On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

Robust control system design for generalized state-space systems

Robustness in multi-variable control system design requires that the solution to the design problem be insensitive to perturbations in the system data. In this paper we discuss measures of robustness for generalized state-space, or descriptor, systems and describe algorithmic techniques for optimizing robustness for various applications.

Weaning diet induces sustained metabolic phenotype shift in the pig and influences host response to Bifidobacterium lactis NCC2818

Background The process of weaning causes a major shift in intestinal microbiota and is a critical period for developing appropriate immune responses in young mammals.Objective To use a new systems approach to provide an overview of host metabolism and the developing immune system in response to nutritional intervention around the weaning period.Design Piglets (n=14) were weaned onto either an egg-based or soya-based diet at 3 weeks until 7 weeks, when all piglets were switched onto a fish-based diet. Half the animals on each weaning diet received Bifidobacterium lactis NCC2818 supplementation from weaning onwards. Immunoglobulin production from immunologically relevant intestinal sites was quantified and the urinary (1)H NMR metabolic profile was obtained from each animal at post mortem (11 weeks).Results Different weaning diets induced divergent and sustained shifts in the metabolic phenotype, which resulted in the alteration of urinary gut microbial co-metabolites, even after 4 weeks of dietary standardisation. B lactis NCC2818 supplementation affected the systemic metabolism of the different weaning diet groups over and above the effects of diet. Additionally, production of gut mucosa-associated IgA and IgM was found to depend upon the weaning diet and on B lactis NCC2818 supplementation.ConclusionThe correlation of urinary (1)H NMR metabolic profile with mucosal immunoglobulin production was demonstrated, thus confirming the value of this multi-platform approach in uncovering non-invasive biomarkers of immunity. This has clear potential for translation into human healthcare with the development of urine testing as a means of assessing mucosal immune status. This might lead to early diagnosis of intestinal dysbiosis and with subsequent intervention, arrest disease development. This system enhances our overall understanding of pathologies under supra-organismal control.

Operator space structure of JC*-triples and TROs, I

We embark upon a systematic investigation of operator space structure of JC*-triples via a study of the TROs (ternary rings of operators) they generate. Our approach is to introduce and develop a variety of universal objects, including universal TROs, by which means we are able to describe all possible operator space structures of a JC*-triple. Via the concept of reversibility we obtain characterisations of universal TROs over a wide range of examples. We apply our results to obtain explicit descriptions of operator space structures of Cartan factors regardless of dimension

On the operator space structure of Hilbert spaces

Operator spaces of Hilbertian JC∗ -triples E are considered in the light of the universal ternary ring of operators (TRO) introduced in recent work. For these operator spaces, it is shown that their triple envelope (in the sense of Hamana) is the TRO they generate, that a complete isometry between any two of them is always the restriction of a TRO isomorphism and that distinct operator space structures on a fixed E are never completely isometric. In the infinite-dimensional cases, operator space structure is shown to be characterized by severe and definite restrictions upon finite-dimensional subspaces. Injective envelopes are explicitly computed.

Universally reversible JC*-triples and operator spaces

Abstract. We prove that the vast majority of JC∗-triples satisfy the condition of universal reversibility. Our characterisation is that a JC∗-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW∗-triples and of TROs (regarded as JC∗-triples). We show that the distinct natural operator space structures on a universally reversible JC∗-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.

Borrowing and shift-induced interference: contrasting patterns in French-Germanic contact in Brussels and Strasbourg

The main aim of the present article is to test hypotheses derived from the model for contact- induced language change as formulated in Thomason and Kaufman (1988 et seq.). As the model correctly predicts the asymmetries between the mutual influences of the Germanic and the Romance varieties in Brussels and Strasbourg it is a very powerful tool for describing the contact patterns in these cities. The analysis shows that the contact patterns are very similar, both from a quantitative and from a qualitative point of view, despite important differences in the sociolinguistic situation of both cities. The striking similarities in the outcome of language contact seem to find a plausible explanation in the fact that the language contact situations in both cities are similar from a typological point of view: in each city a variety of French is in contact with a Germanic variety (Alsatian and Brussels Dutch). Thus, the claim of the present article is that the structure of the languages plays a more prominent role in the outcome of language contact than the sociolinguistic history of the speakers.

Atlantic Ocean influence on a shift in European climate in the 1990s

European climate exhibits variability on a wide range of timescales. Understanding the nature and drivers of this variability is an essential step in developing robust climate predictions and risk assessments. The Atlantic Ocean has been suggested as an important driver of variability in European climate on decadal timescales1, but the importance of this influence in recent decades has been unclear, partly because of difficulties in separating the influence of the Atlantic Ocean from other contributions, for example, from the tropical Pacific Ocean and the stratosphere. Here we analyse four data sets derived from observations to show that, during the 1990s, there was a substantial shift in European climate towards a pattern characterized by anomalously wet summers in northern Europe, and hot, dry, summers in southern Europe, with related shifts in spring and autumn. These changes in climate coincided with a substantial warming of the North Atlantic Ocean, towards a state last seen in the 1950s. The patterns of European climate change in the 1990s are consistent with earlier changes attributed to the influence of the North Atlantic Ocean, and provide compelling evidence that the Atlantic Ocean was the key driver. Our results suggest that the recent pattern of anomalies in European climate will persist as long as the North Atlantic Ocean remains anomalously warm.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Weaning diet induces sustained metabolic phenotype shift in the pig and influences host response to Bifidobacterium lactis NCC2818

Background: The process of weaning causes a major shift in intestinal microbiota and is a critical period for developing appropriate immune responses in young mammals. Objective: To use a new systems approach to provide an overview of host metabolism and the developing immune system in response to nutritional intervention around the weaning period. Design: Piglets (n¼14) were weaned onto either an eggbased or soya-based diet at 3 weeks until 7 weeks, when all piglets were switched onto a fish-based diet. Half the animals on each weaning diet received Bifidobacterium lactis NCC2818 supplementation from weaning onwards. Immunoglobulin production from immunologically relevant intestinal sites was quantified and the urinary 1H NMR metabolic profile was obtained from each animal at post mortem (11 weeks). Results: Different weaning diets induced divergent and sustained shifts in the metabolic phenotype, which resulted in the alteration of urinary gut microbial co-metabolites, even after 4 weeks of dietary standardisation. B lactis NCC2818 supplementation affected the systemic metabolism of the different weaning diet groups over and above the effects of diet. Additionally, production of gut mucosa-associated IgA and IgM was found to depend upon the weaning diet and on B lactis NCC2818 supplementation. Conclusion: The correlation of urinary 1H NMR metabolic profile with mucosal immunoglobulin production was demonstrated, thus confirming the value of this multiplatform approach in uncovering non-invasive biomarkers of immunity. This has clear potential for translation into human healthcare with the development of urine testing as a means of assessing mucosal immune status. This might lead to early diagnosis of intestinal dysbiosis and with subsequent intervention, arrest disease development. This system enhances our overall understanding of pathologies under supra-organismal control.

Perceptual shift in bilingualism: brain potentials reveal plasticity in pre-attentive colour perception

The validity of the linguistic relativity principle continues to stimulate vigorous debate and research. The debate has recently shifted from the behavioural investigation arena to a more biologically grounded field, in which tangible physiological evidence for language effects on perception can be obtained. Using brain potentials in a colour oddball detection task with Greek and English speakers, a recent study suggests that language effects may exist at early stages of perceptual integration [Thierry, G., Athanasopoulos, P., Wiggett, A., Dering, B., & Kuipers, J. (2009). Unconscious effects of language-specific terminology on pre-attentive colour perception. Proceedings of the National Academy of Sciences, 106, 4567–4570]. In this paper, we test whether in Greek speakers exposure to a new cultural environment (UK) with contrasting colour terminology from their native language affects early perceptual processing as indexed by an electrophysiological correlate of visual detection of colour luminance. We also report semantic mapping of native colour terms and colour similarity judgements. Results reveal convergence of linguistic descriptions, cognitive processing, and early perception of colour in bilinguals. This result demonstrates for the first time substantial plasticity in early, pre-attentive colour perception and has important implications for the mechanisms that are involved in perceptual changes during the processes of language learning and acculturation.