Approximating the generalized terminal backup problem via half-integral multiflow relaxation

We consider a network design problem called the generalized terminal backup problem. Whereas earlier work investigated the edge-connectivity constraints only, we consider both edge- and node-connectivity constraints for this problem. A major contribution of this paper is the development of a strongly polynomial-time 4/3-approximation algorithm for the problem. Specifically, we show that a linear programming relaxation of the problem is half-integral, and that the half-integral optimal solution can be rounded to a 4/3-approximate solution. We also prove that the linear programming relaxation of the problem with the edge-connectivity constraints is equivalent to minimizing the cost of half-integral multiflows that satisfy flow demands given from terminals. This observation presents a strongly polynomial-time algorithm for computing a minimum cost half-integral multiflow under flow demand constraints

Spider covers for prize-collecting network activation problem

In the network activation problem, each edge in a graph is associated with an activation function, that decides whether the edge is activated from node-weights assigned to its end-nodes. The feasible solutions of the problem are the node-weights such that the activated edges form graphs of required connectivity, and the objective is to find a feasible solution minimizing its total weight. In this paper, we consider a prize-collecting version of the network activation problem, and present first non- trivial approximation algorithms. Our algorithms are based on a new LP relaxation of the problem. They round optimal solutions for the relaxation by repeatedly computing node-weights activating subgraphs called spiders, which are known to be useful for approximating the network activation problem

Network design with edge-connectivity and degree constraints

We consider the following network design problem; Given a vertex set V with a metric cost c on V, an integer k≥1, and a degree specification b, find a minimum cost k-edge-connected multigraph on V under the constraint that the degree of each vertex v∈V is equal to b(v). This problem generalizes metric TSP. In this paper, we show that the problem admits a ρ-approximation algorithm if b(v)≥2, v∈V, where ρ=2.5 if k is even, and ρ=2.5+1.5/k if k is odd. We also prove that the digraph version of this problem admits a 2.5-approximation algorithm and discuss some generalization of metric TSP

Thermotomaculum hydrothermale gen. nov., sp. nov., a novel heterotrophic thermophile within the phylum Acidobacteria from a deep-sea hydrothermal vent chimney in the Southern Okinawa Trough

http://www.godac.jamstec.go.jp/darwin/cruise/natsushima/nt08-13/

DOCK2 is involved in the host genetics and biology of severe COVID-19

「コロナ制圧タスクフォース」COVID-19疾患感受性遺伝子DOCK2の重症化機序を解明 --アジア最大のバイオレポジトリーでCOVID-19の治療標的を発見--. 京都大学プレスリリース. 2022-08-10.Identifying the host genetic factors underlying severe COVID-19 is an emerging challenge. Here we conducted a genome-wide association study (GWAS) involving 2, 393 cases of COVID-19 in a cohort of Japanese individuals collected during the initial waves of the pandemic, with 3, 289 unaffected controls. We identified a variant on chromosome 5 at 5q35 (rs60200309-A), close to the dedicator of cytokinesis 2 gene (DOCK2), which was associated with severe COVID-19 in patients less than 65 years of age. This risk allele was prevalent in East Asian individuals but rare in Europeans, highlighting the value of genome-wide association studies in non-European populations. RNA-sequencing analysis of 473 bulk peripheral blood samples identified decreased expression of DOCK2 associated with the risk allele in these younger patients. DOCK2 expression was suppressed in patients with severe cases of COVID-19. Single-cell RNA-sequencing analysis (n = 61 individuals) identified cell-type-specific downregulation of DOCK2 and a COVID-19-specific decreasing effect of the risk allele on DOCK2 expression in non-classical monocytes. Immunohistochemistry of lung specimens from patients with severe COVID-19 pneumonia showed suppressed DOCK2 expression. Moreover, inhibition of DOCK2 function with CPYPP increased the severity of pneumonia in a Syrian hamster model of SARS-CoV-2 infection, characterized by weight loss, lung oedema, enhanced viral loads, impaired macrophage recruitment and dysregulated type I interferon responses. We conclude that DOCK2 has an important role in the host immune response to SARS-CoV-2 infection and the development of severe COVID-19, and could be further explored as a potential biomarker and/or therapeutic target

All 4-Edge-Connected HHD-Free Graphs are Z3 -Connected

An undirected graph G = (V, E) is called Z3-connected if for all b : V → Z3 with Σv∈V b(v) = 0, an orientation D = (V, A) of G has a Z3-valued nowhere-zero flow f : A → Z3 − {0} such that Σe∈δ+(v) f(e)−Σe∈δ−(v)f(e) = b(v) for all v ∈ V . We show that all 4-edge-connected HHD-free graphs are Z3-connected. This extends the result due to Lai (2000), which proves the Z3-connectivity for 4-edge-connected chordal graphs

ネットワーク セッケイ モンダイ ニ タイスル キンジ アルゴリズム

京都大学0048新制・課程博士博士(情報学)甲第12719号情博第239号新制||情||50(附属図書館)UT51-2007-C255京都大学大学院情報学研究科数理工学専攻(主査)教授 永持 仁, 教授 福嶋 雅夫, 教授 岩間 一雄学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDFA