相关论文: Ollivier persistent Ricci curvature (OPRC) based m…

Networks with higher-order interactions, prevalent in biological, social, and information systems, are naturally represented as hypergraphs, yet their structural complexity poses fundamental challenges for geometric characterization. While…

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional…

Characterizing shapes of high-dimensional objects via Ricci curvatures plays a critical role in many research areas in mathematics and physics. However, even though several discretizations of Ricci curvatures for discrete combinatorial…

In recent years extensions of manifold Ricci curvature to discrete combinatorial objects such as graphs and hypergraphs (popularly called as "network shapes"), have found a plethora of applications in a wide spectrum of research areas…

Curvature serves as a potent and descriptive invariant, with its efficacy validated both theoretically and practically within graph theory. We employ a definition of generalized Ricci curvature proposed by Ollivier, which Lin and Yau later…

Identifying (a) systemic barriers to quality healthcare access and (b) key indicators of care efficacy in the United States remains a significant challenge. To improve our understanding of regional disparities in care delivery, we introduce…

Artificial intelligence-assisted drug design is revolutionizing the pharmaceutical industry. Effective molecular features are crucial for accurate machine learning predictions, and advanced mathematics plays a key role in designing these…

We introduce ORC-ManL, a new algorithm to prune spurious edges from nearest neighbor graphs using a criterion based on Ollivier-Ricci curvature and estimated metric distortion. Our motivation comes from manifold learning: we show that when…

Optical proximity correction (OPC) is a widely-used resolution enhancement technique (RET) for printability optimization. Recently, rigorous numerical optimization and fast machine learning are the research focus of OPC in both academia and…

Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization to the emerging…

Ricci curvature is a fundamental concept in differential geometry for encoding local geometric structure, and its graph-based analogues have recently gained prominence as practical tools for reweighting, pruning, and reshaping network…

Graph Machine Learning often involves the clustering of nodes based on similarity structure encoded in the graph's topology and the nodes' attributes. On homophilous graphs, the integration of pooling layers has been shown to enhance the…

Accurate prediction of protein-ligand binding affinity remains a central challenge in structure-based drug discovery. The effectiveness of machine learning models critically depends on the quality of molecular descriptors, for which…

Community detection is an important problem in graph neural networks. Recently, algorithms based on Ricci curvature flows have gained significant attention. It was suggested by Ollivier (2009), and applied to community detection by Ni et al…

Persistent homology provides a new approach for the topological simplification of big data via measuring the life time of intrinsic topological features in a filtration process and has found its success in scientific and engineering…

Randomly Wired Neural Networks (RWNNs) serve as a valuable testbed for investigating the impact of network topology in deep learning by capturing how different connectivity patterns impact both learning efficiency and model performance. At…

Machine learning algorithms for generating molecular structures offer a promising new approach to drug discovery. We cast molecular optimization as a translation problem, where the goal is to map an input compound to a target compound with…

The pharmaceutical industry has witnessed exponential growth in transforming operations towards continuous manufacturing to effectively achieve increased profitability, reduced waste, and extended product range. Model Predictive Control…

Classification and Regression Tree (CART), Random Forest (RF) and Gradient Boosting Tree (GBT) are probably the most popular set of statistical learning methods. However, their statistical consistency can only be proved under very…

In this paper, we propose persistent spectral based machine learning (PerSpect ML) models for drug design. Persistent spectral models, including persistent spectral graph, persistent spectral simplicial complex and persistent spectral…