Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals

We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the `Ruijsenaars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BC(n) generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.Comment: Extended version of talk at the conference "Geometry, Integrability and Quantization XIV" (Varna, June 2012), 15 page

Trigonometric Sutherland systems and their Ruijsenaars duals from symplectic reduction

Besides its usual interpretation as a system of $n$ indistinguishable particles moving on the circle, the trigonometric Sutherland system can be viewed alternatively as a system of distinguishable particles on the circle or on the line, and these 3 physically distinct systems are in duality with corresponding variants of the rational Ruijsenaars-Schneider system. We explain that the 3 duality relations, first obtained by Ruijsenaars in 1995, arise naturally from the Kazhdan-Kostant-Sternberg symplectic reductions of the cotangent bundles of the group U(n) and its covering groups $U(1) \times SU(n)$ and ${\mathbb R}\times SU(n)$, respectively. This geometric interpretation enhances our understanding of the duality relations and simplifies Ruijsenaars' original direct arguments that led to their discovery.Comment: 34 pages, minor additions and corrections of typos in v

On the superintegrability of the rational Ruijsenaars-Schneider model

The rational and hyperbolic Ruijsenaars-Schneider models and their non-relativistic limits are maximally superintegrable since they admit action variables with globally well-defined canonical conjugates. In the case of the rational Ruijsenaars-Schneider model we present an alternative proof of the superintegrability by explicitly exhibiting extra conserved quantities relying on a generalization of the construction of Wojciechowski for the rational Calogero model.Comment: added 2 references and some comments in v2, 10 page

Twin-Screw Extrusion Processing of Distillers Dried Grains with Solubles (DDGS)-Based Yellow Perch (Perca flavescens) Feeds

Increases in global aquaculture production, compounded with limited availabilities of fish meal for fish feed, has created the need for alternative protein sources. Twinscrew extrusion studies were performed to investigate the production of nutritionally balanced feeds for juvenile yellow perch (Perca flavescens). Five isocaloric (~3.06 kcal/g) ingredient blends, adjusted to a target protein content of 36.7% db, were formulated with 0%, 10%, 20%, 30%, and 40% distillers dried grains with solubles (DDGS) at an initial moisture content of 5–7%db, with appropriate amounts of fish meal, fish oil, whole wheat flour, corn gluten meal, and vitamin and mineral premixes. During processing, varying amounts of steam (6.9–9.7 kg/h) were injected into the conditioner and water (6.7–13.1 kg/h) into the extruder to modulate the cohesiveness of the final extrudates. Extrusion cooking was performed at 226–298 rpm using a 1.9 mm die. Mass flow rate and processing temperatures generally decreased with progressively higher DDGS content. Moisture content, water activity, unit density, bulk density, expansion ratio, compressive strength and modulus, pellet durability index, water stability, angle of repose, and color were extensively analyzed to quantify the effects of varying DDGS content on the physical properties of the final extrudates. Significant differences (P\u3c0.05) among the blends were observed for color and bulk density for both the raw and extruded material, respectively, and for the unit density of the extruded product. There were also significant changes in brightness (L), redness (a), and yellowness (b) among the final products when increasing the DDGS content of the blends. Expansion ratio and compressive strength of the extrudates were low. On the other hand, all extruded diets resulted in very good water stability properties and nearly all blends achieved high pellet durability indices. In summary, each of the ingredient blends resulted in viable extrudates

Heat Treatment Improvement of Dairy Products via Ohmic Heating Processes : Thermal and Hyrodynamic Effect on Fouling

Fouling and consequently cleaning of heat exchangers in the dairy industry are nowadays a significant issue still not solved for the processing of quite a large variety of products. Ohmic heating processes for food products a priori are well known to minimize the fouling phenomenon due to a totally different way of heating food by admitting the current directly in the product. Such a technology could be a good alternative to counter both fouling and cleaning aspects when pasteurizing or sterilizing dairy desserts known to generate large amounts of soil on heated surfaces. The aim of this experimental study was to investigate the respective roles of both the hydrodynamic parameters and surface electrode temperatures on the fouling phenomenon when heating a simple dairy mix designed to mimic dairy product behaviors

An integrable BC(n) Sutherland model with two types of particles

A hyperbolic BC(n) Sutherland model involving three independent coupling constants that characterize the interactions of two types of particles moving on the half-line is derived by Hamiltonian reduction of the free geodesic motion on the group SU(n,n). The symmetry group underlying the reduction is provided by the direct product of the fixed point subgroups of two commuting involutions of SU(n,n). The derivation implies the integrability of the model and yields a simple algorithm for constructing its solutions.Comment: 14 pages, with minor modifications in v

Improvements in the South African HIV care cascade: findings on 90-90-90 targets from successive population-representative surveys in North West Province.

IntroductionTo achieve epidemic control of HIV by 2030, countries aim to meet 90-90-90 targets to increase knowledge of HIV-positive status, initiation of antiretroviral therapy (ART) and viral suppression by 2020. We assessed the progress towards these targets from 2014 to 2016 in South Africa as expanded treatment policies were introduced using population-representative surveys.MethodsData were collected in January to March 2014 and August to November 2016 in Dr. Ruth Segomotsi Mompati District, North West Province. Each multi-stage cluster sample included 46 enumeration areas (EA), a target of 36 dwelling units (DU) per EA, and a single resident aged 18 to 49 per DU. Data collection included behavioural surveys, rapid HIV antibody testing and dried blood spot collection. We used weighted general linear regression to evaluate differences in the HIV care continuum over time.ResultsOverall, 1044 and 971 participants enrolled in 2014 and 2016 respectively with approximately 77% undergoing HIV testing. Despite increases in reported testing, known status among people living with HIV (PLHIV) remained similar at 68.7% (95% Confidence Interval (CI) = 60.9-75.6) in 2014 and 72.8% (95% CI = 63.6-80.4) in 2016. Men were consistently less likely than women to know their status. Among those with known status, PLHIV on ART increased significantly from 80.9% (95% CI = 71.9-87.4) to 91.5% (95% CI = 84.4-95.5). Viral suppression (<5000 copies/mL using DBS) among those on ART increased significantly from 55.0% (95% CI = 39.6-70.4) in 2014 to 81.4% (95% CI = 72.0-90.8) in 2016. Among all PLHIV an estimated 72.0% (95% CI = 63.8-80.1) of women and 45.8% (95% CI = 27.0-64.7) of men achieved viral suppression by 2016.ConclusionsOver a period during which fixed-dose combination was introduced, ART eligibility expanded, and efforts to streamline treatment were implemented, major improvements in the second and third 90-90-90 targets were achieved. Achieving the first 90 target will require targeted and improved testing models for men

Is abdominal compression useful in lung stereotactic body radiation therapy? A 4DCT and dosimetric lobe-dependent study

International audiencePurpose : To determine the usefulness of abdominal compression in lung stereotactic body radiation therapy (SBRT) depending on lobe tumor location.Materials and methods : Twenty-seven non-small cell lung cancer patients were immobilized in the Stereotactic Body Frame™ (Elekta). Eighteen tumors were located in an upper lobe, one in the middle lobe and nine in a lower lobe (one patient had two lesions). All patients underwent two four-dimensional computed tomography (4DCT) scans, with and without abdominal compression. Three-dimensional tumor motion amplitude was determined using manual landmark annotation. We also determined the internal target volume (ITV) and the influence of abdominal compression on lung dose-volume histograms. Results : The mean reduction of tumor motion amplitude was 3.5 mm (p = 0.009) for lower lobe tumors and 0.8 mm (p = 0.026) for upper/middle lobe locations. Compression increased tumor motion in 5 cases. Mean ITV reduction was 3.6 cm3 (p = 0.039) for lower lobe and 0.2 cm3 (p = 0.048) for upper/middle lobe lesions. Dosimetric gain of the compression for lung sparing was not clinically relevant. Conclusions : The most significant impact of abdominal compression was obtained in patients with lower lobe tumors. However, minor or negative effects of compression were reported for other patients and lung sparing was not substantially improved. At our institute, patients with upper or middle lobe lesions are now systematically treated without compression and the usefulness of compression for lower lobe tumors is evaluated on an individual basis