Single Source Shortest Paths for All Flows with Integer Costs

We consider a shortest path problem for a directed graph with edges labeled with a cost and a capacity. The problem is to push an unsplittable flow $f$ from a specified source to all other vertices with the minimum cost for all f values. Let G = (V, E) with |V| = n and |E| = m. If there are t different capacity values, we can solve the single source shortest path problem t times for all f in O(tm + tn log n) time, which is O(m^2) when t = m. We improve this time to O(min{t, cn}m + cn^2), which is less than O(cmn) if edge costs are non-negative integers bounded by c. Our algorithm performs better for denser graphs

A definition of measures over language space

AbstractAs an attempt to associate a real number with a language, entropies of languages are computed by Banerji, Kuich, and others. As mappings from languages to real numbers, in this paper, measures over languages are presented. These measures satisfy additivity while entropies do not. Two kinds of measures, p-measure and ω-measure, are defined, and the computing method of these measures is shown for regular languages and context-free languages. Some properties of these measures are applied to show the nonregularity of several languages

Solving Shortest Paths Efficiently on Nearly Acyclic Directed Graphs

Shortest path problems can be solved very efficiently when a directed graph is nearly acyclic. Earlier results defined a graph decomposition, now called the 1-dominator set, which consists of a unique collection of acyclic structures with each single acyclic structure dominated by a single associated trigger vertex. In this framework, a specialised shortest path algorithm only spends delete-min operations on trigger vertices, thereby making the computation of shortest paths through non-trigger vertices easier. A previously presented algorithm computed the 1-dominator set in O(mn) worst-case time, which allowed it to be integrated as part of an O(mn + nr log r) time all-pairs algorithm. Here m and n respectively denote the number of edges and vertices in the graph, while r denotes the number of trigger vertices. A new algorithm presented in this paper computes the 1-dominator set in just O(m) time. This can be integrated as part of the O(m+r log r) time spent solving single-source, improving on the value of r obtained by the earlier tree-decomposition single-source algorithm. In addition, a new bi-directional form of 1-dominator set is presented, which further improves the value of r by defining acyclic structures in both directions over edges in the graph. The bi-directional 1-dominator set can similarly be computed in O(m) time and included as part of the O(m + r log r) time spent computing single-source. This paper also presents a new all-pairs algorithm under the more general framework where r is defined as the size of any predetermined feedback vertex set of the graph, improving the previous all-pairs time complexity from O(mn + nr2 ) to O(mn + r 3 )

Interferon-α/β and Anti-Fibroblast Growth Factor Receptor 1 Monoclonal Antibody Suppress Hepatic Cancer Cells In Vitro and In Vivo

Hepatocellular carcinoma (HCC) is the most commonly occurring primary liver cancer and ranks as the fifth most frequently occurring cancer, overall, and the third leading cause of cancer deaths, worldwide. At present, effective therapeutic options available for HCC are limited; consequently, the prognosis for these patients is poor. Our aim in the present study was to identify a novel target for antibody therapy against HCC..Our results suggest that the combined use of an anti-FGFR1 antibody and interferon-α/β is a promising approach to the treatment of HCC

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

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