With respect to experiments, our contributions are twofold.

X)vec (Y) (2) We now proceed with the proof of our result. Work completed during an internship at the A WS Shanghai AI Lab. Note that we apply Roth's column lemma to (11) to derive (12). GNN layers with 16 hidden dimensions. Table 1: Results using different base models (left) and test time comparisons (right).

Work completed during an internship at the A WS Shanghai AI Lab.

Node features are derived from patent metadata.

Graphical models, capable of representing data with complex dependencies, are widely used across domains.

Our research addresses the critical challenge of managing blood transfusions and optimizing allocation in resource-constrained regions. We present heuristic matching algorithms for donor-patient and blood bank selection, alongside machine learning methods to analyze blood transfusion acceptance data and predict potential shortages. We developed simulations to optimize blood bank operations, progressing from random allocation to a system incorporating proximity-based selection, blood type compatibility, expiration prioritization, and rarity scores. Moving from blind matching to a heuristic-based approach yielded a 28.6% marginal improvement in blood request acceptance, while a multi-level heuristic matching resulted in a 47.6% improvement. For shortage prediction, we compared Long Short-Term Memory (LSTM) networks, Linear Regression, and AutoRegressive Integrated Moving Average (ARIMA) models, trained on 170 days of historical data. Linear Regression slightly outperformed others with a 1.40% average absolute percentage difference in predictions. Our solution leverages a Cassandra NoSQL database, integrating heuristic optimization and shortage prediction to proactively manage blood resources. This scalable approach, designed for resource-constrained environments, considers factors such as proximity, blood type compatibility, inventory expiration, and rarity. Future developments will incorporate real-world data and additional variables to improve prediction accuracy and optimization performance.

Graph Neural Networks (GNNs) have demonstrated strong performance in graph mining tasks due to their message-passing mechanism, which is aligned with the homophily assumption that adjacent nodes exhibit similar behaviors. However, in many real-world graphs, connected nodes may display contrasting behaviors, termed as heterophilous patterns, which has attracted increased interest in heterophilous GNNs (HTGNNs). Although the message-passing mechanism seems unsuitable for heterophilous graphs due to the propagation of class-irrelevant information, it is still widely used in many existing HTGNNs and consistently achieves notable success. This raises the question: why does message passing remain effective on heterophilous graphs? To answer this question, in this paper, we revisit the message-passing mechanisms in heterophilous graph neural networks and reformulate them into a unified heterophilious message-passing (HTMP) mechanism. Based on HTMP and empirical analysis, we reveal that the success of message passing in existing HTGNNs is attributed to implicitly enhancing the compatibility matrix among classes. Moreover, we argue that the full potential of the compatibility matrix is not completely achieved due to the existence of incomplete and noisy semantic neighborhoods in real-world heterophilous graphs. To bridge this gap, we introduce a new approach named CMGNN, which operates within the HTMP mechanism to explicitly leverage and improve the compatibility matrix. A thorough evaluation involving 10 benchmark datasets and comparative analysis against 13 well-established baselines highlights the superior performance of the HTMP mechanism and CMGNN method.