Spectral Generalized Multi-Dimensional Scaling

Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances between each pair of points in the set. Distances in the target space can be computed analytically in this setting. Generalized MDS is an extension that allows mapping one metric space into another, that is, multidimensional scaling into target spaces in which distances are evaluated numerically rather than analytically. Here, we propose an efficient approach for computing such mappings between surfaces based on their natural spectral decomposition, where the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS procedure enables efficient embedding by implicitly incorporating smoothness of the mapping into the problem, thereby substantially reducing the complexity involved in its solution while practically overcoming its non-convex nature. The method is compared to existing techniques that compute dense correspondence between shapes. Numerical experiments of the proposed method demonstrate its efficiency and accuracy compared to state-of-the-art approaches

The experience of sibutramine administration in patients with obesity and controlled arterial hypertension

BACKGROUND: Obesity is a metabolic disorder that becomes epidemic. Visceral adiposity increases the risk of arterial hypertension, diabetes mellitus and other comorbidities. According to this, the main aim of obesity treatment is not only a weight loss but also a decrease of the risk of comorbidities. AIMS: to assess the efficiency and safety of sibutramine in patients with obesity and arterial hypertension, to evaluate the drug influence on epicardial fat thickness. MATERIALS AND METHODS: 57 patients aged 35-60 with obesity and arterial hypertension were included in the study. All patients at the beginning and after 7 months of follow-up underwent complex examination including anthropometric measurement, ECG, office and ambulatory blood pressure measurement, echocardiography. Patients with controlled arterial hypertension were included. During the first month of follow-up patients were given general weight loss recommendations. Then sibutramine was added. Control visits to assess efficiency and safety of drug treatment were held after 1 and 6 months of follow-up. RESULTS: Women predominated among the study participants. Visceral adiposity was approved by anthropometric measurements among all patients. Most patients had impaired left ventricle geometry: concentric remodeling or hypertrophy. During the first month of follow-up the weight loss was mild: 2 kg (less than 2%) in average. Sibutramine for 1 month the weight loss increased: 3.7 kg (more than 2%) in average. After 6 months of drug administration the weight loss of patients consisted 8.6 kg (6.2%) in average. According to echocardiography results indexed mass of LV myocardium decreased in all patients more significantly in women. Also in this group of patients significant decrease of epicardial fat thickness was revealed. Adverse events of sibutramine were revealed in 26.3% of patients. The most frequent were constipation (12.3%) and dry mouth (10.6%). The severity of symptoms persisted for 1 month and then decreased, additional therapy was not required. CONCLUSIONS: Sibutramine treatment of obesity promotes effective weight loss, influences the adipose tissue distribution, decreases the progress of associated comorbidities. Sibutramine is an effective and safe drug that can be used in patients with visceral adiposity and controlled arterial hypertension