brief paper zeros of structured linear systems this paper provides a detailed study of transmission zeros in the context of linear structured systems for such systems the entries of the state space model matrices are supposed to be either fixed zeros or free parameters a directed graph can be associated to such systems and structural properties can be studied i e properties which are valid for almost all values of the parameters we show that there exists two kinds of transmission zeros the parameter dependent ones and the constant ones which can only occur in zero moreover the constant transmission zeros can be directly obtained on the associated graph in terms of particular paths and cycles

feedback decoupling of structured systems the feedback decoupling of structured linear systems is considered using results gathered on decoupling and the graph characterization of the structure at infinity a necessary and sufficient decoupling condition for structured systems is developed this condition has a graphical interpretation in terms of shortest input output paths

geometrical properties of pareto distribution the differential geometrical framework for analyzing statistical problems related to pareto distribution is given a classical and intuitive way of description the relationship between the differential geometry and the statistics is introduced publicationes mathematicae debrecen hungary vol 61 2002 1 14 raag mem 4 1968 373 ann statist 10 2 1982 357 springer lecture notes in statistics 1985 tensor n s 57 1996 282 commun statist theor meth 29 4 2000 859 tensor n s 33 1979 347 int j eng sci 19 1981 1609 tensor n s 57 1996 300 differential geometry and statistics 1993 but in a slightly modified manner this is in order to provide an easier introduction for readers not familiar with differential geometry the parameter space of the pareto distribution using its fisher s matrix is defined the riemannian and scalar curvatures to parameter space are calculated the differential equations of the geodesics are obtained and solved the j divergence the geodesic distance and the relations between of them in that space are found a development of the relation between the j divergence and the geodesic distance is illustrated the scalar curvature of the j space is represented

structured systems within the transfer matrix approach application to decoupling abstract we consider a new approach to structured systems within the transfer matrix framework we associate with such a structured system a graph which concentrates both knowledge on structural properties of independent subsystems and on their interconnections the analysis of this associated graph allows to conclude on the decouplability of structured systems

generalized c a b pairs and parameter insensitive disturbance rejection problems with dynamic compensator in the so called geometric approach the notion of the generalized c a b pairs is introduced for uncertain linear systems and its properties are investigated further the parameter insensitive disturbance rejection problem with dynamic compensator is formulated and some sufficient conditions for the problem to be solvable are presented

further analysis of multilevel monte carlo methods for elliptic pdes with random coefficients we consider the application of multilevel monte carlo methods to elliptic pdes with random coefficients we focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter and that only have limited spatial regularity we extend the finite element error analysis for this type of equation carried out in charrier et al siam j numer anal 2013 to more difficult problems posed on non smooth domains and with discontinuities in the coefficient for this wider class of model problem we prove convergence of the multilevel monte carlo algorithm for estimating any bounded linear functional and any continuously frechet differentiable non linear functional of the solution we further improve the performance of the multilevel estimator by introducing level dependent truncations of the karhunen loeve expansion of the random coefficient numerical results complete the paper

bayesian estimation and prediction for pareto data abstract data from a classical pareto distribution are to be used to make inferences about the inequality and precision parameters in addition it is desired to predict the behavior of further observations from the distribution three typical data configurations are considered iid and two types of censoring dependent conjugate prior analyses are reviewed and are compared with an analysis involving independent priors for the inequality and precision parameters it is argued that mathematical tractability should be perhaps a minor consideration in the choice of priors a comparative example is included

survey generic properties and control of linear structured systems a survey in this survey paper we consider linear structured systems in state space form where a linear system is structured when each entry of its matrices like a b c and d is either a fixed zero or a free parameter the location of the fixed zeros in these matrices constitutes the structure of the system indeed a lot of man made physical systems which admit a linear model are structured a structured system is representative of a class of linear systems in the usual sense it is of interest to investigate properties of structured systems which are true for almost any value of the free parameters therefore also called generic properties interestingly a lot of classical properties of linear systems can be studied in terms of genericity moreover these generic properties can in general be checked by means of directed graphs that can be associated to a structured system in a natural way we review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms by properties we mean here system specific properties like controllability the finite and infinite zero structure and so on as well as solvability issues of certain classical control problems like disturbance rejection input output decoupling and so on in this paper we do not try to be exhaustive but instead by a selection of results we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool we emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only moreover the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well known polynomially bounded combinatorial techniques for larger systems

a stochastic collocation method for the second order wave equation with a discontinuous random speed in this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions the speed is piecewise smooth in the physical space and depends on a finite number of random variables the numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials gauss points in the probability space this approach leads to the solution of uncoupled deterministic problems as in the monte carlo method we consider both full and sparse tensor product spaces of orthogonal polynomials we provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data in particular we show that unlike in elliptic and parabolic problems the solution to hyperbolic problems is not in general analytic with respect to the random variables therefore the rate of convergence may only be algebraic an exponential fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data we present numerical examples which confirm the analysis and show that the collocation method is a valid alternative to the more traditional monte carlo method for this class of problems

stochastic galerkin methods for elliptic interface problems with random input in this work we consider random elliptic interface problems namely the media in elliptic equations have both randomness and interfaces a galerkin method using bi orthogonal polynomials is used to convert the random problem into an uncoupled system of deterministic interface problems a principle on how to choose the orders of the approximated polynomial spaces is given based on the sensitivity analysis in random spaces with which the total degree of freedom can be significantly reduced then immersed finite element methods are introduced to solve the resulting system convergence results are given both theoretically and numerically

observer based fault detection and isolation for structured systems fault detection and isolation fdi problems are here consid ered for linear systems with faults and disturbances we design a set of ob server based residuals in such a way that the transfer from the disturbances to the residuals is zero and the transfer from the faults to the residuals al lows fault isolation we are interested in obtaining a transfer function from faults to residuals with either a diagonal structure i e a dedicated struc tured residuals set or a triangular one we deal with this problem when the system under consideration is structured that is the entries of the system matrices are either fixed zeros or free parameters to a structured system one can associate in a natural way a directed graph we can then provide necessary and sufficient conditions under which the fdi problems have a solution for almost any value of the free parameters these conditions are simply expressed in terms of input output paths in the associated graph index terms fault detection and isolation graph theory model based approach structured residuals structured systems

graph theoretic methods for the computation of disturbance decoupling feedback matrices for structured systems abstract structured systems are considered for which the disturbance decoupling problem is known to be generically solvable it is recalled how this generic solvability is in one one correspondence with certain properties of the graph representing the structure of the system further a graph oriented method is derived for the efficient computation of a feedback that actually solves the disturbance decoupling problem it is believed that the method is especially useful in case of sparse system matrices the method may also be advantageous in case some of the entries in the system matrices have an unknown value since the influence of the various entries is easy to establish

analysis of linear structured systems using a primal dual algorithm in this paper we give a polynomial algorithm to compute the infinite structure of a structured system a directed graph is associated with such structured systems the infinite zero orders can be computed on the associated graph via the determination of the minimal length of vertex disjoint input output paths this search corresponds to a minimum cost flow determination on an appropriate directed graph the proposed algorithm is based on the primal dual algorithm linked to linear programming this polynomial algorithm is one of the most efficient for this type of problem moreover it allows an iterative determination of the generic infinite structure which is a key tool for solving numerous control problems

phase type distributions and representations some results and open problems for system theory in this paper we consider phase type distributions these distributions correspond to the random hitting time of an absorbing markov chain they are used for modelling various random times in particular those which appear in manufacturing systems as processing times times to failure repair times etc the markovian nature of these distributions allows the use of very efficient matrix based computer methods for performance evaluation in this paper we give a system theory oriented introduction to phase type distributions we concentrate mainly on the representation problem which consists of finding a markov chain associated with some phase type distribution this is a realization problem in the sense of system theory with a lot of links with the classical linear system theory but also with a number of constraints which make the problem harder but more interesting indeed this problem has strong connections with the positive realization problem in control theory the paper recalls known results gives s

geometrical theory of asymptotic ancillarity and conditional inference summary differential geometry is applied to the problems of defining higher order asymptotic ancillarity and of obtaining the asymptotic conditional distribution of an efficient estimator in multiparameter curved exponential families it is shown that a fundamental role is played in the asymptotic theory of estimation by a one parameter family of affine connexions and curvatures of subspaces asymptotic ancillary statistics of higher order are explicitly constructed with the help of the geometry the conditional distribution of an estimator is given in terms of the exponential curvature of the model and the mixture curvature of the ancillary subspaces associated with the estimator

a geometric approach for structured systems application to disturbance decoupling structured systems described by state space models are considered for these systems the entries of the state space model matrices are supposed to be either fixed zeros or free independent parameters for such systems one can study structural properties i e properties that are valid for almost any value of the parameters we revisit the classical geometric theory in the context of structured systems in particular the well known notions of a b invariant and c a invariant subspaces are redefined and analysed in this context we characterize fixed subspaces included or containing these invariant subspaces and show that they play a key role in solving control problems as an application of this geometric approach for structured systems we propose new solutions to the disturbance decoupling problems by state feedback and by output measurement feedback the solvability conditions are easily checked on the associated graph of the system

high order fem bem computer models for wave propagation in unbounded and heterogeneous media efficient computational models that retain essential physics of the associated continuous mathematical models are important for several applications including acoustic horn optimization for heterogeneous wave propagation models that are naturally posed on unbounded domains a crucial physical requirement is that the scattered fields are radiating and satisfy a radiation condition at infinity we describe and implement an efficient high order coupled computer model for acoustic wave propagation in an unbounded region comprising bounded heterogeneous media with several obstacles our unbounded and heterogeneous media computer model retains the radiation condition exactly and hence is readily applicable for the celebrated acoustic horn problem this approach is more suitable than using a standard low order approximation of the radiation condition using parallel computing environments we demonstrate the high order algorithm with extensive numerical experiments and computational analysis including the model horn problem with several material property parameters our efficient computer models and validation in this work lead to some interesting mathematical and numerical analysis problems for the acoustic system defined on unbounded and heterogeneous media comprising smooth non smooth horn impenetrable and penetrable obstacles

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

bayesian inference for pareto populations abstract bayesian techniques for samples from classical generalized and multivariate pareto distributions are described we place emphasis on choosing proper prior distributions that do not lead to anomalous posterior densities

a stochastic collocation algorithm with multifidelity models we present a numerical method for utilizing stochastic models with differing fideli ties to approximate parameterized functions a representative case is where a high fidelity and a low fidelity model are available the low fidelity model represents a coarse and rather crude ap proximation to the underlying physical system however it is easy to compute and consumes little simulation time on the other hand the high fidelity model is a much more accurate representation of the physics but can be highly time consuming to simulate our approach is nonintrusive and is therefore applicable to stochastic collocation settings where the parameters are random variables we provide sufficient conditions for convergence of the method and present several examples that are of practical interest including multifidelity approximations and dimensionality reduction

a sparse grid stochastic collocation method for partial differential equations with random input data this work proposes and analyzes a smolyak type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms input data of the model to compute solution statistics the sparse grid stochastic collocation method uses approximate solutions produced here by finite elements corresponding to a deterministic set of points in the random input space this naturally requires solving uncoupled deterministic problems as in the monte carlo method if the number of random variables needed to describe the input data is moderately large full tensor product spaces are computationally expensive to use due to the curse of dimensionality in this case the sparse grid approach is still expected to be competitive with the classical monte carlo method therefore it is of major practical relevance to understand in which situations the sparse grid stochastic collocation method is more efficient than monte carlo this work provides error estimates for the fully discrete solution using l q norms and analyzes the computational efficiency of the proposed method in particular it demonstrates algebraic convergence with respect to the total number of collocation points and quantifies the effect of the dimension of the problem number of input random variables in the final estimates the derived estimates are then used to compare the method with monte carlo indicating for which problems the former is more efficient than the latter computational evidence complements the present theory and shows the effectiveness of the sparse grid stochastic collocation method compared to full tensor and monte carlo approaches

interval prediction for pareto and exponential observables abstract the prediction of single and multiple pareto or translated exponential observables is addressed within a bayesian framework in particular the probability that a given fraction out of a finite number of potential observables be in a prescribed finite or infinite interval is calculated this generalizes previous work which we restricted to the one sided infinite interval case

disturbance decoupling by measurement feedback for structured transfer matrix systems structured transfer matrix systems are linear systems given by transfer matrices of which the infinite zero order of each nonzero entry is known while the associated infinite gains are unknown and assumed mutually independent in this paper necessary and sufficient conditions are derived for the generic solvability of the well known disturbance decoupling problem by measurement feedback for structured transfer matrix systems generic solvability here means solvability for almost all possible values for the infinite gains of the nonzero transfer matrix entries the conditions will be stated in terms of a bipartite graph that can be easily associated with a structured transfer matrix system the advantage of this is that the conditions then can be verified by means of graph theoretic algorithms

differential geometry of curved exponential families curvatures and information loss the differential geometrical framework is given for analyzing statistical problems related to multi parameter families of distributions the dualistic structures of the exponential families and curved exponential families are elucidated from the geometrical viewpoint the duality connected by the legendre transformation is thus extended to include two kinds of affine connections and two kinds of curvatures the second order information loss is calculated for fisher efficient estimators and is decomposed into the sum of two non negative terms one is related to the exponential curvature of the statistical model and the other is related to the mixture curvature of the estimator only the latter term depends on the estimator and vanishes for the maximum likelihood estimator a set of statistics which recover the second order information loss are given the second order efficiency also is obtained the differential geometry of the function space of distributions is discussed

a weighted reduced basis method for elliptic partial differential equations with random input data in this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations pdes with random input data the pdes are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights to the samples in the greedy sampling procedure a priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and the stochastic collocation method in both univariate and multivariate stochastic problems

multilevel and weighted reduced basis method for stochastic optimal control problems constrained by stokes equations in this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by stokes equations we prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data the finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space respectively resulting in many large scale optimality systems to solve in order to reduce the unaffordable computational effort we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse grid techniques a weighted a posteriori error bound highlights the contribution stemming from each method numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient especially for solving high dimensional and large scale optimization problems

simultaneous decoupling and disturbance rejection a structural approach abstract the combined problem of disturbance rejection and decoupling for linear systems is considered new necessary and sufficient conditions are derived for the existence of a state feedback controller that rejects the disturbances and simultaneously decouples the closed loop system these conditions are simple intuitively appealing and are expressed in terms of system structural invariants such as infinite zero orders then we consider the disturbance rejection with simultaneous decoupling problem for structured linear systems necessary and sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

output feedback disturbance decoupling graph interpretation for structured systems abstract in this paper we consider first the output feedback disturbance decoupling problem for linear systems we derive a set of new necessary or sufficient conditions for the solvability of this problem these conditions are expressed in terms of system structural invariants such as infinite zero orders and essential orders then we consider the output feedback disturbance decoupling problem for structured linear systems necessary or sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

combinatorial relaxation algorithm for mixed polynomial matrices the notion of mixed polynomial matrices is a mathematical tool for faithful description of discrete physical engineering dynamical systems it distinguishes two kinds of numbers fixed constants that account for conservation laws and independent parameters that represent physical characteristics

disturbance rejection for structured systems the disturbance rejection problem for structured systems is solved a graph is associated with such a structured system disturbance rejection is shown to be solvable by state feedback whenever the control inputs reach the outputs more quickly than the disturbances in the associated graph the infinite structure of a structured system is characterized in terms of input output paths in the associated graph

a stochastic collocation method for elliptic partial differential equations with random input data in this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms input data of the model the input data are assumed to depend on a finite number of random variables the method consists in a galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials gauss points in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the monte carlo approach it can be seen as a generalization of the stochastic galerkin method proposed in i babuscka r tempone and g e zouraris siam j numer anal 42 2004 pp 800 825 and allows one to treat easily a wider range of situations such as input data that depend nonlinearly on the random variables diffusivity coefficients with unbounded second moments and random variables that are correlated or even unbounded we provide a rigorous convergence analysis and demonstrate exponential convergence of the probability error with respect to the number of gauss points in each direction in the probability space under some regularity assumptions on the random input data numerical examples show the effectiveness of the method

an offline online algorithm for a class of stochastic multiple obstacle scattering configurations in the half plane efficient computational models are required to understand quantities of interest qoi such as the intensity of sound radiated by non deterministic configurations comprising multiple obstacles in the half plane the stochastic nature of the configurations requires tens of thousands of realizations to compute the expected value and standard deviation of the random qoi the acoustic wave scattering configuration usually comprises multiple deterministic structures whose locations in the half plane are non deterministic thus understanding the nature of the deterministic structures is intrinsically an offline process whilst understanding the nature of the resulting qoi is an online process the online process includes interactions between the structures and the half plane boundary in accordance with the physical offline online process we develop a computational t matrix based offline online reduced order model for large realizations of stochastic acoustic wave scattering configurations in the half plane we present results with more than 60 000 monte carlo mc quasi mc qmc and generalized polynomial chaos gpc simulations which are evaluated using our efficient online scheme for the acoustic scattering half plane model our offline online deterministic and stochastic framework can be used in conjunction with any numerical method for the offline simulations of scattering from a single obstacle in free space

decoupling of structured systems by parameter independent precompensation and state feedback in this paper structured systems described by state space models are considered for these systems the entries of the state space model matrices are assumed to be either fixed zeros or free independent parameters we study the dynamic decoupling of structured linear systems it turns out that a large class of systems which is not state feedback decouplable can be made decouplable by the addition of a simple structured precompensator such a precompensator then has the property to be independent of the system parameters we give a necessary and sufficient condition for a structured system to be made feedback decouplable using a parameter independent precompensator furthermore we prove that when such a solution exists the precompensator can be chosen to be diagonal in this case the precompensator is constructed via a simple combinatorial algorithm our approach is based on a graph representation of the structured system all the results of this paper are related to some particular shortest sets of input output paths in the graph associated with the structured system

change of measure technique in characterizations of the gamma and kummer distributions abstract if x and y are independent random variables with distributions nd then u x y and v x y are also independent for some transformations and properties of this type are known for many important probability distributions and also related characterization questions have been widely investigated these are questions of the form let x and y be independent and let u and v be also independent are the distributions of x and y necessarily and respectively recently two new properties and characterizations of this kind involving the kummer distribution appeared in the literature for independent x and y with gamma and kummer distributions koudou and vallois in 17 observed that u 1 x y 1 1 x 1 and v x y are also independent and hamza and vallois in 13 observed that u y 1 x and v x 1 y 1 x are independent in 16 and 17 characterizations related to the first property were proved while the characterizations in the second setting have been recently given in 29 these results were not fully satisfactory since in both cases technical assumptions on smoothness properties of densities of x and y were needed in 31 the assumption of independence of u and v in the first setting was weakened to constancy of regressions of u and u 1 given v with no density assumptions however the additional assumption e x 1 was introduced in the present paper we provide a complete answer to the characterization question in both settings without any additional technical assumptions regarding smoothness or existence of moments the approach is first via characterizations exploiting some conditions imposed on regressions of u given v which are weaker than independence but for which moment assumptions are necessary second using a technique of change of measure we show that the moment assumptions can be avoided

quasi monte carlo finite element methods for a class of elliptic partial differential equations with random coefficients in this paper quasi monte carlo qmc methods are applied to a class of elliptic partial differential equations pdes with random coefficients where the random coefficient is parametrized by a co