minimal completion problem for quasi regular matrix pencils abstract in this paper we study the problem of completion of an arbitrary matrix pencil by rows and columns in order to obtain a quasi regular matrix pencil in the case when the number of added columns or rows is the minimal possible to obtain a quasi regular matrix pencil in the solution we use combinatorial methods involving lr coefficients a solution of the carlson problem and localization techniques the result is given over algebraically closed fields

characteristic polynomials and controlability of partially prescribed matrices abstract in a previous paper it was proved that n 1 arbitrary entries and the characteristic polynomial of a n n matrix over a field f can be arbitrarily prescribed except if all the nonprincipal entries of a row or column are prescribed equal to zero and the characteristic polynomial does not have a root in f this paper describes the possible characteristic polynomials of a pk pk matrix partitioned into k k blocks of size p p when k 1 blocks are fixed and the others vary it also studies the possibility of a pair of matrices a 1 a 2 where a 1 is square and a 1 a 2 is partitioned into k k 1 blocks of size p p being completely controllable when some of the blocks are prescribed and the others vary

realizations of perturbations of an observable pair with prescribed indices it is well known that when a full rank observable pair c a is slightly perturbed the new observability indices k are majorized by the initial ones k k k conversely any indices k majorized by k can be obtained by perturbing c a the aim of this paper is the explicit construction of perturbations of c a which have the desired indices k by means of a sequence of uniparametrical versal perturbations even more using versal deformations we refine this construction in such a way that the perturbation has the maximum possible number of zeros and no parameters in the square part

some generic invariant factor assignment results using dynamic output feedback abstract working with input output transfer functions in the frequency domain and exploiting a formulation involving generalized sylvester resultants we are able to derive necessary and sufficient conditions for generic invariant factor assignment in several cases using proper dynamic output feedback compensators

marginalized binary mixed effects models with covariate dependent random effects and likelihood inference les modeles marginaux et les modeles a effets mixtes conditionnels sont couramment utilises pour des donnees binaires agregees cependant les parametres de regression et les predictions de modeles non lineaires a effets mixtes n ont pas habituellement une interpretation marginale directe des que la forme fonctionnelle conditionnelle ne peut etre transposee a la marge une approche unifiee est interessante des que l on est interesse a la fois par des inferences marginales et conditionnelles a cette fin nous avons etudie une parametrisation de modeles lineaires generalises mixtes avec une distribution structuree de l intercept aleatoire qui apparie les formes conditionnelles et marginales nous modelisons la distribution des reponses moyennes marginales et selectionnons la distribution des intercept pour realiser l appariement et aussi pour modeliser des effets aleatoires de covariables nous discutons la relation entre cette approche et quelques modeles existant et comparons ces approches sur deux jeux de donnees

strong and weak constraint variational assimilations for reduced order fluid flow modeling in this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a galerkin projection of the navier stokes equation the techniques proposed differ in the control variables they involve the first one introduces a weak dynamical model defined only up to an additional uncertainty time dependent function whereas the second one handles a strong dynamical constraint in which the dynamical system s coefficients constitute the control variables both choices correspond to different approximations of the relation between the reduced basis on which is expressed the motion field and the basis components that have been neglected in the reduced order model construction the techniques have been assessed on numerical data and for real experimental conditions with noisy particle image velocimetry data

bridging conditional and marginal inference for spatially referenced binary data spatially referenced binary data are common in epidemiology and public health owing to its elegant log odds interpretation of the regression coefficients a natural model for these data is logistic regression to account for missing confounding variables that might exhibit a spatial pattern say socioeconomic biological or environmental conditions it is customary to include a gaussian spatial random effect conditioned on the spatial random effect the coefficients may be interpreted as log odds ratios however marginally over the random effects the coefficients no longer preserve the log odds interpretation and the estimates are hard to interpret and generalize to other spatial regions to resolve this issue we propose a new spatial random effect distribution through a copula framework which ensures that the regression coefficients maintain the log odds interpretation both conditional on and marginally over the spatial random effects we present simulations to assess the robustness of our approach to various random effects and apply it to an interesting dataset assessing periodontal health of gullah speaking african americans the proposed methodology is flexible enough to handle areal or geo statistical datasets and hierarchical models with multiple random intercepts

bayesian multivariate logistic regression bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes in addition difficulties arise when simple noninformative priors are chosen for the covariance parameters motivated by these problems we propose a new type of multivariate logistic distribution that can be used to construct a likelihood for multivariate logistic regression analysis of binary and categorical data the model for individual outcomes has a marginal logistic structure simplifying interpretation we follow a bayesian approach to estimation and inference developing an efficient data augmentation algorithm for posterior computation the method is illustrated with application to a neurotoxicology study

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

feedback invariants of matrices with prescribed rows abstract let a f n n b f n m where f is an arbitrary field in this paper we solve the problem of the existence of the matrix a b when its feedback invariants and some rows are prescribed

matrices with prescribed eigenvalues and blocks abstract we solve the following problem proposed by oliveira under what conditions does there exist a square matrix a a ij i j 1 2 a 11 is principal over an arbitrary field with prescribed eigenvalues and prescribed submatrices a 11 a 12 and a 22

discrete adjoint of fractional step incompressible navier stokes solver in curvilinear coordinates and application to data assimilation abstract the discrete adjoint of an incompressible navier stokes algorithm in generalized coordinates is derived and applied to estimate the states of saturated and turbulent circular couette flows the forward navier stokes model is based on the fractional step algorithm in curvilinear coordinates on a structured grid 1 which has been widely adopted in direct numerical simulations of transitional and turbulent flows the discrete adjoint equations adopt the same stencil and temporal scheme as the forward discretization and expressions are derived that relate the discrete adjoint variables to their continuous counterpart the key ingredients of the forward algorithm can be retained in the adjoint including the computation of the cell geometry the approximate factorization method and the parallelization strategy the accuracy efficiency and stability of the adjoint solver are also commensurate with the forward model in addition a novel symmetric projector is proposed to guarantee that the the outcome of the adjoint algorithm is divergence free the implementation of the algorithm in double precision satisfies the forward adjoint relation up to eight significant figures and further validation is performed using circular couette flow the forward and adjoint growth rates of instability modes from linear theory are accurately reproduced in addition an adjoint variational data assimilation algorithm 4dvar is adopted to reconstruct the initial condition of circular couette flows from limited measurements obtained from an independent simulation when the flow is comprised of saturated wavy vortices wall measurements are sufficient to reconstruct an initial condition that latches onto the target state after a short time for the more challenging turbulent case coarse grained velocity data are used to estimate the initial condition

perturbation of linear control systems abstract we study the variation of the controllability indices and the jordan structure of a pair of matrices a b under small perturbations

linear systems some algebraic aspects abstract in the past twenty years mathematically minded engineers working in control theory have discovered a number of results of a purely algebraic nature the present article aims at giving a survey of this area for readers interested in linear algebra but without previous knowledge of this topic

similarity and block similarity we present some equivalent characterizations of the block similarity of matrix pairs with an application to a characterization of the similarity of two square matrices also a survey of some generalizations of properties of the invariants of similarity to the invariants of block similarity is presented

the change of the jordan structure under one row perturbations we study the variation of the jordan structure of a complex square matrix when we make small perturbations on the elements of one row

likelihood methods for binary responses of present components in a cluster in some biomedical studies involving clustered binary responses say disease status the cluster sizes can vary because some components of the cluster can be absent when both the presence of a cluster component as well as the binary disease status of a present component are treated as responses of interest we propose a novel two stage random effects logistic regression framework for the ease of interpretation of regression effects both the marginal probability of presence absence of a component as well as the conditional probability of disease status of a present component preserve the approximate logistic regression forms we present a maximum likelihood method of estimation implementable using standard statistical software we compare our models and the physical interpretation of regression effects with competing methods from literature we also present a simulation study to assess the robustness of our procedure to wrong specification of the random effects distribution and to compare finite sample performances of estimates with existing methods the methodology is illustrated via analyzing a study of the periodontal health status in a diabetic gullah population

matching conditional and marginal shapes in binary random intercept models using a bridge distribution function summary random effects logistic regression models are often used to model clustered binary response data regression parameters in these models have a conditional subject specific interpretation in that they quantify regression effects for each cluster very often the logistic functional shape conditional on the random effects does not carry over to the marginal scale thus parameters in these models usually do not have an explicit marginal population averaged interpretation we study a bridge distribution function for the random effect in the random intercept logistic regression model under this distributional assumption the marginal functional shape is still of logistic form and thus regression parameters have an explicit marginal interpretation the main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework the generality of the results and some properties of the bridge distribution functions are discussed an example is used for illustration

on a b t invariant subspaces having extendible brunovsky bases we consider a by invariant subspaces having a brunovsky basis which can be extended to a brunovsky basis of the whole space we obtain a geometrical characterization of this class of a by invariant subspaces and a complete family of numerical invariants to classify them 0 elsevier science inc 1997

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

a bayesian tutorial for data assimilation data assimilation is the process by which observational data are fused with scientific information the bayesian paradigm provides a coherent probabilistic approach for combining information and thus is an appropriate framework for data assimilation viewing data assimilation as a problem in bayesian statistics is not new however the field of bayesian statistics is rapidly evolving and new approaches for model construction and sampling have been utilized recently in a wide variety of disciplines to combine information this article includes a brief introduction to bayesian methods paying particular attention to data assimilation we review linkages to optimal interpolation kriging kalman filtering smoothing and variational analysis discussion is provided concerning monte carlo methods for implementing bayesian analysis including importance sampling particle filtering ensemble kalman filtering and markov chain monte carlo sampling finally hierarchical bayesian modeling is reviewed we indicate how this approach can be used to incorporate significant physically based prior information into statistical models thereby accounting for uncertainty the approach is illustrated in a simplified advection diffusion model

the change of the jordan structure of a mtrix under small perturbations abstract in this paper a complete description including multiplicity is given for the jordan structure of a matrix which is a small perturbation of a matrix of known jordan structure the problem solved here was solved independently as noted and the other solution has been published in english however the solutions are different the problem is important and it seems desirable to have this solution widely available

jordan forms of completions of partial upper triangular matrices abstract the possible jordan forms of completions of a matrix prescribed in its upper triangular part are studied it is shown that there always exists a nonderogatory completion for such a matrix jordan forms of nilpotent completions are considered as well

reconstruction of unsteady viscous flows using data assimilation schemes this paper investigates the use of various data assimilation da approaches for the reconstruction of the unsteady flow past a cylinder in the presence of incident coherent gusts variational ensemble kalman filter based and ensemble based variational da techniques are deployed along with a 2d compressible navier stokes flow solver which is also used to generate synthetic observations of a reference flow the performance of these da schemes is thoroughly analyzed for various types of observations ranging from the global aerodynamic coefficients of the cylinder to the full 2d flow field moreover different reconstruction scenarios are investigated in order to assess the robustness of these methods for large scale da problems with up to 105 control variables in particular we show how an iterative procedure can be used within the framework of ensemble based methods to deal with both non uniform unsteady boundary conditions and initial field reconstruction the different methodologies developed and assessed in this work give a review of what can be done with da schemes in computational fluid dynamics cfd paradigm in the same time this work also provides useful information which can also turn out to be rational arguments in the da scheme choice dedicated to a specific cfd application

the effects of mixture distribution misspecification when fitting mixed effects logistic models summary mixed effects logistic models are often used to analyze binary response data which have been gathered in clusters or groups responses are assumed to follow a logistic model within clusters with an intercept which varies across clusters according to a specified probability distribution g in this paper we examine the performance of mixed effects logistic regression analysis when a main component of the model the mixture distribution is misspecified we show that when the mixture distribution is misspecified estimates of model parameters including the effects of covariates typically are asymptotically biased i e inconsistent however we present some approximations which suggest that the magnitude of the bias in the estimated covariate effects is typically small these findings are corroborated by a set of simulations which also suggest that valid variance estimates of estimated covariate effects can be obtained when the mixture distribution is misspecified

association models for clustered data with binary and continuous responses we consider analysis of clustered data with mixed bivariate responses i e where each member of the cluster has a binary and a continuous outcome we propose a new bivariate random effects model that induces associations among the binary outcomes within a cluster among the continuous outcomes within a cluster between a binary outcome and a continuous outcome from different subjects within a cluster as well as the direct association between the binary and continuous outcomes within the same subject for the ease of interpretations of the regression effects the marginal model of the binary response probability integrated over the random effects preserves the logistic form and the marginal expectation of the continuous response preserves the linear form we implement maximum likelihood estimation of our model parameters using standard software such as proc nlmixed of sas our simulation study demonstrates the robustness of our method with respect to the misspecification of the regression model as well as the random effects model we illustrate our methodology by analyzing a developmental toxicity study of ethylene glycol in mice

global analytic block similarity to a brunoovsky form abstract necessary and sufficient conditions for reducing a pair of analytic matrix functions a z b z to a brunovsky canonical form by means of analytic passage matrices are given

the topology of the set of conditioned invariant subspaces we consider the topology of the set of conditioned invariant subspaces of an observable pair c a of a fixed dimension by fixing the observability indices of the restricted system a stratification by finitely many smooth manifolds is obtained termed brunovsky strata it is shown that each brunovsky stratum is homotopy equivalent to a generalized flag manifold from this description an effective formula for the betti numbers of the brunovsky strata can be derived

interlacing inequalities matrix groups abstract this paper has two parts 1 interlacing inequalities in linear algebra eigenvalues singular values invariant polynomials attempts to construct a unifying theory 2 subgroups of the full linear group defined by polynomial identities

similarity of non everywhere defined linear maps abstract the equivalence between linear maps defined only on a subspace or by duality defined modulo a subspace is studied and applied to block similarity of rectangular matrices in that way we find the complete families of invariants obtained by brunovsky and zaballa and the results of gohberg and others for this particular case also we describe explicit methods for obtaining the reduced matrix and the corresponding bases

differentiable structure of the set of controllable a b t invariant subspaces abstract given a b t hom c n c n m observable we prove that the set of a b t invariant subspaces having a fixed brunovsky kronecker structure is a connected manifold and we compute its dimension also we include some applications of these results

pencils of complex and real symmetric and skew matrices abstract this expository paper establishes the canonical forms under congruence for pairs of complex or real symmetric or skew matrices the treatment is in the spirit of the well known book of gantmacher on matrix theory and may be regarded as a supplement to gantmacher s chapters on pencils of matrices

on pole structure assignment in linear systems the problem of pole structure assignment psa by state feedback in implicit linear and uncontrollable systems is discussed in the article it is shown that the problem is solvable if the system is regularisable then necessary and sufficient conditions for characteristic polynomial assignment are established in the case of psa invariant polynomials assignment just necessary conditions have been obtained but it turns out that these conditions are also sufficient in some special cases this happens for example when the system does not possess any non proper controllability indexes a possible application of the achieved results to modelling a constrained movement of a robot arm is outlined too

marginally specified logistic normal models for longitudinal binary data summary likelihood based inference for longitudinal binary data can be obtained using a generalized linear mixed model breslow n and clayton d g 1993 journal of the american statistical association88 9 25 wolfinger r and o connell m 1993 journal of statistical computation and simulation48 233 243 given the recent improvements in computational approaches alternatively fitzmaurice and laird 1993 biometrika80 141 151 molenberghs and lesaffre 1994 journal of the american statistical association89 633 644 and heagerty and zeger 1996 journal of the american statistical association91 1024 1036 have developed a likelihood based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and or marginal higher moment assumptions each of these marginal approaches is computationally intense and currently limited to small cluster sizes in this manuscript an alternative parameterization of the logistic normal random effects model is adopted and both likelihood and estimating equation approaches to parameter estimation are studied a key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual level predictions or contrasts an example is presented where scientific interest is in both the mean response and the covariance among repeated measurements

interlacing inequalities and control theory abstract given a p by p matrix a we solve the problem of the existence of a p by q matrix b such that a b has prescribed controllability indices and i p a b has prescribed invariant polynomials the solution of this problem together with an earlier theorem of the author s is used to provide a new proof of the sa thompson interlacing inequalities for invariant polynomials

spatial analyses of periodontal data using conditionally autoregressive priors having two classes of neighbor relations attachment loss the extent of a tooth s root in millimeters that is no longer attached to surrounding bone by periodontal ligament is often used to measure the current state of a patient s periodontal disease and monitor disease progression attachment loss data can be analyzed using a conditionally autoregressive car prior distribution that smooths fitted values toward neighboring values however it may be desirable to have more than one class of neighbor relation in the spatial structure so the different classes of neighbor relations can induce different degrees of smoothing for example we may wish to allow smoothing of neighbor pairs bridging the gap between teeth to differ from smoothing of pairs that do not bridge such gaps adequately modeling the spatial structure may improve the monitoring of periodontal disease progression this article develops a two neighbor relation car model to handle this situation and presents associated theory to help explain the sometimes unusual posterior distr

the number of linear transformations defined on a subspace with given invariant factors abstract given a finite dimensional vector space v over the finite field f q and a subspace w of v we consider the problem of counting linear transformations t w v which have prescribed invariant factors the case w v is a well studied problem that is essentially equivalent to counting the number of square matrices over f q in a conjugacy class and an explicit formula is known in this case on the other hand the case of general w is also an interesting problem and there hasn t been substantive progress in this case for over two decades barring a special case where all the invariant factors of t are of degree zero we extend this result to the case of arbitrary w by giving an explicit counting formula as an application of our results we give new proofs of some recent enumerative results in linear control theory and derive an extension of the gerstenhaber reiner formula for the number of square matrices over f q with given characteristic polynomial

a reduced order model based on kalman filtering for sequential data assimilation of turbulent flows abstract a kalman filter based sequential estimator is presented in this work the estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows this technique provides an augmented flow state integrating available observation in the cfd model naturally preserving a zero divergence condition for the velocity field because of the prohibitive costs associated with a complete kalman filter application two model reduction strategies have been proposed and assessed these strategies dramatically reduce the increase in computational costs of the model which can be quantified in an augmentation of 10 15 with respect to the classical numerical simulation in addition an extended analysis of the behavior of the numerical model covariance q has been performed optimized values are strongly linked to the truncation error of the discretization procedure the estimator has been applied to the analysis of a number of test cases exhibiting increasing complexity including turbulent flow configurations the results show that the augmented flow successfully improves the prediction of the physical quantities investigated even when the observation is provided in a limited region of the physical domain in addition the present work suggests that these data assimilation techniques which are at an embryonic stage of development in cfd may have the potential to be pushed even further using the augmented prediction as a powerful tool for the optimization of the free parameters in the numerical simulation

the number of nonconstant invariant polynomials of matrices with several prescribed blocks abstract consider a n n matrix partitioned into k k blocks c c i j where c 1 1 c k k are square this paper studies the possible numbers of nonconstant invariant polynomials of c when a diagonal of blocks c i j is fixed and the others vary

global reduction to the kronecker canonical form of a cr family of time invariant linear systems abstract we present an approach to the kronecker equivalence of quadruples of matrices a b c d based on a natural equivalence relation between pairs of linear mappings we apply this approach to smooth families of quadruples of constant kronecker type obtaining smooth families of transformation matrices that pointwise reduce each quadruple to its kronecker canonical form

interlacing and majorization in invariant factor assignment problems this paper shows some connections between pole assignment in control theory and assignment of invariant factors on matrices with some prescribed submatrices the majorization in the hardy littlewood polya sense and the interlacing inequalities for invariant factors play a fundamental role in the solution of some problems common to both theories

bayesian modeling of multivariate spatial binary data with applications to dental caries dental research gives rise to data with potentially complex correlation structure assessments of dental caries yield a binary outcome indicating the presence or absence of caries experience for each surface of each tooth in a subject s mouth in addition to this nesting caries outcome exhibit spatial structure among neighboring teeth we develop a bayesian multivariate model for spatial binary data using random effects autologistic regression that controls for the correlation within tooth surfaces and spatial correlation among neighboring teeth using a sample from a clinical study conducted at the medical university of south carolina we compare this autologistic model with covariates to alternative models to demonstrate the improvement in predictions and also to assess the effects of covariates on caries experience

matrix pencils completion problems ii in this paper we give new simple and explicit necessary and sufficient conditions for the existence of a matrix pencil with prescribed kronecker invariants and a regular subpencil moreover we explicitly solve the problem of describing the possible kronecker invariants of a pencil with a prescribed subpencil in the case of the existence of an intermediate regular pencil all the results are obtained over algebraically closed fields

on the number of invariant polynomials of partially prescribed matrices abstract we study the number of invariant polynomials of a i j i j 1 2 when the submatrices a 1 1 a 1 2 a 2 2 are prescribed

matrices with prescribed rows and invariant factors abstract in this paper we solve the problem of the existence of an n n matrix over an arbitrary field when its invariant polynomials and either some rows or columns are prescribed the solution is given in terms of invariant factor inequalities and of majorization inequalities involving controllability indices and the degrees of the invariant polynomials

equivalence of quadruples and feedback equivalence of related pairs in this paper we look for a generalization of a property of matrix pairs to quadruples of matrices it is known that it is possible to analyze the feedback equivalence of matrix pairs in terms of the similarity of the square matrices belonging to sets related to the pairs we will determine when it is possible to analyze the equivalence of matrix quadruples in terms of the feedback equivalence of matrix pairs

invariants of the block tensor product abstract we are concerned with the following problem let xi i 1 2 be vector spaces over c yi subspaces of xi i 1 2 and fi yi xi i 1 2 linear m defined on a subspace we characterize the invariants of block similarity of f1 f2 y1 y2 x1 x2 in terms of the block similarity invariants of f1 and f2

the number of invariant polynomials of a matrix with prescribed complementary principal submatrices abstract we study the number of invariant polynomials of a i j i j 1 2 when the submatrices a 1 1 and a 2 2 are prescribed

on the number of invariant factors of partially prescribed matrices and control theory abstract let a and b be matrices of sizes m m and m u respectively over an infinite field let i a b be the number of invariant factors of xi a b different from 1 this paper gives a necessary and sufficient condition for the existence of a matrix a b with a prescribed submatrix on the right lower corner such that i a b in particular this paper studies the possibility of a linear system t a t b t being completely controllable when a submatrix on the right lower corner of a b is unknown and all the other entries are prescribed

inflow and initial conditions for direct numerical simulation based on adjoint data assimilation a method for generating inflow conditions for direct numerical simulations dns of spatially developing flows is presented the proposed method is based on variational data assimilation and adjoint based optimization the estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system defined by the adjoint of the discrete scheme associated to the dynamical system the approach s robustness is evaluated on two synthetic velocity field sequences provided by numerical simulation of a mixing layer and a wake flow behind a cylinder the performance of the technique is also illustrated in a real world application by using noisy large scale piv measurements this method denoises experimental velocity fields and reconstructs a continuous trajectory of motion fields from discrete and unstable measurements

on feedback equivalence and completion problems abstract in 1987 i zaballa characterized the possible similarity classes of a square matrix with some prescribed rows in 1988 the same author characterized the possible feedback equivalence classes of a b where a is a fixed square matrix and b varies firstly in this paper we observe that these results are equivalent that is each one of them can be obtained as a corollary of the other then we apply similar arguments to other inverse problems in particular we study the possible invariant polynomials and the possible characteristic polynomials of a bx yc when x and y vary and we study the linear systems that can become completely observable with a suitable choice of linear state feedback control

singular systems state feedback problem in this paper the problem of kronecker invariants assignment by state feedback in singular linear systems is studied and resolved this result presents a generalization of the previous results of state feedback action on singular systems

hermite indices and the action of the feedback group the controllability indices are a complete system of invariants for the feedback equivalence relation of controllable matrix pairs the hermite indices are invariant for the similarity of matrix pairs but they are not invariant by changing bases on the input space and performing state feedback the aim of this work is to partially characterize the hermite indices of a controllable matrix pair when transformations of the feedback group are performed on it

matrices with prescribed lower triangular part abstract we give a necessary and sufficient condition for the existence of a square matrix with prescribed characteristic polynomial and prescribed entries on and below the main diagonal

possible block similarity classes of a matrix with a prescribed nonprincipal submatrix ii abstract this paper gives necessary and sufficient conditions for the existence of a matrix a 1 a 2 where a 1 is square with prescribed block similarity class and a prescribed submatrix that does not contain principal entries of a 1

completion problems for real matrices ii abstract thirty years ago g n de oliveira has proposed the following completion problems describe the possible characteristic polynomials of c i j i j 1 2 where c 1 1 and c 2 2 are square submatrices when some of the blocks c i j are fixed and the others vary several of these problems remain unsolved this paper gives the solution over the field of real numbers of oliveira s problem where the blocks c 1 1 c 2 2 are fixed and the others vary

matrices with prescribed submatrices and number of invariant polynomials abstract we give necessary and sufficient conditions for the existence of a matrix a b over a field where a is a square matrix such that a b has a prescribed submatrix and the pencil xi a b has a prescribed number of invariant factors different from 1 as a corollary we give a necessary and sufficient condition for the existence of a completely controllable pair a b such that a b has a prescribed submatrix

a cellular decomposition of the manifold of observable conditioned invariant subspaces abstract given an observable system defined by a pair of matrices c a we obtain a cellular decomposition of the manifold of c a conditioned invariant subspaces with fixed observability indices of the restricted system and we apply this decomposition to compute their homology groups

the characteristic polynomial of a matrix with prescribed off diagonal blocks abstract we present new sufficient conditions for the existence of a matrix with prescribed complementary off diagonal blocks and characteristic polynomial

completion up to a matrix pencil with column minimal indices as the only nontrivial kronecker invariants abstract in this paper we give explicit necessary and sufficient conditions for a completion of an arbitrary matrix pencil up to a pencil with a prescribed set of kronecker invariants in the case when the only nontrivial invariants of the resulting pencil are its column row minimal indices the result is given over arbitrary fields

unified theorems on completions of matrix pencils abstract we generalize and unify some theorems concerned with the existence of a pencil with a prescribed subpencil and prescribed strict equivalence class

a coordinate atlas of the manifold of observable conditioned invariant subspaces given an observable system c a k mxn x k nxn with k r or c the set of c a invariant subspaces having the restricted system fixed observability indices is a smooth manifold embedded on the corresponding grassmannian we obtain an explicit parametrization of it by means of an atlas of corresponding charts as an application we obtain the set of maximal dimensional outputs making solvable a generic disturbance decoupling problem

structural stability of c a marked subspaces abstract given an observable pair of matrices c a we consider the manifold of c a invariant subspaces having a fixed brunovsky kronecker structure using arnold techniques we obtain the explicit form of a miniversal deformation of a marked c a invariant subspace with respect to the usual equivalence relation as an application we obtain the dimension of the orbit and we characterize the structurally stable subspaces those with open orbit

a completion problem over the field of real numbers let f be a field almost 25 years ago g n de oliveira has proposed the following completion problems describe the possible characteristic polynomials of ai j i j 1 2 where a1 1 and a2 2 are square submatrices when some of the blocks ai j are fixed and the others vary cf linear multilinear algebra 2 1975 357 several of these problems remain unsolved this paper gives the solution over the field of real numbers of oliveira s problem where the blocks a1 2 a2 1 are fixed and the others vary

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

block similarity invariants of restrictions to a b invariant subspaces we generalize some properties of invariant subspaces of endomorphisms to a b invariant subspaces in particular we show that in appropriate bases the pair a b can be written as