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

Hadronic decays of B→a1(1260)b1(1235)B \to a_1(1260) b_1(1235) in the perturbative QCD approach

We calculate the branching ratios and polarization fractions of the $B \to a_1 b_1$ decays in the perturbative QCD(pQCD) approach at leading order, where $a_1$($b_1$) stands for the axial-vector $a_1(1260)[b_1(1235)]$ state. By combining the phenomenological analyses with the perturbative calculations, we find the following results: (a) the large decay rates around $10^{-5}$ to $10^{-6}$ of the $B \to a_1 b_1$ decays dominated by the longitudinal polarization(except for the $B^+ \to b_1^+ a_1^0$ mode) are predicted and basically consistent with those in the QCD factorization(QCDF) within errors, which are expected to be tested by the Large Hadron Collider and Belle-II experiments. The large $B^0 \to a_1^0 b_1^0$ branching ratio could provide hints to help explore the mechanism of the color-suppressed decays. (b) the rather different QCD behaviors between the $a_1$ and $b_1$ mesons result in the destructive(constructive) contributions in the nonfactorizable spectator diagrams with $a_1(b_1)$ emission. Therefore, an interesting pattern of the branching ratios appears for the color-suppressed $B^0 \to a_1^0 a_1^0, a_1^0 b_1^0,$ and $b_1^0 b_1^0$ modes in the pQCD approach, $Br(B^0 \to b_1^0 b_1^0) > Br(B^0 \to a_1^0 b_1^0) \gtrsim Br(B^0 \to a_1^0 a_1^0)$, which is different from $Br(B^0 \to b_1^0 b_1^0) \sim Br(B^0 \to a_1^0 b_1^0) \gtrsim Br(B^0 \to a_1^0 a_1^0)$ in the QCDF and would be verified at future experiments. (c) the large naive factorization breaking effects are observed in these $B \to a_1 b_1$ decays. Specifically, the large nonfactorizable spectator(weak annihilation) amplitudes contribute to the $B^0 \to b_1^+ a_1^-(B^+ \to a_1^+ b_1^0\; {\rm and}\; B^+ \to b_1^+ a_1^0)$ mode(s), which demand confirmations via the precise measurements.Comment: 13 pages, 1 figure, 5 tables, revtex fil

Genetic Diversity and Differentiation of the Ryukyu Endemic Frog Babina holsti as Revealed by Mitochondrial DNA

We surveyed the genetic diversity and genetic differentiation of an endangered frog, Babina holsti, endemic to Okinawajima and Tokashikijima Islands of the Ryukyus, to elucidate its divergence history and obtain basic data for its conservation. Genetic differentiation between the two island lineages is moderate (3. 1% p-distance in the cyt b gene). This result suggests that the two island lineages have been isolated between the late Pliocene and the middle Pleistocene and have never migrated between the current northern part of Okinawajima and Tokashikijima Islands, which were once connected in the late Pleistocene glacial age. On Okinawajima Island, the southernmost sample was constituted by a unique haplotype, without considerable genetic distance from haplotypes detected from northern samples. This unique haplotype composition in the southernmost sample would have resulted from the restricted gene flow between the southernmost population and the other populations in Okinawajima Island. Furthermore, the absence of genetic diversity within the southernmost sample indicates that this population has recently experienced population size reduction, possibly by predation pressure from an introduced mongoose, which is more abundant in the southern part than in the northern part of the island. Lower genetic diversity in the Tokashikijima sample implies a small effective population size for mitochondrial DNA (mtDNA) in B. holsti on the island. Immediate conservation measures should be taken for the populations from the southernmost range in Okinawajima and Tokashikijima

DeWitt boundary condition is consistent in Hořava-Lifshitz quantum gravity

In quantum cosmology the DeWitt boundary condition is a proposal to set the wave function of the universe to vanish at the classical big-bang singularity. In this Letter, we show that in many gravitational theories including general relativity, the DeWitt wave function does not take a desired form once tensor perturbations around a homogeneous and isotropic closed universe are taken into account: anisotropies and inhomogeneities due to the perturbations are not suppressed near the classical singularity. We then show that Hořava-Lifshitz gravity provides a satisfactory DeWitt wave function. In particular, in the limit of z = 3 anisotropic scaling, we find an exact analytic expression for the DeWitt wave function of the universe with scale-invariant perturbations. In general cases with relevant deformations, we show that the DeWitt wave function can be systematically expanded around the classical big-bang singularity with perturbations under control

An Interactive Fuzzy Satisficing Method for Multiobjective Stochastic Integer Programming Problems through Simple Recourse Model

Two major approaches to deal with randomness or impression involved in mathematical programming problems have been developed. The one is called stochastic programming, and the other is called fuzzy programming. In this paper, we focus on multiobjective integer programming problems involving random variable coefficients in constraints. Using the concept of simple recourse, such multiobjective stochastic integer programming problems are transformed into deterministic ones. As a fusion of stochastic programming and fuzzy one, after introducing fuzzy goals to reflect the ambiguity of the decision maker's judgments for objective functions, we propose an interactive fuzzy satisficing method to derive a satisficing solution for the decision maker by updating the reference membership levels

Regulation of Mitochondrial Dynamics and Neurodegenerative Diseases

Mitochondria are important cellular organelles in most metabolic processes and have a highly dynamic nature, undergoing frequent fission and fusion. The dynamic balance between fission and fusion plays critical roles in mitochondrial functions. In recent studies, several large GTPases have been identified as key molecular factors in mitochondrial fission and fusion. Moreover, the posttranslational modifications of these large GTPases, including phosphorylation, ubiquitination and SUMOylation, have been shown to be involved in the regulation of mitochondrial dynamics. Neurons are particularly sensitive and vulnerable to any abnormalities in mitochondrial dynamics, due to their large energy demand and long extended processes. Emerging evidences have thus indicated a strong linkage between mitochondria and neurodegenerative diseases, including Alzheimer's disease, Parkinson's disease and Huntington's disease. In this review, we will describe the regulation of mitochondrial dynamics and its role in neurodegenerative diseases

A comparative study of child-nurturing considerations of mothers and fathers of children with disabilities : Qualitative Analysis by Focus Group Interview <Research papers>

The purpose of this study was to examine the important aspects of the support of children with disabilities from the perspective of their mothers and fathers. A focus group method was used to interview the mothers and fathers of six families separately. The interview data were analyzed according to aspects addressed during the focus group interview. Eight categories were considered important by mothers (“pleasure of my child’s life now,” “influence arising from the behavior of others,” “worry of brothers and sisters,” “gratitude for institutional support,” “respite care,” “difficulty of gathering information,” “not letting father do the housework,” and “support from brothers and sisters”). Six categories were considered important by fathers (“worry about the future of the child,” “sports that father plays,” “dissatisfaction with institutional support,” “respite care for my wife,” “I feel that I should not do housework,” and “work-life balance”). Three complementary results were found. First, mothers consider the “now” while fathers consider “the future” of the child. Second, mothers are “grateful” while fathers are “dissatisfied” with institutional support. Third, both mothers and fathers consider that fathers “must not do housework.”本稿の一部は，日本特殊教育学会第50回研究大会にて報告された。なお，本研究は，平成21～23年度文部科学省科学研究費補助金基盤研究（B）（課題番号21402045　代表　七木田敦）の補助を受けて行われたものである