Additive Approximation Algorithms for Modularity Maximization

The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). Community detection in graphs is now often conducted through modularity maximization: given an undirected graph $G=(V,E)$, we are asked to find a partition $\mathcal{C}$ of $V$ that maximizes the modularity. Although numerous algorithms have been developed to date, most of them have no theoretical approximation guarantee. Recently, to overcome this issue, the design of modularity maximization algorithms with provable approximation guarantees has attracted significant attention in the computer science community. In this study, we further investigate the approximability of modularity maximization. More specifically, we propose a polynomial-time $\left(\cos\left(\frac{3-\sqrt{5}}{4}\pi\right) - \frac{1+\sqrt{5}}{8}\right)$-additive approximation algorithm for the modularity maximization problem. Note here that $\cos\left(\frac{3-\sqrt{5}}{4}\pi\right) - \frac{1+\sqrt{5}}{8} < 0.42084$ holds. This improves the current best additive approximation error of $0.4672$, which was recently provided by Dinh, Li, and Thai (2015). Interestingly, our analysis also demonstrates that the proposed algorithm obtains a nearly-optimal solution for any instance with a very high modularity value. Moreover, we propose a polynomial-time $0.16598$-additive approximation algorithm for the maximum modularity cut problem. It should be noted that this is the first non-trivial approximability result for the problem. Finally, we demonstrate that our approximation algorithm can be extended to some related problems.Comment: 23 pages, 4 figure

Characterizing Delaunay Graphs via Fixed Point Theorem

Abstract This paper discusses a problem for determining whether a given plane graph is a Delaunay graph, i.e., whether it is topologically equivalent to a Delaunay triangulation. There exists a theorem which characterizes Delaunay graphs and yields a polynomial time algorithm for the problem only by solving a certain linear inequality system. The theorem was proved by Rivin based on arguments of hyperbolic geometry. Independently, Hiroshima, Miyamoto and Sugihara gave another proof of the theorem based on primitive arguments on Euclidean geometry. Unfortunately, the existing proofs of the theorem are rather difficult or long. In this paper, we give a simple proof of the theorem characterizing Delaunay graphs, which is based on the fixed point theorem

Region-specific and state-dependent astrocyte Ca2+ dynamics during the sleep-wake cycle in mice

Neural activity is diverse, and varies depending on brain regions and sleep/wakefulness states. However, whether astrocyte activity differs between sleep/wakefulness states, and whether there are differences in astrocyte activity among brain regions remain poorly understood. Therefore, in this study, we recorded astrocyte intracellular calcium (Ca2+) concentrations of mice during sleep/wakefulness states in the cortex, hippocampus, hypothalamus, cerebellum, and pons using fiber photometry. For this purpose, male transgenic mice expressing the genetically encoded ratiometric Ca2+ sensor YCnano50 specifically in their astrocytes were used. We demonstrated that Ca2+ levels in astrocytes substantially decrease during rapid eye movement (REM) sleep, and increase after the onset of wakefulness. In contrast, differences in Ca2+ levels during non-rapid eye movement (NREM) sleep were observed among the different brain regions, and no significant decrease was observed in the hypothalamus and pons. Further analyses focusing on the transition between sleep/wakefulness states and correlation analysis with the duration of REM sleep showed that Ca2+ dynamics differs among brain regions, suggesting the existence of several clusters; i.e., the first comprising the cortex and hippocampus, the second comprising the hypothalamus and pons, and the third comprising the cerebellum. Our study thus demonstrated that astrocyte Ca2+ levels change substantially according to sleep/wakefulness states. These changes were consistent in general unlike neural activity. However, we also clarified that Ca2+ dynamics varies depending on the brain region, implying that astrocytes may play various physiological roles in sleep

Mouse in Utero Electroporation: Controlled Spatiotemporal Gene Transfection

In order to understand the function of genes expressed in specific region of the developing brain, including signaling molecules and axon guidance molecules, local gene transfer or knock- out is required. Gene targeting knock-in or knock-out into local regions is possible to perform with combination with a specific CRE line, which is laborious, costly, and time consuming. Therefore, a simple transfection method, an in utero electroporation technique, which can be performed with short time, will be handy to test the possible function of candidate genes prior to the generation of transgenic animals 1,2. In addition to this, in utero electroporation targets areas of the brain where no specific CRE line exists, and will limit embryonic lethality 3,4. Here, we present a method of in utero electroporation combining two different types of electrodes for simple and convenient gene transfer into target areas of the developing brain. First, a unique holding method of embryos using an optic fiber optic light cable will make small embryos (from E9.5) visible for targeted DNA solution injection into ventricles and needle type electrodes insertion to the targeted brain area 5,6. The patterning of the brain such as cortical area occur at early embryonic stage, therefore, these early electroporation from E9.5 make a big contribution to understand entire area patterning event. Second, the precise shape of a capillary prevents uterine damage by making holes by insertion of the capillary. Furthermore, the precise shape of the needle electrodes are created with tungsten and platinum wire and sharpened using sand paper and insulated with nail polish 7, a method which is described in great detail in this protocol. This unique technique allows transfection of plasmid DNA into restricted areas of the brain and will enable small embryos to be electroporated. This will help to, open a new window for many scientists who are working on cell differentiation, cell migration, axon guidance in very early embryonic stage. Moreover, this technique will allow scientists to transfect plasmid DNA into deep parts of the developing brain such as thalamus and hypothalamus, where not many region-specific CRE lines exist for gain of function (GOF) or loss of function (LOF) analyses

Lower Bounds for Bruss' Odds Problem with Multiple Stoppings

We give asymptotic lower bounds of the value for Bruss' optimal stopping problem with multiple stopping chances. It interestingly consists of the asymptotic threshold values in the optimal multiple stopping strategy. Another interesting implication of the result is that the asymptotic value for each secretary problem with multiple stoppings is in fact a typical lower bound in a much more general class of multiple stopping problems as modifications of odds problem.Comment: 41 pages, 4 figure

糖尿病ケアにおける看護師のソーシャルスキルおよび批判的思考態度の実態と糖尿病教育スタイルとの関係

本研究の目的は、糖尿病看護に携わっている看護師のソーシャルスキルおよび批判的思考 態度の実態と看護師の糖尿病教育スタイルとの関係を明らかにすることである。糖尿病教育 スタイルとは、糖尿病看護に携わっている看護師の患者教育における意識や行動の特徴であ り、3 つのスタイルで識別される。 糖尿病看護に携わっている看護師を対象に自記式質問紙調査を実施した。223 施設に質問 紙を送付し、返送された1115 名中、有効回答848 名（有効回答率76.0%）を分析対象とした。 基本属性、ソーシャルスキル9 下位尺度27 項目、批判的思考態度4 下位尺度33 項目、糖尿 病教育スタイル自己評価18 項目について調査した。 その結果、あてはまるとの回答が80% 以上だった項目は、ソーシャルスキルでは皆無で あり、批判的思考態度においてもわずか４項目であった。また、批判的思考態度においては、 年齢、糖尿病看護経験年数、CDEJ、糖尿病看護認定看護師と相関がみとめられた。しかしソー シャルスキルにおいて相関のみとめられたのは糖尿病看護経験年数のみであった。また、糖 尿病教育スタイルとこれら2 つのスキルとの相関においては、いずれも生活心情がみえてい るスタイルとの正の相関が最も高かったが、批判的思考態度の下位尺度「証拠の重視」にの み相関はみとめられなかった。 以上より、看護師のソーシャルスキルおよび批判的思考態度の自己評価は高いとはいえな いことが明らかになった。また、資格よりむしろ糖尿病看護経験年数がスキルの高さに関与 する可能性が示された。さらに、これら2 尺度の得点と最も相関が高かった生活心情がみえ ている教育スタイルがのぞましいことが確認された

A 2.75-Approximation Algorithm for the Unconstrained Traveling Tournament Problem

A 2.75-approximation algorithm is proposed for the unconstrained traveling tournament problem, which is a variant of the traveling tournament problem. For the unconstrained traveling tournament problem, this is the first proposal of an approximation algorithm with a constant approximation ratio. In addition, the proposed algorithm yields a solution that meets both the no-repeater and mirrored constraints. Computational experiments show that the algorithm generates solutions of good quality.Comment: 12 pages, 1 figur

Nazım Hikmet'in vatan hainliği

Taha Toros Arşivi, Dosya Adı: Nazım Hikmet. Not: Gazetenin "Tersi Yüzü" köşesinde yayımlanmıştır.İstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033