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We present convergence estimates of two types of greedy algorithms in terms of the entropy numbers of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the entropy numbers of the solution manifold in Banach spaces. This contrasts with the classical analysis based on the Kolmogorov [Formula: see text]-widths and enables us to obtain direct comparisons between the algorithm error and the entropy numbers, where the multiplicative constants are explicit and simple. The entropy-based convergence estimate is sharp and improves upon the classical width-based analysis of reduced basis methods for elliptic model problems. In the second part, we derive a novel and simple convergence analysis of the classical orthogonal greedy algorithm for nonlinear dictionary approximation using the entropy numbers of the symmetric convex hull of the dictionary. This also improves upon existing results by giving a direct comparison between the algorithm error and the entropy numbers. 

This paper describes an open-access database for seismo-cardiogram (SCG) and gyro-cardiogram (GCG) signals. The archive comprises SCG and GCG recordings sourced from and processed at multiple sites worldwide, including Columbia University Medical Center and Stevens Institute of Technology in the United States, as well as Southeast University, Nanjing Medical University, and the first affiliated hospital of Nanjing Medical University in China. It includes electrocardiogram (ECG), SCG, and GCG recordings collected from 100 patients with various conditions of valvular heart diseases such as aortic and mitral stenosis. The recordings were collected from clinical environments with the same types of wearable sensor patch. Besides the raw recordings of ECG, SCG, and GCG signals, a set of hand-corrected fiducial point annotations is provided by manually checking the results of the annotated algorithm. The database also includes relevant echocardiogram parameters associated with each subject such as ejection fraction, valve area, and mean gradient pressure. 

Abstract We present residual-based a posteriori error estimates of mixed finite element methods for the three-field formulation of Biot’s consolidation model. The error estimator are upper and lower bounds of the space-time discretization error up to data oscillation. As a by-product, we also obtain a new a posteriori error estimate of mixed finite element methods for the heat equation. 

A laser-induced microbubble refers to a bubble that is generated in a liquid solution by CW laser illumination to light absorptive materials. In this study, we use the gold nanoparticles solutions and gold nanoparticle film as the materials to absorb the heat under illumination. Heat transfer from the gold nanoparticles to surroundings induces a sharp increase in temperature, which results the generation of the microbubbles in the solutions. Therefore, the size and position of the surface bubble can be dynamically adjusted by changing the power and position of the laser spots. Convection currents around microbubble can make the gold nanoparticles pinned to the substrate surface, which can generate the Roman ring-shape structure. And then shine the CW laser of different power on the structure, the characteristics of the structure can be changed. These effects can be used for a wide variety of applications including micro/nano-particle manipulation, active microfluidic control, as well as cell stretching and sorting.