We train machine learning models to predict the order of the Shafarevich-Tate group of an elliptic curve over $\mathbb{Q}$. Building on earlier work of He, Lee, and Oliver, we show that a feed-forward neural network classifier trained on subsets of the invariants arising in the Birch--Swinnerton-Dyer conjectural formula yields higher accuracies ($> 0.9$) than any model previously studied. In addition, we develop a regression model that may be used to predict orders of this group not seen during training and apply this to the elliptic curve of rank 29 recently discovered by Elkies and Klagsbrun. Finally we conduct some exploratory data analyses and visualizations on our dataset. We use the elliptic curve dataset from the L-functions and modular forms database (LMFDB).

The integration of social media and artificial intelligence (AI) into disaster management, particularly for earthquake response, represents a profound evolution in emergency management practices. In the digital age, real-time information sharing has reached unprecedented levels, with social media platforms emerging as crucial communication channels during crises. This shift has transformed traditional, centralized emergency services into more decentralized, participatory models of disaster situational awareness. Our study includes an experimental analysis of 8,900 social media interactions, including 2,920 posts and 5,980 replies on X (formerly Twitter), following a magnitude 5.1 earthquake in Oklahoma on February 2, 2024. The analysis covers data from the immediate aftermath and extends over the following seven days, illustrating the critical role of digital platforms in modern disaster response. The results demonstrate that social media platforms can be effectively used as real-time situational awareness tools, delivering critical information to society and authorities during emergencies.

--Node classification on static graphs has achieved significant success, but achieving accurate node classification on dynamic graphs where node topology, attributes, and labels change over time has not been well addressed. Existing methods based on RNNs and self-attention only aggregate features of the same node across different time slices, which cannot adequately address and capture the diverse dynamic changes in dynamic graphs. Therefore, we propose a novel model named Hypergraph-Based Multi-granularity Dynamic Graph Node Classification (HYDG). More accurate representations are obtained through weighted information propagation and aggregation by the hypergraph neural network. Extensive experiments on five real dynamic graph datasets using two GNN backbones demonstrate the superiority of our proposed framework.

Regularization is a widely recognized technique in mathematical optimization. It can be used to smooth out objective functions, refine the feasible solution set, or prevent overfitting in machine learning models. Due to its simplicity and robustness, the gradient descent (GD) method is one of the primary methods used for numerical optimization of differentiable objective functions. However, GD is not well-suited for solving $\ell^1$ regularized optimization problems since these problems are non-differentiable at zero, causing iteration updates to oscillate or fail to converge. Instead, a more effective version of GD, called the proximal gradient descent employs a technique known as soft-thresholding to shrink the iteration updates toward zero, thus enabling sparsity in the solution. Motivated by the widespread applications of proximal GD in sparse and low-rank recovery across various engineering disciplines, we provide an overview of the GD and proximal GD methods for solving regularized optimization problems. Furthermore, this paper proposes a novel algorithm for the proximal GD method that incorporates a variable step size. Unlike conventional proximal GD, which uses a fixed step size based on the global Lipschitz constant, our method estimates the Lipschitz constant locally at each iteration and uses its reciprocal as the step size. This eliminates the need for a global Lipschitz constant, which can be impractical to compute. Numerical experiments we performed on synthetic and real-data sets show notable performance improvement of the proposed method compared to the conventional proximal GD with constant step size, both in terms of number of iterations and in time requirements.

Air pollution in cities, especially NO\textsubscript{2}, is linked to numerous health problems, ranging from mortality to mental health challenges and attention deficits in children. While cities globally have initiated policies to curtail emissions, real-time monitoring remains challenging due to limited environmental sensors and their inconsistent distribution. This gap hinders the creation of adaptive urban policies that respond to the sequence of events and daily activities affecting pollution in cities. Here, we demonstrate how city CCTV cameras can act as a pseudo-NO\textsubscript{2} sensors. Using a predictive graph deep model, we utilised traffic flow from London's cameras in addition to environmental and spatial factors, generating NO\textsubscript{2} predictions from over 133 million frames. Our analysis of London's mobility patterns unveiled critical spatiotemporal connections, showing how specific traffic patterns affect NO\textsubscript{2} levels, sometimes with temporal lags of up to 6 hours. For instance, if trucks only drive at night, their effects on NO\textsubscript{2} levels are most likely to be seen in the morning when people commute. These findings cast doubt on the efficacy of some of the urban policies currently being implemented to reduce pollution. By leveraging existing camera infrastructure and our introduced methods, city planners and policymakers could cost-effectively monitor and mitigate the impact of NO\textsubscript{2} and other pollutants.

Learning to move is a primary goal for animals and robots, where ensuring safety is often important when optimizing control policies on the embodied systems. For complex tasks such as the control of human or humanoid control, the high-dimensional parameter space adds complexity to the safe optimization effort. Current safe exploration algorithms exhibit inefficiency and may even become infeasible with large high-dimensional input spaces. Furthermore, existing high-dimensional constrained optimization methods neglect safety in the search process. In this paper, we propose High-dimensional Safe Bayesian Optimization with local optimistic exploration (HdSafeBO), a novel approach designed to handle high-dimensional sampling problems under probabilistic safety constraints. We introduce a local optimistic strategy to efficiently and safely optimize the objective function, providing a probabilistic safety guarantee and a cumulative safety violation bound. Through the use of isometric embedding, HdSafeBO addresses problems ranging from a few hundred to several thousand dimensions while maintaining safety guarantees. To our knowledge, HdSafeBO is the first algorithm capable of optimizing the control of high-dimensional musculoskeletal systems with high safety probability. We also demonstrate the real-world applicability of HdSafeBO through its use in the safe online optimization of neural stimulation induced human motion control.

Federated Clustering (FC) is crucial to mining knowledge from unlabeled non-Independent Identically Distributed (non-IID) data provided by multiple clients while preserving their privacy. Most existing attempts learn cluster distributions at local clients, and then securely pass the desensitized information to the server for aggregation. However, some tricky but common FC problems are still relatively unexplored, including the heterogeneity in terms of clients' communication capacity and the unknown number of proper clusters $k^*$. To further bridge the gap between FC and real application scenarios, this paper first shows that the clients' communication asynchrony and unknown $k^*$ are complex coupling problems, and then proposes an Asynchronous Federated Cluster Learning (AFCL) method accordingly. It spreads the excessive number of seed points to the clients as a learning medium and coordinates them across the clients to form a consensus. To alleviate the distribution imbalance cumulated due to the unforeseen asynchronous uploading from the heterogeneous clients, we also design a balancing mechanism for seeds updating. As a result, the seeds gradually adapt to each other to reveal a proper number of clusters. Extensive experiments demonstrate the efficacy of AFCL.

If the state-of-the-art research in Machine and Deep Learning for finance has reached interesting results about Credit Scoring models, usage of such models in a heavily regulated context ([5], [1], [3], [4]) such as the one in banks has never been done so far. Our work is thus a tentative to challenge the current regulatory status-quo and introduce new BASEL 2 and 3 compliant techniques, while still answering the Federal Reserve Bank and the European Central Bank requirements. With the help of Gradient Boosting Machines (mainly XGBoost [9]) we challenge an actual model used by BANK A for scoring through the door Auto Loan applicants. We prove that the usage of such algorithms for Credit Scoring models drastically improves performance and default capture rate. Furthermore, we leverage the power of Shapley Values [16] to prove that these relatively simple models are not as black-box as the current regulatory system thinks they are, and we attempt to explain the model outputs and Credit Scores within the BANK A Model Design and Validation framework.

Federated Learning (FL) has received much attention in recent years. However, although clients are not required to share their data in FL, the global model itself can implicitly remember clients' local data. Therefore, it's necessary to effectively remove the target client's data from the FL global model to ease the risk of privacy leakage and implement ``the right to be forgotten". Federated Unlearning (FU) has been considered a promising way to remove data without full retraining. But the model utility easily suffers significant reduction during unlearning due to the gradient conflicts. Furthermore, when conducting the post-training to recover the model utility, the model is prone to move back and revert what has already been unlearned. To address these issues, we propose Federated Unlearning with Orthogonal Steepest Descent (FedOSD). We first design an unlearning Cross-Entropy loss to overcome the convergence issue of the gradient ascent. A steepest descent direction for unlearning is then calculated in the condition of being non-conflicting with other clients' gradients and closest to the target client's gradient. This benefits to efficiently unlearn and mitigate the model utility reduction. After unlearning, we recover the model utility by maintaining the achievement of unlearning. Finally, extensive experiments in several FL scenarios verify that FedOSD outperforms the SOTA FU algorithms in terms of unlearning and model utility.

Raman scattering is based on molecular vibration spectroscopy and provides a powerful technology for pathogenic bacteria diagnosis using the unique molecular fingerprint information of a substance. The integration of deep learning technology has significantly improved the efficiency and accuracy of intelligent Raman spectroscopy (RS) recognition. However, the current RS recognition methods based on deep neural networks still require the annotation of a large amount of spectral data, which is labor-intensive. This paper presents a novel annotation-efficient Self-Calibrated Dual Contrasting (SCDC) method for RS recognition that operates effectively with few or no annotation. Our core motivation is to represent the spectrum from two different perspectives in two distinct subspaces: embedding and category. The embedding perspective captures instance-level information, while the category perspective reflects category-level information. Accordingly, we have implemented a dual contrastive learning approach from two perspectives to obtain discriminative representations, which are applicable for Raman spectroscopy recognition under both unsupervised and semi-supervised learning conditions. Furthermore, a self-calibration mechanism is proposed to enhance robustness. Validation of the identification task on three large-scale bacterial Raman spectroscopy datasets demonstrates that our SCDC method achieves robust recognition performance with very few (5$\%$ or 10$\%$) or no annotations, highlighting the potential of the proposed method for biospectral identification in annotation-efficient clinical scenarios.