Quaternionic Salkowski Curves and Quaternionic Similar Curves

In this paper, we give the definitions and characterizations of quaternionic Salkowski, quaternionic anti-Salkowski and quaternionic similar curves in the Euclidean spaces E^3 and E^4. We obtain relationships between these curves and some special quaternionic curves such as quaternionic slant helices and quaternionic B2-slant helices.Comment: 17 page

On the computation of zone and double zone diagrams

Classical objects in computational geometry are defined by explicit relations. Several years ago the pioneering works of T. Asano, J. Matousek and T. Tokuyama introduced "implicit computational geometry", in which the geometric objects are defined by implicit relations involving sets. An important member in this family is called "a zone diagram". The implicit nature of zone diagrams implies, as already observed in the original works, that their computation is a challenging task. In a continuous setting this task has been addressed (briefly) only by these authors in the Euclidean plane with point sites. We discuss the possibility to compute zone diagrams in a wide class of spaces and also shed new light on their computation in the original setting. The class of spaces, which is introduced here, includes, in particular, Euclidean spheres and finite dimensional strictly convex normed spaces. Sites of a general form are allowed and it is shown that a generalization of the iterative method suggested by Asano, Matousek and Tokuyama converges to a double zone diagram, another implicit geometric object whose existence is known in general. Occasionally a zone diagram can be obtained from this procedure. The actual (approximate) computation of the iterations is based on a simple algorithm which enables the approximate computation of Voronoi diagrams in a general setting. Our analysis also yields a few byproducts of independent interest, such as certain topological properties of Voronoi cells (e.g., that in the considered setting their boundaries cannot be "fat").Comment: Very slight improvements (mainly correction of a few typos); add DOI; Ref [51] points to a freely available computer application which implements the algorithms; to appear in Discrete & Computational Geometry (available online

Supercoherent States, Super K\"ahler Geometry and Geometric Quantization

Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view is extended to the supersymmetric context, through the study of the OSp(2/2) coherent states. These are explicitly constructed starting from the known abstract typical and atypical representations of osp(2/2). Their underlying geometries turn out to be those of supersymplectic OSp(2/2) homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of OSp(2/2) are exhibited via Berezin's symbols. When considered within Rothstein's general paradigm, these results lead to a natural general definition of a super K\"ahler supermanifold, the supergeometry of which is determined in terms of the usual geometry of holomorphic Hermitian vector bundles over K\"ahler manifolds. In particular, the supergeometry of the above orbits is interpreted in terms of the geometry of Einstein-Hermitian vector bundles. In the second part, an extension of the full geometric quantization procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler character of the latter, this procedure leads to explicit super unitary irreducible representations of OSp(2/2) in super Hilbert spaces of $L^2$ superholomorphic sections of prequantum bundles of the Kostant type. This work lays the foundations of a program aimed at classifying Lie supergroups' coadjoint orbits and their associated irreducible representations, ultimately leading to harmonic superanalysis. For this purpose a set of consistent conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts

Superization of Homogeneous Spin Manifolds and Geometry of Homogeneous Supermanifolds

Let M_0=G_0/H be a (pseudo)-Riemannian homogeneous spin manifold, with reductive decomposition g_0=h+m and let S(M_0) be the spin bundle defined by the spin representation Ad:H->\GL_R(S) of the stabilizer H. This article studies the superizations of M_0, i.e. its extensions to a homogeneous supermanifold M=G/H whose sheaf of superfunctions is isomorphic to Lambda(S^*(M_0)). Here G is the Lie supergroup associated with a certain extension of the Lie algebra of symmetry g_0 to an algebra of supersymmetry g=g_0+g_1=g_0+S via the Kostant-Koszul construction. Each algebra of supersymmetry naturally determines a flat connection nabla^{S} in the spin bundle S(M_0). Killing vectors together with generalized Killing spinors (i.e. nabla^{S}-parallel spinors) are interpreted as the values of appropriate geometric symmetries of M, namely even and odd Killing fields. An explicit formula for the Killing representation of the algebra of supersymmetry is obtained, generalizing some results of Koszul. The generalized spin connection nabla^{S} defines a superconnection on M, via the super-version of a theorem of Wang.Comment: 50 page

Evaluation of integrated care services in Catalonia: Population-based and service-based real-life deployment protocols

Background: Comprehensive assessment of integrated care deployment constitutes a major challenge to ensure quality, sustainability and transferability of both healthcare policies and services in the transition toward a coordinated service delivery scenario. To this end, the manuscript articulates four different protocols aiming at assessing large-scale implementation of integrated care, which are being developed within the umbrella of the regional project Nextcare (2016-2019), undertaken to foster innovation in technologically-supported services for chronic multimorbid patients in Catalonia (ES) (7.5 M inhabitants). Whereas one of the assessment protocols is designed to evaluate population-based deployment of care coordination at regional level during the period 2011-2017, the other three are service-based protocols addressing: i) Home hospitalization; ii) Prehabilitation for major surgery; and, iii) Community-based interventions for frail elderly chronic patients. All three services have demonstrated efficacy and potential for health value generation. They reflect different implementation maturity levels. While full coverage of the entire urban health district of Barcelona-Esquerra (52

Effectiveness of an mHealth intervention combining a smartphone app and smart band on body composition in an overweight and obese population: Randomized controlled trial (EVIDENT 3 study)

Background: Mobile health (mHealth) is currently among the supporting elements that may contribute to an improvement in health markers by helping people adopt healthier lifestyles. mHealth interventions have been widely reported to achieve greater weight loss than other approaches, but their effect on body composition remains unclear. Objective: This study aimed to assess the short-term (3 months) effectiveness of a mobile app and a smart band for losing weight and changing body composition in sedentary Spanish adults who are overweight or obese. Methods: A randomized controlled, multicenter clinical trial was conducted involving the participation of 440 subjects from primary care centers, with 231 subjects in the intervention group (IG; counselling with smartphone app and smart band) and 209 in the control group (CG; counselling only). Both groups were counselled about healthy diet and physical activity. For the 3-month intervention period, the IG was trained to use a smartphone app that involved self-monitoring and tailored feedback, as well as a smart band that recorded daily physical activity (Mi Band 2, Xiaomi). Body composition was measured using the InBody 230 bioimpedance device (InBody Co., Ltd), and physical activity was measured using the International Physical Activity Questionnaire. Results: The mHealth intervention produced a greater loss of body weight (–1.97 kg, 95% CI –2.39 to –1.54) relative to standard counselling at 3 months (–1.13 kg, 95% CI –1.56 to –0.69). Comparing groups, the IG achieved a weight loss of 0.84 kg more than the CG at 3 months. The IG showed a decrease in body fat mass (BFM; –1.84 kg, 95% CI –2.48 to –1.20), percentage of body fat (PBF; –1.22%, 95% CI –1.82% to 0.62%), and BMI (–0.77 kg/m2, 95% CI –0.96 to 0.57). No significant changes were observed in any of these parameters in men; among women, there was a significant decrease in BMI in the IG compared with the CG. When subjects were grouped according to baseline BMI, the overweight group experienced a change in BFM of –1.18 kg (95% CI –2.30 to –0.06) and BMI of –0.47 kg/m2 (95% CI –0.80 to –0.13), whereas the obese group only experienced a change in BMI of –0.53 kg/m2 (95% CI –0.86 to –0.19). When the data were analyzed according to physical activity, the moderate-vigorous physical activity group showed significant changes in BFM of –1.03 kg (95% CI –1.74 to –0.33), PBF of –0.76% (95% CI –1.32% to –0.20%), and BMI of –0.5 kg/m2 (95% CI –0.83 to –0.19). Conclusions: The results from this multicenter, randomized controlled clinical trial study show that compared with standard counselling alone, adding a self-reported app and a smart band obtained beneficial results in terms of weight loss and a reduction in BFM and PBF in female subjects with a BMI less than 30 kg/m2 and a moderate-vigorous physical activity level. Nevertheless, further studies are needed to ensure that this profile benefits more than others from this intervention and to investigate modifications of this intervention to achieve a global effect

A Pilot Randomized Controlled Trial to Explore Cognitive and Emotional Effects of Probiotics in Fibromyalgia

It has recently been found that microbes in the gut may regulate brain processes through the gut microbiota–brain axis, which modulates affection, motivation and higher cognitive functions. According to this finding, the use of probiotics may be a potential treatment to improve physical, psychological and cognitive status in clinical populations with altered microbiota balance such as those with fibromyalgia (FMS). Thus, the aim of the present pilot study with a double-blind, placebo-controlled, randomised design was to test whether a multispecies probiotic may improve cognition, emotional symptoms and functional state in a sample of patients diagnosed with FMS. Pain, impact of FMS, quality of life, anxiety and depressive symptoms were measured during the pre- and post-intervention phases; participants also completed two computerised cognitive tasks to assess impulsive choice and decision-making. Finally, urinary cortisol concentration was determined. To our knowledge, this is the first study that explore the effect of a multispecies probiotic in FMS patients. Our results indicated that probiotics improved impulsivity and decision-making in these patients. However, more research is needed to further explore the potential effects of probiotics on other cognitive functions affected in FMS as well as in other clinical populations

Synthesis of optically pure 4-hydroxymethyl-3-phenoxy-2-azetidinone from D-glucal

A convenient approach to enantiomerically pure 4-hydroxymethyl- 3-phenoxy-2-azetidinone has been carried out using the easily available aldehyde 5 as chiral starting material