Coding and Compression of Three Dimensional Meshes by Planes

The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D convex polyhedron by means of planes, containing only its faces. This allows not to consider topological aspects of the problem (connectivity information among vertices and edges) since by means of the planes we construct the polyhedron uniquely. Due to the fact that the topological data is ignored this representation provides high degree of compression. Also planes based representation provides a compression of geometrical data because most of the faces of the polyhedron are not triangles but polygons with more than three vertices.Comment: 10 pages, 7 figure

Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of

We obtain weighted integral representations for spaces of functions holomorphic in the unit ball and belonging to area-integrable weighted -classes with “anisotropic” weight function of the type ∏=1(1−|1|2−|2|2−⋯−||2), =(1,2,…,)∈. The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for =2)

Relationships between pulmonary hypertension risk, clinical profiles, and outcomes in dilated cardiomyopathy

Pulmonary hypertension (PH) in patients with heart failure (HF) contributes to a poorer prognosis. However, in those with dilated cardiomyopathy (DCM), the true prevalence and role of PH is unclear. Therefore, this study aimed to analyze the profile of DCM patients at various levels of PH risk, determined via echocardiography, and its impact on outcomes. The 502 DCM in- and out-patient records were retrospectively analyzed. Information on patient status was gathered after 45.9 ± 31.3 months. Patients were divided into 3 PH-risk groups based on results from echocardiography measurements: low (L, n = 239, 47.6%), intermediate (I, n = 153, 30.5%), and high (H, n = 110, 21.9%). Symptom duration, atrial fibrillation, ventricular tachyarrhythmia, ejection fraction, right atrial area, and moderate or severe mitral regurgitation were found to be independently associated with PH risk. During the follow-up period, 83 (16.5%) DCM patients died: 29 (12.1%) in L, 31 (20.3%) in I, and 23 (20.9%) in H. L-patients had a significantly lower risk of all-cause death (L to H: HR 0.55 (95%CI 0.32–0.98), p = 0.01), while no differences in prognosis were found between I and H. In conclusion, over one in five DCM patients had a high PH risk, and low PH risk was associated with better prognoses

Weighted -Integral Representations of -Functions in

For 1-functions , given in the complex space , integral representations of the form =()−() are obtained. Here, is the orthogonal projector of the space 2{;−||||()} onto its subspace of entire functions and the integral operator appears by means of explicitly constructed kernel Φ which is investigated in detail

The burden of atrial fibrillation and its prognostic value in patients with dilated cardiomyopathy

Background: Atrial fibrillation (AF) is the most common arrhythmia in patients with dilated cardiomyopathy (DCM). However, the epidemiology as well as clinical and prognostic significance of AF in DCM are poorly defined. Aims: We aimed to assess the impact and prognostic value of AF in DCM as well as to investigate the concept of AF‑induced DCM. Methods: Hospital records of 285 patients with DCM from 2012 to 2018 with follow-up were analyzed. Results: Atrial fibrillation was present in 89 patients (31%). They were older, more frequently male, hadhigher body mass index, New York Heart Association class, heart rate (HR), creatinine levels, and larger atria (all P < 0.05) than patients without AF. During follow‑up (mean [SD], 35 [24] months), death occurred in 20 of the 82 available patients with AF and 22 of the 188 patients without AF (24% and 12%, respectively; P = 0.007). Atrial fibrillation was independently associated with a worse outcome (hazard ratio, 2.4; 95% CI, 1.3–4.3) and was found to be the major cause of DCM in 21 patients (24%). The diagnostic accuracy of the most optimal predictive model for AF‑induced DCM was 0.935 (95% CI, 0.903–0.967). Despite numerical differences, survival was similar in DCM patients with and without AF (P = 0.15). Conclusions: Almost one‑third of patients with DCM had AF. Most of the parameters analyzed differed between patients with and without AF, and AF was found to be an independent prognostic factor of DCM. One‑fourth of patients with DCM and AF met the diagnostic criteria for AF‑induced DCM

Lack of Relationship between Fibrosis-Related Biomarkers and Cardiac Magnetic Resonance-Assessed Replacement and Interstitial Fibrosis in Dilated Cardiomyopathy

The relationship between circulating fibrosis-related molecules and magnetic resonance-assessed cardiac fibrosis in dilated cardiomyopathy (DCM) is poorly understood. To compare circulating biomarkers between DCM patients with high and low fibrosis burdens, we performed a prospective, single-center, observational study. The study population was composed of 100 DCM patients (87 male, mean age 45.2 ± 11.8 years, mean ejection fraction 29.7% ± 10.1%). Replacement fibrosis was quantified by means of late gadolinium enhancement (LGE), whereas interstitial fibrosis was assessed via extracellular volume (ECV). Plasma concentrations of cardiotrophin-1, growth differentiation factor-15, platelet-derived growth factor, procollagen I C-terminal propeptide, procollagen III N-terminal propeptide, and C-terminal telopeptide of type I collagen were measured. There were 44% patients with LGE and the median ECV was 27.7%. None of analyzed fibrosis serum biomarkers were associated with the LGE or ECV, whereas NT-proBNP was independently associated with both LGE and ECV, and troponin T was associated with ECV. None of the circulating fibrosis markers differentiated between DCM patients with and without replacement fibrosis, or patients stratified according to median ECV. However, cardiac-specific markers, such as NT-proBNP and hs-TnT, were associated with fibrosis. Levels of circulating markers of fibrosis seem to have no utility in the diagnosis and monitoring of cardiac fibrosis in DCM