By counting with triangles and the octohedral axiom, we find a direct way to prove the formula of Toën in [13] for a triangulated category with (left) homological-finite condition.

MotivationSuper-resolution fluorescence microscopy with a resolution beyond the diffraction limit of light, has become an indispensable tool to directly visualize biological structures in living cells at a nanometer-scale resolution. Despite advances in high-density super-resolution fluorescent techniques, existing methods still have bottlenecks, including extremely long execution time, artificial thinning and thickening of structures, and lack of ability to capture latent structures.ResultsHere, we propose a novel deep learning guided Bayesian inference (DLBI) approach, for the time-series analysis of high-density fluorescent images. Our method combines the strength of deep learning and statistical inference, where deep learning captures the underlying distribution of the fluorophores that are consistent with the observed time-series fluorescent images by exploring local features and correlation along time-axis, and statistical inference further refines the ultrastructure extracted by deep learning and endues physical meaning to the final image. In particular, our method contains three main components. The first one is a simulator that takes a high-resolution image as the input, and simulates time-series low-resolution fluorescent images based on experimentally calibrated parameters, which provides supervised training data to the deep learning model. The second one is a multi-scale deep learning module to capture both spatial information in each input low-resolution image as well as temporal information among the time-series images. And the third one is a Bayesian inference module that takes the image from the deep learning module as the initial localization of fluorophores and removes artifacts by statistical inference. Comprehensive experimental results on both real and simulated datasets demonstrate that our method provides more accurate and realistic local patch and large-field reconstruction than the state-of-the-art method, the 3B analysis, while our method is more than two orders of magnitude faster.Availability and implementationThe main program is available at https://github.com/lykaust15/DLBISupplementary information Supplementary data are available at Bioinformatics online.

Single-molecule localization microscopy is a powerful tool for visualizing subcellular structures, interactions, and protein functions in biological research. However, inhomogeneous refractive indices inside cells and tissues distort the fluorescent signal emitted from single-molecule probes, which rapidly deteriorates resolution with increasing depth. We propose a method that enables the construction of an in situ 3D response of single emitters directly from single-molecule blinking datasets and therefore allows their locations to be pin-pointed with precision that achieves the Cramer-Rao lower bound and uncompromised fidelity. We demonstrate this method, named in situ PSF retrieval (INSPR), across a range of cellular and tissue architectures from mitochondrial networks and nuclear pores in mammalian cells, to amyloid β plaques and dendrites in brain tissues, and elastic fibers in developing cartilage of mice. This advancement expands the routine applicability of super-resolution microscopy from selected cellular targets near coverslips to intra- and extra-cellular targets deep inside tissues.

The tribovoltaic effect at the dynamic semiconductor interfaces has been an emerging hot topic due to its potential impact in energy harvesting and smart electronics. Previously, this effect is mainly...

In [CK] and [SZ], the authors constructed the bases of cluster algebras of finite types and of type A 1,1 , respectively. In this paper, we will deduce Z-bases for cluster algebras of affine types.

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ABSTRACTSingle-molecule localization microscopy is a powerful tool in visualizing organelle structures, interactions, and protein functions in biological research. However, whole-cell and tissue specimens challenge the achievable resolution and depth of nanoscopy methods. As imaging depth increases, photons emitted by fluorescent probes, the sole source of molecular positions, were scattered and aberrated, resulting in image artifacts and rapidly deteriorating resolution. We propose a method to allow constructing the in situ 3D response of single emitters directly from single-molecule dataset and therefore allow pin-pointing single-molecule locations with limit-achieving precision and uncompromised fidelity through whole cells and tissues. This advancement expands the routine applicability of super-resolution imaging from selected cellular targets near coverslips to intra- and extra-cellular targets deep inside tissues. We demonstrate this across a range of cellular-tissue architectures from mitochondrial networks, microtubules, and nuclear pores in 2D and 3D cultures, amyloid-β plaques in mouse brains to developing cartilage in mouse forelimbs.

Liquid catalyzed fuel cell (LCFC) is a kind of redox flow fuel cell directly converting carbohydrates to electricity. To improve its efficiency, ferric chloride (FeCl3) was introduced as main catalyst. As mono catalyst, phosphomolybdic acid (PMo12) was much better than phosphotungstic acid (PW12) and FeCl3 was intermediate between them. Compared with PMo12 at the optimal dose of 0.30 mol/L, the combination of FeCl3 (1.00 mol/L) and PW12 (0.06 mol/L) achieved similar power output from glucose (2.59 mW/cm2) or starch (1.57 mW/cm2), and even improved the maximum power density by 57% from 0.46 to 0.72 mW/cm2 when using cellulose as the fuel. Long-term continuous operation of the LCFC indicated that carbohydrates can be hydrolyzed to glucose and then oxidized stepwise to carbon dioxide. At the latter stage, there was a linear relationship between the electron transfer number from glucose to catalyst and the subsequent cell performance. Based on these findings, the contribution of FeCl3 to LCFC should be derived from the accelerated hydrolysis and oxidation of carbohydrates and the enhanced electron transfer from glucose to anode. The addition of FeCl3 reduced the usage of polyoxometalates by 80%, and the replacement implied that LCFC can be operated less toxically and more economically.