Nonlinear O(3)O(3) sigma model in discrete complex analysis

We examine a discrete version of the two-dimensional nonlinear $O(3)$ sigma model derived from discrete complex analysis. We adopt two lattices, one rectangular, the other polar. We define a discrete energy $E({f})^{\rm disc.}$ and a discrete area ${\cal{A}}({f})^{\rm disc.}$, where the function $f$ is related to a stereographic projection governed by a unit vector of the model. The discrete energy and area satisfy the inequality $E({f})^{\rm disc.} \ge |{\cal{A}}({f})^{\rm disc.}|$, which is saturated if and only if the function $f$ is discrete (anti-)holomorphic. We show for the rectangular lattice that, except for a factor 2, the discrete energy and the area tend to the usual continuous energy $E({f})$ and the area ${\cal{A}}({f})=4 \pi N, \,\,N\in \pi_2(S^2)$ as the lattice spacings tend to zero. In the polar lattice, we section the plane by $2M$ lines passing through the origin into $2M$ equal sectors and place vertices radially in a geometric progression with a common ratio $q$. For this polar lattice, the Euler--Lagrange equation derived from the discrete energy $E({f})^{\rm disc.}$ yields rotationally symmetric (anti-)holomorphic solutions $f(z)=Cz^{\pm 1}\,\,(C\bar{z}^{\pm 1})$ in the zeroth order of $\kappa:=q^{-1}-q$. We find that the discrete area evaluated by these zeroth-order solutions is expressible as a $q$-integral (the Jackson integral). Moreover, the area tends to $\pm 2\cdot 4\pi$ in the continuum limit ($M \to \infty$ and $q \to 1\!-0$) with fixed discrete conformal structure $\rho_0 =2 \sin{(\pi/M)}/ \kappa$.Comment: v1. 10 pages, 2 figures v2. New title, 19 pages and 3 figures, Sec.2.3 (EL eq. and its continuum limt) and Sec.3 (polar lattice) adde

Fate of Polycyclic Aromatic Hydrocarbons and Radionuclides through Loess over Pan-Japan Sea Area -Reaction, Transportation and Deposition-

金沢大学大学院自然科学研究科金沢大学工学部Nankai, UniversityChinese Academy of SciencesScedule:17-18 March 2003, Vemue: Kanazawa, Japan, Kanazawa Citymonde Hotel, Project Leader : Hayakawa, Kazuichi, Symposium Secretariat: XO kamata, Naoto, Edited by:Kamata, Naoto

The whole blood transcriptional regulation landscape in 465 COVID-19 infected samples from Japan COVID-19 Task Force

「コロナ制圧タスクフォース」COVID-19患者由来の血液細胞における遺伝子発現の網羅的解析 --重症度に応じた遺伝子発現の変化には、ヒトゲノム配列の個人差が影響する--. 京都大学プレスリリース. 2022-08-23.Coronavirus disease 2019 (COVID-19) is a recently-emerged infectious disease that has caused millions of deaths, where comprehensive understanding of disease mechanisms is still unestablished. In particular, studies of gene expression dynamics and regulation landscape in COVID-19 infected individuals are limited. Here, we report on a thorough analysis of whole blood RNA-seq data from 465 genotyped samples from the Japan COVID-19 Task Force, including 359 severe and 106 non-severe COVID-19 cases. We discover 1169 putative causal expression quantitative trait loci (eQTLs) including 34 possible colocalizations with biobank fine-mapping results of hematopoietic traits in a Japanese population, 1549 putative causal splice QTLs (sQTLs; e.g. two independent sQTLs at TOR1AIP1), as well as biologically interpretable trans-eQTL examples (e.g., REST and STING1), all fine-mapped at single variant resolution. We perform differential gene expression analysis to elucidate 198 genes with increased expression in severe COVID-19 cases and enriched for innate immune-related functions. Finally, we evaluate the limited but non-zero effect of COVID-19 phenotype on eQTL discovery, and highlight the presence of COVID-19 severity-interaction eQTLs (ieQTLs; e.g., CLEC4C and MYBL2). Our study provides a comprehensive catalog of whole blood regulatory variants in Japanese, as well as a reference for transcriptional landscapes in response to COVID-19 infection