Quotients of Étale Groupoids and The Abelianizations of Groupoid C*-Algebras

In this paper, we introduce quotients of étale groupoids. Using the notion of quotients, we describe the abelianizations of groupoid C*-algebras. As another application, we obtain a simple proof that effectiveness of an étale groupoid is implied by a Cuntz–Krieger uniqueness theorem for a universal groupoid C*-algebra.journal articl

Submodules of normalisers in groupoid C*-algebras and discrete group coactions

In this paper, we investigate certain submodules in C*-algebras associated to effective étale groupoids. First, we show that a submodule generated by normalizers is a closure of the set of compactly supported continuous functions on some open set. As a corollary, we show that discrete group coactions on groupoid C*-algebras are induced by cocycles of étale groupoids if the fixed point algebras contain C*-subalgebras of continuous functions vanishing at infinity on the unit spaces. In the latter part, we prove the Galois correspondence result for discrete group coactions on groupoid C*-algebras.journal articl

Weyl groups of groupoid C*-algebras

In the theory of C*-algebras, the Weyl groups were defined for the Cuntz algebras and graph algebras by Cuntz and Conti et al. respectively. In this paper, we introduce and investigate the Weyl groups of groupoid C*-algebras as a natural generalization of the existing Weyl groups. Then we analyse several groups of automorphisms on groupoid C*-algebras. Finally, we apply our results to Cuntz algebras, graph algebras and C*-algebras associated with Deaconu–Renault systems.journal articl

A correspondence between inverse subsemigroups, open wide subgroupoids and cartan intermediate C*-subalgebras

For a given inverse semigroup action on a topological space, one can associate an étale groupoid. We prove that there exists a correspondence between the certain subsemigroups and the open wide subgroupoids in case that the action is strongly tight. Combining with the recent result of Brown et al., we obtain a correspondence between the certain subsemigroups of an inverse semigroup and the Cartan intermediate subalgebras of a groupoid C*-algebra.journal articl

Invariant Sets and Normal Subgroupoids of Universal Étale Groupoids Induced by Congruences of Inverse Semigroups

For a given inverse semigroup, one can associate an étale groupoid which is called the universal groupoid. Our motivation is studying the relation between inverse semigroups and associated étale groupoids. In this paper, we focus on congruences of inverse semigroups, which is a fundamental concept for considering quotients of inverse semigroups. We prove that a congruence of an inverse semigroup induces a closed invariant set and a normal subgroupoid of the universal groupoid. Then we show that the universal groupoid associated to a quotient inverse semigroup is described by the restriction and quotient of the original universal groupoid. Finally we compute invariant sets and normal subgroupoids induced by special congruences including abelianization.journal articl

M.ヴェーバーの文化科学と価値関係論（上） : M.ヴェーバーの科学論の構図と理念型論 : 多元主義的存在論の視点からの再解釈の試み（その１）

departmental bulletin pape

Reproducing kernel Hilbert C*-module and kernel mean embeddings

Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with reproducing kernel Hilbert C∗-module (RKHM) and kernel mean embedding (KME) in RKHM. Since RKHM contains richer information than RKHS or vector-valued RKHS (vvRKHS), analysis with RKHM enables us to capture and extract structural properties in such as functional data. We show a branch of theories for RKHM to apply to data analysis, including the representer theorem, and the injectivity and universality of the proposed KME. We also show RKHM generalizes RKHS and vvRKHS. Then, we provide concrete procedures for employing RKHM and the proposed KME to data analysis.journal articl

Observation of B+ → χc0K+

journal articl

研究解説 : 乱流とコンピュータ

乱流シミュレーションは、物理学・工学の重要な研究テーマである乱流現象を解明する鍵となる技術であり、乱流の統計理論およびそれに基づくコンピュータ・ソフトウェアの研究に支えられて独自の研究分野を築きつつある。これを理工学のさまざまな分野での実用的ツールに成長させるためには乱流のモデリングと数億計算手法の両面からリファインすることが必要である。この乱流の数値シミュレーションの現状と課題を概説するdepartmental bulletin pape

A LSTM Neural Network applied to Mobile Robots Path Planning

Mobile robots path planning is a central problem in every situation where human intervention is not desired or not possible to accept: full automated industrial warehouses or general stocking areas and every domestic application that involves a mobile robot and special cases where environment is prohibited for human accessing like toxic wastes and bombs defusing [1]. Currently, neural networks are applied to problems related to mobile robot navigation. However, they are not as popular as in applications like image processing, speech recognition or machine translation, where they are commercially relevant. In this paper we propose a Long Short-Term Memory (LSTM) neural network as an online search agent to tackle the problem of mobile robots path planning in unknown environments, meaning that the agent relies only on local map awareness realized with a LRF sensor and relative information between robot and goal position. Specifically, a final structure of LSTM network is analyzed and its performance is compared with the A* algorithm, a widely known method that follows the best-first search approach. Subsequently, an analysis of the method developed on a real robot is described.journal articl