Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

MB-MDR: Model-Based Multifactor Dimensionality Reduction for detecting interactions in high-dimensional genomic data

L’anàlisi de l’efecte dels gens i els factors ambientals en el desenvolupament de malalties complexes és un gran repte estadístic i computacional. Entre les diverses metodologies de mineria de dades que s’han proposat per a l’anàlisi d’interaccions una de les més populars és el mètode Multifactor Dimensionality Reduction, MDR, (Ritchie i al. 2001). L’estratègia d’aquest mètode és reduir la dimensió multifactorial a u mitjançant l’agrupació dels diferents genotips en dos grups de risc: alt i baix. Tot i la seva utilitat demostrada, el mètode MDR té alguns inconvenients entre els quals l’agrupació excessiva de genotips pot fer que algunes interaccions importants no siguin detectades i que no permet ajustar per efectes principals ni per variables confusores. En aquest article il•lustrem les limitacions de l’estratègia MDR i d’altres aproximacions no paramètriques i demostrem la conveniència d’utilitzar metodologies parametriques per analitzar interaccions en estudis cas-control on es requereix l’ajust per variables confusores i per efectes principals. Proposem una nova metodologia, una versió paramètrica del mètode MDR, que anomenem Model-Based Multifactor Dimensionality Reduction (MB-MDR). La metodologia proposada té com a objectiu la identificació de genotips específics que estiguin associats a la malaltia i permet ajustar per efectes marginals i variables confusores. La nova metodologia s’il•lustra amb dades de l’Estudi Espanyol de Cancer de Bufeta.

Glucose-dependent insulinotropic polypeptide receptor deficiency leads to modifications of trabecular bone volume and quality in mice.

A role for the gastro-intestinal tract in controlling bone remodeling is suspected since serum levels of bone remodeling markers are affected rapidly after a meal. Glucose-dependent insulinotropic polypeptide (GIP) represents a suitable candidate in mediating this effect. The aim of the present study was to investigate the effect of total inhibition of GIP signaling on trabecular bone volume, microarchitecture and quality. We used GIP receptor (GIPR) knockout mice and investigated trabecular bone volume and microarchitecture by microCT and histomorphometry. GIPR-deficient animals at 16 weeks of age presented with a significant (20%) increase in trabecular bone mass accompanied by an increase (17%) in trabecular number. In addition, the number of osteoclasts and bone formation rate was significantly reduced and augmented, respectively in these animals when compared with wild-type littermates. These modifications of trabecular bone microarchitecture are linked to a remodeling in the expression pattern of adipokines in the GIPR-deficient mice. On the other hand, despite significant enhancement in bone volume, intrinsic mechanical properties of the bone matrix was reduced as well as the distribution of bone mineral density and the ratio of mature/immature collagen cross-links. Taken together, these results indicate an increase in trabecular bone volume in GIPR KO animals associated with a reduction in bone quality.

Pharmacokinetics and pharmacogenomics of once-daily raltegravir and atazanavir in healthy volunteers.

Atazanavir inhibits UDP-glucuronyl-transferase-1A1 (UGT1A1), which metabolizes raltegravir, but the magnitude of steady-state inhibition and role of the UGT1A1 genotype are unknown. Sufficient inhibition could lead to reduced-dose and -cost raltegravir regimens. Nineteen healthy volunteers, age 24 to 51 years, took raltegravir 400 mg twice daily (arm A) and 400 mg plus atazanavir 400 mg once daily (arm B), separated by ?3 days, in a crossover design. After 1 week on each regimen, raltegravir and raltegravir-glucuronide plasma and urine concentrations were measured by liquid chromatography-tandem mass spectrometry in multiple samples obtained over 12 h (arm A) or 24 h (arm B) and analyzed by noncompartmental methods. UGT1A1 promoter variants were detected with a commercially available kit and published primers. The primary outcome was the ratio of plasma raltegravir C(tau), or concentration at the end of the dosing interval, for arm B (24 h) versus arm A (12 h). The arm B-to-arm A geometric mean ratios (95% confidence interval, P value) for plasma raltegravir C(tau), area under the concentration-time curve from 0 to 12 h (AUC(0-12)), and raltegravir-glucuronide/raltegravir AUC(0-12) were 0.38 (0.22 to 0.65, 0.001), 1.32 (0.62 to 2.81, 0.45), and 0.47 (0.38 to 0.59, <0.001), respectively. Nine volunteers were heterozygous and one was homozygous for a UGT1A1 reduction-of-function allele, but these were not associated with metabolite formation. Although atazanavir significantly reduced the formation of the glucuronide metabolite, its steady-state boosting of plasma raltegravir did not render the C(tau) with a once-daily raltegravir dose of 400 mg similar to the C(tau) with the standard twice-daily dose. UGT1A1 promoter variants did not significantly influence this interaction.

Label Space Reduction in All-Optical Label Switchiing Networks

Report for the scientific sojourn at the Department of Information Technology (INTEC) at the Ghent University, Belgium, from january to june 2007. All-Optical Label Swapping (AOLS) forms a key technology towards the implementation of All-Optical Packet Switching nodes (AOPS) for the future optical Internet. The capital expenditures of the deployment of AOLS increases with the size of the label spaces (i.e. the number of used labels), since a special optical device is needed for each recognized label on every node. Label space sizes are affected by the wayin which demands are routed. For instance, while shortest-path routing leads to the usage of fewer labels but high link utilization, minimum interference routing leads to the opposite. This project studies and proposes All-Optical Label Stacking (AOLStack), which is an extension of the AOLS architecture. AOLStack aims at reducing label spaces while easing the compromise with link utilization. In this project, an Integer Lineal Program is proposed with the objective of analyzing the softening of the aforementioned trade-off due to AOLStack. Furthermore, a heuristic aiming at finding good solutions in polynomial-time is proposed as well. Simulation results show that AOLStack either a) reduces the label spaces with a low increase in the link utilization or, similarly, b) uses better the residual bandwidth to decrease the number of labels even more.

Metabolic and respiratory effects of infused sodium acetate in healthy human subjects.

The metabolic and respiratory effects of intravenous 0.5 M sodium acetate (at a rate of 2.5 mmol/min during 120 min) were studied in nine normal human subjects. O2 consumption (VO2) and CO2 production (VCO2) were measured continuously by open-circuit indirect calorimetry. VO2 increased from 251 +/- 9 to 281 +/- 9 ml/min (P < 0.001), energy expenditure increased from 4.95 +/- 0.17 kJ/min baseline to 5.58 +/- 0.16 kJ/min (P < 0.001), and VCO2 decreased nonsignificantly (211 +/- 7 ml/min vs. 202 +/- 7 ml/min, NS). The extrapulmonary CO2 loss (i.e., bicarbonate generation and excretion) was estimated at 48 +/- 5 ml/min. This observation is consistent with 1 mol of bicarbonate generated from 1 mol of acetate metabolized. Alveolar ventilation decreased from 3.5 +/- 0.2 l/min basal to 3.1 +/- 0.2 l/min (P < 0.001). The minute ventilation (VE) to VO2 ratio decreased from 22.9 +/- 1.3 to 17.6 +/- 0.9 l/l (P < 0.005), arterial PO2 decreased from 93.2 +/- 1.9 to 78.7 +/- 1.6 mmHg (P < 0.0001), arterial PCO2 increased from 39.2 +/- 0.7 to 42.1 +/- 1.1 mmHg (P < 0.0001), pH from 7.40 +/- 0.005 to 7.50 +/- 0.007 (P < 0.005), and arterial bicarbonate concentration from 24.2 +/- 0.7 to 32.9 +/- 1.1 (P < 0.0001). These observations indicate that sodium acetate infusion results in substantial extrapulmonary CO2 loss, which leads to a relative decrease of total and alveolar ventilation.

Detection of testosterone administration based on the carbon isotope ratio profiling of endogenous steroids: international reference populations of professional soccer players.

BACKGROUND AND OBJECTIVES: The determination of the carbon isotope ratio in androgen metabolites has been previously shown to be a reliable, direct method to detect testosterone misuse in the context of antidoping testing. Here, the variability in the 13C/12C ratios in urinary steroids in a widely heterogeneous cohort of professional soccer players residing in different countries (Argentina, Italy, Japan, South Africa, Switzerland and Uganda) is examined. METHODS: Carbon isotope ratios of selected androgens in urine specimens were determined using gas chromatography/combustion/isotope ratio mass spectrometry (GC-C-IRMS). RESULTS: Urinary steroids in Italian and Swiss populations were found to be enriched in 13C relative to other groups, reflecting higher consumption of C3 plants in these two countries. Importantly, detection criteria based on the difference in the carbon isotope ratio of androsterone and pregnanediol for each population were found to be well below the established threshold value for positive cases. CONCLUSIONS: The results obtained with the tested diet groups highlight the importance of adapting the criteria if one wishes to increase the sensitivity of exogenous testosterone detection. In addition, confirmatory tests might be rendered more efficient by combining isotope ratio mass spectrometry with refined interpretation criteria for positivity and subject-based profiling of steroids.

An extension of the Marsden-Ratiu reduction for Poisson manifolds

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure effectively dependent on the distribution. Different applications are discussed, as well as the algebraic interpretation of the procedure and its formulation in terms of Dirac structures.

Fatigue et réduction de la performance motrice chez le sportif, syndrome de surentraînement [Fatigue and reduction in motor performance in sportspeople or overtraining syndrome].

The main goal of training activities is to improve motor performance. After strenuous workouts, it is physiological to experience fatigue, which relieves within two weeks, and then induce an improvement in motor capacities. An overtraining syndrome is diagnosed when fatigue is postponed beyond two weeks, and affects mainly endurance athletes. It is a condition of chronic fatigue, underperformance and an increased vulnerability to infection leading to recurrent infections. The whole observed spectrum of symptoms is physiological, psychological, endocrinogical and immunological. All play a role in the failure to recover. Monitoring of athletes activities helps to prevent the syndrome with days with no sports. Rest, patience and empathy are the only ways of treatment options.

Is the consumption-income ratio stationary? Evidence from linear and nonlinear panel unit root tests for OECD and non-OECD countries

This paper applies recently developed heterogeneous nonlinear and linear panel unit root tests that account for cross-sectional dependence to 24 OECD and 33 non-OECD countries’ consumption-income ratios over the period 1951–2003. We apply a recently developed methodology that facilitates the use of panel tests to identify which individual cross-sectional units are stationary and which are nonstationary. This extends evidence provided in the recent literature to consider both linear and nonlinear adjustment in panel unit root tests, to address the issue of cross-sectional dependence, and to substantially expand both time-series and cross sectional dimensions of the data analysed. We find that the majority (65%) of the series are nonstationary with slightly fewer OECD countries’ (61%) series exhibiting a unit root than non-OECD countries (68%).

Measurement of 13CO2 in expired air as an index of compliance to a high carbohydrate diet naturally enriched in 13C.

The aim of this study was to determine whether breath 13CO2 measurements could be used to assess the compliance to a diet containing carbohydrates naturally enriched in 13C. The study was divided into two periods: Period 1 (baseline of 4 days) with low 13C/12C ratio carbohydrates. Period 2 (5 days) isocaloric diet with a high 13C/12C ratio (corn, cane sugar, pineapple, millet) carbohydrates. Measurements were made of respiratory gas exchange by indirect calorimetry, urinary nitrogen excretion and breath 13CO2 every morning in post-absorptive conditions, both in resting state and during a 45-min low intensity exercise (walking on a treadmill). The subjects were 10 healthy lean women (BMI 20.4 +/- 1.7 kg/m2, % body fat 24.4 +/- 1.3%), the 13C enrichment of oxidized carbohydrate and breath 13CO2 were compared to the enrichment of exogenous dietary carbohydrates. At rest the enrichment of oxidized carbohydrate increased significantly after one day of 13C carbohydrate enriched diet and reached a steady value (103 +/- 16%) similar to the enrichment of exogenous carbohydrates. During exercise, the 13C enrichment of oxidized carbohydrate remained significantly lower (68 +/- 17%) than that of dietary carbohydrates. The compliance to a diet with a high content of carbohydrates naturally enriched in 13C may be assessed from the measurement of breath 13CO2 enrichment combined with respiratory gas exchange in resting, postabsorptive conditions.

The use of the likelihood ratio for evaluative and investigative purposes in comparative forensic handwriting examination

This paper extends previous research and discussion on the use of multivariate continuous data, which are about to become more prevalent in forensic science. As an illustrative example, attention is drawn here on the area of comparative handwriting examinations. Multivariate continuous data can be obtained in this field by analysing the contour shape of loop characters through Fourier analysis. This methodology, based on existing research in this area, allows one describe in detail the morphology of character contours throughout a set of variables. This paper uses data collected from female and male writers to conduct a comparative analysis of likelihood ratio based evidence assessment procedures in both, evaluative and investigative proceedings. While the use of likelihood ratios in the former situation is now rather well established (typically, in order to discriminate between propositions of authorship of a given individual versus another, unknown individual), focus on the investigative setting still remains rather beyond considerations in practice. This paper seeks to highlight that investigative settings, too, can represent an area of application for which the likelihood ratio can offer a logical support. As an example, the inference of gender of the writer of an incriminated handwritten text is forwarded, analysed and discussed in this paper. The more general viewpoint according to which likelihood ratio analyses can be helpful for investigative proceedings is supported here through various simulations. These offer a characterisation of the robustness of the proposed likelihood ratio methodology.

Class-size Reduction Policies and the Quality of Entering Teachers

State-wide class-size reduction (CSR) policies have typically failed to produce large achievement gains. One explanation is that the introduction of such policies forces schools to hire relatively low-quality teachers. This paper uses data from an anonymous state to explore whether teacher quality suff ered from the introduction of CSR. We find that it did, but not nearly enough to explain the small achievement effects of CSR. The combined fall in achievement due to hiring lower quality teachers and more inexperienced teachers is small relative to the unrealized gains. Furthermore, between-school diff erences in the quality of incoming teachers cannot explain the poor estimated CSR performance from previous quasi-experimental treatment-control comparisons.