Landis-type conjecture for the half-Laplacian

In this paper, we study the Landis-type conjecture, i.e., unique continuation property from infinity, of the fractional Schr\"{o}dinger equation with drift and potential terms. We show that if any solution of the equation decays at a certain exponential rate, then it must be trivial. The main ingredients of our proof are the Caffarelli-Silvestre extension and Armitage's Liouville-type theorem

Identification of driving factors of algal growth in the South-to-North Water Diversion Project by Transformer-based deep learning

Accurate and credible identification of the drivers of algal growth is essential for sustainable utilization and scientific management of freshwater. In this study, we developed a deep learning-based Transformer model, named Bloomformer-1, for end-to-end identification of the drivers of algal growth without the needing extensive a priori knowledge or prior experiments. The Middle Route of the South-to-North Water Diversion Project (MRP) was used as the study site to demonstrate that Bloomformer-1 exhibited more robust performance (with the highest R$^{2}$, 0.80 to 0.94, and the lowest RMSE, 0.22–0.43 ​μg/L) compared to four widely used traditional machine learning models, namely extra trees regression (ETR), gradient boosting regression tree (GBRT), support vector regression (SVR), and multiple linear regression (MLR). In addition, Bloomformer-1 had higher interpretability (including higher transferability and understandability) than the four traditional machine learning models, which meant that it was trustworthy and the results could be directly applied to real scenarios. Finally, it was determined that total phosphorus (TP) was the most important driver for the MRP, especially in Henan section of the canal, although total nitrogen (TN) had the highest effect on algal growth in the Hebei section. Based on these results, phosphorus loading controlling in the whole MRP was proposed as an algal control strategy

Lifelong Person Re-Identification via Adaptive Knowledge Accumulation

Person ReID methods always learn through a stationary domain that is fixed by the choice of a given dataset. In many contexts (e.g., lifelong learning), those methods are ineffective because the domain is continually changing in which case incremental learning over multiple domains is required potentially. In this work we explore a new and challenging ReID task, namely lifelong person re-identification (LReID), which enables to learn continuously across multiple domains and even generalise on new and unseen domains. Following the cognitive processes in the human brain, we design an Adaptive Knowledge Accumulation (AKA) framework that is endowed with two crucial abilities: knowledge representation and knowledge operation. Our method alleviates catastrophic forgetting on seen domains and demonstrates the ability to generalize to unseen domains. Correspondingly, we also provide a new and large-scale benchmark for LReID. Extensive experiments demonstrate our method outperforms other competitors by a margin of 5.8% mAP in generalising evaluation.Comment: 10 pages, 5 figures, Accepted by CVPR202

PREPRINT: Comparison of deep learning and hand crafted features for mining simulation data

Computational Fluid Dynamics (CFD) simulations are a very important tool for many industrial applications, such as aerodynamic optimization of engineering designs like cars shapes, airplanes parts etc. The output of such simulations, in particular the calculated flow fields, are usually very complex and hard to interpret for realistic three-dimensional real-world applications, especially if time-dependent simulations are investigated. Automated data analysis methods are warranted but a non-trivial obstacle is given by the very large dimensionality of the data. A flow field typically consists of six measurement values for each point of the computational grid in 3D space and time (velocity vector values, turbulent kinetic energy, pressure and viscosity). In this paper we address the task of extracting meaningful results in an automated manner from such high dimensional data sets. We propose deep learning methods which are capable of processing such data and which can be trained to solve relevant tasks on simulation data, i.e. predicting drag and lift forces applied on an airfoil. We also propose an adaptation of the classical hand crafted features known from computer vision to address the same problem and compare a large variety of descriptors and detectors. Finally, we compile a large dataset of 2D simulations of the flow field around airfoils which contains 16000 flow fields with which we tested and compared approaches. Our results show that the deep learning-based methods, as well as hand crafted feature based approaches, are well-capable to accurately describe the content of the CFD simulation output on the proposed dataset

Dual Gaussian-based Variational Subspace Disentanglement for Visible-Infrared Person Re-Identification

Visible-infrared person re-identification (VI-ReID) is a challenging and essential task in night-time intelligent surveillance systems. Except for the intra-modality variance that RGB-RGB person re-identification mainly overcomes, VI-ReID suffers from additional inter-modality variance caused by the inherent heterogeneous gap. To solve the problem, we present a carefully designed dual Gaussian-based variational auto-encoder (DG-VAE), which disentangles an identity-discriminable and an identity-ambiguous cross-modality feature subspace, following a mixture-of-Gaussians (MoG) prior and a standard Gaussian distribution prior, respectively. Disentangling cross-modality identity-discriminable features leads to more robust retrieval for VI-ReID. To achieve efficient optimization like conventional VAE, we theoretically derive two variational inference terms for the MoG prior under the supervised setting, which not only restricts the identity-discriminable subspace so that the model explicitly handles the cross-modality intra-identity variance, but also enables the MoG distribution to avoid posterior collapse. Furthermore, we propose a triplet swap reconstruction (TSR) strategy to promote the above disentangling process. Extensive experiments demonstrate that our method outperforms state-of-the-art methods on two VI-ReID datasets.Comment: Accepted by ACM MM 2020 poster. 12 pages, 10 appendixe