs and outputs in this paper we introduce two new nonparametric techniques which borrow ideas from a recently introduced kernel estimator called stable spline as well as from sparsity inducing priors which use 1 type penalties numerical experiments regarding estimation of large scale sparse armax models show that this technique provides a definite advantage over a group lar algorithm and state of the art parametric identification techniques based on prediction error minimization

representations of jointly stationary stochastic feedback processes abstract stable constant linear closed loop systems relating an input vector u to an output vector u and vice versa produce a jointly stationary y u procoss on the other hand it is often natural to split up a stationary vector random process z into component vectors yand u and to examine the closed loop relations between y and u this paper presents a number of new results on the spectral factorization and the closed loop representation of a jointly stationary vector y u proccss conditions are derived on the closed loop models for the joint process model to bo oe minimal degree stable and minimum phase relations between different joint process models producing the same spectrum yu z are established

on the problem of reconstructing an unknown topology via locality properties of the wiener filter determining interrelatedness structure of various entities from multiple time series data is of significant interest to many areas knowledge of such a structure can aid in identifying cause and effect relationships clustering of similar entities identification of representative elements and model reduction the majority of existing results are based on correlation based indices which effectively assume a static relationship between the time series data and are not suitable for detecting interrelatedness when the time series are dynamically related or when the time series involve loops in this paper a methodology for identifying the interrelatedness structure of dynamically related time series data is presented that also allows for the presence of loops in the connectivity structure a linear dynamic graph model is presented where it is assumed that each time series data is the sum of an independent stochastic noise source and a dynamically weighted sum of other time series data a link is assumed to be present between two time series if the weight of a time series which is a linear time invariant filter is nonzero in the formation of the other reconstruction of the link connectivity structure under various scenarios is considered it is shown that when the linear dynamic graph is allowed to admit non causal weights then the links structure can be recovered with the possibility of identifying spurious connections however it is shown that the spurious links remain local where a spurious link is restricted to be within one hop of a true link furthermore strategies for exact reconstruction of the link structure when the weights are restricted to be causal are developed the main tools for determining the network topology are based on variations of wiener filtering a significant insight provided by the article is that in the class of network models considered in the paper the wiener filter estimating a stochastic process based on other processes remains local in the sense that the wiener filter utilizes only measurements local to the node being estimated

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

some applications of persistent random walks and the telegrapher s equation abstract a persistent random walk can be regarded as a multidimensional markov process the bias free telegraphers equation is 2 p t 2 1 t p t v 2 2 p it can be regarded as interpolating between the wave equation t and the diffusion equation t 0 previously it has found application in thermodynamics cf the review in rev mod phys 61 1989 41 62 1990 375 more recent applications are reviewed in the present article

infinite hypergraphs i basic properties abstract basic properties of the category of infinite directed hyperedge labelled hypergraphs are studied an algebraic structure is given which enables us to describe such hypergraphs by means of infinite expressions it is then shown that two expressions define the same hypergraphs if and only if they are congruent with respect to some rewriting system these results will be used in the second part of this paper to solve systems of recursive equations on hypergraphs and characterize their solutions

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

node rewriting in graphs and hypergraphs a categorical framework vertex rewriting in graphs is a very powerful mechanism which has been studied for quite a long time in this paper we eventually provide a categorical theory of vertex rewriting and show how it can extend in a uniform way to node and pattern rewriting mechanisms in hypergraphs copyright 2001 elsevier science b v

residence time densities for non markovian systems ii the n state system we study dynamical system which makes transitions between two states at random times we analyze properties of the cumulative time spent by the system in a given state up to time t when the probability density for the residence time in a single sojourn in the given state differs from a negative exponential the system will be non markovian simple analytical expressions are derived for the laplace transform with respect to t of moments of the cumulative residence time an exact fourier laplace transform of the probability densities for at a fixed t are also found it can be inferred from this expression that at sufficiently large t the probability densities tend towards a gaussian the parameters that define the gaussian are also given

brief paper variance results for identification of cascade systems the objective of this contribution is to analyze statistical properties of estimated models of cascade systems models of such systems are important in for example cascade control applications the aim is to present and analyze some fundamental limitations in the quality of an identified model of a cascade system under the condition that the true subsystems have certain common dynamics the model quality is analyzed by studying the asymptotic large data covariance matrix of the prediction error method parameter estimate the analysis will focus on cascade systems with three subsystems the main result is that if the true transfer functions of the first and second subsystem are identical the output signal information from the second and third subsystems will not affect the asymptotic variance of the estimated model of the first subsystem this result implies that for a cascade system with two subsystems where the dynamics of the first subsystem is a factor of the dynamics of the second one the output signal information from the second subsystem will not improve the asymptotic quality of the estimate of the first subsystem the results are illustrated by some simple fir examples

infinite hypergraphs ii systems of recursive equations abstract the results and tools which were developed in part i of this paper 4 are used to solve systems of recursive equations on hypergraphs and to characterize their solutions completely a hypergraph s initial solutions are called equational hypergraphs it is then shown that the context free graphs of muller and schupp 15 are equational

on covariance function tests used in system identification abstract tests on the autocovariance function of the residuals of an estimated model or on the cross covariance function between the model residuals and the past values of the input signal are frequently used in system identification for model validation purposes usually the threshold of such a test is derived under the assumption that the model and the identified system coincide the present paper shows that this simplifying assumption leads to a risk of overfitting less than expected and accordingly to a greater risk of underfitting the correct test threshold is problem dependent and cannot be determined easily in the general case however it can be shown to lie in a certain interval and to be equal to one of the bounds defining this interval under certain sufficient conditions the implication of these results for model validation based on covariance tests is discussed and illustrated by means of some numerical examples

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

estimation for the multivariate errors in variables model with estimated error covariance matrix the errors in variables model in which the unobserved true values satisfy multiple linear restrictions is considered under the assumptions that the unobservable true values are normally distributed and that an estimator of the covariance matrix of the measurement error is available the maximum likelihood estimators are derived the limiting properties of the estimators are obtained for a wide range of assumptions including the assumption of fixed true values

a comparison of boundary graph grammars and context free hypergraph grammars context free hypergraph grammars and boundary graph grammars of bounded nonterminal degree have the same power both for generating sets of graphs and for generating sets of hypergraphs arbitrary boundary graph grammars have more graph generating power than context free hypergraph grammars but they have the same hypergraph generating power to obtain these results several normal forms for boundary graph grammars are given it is also shown that the class of boundary graph languages is closed under the operation of edge contraction where the label of the edge indicates whether or not the edge should be contracted

an axiomatic definition of context free rewriting and its application to nlc graph grammars abstract an abstract notion of context free grammar is introduced it deals with abstract objects that can be words trees graphs or other combinatorial objects it is applied to nlc graph grammars introduced by rozenberg and janssens the monadic second order theory of a context free nlc set of graphs is decidable

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

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

frequency domain system identification using non parametric noise models estimated from a small number of data sets abstract this paper discusses the problem of identifying a linear system from the frequency data when the measurements of the input and the output signals are both disturbed with noise a typical example of such a problem is the identification of a system in a feedback loop it is known that this problem can be solved using errors in varaibles methods if the covariance matrices of the disturbing noise on input and output measurements are a priori known it is shown that the exact covariance matrices can be replaced by the sample covariance matrices the system can be identified from the sample means and sample covariance matrices calculated from a small number m of independently repeated experiments it is shown that under these conditions the estimates are still strongly consistent for an increasing number of data points n in each experiment n if m 4 the loss in efficiency is quantified m 6 and the expected value of the cost function m 4 and its variance m 6 are calculated