Progressive Wasserstein Barycenters of Persistence Diagrams

This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data. Given a set of scalar fields, our approach enables the computation of a persistence diagram which is representative of the set, and which visually conveys the number, data ranges and saliences of the main features of interest found in the set. Such representative diagrams are obtained by computing explicitly the discrete Wasserstein barycenter of the set of persistence diagrams, a notoriously computationally intensive task. In particular, we revisit efficient algorithms for Wasserstein distance approximation [12,51] to extend previous work on barycenter estimation [94]. We present a new fast algorithm, which progressively approximates the barycenter by iteratively increasing the computation accuracy as well as the number of persistent features in the output diagram. Such a progressivity drastically improves convergence in practice and allows to design an interruptible algorithm, capable of respecting computation time constraints. This enables the approximation of Wasserstein barycenters within interactive times. We present an application to ensemble clustering where we revisit the k-means algorithm to exploit our barycenters and compute, within execution time constraints, meaningful clusters of ensemble data along with their barycenter diagram. Extensive experiments on synthetic and real-life data sets report that our algorithm converges to barycenters that are qualitatively meaningful with regard to the applications, and quantitatively comparable to previous techniques, while offering an order of magnitude speedup when run until convergence (without time constraint). Our algorithm can be trivially parallelized to provide additional speedups in practice on standard workstations. [...

Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)

This paper presents a computational framework for the Principal Geodesic Analysis of merge trees (MT-PGA), a novel adaptation of the celebrated Principal Component Analysis (PCA) framework [87] to the Wasserstein metric space of merge trees [92]. We formulate MT-PGA computation as a constrained optimization problem, aiming at adjusting a basis of orthogonal geodesic axes, while minimizing a fitting energy. We introduce an efficient, iterative algorithm which exploits shared-memory parallelism, as well as an analytic expression of the fitting energy gradient, to ensure fast iterations. Our approach also trivially extends to extremum persistence diagrams. Extensive experiments on public ensembles demonstrate the efficiency of our approach - with MT-PGA computations in the orders of minutes for the largest examples. We show the utility of our contributions by extending to merge trees two typical PCA applications. First, we apply MT-PGA to data reduction and reliably compress merge trees by concisely representing them by their first coordinates in the MT-PGA basis. Second, we present a dimensionality reduction framework exploiting the first two directions of the MT-PGA basis to generate two-dimensional layouts of the ensemble. We augment these layouts with persistence correlation views, enabling global and local visual inspections of the feature variability in the ensemble. In both applications, quantitative experiments assess the relevance of our framework. Finally, we provide a lightweight C++ implementation that can be used to reproduce our results

Statistical Parameter Selection for Clustering Persistence Diagrams

International audienceIn urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will analyze the output of ensemble simulations by considering so-called persistence diagrams, which are reduced representations of the original data, motivated by the extraction of topological features. Based on a recently published progressive algorithm for the clustering of persistence diagrams, we determine the optimal number of clusters, and therefore the number of significantly different outcome scenarios, by the minimization of established statistical score functions. Furthermore, we present a proof-of-concept prototype implementation of the statistical selection of the number of clusters and provide the results of an experimental study, where this implementation has been applied to real-world ensemble data sets

Noncooperative thermodynamics and kinetic models of ligand binding to polymers: Connecting McGhee-von Hippel model with the Tonks gas model

Ligand binding to polymers modifies the physical and chemical properties of the polymers, leading to physical, chemical, and biological implications. McGhee and von Hippel obtained the equilibrium coverage as a function of the ligand affinity, through the computation of the possible binding sites for the ligand. Here, we complete this theory deriving the kinetic model for the ligand-binding dynamics and the associated equilibrium chemical potential, which turns out to be of the Tonks gas model type. At low coverage, the Tonks chemical potential becomes the Fermi chemical potential and even the ideal gas chemical potential. We also discuss kinetic models associated with these chemical potentials. These results clarify the kinetic models of ligand binding, their relations with the chemical potentials, and their range of validity. Our results highlight the inaccuracy of ideal and simplified kinetic approaches for medium and high coverages

PREVALÊNCIA E FATORES ASSOCIADOS À ADESÃO AO TRATAMENTO MEDICAMENTOSO POR PACIENTES COM HIPERTENSÃO ARTERIAL

Objetivou-se avaliar a prevalência e os fatores associados à adesão ao tratamento entre pessoas acometidas por hipertensão arterial sistêmica. Estudo transversal, descritivo, realizado com 92 usuários atendidos em uma Unidade Básica de Saúde. Utilizou-se questionário contendo características sociodemográficas, econômicas, de saúde e o Teste de Morisky-Green. Aferiu-se a pressão arterial pelo método indireto. A prevalência de adesão ao tratamento foi 72,8%. Evidenciou-se diferenças significativas na adesão ao tratamento segundo situação marital de união estável (p= 0,043), forma de controle da pressão arterial por meio de tratamento medicamentoso combinado com mudanças no estilo de vida (p=0,003) e tempo de diagnóstico da hipertensão inferior a 10 anos (

Optimal or standard control of systolic and diastolic blood pressure across risk factor categories in patients with chronic coronary syndromes

Aims: Guidelines have lowered blood pressure (BP) targets to <130/80 mmHg. We examined the benefit of intensive control for each BP component, versus the burden of other modifiable risk factors, in patients with chronic coronary syndromes (CCS). Methods and results: The CLARIFY registry (ISRCTN43070564) enrolled 32 703 CCS patients, from 2009−2010, with a 5-year follow-up. Patients with either BP component below European guideline safety boundaries (120/70 mmHg) were excluded, leaving 19 167 patients (mean age 63.8 ± 10.1 years, 78% men) in the present analysis. A multivariable-adjusted Cox proportional hazards model showed a gradual increase in cardiovascular risk (cardiovascular death, myocardial infarction, or stroke) when the number of uncontrolled risk factors (active smoking, no physical activity, low-density lipoprotein cholesterol ≥100 mg/dL, and diabetes with glycated haemoglobin ≥7%) increased [adjusted hazard ratio (HR): 1.34; 95% confidence interval (CI): 1.17−1.52, 1.65 (1.40−1.94), and 2.47 (1.90−3.21) for 1, 2, and 3 or 4 uncontrolled risk factors, respectively, versus 0], without significant interaction with BP. Although uncontrolled systolic (≥140 mmHg) and diastolic (≥90 mmHg) BP were both associated with higher risk than standard BP, standard BP was associated with higher risk than optimal control for only the diastolic component (adjusted HR: 1.08; 95% CI: 0.94−1.25 for systolic BP 130−139 versus 120−129 mmHg and 1.43; 95% CI: 1.27−1.62 for diastolic BP 80−89 versus 70−79 mmHg). Conclusions: Our results suggest that optimal BP target in CCS may be ≤139/79 mmHg, and that optimizing the burden of other risk factors should be prioritized over further reduction of systolic BP