analysis of subspace fitting and ml techniques for parameter estimation from sensor array data it is shown that the multidimensional signal subspace method termed weighted subspace fitting wsf is asymptotically efficient this results in a novel compact matrix expression for the cramer rao bound crb on the estimation error variance the asymptotic analysis of the maximum likelihood ml and wsf methods is extended to deterministic emitter signals the asymptotic properties of the estimates for this case are shown to be identical to the gaussian emitter signal case i e independent of the actual signal waveforms conclusions concerning the modeling aspect of the sensor array problem are drawn

time series based damage detection and localization algorithm with application to the asce benchmark structure abstract in this paper a time series algorithm is presented for damage identification and localization the vibration signals obtained from sensors are modeled as autoregressive moving average arma time series a new damage sensitive feature dsf is defined as a function of the first three auto regressive ar components it is found that the mean values of the dsf for the damaged and undamaged signals are different thus a hypothesis test involving the t test is used to obtain a damage decision two damage localization indices li 1 and li 2 are introduced based on the ar coefficients at the sensor locations where damage is introduced the values of li 1 and li 2 appear to increase from their values obtained at the undamaged baseline state the damage detection and localization algorithms are valid for stationary signals obtained from linear systems to test the efficacy of the damage detection and localization methodologies the algorithm has been tested on the analytical and experimental results of the asce benchmark structure in contrast to prior pattern classification and statistical signal processing algorithms that have been able to identify primarily severe damage and have not been able to localize the damage effectively the proposed algorithm is able to identify and localize minor to severe damage as defined for the benchmark structure

model reduction of nonlinear systems with external periodic excitations via construction of invariant manifolds abstract a methodology for determining reduced order models of periodically excited nonlinear systems with constant as well as periodic coefficients is presented the approach is based on the construction of an invariant manifold such that the projected dynamics is governed by a fewer number of ordinary differential equations due to the existence of external and parametric periodic excitations however the geometry of the manifold varies with time as a result the manifold is constructed in terms of temporal and dominant state variables the governing partial differential equation pde for the manifold is nonlinear and contains time varying coefficients an approximate technique to find solution of this pde using a multivariable taylor fourier series is suggested it is shown that in certain cases it is possible to obtain various reducibility conditions in a closed form the case of time periodic systems is handled through the use of lyapunov floquet l f transformation application of the l f transformation produces a dynamically equivalent system in which the linear part of the system is time invariant however the nonlinear terms get multiplied by a truncated fourier series containing multiple parametric excitation frequencies this warrants some structural changes in the proposed manifold but the solution procedure remains the same two examples namely a 2 dof mass spring damper system and an inverted pendulum with periodic loads are used to illustrate applications of the technique for systems with constant and periodic coefficients respectively results show that the dynamics of these 2 dof systems can be accurately approximated by equivalent 1 dof systems using the proposed methodology

brief paper state estimation for linear systems with state equality constraints this paper deals with the state estimation problem for linear systems with linear state equality constraints using noisy measurements which are available from the observable system we construct the optimal estimate which also satisfies linear equality constraints for this purpose after reviewing modeling problems in linear stochastic systems with state equality constraints we formulate a projected system representation by using the constrained kalman filter for the projected system and comparing its filter riccati equation with those of the unconstrained and the projected kalman filters we clearly show without using optimality that the constrained estimator outperforms the other filters for estimating the constrained system state finally a numerical example is presented which demonstrates performance differences among those filters

on consistency of stochastic dominance and mean semideviation models we analyze relations between two methods frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches new necessary conditions for stochastic dominance are developed these conditions compare values of a certain functional which contains two components the expected value of a random outcome and a risk term represented by the central semideviation of the corresponding degree if the weight of the semideviation in the composite objective does not exceed the weight of the expected value maximization of such a functional yields solutions which are efficient in terms of stochastic dominance the results are illustrated graphically

robustness of optimal portfolios under risk and stochastic dominance constraints abstract solutions of portfolio optimization problems are often influenced by a model misspecification or by errors due to approximation estimation and incomplete information the obtained results recommendations for the risk and portfolio manager should be then carefully analyzed we shall deal with output analysis and stress testing with respect to uncertainty or perturbations of input data for static risk constrained portfolio optimization problems by means of the contamination technique dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of convexity based global contamination bounds results obtained in our paper dupacova j kopa m 2012 robustness in stochastic programs with risk constraints annals of operations research 200 55 74 were derived for the risk and second order stochastic dominance constraints under suitable smoothness and or convexity assumptions that are fulfilled e g for the markowitz mean variance model in this paper we relax these assumptions having in mind the first order stochastic dominance and probabilistic risk constraints local bounds for problems of a special structure are obtained under suitable conditions on the structure of the problem and for discrete distributions we shall exploit the contamination technique to derive a new robust first order stochastic dominance portfolio efficiency test

application of the variable projection method for updating models of mechanical systems to update the parameters of a mathematical model of a mechanical system usually a cost function is minimised which consists of the difference between calculated and measured quantities this paper deals with the special case where the forces are unknown instead of following the usual way of handling this type of updating problem by assuming a model for the forces in this paper the variable projection method is applied to estimate the unknown forces in addition to the model parameters under certain conditions this two fold inverse problem can be solved by eliminating the force from the parameter estimation process the remaining equation to estimate the model parameters consists of the projection of the response data where the associated projector depends on the model parameters this application of the variable projection method is essentially an extension of the output residual method and leads to an estimation equation which is non linear with respect to the model parameters the variable projection method is introduced and investigated for two general types of unknown forces two theoretical examples wind excitation of a tower and a rotary machine under unknown unbalance configuration and the experimental case of a free free steel beam tested by hammer excitation are presented and discussed

non parametric identification of viscoelastic materials from wave propagation experiments we investigate how the frequency dependent wave propagation coefficient and complex modulus for a linearly viscoelastic material can be estimated from wave propagation experiments the strains at different sections of a bar specimen are measured as functions of time the time series are transformed into the frequency domain where a non parametric identification is made a thorough analysis of the quality of the non parametric estimate is made in which approximate expressions for the covariance matrices of the wave propagation coefficient and the complex modulus are derived the validity of these expressions are confirmed by numerical studies and real experiments

frontiers of stochastically nondominated portfolios we consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution we propose mean risk models that are solvable by linear programming and generate portfolios whose returns are nondomi nated in the sense of second order stochastic dominance next we develop a specialized parametric method for recovering the entire mean risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and real izations the problem of optimizing a portfolio of finitely many assets is a classical problem in theoretical and computational finance since the seminal work of markowitz 1952 it is generally agreed that portfolio performance should be measured in two distinct dimen sions the mean describing the expected return and the risk which measures the uncer tainty of the return in the mean risk approach we select from the universe of all possible portfolios those that are efficient for a given value of the mean they minimize the risk or equivalently for a given value of risk they maximize the mean such an approach has many advantages it allows one to formulate the problem as a parametric optimization problem and it facilitates the trade off analysis between mean and risk markowitz used the variance of the return as the measure of the risk it is easy to compute and it reduces the portfolio selection problem to a parametric quadratic pro gramming problem one can however construct simple counterexamples that show the imperfection of the variance as the risk measure it treats over performance equally as under performance and more importantly its use may suggest a portfolio that is always outperformed by another portfolio the use of the semivariance rather than the variance was already recommended by markowitz 1959 but even in this case significant deficien cies remain as we shall explain another theoretical approach to the portfolio selection problem is that of stochastic dominance see whitmore and findlay 1978 levy 1992 the usual first order defi nition of stochastic dominance gives a partial order in the space of real random variables more important from the portfolio point of view is the notion of second order dominance which is also defined as a partial order but which is equivalent to this statement a random variable y dominates the random variable z if e u y e u z for all nondecreasing concave functions u for which these expected values are finite thus no risk averse decision marker will prefer a portfolio with return z over a portfolio with return y while

brief paper bayesian approaches for identification of the complex modulus of viscoelastic materials frequency domain identification of the complex young s modulus of a viscoelastic solid from wave propagation experiment data is considered in this paper the conventional techniques use a non parametric approach where the estimate at a particular frequency is independent of the estimate at another frequency here we show that the estimation accuracy can be improved significantly by taking the continuity of the complex modulus into account in particular we propose bayesian estimation approaches to impose the continuity property the estimation algorithms are computationally efficient the analytical claims are also substantiated in experimental studies

the mapping dynamics of periodic motions for a three piecewise linear system under a periodic excitation in this paper the mapping dynamics of periodic motions for a three piecewise linear system under a periodic excitation is developed and the mapping structures for specified periodic motions are constructed based on the mapping structures an analytical prediction of all possible stable and unstable periodic motions is given the symmetry for the stable asymmetrical periodic motions of such a system is observed however the unstable periodic motions do not have such symmetry the methodology presented in this paper is applicable to other non smooth systems such as friction induced vibration impact oscillator and power control systems in addition the mapping dynamics provides a useful and efficient tool for the co existence of periodic motions and or chaotic motions in nonlinear dynamical systems

from stochastic dominance to mean risk models semideviations as risk measures abstract two methods are frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches the former is based on an axiomatic model of risk averse preferences but does not provide a convenient computational recipe the latter quantifies the problem in a lucid form of two criteria with possible trade off analysis but cannot model all risk averse preferences in particular if variance is used as a measure of risk the resulting mean variance markowitz model is in general not consistent with stochastic dominance rules this paper shows that the standard semideviation square root of the semivariance as the risk measure makes the mean risk model consistent with the second degree stochastic dominance provided that the trade off coefficient is bounded by a certain constant similar results are obtained for the absolute semideviation and for the absolute and standard deviations in the case of symmetric or bounded distributions in the analysis we use a new tool the outcome risk o r diagram which appears to be particularly useful for comparing uncertain outcomes

further results and insights on subspace based sinusoidal frequency estimation subspace based methods for parameter identification have received considerable attention in the literature starting with a scalar valued process it is well known that subspace based identification of sinusoidal frequencies is possible if the scalar valued data is windowed to form a low rank vector valued process music and esprit like estimators have for some time been applied to this vector model in addition a statistically attractive markov like procedure for this class of methods has been proposed herein the markov like procedure is reinvestigated several results regarding rank performance and structure are given in a compact manner the large sample equivalence with the approximate maximum likelihood method by stoica et al 1988 is also established

optimization with stochastic dominance constraints we introduce stochastic optimization problems involving stochastic dominance constraints we develop necessary and sufficient conditions of optimality and duality theory for these models and show that the lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions the models and results are illustrated on a portfolio optimization problem

on the tautological ring of mg we prove that any product of tautological classes of g of degreed in the chow ring of g with rational coefficients vanishes ford g 2 and is proportional to the class of the hyperelliptic locus in degreeg 2

computationally efficient estimation of wave propagation functions from 1 d wave experiments on viscoelastic materials least squares based non parametric estimation of the wave propagation functions of a viscoelastic material is considered in this paper widely used nonlinear least squares based algorithms are often computationally expensive and suffer from numerical problems in this paper we propose a class of subspace estimators which assume equidistant sensor configuration the proposed estimator is computationally economical and numerically robust analytical expressions for the estimation accuracy have been derived it is also shown that the subspace estimator achieves the optimal accuracy under the optimal weighting the algorithm is employed on simulated data as well as on real experimental data the results therefrom are shown to confirm the analytical results

tractable almost stochastic dominance abstract ll almost stochastic dominance ll asd is a relaxation of the stochastic dominance sd concept proposed by leshno and levy that explains more of realistic preferences observed in practice than sd alone does unfortunately numerical applications of this concept such as identifying if a given portfolio is efficient or determining a marketed portfolio that dominates a given benchmark are computationally prohibitive due to the structure of ll asd we propose a new almost stochastic dominance asd concept that is computationally tractable for instance a marketed dominating portfolio can be identified by solving a simple linear programming problem moreover the new concept performs well on all the intuitive examples from the literature and in some cases leads to more realistic predictions than the earlier concept we develop some properties of asd formulate efficient optimization models and apply the concept to analyzing investors preferences between bonds and stocks for the long run

on the end performance metric estimator selection it is well known that appropriately biasing an estimator can potentially lead to a lower mean square error mse than the achievable mse within the class of unbiased estimators nevertheless the choice of an appropriate bias is generally unclear and only recently there have been attempts to systematize such a selection these systematic approaches aim at introducing mse bounds that are lower than the unbiased cramer rao bound crb for all values of the unknown parameters and at choosing biased estimators that beat the standard maximum likelihood ml and or least squares ls estimators in the finite sample case in this paper we take these approaches one step further and investigate the same problem from the aspect of an end performance metric different than the classical mse this study is motivated by recent advances in the area of system identification indicating that the optimal experiment design should be done by taking into account the end performance metric of interest and not by quantifying a quadratic distance of the unknown model from the true one

improved estimation performance using known linear constraints the additional information available in the form of linear or nonlinear constraints are often remain unexplored in the parameter identification problems related to linear dynamic systems our goal in this work is to explore the knowledge of the linear constraints to achieve significant improvement in the accuracy of the parameter estimates in the class of problems being addressed here the unknown boundary conditions appear as nuisance parameters in practice these nuisance parameters are eliminated from the loss function to get a variable projection optimization problem in the parameters of interest in this work we solve a constrained optimization problem instead where the additional linear constraints are imposed in the form of partially known boundary conditions in the process we show how the accuracy of the estimates is improved by taking the constraints into account the theoretical methodology is successfully applied also to numerical simulations as well as in real world experiments

second order stochastic dominance constrained portfolio optimization theory and computational tests abstract due to the definition of second order stochastic dominance ssd in terms of utility theory portfolio optimization with ssd constraints is of major practical interest we contribute to the field in two ways first we present a self contained theory with some new results and new proofs of known results second we perform a set of tests for computational efficiency we provide new and simple arguments for the formulation of ssd constraints in a mathematical programming framework for many individuals an ssd constraint may seem too severe wherefore various relaxations assd have been proposed we introduce yet another relaxation directional ssd where a candidate portfolio is admissible if a step from the benchmark in the direction of the candidate yields a dominating portfolio optimal step size depends on individual preferences reflected by the objective function we compare computational efficiency of seven approaches for sd constrained portfolio problems including ssd and assd constrained cases

differential constraints for bounded recursive identification with multivariate splines the ability to perform online model identification for nonlinear systems with unknown dynamics is essential to any adaptive model based control system in this paper a new differential equality constrained recursive least squares estimator for multivariate simplex splines is presented that is able to perform online model identification and bounded model extrapolation in the framework of a model based control system a new type of linear constraints the differential constraints are used as differential boundary conditions within the recursive estimator which limit polynomial divergence when extrapolating data the differential constraints are derived with a new one step matrix form of the de casteljau algorithm which reduces their formulation into a single matrix multiplication the recursive estimator is demonstrated on a bivariate dataset where it is shown to provide a speedup of two orders of magnitude over an ordinary least squares batch method additionally it is demonstrated that inclusion of differential constraints in the least squares optimization scheme can prevent polynomial divergence close to edges of the model domain where local data coverage may be insufficient a situation often encountered with global recursive data approximation

a novel sensitivity based method for damage detection of structures under unknown periodic excitations abstract this paper presents a technique for damage detection in structures under unknown periodic excitations using the transient displacement response the method is capable of identifying the damage parameters without finding the input excitations we first define the concept of displacement space as a linear space in which each point represents displacements of structure under an excitation and initial condition roughly speaking the method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space considering this novel geometrical viewpoint an equation called kernel parallelization equation kpe is derived for damage detection under unknown periodic excitations and a sensitivity based algorithm for solving kpe is proposed accordingly the method is evaluated via three case studies under periodic excitations which confirm the efficiency of the proposed method

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

markov based eigenanalysis method for frequency estimation this paper proposes an eigenanalysis based method for estimating the frequencies of complex valued sine waves the basic idea behind this method consists of using a set of linearly independent vectors that are orthogonal to the signal subspace spanned by the principal eigenvectors of the data covariance matrix exploiting that orthogonality condition gives an overdetermined system of linear equations the unknown parameters of which are uniquely related to the frequencies analytical expressions are derived for the covariances of the equation errors in the sample version of the aforementioned linear system of equations based on these expressions a markov like estimate of the unknown parameters is introduced which asymptotically with respect to either the number of data samples or the signal to noise ratio provides the minimum variance frequency estimates in a fairly large class of consistent estimators the paper includes monte carlo simulations that support the theoretical analysis results and show that those results may apply to scenarios with rather low values of the number of data samples and the signal to noise ratio

dual stochastic dominance and related mean risk models we consider the problem of constructing mean risk models which are consistent with the second degree stochastic dominance relation by exploiting duality relations of convex analysis we develop the quantile model of stochastic dominance for general distributions this allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation we also provide stochastic linear programming formulations of these models

the noether lefschetz conjecture and generalizations we prove the noether lefschetz conjecture on the moduli space of quasi polarized k3 surfaces this is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal type are dual to the classes of special cycles i e sub arithmetic manifolds of the same type for compact manifolds this was proved in 3 here we extend the results of 3 to non compact manifolds this allows us to apply our results to the moduli spaces of quasi polarized k3 surfaces

new formulations for optimization under stochastic dominance constraints stochastic dominance constraints allow a decision maker to manage risk in an optimization setting by requiring his or her decision to yield a random outcome which stochastically dominates a reference random outcome we present new integer and linear programming formulations for optimization under first and second order stochastic dominance constraints respectively these formulations are more compact than existing formulations and relaxing integrality in the first order formulation yields a second order formulation demonstrating the tightness of this formulation we also present a specialized branching strategy and heuristics which can be used with the new first order formulation computational tests illustrate the potential benefits of the new formulations

generalized almost stochastic dominance almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them while the idea behind almost stochastic dominance is quite promising it has not caught on in practice implementation issues and inconsistencies between integral conditions and their associated utility classes contribute to this situation we develop generalized almost second degree stochastic dominance and almost second degree risk in terms of the appropriate utility classes and their corresponding integral conditions and extend these concepts to higher degrees we address implementation issues and show that generalized almost stochastic dominance inherits the appealing properties of stochastic dominance finally we define convex generalized almost stochastic dominance to deal with risk prone preferences generalized almost stochastic dominance could be useful in decision analysis empirical researc

le lemme fondamental pondere ii enonces cohomologiques dans cet article on etudie la cohomologie de la fibration de hitchin tronquee introduite dans un article precedent on etend les principaux theoremes de ngo sur la cohomologie de la partie elliptique de la fibration de hitchin comme consequence on obtient une demonstration du lemme fondamental pondere d arthur in this paper we study the cohomology of the truncated hitchin fibration which was introduced in a previous paper we extend ngo s main theorems on the cohomology of the elliptic part of the hitchin fibration as a consequence we get a proof of arthur s weighted fundamental lemma