This paper introduces the RAG-RLRC-LaySum framework, designed to make complex biomedical research understandable to laymen through advanced Natural Language Processing (NLP) techniques. Our Retrieval Augmented Generation (RAG) solution, enhanced by a reranking method, utilizes multiple knowledge sources to ensure the precision and pertinence of lay summaries. Additionally, our Reinforcement Learning for Readability Control (RLRC) strategy improves readability, making scientific content comprehensible to non-specialists. Evaluations using the publicly accessible PLOS and eLife datasets show that our methods surpass Plain Gemini model, demonstrating a 20% increase in readability scores, a 15% improvement in ROUGE-2 relevance scores, and a 10% enhancement in factual accuracy. The RAG-RLRC-LaySum framework effectively democratizes scientific knowledge, enhancing public engagement with biomedical discoveries.

We developed a convolution neural network (CNN) on semi-regular triangulated meshes whose vertices have 6 neighbours. The key blocks of the proposed CNN, including convolution and down-sampling, are directly defined in a vertex domain. By exploiting the ordering property of semi-regular meshes, the convolution is defined on a vertex domain with strong motivation from the spatial definition of classic convolution. Moreover, the down-sampling of a semi-regular mesh embedded in a 3D Euclidean space can achieve a down-sampling rate of 4, 16, 64, etc. We demonstrated the use of this vertex-based graph CNN for the classification of mild cognitive impairment (MCI) and Alzheimer's disease (AD) based on 3169 MRI scans of the Alzheimer's Disease Neuroimaging Initiative (ADNI). We compared the performance of the vertex-based graph CNN with that of the spectral graph CNN.

Data clustering is a fundamental problem with a wide range of applications. Standard methods, eg the $k$-means method, usually require solving a non-convex optimization problem. Recently, total variation based convex relaxation to the $k$-means model has emerged as an attractive alternative for data clustering. However, the existing results on its exact clustering property, ie, the condition imposed on data so that the method can provably give correct identification of all cluster memberships, is only applicable to very specific data and is also much more restrictive than that of some other methods. This paper aims at the revisit of total variation based convex clustering, by proposing a weighted sum-of-$\ell_1$-norm relating convex model. Its exact clustering property established in this paper, in both deterministic and probabilistic context, is applicable to general data and is much sharper than the existing results. These results provided good insights to advance the research on convex clustering. Moreover, the experiments also demonstrated that the proposed convex model has better empirical performance when be compared to standard clustering methods, and thus it can see its potential in practice.