Approximating the minimum directed tree cover

Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a rooted directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover problem (DTCP) is to find a directed tree cover of minimum cost. The problem is known to be $NP$-hard. In this paper, we show that the weighted Set Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to approximate DTCP with the same ratio as for SCP. We show that this expectation can be satisfied in some way by designing a purely combinatorial approximation algorithm for the DTCP and proving that the approximation ratio of the algorithm is $\max\{2, \ln(D^+)\}$ with $D^+$ is the maximum outgoing degree of the nodes in $G$.Comment: 13 page

The Fewest Clues Problem of Picross 3D

Picross 3D is a popular single-player puzzle video game for the Nintendo DS. It is a 3D variant of Nonogram, which is a popular pencil-and-paper puzzle. While Nonogram provides a rectangular grid of squares that must be filled in to create a picture, Picross 3D presents a rectangular parallelepiped (i.e., rectangular box) made of unit cubes, some of which must be removed to construct an image in three dimensions. Each row or column has at most one integer on it, and the integer indicates how many cubes in the corresponding 1D slice remain when the image is complete. It is shown by Kusano et al. that Picross 3D is NP-complete. We in this paper show that the fewest clues problem of Picross 3D is Sigma_2^P-complete and that the counting version and the another solution problem of Picross 3D are #P-complete and NP-complete, respectively

On the best possible competitive ratio for the multislope ski-rental problem

The multislope ski-rental problem is an extension of the classical ski-rental problem, where the player has several lease options besides the pure rent and buy options. In this problem the hardness of an instance, which is the setting of options, significantly affects the player's performance. There is an algorithm that for a given instance, computes the best possible strategy. However, the output is given as numerical values and therefore the relational nature between an instance and the best possible performance for it has not been known. In this paper we prove that even for the easiest instance, a competitive ratio smaller than cannot be achieved. More precisely, a tight lower bound on the best possible performance is obtained in a closed form parametrized by the number of options. Furthermore, we establish a matching upper and lower bound on the competitive ratio each for the 3-option and 4-option problems.ArticleJOURNAL OF COMBINATORIAL OPTIMIZATION. 31(2): 463-490 (2016)journal articl

Learning-Dependent Gene Expression of CREB1 Isoforms in the Molluscan Brain

Cyclic AMP-responsive element binding protein1 (CREB1) has multiple functions in gene regulation. Various studies have reported that CREB1-dependent gene induction is necessary for memory formation and long-lasting behavioral changes in both vertebrates and invertebrates. In the present study, we characterized Lymnaea CREB1 (LymCREB1) mRNA isoforms of spliced variants in the central nervous system (CNS) of the pond snail Lymnaea stagnalis. Among these spliced variants, the three isoforms that code a whole LymCREB1 protein are considered to be the activators for gene regulation. The other four isoforms, which code truncated LymCREB1 proteins with no kinase inducible domain, are the repressors. For a better understanding of the possible roles of different LymCREB1 isoforms, the expression level of these isoform mRNAs was investigated by a real-time quantitative RT-PCR method. Further, we examined the changes in gene expression for all the isoforms in the CNS after conditioned taste aversion (CTA) learning or backward conditioning as a control. The results showed that CTA learning increased LymCREB1 gene expression, but it did not change the activator/repressor ratio. Our findings showed that the repressor isoforms, as well as the activator ones, are expressed in large amounts in the CNS, and the gene expression of CREB1 isoforms appeared to be specific for the given stimulus. This was the first quantitative analysis of the expression patterns of CREB1 isoforms at the mRNA level and their association with learning behavior

A Case of a Giant Congenital Melanocytic Nevus Treated by Curettage with the Application of Cultured Epidermal Autografts before 6 Months of Age

Curettage is common in the treatment of a giant congenital melanocytic nevus (GCMN) in infants and should generally be performed before 6 months of age. Post-curettage retarded epithelialization often interferes with the ability to perform multiple operations within a short interval, and thus, it is difficult to treat large lesions in the neonatal period. We herein report a case of a GCMN comprising 20% of the total body surface area, which required multi-stage curettage, in which a cultured epithelial autograft was used to promote epithelialization of the post-curettage wound. The patient was a 1-month-old boy with a GCMN in his head, neck, chest, back, buttock, left upper arm, and a few satellite lesions. A four-stage operation was performed between 3 and 6 months of age; the cultured epithelial autograft took well after each operation, and complete epithelialization was observed at postoperative days 20, 23, 27, and 12, respectively. Seven months after the last surgery, hypertrophic scar formation was only observed in a small area of the left upper arm without axillary contracture. The color of the treated area improved, except for slight partial re-pigmentation. A skin biopsy was obtained from the re-pigmented area. The results demonstrated that nevus cells remained in the basal layer of the epidermis, hair follicles, and deep layer of the remaining dermis, suggesting that the recurrent nevus cells in the regenerated epidermis migrated from hair follicles. We conclude that the combination of curettage and the application of a cultured epithelial autograft is a promising option for GCMN treatment

コロナ禍におけるエルサルバドル教育セクターのニーズ分析

2019年12月に新型コロナウイルス感染症（COVID-19）が確認されてから世界的なパンデミックに見舞われ，現在も流行が続いている．エルサルバドルでは，学校閉鎖の影響により約1年間の授業機会が失われている状況である．遠隔教育が普及されつつある中，インターネットへのアクセスや，保護者の支援等が児童生徒に必要となっている． エルサルバドルではオンライン教育が実施される中でインターネット環境や保護者の支援など様々な課題に直面している．本研究ではコロナ禍におけるエルサルバドルの現状と課題を明らかにし，教員が求めているニーズについて調査した．その結果，児童生徒側のみならず学校・教員側のインターネットアクセスは喫緊の課題であり，オフラインでの授業・活動に限られる状況下では，紙媒体の教材の使用に限られることが明らかとなった．また，児童生徒にとって自立した学習時間の管理は難しく，欠席率の高さも課 題であることが分かった．ICT（Information Communication Technology）リテラシーの欠如は，児童生徒だけでなく教員側にも顕著であり，ICT 機器の配備のみならず使い方の向上が重要な課題であることが明らかとなった

Covering problems in edge- and node-weighted graphs

This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large integrality gap of a natural linear programming (LP) relaxation, LP rounding algorithms based on the relaxation yield poor performance. Here we propose a stronger LP relaxation for the graph covering problem. The proposed relaxation is applied to designing primal-dual algorithms for two fundamental graph covering problems: the prize-collecting edge dominating set problem and the multicut problem in trees. Our algorithms are an exact polynomial-time algorithm for the former problem, and a 2-approximation algorithm for the latter problem, respectively. These results match the currently known best results for purely edge-weighted graphs.Comment: To appear in SWAT 201

Inhibition of cell movement and proliferation by cell–cell contact-induced interaction of Necl-5 with nectin-3

Immunoglobulin-like Necl-5/Tage4/poliovirus receptor (PVR)/CD155, originally identified as the PVR, has been shown to be up-regulated in cancer cells and to enhance growth factor–induced cell movement and proliferation. In addition, Necl-5 heterophilically trans-interacts with nectin-3, a cell–cell adhesion molecule known to form adherens junctions in cooperation with cadherin. We show here that Necl-5 was down-regulated from cell surface upon cell–cell contacts in NIH3T3 cells. This down-regulation of Necl-5 was initiated by its interaction with nectin-3 and was mainly mediated by clathrin-dependent endocytosis. Then, the down-regulation of Necl-5 induced in this way reduced movement and proliferation of NIH3T3 cells. These results indicate that the down-regulation of Necl-5 induced by its interaction with nectin-3 upon cell–cell contacts may be at least one mechanism underlying contact inhibition of cell movement and proliferation