On reduction complexity of Heegaard splittings

AbstractLet ∪F W be a Heegaard splitting of a closed, connected, orientable 3-manifold M with genus n. We introduce a reduction complexity, δ, for the Heegaard splitting, and conclude that: 1.(1) δ ⩾ max{2, n} if and only if V ∪F W is reducible;2.(2) δ ⩾ 2 if and only if V ∪F W is weakly reducible,3.(3) δ > n if and only if M has exactly δ − n connected sum factors which are homeomorphic to S1 × S2

Persistent hypergraph homology and its applications

Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as persistent barcodes. However, many datasets contain complex systems of multi-way interactions, making these datasets more naturally and faithfully modeled by hypergraphs. In this article, we investigate the persistent hypergraph model, an important generalization of the classical persistent homology on simplicial complexes. We introduce a new homology, $\hat{H}$, on hypergraphs and an efficient algorithm to compute both persistent barcodes and $\hat{H}$ barcodes. As example, our theory is demonstrated by analyzing face-to-face interactions of different populations. The datasets that we select consist of baboons in primate center, people from rural Malawi, scientific conference, workplace and high school.Comment: 21 page

Mechanisms of Kaposi's Sarcoma-Associated Herpesvirus Latency and Reactivation

The life cycle of Kaposi's sarcoma-associated herpesvirus (KSHV) consists of latent and lytic replication phases. During latent infection, only a limited number of KSHV genes are expressed. However, this phase of replication is essential for persistent infection, evasion of host immune response, and induction of KSHV-related malignancies. KSHV reactivation from latency produces a wide range of viral products and infectious virions. The resulting de novo infection and viral lytic products modulate diverse cellular pathways and stromal microenvironment, which promote the development of Kaposi's sarcoma (KS). The mechanisms controlling KSHV latency and reactivation are complex, involving both viral and host factors, and are modulated by diverse environmental factors. Here, we review the cellular and molecular basis of KSHV latency and reactivation with a focus on the most recent advancements in the field

Review of the role of collagen in tumorigenesis and development

Collagen is one of the most abundant proteins in the body and is the main component of the extracellular matrix. Collagen regulates cellular behavior, and its dysregulation can cause a variety of diseases, including cancer. Collagen in tumors is mainly produced by fibroblasts and plays an important role in cancer progression and metastasis. Collagen can act as a prognostic predictor for cancer patients and may be an effective target for the treatment and prevention of tumor progression and metastasis. Anti-tumor drugs targeting collagen and its receptors may be developed in the future. This review focuses on the newly discovered role of collagen in cancer in recent years, specifically the role of collagen in tumor cell dormancy and immune evasion, and the participation of collagen in tumor cell metabolism