Samelson products in p-regular exceptional Lie groups

The (non)triviality of Samelson products of the inclusions of the spheres into p-regular exceptional Lie groups is completely determined, where a connected Lie group is called p-regular if it has the p-local homotopy type of a product of spheres.Comment: 15 pages, 0 figur

Multi-scale interactions between turbulence and magnetohydrodynamic instability driven by energetic particles

In order to realize high performance burning plasmas in magnetic-confinement fusion devices, such as tokamaks, both bulk plasma transport and that of energetic fusion alpha-particles, which result from different scale fluctuations with different free energy sources, have to be reduced simultaneously. Utilizing the advantage of global toroidal non-linear simulations covering a whole torus, here, we found a new coupling mechanism between the low-frequency micro-scale electromagnetic drift-wave fluctuations regulating the former, while the high-frequency macro-scale toroidal Alfven eigenmode (TAE) regulates the latter. This results from the dual spread of micro-scale turbulence due to the macro-scale TAE not only in wavenumber space representing local eddy size but also in configuration space with global profile variations. Consequently, a new class of turbulent state is found to be established, where the turbulence is homogenized on the poloidal cross-section with exhibiting large-scale structure, which increases fluctuation levels and then both transports, leading to deterioration in the fusion performance

Improving Molecular Properties Prediction Through Latent Space Fusion

Pre-trained Language Models have emerged as promising tools for predicting molecular properties, yet their development is in its early stages, necessitating further research to enhance their efficacy and address challenges such as generalization and sample efficiency. In this paper, we present a multi-view approach that combines latent spaces derived from state-of-the-art chemical models. Our approach relies on two pivotal elements: the embeddings derived from MHG-GNN, which represent molecular structures as graphs, and MoLFormer embeddings rooted in chemical language. The attention mechanism of MoLFormer is able to identify relations between two atoms even when their distance is far apart, while the GNN of MHG-GNN can more precisely capture relations among multiple atoms closely located. In this work, we demonstrate the superior performance of our proposed multi-view approach compared to existing state-of-the-art methods, including MoLFormer-XL, which was trained on 1.1 billion molecules, particularly in intricate tasks such as predicting clinical trial drug toxicity and inhibiting HIV replication. We assessed our approach using six benchmark datasets from MoleculeNet, where it outperformed competitors in five of them. Our study highlights the potential of latent space fusion and feature integration for advancing molecular property prediction. In this work, we use small versions of MHG-GNN and MoLFormer, which opens up an opportunity for further improvement when our approach uses a larger-scale dataset.Comment: 8 Pages, 4 Figures - Submited to the AI4Science Workshop - Neurips 202