comments on mfd models and time delays some consequences for identification janssen 1987 proposed a method for the incorporation of time delays and causality in mfd models for the purpose of equation error identification this method is shown not to be completely adequate since it retains linearity in the parameters by sacrificing optimality of the solution

e factor of representations of classical groups abstract we let g be the isometry group of a nondegenerate symmetric or skew symmetric form h on a space v over some local or global field k i e g u v h we let lg be the l group of go the identity component of g and r be the natural representation of this group we develop here a theory of l functions and e factors attached to this r in particular we develop a theory of local and global zeta integrals for such g we use very special intertwining operators therein we require an analysis of the proper normalization of such operators with such techniques we determine the correct e factors associated to local representations the issue of the correct local l factor is discussed

analysis of a darcy flow model with a dynamic pressure saturation relation we consider a new model for groundwater flow the model differs from previous models in that the saturation pressure relation is extended with a dynamic term namely the time derivative of the saturation the resulting model equation is of nonlinear degenerate pseudoparabolic type we give a rigorous analysis of travelling wave solutions and the local behavior near fronts part of this analysis is then used in a formal asymptotic analysis of solutions with initial support in a half line as an illustrative special case we also consider heaviside initial data

on the genericity of cuspidal automorphic forms of so2n 1 this is a sequel of our work js06 we extend moeglin s results m97a and m97b from the even orthogonal groups to old orthogonal groups and complete our proof of the cap conjecture for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models we also give characterization of the vanishing of the central value of the standard l function of so2n 1 a in terms of theta correspondence as result we obtain the weak langlands functorial transfer from so2n 1 a to gl2n a for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models

arma canonical forms obtained from constructibility invariants in recent approaches multivariable arma models have been derived from observable canonical mfds but it was realized that these models have a number of serious limitations and disadvantages this paper presents a new approach based on the idea of observing the state from past outputs which leads to the construction of monic arma models defined by the constructibility invariants the derivation and structural properties of these constructibility forms are investigated

the frisch scheme in dynamic system identification abstract the use of the frisch scheme in the identification of linear dynamic systems is investigated in order to describe the whole family of models that can explain given input output noisy sequences unlike the algebraic case it is shown that in general only a single model is compatible with the data these results are first proposed for single input single output systems and then generalized to the multivariable case

structure and order estimation of multivariable stochastic processes an easy to implement numerically efficient algorithm which estimates the kronecker invariants is presented a procedure allowing estimation of the structure of a state space representation for a multivariable stationary stochastic process from measured output data is presented it is assumed that the observed vector time series is a realization of a process with rational spectrum or the output of a stable time invariant linear system driven by white noise an algorithm is proposed which selects a maximal set of linearly independent rows of the hankel matrix built upon the estimated covariance sequence and thus yields estimates of the kronecker invariants when applied to simulated examples it systematically yielded the good structure without any ambiguity i e with a surprising robustness with respect to the choice of the probability of false alarm the numerical efficiency of the procedure is remarkable and no exhaustive search over the set of all possible kronecker indexes has to be performed

strong consistency of ml estimators using partial fraction and elementary subsystem representation of multivariable systems the strong consistency of ml estimators for partial fraction matrix pfm and elementary subsystem ess representations of vector arma processes will be discussed for the case when the structure is overestimated the main results of the paper are the off line strong consistency theorems of ml estimators for pfm representation when the number of poles is overestimated and for the ess representations when the number of ess s associated with the poles is overestimated

estimation and identification for 2 d block kalman filtering the development of a recursive identification and estimation procedure for two dimensional block kalman filtering is discussed the recursive identification scheme can be used online to update the image model parameters at each iteration based on the local statistics within a block of the observed noisy image the covariance matrix of the driving noise can also be estimated at each iteration of this algorithm a recursive procedure for computing the parameters of the higher order models is given simulation results are also provided

brief identification of dynamic errors in variables models approaches based on two dimensional arma modeling of the data in this paper we propose a parametric and a non parametric identification algorithm for dynamic errors in variables model we show that the two dimensional process composed of the input output data admits a finite order arma representation the non parametric method uses the arma structure to compute a consistent estimate of the joint spectrum of the input and the output a frisch scheme is then employed to extract an estimate of the joint spectrum of the noise free input output data which in turn is used to estimate the transfer function of the system the parametric method exploits the arma structure to give estimates of the system parameters the performances of the algorithms are illustrated using the results obtained from a numerical simulation study

remarks on classical invariant theory a uniform formulation applying to all classical groups simultaneously of the first fundamental theory of classical invariant theory is given in terms of the weyl algebra the formulation also allows skew symmetric as well as symmetric variables examples illustrate the scope of this formulation

a summation formula for triples of quadratic spaces abstract let v 1 v 2 v 3 be a triple of even dimensional vector spaces over a number field f equipped with nondegenerate quadratic forms q 1 q 2 q 3 respectively let y i 1 v i be the closed subscheme consisting of v 1 v 2 v 3 on which q 1 v 1 q 2 v 2 q 3 v 3 motivated by conjectures of braverman and kazhdan and related work of lafforgue ngo and sakellaridis we prove an analogue of the poisson summation formula for certain functions on this space

paper uniquely identifiable state space and arma parametrizations for multivariable linear systems multivariable systems can be represented in a uniquely identifiable way either by canonical forms or by so called overlapping forms the advantage of the latter is that they do not require the a priori estimation of a set of structural invariants e g kronecker invariants we show here how to define uniquely identifiable overlapping parametrizations for state space and arma models we show that these parametrizations are all related to a set of intrinsic invariants which are obtained from the markov parameters of the system different forms of overlapping arma parametrizations are derived and their properties discussed

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

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

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

on line structure selection for multivariable state space models an algorithm is described for the selection of model structure for identifying state space models of black box character the algorithm receives as input a given system in a given parametrization it is then tested whether this parametrization is suitable well conditioned for identification purposes if not a better one is selected and the transformation of the system to the new representation is performed this algorithm can be used as a block both in an iterative off line identification procedure and for recursive on line identification it can be called whenever there is some indication that the model structure is ill conditioned it is discussed how the model structure selection algorithm can be interfaced with an off line identification procedure a complete procedure is described and tested on real and simulated data

the buckley leverett equation with dynamic capillary pressure the buckley leverett equation for two phase flow in a porous medium is modified by including dependence of the capillary pressure on the rate of change of saturation this model due to hassanizadeh and gray results in a nonlinear pseudoparabolic partial differential equation phase plane analysis including a separation function to measure the distance between invariant manifolds is used to determine when the equation supports traveling waves corresponding to undercompressive shocks the riemann problem for the underlying conservation law is solved and the structures of the various solutions are confirmed with numerical simulations of the partial differential equation

paper pseudo canonical forms identifiable parametrizations and simple parameter estimation for linear multivariable systems input output models this paper examines the use of pseudo canonical forms as opposed to canonical forms in the identification of linear discrete time multivariable systems firstly a relationship is established between state space models in a pseudo canonical form and a set of corresponding matrix fraction descriptions or equivalently finite difference equations the causality of the systems implies that there will be dependencies amongst the parameters in the matrix fraction description in certain circumstances by introducing an ordering of the output variables and associated parameters this dependency can be handled sequentially in simple parameter estimation algorithms

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

on admissibility of pseudoobservability and pseudocontrollability indexes it has been shown recently that a given mimo system may be represented by several equivalent state space representations referred to as overlapping or pseudocanonical forms instead of the unique observability controllability canonical form the structure of a pseudocanonical form is determined by a set of pseudoobservability controllability indexes analogous to the observability controllability indexes determining the structure of the canonical form a mimo system can be represented by several different pseudocanonical forms specified by their structure indexes in this note we give an upper bound on the admissible structure indexes of a given system in terms of a new set of invariants of this system an illustrative example is included

on the formal arc space of a reductive monoid let x be a scheme of finite type over a finite field k and let cal l x denote its arc space in particular cal l x k x k t using the theory of grinberg kazhdan and drinfeld on the finite dimensionality of singularities of cal l x in the neighborhood of non degenerate arcs we show that a canonical basic function can be defined on the non degenerate locus of cal l x k which corresponds to the trace of frobenius on the stalks of the intersection complex of any finite dimensional model we then proceed to compute this function when x is an affine toric variety or an l monoid our computation confirms the expectation that the basic function is a generating function for a local unramified l function in particular in the case of an l monoid we prove a conjecture formulated by the second author

the range error test in the structural identification of linear multivariable systems among the approaches that have been proposed in recent years for the identification of discrete time linear multivariable systems very efficient procedures are based on the introduction of a set of input output canonical models and on the separate determination of the process structure structural identification and parameters parametric identification this paper introduces a new simple test which allows us to perform the structural identification without the drawbacks usually associated with singularity tests the proposed test gives an a priori prediction of the model performance in order to avoid trial and error procedures in the determination of a suitable structure for the process to be identified

exact modelling and identifiability of linear systems in this paper we consider the question of identifiability of a system on the basis of observed data in particular we present a framework for exact modelling and identifiability of finite dimensional linear time invariant systems on the basis of time series of infinite or finite length systems are characterized in terms of their behaviour i e the set of time series which are allowed by the system in this behavioural approach no a priori distinction is made between input and output variables and also non controllable systems can be considered we describe identification procedures for exact modelling of multivariable time series of infinite or finite length these procedures are based on the concept of corroboration of models by data reflecting that the data should incorporate evidence for the acceptability of the identified models the assumed a priori information on the data generating system consists of the qualitative behavioural properties of linearity time invariance and completeness no knowledge is required concerning quantitative properties like the number of input and output variables the number of state variables or the observability indices a complete characterization is obtained of the minimal number of time series required for system identifiability the class of systems identifiable by one time series contains the controllable systems as a strict subclass

transcending classical invariant theory let sp2 r sp2 sp be the real symplectic group of rank n let sp denote the two fold cover of sp there is a unitary representation constructed by shale sh and weil wa of sp that is of considerable interest in the theory of automorphic forms we denote this representation by co and call it the oscillator representation the purpose of this paper is to establish about c a fact that should be useful for clarifying the structure of spaces of automorphic forms constructed using co we begin by formulating the result let e be a reductive subgroup of sp and let e denote the inverse image of e in sp denote by r e the set of infinitesimal equivalence classes of continuous irreducible admissible representations of e on locally convex spaces let co be the smooth representation of sp associated to co let co be realized on a hilbert space and let the subspace of smooth vectors on which space co is defined be written denote by r9 e co the set of elements of e which are realized as quotients by co e invariant closed subspaces of t g consider a reductive dual pair g g c sp h2 it is not hard to show that g and g commute with one another hence we may regard co i g g as a representation of gx g it is well known f that r gx g s9 g xr9 g the identification associates to p e r g and p e i g the tensor product p x p we note that p x p is not defined as a topological vector space nevertheless the infinitesimal equivalence class of p op is well defined select p x p e g x g suppose that in fact p p e 9 g g c then clearly p e r g c and p e 9 g c hence g co defines the graph of a correspondence between certain subsets of r9 g cv and j g co in fact the situation is quite precise

mfd models and time delays some consequences for identification a general relationship is established between the coefficients of a general mfd model and its associated markov parameters this result is used to derive necessary and sufficient conditions for the appearance of time delays in general mfd models these conditions involve dependencies between some coefficients of the mfd models finally it is indicated how these dependencies can possibly be incorporated in equation error identification techniques retaining the favourable property of linearity in the parameters

invariants and canonical forms for systems structural and parametric identification the basic definitions regarding invariant functions and canonical forms for an equivalence relation on a generic set are first recalled with reference to observable state space models and to the equivalence relation induced by a change of basis it is then shown how the image of a complete set of independent invariants for the considered equivalence relation can be used to parametrize a subset of canonical forms in the given set then the set of polynomial input output models of the type p z y t q z u t and the equivalence relation induced by the premultiplication of p and q by a unimodular matrix are considered and canonical forms parametrized by a complete set of independent invariants introduced since the two sets of canonical forms share common sets of complete independent invariants very simple algebraical links between state space and input output canonical forms can be deduced the previous results are used to design efficient algorithms solving the problem of the canonical structural and parametric realization and identification of generic input output sequences generated by a linear discrete time invariant multivariable system the results obtained in the identification of a real process are then reported

l functions and theta correspondence for classical groups using the doubling method of piatetski shapiro and rallis we develop a theory of local factors of representations of classical groups and apply it to give a necessary and sufficient condition for nonvanishing of global theta liftings in terms of analytic properties of the l functions and local theta correspondence

model sets and parametrizations for identification of multivariable equation error models abstract equation error or linear regression models are known to inherently require the a priori choice for specific signal variables to be considered as regressand and or regressor this implies that a model set should be a priori restricted in some way in order to define an acceptable identification problem in the case of approximate identification i e the system to be modelled is not contained in the model set this restriction acts as a design variable with the identified models being dependent on its specific choice in this paper the necessity of this restriction is quantified by the property of discriminability i e the ability of an identification criterion to distinguish between all the different models in a model set employing a deterministic signal oriented framework several sets of sufficient conditions are derived for model sets to be discriminable by a least squares identification criterion to this end use is made of polynomial model representations in two shift operators although it is of a different nature the problem discussed is shown to be closely related to the problem of constructing identifiable parametrizations for sets of rational transfer functions it is shown that the pseudo canonical or overlapping parametrization of all transfer functions with fixed mcmillan degree constitutes a nonoverlapping set of equation error models that is discriminable by a least squares identification criterion

some local global non vanishing results for theta lifts from orthogonal groups we firstly improve a theorem of b roberts which characterizes non vanishing of a global theta lift from o x to sp n in terms of non vanishing of local theta lifts in particular we will remove all the archimedean conditions imposed upon his theorem sec ondly following roberts we will apply our theorem to theta lifting of low rank similitude groups namely we characterize the non vanishing condition of a global theta lift from go 4 to gsp 2 in our improved setting also we consider non vanishing conditions of a global theta lift from go 4 to gsp 1 and explicitly compute the lift when it exists

faltings heights of abelian varieties with complex multiplication let m be the shimura variety associated with the group of spinor similitudes of a quadratic space over q of signature n 2 we prove a conjecture of bruinier kudla yang relating the arithmetic intersection multiplicities of special divisors and big cm points on m to the central derivatives of certain l functions as an application of this result we prove an averaged version of colmez s conjecture on the faltings heights of cm abelian varieties

transformations between input output multistructural models properties and applications some general properties of recently introduced inputs output multistructural overlapping models are analysed and compared with the properties of the well known input output canonical forms algorithms for the transformation of a generic input output model to a multi structural one and for transformation between adjacent multistructural models are then proposed the use of the models in on line multivariate identification is also discussed and a numerical example given

generalised form of a conjecture of jacquet and a local consequence following the work of harris and kudla we prove a general form of a conjecture of jacquet relating the non vanishing of a certain period integral to non vanishing of the central critical value of a certain l function as a consequence we deduce a theorem relating the existence of gl 2 k invariant linear forms on irreducible admissible representations of gl 2 k for a commutative semi simple cubic algebra k over a non archimedean local field k in terms of local epsilon factors which was proved only in some cases by the first author in his earlier work in d prasad invariant forms for representations of gl 2 over a local field amer j math 114 1992 no 6 1317 1363 this has been achieved by globalising a locally distinguished supercuspidal representation to a globally distinguished representation a result of independent interest which is proved by an application of the relative trace formula

the hodge conjecture and arithmetic quotients of complex balls let s be a closed shimura variety uniformized by the complex n ball associated with a standard unitary group the hodge conjecture predicts that every hodge class in h 2k s mathbb q k 0 dots n is algebraic we show that this holds for all degrees k away from the neighborhood bigl tfrac13n tfrac23n bigr of the middle degree we also prove the tate conjecture for the same degrees as the hodge conjecture and the generalized form of the hodge conjecture in degrees away from an interval depending on the codimension c of the subvariety centered at the middle dimension of s these results are derived from a general theorem that applies to all shimura varieties associated with standard unitary groups of any signature the proofs make use of arthur s endoscopic classification of automorphic representations of classical groups as such our results rely on the stabilization of the trace formula for the disconnected groups gl n rtimes langle theta rangle associated with base change

parameter and structure identification of linear multivariable systems abstract in this paper a parameter and structure identification scheme which can be used for both continuous and discrete time systems is presented this scheme has an on line nature and it incorporates standard techniques such as state variable filters and adaptation laws developed through stability analysis the canonical form being used is based on the output injection which is constructed to assign all the poles of the system to an arbitrary chosen real number it is therefore named the canonical form

criterion based equivalence for equation error models the problem of modeling an input output data sequence is considered when applying equation error least squares identification methods to matrix fraction description mfd models in the case that a set of models has been parametrized using the notion of i o input output equivalence it is shown that the identified model will be essentially dependent on the specific parameterization chosen as an alternative a notion of model equivalence is introduced that is related to the identification criterion the pseudocanonical or overlapping parametrization of mfd models appears to constitute a set of canonical forms for this least squares based model equivalence

system identifiability from finite time series in this paper we investigate the identification of systems from time series observed over a finite time interval the data generating system is supposed to be finite dimensional linear and time invariant but not necessarily controllable the minimal number of time series needed to identify a system is characterized by the identifiability index of a system which measures the rank drop of autoregressive representations we formulate a procedure for modelling finite time series which takes the corroboration of system restrictions into account this also gives a new solution for the partial realization problem

on the exactly solvable equation s_t beta s gamma 2 s_x _x alpha beta s gamma 2 s_x occurring in two phase flow in porous media the symmetry approach of fokas j math phys 21 1980 pp 1318 1325 is used to show that the most general equation of the form s t g s s xx f s s x dg ds ne 0 which is exactly solvable is equivalent to the equation s t beta s gamma 2 s x x alpha beta s gamma 2 s x this equation is then mapped to the linear heat equation through a series of backlund transformations the above result is used to solve an initial boundary value problem modeling the process of waterflooding i e the displacement of oil initially in a porous reservoir by continuously injected water

universal scaling of spontaneous imbibition for water wet systems 1 spontaneous counter current imbibition si is a key mechanism in many multiphase flow processes such as cleanup of nonaqueous phase liquids napls bioremediation or co2 storage for interpreting and upscaling laboratory si data and modeling and prediction purposes scaling groups are an essential tool the question of how to formulate a general scaling group has been debated for over 90 years here we propose the first scaling group that incorporates the influence of all parameters on si that are present in the two phase darcy model the group is derived rigorously from the only known exact analytical solution for spontaneous imbibition by relating the cumulative water phase imbibed to the normalized pore volume we show the validity of the group by applying it to 42 published si studies for water oil and water air experiments for a wide range of viscosity ratios different materials different initial water saturations and different length scales in all cases water was the wetting phase our group serves as a master equation whose generality allows the rigorous prediction of the validity of a large number of specialized scaling groups proposed during the last 90 years furthermore our results give strong evidence that the darcy model is suitable for describing si and that including dynamic effects in capillary pressure is not necessary for counter current si contrary to what has been hypothesized two key applications of the group are discussed first the group can serve as the long sought after general transfer rate for imbibition used in dual porosity models second it is the so far missing proportionality constant in imbibition germination models for plant seeds