Cluster realizations of Weyl groups and higher Teichm\"uller theory

For a symmetrizable Kac-Moody Lie algebra $\mathfrak{g}$, we construct a family of weighted quivers $Q_m(\mathfrak{g})$ ($m \geq 2$) whose cluster modular group $\Gamma_{Q_m(\mathfrak{g})}$ contains the Weyl group $W(\mathfrak{g})$ as a subgroup. We compute explicit formulae for the corresponding cluster $\mathcal{A}$- and $\mathcal{X}$-transformations. As a result, we obtain green sequences and the cluster Donaldson-Thomas transformation for $Q_m(\mathfrak{g})$ in a systematic way when $\mathfrak{g}$ is of finite type. Moreover if $\mathfrak{g}$ is of classical finite type with the Coxeter number $h$, the quiver $Q_{kh}(\mathfrak{g})$ ($k \geq 1$) is mutation-equivalent to a quiver encoding the cluster structure of the higher Teichm\"uller space of a once-punctured disk with $2k$ marked points on the boundary, up to frozen vertices. This correspondence induces the action of direct products of Weyl groups on the higher Teichm\"uller space of a general marked surface. We finally prove that this action coincides with the one constructed in [GS18] from the geometrical viewpoint.Comment: 70 pages, 28 figures. Final version. To appear in Selecta Mathematica, New Serie

Mining Coding Patterns to Detect Crosscutting Concerns in Java Programs

Reverse Engineering, 2008. WCRE '08. 15th Working Conference onDate of Conference:15-18 Oct. 2008Conference Location :Antwer

Mining Application-Specific Coding Patterns for Software Maintenance

LATE '08 Proceedings of the 2008 AOSD workshop on Linking aspect technology and evolutio

An energy landscape approach to understanding variety and robustness in tissue morphogenesis

During morphogenesis in development, multicellular tissues deform by mechanical forces induced by spatiotemporally regulated cellular activities, such as cell proliferation and constriction. Various morphologies are formed because of various spatiotemporal combinations and sequences of multicellular activities. Despite its potential to variations, morphogenesis is a surprisingly robust process, in which qualitatively similar morphologies are reproducibly formed even under spatiotemporal fluctuation of multicellular activities. To understand these essential characteristics of tissue morphogenesis, which involves the coexistence of various morphologies and robustness of the morphogenetic process, in this study, we propose a novel approach to capture the overall view of morphogenesis from mechanical viewpoints. This approach will enable visualization of the energy landscape, which includes morphogenetic processes induced by admissible histories of cellular activities. This approach was applied to investigate the morphogenesis of a sheet-like tissue with curvature, where it deformed to a concave or convex morphology depending on the history of growth and constriction. Qualitatively different morphologies were produced by bifurcation of the valley in the energy landscape. The depth and steepness of the valley near the stable states represented the degree of robustness to fluctuations of multicellular activities. Furthermore, as a realistic example, we showed an application of this approach to luminal folding observed in the initial stage of intestinal villus formation. This approach will be helpful to understand the mechanism of how various morphologies are formed and how tissues reproducibly achieve specific morphologies

Choosing a theme and designing its instructional units in Life-Unit Learning : Analyzing the impact on what and how students with intellectual disabilities have learned

本研究では、知的障害特別支援学校中学部において、同一集団、同一指導者によって2年間実践された「生活上の課題をもとにした」22 の生活単元学習の授業評価を行い、その結果を踏まえて、単元設定や単元構成の在り方について検討した。3 観点からなる観点別個別評価結果を基に各単元の評価を行った結果、観点別評価による各単元の特徴及び生徒個々の活動への取り組み方を確かめることができた。また、個々の単元の評価結果と、単元の活動経験の有無、活動の種類、単元目的の具体性、教師と生徒のいずれが提案した単元であるかという視点との明確な関連性は見られなかった。一方で、生徒が見通しをもつことのできる単純な単元構成、集団全体の課題解決場面の設定、人と関わりの多い場面設定と単元の評価結果との関連性が見られ、単元設定、単元構成におけるこれらの重要性が示唆された

Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings

We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the existence of Lyapunov function. We also give applications of a mapping with an adjusted parameter, a probabilistic mapping and coupled mappings.Comment: submitted to Physica

Latent trajectory modelling of pulmonary artery pressure in systemic sclerosis: a retrospective cohort study

OBJECTIVES: To visualise the trajectories of pulmonary arterial pressure (PAP) in systemic sclerosis (SSc) and identify the clinical phenotypes for each trajectory, by applying latent trajectory modelling for PAP repeatedly estimated by echocardiography. METHODS: This was a multicentre, retrospective cohort study conducted at four referral hospitals in Kyoto, Japan. Patients with SSc who were treated at study sites between 2008 and 2021 and who had at least three echocardiographic measurements of systolic PAP (sPAP) were included. A group-based trajectory model was applied to the change in sPAP over time, and patients were classified into distinct subgroups that followed similar trajectories. Pulmonary hypertension (PH)-free survival was compared for each trajectory. Multinomial logistic regression analysis was performed for baseline clinical characteristics associated with trajectory assignment. RESULTS: A total of 236 patients with 1097 sPAP measurements were included. We identified five trajectories: rapid progression (n=9, 3.8%), early elevation (n=30, 12.7%), middle elevation (n=54, 22.9%), late elevation (n=24, 10.2%) and low stable (n=119, 50.4%). The trajectories, in the listed order, showed progressively earlier elevation of sPAP and shorter PH-free survival. In the multinomial logistic regression analysis with the low stable as a reference, cardiac involvement was associated with rapid progression, diffuse cutaneous SSc was associated with early elevation and anti-centromere antibody was associated with middle elevation; older age of onset was associated with all three of these trajectories. CONCLUSION: The pattern of changes in PAP over time in SSc can be classified into five trajectories with distinctly different clinical characteristics and outcomes

Clinical significance of IDC-P as predictive factor after intensity-modulated radiation therapy

The clinical significance of intraductal carcinoma of the prostate (IDC-P) in men with nonmetastatic prostate cancer (PCa) treated with high-dose external-beam radiation therapy remains unclear. The aim of this study was to evaluate the impact of IDC-P in men who received intensity-modulated radiation therapy (IMRT) for nonmetastatic PCa. All patients with high-risk (H-R) and very high–risk (VH-R) PCa who received IMRT between September 2000 and December 2013 at our institution were analyzed retrospectively. We re-reviewed biopsy cores for the presence of IDC-P. Treatment consisted of IMRT (median: 78 Gy at 2 Gy per fraction) plus 6-month neoadjuvant hormonal therapy (HT). In total, 154 consecutive patients with H-R and VH-R PCa were analyzed. Intraductal carcinoma of the prostate was present in 27.9% (n = 43). The median follow-up period was 8.4 years. The 10-year PCa-specific survival, biochemical failure (BF), clinical failure, and castration-resistant PCa rates were 90.0%, 47.8%, 27.5%, and 24.5% in patients with IDC-P, and 96.6%, 32.6%, 10.8%, and 7.0% in those without IDC-P, respectively (p = 0.12, 0.04, 0.0031, and 0.012, respectively). In multivariable analysis, IDC-P was not identified as an independent predictive factor for BF (p = 0.26). The presence of IDC-P was correlated with a significantly higher incidence of disease progression in men with H-R and VH-R PCa who received IMRT, although it was not identified as an independent predictive factor for BF. Further investigations are needed to determine the significance of IDC-P as an independent predictive factor for survival outcomes