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\"Probability theory and mathematical statistics\" is an important public compulsory course of arithmetical foundation. MATLAB software is introduced into the teaching process to make some abstract concepts and theorems expressed in the form of graphics to achieve visualization effect. This method makes it easy for students to understand, improve their learning enthusiasm and achieve twice the result with half the effort.

We propose a technique for producing ‘visual explanations’ for decisions from a large class of Convolutional Neural Network (CNN)-based models, making them more transparent and explainable. Our approach—Gradient-weighted Class Activation Mapping (Grad-CAM), uses the gradients of any target concept (say ‘dog’ in a classification network or a sequence of words in captioning network) flowing into the final convolutional layer to produce a coarse localization map highlighting the important regions in the image for predicting the concept. Unlike previous approaches, Grad-CAM is applicable to a wide variety of CNN model-families: (1) CNNs with fully-connected layers (e.g.VGG), (2) CNNs used for structured outputs (e.g.captioning), (3) CNNs used in tasks with multi-modal inputs (e.g.visual question answering) or reinforcement learning, all without architectural changes or re-training. We combine Grad-CAM with existing fine-grained visualizations to create a high-resolution class-discriminative visualization, Guided Grad-CAM, and apply it to image classification, image captioning, and visual question answering (VQA) models, including ResNet-based architectures. In the context of image classification models, our visualizations (a) lend insights into failure modes of these models (showing that seemingly unreasonable predictions have reasonable explanations), (b) outperform previous methods on the ILSVRC-15 weakly-supervised localization task, (c) are robust to adversarial perturbations, (d) are more faithful to the underlying model, and (e) help achieve model generalization by identifying dataset bias. For image captioning and VQA, our visualizations show that even non-attention based models learn to localize discriminative regions of input image. We devise a way to identify important neurons through Grad-CAM and combine it with neuron names (Bau et al. in Computer vision and pattern recognition, 2017) to provide textual explanations for model decisions. Finally, we design and conduct human studies to measure if Grad-CAM explanations help users establish appropriate trust in predictions from deep networks and show that Grad-CAM helps untrained users successfully discern a ‘stronger’ deep network from a ‘weaker’ one even when both make identical predictions. Our code is available at https://github.com/ramprs/grad-cam/, along with a demo on CloudCV (Agrawal et al., in: Mobile cloud visual media computing, pp 265–290. Springer, 2015) (http://gradcam.cloudcv.org) and a video at http://youtu.be/COjUB9Izk6E.

Heterostructures comprising different monolayer semiconductors provide an attractive setting for fundamental science and device technologies, such as in the emerging field of valleytronics. We realized valley-specific interlayer excitons in monolayer WSe₂-MoSe₂ vertical heterostructures. We created interlayer exciton spin-valley polarization by means of circularly polarized optical pumping and determined a valley lifetime of 40 nanoseconds. This long-lived polarization enables the visualization of the expansion of a valley-polarized exciton cloud over several micrometers. The spatial pattern of the polarization evolves into a ring with increasing exciton density, a manifestation of valley exciton exchange interactions. Our work introduces van der Waals heterostructures as a promising platform from which to study valley exciton physics.

In recent years, with the massive growth of data, the world today has entered the era of big data. Big data has brought tremendous value to all fields of today’s society, and it has also brought enormous challenges, which has attracted great attention from all walks of life. Analyze and forecast the research hotspots and future development trends in the field of big data, and understand the development changes and priorities in the field of big data research, which will play a significant role in promoting the development of social development and scientific research. In the era of big data, how to extract information from huge amounts of complex data and present complex information more clearly and clearly, the most effective way is to use visualization technology. The article uses the information visualization software Citespace to study the data related to big data in the Web of Science and CNKI database from 2008 to 2017 for 10 years, from macro to micro to the representative countries of the literature, keywords and co-cited documents. Through visualization analysis, the article clarifies the key research directions, key documents and hot spot frontiers in the field of big data research, forecasts the future development trends in this field, and compares the research situation at home and abroad, in order to provide readers and other researchers with certain reference and help.

The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics 1 – 15 . Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry 14 , 15 . However, quantum materials hosting ideal spin–orbit-coupled kagome lattices with strong out-of-plane magnetization are lacking 16 – 21 . Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn 6 Sn 6 , that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk–boundary correspondence between the Chern gap and the topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn 6 Sn 6 , and may enable the observation of topological quantum phenomena in the RMn 6 Sn 6 (where R is a rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk–boundary–Berry correspondence covering real space and momentum space demonstrates a proof-of-principle method for revealing topological magnets. Scanning tunnelling microscopy is used to reveal a new topological kagome magnet with an intrinsic Chern quantum phase, which shows a distinct Landau fan structure with a large Chern gap.

Super-resolution microscopy has overcome a long-held resolution barrier—the diffraction limit—in light microscopy and enabled visualization of previously invisible molecular details in biological systems. Since their conception, super-resolution imaging methods have continually evolved and can now be used to image cellular structures in three dimensions, multiple colors, and living systems with nanometer-scale resolution. These methods have been applied to answer questions involving the organization, interaction, stoichiometry, and dynamics of individual molecular building blocks and their integration into functional machineries in cells and tissues. In this Review, we provide an overview of super-resolution methods, their state-of-the-art capabilities, and their constantly expanding applications to biology, with a focus on the latter. We will also describe the current technical challenges and future advances anticipated in super-resolution imaging.

We used ultrahigh-speed synchrotron x-ray imaging to quantify the phenomenon of vapor depressions (also known as keyholes) during laser melting of metals as practiced in additive manufacturing. Although expected from welding and inferred from postmortem cross sections of fusion zones, the direct visualization of the keyhole morphology and dynamics with high-energy x-rays shows that (i) keyholes are present across the range of power and scanning velocity used in laser powder bed fusion; (ii) there is a well-defined threshold from conduction mode to keyhole based on laser power density; and (iii) the transition follows the sequence of vaporization, depression of the liquid surface, instability, and then deep keyhole formation. These and other aspects provide a physical basis for three-dimensional printing in laser powder bed machines.

This study offers a systematic review of academic research on platforms in management, business and economics. By using two visualization tools named VOSviewer and CiteSpace, we analyzed 619 articles on platform research with associated 23,093 references from the Web of Science database. We have discerned the most impact publications, authors, journals, institutions and countries in the platform research. In addition, we have explored the structures of the cited references, cited authors and cited journals to further understand the theoretical basis of the platform research. Moreover, by evolution analysis through CiteSpace and co-occurrence analysis through VOSViewer, we explored the evolution process of platform research and predicted the future development trends. The results conjunctively achieved by VOSviewer and CiteSpace will enhance understanding of platform research and enable future developments for both theorists and practitioners.