Topological Abel-Jacobi map and mixed Hodge structures

For a smooth projective variety $X$ of dimension $2n-1$, Zhao defined topological Abel-Jacobi map, which sends vanishing cycles on a smooth hyperplane section $Y$ of $X$ to the middle dimensional primitive intermediate Jacobian of $X$. When the vanishing cycles are algebraic, it agrees with Griffiths Abel-Jacobi map. On the other hand, Schnell defined a topological Abel-Jacobi map using the $mathbb R$-splitting property of the mixed Hodge structure on $H^{2n-1}(Xsetminus Y)$. We show that the two definitions coincide, which answers a question of Schnell.

Transverse mode selective laser with gain regulation by a digital micromirror device

A transverse mode selective laser system with gain regulation by a digital micromirror device (DMD) is presented in this letter. The gain regulation in laser medium is adjusted by the switch of the patterns loaded on DMD. Structured pump beam patterns can be obtained after the reflection of the loaded patterns on DMD, and then its defocused into a microchip laser medium by a short focal lens, so that the pump patterns can be transferred to the gain medium to regulate the gain distribution. Corresponding structured laser beams can be generated by this laser system. The laser beam pattern can be regulated easily and quickly, by switching the loaded patterns on DMD. Through this method, we show a simple and flexible laser system to generate on-demand laser beam patterns.

On the new identities of Dirichlet $L$-functions

Let $qge3$ be an integer, $chi$ be a Dirichlet character modulo $q$, and $L(s,chi)$ denote the Dirichlet $L$-functions corresponding to $chi$. In this paper, we show some special function series, and give some new identities for the Dirichlet $L$-functions involving Gauss sums. Specially, we give specific identities for $L(2,chi)$.

Group Fisher Pruning for Practical Network Compression

Network compression has been widely studied since it is able to reduce the memory and computation cost during inference. However, previous methods seldom deal with complicated structures like residual connections, group/depth-wise convolution and feature pyramid network, where channels of multiple layers are coupled and need to be pruned simultaneously. In this paper, we present a general channel pruning approach that can be applied to various complicated structures. Particularly, we propose a layer grouping algorithm to find coupled channels automatically. Then we derive a unified metric based on Fisher information to evaluate the importance of a single channel and coupled channels. Moreover, we find that inference speedup on GPUs is more correlated with the reduction of memory rather than FLOPs, and thus we employ the memory reduction of each channel to normalize the importance. Our method can be used to prune any structures including those with coupled channels. We conduct extensive experiments on various backbones, including the classic ResNet and ResNeXt, mobile-friendly MobileNetV2, and the NAS-based RegNet, both on image classification and object detection which is under-explored. Experimental results validate that our method can effectively prune sophisticated networks, boosting inference speed without sacrificing accuracy.

Neural Differential Equations for Inverse Modeling in Model Combustors

Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal resolution. This work proposes an approach based on neural differential equations to approximate the unknown quantities from available sparse measurements. The approach tackles the challenges of nonlinearity and the curse of dimensionality in inverse modeling by representing the dynamic signal using neural network models. In addition, we augment physical models for combustion with neural differential equations to enable learning from sparse measurements. We demonstrated the inverse modeling approach in a model combustor system by simulating the oscillation of an industrial combustor with a perfectly stirred reactor. Given the sparse measurements of the temperature inside the combustor, upstream fluctuations in compositions and/or flow rates can be inferred. Various types of fluctuations in the upstream, as well as the responses in the combustor, were synthesized to train and validate the algorithm. The results demonstrated that the approach can efficiently and accurately infer the dynamics of the unknown inlet boundary conditions, even without assuming the types of fluctuations. Those demonstrations shall open a lot of opportunities in utilizing neural differential equations for fault diagnostics and model-based dynamic control of industrial power systems.

RankSRGAN: Super Resolution Generative Adversarial Networks with Learning to Rank

Generative Adversarial Networks (GAN) have demonstrated the potential to recover realistic details for single image super-resolution (SISR). To further improve the visual quality of super-resolved results, PIRM2018-SR Challenge employed perceptual metrics to assess the perceptual quality, such as PI, NIQE, and Ma. However, existing methods cannot directly optimize these indifferentiable perceptual metrics, which are shown to be highly correlated with human ratings. To address the problem, we propose Super-Resolution Generative Adversarial Networks with Ranker (RankSRGAN) to optimize generator in the direction of different perceptual metrics. Specifically, we first train a Ranker which can learn the behaviour of perceptual metrics and then introduce a novel rank-content loss to optimize the perceptual quality. The most appealing part is that the proposed method can combine the strengths of different SR methods to generate better results. Furthermore, we extend our method to multiple Rankers to provide multi-dimension constraints for the generator. Extensive experiments show that RankSRGAN achieves visually pleasing results and reaches state-of-the-art performance in perceptual metrics and quality. Project page: https://wenlongzhang0517.github.io/Projects/RankSRGAN

Physically-motivated Recursively Embedded Atom Neural Networks: Incorporating Local Completeness and Nonlocality

Recent advances in machine-learned interatomic potentials largely benefit from the atomistic representation and locally invariant many-body descriptors. It was however recently argued that including three- (or even four-) body features is incomplete to distinguish specific local structures. Utilizing an embedded density descriptor made by linear combinations of neighboring atomic orbitals and realizing that each orbital coefficient physically depends on its own local environment, we propose a recursively embedded atom neural network model. We formally prove that this model can efficiently incorporate complete many-body correlations without explicitly computing high-order terms. This model not only successfully addresses challenges regarding local completeness and nonlocality in representative systems, but also provides an easy and general way to update local many-body descriptors to have a message-passing form without changing their basic structures.

Feature Space Targeted Attacks by Statistic Alignment

By adding human-imperceptible perturbations to images, DNNs can be easily fooled. As one of the mainstream methods, feature space targeted attacks perturb images by modulating their intermediate feature maps, for the discrepancy between the intermediate source and target features is minimized. However, the current choice of pixel-wise Euclidean Distance to measure the discrepancy is questionable because it unreasonably imposes a spatial-consistency constraint on the source and target features. Intuitively, an image can be categorized as cat no matter the cat is on the left or right of the image. To address this issue, we propose to measure this discrepancy using statistic alignment. Specifically, we design two novel approaches called Pair-wise Alignment Attack and Global-wise Alignment Attack, which attempt to measure similarities between feature maps by high-order statistics with translation invariance. Furthermore, we systematically analyze the layer-wise transferability with varied difficulties to obtain highly reliable attacks. Extensive experiments verify the effectiveness of our proposed method, and it outperforms the state-of-the-art algorithms by a large margin. Our code is publicly available at https://github.com/yaya-cheng/PAA-GAA.

Blockchain Systems, Technologies and Applications: A Methodology Perspective

In the past decade, blockchain has shown a promising vision greatly to build the trust without any powerful third party in a secure, decentralized and salable manner. However, due to the wide application and future development from cryptocurrency to Internet of Things, blockchain is an extremely complex system enabling integration with mathematics, finance, computer science, communication and network engineering, etc. As a result, it is a challenge for engineer, expert and researcher to fully understand the blockchain process in a systematic view from top to down. First, this article introduces how blockchain works, the research activity and challenge, and illustrates the roadmap involving the classic methodology with typical blockchain use cases and topics. Second, in blockchain system, how to adopt stochastic process, game theory, optimization, machine learning and cryptography to study blockchain running process and design blockchain protocol/algorithm are discussed in details. Moreover, the advantage and limitation using these methods are also summarized as the guide of future work to further considered. Finally, some remaining problems from technical, commercial and political views are discussed as the open issues. The main findings of this article will provide an overview in a methodology perspective to study theoretical model for blockchain fundamentals understanding, design network service for blockchain-based mechanisms and algorithms, as well as apply blockchain for Internet of Things, etc.

Berry curvature generation detected by Nernst responses in ferroelectric Weyl semimetal

The quest for nonmagnetic Weyl semimetals with high tunability of phase has remained a demanding challenge. As the symmetry breaking control parameter, the ferroelectric order can be steered to turn on/off the Weyl semimetals phase, adjust the band structures around the Fermi level, and enlarge/shrink the momentum separation of Weyl nodes which generate the Berry curvature as the emergent magnetic field. Here, we report the realization of a ferroelectric nonmagnetic Weyl semimetal based on indium doped Pb1 xSnxTe alloy where the underlying inversion symmetry as well as mirror symmetry is broken with the strength of ferroelectricity adjustable via tuning indium doping level and Sn/Pb ratio. The transverse thermoelectric effect, i.e., Nernst effect both for out of plane and in plane magnetic field geometry, is exploited as a Berry curvature sensitive experimental probe to manifest the generation of Berry curvature via the redistribution of Weyl nodes under magnetic fields. The results demonstrate a clean non-magnetic Weyl semimetal coupled with highly tunable ferroelectric order, providing an ideal platform for manipulating the Weyl fermions in nonmagnetic system.