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We provide an example to show that the monotone Sokolov property is not necessarily preserved under compact continuous images. Furthermore, we prove that if X 2 ∖ Δ X is either monotonically Sokolov or monotonically retractable, then X must be cosmic; and that if X is either hereditarily monotonically Sokolov or hereditarily monotonically retractable, then X has a countable network. Moreover, we characterize the Lindelof Σ-property in C p -spaces on Alexandrov doubles, and show that the L Σ ( L Σ ( ⩽ ω ) ) -property is equivalent to the L Σ ( ⩽ ω ) -property for the class of C p -spaces and for the class of Gul'ko spaces. These results solve some problems published by Kalenda [7] , Tkachuk [23] , Garcia-Ferreira and Rojas-Hernandez [5] , and Molina-Lara and Okunev [11] .

The problem of estimating the largest gain of an unknown linear and time-invariant filter is studied, known as the ${{\mathcal{H}}_\infty }$-norm estimation problem. The approach presented in this paper is iterative and corresponds to the combination of two state-of-the-art methods: Power Iterations and Weighted Thompson Sampling. The combination is done by means of a well-known technique in communications known as a cyclic prefix, in which the last points of a signal are prepended to it. This allows to take considerably more exact measurements of the frequency response of the system at a set of equispaced frequencies. The discussion is complemented with a simulation study, showing that the proposed algorithm has an increased speed of convergence to the quantity of interest.

In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by at least a positive e from its true value. Our results consider both stable and unstable processes. Afterwards, we obtain problem-dependent non-asymptotic bounds on the variance of this estimator, valid for sample sizes greater than or equal to seven. Via simulations we analyze the conservatism of our bounds, and show that they reliably capture the true behavior of the quantities of interest.

A space Z is weakly pseudocompact if Z is G δ -dense in at least one of its compactifications. In 1996 F.W. Eckertson [3] proposed the following problem: Find examples of Baire non Lindelof spaces which are not weakly pseudocompact. Eckertson proposed a list of natural candidates. In this article we show that part of this list produces examples of this type by providing examples of product spaces which are Baire non-Lindelof and not weakly pseudocompact.

Given compact spaces X and Y, if X is Eberlein compact and C p , n ( X ) is homeomorphic to C p , n ( Y ) for some natural n, then Y is also Eberlein compact; this result answers a question posed by Tkachuk. Assuming existence of a Souslin line, we give an example of a Corson compact space with a Lindelof subspace that fails to be Lindelof Σ; this gives a consistent answer to another question of Tkachuk. We establish that every Σ s -product of K-analytic spaces is Lindelof Σ and C p ( X ) is a Lindelof Σ-space for every Lindelof Σ-space X contained in a Σ s -product of real lines. We show that C p ( X ) is Lindelof for each Lindelof Σ-space X contained in a Σ-product of real lines. We prove that C p ( X ) has the Collins–Roscoe property for every dyadic compact space X and generalize a result of Tkachenko by showing, with a different method, that the inequality w ( X ) ≤ n w ( X ) N a g ( X ) holds for regular spaces.

We consider identification of linear systems with a certain order from a set of noisy input-output observations. We utilize the fact that the system order corresponds to the rank of the Hankel matr ...

A set Y ⊂ C p ( X ) is uniformly dense in C p ( X ) if it is dense in the uniform topology on C ( X ) . We construct a zero-dimensional σ-compact space X such that C p ( X ) has a uniformly dense Lindelof subspace while C p ( X ) is not normal. This example answers several published open questions. Additionally, we obtain a version of a theorem of Reznichenko on ω-monolithicity, under M A + ¬ C H , of a compact space X if C p ( X ) has a uniformly dense Lindelof subspace. We also prove that if X is a dyadic compact then C p ( X ) has a uniformly dense subspace of countable pseudocharacter.

In this paper, we shall consider the hyperspace of all nontrivial convergent sequences S c ( X ) of a Frechet-Urysohn nondiscrete space X, which is equipped with the Vietoris topology. We study the spaces X for which S c ( X ) is Baire: this kind of spaces have a dense subset of isolated points (see [12] ). We characterize the spaces X for which S c ( X ) is Baire. This characterization uses a topological game inspired by the Banach-Mazur game. As a consequence, we obtain that if X is completely metrizable and has a dense subset of isolated points, then S c ( X ) is Baire. Our last main result shows that S c ( X ) is pseudocompact iff X is homeomorphic to the one-point compactification of a discrete space of uncountable size. This last assertion provides a characterization of the one-point compactification of a discrete space of uncountable size.

We provide simple characterizations of spaces admitting full r-skeletons, c-skeletons and q-skeletons, by using ω-monotone functions. We use this characterization to prove that every countably compact space admitting a full r-skeleton is proximal; furthermore the characterizations are used to show that the class of spaces admitting full c-skeletons is invariant under subspaces, disjoint topological sums and Σ-products, in addition to prove that the class of spaces admitting full q-skeletons is closed under extensions, continuous images and one-point Lindelof extensions of disjoint topological sums. These characterizations also yield some positive results for products.

In this paper we improve several results presented in [7] and in [9] related to the characterization of several kinds of pseudocompleteness and compactness properties in spaces of continuous functions of the form C p ( X , Y ) . In particular, we prove that for every Tychonoff space X and every separable metrizable topological group G for which C p ( X , G ) is dense in G X , C p ( X , G ) is weakly α-favorable if and only if X is u G -discrete. This result helps us to obtain two generalizations of a theorem due to V.V. Tkachuk in [24] : Theorem I 5.5 Let G be a separable completely metrizable topological group and X a set. If H is a dense subgroup of G X and H is homeomorphic to G Y for some set Y, then H = G X . A particular and interesting case is when X is a Tychonoff space and H = C p ( X , G ) is dense in G X . Theorem II 6.9 Let G be a realcompact Cech-complete weakly α-favorable topological group with countable pseudocharacter and let X be regular C ω G -discrete. Then, C p ( X , G ) ≅ G κ if and only if X is a discrete space of cardinality κ. Besides, we obtain several applications to weakly pseudocompact spaces.

Identification of an output error model using the prediction error method leads to an optimization problem built on input/output data collected from the system to be identified. It is often hard to ...

We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction bounds for the least-squares estimator of the parameters. Our results are based on two concentration inequalities on the norm of sums of dependent covariate vectors and on the singular values of their covariance operator that are of independent value on their own and where the dependence arises from the time shift structure of the time series. These results generalize the known bounds for the independent case., 23 pages

We develop Bayesian learning methods for low-rank matrix reconstruction and completion from linear measurements. For under-determined systems, the developed methods reconstruct low-rank matrices when neither the rank nor the noise power is known a priori. We derive relations between the proposed Bayesian models and low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian-based prior. In the methods, we use expectation maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations on synthetic and real data. QC 20161017

In this article, we mainly study certain families of continuous retractions ($r$-skeletons) having certain rich properties. By using monotonically retractable spaces we solve a question posed by R. Z. Buzyakova in \cite{buz} concerning the Alexandroff duplicate of a space. Certainly, it is shown that if the space $X$ has a full $r$-skeleton, then its Alexandroff duplicate also has a full $r$-skeleton and, in a very similar way, it is proved that the Alexandroff duplicate of a monotonically retractable space is monotonically retractable. The notion of $q$-skeleton is introduced and it is shown that every compact subspace of $C_p(X)$ is Corson when $X$ has a full $q$-skeleton. The notion of strong $r$-skeleton is also introduced to answer a question suggested by F. Casarrubias-Segura and R. Rojas-Hern\'andez in their paper \cite{cas-rjs} by establishing that a space $X$ is monotonically Sokolov iff it is monotonically $\omega$-monolithic and has a strong $r$-skeleton. The techniques used here allow us to give a topological proof of a result of I. Bandlow \cite{ban} who used elementary submodels and uniform spaces.

This paper focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas from the alternating direction method of multipliers (ADMM) to recover low-rank matrices with linear parameterized structures, such as Hankel matrices. The use of ADMM helps to improve the estimate in each iteration due to its capability of incorporating information about the direction of estimates achieved in previous iterations. We show that merging these two alternating strategies leads to a better performance and less consumed time than the existing alternating least squares (ALS) strategy. The improved performance is verified via numerical simulations with varying sampling rates and real applications. HighlightsAlternating optimization strategies are good for recovering matrices.Matrices in consideration are low-rank matrices with linear parameterized structures.The algorithm combines an alternating least-squares based strategy with ideas from ADMM.Merging these two strategies leads to a better performance and less consumed time.

The lacunarity index (monolacunarity) averages the behavior of variable size structures in a binary image. The generalized lacunarity concept (multilacunarity) on the basis of generalized distribution moments is an appealing model that can account for differences in the mass content at different scales. The model was tested previously on natural images [J. Vernon-Carter et al., Physica A 388, 4305 (2009)]. Here, the computational aspects of multilacunarity are validated using synthetic binary images that consist of random maps, spatial stochastic patterns, patterns with circular or polygonal elements, and a plane fractal. Furthermore, monolacunarity and detrended fluctuation analysis were employed to quantify the mesostructural changes in the intercellular air spaces of frozen-thawed parenchymatous tissue of pome fruit [N. A. Valous et al., J. Appl. Phys. 115, 064901 (2014)]. Here, the aim is to further examine the coherence of the multilacunarity model for quantifying the mesostructural changes in the intercellular air spaces of parenchymatous tissue of pome and stone fruit, acquired with X-ray microcomputed tomography, after storage and ripening, respectively. The multilacunarity morphometric is a multiscale multi-mass fingerprint of spatial pattern composition, assisting the exploration of the effects of metabolic and physiological activity on the pore space of plant parenchyma tissue. ispartof: Chaos vol:28 issue:9 ispartof: location:United States status: published

We study the problem of estimating the largest gain of an unknown linear and time-invariant filter, which is also known as the H ∞ norm of the system. By using ideas from the stochastic multi-armed bandit framework, we present a new algorithm that sequentially designs an input signal in order to estimate this quantity by means of input-output data. The algorithm is shown empirically to beat an asymptotically optimal method, known as Thompson Sampling, in the sense of its cumulative regret function. Finally, for a general class of algorithms, a lower bound on the performance of finding the H ∞ norm is derived.

We consider a class of weighted nuclear norm optimization problems with important applications in signal processing, system identification, and model order reduction. The nuclear norm is commonly used as a convex heuristic for matrix rank constraints. Our objective is to minimize a quadratic cost subject to a nuclear norm constraint on a linear function of the decision variables, where the trade-off between the fit and the constraint is governed by a regularization parameter. The main contribution is an algorithm to determine the so-called approximate regularization path, which is the optimal solution up to a given error tolerance as a function of the regularization parameter. The advantage is that we only have to solve the optimization problem for a fixed number of values of the regularization parameter, with guaranteed error tolerance. The algorithm is exemplified on a weighted Hankel matrix model order reduction problem.

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.

Designing the optimal experiment for the recovery of an unknown system with respect to the end performance metric of interest is a recently established practice in the system identification literature. This practice leads to superior end performance to designing the experiment with respect to some generic metric quantifying the distance of the estimated model from the true one. This is usually done by choosing and fixing the estimation method to either a standard maximum likelihood (ML) or a Bayesian estimator. In this paper, we pose the intuitive question: Can we design better estimators than the usual ones with respect to an end performance metric of interest? Based on a simple linear regression example we affirmatively answer this question.

The accuracy of identified linear time-invariant single-input multi-output (SIMO) models can be improved when the disturbances affecting the output measurements are spatially correlated. Given a li ...

In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound for the traditional SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound.

We introduce the monotone Sokolov property and show that it is dual to monotone retractability in the sense that X is monotonically retractable if and only if C p ( X ) is monotonically Sokolov. Besides, a space X is monotonically Sokolov if and only if C p ( X ) is monotonically retractable. Monotone retractability and monotone Sokolov property are shown to be preserved by R -quotient images and F σ -subspaces. Furthermore, every monotonically retractable space is Sokolov so it is collectionwise normal and has countable extent. We also establish that if X and C p ( X ) are Lindelof Σ -spaces then they are both monotonically retractable and have the monotone Sokolov property. An example is given of a space X such that C p ( X ) has the Lindelof Σ -property but neither X nor C p ( X ) is monotonically retractable. We also establish that every Lindelof Σ -space with a unique non-isolated point is monotonically retractable. On the other hand, each Lindelof space with a unique non-isolated point is monotonically Sokolov.

The notion of monotonically monolithic space was introduced by V.V. Tkachuk in 2009 [8] . In this paper we introduce the notion of monotone stability and show that a space C p ( X ) is monotonically monolithic if and only if X is monotonically stable. As a consequence, a space C p ( X ) is monotonically stable if and only if X is monotonically monolithic. We also prove that C p ( X ) is monotonically monolithic when X is a Σ κ -product of a family of Lindelof Σ-spaces. These results answer some questions posed by A. Tamariz-Mascarua and the author in a previous paper [7] .

Let CL(X) and K(X) denote the hyperspaces of non-empty closed and non-empty compact subsets of X, respectively, with the Vietoris topology. In this paper we show that, given an ordinal number γ, the space K([0,γ)) is C-embedded in CL([0,γ)) if and only if cof(γ)≠ω. Moreover we answer some problems posed by the first author and Jun Terasawa.

Estimating unstable systems typically requires additional system identification techniques. In this paper, we consider the weighted null-space fitting method, a three step method that is asymptotically efficient for stable systems. This method first estimates a high order ARX model and then reduces it to a structured model with lower variance using weighted least squares. However, with unstable systems, the method cannot be used to simultaneously estimate the stable and unstable poles. To solve this, we observe that the unstable poles can be estimated from the high order ARX model with relative high accuracy, and use this as an estimate for the unstable poles of the model of interest. Then, the remaining parameters in this model can be estimated by weighted least squares. Because the complete set of parameters is not estimated jointly, asymptotic efficiency is lost. Nevertheless, a simulation study shows good performance.

Recently, the application-oriented framework for pilot design in communication systems has been introduced. This framework is mostly appropriate for such a design since the training sequences are selected to optimize a final performance metric of interest and not some of the classical metrics quantifying the distance between the estimated model and the true one, e.g., the mean square error (MSE). In this perspective, the known pilot sequences that are optimal for any communication system and for any estimation task have to be reexamined. In this paper, the problem of training pilot design for the task of channel estimation in cyclic prefixed orthogonal frequency division multiplexing (CP-OFDM) systems is revisited. So far, the optimal training sequences for least squares (LS) channel estimation with respect to minimizing the channel MSE under a training energy constraint have been derived. Here, we investigate the same problem for the LS channel estimator, but when the design takes into account an end performance metric of interest, namely, the symbol estimate MSE due to the use of per subcarrier zero forcing (ZF) symbol estimators/equalizers at the receiver side. Based on some convex approximations, we verify that the optimal full preamble, i.e, the preamble employing pilots on all sub carriers, for LS channel estimation in its classical context are near optimal in the aforementioned application-oriented context for the ZF symbol estimate MSE in certain target signal-to-noise ratio (SNR) operating intervals.

groupe Cigognes France; International audience; How the spatial expansion of a species changes at a human time scale is a process difficult to determine. We studied the dispersal pattern of the French white stork population, using a 21-year ringing/resighting dataset. We used the graph-theory to investigate the strength of links between 5 populations (NorthEast , NorthWest , Centre, West, and South) and to determine factors important for the birds' movements. Two clusters of populations were identified within the metapopulation, with most frequent movements of individuals between NorthEastern and Centre populations, and between NorthWestern and Western populations. Exchanges of individuals between populations were asymmetrical, where NorthEast -ern and NorthWestern populations provided more emigrants than they received immigrants. Neither the geographical distance between populations, nor the difference in densities influenced the number of individuals exchanging between populations. The graph-theory approach provides a dynamic view of individual movements within a metapopulation and might be useful for future population studies in the context of conservation.

In this paper, we consider the recovery of piecewise sparse signals from incomplete noisy measurements via a greedy algorithm. Here piecewise sparse means that the signal can be approximated in certain domain with known number of nonzero entries in each piece/segment. This paper makes a two-fold contribution to this problem: 1) formulating a piecewise sparse model in the framework of compressed sensing and providing the theoretical analysis of corresponding sensing matrices; 2) developing a greedy algorithm called piecewise orthogonal matching pursuit (POMP) for the recovery of piecewise sparse signals. Experimental simulations verify the effectiveness of the proposed algorithms.

In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the $\ell_0$ norm can be controlled. We prove that the series of the approximations asymptotically coincides with the $\ell_1$ and $\ell_0$ norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed which leads to a number of weighted $\ell_1$ minimization programs, whereas, in the presence of noise, we propose two iterative thresholding methods that are computationally appealing. A convergence guarantee for the iterative thresholding method is provided, and, for a particular function in the class of the approximating functions, we derive the closed-form thresholding operator. We further present some theoretical analyses via the restricted isometry, null space, and spherical section properties. Our extensive numerical simulations indicate that the proposed algorithm closely follows the performance of the oracle estimator for a range of sparsity levels wider than those of the state-of-the-art algorithms., Comment: Submitted to IEEE Trans. on Signal Processing

We address the problem of identifying a specific module in a dynamic network, assuming known topology. We express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the ExpectationMaximization algorithm. Numerical experiments illustrate the effectiveness of the proposed method. QC 20170613

$\ell_1$ mean filtering is a conventional, optimization-based method to estimate the positions of jumps in a piecewise constant signal perturbed by additive noise. In this method, the $\ell_1$ norm penalizes sparsity of the first-order derivative of the signal. Theoretical results, however, show that in some situations, which can occur frequently in practice, even when the jump amplitudes tend to $\infty$, the conventional method identifies false change points. This issue is referred to as stair-casing problem and restricts practical importance of $\ell_1$ mean filtering. In this paper, sparsity is penalized more tightly than the $\ell_1$ norm by exploiting a certain class of nonconvex functions, while the strict convexity of the consequent optimization problem is preserved. This results in a higher performance in detecting change points. To theoretically justify the performance improvements over $\ell_1$ mean filtering, deterministic and stochastic sufficient conditions for exact change point recovery are derived. In particular, theoretical results show that in the stair-casing problem, our approach might be able to exclude the false change points, while $\ell_1$ mean filtering may fail. A number of numerical simulations assist to show superiority of our method over $\ell_1$ mean filtering and another state-of-the-art algorithm that promotes sparsity tighter than the $\ell_1$ norm. Specifically, it is shown that our approach can consistently detect change points when the jump amplitudes become sufficiently large, while the two other competitors cannot., Submitted to IEEE Transactions on Signal Processing

We give a new characterization of Valdivia compact spaces: A compact space is Valdivia if and only if it has a dense commutatively monotonically retractable subspace. This result solves Problem 5.12 from [6] . Besides, we introduce the notion of full c -skeleton and prove that a compact space is Corson if and only if it has a full c -skeleton.

Many iterative approaches in the field of system identification for control have been developed. Although successful implementations have been reported, a solid analysis with respect to the convergence of these iterations has not been established. The aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric H ∞ -norm estimation. The pursued methodology involves a novel frequency domain approach that addresses both additive stochastic disturbances and input normalization. The results of the convergence analysis are twofold: (1) the presence of additive disturbances introduces a bias in the estimation procedure, and (2) the iterative procedure can be interpreted as experiment design for H ∞ -norm estimation, revealing the value of iterations and limits of accuracy in terms of the Fisher information matrix. The results are confirmed by means of a simulation example.

In many practical situations, it is highly desirable to estimate an accurate mathematical model of a real system using as few parameters as possible. This can be motivated either from appealing to ...

The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The existence of local minima, and hence the difficulty in solving the optimization, depends mainly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. It is therefore possible to avoid the existence of local minima by properly choosing the spectrum of the input; in this paper we show how to perform this choice. We present sufficient conditions for the convergence of PEM to the global minimum and from these conditions we derive two approaches to avoid the existence of nonglobal minima. We present the application of one of these two approaches to a case study where standard identification toolboxes tend to get trapped in nonglobal minima.

In this paper, the problem of input signal design with the property that the estimated model satisfies a given performance level with a prescribed probability is studied. The aforementioned performance level is associated with a particular application. This problem is well-known to fall within the class of chance-constrained optimization problems, which are nonconvex in most cases. Convexification is attempted based on a Markov inequality, leading to semidefinite programming (SDP) relaxation formulations. As applications, we focus on the identification of multiple input multiple output (MIMO) wireless communication channel models for minimum mean square error (MMSE) channel equalization and zero-forcing (ZF) precoding.

In this contribution we present a method to estimate structured high order ARX models. By this we mean that the estimated model, despite its high order is close to a low order model. This is achieved by adding two terms to the least-squares cost function. These two terms correspond to nuclear norms of two Hankel matrices. These Hankel matrices are constructed from the impulse response coefficients of the inverse noise model, and the numerator polynomial of the model dynamics, respectively. In a simulation study the method is shown to be competitive as compared to the prediction error method. In particular, in the study the performance degrades more gracefully than for the Prediction Error Method when the signal to noise ratio decreases.

In this paper, we study the accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation. We present a frequency-domain representation for the information matrix for general linear MIMO models. We show that the variance of estimated parametric models for linear MIMO systems satisfies a fundamental integral trade-off. This trade-off is expressed as a multivariable 'water-bed' effect. An extension to spectral estimation is also discussed.

In this paper, the extended finite element method (X-FEM) is implemented to analyze fracture mechanics problems in elastic materials that exhibit general anisotropy. In the X-FEM, crack modeling is addressed by adding discontinuous enrichment functions to the standard FE polynomial approximation within the framework of partition of unity. In particular, the crack interior is represented by the Heaviside function, whereas the crack-tip is modeled by the so-called crack-tip enrichment functions. These functions have previously been obtained in the literature for isotropic, orthotropic, piezoelectric and magnetoelectroelastic materials. In the present work, the crack-tip functions are determined by means of the Stroh's formalism for fully anisotropic materials, thus providing a new set of enrichment functions in a concise and compact form. The proposed formulation is validated by comparing the obtained results with other analytical and numerical solutions. Convergence rates for both topological and geometrical enrichments are presented. Performance of the newly derived enrichment functions is studied, and comparisons are made to the well-known classical crack-tip functions for isotropic materials.

An efficient numerical tool based on the hypersingular formulation of the Boundary Element Method (BEM) for the analysis of different crack face boundary conditions in 2D magnetoelectroelastic media is presented. A new algorithm for the resolution of multiple semipermeable cracks is derived and implemented. The accuracy of the proposed formulation is confirmed by comparison with analytical solutions available in literature. The new results presented in this work may be of interest for the understanding of magnetoelectroelastic cracked solids behavior and the consequent improvements in the design and maintenance of novel devices.

We study the accuracy of identified linear time-invariant multi-input multi-output (MIMO) systems. Under a stochastic framework, we quantify the effect of the spatial correlation and choice of model structure on the covariance matrix of the transfer function estimates. In particular, it is shown how the variance of a transfer function estimate depends on signal properties and model orders of other modules composing the MIMO system.

Errors-in-variables estimation problems for single-input-single-output systems with Gaussian signals are considered in this contribution. It is shown that the Fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated. Furthermore, it is shown that Whittle's formula for the Fisher information matrix can be represented as a Gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators. Finally, the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases: (i) when the model includes white measurement noise on the input and the variance of the noise is estimated, and (ii) when the model includes only measurement noise on the output. In both cases, asymptotically efficient estimators are assumed. An explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output.

In this paper we investigate the cost of complexity, which is defined as the minimum amount of input power required to estimate the frequency response of a given linear time invariant system of order n with a prescribed degree of accuracy. In particular we require that the asymptotic (in the data length) variance is less or equal to γ over a prespecified frequency range 0 , ω B ] . The models considered here are Output Error models, with an emphasis on fixed denominator and Laguerre models. Several properties of the cost are derived. For instance, we present an expression which shows how the pole of the Laguerre model affects the cost. These results quantify how the cost of the system identification experiment depends on n and on the model structure. Also, they show the relation between the cost and the amount of information we would like to extract from the system (in terms of ω B and γ ). For simplicity we assume that there is no undermodelling.

An adaptive algorithm, consisting of a recursive estimator for a finite impulse response model having two non-zero lags only, and an adaptive input are presented. The model is parametrized in terms of the first impulse response coefficient and the model zero. For linear time-invariant single-input single-output systems with real rational transfer functions possessing at least one real-valued non-minimum phase zero of multiplicity one, it is shown that the model zero converges to such a zero of the true system. In the case of multiple non-minimum phase zeros, the algorithm can be tailored to converge to a particular zero. The result is shown to hold for systems and noise spectra of arbitrary degree. The algorithm requires prior knowledge of the sign of the high frequency gain of the system as well as an interval to which the non-minimum phase zero of interest belongs.

Static fracture analyses in two-dimensional linear magnetoelectroelastic (MEE) solids is studied by means of the extended finite element method (X-FEM). In the X-FEM, crack modeling is facilitated by adding a discontinuous function and the crack-tip asymptotic functions to the standard finite element approximation using the framework of partition of unity. In this study, media possessing fully coupled piezoelectric, piezomagnetic and magnetoelectric effects are considered. New enrichment functions for cracks in transversely isotropic MEE materials are derived, and the computation of fracture parameters using the domain form of the contour interaction integral is presented. The convergence rates in energy for topological and geometric enrichments are studied. Excellent accuracy of the proposed formulation is demonstrated on benchmark crack problems through comparisons with both analytical solutions and numerical results obtained by the dual boundary element method. Copyright © 2011 John Wiley & Sons, Ltd.

It is well known that if we intend to use a minimum variance control strategy, which is designed based on a model obtained from an identification experiment, the best experiment which can be performed on the system to determine such a model (subject to output power constraints, or for some specific model structures) is to use the true minimum variance controller. This result has been derived under several circumstances, first using asymptotic (in model order) variance expressions but also more recently for ARMAX models of finite order. In this paper we re-approach this problem using a recently developed expression for the variance of parametric frequency function estimates. This allows a geometric analysis of the problem and the generalization of the aforementioned finite model order ARMAX results to general linear model structures.

In this paper, we consider full order modeling, i.e., when the true system belongs to the model set. We investigate the minimum amount of input energy required to estimate a given linear system with a full order model within a prescribed degree of accuracy γ, as a function of the model complexity. This quantity we define to be the “cost of complexity.” The degree of accuracy is measured by the inverse of the maximum variance of the discrete-time frequency function estimator over a given frequency range [-ωB,ωB]. It is commonly believed that the cost increases as the model complexity increases. However, the amount of information that is to be extracted from the system also influences the cost. The objective of this paper is to quantify these dependencies for systems described by finite-impulse response models. It is shown that, asymptotically in the model order n and sample size, the cost is well approximated by γσo2nωB/π where σo2 is the noise variance. This expression can be used as a simple rule of thumb for assessing trade-offs that have to be made in a system identification project where full order models are used. For example, for given experiment duration, excitation level and desired accuracy, one can assess how the achievable frequency range depends on the required model order. This type of consideration is useful when formally planning experiments. In addition, we establish several properties of the cost of complexity. We find, for example, that if ωB is very close (but not necessarily equal) to π, the optimal input satisfies the model quality constraint for all frequencies.

In this technical note fundamental integral limitations are derived on the variance of estimated parametric models, for both open and closed loop identification. As an application of these results we show that, for multisine inputs, a well known asymptotic (in model order) variance expression provides upper bounds on the actual variance of the estimated models for finite model orders. The fundamental limitations established here give rise to a dasiawater-bedpsila effect, which is illustrated in an example.