arXiv subjects
Publications and source records attributed to Jiaping Lu.
Let I be a finite partially ordered set and let (Sym({\Delta}i),{\Delta}i)i be a sequence of symmetric groups indexed by I. Construct the generalised wreath product (F, {\Delta}) on this sequence of permutation groups. We determine the minimum number d(F) of generators required for this generalised wreath product.
Let G1, G2, ... be a sequence of almost simple groups and construct a sequence (Wi) of wreath products via W1 = G1 and, for each i > 1, Wi+1 = Gi+1 wr Wi via the regular action of each Gi. We determine the minimum number d(Wi) of generators required for each wreath product in this sequence.
Let $G_{1}$, $G_{2}$, ... be a sequence of groups each of which is either an alternating group, a symmetric group or a cyclic group and construct a sequence $(W_{i})$ of wreath products via $W_{1} = G_{1}$ and, for each $i \geq 1$, $W_{i+1} = G_{i+1} \operatorname{wr} G_{i}$ via the natural permutation action. We determine the minimum number $d(W_{i})$ of generators required for each wreath product in this sequence.
Diabetes is a chronic disease with a significant global health burden, requiring multi-stakeholder collaboration for optimal management. Large language models (LLMs) have shown promise in various healthcare scenarios, but their effectiveness across diverse diabetes tasks remains unproven. Our study introduced a framework to train and validate diabetes-specific LLMs. We first developed a comprehensive data processing pipeline that includes data collection, filtering, augmentation and refinement. This created a high-quality, diabetes-specific dataset and evaluation benchmarks from scratch. Fine-tuned on the collected training dataset, our diabetes-specific LLM family demonstrated state-of-the-art proficiency in processing various diabetes tasks compared to other LLMs. Furthermore, clinical studies revealed the potential applications of our models in diabetes care, including providing personalized healthcare, assisting medical education, and streamlining clinical tasks. Generally, our introduced framework helps develop diabetes-specific LLMs and highlights their potential to enhance clinical practice and provide personalized, data-driven support for diabetes management across different end users. Our codes, benchmarks and models are available at https://github.com/waltonfuture/Diabetica.
An extension of the Kadomtsev-Petviashvili (KP) hierarchy defined via scalar pseudo-differential operators was studied in [16, 20]. In this paper, we represent the extended KP hierarchy into the form of bilinear equation of (adjoint) Baker-Akhiezer functions, and construct its additional symmetries. As a byproduct, we derive the Virasoro symmetries for the constrained KP hierarchies.