Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

Peptidomimetic design of unusual turns by incorporating flexible and rigid omega-amino acids simultaneously

The tripeptides Boc-Gly-Aib-m-ABA-OMe (I), Boc-beta Ala-Aib-m-ABA-OMe (II) and Boc-gamma Abu-Aib-rn-ABA-OMe (III) (Aib: alpha-aminoisobutyric acid, beta Ala: beta-alanine, gamma Abu: gamma-aminobutyric acid, m-ABA: meta-aminobenzoic acid) with homologated amino acids at the N-terminus, the rigid gamma-amino acid m-ABA at the C-terminus and the helicogenic Aib at the central position have been chosen to create unusual turns. Single crystal X-ray diffraction studies, solvent dependent NMR titrations and 2D NMR analysis reveal that peptides II and III adopt unusual turns of 11- and 12-membered rings stabilized by modified 4 -> 1 type intramolecular hydrogen bonds. Solution phase studies indicate that peptide I exists in the beta-turn conformation stabilized by 10-membered intramolecular hydrogen bonding.

Glucokinase Regulatory Protein genetic variant interacts with omega-3 PUFA to influence insulin resistance and inflammation in metabolic syndrome

Glucokinase Regulatory Protein (GCKR) plays a central role regulating both hepatic triglyceride and glucose metabolism. Fatty acids are key metabolic regulators, which interact with genetic factors and influence glucose metabolism and other metabolic traits. Omega-3 polyunsaturated fatty acids (n-3 PUFA) have been of considerable interest, due to their potential to reduce metabolic syndrome (MetS) risk. Objective To examine whether genetic variability at the GCKR gene locus was associated with the degree of insulin resistance, plasma concentrations of C-reactive protein (CRP) and n-3 PUFA in MetS subjects. Design Homeostasis model assessment of insulin resistance (HOMA-IR), HOMA-B, plasma concentrations of C-peptide, CRP, fatty acid composition and the GCKR rs1260326-P446L polymorphism, were determined in a cross-sectional analysis of 379 subjects with MetS participating in the LIPGENE dietary cohort. Results Among subjects with n-3 PUFA levels below the population median, carriers of the common C/C genotype had higher plasma concentrations of fasting insulin (P = 0.019), C-peptide (P = 0.004), HOMA-IR (P = 0.008) and CRP (P = 0.032) as compared with subjects carrying the minor T-allele (Leu446). In contrast, homozygous C/C carriers with n-3 PUFA levels above the median showed lower plasma concentrations of fasting insulin, peptide C, HOMA-IR and CRP, as compared with individuals with the T-allele. Conclusions We have demonstrated a significant interaction between the GCKR rs1260326-P446L polymorphism and plasma n-3 PUFA levels modulating insulin resistance and inflammatory markers in MetS subjects. Further studies are needed to confirm this gene-diet interaction in the general population and whether targeted dietary recommendations can prevent MetS in genetically susceptible individuals.

Effects of omega-3 fatty acids on immune function in broiler chickens

There is interest in the enrichment of poultry meat with long-chain n-3 polyunsaturated fatty acids in order to increase the consumption of these fatty acids by humans. However, there is concern that high levels of n-3 polyunsaturated fatty acids may have detrimental effects on immune function in chickens. The effect of feeding increasing levels of fish oil (FO) on immune function was investigated in broiler chickens. Three-week-old broilers were fed 1 of 4 wheat-soybean basal diets that contained 0, 30, 50, or 60 g/kg of FO until slaughter. At slaughter, samples of blood, bursa of Fabricius, spleen, and thymus were collected from each bird. A range of immune parameters, including immune tissue weight, immuno-phenotyping, phagocytosis, and cell proliferation, were assessed. The pattern of fatty acid incorporation reflected the fatty acid composition of the diet. The FO did not affect the weight of the spleen, but it did increase thymus weight when fed at 50 g/kg (P < 0.001). Fish oil also lowered bursal weights when fed at 50 or 60 g/kg (P < 0.001). There was no significant effect of FO on immune cell phenotypes in the spleen, thymus, bursa, or blood. Feeding 60 g/kg of FO significantly decreased the percentage of monocytes engaged in phagocytosis, but it increased their mean fluorescence intensity relative to that of broilers fed 50 g/kg of FO. Lymphocyte proliferation was significantly decreased after feeding broiler chickens diets rich in FO when expressed as division index or proliferation index, although there was no significant effect of FO on the percentage of divided cells. In conclusion, dietary n-3 polyunsaturated fatty acids decrease phagocytosis and lymphocyte proliferation in broiler chickens, highlighting the need for the poultry industry to consider the health status of poultry when poultry meat is being enriched with FO.

A search for invariant relative satellite motion

This report presents the canonical Hamiltonian formulation of relative satellite motion. The unperturbed Hamiltonian model is shown to be equivalent to the well known Hill-Clohessy-Wilshire (HCW) linear formulation. The in°uence of perturbations of the nonlinear Gravitational potential and the oblateness of the Earth; J2 perturbations are also modelled within the Hamiltonian formulation. The modelling incorporates eccentricity of the reference orbit. The corresponding Hamiltonian vector ¯elds are computed and implemented in Simulink. A numerical method is presented aimed at locating periodic or quasi-periodic relative satellite motion. The numerical method outlined in this paper is applied to the Hamiltonian system. Although the orbits considered here are weakly unstable at best, in the case of eccentricity only, the method ¯nds exact periodic orbits. When other perturbations such as nonlinear gravitational terms are added, drift is signicantly reduced and in the case of the J2 perturbation with and without the nonlinear gravitational potential term, bounded quasi-periodic solutions are found. Advantages of using Newton's method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, repeatability of solutions due to its non-random nature, and fast convergence. Given that the use of bounded or drifting trajectories as control references carries practical di±culties over long-term missions, Principal Component Analysis (PCA) is applied to the quasi-periodic or slowly drifting trajectories to help provide a closed reference trajectory for the implementation of closed loop control. In order to evaluate the e®ect of the quality of the model used to generate the periodic reference trajectory, a study involving closed loop control of a simulated master/follower formation was performed. 2 The results of the closed loop control study indicate that the quality of the model employed for generating the reference trajectory used for control purposes has an important in°uence on the resulting amount of fuel required to track the reference trajectory. The model used to generate LQR controller gains also has an e®ect on the e±ciency of the controller.

Spectrally invariant approximation within atmospheric radiative transfer

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These ‘‘spectrally invariant relationships’’ are the consequence of wavelength independence of the extinction coefficient and scattering phase function in veg- etation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accu- rately describe the extinction and scattering properties of cloudy atmospheres. The validity of the as- sumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

Marine omega-3 fatty acids and coronary heart disease

Purpose of review: To provide an overview of the key earlier intervention studies with marine omega-3 fatty acids and to review and comment on recent studies reporting on mortality outcomes and on selected underlying mechanisms of action. Recent findings: Studies relating marine omega-3 fatty acid status to current or future outcomes continue to indicate benefits, for example, on incident heart failure, congestive heart failure, acute coronary syndrome, and all-cause mortality. New mechanistic insights into the actions of marine omega-3 fatty acids have been gained. Three fairly large secondary prevention trials have not confirmed the previously reported benefit of marine omega-3 fatty acids towards mortality in survivors of myocardial infarction. Studies of marine omega-3 fatty acids in atrial fibrillation and in cardiac surgery-induced atrial fibrillation have produced inconsistent findings and meta-analyses demonstrate no benefit. A study confirmed that marine omega-3 fatty acids reduce the inflammatory burden with advanced atherosclerotic plaques, so inducing greater stability. Summary: Recent studies of marine omega-3 fatty acids on morbidity of, and mortality from, coronary and cardiovascular disease have produced mixed findings. These studies raise new issues to be addressed in future research.

On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

A time-invariant visco-elastic windkessel model relating blood flow and blood volume

The difference between the rate of change of cerebral blood volume (CBV) and cerebral blood flow (CBF) following stimulation is thought to be due to circumferential stress relaxation in veins (Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679–689). In this paper we explore the visco-elastic properties of blood vessels, and present a dynamic model relating changes in CBF to changes in CBV. We refer to this model as the visco-elastic windkessel (VW) model. A novel feature of this model is that the parameter characterising the pressure–volume relationship of blood vessels is treated as a state variable dependent on the rate of change of CBV, producing hysteresis in the pressure–volume space during vessel dilation and contraction. The VW model is nonlinear time-invariant, and is able to predict the observed differences between the time series of CBV and that of CBF measurements following changes in neural activity. Like the windkessel model derived by Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679–689, the VW model is primarily a model of haemodynamic changes in the venous compartment. The VW model is demonstrated to have the following characteristics typical of visco-elastic materials: (1) hysteresis, (2) creep, and (3) stress relaxation, hence it provides a unified model of the visco-elastic properties of the vasculature. The model will not only contribute to the interpretation of the Blood Oxygen Level Dependent (BOLD) signals from functional Magnetic Resonance Imaging (fMRI) experiments, but also find applications in the study and modelling of the brain vasculature and the haemodynamics of circulatory and cardiovascular systems.

Postprandial enrichment of triacylglycerol-rich lipoproteins with omega-3 fatty acids: lack of an interaction with apolipoprotein E genotype?

Background: We have previously demonstrated that carrying the apolipoprotein (apo) E epsilon 4 (E4+) genotype disrupts omega-3 fatty acids (n − 3 PUFA) metabolism. Here we hypothesise that the postprandial clearance of n − 3 PUFA from the circulation is faster in E4+ compared to non-carriers (E4−). The objective of the study was to investigate the fasted and postprandial fatty acid (FA) profile of triacylglycerol-rich lipoprotein (TRL) fractions: Sf >400 (predominately chylomicron CM), Sf 60 − 400 (VLDL1), and Sf 20 − 60 (VLDL2) according to APOE genotype. Methods: Postprandial TRL fractions were obtained in 11 E4+ (ε3/ε4) and 12 E4− (ε3/ε3) male from the SATgenε study following high saturated fat diet + 3.45 g/d of docosahexaenoic acid (DHA) for 8-wk. Blood samples were taken at fasting and 5-h after consuming a test-meal representative of the dietary intervention. FA were characterized by gas chromatography. Results: At fasting, there was a 2-fold higher ratio of eicosapentaenoic acid (EPA) to arachidonic acid (P = 0.046) as well as a trend towards higher relative% of EPA (P=0.063) in theSf >400 fraction of E4+. Total n − 3 PUFA in the Sf 60 − 400 and Sf 20 − 60 fractions were not APOE genotype dependant. At 5 h, there was a trend towards a time × genotype interaction (P=0.081) for EPA in theSf >400 fraction. When sub-groups were form based on the level of EPA at baseline within the Sf >400 fraction, postprandial EPA (%) was significantly reduced only in the high-EPA group. EPA at baseline significantly predicted the postprandial response in EPA only in E4+ subjects (R2 = 0.816). Conclusion: Despite the DHA supplement contain very low levels of EPA, E4+ subjects with high EPA at fasting potentially have disrupted postprandial n − 3 PUFA metabolism after receiving a high-dose of DHA. Trial registration: Registered at clinicaltrials.gov/show/NCT01544855.

Spectral design of temperature-invariant narrow bandpass filters for the mid-infrared

The ability of narrow bandpass filters to discriminate wavelengths between closely-separated gas absorption lines is crucial in many areas of infrared spectroscopy. As improvements to the sensitivity of infrared detectors enables operation in uncontrolled high-temperature environments, this imposes demands on the explicit bandpass design to provide temperature-invariant behavior. The unique negative temperature coefficient (dn/dT<0) of Lead-based (Pb) salts, in combination with dielectric materials enable bandpass filters with exclusive immunity to shifts in wavelength with temperature. This paper presents the results of an investigation into the interdependence between multilayer bandpass design and optical materials together with a review on invariance at elevated temperatures.

Higher PUFA and omega-3 PUFA, CLA, α-tocopherol and iron, but lower iodine and selenium concentrations in organic milk: a systematic literature review and meta- and redundancy analyses

Demand for organic milk is partially driven by consumer perceptions that it is more nutritious. However, there is still considerable uncertainty over whether the use of organic production standards affects milk quality. Here we report results of meta-analyses based on 170 published studies comparing the nutrient content of organic and conventional bovine milk. There were no significant differences in total SFA and MUFA concentrations between organic and conventional milk. However, concentrations of total PUFA and n-3 PUFA were significantly higher in organic milk, by an estimated 7 (95 % CI −1, 15) % and 56 (95 % CI 38, 74) %, respectively. Concentrations of α-linolenic acid (ALA), very long-chain n-3 fatty acids (EPA+DPA+DHA) and conjugated linoleic acid were also significantly higher in organic milk, by an 69 (95 % CI 53, 84) %, 57 (95 % CI 27, 87) % and 41 (95 % CI 14, 68) %, respectively. As there were no significant differences in total n-6 PUFA and linoleic acid (LA) concentrations, the n-6:n-3 and LA:ALA ratios were lower in organic milk, by an estimated 71 (95 % CI −122, −20) % and 93 (95 % CI −116, −70) %. It is concluded that organic bovine milk has a more desirable fatty acid composition than conventional milk. Meta-analyses also showed that organic milk has significantly higher α-tocopherol and Fe, but lower I and Se concentrations. Redundancy analysis of data from a large cross-European milk quality survey indicates that the higher grazing/conserved forage intakes in organic systems were the main reason for milk composition differences.