On the Hausdorff volume in sub-Riemannian geometry

For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous function. We then prove that up to dimension 4 it is smooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4 on every smooth curve) but in general not C^5. These results answer to a question addressed by Montgomery about the relation between two intrinsic volumes that can be defined in a sub-Riemannian manifold, namely the Popp and the Hausdorff volume. If the nilpotent approximation depends on the point (that may happen starting from dimension 5), then they are not proportional, in general.Comment: Accepted on Calculus and Variations and PD

Continuity of Optimal Control Costs and its application to Weak KAM Theory

We prove continuity of certain cost functions arising from optimal control of affine control systems. We give sharp sufficient conditions for this continuity. As an application, we prove a version of weak KAM theorem and consider the Aubry-Mather problems corresponding to these systems.Comment: 23 pages, 1 figures, added explanations in the proofs of the main theorem and the exampl

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Effectiveness and cost-effectiveness of daily all-over-body application of emollient during the first year of life for preventing atopic eczema in high-risk children (The BEEP trial): protocol for a randomised controlled trial.

BACKGROUND: Atopic eczema (AE) is a common skin problem that impairs quality of life and is associated with the development of other atopic diseases including asthma, food allergy and allergic rhinitis. AE treatment is a significant cost burden for health care providers. The purpose of the trial is to investigate whether daily application of emollients for the first year of life can prevent AE developing in high-risk infants (first-degree relative with asthma, AE or allergic rhinitis). METHODS: This is a protocol for a pragmatic, two-arm, randomised controlled, multicentre trial. Up to 1400 term infants at high risk of developing AE will be recruited through the community, primary and secondary care in England. Participating families will be randomised in a 1:1 ratio to receive general infant skin-care advice, or general skin-care advice plus emollients with advice to apply daily to the infant for the first year of life. Families will not be blinded to treatment allocation. The primary outcome will be a blinded assessment of AE at 24 months of age using the UK Working Party Diagnostic Criteria for Atopic Eczema. Secondary outcomes are other definitions of AE, time to AE onset, severity of AE (EASI and POEM), presence of other allergic diseases including food allergy, asthma and hay fever, allergic sensitisation, quality of life, cost-effectiveness and safety of the emollients. Subgroup analyses are planned for the primary outcome according to filaggrin genotype and the number of first-degree relatives with AE and other atopic diseases. Families will be followed up by online and postal questionnaire at 3, 6, 12 and 18 months with a face-to-face visit at 24 months. Long-term follow-up until 60 months will be via annual questionnaires. DISCUSSION: This trial will demonstrate whether skin-barrier enhancement through daily emollient for the first year of life can prevent AE from developing in high-risk infants. If effective, this simple and cheap intervention has the potential to result in significant cost savings for health care providers throughout the world by preventing AE and possibly other associated allergic diseases. TRIAL REGISTRATION: ISRCTN registry; ID: ISRCTN21528841 . Registered on 25 July 2014

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Sedentary time and markers of inflammation in people with newly diagnosed type 2 diabetes

AbstractBackground and aimsWe investigated whether objectively measured sedentary time was associated with markers of inflammation in adults with newly diagnosed type 2 diabetes.Methods and resultsWe studied 285 adults (184 men, 101 women, mean age 59.0 ± 9.7) who had been recruited to the Early ACTivity in Diabetes (Early ACTID) randomised controlled trial. C-reactive protein (CRP), adiponectin, soluble intracellular adhesion molecule-1 (sICAM-1), interleukin-6 (IL-6), and accelerometer-determined sedentary time and moderate-vigorous physical activity (MVPA) were measured at baseline and after six-months. Linear regression analysis was used to investigate the independent cross-sectional and longitudinal associations of sedentary time with markers of inflammation.At baseline, associations between sedentary time and IL-6 were observed in men and women, an association that was attenuated following adjustment for waist circumference. After 6 months of follow-up, sedentary time was reduced by 0.4 ± 1.2 h per day in women, with the change in sedentary time predicting CRP at follow-up. Every hour decrease in sedentary time between baseline and six-months was associated with 24% (1, 48) lower CRP. No changes in sedentary time between baseline and 6 months were seen in men.ConclusionsHigher sedentary time is associated with IL-6 in men and women with type 2 diabetes, and reducing sedentary time is associated with improved levels of CRP in women. Interventions to reduce sedentary time may help to reduce inflammation in women with type 2 diabetes

Eicosapentaenoic acid and aspirin, alone and in combination, for the prevention of colorectal adenomas (seAFOod Polyp Prevention trial): a multicentre, randomised, double-blind, placebo-controlled, 2 × 2 factorial trial

YesBackground: The omega-3 polyunsaturated fatty acid eicosapentaenoic acid (EPA) and aspirin both have proof of concept for colorectal cancer chemoprevention, aligned with an excellent safety profile. Therefore, we aimed to test the efficacy of EPA and aspirin, alone and in combination and compared with a placebo, in individuals with sporadic colorectal neoplasia detected at colonoscopy. Methods: In a multicentre, randomised, double-blind, placebo-controlled, 2 × 2 factorial trial, patients aged 55–73 years who were identified during colonoscopy as being at high risk in the English Bowel Cancer Screening Programme (BCSP; ≥3 adenomas if at least one was ≥10 mm in diameter or ≥5 adenomas if these were <10 mm in diameter) were recruited from 53 BCSP endoscopy units in England, UK. Patients were randomly allocated (1:1:1:1) using a secure web-based server to receive 2 g EPA-free fatty acid (FFA) per day (either as the FFA or triglyceride), 300 mg aspirin per day, both treatments in combination, or placebo for 12 months using random permuted blocks of randomly varying size, and stratified by BCSP site. Research staff and participants were masked to group assignment. The primary endpoint was the adenoma detection rate (ADR; the proportion of participants with any adenoma) at 1 year surveillance colonoscopy analysed in all participants with observable follow-up data using a so-called at-the-margins approach, adjusted for BCSP site and repeat endoscopy at baseline. The safety population included all participants who received at least one dose of study drug. The trial is registered with the International Standard Randomised Controlled Trials Number registry, number ISRCTN05926847. Findings: Between Nov 11, 2011, and June 10, 2016, 709 participants were randomly assigned to four treatment groups (176 to placebo, 179 to EPA, 177 to aspirin, and 177 to EPA plus aspirin). Adenoma outcome data were available for 163 (93%) patients in the placebo group, 153 (85%) in the EPA group, 163 (92%) in the aspirin group, and 161 (91%) in the EPA plus aspirin group. The ADR was 61% (100 of 163) in the placebo group, 63% (97 of 153) in the EPA group, 61% (100 of 163) in the aspirin group, and 61% (98 of 161) in the EPA plus aspirin group, with no evidence of any effect for EPA (risk ratio [RR] 0·98, 95% CI 0·87 to 1·12; risk difference –0·9%, –8·8 to 6·9; p=0·81) or aspirin (RR 0·99 (0·87 to 1·12; risk difference –0·6%, –8·5 to 7·2; p=0·88). EPA and aspirin were well tolerated (78 [44%] of 176 had ≥1 adverse event in the placebo group compared with 82 [46%] in the EPA group, 68 [39%] in the aspirin group, and 76 [45%] in the EPA plus aspirin group), although the number of gastrointestinal adverse events was increased in the EPA alone group at 146 events (compared with 85 in the placebo group, 86 in the aspirin group, and 68 in the aspirin plus placebo group). Six upper-gastrointestinal bleeding events were reported across the treatment groups (two in the EPA group, three in the aspirin group, and one in the placebo group). Interpretation Neither EPA nor aspirin treatment were associated with a reduction in the proportion of patients with at least one colorectal adenoma. Further research is needed regarding the effect on colorectal adenoma number according to adenoma type and location. Optimal use of EPA and aspirin might need a precision medicine approach to adenoma recurrence.Efficacy and Mechanism Evaluation Programme, a UK Medical Research Council and National Institute for Health Research partnership.Research Development Fund Publication Prize Award winner, November 2018

Evidence of Color Coherence Effects in W+jets Events from ppbar Collisions at sqrt(s) = 1.8 TeV

We report the results of a study of color coherence effects in ppbar collisions based on data collected by the D0 detector during the 1994-1995 run of the Fermilab Tevatron Collider, at a center of mass energy sqrt(s) = 1.8 TeV. Initial-to-final state color interference effects are studied by examining particle distribution patterns in events with a W boson and at least one jet. The data are compared to Monte Carlo simulations with different color coherence implementations and to an analytic modified-leading-logarithm perturbative calculation based on the local parton-hadron duality hypothesis.Comment: 13 pages, 6 figures. Submitted to Physics Letters

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) ows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several special applications in heliophysics and astrophysics, assessing triumphs, challenges,and future directions