Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras

Darboux coordinates are constructed on rational coadjoint orbits of the positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by the values of the spectral parameters at the divisors corresponding to eigenvector line bundles over the associated spectral curves, defined within a given matrix representation. A Liouville generating function is obtained in completely separated form and shown, through the Liouville-Arnold integration method, to lead to the Abel map linearization of all Hamiltonian flows induced by the spectral invariants. Serre duality is used to define a natural symplectic structure on the space of line bundles of suitable degree over a permissible class of spectral curves, and this is shown to be equivalent to the Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general construction is given for $\frak{g}=\frak{gl}(r)$ or $\frak{sl}(r)$, with reductions to orbits of subalgebras determined as invariant fixed point sets under involutive automorphisms. The case $\frak{g=sl}(2)$ is shown to reproduce the classical integration methods for finite dimensional systems defined on quadrics, as well as the quasi-periodic solutions of the cubically nonlinear Schr\"odinger equation. For $\frak{g=sl}(3)$, the method is applied to the computation of quasi-periodic solutions of the two component coupled nonlinear Schr\"odinger equation.Comment: 61 pg

Optimisation of Nutrient Supply for Beef Cattle Fed Grass or Silage.

End of Project ReportSince forage forms a large part of growing ruminant rations in Ireland, the trust of this project was to examine the effect of ensilage on ruminal digestion of grass and to examine ruminal microbial protein and intestinally absorbable protein supplied by grass and/or clover. A range of in vitro and in vivo techniques were employed and strategies used by commercial beef producers to optimise cattle growth (and nutrient supply) were also documented. To accomplish the aims of this project, a range of methodology developments/ modifications in vitro and in vivo was carried out. From in vitro methodology development it was concluded that : (i) Compared with fresh silage, drying per se may give artifically higher rates of dry matter (DM) digestion. (ii) Greater experimental precision can be obtained by ensuring a greater substrate surface area to reaction volume ratio in each reaction vessel. (iii) For studies where the rate of digestion is of greatest importance, pre-incubation of frozen inoculum in a nutrient medium best simulated the cellulolytic activity of unfrozen inoculum. In studies that require large volumes of inoculum for extended work, freezing directly is justified. (iv) Neutral detergent extraction altered in vitro digestion characteristics of silage. The residue after washing with water at 70°C has a high residual fibre concentration and is more representative of the structural components of silage ingested by ruminants. (v) A semi-continuous culture system developed at Grange Research Centre can successfully model in vitro ruminal digestion of fibre and starch-based diets in a controlled environment. From in vivo methodology development it was concluded that : (i) Oven drying at 60°C and correction for loss of volatiles gives a good estimation of DM concentration of ruminal particulate digesta. This procedure has the added advantage that drying at 60°C allows the residual materials to be analysed for fibre fractions without concern for heat damage which can occur at a higher drying temperature. (ii) A naso-ruminal sampling device can be used to measure the relative patterns of fermentation of contrasting diet types when in situ for up to 7 days. (ii) Application of a vacuum to withdraw samples had no negative effect on ruminal fluid variables. From in vitro studies on grass digestion, it was concluded that : (i) Ensiling of grass decreased the apparent extent of digestion of cell walls when in the presence of the whole plant and that this largely reflected an increase in the lag time before digestion commenced. (ii) Ensiling of grass did not negatively affect the digestion of isolated cell walls. (iii) There is a negative impact of ensiling on microbial protein production from the water soluble carbohydrate fraction of grass. (iv) Supplementation with the water soluble fraction of grass significantly improved the apparent extent of digestion for ensiled forages when compared with the supplementation of the post-ensiling fraction in a batch culture system. (v) There is a negative impact of maturity on the pattern of cell wall fermentation and that this impact can be decreased by ensiling method. From studies on herbage digestion in vivo it was concluded that : (i) Grass silage type had a greater effect than the rate of concentrate fermentation on ruminal microbal protein synthesis. (ii) Harvesting time had a bigger impact on nutrient supply from herbage than sward type (grass or grass/clover). (iii) Increasing clover content in the herbage decreased the biological value (g nitrogen retained/kg absorbed) of dietary protein. Diverse stratgies were used on commercial beef farms to optimise nutrient supply and animal growth. Average animal performance on individual farms was not better than would be typically recorded in a research environment. There was scope on many of the farms to improve technical performance and to decrease the costs of production.European Union Structural Funds (EAGGF

Comparison of the cardiometabolic profiles of adolescents conceived through ART with those of a non-ART cohort

STUDY QUESTION Is the cardiometabolic health of adolescents conceived through ART worse than that of their counterparts conceived without ART? SUMMARY ANSWER The majority of cardiometabolic and vascular health parameters of adolescents conceived through ART are similar or more favourable, than those of their counterparts of similar age and conceived without ART. WHAT IS KNOWN ALREADY It has been proposed that the cardiometabolic health of offspring conceived with ART may be unfavourable compared to that of their counterparts conceived without ART. The literature pertaining to cardiometabolic health of offspring conceived after ART is contradictory, but generally suggests unfavourable cardiometabolic health parameters, such as an increase in blood pressure (BP), vascular dysfunction and adiposity, as well as unfavourable glucose and lipid profiles. With over 8 million children and adults born through ART worldwide, it is important to investigate whether these early signs of adverse cardiometabolic differences persist into adolescence and beyond. STUDY DESIGN, SIZE, DURATION The Growing Up Healthy Study (GUHS) is a prospective cohort study that recruited 303 adolescents and young adults conceived after ART (aged 13–21 years) and born between 1991 and 2001 in Western Australia. Their health parameters, including cardiometabolic factors, were assessed and compared with counterparts from the Raine Study Generation 2 (Gen2). The 2868 Gen2 participants were born 1989–1992 and are representative of the Western Australian adolescent population. At ∼17 years of age (2013–2017), 163 GUHS participants replicated assessments previously completed by Gen2 at a similar age. PARTICIPANTS/MATERIALS, SETTING, METHODS Cardiometabolic parameters were compared between a total of 163 GUHS and 1457 Gen2 adolescents. Separate male (GUHS n = 81, Gen2 n = 735) and female (GUHS n = 82, Gen2 n = 722) analyses were conducted. Assessments consisted of a detailed questionnaire including health, lifestyle and demographic parameters, anthropometric assessments (height, weight, BMI, waist circumference and skinfold thickness), fasting serum biochemistry, arterial stiffness and BP (assessed using applanation tonometry). Abdominal ultrasonography was used to assess the presence and severity of hepatic steatosis, and thickness of abdominal fat compartments. Non-alcoholic fatty liver disease (NAFLD) was diagnosed if there was sonographic fatty liver in the absence of significant alcohol consumption. Chi2, Fisher’s exact and Mann–Whitney U tests, performed in SPSS V25, examined cohort differences and generalized estimating equations adjusted for the following covariates: singleton vs non-singleton pregnancy, birthweight (z-score), gestational age, BMI, smoking, alcohol consumption in the past 6 months and parent cardiovascular status. Arterial stiffness measures and waist circumference were additionally adjusted for height, and female analyses were additionally adjusted for use of oral contraceptives in the preceding 6 months. MAIN RESULTS AND THE ROLE OF CHANCE In adjusted analyses, GUHS females had a lower BMI (22.1 vs 23.3 kg/m2, P = 0.014), and thinner skinfolds (triceps, subscapular, mid-abdominal; 16.9 vs 18.7 mm, P = 0.021, 13.4 vs 15.0 mm, P = 0.027, 19.7 vs 23.2 mm, P < 0.001, respectively), whereas males were not significantly different. Waist circumference was lower in GUHS adolescents (males: 78.1 vs 81.3 cm, P = 0.008, females: 76.7 vs 83.3 cm, P = 0.007). There were no significant differences between the two groups in glucose, insulin, homeostatic model assessment for insulin resistance, low-density lipoprotein cholesterol, non-high-density lipoprotein cholesterol (non-HDL-C), total cholesterol (TC), alanine aminotransferase and high-sensitivity C-reactive protein in both sexes. In females, serum triglycerides were lower in GUHS adolescents (1.0 vs 1.2 mmol/l, P = 0.029). GUHS males had higher serum HDL-C (1.1 vs 1.0 mmol/l, P = 0.004) and a lower TC/HDL-C ratio (3.2 vs 3.6, P = 0.036). There were no significant differences in the prevalence of NAFLD or steatosis severity scores between the cohorts in males and females. GUHS females had less subcutaneous adipose tissue (9.4 vs 17.9 mm, P < 0.001), whereas GUHS males had greater visceral adipose thickness (44.7 vs 36.3 mm, P < 0.001). There was no significant difference in pre-peritoneal adipose thickness. Pulse wave velocity was lower in GUHS males (5.8 vs 6.3 m/s, P < 0.001) and heart rate corrected augmentation index was lower in GUHS females (−8.4 vs −2.7%, P = 0.048). There were no significant differences in BP or heart rate in males or females between the two groups. LIMITATIONS, REASONS FOR CAUTION Despite the substantial study size and the unique study design of the ART cohort, we were unable to differentiate between different types of ART, due to the low number of ICSI cycles (e.g. IVF vs ICSI), draw definite conclusions, or relate the outcomes to the cause of infertility. Considering the differences in time points when both cohorts were studied, external factors could have changed, which could not be accounted for. Given the observational nature of this study, causation cannot be proven. WIDER IMPLICATIONS OF THE FINDINGS Contrary to our hypothesis and previous findings focussing mainly on childhood, this study reports mostly similar or favourable cardiometabolic markers in adolescents conceived with ART compared to those conceived without ART. The greater visceral adipose thickness, particularly present in males, requires further investigation. While these findings are generally reassuring, future well-designed and appropriately powered studies are required to definitively address the issue of cardiometabolic health in ART adults. STUDY FUNDING/COMPETING INTEREST(S) This project was supported by NHMRC project grant number 1042269 and R.J.H. received education grant funding support from Ferring Pharmaceuticals. R.J.H. is the Medical Director of Fertility Specialists of Western Australia and a shareholder in Western IVF. He has received educational sponsorship from MSD, Merck-Serono and Ferring Pharmaceuticals. P.B. is the Scientific Director of Concept Fertility Centre, Subiaco, Western Australia. J.L.Y. is the Medical Director of PIVET Medical Centre, Perth, Western Australia

Boost Invariance and Multiplicity Dependence of the Charge Balance Functionin π+p\pi^{+}p and K+pK^{+}p Collisions at s=22\sqrt s= 22 GeV/c

Boost invariance and multiplicity dependence of the charge balance function are studied in \pi^{+}\rp and \rK^{+}\rp collisions at 250 GeV/$c$ incident beam momentum. Charge balance, as well as charge fluctuations, are found to be boost invariant over the whole rapidity region, but both depend on the size of the rapidity window. It is also found that the balance function becomes narrower with increasing multiplicity, consistent with the narrowing of the balance function when centrality and/or system size increase, as observed in current relativistic heavy ion experiments.Comment: 4 pages, 5 figures, Revte

Leading strategies in competitive on-line prediction

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.Comment: 20 pages; a conference version is to appear in the ALT'2006 proceeding

Entropic Interactions in Suspensions of Semi-Flexible Rods: Short-Range Effects of Flexibility

We compute the entropic interactions between two colloidal spheres immersed in a dilute suspension of semi-flexible rods. Our model treats the semi-flexible rod as a bent rod at fixed angle, set by the rod contour and persistence lengths. The entropic forces arising from this additional rotational degree of freedom are captured quantitatively by the model, and account for observations at short range in a recent experiment. Global fits to the interaction potential data suggest the persistence length of fd-virus is about two to three times smaller than the commonly used value of $2.2 \mu {m}$.Comment: 4 pages, 5 figures, submitted to PRE rapid communication

Nonlocal Equation of State in Anisotropic Static Fluid Spheres in General Relativity

We show that it is possible to obtain credible static anisotropic spherically symmetric matter configurations starting from known density profiles and satisfying a nonlocal equation of state. These particular types of equation of state describe, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. To establish the physical plausibility of the proposed family of solutions satisfying nonlocal equation of state, we study the constraints imposed by the junction and energy conditions on these bounded matter distributions. We also show that it is possible to obtain physically plausible static anisotropic spherically symmetric matter configurations, having nonlocal equations of state\textit{,}concerning the particular cases where the radial pressure vanishes and, other where the tangential pressures vanishes. The later very particular type of relativistic sphere with vanishing tangential stresses is inspired by some of the models proposed to describe extremely magnetized neutron stars (magnetars) during the transverse quantum collapse.Comment: 21 pages, 1 figure, minor changes in the text, references added, two new solutions studie