Synthesis of N-heterocycles through cyclization-triggered tandem additions to alkynes and the study of promoters in ionic reactions.

Our research mainly focused on three parts related to the rapid construction of N-heterocycles and the search for ionic reaction promoters. First, N-heterocycles of different ring sizes and with different substitution patterns constitute extremely important structure classes (e.g., alkaloids) in the search for bioactivity. A contemporary challenge in organic synthesis is the mapping of new chemical spaces through tandem or cascade reactions in an atom economical fashion. Our strategy to access these biologically important heterocycles is through a cyclization-triggered tandem addition to alkynes catalyzed by readily available alkynophilic coinage metals like copper. In this manner, a variety of functional groups could be introduced to the ring system through a carbon-carbon forming reaction. Second, in chemistry, a promoter is defined as a substance added to a catalyst to improve its performance in a chemical reaction. Promoters interact with active components of catalysts and thereby alter their chemical effect on the catalyzed substance. In our studies, we found KCTf3 is an ideal promoter that is readily available and able to tolerate harsh reaction conditions. When KCTf3 is added to reaction system, a reshuffling of ions occurs and a CTf3- reactive cationic species will be generated in situ, which improves the efficiency of a reaction. Third, silver-mediated halogen abstraction is the most preferred method to generate cationic gold from a gold catalyst precursor. However, the use of silver activators is problematic because of its high cost, generation of unwanted side reactions and Au-Ag intermediates. We found that a gold phthalimide complex (L-Au-Pht) could be easily synthesized, and upon contact with either a Brønsted acid or a Lewis acid it generates an active gold phthalimide complex that not only avoid problems caused by silver promoters but also yields an efficient and highly reactive gold catalyst for the most popular types of gold-catalyzed reactions, including X-H (X = O, N, C) additions to C-C unsaturated compounds (alkyne/allene/alkene), and cycloisomerizations

From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is being iteratively aggregated to central nodes from their neighbourhood. Such a scheme has been found to be intrinsically linked to a physical process known as heat diffusion, where the propagation of GNNs naturally corresponds to the evolution of heat density. Analogizing the process of message passing to the heat dynamics allows to fundamentally understand the power and pitfalls of GNNs and consequently informs better model design. Recently, there emerges a plethora of works that proposes GNNs inspired from the continuous dynamics formulation, in an attempt to mitigate the known limitations of GNNs, such as oversmoothing and oversquashing. In this survey, we provide the first systematic and comprehensive review of studies that leverage the continuous perspective of GNNs. To this end, we introduce foundational ingredients for adapting continuous dynamics to GNNs, along with a general framework for the design of graph neural dynamics. We then review and categorize existing works based on their driven mechanisms and underlying dynamics. We also summarize how the limitations of classic GNNs can be addressed under the continuous framework. We conclude by identifying multiple open research directions

Generalized energy and gradient flow via graph framelets

In this work, we provide a theoretical understanding of the framelet-based graph neural networks through the perspective of energy gradient flow. By viewing the framelet-based models as discretized gradient flows of some energy, we show it can induce both low-frequency and high-frequency-dominated dynamics, via the separate weight matrices for different frequency components. This substantiates its good empirical performance on both homophilic and heterophilic graphs. We then propose a generalized energy via framelet decomposition and show its gradient flow leads to a novel graph neural network, which includes many existing models as special cases. We then explain how the proposed model generally leads to more flexible dynamics, thus potentially enhancing the representation power of graph neural networks

Generalized Bures-Wasserstein Geometry for Positive Definite Matrices

This paper proposes a generalized Bures-Wasserstein (BW) Riemannian geometry for the manifold of symmetric positive definite matrices. We explore the generalization of the BW geometry in three different ways: 1) by generalizing the Lyapunov operator in the metric, 2) by generalizing the orthogonal Procrustes distance, and 3) by generalizing the Wasserstein distance between the Gaussians. We show that they all lead to the same geometry. The proposed generalization is parameterized by a symmetric positive definite matrix $\mathbf{M}$ such that when $\mathbf{M} = \mathbf{I}$, we recover the BW geometry. We derive expressions for the distance, geodesic, exponential/logarithm maps, Levi-Civita connection, and sectional curvature under the generalized BW geometry. We also present applications and experiments that illustrate the efficacy of the proposed geometry

Generalized Laplacian Regularized Framelet GCNs

This paper introduces a novel Framelet Graph approach based on p-Laplacian GNN. The proposed two models, named p-Laplacian undecimated framelet graph convolution (pL-UFG) and generalized p-Laplacian undecimated framelet graph convolution (pL-fUFG) inherit the nature of p-Laplacian with the expressive power of multi-resolution decomposition of graph signals. The empirical study highlights the excellent performance of the pL-UFG and pL-fUFG in different graph learning tasks including node classification and signal denoising

Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challenges

Graph-based message-passing neural networks (MPNNs) have achieved remarkable success in both node and graph-level learning tasks. However, several identified problems, including over-smoothing (OSM), limited expressive power, and over-squashing (OSQ), still limit the performance of MPNNs. In particular, OSQ serves as the latest identified problem, where MPNNs gradually lose their learning accuracy when long-range dependencies between graph nodes are required. In this work, we provide an exposition on the OSQ problem by summarizing different formulations of OSQ from current literature, as well as the three different categories of approaches for addressing the OSQ problem. In addition, we also discuss the alignment between OSQ and expressive power and the trade-off between OSQ and OSM. Furthermore, we summarize the empirical methods leveraged from existing works to verify the efficiency of OSQ mitigation approaches, with illustrations of their computational complexities. Lastly, we list some open questions that are of interest for further exploration of the OSQ problem along with potential directions from the best of our knowledge