An asymptotic analysis for an integrable variant of the Lotka-Volterra prey-predator model via a determinant expansion technique

Abstract: The Hankel determinant appears in representations of solutions to several integrable systems. An asymptotic expansion of the Hankel determinant thus plays a key role in the investigation of asymptotic analysis of such integrable systems. This paper presents an asymptotic expansion formula of a certain Casorati determinant as an extension of the Hankel case. This Casorati determinant is then shown to be associated with the solution to the discrete hungry Lotka-Volterra (dhLV) system, which is an integrable variant of the famous prey-predator model in mathematical biology. Finally, the asymptotic behavior of the dhLV system is clarified using the expansion formula for the Casorati determinant

Nesfatin-1 evokes Ca2+ signaling in isolated vagal afferent neurons via Ca2+ influx through N-type channels

金沢大学医薬保健研究域医学系Nesfatin-1, processed from nucleobindin 2, is an anorexigenic peptide expressed in the brain and several peripheral tissues including the stomach and pancreas. Peripheral, as well as intracerebroventricular, administration of nesfatin-1 suppresses feeding behavior, though underlying mechanisms are unknown. In this study, we examined effects of nesfatin-1 on cytosolic Ca2+ concentration ([Ca2+]i) in the neurons isolated from the vagal afferent nodose ganglion of mice. Nesfatin-1 at 10-10-10-8 M increased [Ca2+]i in the isolated neurons in a concentration-dependent manner, and at 10-8 M it increased [Ca2+]i in 33 out of 263 (12.5%) neurons. These responses were inhibited under Ca2+-free conditions and by N-type Ca2+ channel blocker, ω-conotoxin GVIA. All the nesfatin-1-responsive neurons also exhibited [Ca2+]i responses to capsaicin and cholecystokinin-8. These results provide direct evidence that nesfatin-1 activates vagal afferent neurons by stimulating Ca2+ influx through N-type channels, demonstrating the machinery through which peripheral nesfatin-1 can convey signals to the brain. © 2009 Elsevier Inc. All rights reserved

帯行列の固有値を計算する離散可積分系について

九州大学応用力学研究所研究集会報告 No.21ME-S7 「非線形波動研究の現状と将来 : 次の10 年への展望」RIAM Symposium No.21ME-S7 Current and Future Research on Nonlinear Waves : Perspectives for the Next Decade離散可積分系に分類される離散ハングリーロトカ・ボルテラ系及び離散ハングリー戸田方程式の時間発展は，あるクラスの帯行列の相似変形を与える。この性質を利用して定式化された帯行列の固有値計算アルゴリズムを紹介する

箱に番号が付いた新しい箱玉系について

九州大学応用力学研究所研究集会報告 No.25AO-S2 「非線形波動研究の拡がり」Reports of RIAM Symposium No.25AO-S2 The breadth and depth of nonlinear wave scienceProceedings of a symposium held at Chikushi Campus, Kyushu Universiy, Kasuga, Fukuoka, Japan, October 31 - November 2, 2013離散ハングリー戸田方程式の超離散版は玉に番号が付いた箱玉系の運動方程式として知られている．本報告では，離散ハングリー戸田方程式のある変形版を導入し，その超離散化を通じて箱を番号付けで区別した新しい箱玉系を導く．また，離散ハングリー戸田方程式の変形版の保存量を求め，その超離散化によって新しい箱玉系の保存量を明らかにする．保存量を求める過程において，離散ハングリーロトカ・ボルテラ系と離散ハングリー戸田方程式の変形版を結ぶベックルント変換も示す．さらに，玉に番号が付いた箱玉系と新しい箱玉系の関係についても述べる

8-oxoguanine causes spontaneous de novo germline mutations in mice.

Spontaneous germline mutations generate genetic diversity in populations of sexually reproductive organisms, and are thus regarded as a driving force of evolution. However, the cause and mechanism remain unclear. 8-oxoguanine (8-oxoG) is a candidate molecule that causes germline mutations, because it makes DNA more prone to mutation and is constantly generated by reactive oxygen species in vivo. We show here that endogenous 8-oxoG caused de novo spontaneous and heritable G to T mutations in mice, which occurred at different stages in the germ cell lineage and were distributed throughout the chromosomes. Using exome analyses covering 40.9 Mb of mouse transcribed regions, we found increased frequencies of G to T mutations at a rate of 2 × 10(-7) mutations/base/generation in offspring of Mth1/Ogg1/Mutyh triple knockout (TOY-KO) mice, which accumulate 8-oxoG in the nuclear DNA of gonadal cells. The roles of MTH1, OGG1, and MUTYH are specific for the prevention of 8-oxoG-induced mutation, and 99% of the mutations observed in TOY-KO mice were G to T transversions caused by 8-oxoG; therefore, we concluded that 8-oxoG is a causative molecule for spontaneous and inheritable mutations of the germ lineage cells

Convergence acceleration of shifted LRLR transformations for totally nonnegative Hessenberg matrices

summary:We design shifted $LR$ transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted $LR$ transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted $LR$ transformations by considering the concept of the Newton shift. We show that the shifted $LR$ transformations with the resulting shift strategy converge with order $2-\epsilon$ for arbitrary $\epsilon >0$