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

Textual Knowledge Matters: Cross-Modality Co-Teaching for Generalized Visual Class Discovery

In this paper, we study the problem of Generalized Category Discovery (GCD), which aims to cluster unlabeled data from both known and unknown categories using the knowledge of labeled data from known categories. Current GCD methods rely on only visual cues, which however neglect the multi-modality perceptive nature of human cognitive processes in discovering novel visual categories. To address this, we propose a two-phase TextGCD framework to accomplish multi-modality GCD by exploiting powerful Visual-Language Models. TextGCD mainly includes a retrieval-based text generation (RTG) phase and a cross-modality co-teaching (CCT) phase. First, RTG constructs a visual lexicon using category tags from diverse datasets and attributes from Large Language Models, generating descriptive texts for images in a retrieval manner. Second, CCT leverages disparities between textual and visual modalities to foster mutual learning, thereby enhancing visual GCD. In addition, we design an adaptive class aligning strategy to ensure the alignment of category perceptions between modalities as well as a soft-voting mechanism to integrate multi-modality cues. Experiments on eight datasets show the large superiority of our approach over state-of-the-art methods. Notably, our approach outperforms the best competitor, by 7.7% and 10.8% in All accuracy on ImageNet-1k and CUB, respectively

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

A Generative Deep Learning Approach for Crash Severity Modeling with Imbalanced Data

Crash data is often greatly imbalanced, with the majority of crashes being non-fatal crashes, and only a small number being fatal crashes due to their rarity. Such data imbalance issue poses a challenge for crash severity modeling since it struggles to fit and interpret fatal crash outcomes with very limited samples. Usually, such data imbalance issues are addressed by data resampling methods, such as under-sampling and over-sampling techniques. However, most traditional and deep learning-based data resampling methods, such as synthetic minority oversampling technique (SMOTE) and generative Adversarial Networks (GAN) are designed dedicated to processing continuous variables. Though some resampling methods have improved to handle both continuous and discrete variables, they may have difficulties in dealing with the collapse issue associated with sparse discrete risk factors. Moreover, there is a lack of comprehensive studies that compare the performance of various resampling methods in crash severity modeling. To address the aforementioned issues, the current study proposes a crash data generation method based on the Conditional Tabular GAN. After data balancing, a crash severity model is employed to estimate the performance of classification and interpretation. A comparative study is conducted to assess classification accuracy and distribution consistency of the proposed generation method using a 4-year imbalanced crash dataset collected in Washington State, U.S. Additionally, Monte Carlo simulation is employed to estimate the performance of parameter and probability estimation in both two- and three-class imbalance scenarios. The results indicate that using synthetic data generated by CTGAN-RU for crash severity modeling outperforms using original data or synthetic data generated by other resampling methods

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

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

tau-FPL: Tolerance-Constrained Learning in Linear Time

Learning a classifier with control on the false-positive rate plays a critical role in many machine learning applications. Existing approaches either introduce prior knowledge dependent label cost or tune parameters based on traditional classifiers, which lack consistency in methodology because they do not strictly adhere to the false-positive rate constraint. In this paper, we propose a novel scoring-thresholding approach, tau-False Positive Learning (tau-FPL) to address this problem. We show the scoring problem which takes the false-positive rate tolerance into accounts can be efficiently solved in linear time, also an out-of-bootstrap thresholding method can transform the learned ranking function into a low false-positive classifier. Both theoretical analysis and experimental results show superior performance of the proposed tau-FPL over existing approaches.Comment: 32 pages, 3 figures. This is an extended version of our paper published in AAAI-1