Degenerate bifurcations of two-fold doubly-connected vortex patches

In this paper we consider the existence of uniformly rotating doubly-connected vortex patch near some annuli. Such annuli correspond to a very degenerate case in the scenario of linearization. Upon a careful analysis on the nonlinear structure of the functional, we prove that there exists a family of two-fold uniformly rotating doubly-connected vortex patch emanating from these annuli. This result partially answers an open problem proposed by Hmidi and Mateu in \cite{Hmidi2016a}

Boundary regularity of uniformly rotating vortex patch

In this paper we consider the singularities on the boundary of limiting $V$-states of the 2-dim incompressible Euler equation. By setting up a Weiss-type monotoncity formula for a sign-changing unstable elliptic free boundary problem, we obtain the classification of singular points on the free boundary: the boundary of vortical domain would form either a right angle ($90^\circ$) or a cusp ($0^\circ$) near these points in the limiting sense. For the first alternative, we further prove the uniformly regularity of the free boundary near these isolated singular points

Recent advances in drug delivery of celastrol for enhancing efficiency and reducing the toxicity

Celastrol is a quinone methyl triterpenoid monomeric ingredient extracted from the root of Tripterygium wilfordii. Celastrol shows potential pharmacological activities in various diseases, which include inflammatory, obesity, cancer, and bacterial diseases. However, the application prospect of celastrol is largely limited by its low bioavailability, poor water solubility, and undesired off-target cytotoxicity. To address these problems, a number of drug delivery methods and technologies have been reported to enhance the efficiency and reduce the toxicity of celastrol. We classified the current drug delivery technologies into two parts. The direct chemical modification includes nucleic acid aptamer–celastrol conjugate, nucleic acid aptamer–dendrimer–celastrol conjugate, and glucolipid–celastrol conjugate. The indirect modification includes dendrimers, polymers, albumins, and vesicular carriers. The current technologies can covalently bond or encapsulate celastrol, which improves its selectivity. Here, we present a review that focalizes the recent advances of drug delivery strategies in enhancing the efficiency and reducing the toxicity of celastrol

Federated Knowledge Graph Completion via Latent Embedding Sharing and Tensor Factorization

Knowledge graphs (KGs), which consist of triples, are inherently incomplete and always require completion procedure to predict missing triples. In real-world scenarios, KGs are distributed across clients, complicating completion tasks due to privacy restrictions. Many frameworks have been proposed to address the issue of federated knowledge graph completion. However, the existing frameworks, including FedE, FedR, and FEKG, have certain limitations. = FedE poses a risk of information leakage, FedR's optimization efficacy diminishes when there is minimal overlap among relations, and FKGE suffers from computational costs and mode collapse issues. To address these issues, we propose a novel method, i.e., Federated Latent Embedding Sharing Tensor factorization (FLEST), which is a novel approach using federated tensor factorization for KG completion. FLEST decompose the embedding matrix and enables sharing of latent dictionary embeddings to lower privacy risks. Empirical results demonstrate FLEST's effectiveness and efficiency, offering a balanced solution between performance and privacy. FLEST expands the application of federated tensor factorization in KG completion tasks.Comment: Accepted by ICDM 202