450 research outputs found

    Time-optimal path planning in dynamic flows using level set equations: theory and schemes

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    We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.United States. Office of Naval Research (Grant N00014-09-1-0676 (Science of Autonomy - A-MISSION))United States. Office of Naval Research (Grant N00014-12-1-0944 (ONR6.2))Natural Sciences and Engineering Research Council of Canada (Postgraduate Fellowship

    Generalized Huygens principle with pulsed-beam wavelets

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    Huygens' principle has a well-known problem with back-propagation due to the spherical nature of the secondary wavelets. We solve this by analytically continuing the surface of integration. If the surface is a sphere of radius RR, this is done by complexifying RR to R+iaR+ia. The resulting complex sphere is shown to be a real bundle of disks with radius aa tangent to the sphere. Huygens' "secondary source points" are thus replaced by disks, and his spherical wavelets by well-focused pulsed beams propagating outward. This solves the back-propagation problem. The extended Huygens principle is a completeness relation for pulsed beams, giving a representation of a general radiation field as a superposition of such beams. Furthermore, it naturally yields a very efficient way to compute radiation fields because all pulsed beams missing a given observer can be ignored. Increasing aa sharpens the focus of the pulsed beams, which in turn raises the compression of the representation.Comment: 49 pages, 14 figure

    Differential Adaptation of Human Gut Microbiota to Bariatric Surgery–Induced Weight Loss: Links With Metabolic and Low-Grade Inflammation Markers

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    International audienceOBJECTIVE Obesity alters gut microbiota ecology and associates with low-grade inflammation in humans. Roux-en-Y gastric bypass (RYGB) surgery is one of the most efficient procedures for the treatment of morbid obesity resulting in drastic weight loss and improvement of metabolic and inflammatory status. We analyzed the impact of RYGB on the modifications of gut microbiota and examined links with adaptations associated with this procedure. RESEARCH DESIGN AND METHODS Gut microbiota was profiled from fecal samples by real-time quantitative PCR in 13 lean control subjects and in 30 obese individuals (with seven type 2 diabetics) explored before (M0), 3 months (M3), and 6 months (M6) after RYGB. RESULTS Four major findings are highlighted: 1) Bacteroides/Prevotella group was lower in obese subjects than in control subjects at MO and increased at M3. It was negatively correlated with corpulence, but the correlation depended highly on caloric intake; 2) Escherichia coli species increased at M3 and inversely correlated with fat mass and leptin levels independently of changes in food intake; 3) lactic acid bacteria including Lacto-bacillus/Leuconostoc/Pediococcus group and Bifidobacterium genus decreased at M3; and 4) Faecalibacterium prausnitzii species was lower in subjects with diabetes and associated negatively with inflammatory markers at MO and throughout the follow-up after surgery independently of changes in food intake. CONCLUSIONS These results suggest that components of the dominant gut microbiota rapidly adapt in a starvation-like situation induced by RYGB while the F. prausnitzii species is directly linked to the reduction in low-grade inflammation state in obesity and diabetes independently of calorie intake. Diabetes 59:3049-3057, 201
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