Birational Weyl group actions via mutation combinatorics in cluster algebras

A cluster algebra is an algebraic structure generated by operations of a quiver (a directed graph) called the mutations and their associated simple birational mappings. By using a graph-combinatorial approach, we present a systematic way to derive a tropical, i.e. subtraction-free birational, representation of Weyl groups from cluster algebras. Our result provides a broad class of Weyl group actions including previously known examples acting on certain rational varieties [28, 30] and hence it is relevant to q-Painleve equations and their higher-order extensions. Key ingredients of the argument are the combinatorial aspects of the reflection associated with a cycle subgraph in the quiver. We also discuss symplectic structures of the discrete dynamical systems thus obtained.Comment: 28 pages; typos were corrected and the definition of the polynomials F_k(y) in Section 3.2 was slightly modifie

Cluster algebras and higher order generalizations of the qq-Painleve equations of type A7(1)A_7^{(1)} and A6(1)A_6^{(1)} (Mathematical structures of integrable systems, its deepening and expansion)

Mathematical structures of integrable systems, its deepening and expansion. September 9-11, 2019. edited by Takao Suzuki. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.We construct higher order generalizations of the q-Painlevé equations of surface type A₇(¹) and A₆(¹) based on the cluster algebras corresponding to certain quivers. These equations possess the affine Weyl group symmetries of type A₁(¹) and (A1 + A′1)(¹), respectively. We show that these equations and symmetries can be realized as birational canonical transformations. A relationship between the quivers and the discrete KdV equation is also discussed

クラスター代数およびその拡張に付随する離散可積分方程式

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 時弘 哲治, 東京大学教授 WILLOX RALPH, 東京大学准教授 加藤 晃史, 東京大学准教授 白石 潤一, 東京大学准教授 坂井 秀隆, 青山学院大学准教授 増田 哲University of Tokyo(東京大学

Dentin Materials as Biological Scaffolds for Tissue Engineering

Vital tooth-derived demineralized dentin matrix (DDM) has a bone-inductive ability, while non-vital tooth-derived DDM lost it. Acid treatment for dentin provides the increase of surface area, the release of matrix-binding growth factors such as BMPs, and the decrease of the infection risk. Human autograft of vital tooth-derived DDM was achieved first in Japan 2002, while first bone autograft was noted in Italy 1820. This paper introduced dentin/bone biology and a unique clinical case, combined with two types of non-vital tooth-derived DDM (roots, granules) for lateral bone augmentation. A 63-year-old woman revealed highly atrophic mandible in 2015. Three non-vital teeth were extracted, changed in shape, demineralized in 2% HNO3, were rinsed, and were grafted immediately. The CT images at 3 months after the graft showed remarkable lateral augmentation. DDM scaffolds were received to host, and two fixtures were placed into the DDM-augmented bone. The patient was successfully restored with their own DDM scaffolds and implant surgery

L-carnitine prevents lenvatinib-induced muscle toxicity without impairment of the anti-angiogenic efficacy

Lenvatinib is an oral tyrosine kinase inhibitor that acts on multiple receptors involved in angiogenesis. Lenvatinib is a standard agent for the treatment of several types of advanced cancers; however, it frequently causes muscle-related adverse reactions. Our previous study revealed that lenvatinib treatment reduced carnitine content and the expression of carnitine-related and oxidative phosphorylation (OXPHOS) proteins in the skeletal muscle of rats. Therefore, this study aimed to evaluate the effects of L-carnitine on myotoxic and anti-angiogenic actions of lenvatinib. Co-administration of L-carnitine in rats treated with lenvatinib for 2 weeks completely prevented the decrease in carnitine content and expression levels of carnitine-related and OXPHOS proteins, including carnitine/organic cation transporter 2, in the skeletal muscle. Moreover, L-carnitine counteracted lenvatinib-induced protein synthesis inhibition, mitochondrial dysfunction, and cell toxicity in C2C12 myocytes. In contrast, L-carnitine had no influence on either lenvatinib-induced inhibition of vascular endothelial growth factor receptor 2 phosphorylation in human umbilical vein endothelial cells or angiogenesis in endothelial tube formation and mouse aortic ring assays. These results suggest that L-carnitine supplementation could prevent lenvatinib-induced muscle toxicity without diminishing its antineoplastic activity, although further clinical studies are needed to validate these findings