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Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as −log(B/A), where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with m+1, for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require O(N2) or O(N2−1m+1) computational complexity, where N is the length of the time series analyzed. When N is big, the computational costs of these algorithms are large. We propose a super fast algorithm to estimate sample entropy based on Monte Carlo, with computational costs independent of N (the length of the time series) and the estimation converging to the exact sample entropy as the number of repeating experiments becomes large. The convergence rate of the algorithm is also established. Numerical experiments are performed for electrocardiogram time series, electroencephalogram time series, cardiac inter-beat time series, mechanical vibration signals (MVS), meteorological data (MD), and 1/f noise. Numerical results show that the proposed algorithm can gain 100–1000 times speedup compared to the kd-tree and assisted sliding box algorithms while providing satisfactory approximate accuracy. 

Abstract We have performed sound velocity and unit cell volume measurements of three synthetic, ultrafine micro/nanocrystalline grossular samples up to 50 GPa using Brillouin spectroscopy and synchrotron X-ray diffraction. The samples are characterized by average grain sizes of 90 nm, 93 nm and 179 nm (hereinafter referred to as samples Gr90, Gr93, and Gr179, respectively). The experimentally determined sound velocities and elastic properties of Gr179 sample are comparable with previous measurements, but slightly higher than those of Gr90 and Gr93 under ambient conditions. However, the differences diminish with increasing pressure, and the velocity crossover eventually takes place at approximately 20–30 GPa. The X-ray diffraction peaks of the ultrafine micro/nanocrystalline grossular samples significantly broaden between 15–40 GPa, especially for Gr179. The velocity or elasticity crossover observed at pressures over 30 GPa might be explained by different grain size reduction and/or inhomogeneous strain within the individual grains for the three grossular samples, which is supported by both the pressure-induced peak broadening observed in the X-ray diffraction experiments and transmission electron microscopy observations. The elastic behavior of ultrafine micro/nanocrystalline silicates, in this case, grossular, is both grain size and pressure dependent. 

The crystal chemistry of carnotite (prototype formula: K2(UO2)2(VO4)2·3H2O) occurring in mine wastes collected from Northeastern Arizona was investigated by integrating spectroscopy, electron microscopy, and x-ray diffraction analyses. Raman spectroscopy confirms that the uranyl vanadate phase present in the mine waste is carnotite, rather than the rarer polymorph vandermeerscheite. X-ray diffraction patterns of the carnotite occurring in these mine wastes are in agreement with those reported in the literature for a synthetic analog. Carbon detected in this carnotite was identified as organic carbon inclusions using transmission electron microscopy (TEM) and electron energy loss spectroscopy (EELS) analyses. After excluding C and correcting for K-drift from the electron microprobe analyses, the composition of the carnotite was determined as 8.64% K2O, 0.26% CaO, 61.43% UO3, 20.26% V2O5, 0.38% Fe2O3, and 8.23% H2O. The empirical formula, (K1.66Ca0.043Al(OH)2+0.145 Fe(OH)2+0.044)((U0.97)O2)2((V1.005)O4)2·4H2O of the studied carnotite, with an atomic ratio 1.9:2:2 for K:U:V, is similar to the that of carnotite (K2(UO2)2(VO4)2·3H2O) reported in the literature. Lattice spacing data determined using selected area electron diffraction (SAED)-TEM suggests: (1) complete amorphization of the carnotite within 120 s of exposure to the electron beam and (2) good agreement of the measured d-spacings for carnotite in the literature. Small differences between the measured and literature d-spacing values are likely due to the varying degree of hydration between natural and synthetic materials. Such information about the crystal chemistry of carnotite in mine wastes is important for an improved understanding of the occurrence and reactivity of U, V, and other elements in the environment. 

Salient segmentation is a critical step in biomedical image analysis, aiming to cut out regions that are most interesting to humans. Recently, supervised methods have achieved promising results in biomedical areas, but they depend on annotated training data sets, which requires labor and proficiency in related background knowledge. In contrast, unsupervised learning makes data-driven decisions by obtaining insights directly from the data themselves. In this paper, we propose a completely unsupervised self-aware network based on pre-training and attentional backpropagation for biomedical salient segmentation, named as PUB-SalNet. Firstly, we aggregate a new biomedical data set from several simulated Cellular Electron Cryo-Tomography (CECT) data sets featuring rich salient objects, different SNR settings, and various resolutions, which is called SalSeg-CECT. Based on the SalSeg-CECT data set, we then pre-train a model specially designed for biomedical tasks as a backbone module to initialize network parameters. Next, we present a U-SalNet network to learn to selectively attend to salient objects. It includes two types of attention modules to facilitate learning saliency through global contrast and local similarity. Lastly, we jointly refine the salient regions together with feature representations from U-SalNet, with the parameters updated by self-aware attentional backpropagation. We apply PUB-SalNet for analysis of 2D simulated and real images and achieve state-of-the-art performance on simulated biomedical data sets. Furthermore, our proposed PUB-SalNet can be easily extended to 3D images. The experimental results on the 2d and 3d data sets also demonstrate the generalization ability and robustness of our method. 

Abstract A bidirectional brain interface with both “write” and “read” functions can be an important tool for fundamental studies and potential clinical treatments for neurological diseases. Herein, a miniaturized multifunctional fiber‐based optoacoustic emitter (mFOE) is reported thatintegrates simultaneous optoacoustic stimulation for “write” and electrophysiology recording of neural circuits for “read”. Because of the intrinsic ability of neurons to respond to acoustic wave, there is no requirement of the viral transfection. The orthogonality between optoacoustic waves and electrical field provides a solution to avoid the interference between electrical stimulation and recording. The stimulation function of the mFOE is first validated in cultured ratcortical neurons using calcium imaging. In vivo application of mFOE for successful simultaneous optoacoustic stimulation and electrical recording of brain activities is confirmed in mouse hippocampus in both acute and chronical applications up to 1 month. Minor brain tissue damage is confirmed after these applications. The capability of simultaneous neural stimulation and recording enabled by mFOE opens up new possibilities for the investigation of neural circuits and brings new insights into the study of ultrasound neurostimulation.