Ramsey-Tur\'an Problems with small independence numbers

Given a graph $H$ and a function $f(n)$, the Ramsey-Tur\'an number $RT(n,H,f(n))$ is the maximum number of edges in an $n$-vertex $H$-free graph with independence number at most $f(n)$. For $H$ being a small clique, many results about $RT(n,H,f(n))$ are known and we focus our attention on $H=K_s$ for $s\leq 13$. By applying Szemer\'edi's Regularity Lemma, the dependent random choice method and some weighted Tur\'an-type results, we prove that these cliques have the so-called phase transitions when $f(n)$ is around the inverse function of the off-diagonal Ramsey number of $K_r$ versus a large clique $K_n$ for some $r\leq s$.Comment: 20 page

Multiple Dynamics in Tumor Microenvironment Under Radiotherapy.

The tumor microenvironment (TME) is an evolutionally low-level and embryonically featured tissue comprising heterogenic populations of malignant and stromal cells as well as noncellular components. Under radiotherapy (RT), the major modality for the treatment of malignant diseases [1], TME shows an adaptive response in multiple aspects that affect the efficacy of RT. With the potential clinical benefits, interests in RT combined with immunotherapy (IT) are intensified with a large scale of clinical trials underway for an array of cancer types. A better understanding of the multiple molecular aspects, especially the cross talks of RT-mediated energy reprogramming and immunoregulation in the irradiated TME (ITME), will be necessary for further enhancing the benefit of RT-IT modality. Coming studies should further reveal more mechanistic insights of radiation-induced instant or permanent consequence in tumor and stromal cells. Results from these studies will help to identify critical molecular pathways including cancer stem cell repopulation, metabolic rewiring, and specific communication between radioresistant cancer cells and the infiltrated immune active lymphocytes. In this chapter, we will focus on the following aspects: radiation-repopulated cancer stem cells (CSCs), hypoxia and re-oxygenation, reprogramming metabolism, and radiation-induced immune regulation, in which we summarize the current literature to illustrate an integrated image of the ITME. We hope that the contents in this chapter will be informative for physicians and translational researchers in cancer radiotherapy or immunotherapy