Regularization of descriptor systems by output feedback

Conditions are given under which a descriptor, or generalized state-space system can be regularized by output feedback. It is shown that under these conditions, proportional and derivative output feedback controls can be constructed such that the closed-loop system is regular and has index at most one. This property ensures the solvability of the resulting system of dynamic-algebraic equations. A reduced form is given that allows the system properties as well as the feedback to be determined. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way.

Regularization of Descriptor Systems by Derivative and Proportional State Feedback

For linear multivariable time-invariant continuous or discrete-time singular systems it is customary to use a proportional feedback control in order to achieve a desired closed loop behaviour. Derivative feedback is rarely considered. This paper examines how derivative feedback in descriptor systems can be used to alter the structure of the system pencil under various controllability conditions. It is shown that derivative and proportional feedback controls can be constructed such that the closed loop system has a given form and is also regular and has index at most 1. This property ensures the solvability of the resulting system of dynamic-algebraic equations. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. The problem of pole placement with derivative feedback alone and in combination with proportional state feedback is also investigated. A computational algorithm for improving the “conditioning” of the regularized closed loop system is derived.

Can L2 learners learn new ways to conceptualise events? Evidence from motion event construal among English-speaking learners of French

This study tests Slobin’s (1996) claim that L2 learners struggle with conceptual restructuring in L2 acquisition. We suggest that learners can find themselves in four different reconceptualisation scenarios: the TRANSFER, RESTRUCTURING, CREATIVE/HYBRID and CONVERGENCE SCENARIOS. To test this proposal in the field of event conceptualisation, a comprehensive analysis was made of the frequency distribution of path, manner, caused motion and deictic verbs in narratives elicited from intermediate (N=20) and advanced learners (N=21) of French, as well as native speakers of French (N=23) and English (N=30). The productions of the intermediate level learners were found to correspond to the creative/hybrid scenario because they differed significantly in their motion expressions from English as well as French native speakers, except for path, which was verbalised in target-like ways early on. Advanced learners were found to be able to reconceptualise motion in the L2, as far as manner and path are concerned, but continued to struggle with deictic verbs and caused motion. The clearest evidence for transfer from the L1 was found in verbalisations among intermediate level learners of events which involved a boundary crossing.

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ∈ X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

Processing empty categories in a second language: When naturalistic exposure fills the (intermediate) gap

An ongoing debate on second language (L2) processing revolves around whether or not L2 learners process syntactic information similarly to monolinguals (L1), and what factors lead to a native-like processing. According to the Shallow Structure Hypothesis (Clahsen & Felser, 2006a), L2 learners’ processing does not include abstract syntactic features, such as intermediate gaps of wh-movement, but relies more on lexical/semantic information. Other researchers have suggested that naturalistic L2 exposure can lead to native-like processing (Dussias, 2003). This study investigates the effect of naturalistic exposure in processing wh-dependencies. Twenty-six advanced Greek learners of L2 English with an average nine years of naturalistic exposure, 30 with classroom exposure, and 30 native speakers of English completed a self-paced reading task with sentences involving intermediate gaps. L2 learners with naturalistic exposure showed evidence of native-like processing of the intermediate gaps, suggesting that linguistic immersion can lead to native-like abstract syntactic processing in the L2.

Resolution of sharp fronts in the presence of model error in variational data assimilation

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

Bilingual 'tagging' of financial accounts in Demotic and Greek

‘Bilingual’ documents, with text in both Demotic and Greek, can be of several sorts, ranging from complete translations of the same information (e.g. Ptolemaic decrees) to those where the information presented in the two languages is complementary (e.g. mummy labels). The texts discussed in this paper consist of a number of examples of financial records where a full account in one language (L1) is annotated with brief pieces of information in a second language (L2). These L2 ‘tags’ are designed to facilitate extraction of summary data at another level of the administration, functioning in a different language, and probably also to make the document accessible to those who are not literate in the L1.

Second tier professionals: English teachers in England

The policy context for mother-tongue educators at all levels in England has been dominated by a matrix with four key elements,running along two spectra, one of learning (content↘assessment) and one of teaching (autonomy↘accountability). In each case the trend has been towards increasing external control and decreasing professional autonomy. Whilst some imposed changes have been recognised as intrinsically valuable, the majority are viewed as detrimental to teachers' status and obstructive for students. The research community has been largely marginalised and has had little scope to influence proceedings. A rapidly developing crisis in teacher retention may yet reverse these trends as the government is forced to recognise the long-term implications of their treatment of the profession.

Cooperative metal-ligand-induced properties of heteroleptic copper(I) xanthate/dithiocarbamate PPh3 complexes

Four new heteroleptic mononuclear complexes, [Cu(PPh3)2L1](1) {L1 = (C9H11O2CS2), [2-(4-methoxyphenyl)ethyl]xanthate}, [Cu(PPh3)2L2] (2) [L2 = (C6H7OCS2), benzylxanthate], [Cu(PPh3)2L3] (3) [L3 = (C5H9OCS2), (cyclobutylmethyl)xanthate] and [Cu(PPh3)2L4] (4) [L4 = (NC13H13NCS2), N-benzyl-N-(4-pyridylmethyl)dithiocarbamate], have been synthesized and characterized by using microanalysis, IR, UV/Vis, 1H, 13C and 31P NMR spectroscopy and X-ray crystallography; their photoluminescent behaviour and molecular electrical conductivity have been investigated. CuI possesses four-coordinate distorted tetrahedral geometry in all the complexes. All are weakly conducting and exhibit semiconductor behaviour in the studied 303363 K temperature range. Complex 4 shows striking luminescent behaviour emitting bluish green light at 480 nm in CH2Cl2 solution at room temperature

Synthesis and properties of new Mo(II) complexes with N-heterocyclic and ferrocenyl ligands

New Mo(II) complexes with 2,2'-dipyridylamine (L1), [Mo(CH(3)CN)(eta(3)-C(3)H(5))(CO)(2)(L1)]OTf (C1a) and [{MoBr(eta(3)-C(3)H(5))(CO)(2)(L1)}(2)(4,4'-bipy)](PF(6))(2) (C1b), with {[bis(2-pyridyl)amino]carbonyl}ferrocene (L2), [MoBr(eta(3)-C(3)H(5))(CO)(2)(L2)] (C2), and with the new ligand N,N-bis(ferrocenecarbonyl)-2-aminopyridine (L3), [MoBr(eta(3)-C(3)H(5))(CO)(2)(L3)] (C3), were prepared and characterized by FTIR and (1)H and (13)C NMR spectroscopy. C1a, C1b, L3, and C2 were also structurally characterized by single crystal X-ray diffraction. The Mo(II) coordination sphere in all complexes features the facial arrangement of allyl and carbonyl ligands, with the axial isomer present in C1a and C2, and the equatorial in the binuclear C1b. In both C1a and C1b complexes, the L1 ligand is bonded to Mo(II) through the nitrogen atoms and the NH group is involved in hydrogen bonds. The X-ray single crystal structure of C2 shows that L2 is coordinated in a kappa(2)-N,N-bidentate chelating fashion. Complex C3 was characterized as [MoBr(eta(3)-C(3)H(5))(CO)(2)(L3)] with L3 acting as a kappa(2)-N,O-bidentate ligand, based on the spectroscopic data, complemented by DFT calculations. The electrochemical behavior of the monoferrocenyl and diferrocenyl ligands L2 and L3 has been studied together with that of their Mo(II) complexes C2 and C3. As much as possible, the nature of the different redox changes has been confirmed by spectrophotometric measurements. The nature of the frontier orbitals, namely the localization of the HOMO in Mo for both in C2 and C3, was determined by DFT studies.

Sparse shape representation using the Laplace-Beltrami eigenfunctions and its application to modeling subcortical structures

We present a new sparse shape modeling framework on the Laplace-Beltrami (LB) eigenfunctions. Traditionally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes by forming a Fourier series expansion. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we propose to filter out only the significant eigenfunctions by imposing l1-penalty. The new sparse framework can further avoid additional surface-based smoothing often used in the field. The proposed approach is applied in investigating the influence of age (38-79 years) and gender on amygdala and hippocampus shapes in the normal population. In addition, we show how the emotional response is related to the anatomy of the subcortical structures.

Parsing the passive: comparing children with Specific Language Impairment to sequential bilingual children

25 monolingual (L1) children with Specific Language Impairment (SLI), 32 sequential bilingual (L2) children, and 29 L1 controls completed the Test of Active & Passive Sentences-Revised (van der Lely, 1996) and the self-paced listening task with picture verification for actives and passives (Marinis, 2007). These revealed important between-group differences in both tasks. The children with SLI showed difficulties in both actives and passives when they had to reanalyse thematic roles on-line. Their error pattern provided evidence for working memory limitations. The L2 children showed difficulties only in passives both on-line and off-line. We suggest that these relate to the complex syntactic algorithm in passives and reflect an earlier developmental stage due to reduced exposure to the L2. The results are discussed in relation to theories of SLI and can be best accommodated within accounts proposing that difficulties in the comprehension of passives stem from processing limitations.

In vitro effects of extracts and purified tannins of sainfoin (Onobrychis viciifolia) against two cattle nematodes

Sainfoin (Onobrychis viciifolia) is a condensed tannin (CT)-containing legume and has anthelmintic potential against gastrointestinal nematodes of ruminants. This study investigated in vitro effects of acetone/water extracts and derived CT fractions from different types of sainfoin (i.e. accessions) against larvae of Cooperia oncophora and Ostertagia ostertagi by applying the larval feeding inhibition assay (LFIA). Seven sainfoin accessions were extracted and tested with L1 larvae at 10 and 40 μg extract/ml. In addition, CT in extracts from 4 accessions were fractionated according to polymer size and tested by LFIA at two concentrations (2 and 10 μg CT fraction/ml). All sainfoin extracts caused significant inhibition of L1-feeding of both C. oncophora and O. ostertagi with varying intensity compared to the control (phosphate buffered saline). For both nematode species the in vitro effect was positively correlated with CT content in the extracts, but not with any of the structural CT parameters. In contrast, the 16 CT fractions revealed significant correlations between in vitro effect and CT content, polymer size (mean degree of polymerisation, mDP) and monomeric composition (prodelphinidin percentage, % PD). These differences between crude extracts and purified fractions may stem from the fact that extracts contain complex CT mixtures, which may mask and thus suppress CT structural effects. This study provides the first indication that, apart from CT and % PD content, polymer size also contributes to anthelmintic activity of CTs. The results, therefore, suggest that the inter-accession variability in CT content and composition needs to be taken into account in future plant breeding programmes which seek to enhance the anthelmintic properties of sainfoin

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.