Searcharxiv⌕ Search

arXiv subjects

Kentaro Wada

Publications and source records attributed to Kentaro Wada.

35 records · Page 2Linked to original sources
arXiv2020

3D Object Segmentation for Shelf Bin Picking by Humanoid with Deep Learning and Occupancy Voxel Grid Map

Picking objects in a narrow space such as shelf bins is an important task for humanoid to extract target object from environment. In those situations, however, there are many occlusions between the camera and objects, and this makes it difficult to segment the target object three dimensionally because of the lack of three dimentional sensor inputs. We address this problem with accumulating segmentation result with multiple camera angles, and generating voxel model of the target object. Our approach consists of two components: first is object probability prediction for input image with convolutional networks, and second is generating voxel grid map which is designed for object segmentation. We evaluated the method with the picking task experiment for target objects in narrow shelf bins. Our method generates dense 3D object segments even with occlusions, and the real robot successfuly picked target objects from the narrow space.

cs.RO↗
arXiv2020

Probabilistic 3D Multilabel Real-time Mapping for Multi-object Manipulation

Probabilistic 3D map has been applied to object segmentation with multiple camera viewpoints, however, conventional methods lack of real-time efficiency and functionality of multilabel object mapping. In this paper, we propose a method to generate three-dimensional map with multilabel occupancy in real-time. Extending our previous work in which only target label occupancy is mapped, we achieve multilabel object segmentation in a single looking around action. We evaluate our method by testing segmentation accuracy with 39 different objects, and applying it to a manipulation task of multiple objects in the experiments. Our mapping-based method outperforms the conventional projection-based method by 40 - 96\% relative (12.6 mean $IU_{3d}$), and robot successfully recognizes (86.9\%) and manipulates multiple objects (60.7\%) in an environment with heavy occlusions.

cs.RO↗
arXiv2018

On the Mackey formulas for cyclotomic Hecke algebras and categories O of rational Cherednik algebras

In this paper, we shall establish the Mackey formulas in the following two set ups: (i) on the tensor induction and restriction functors on the modules over cyclotomic Hecke algebras (Ariki-Koike algebras) and their standard subalgebras of parabolic subgroups. (ii) on the Bezrukavnikov-Etingof induction and restriction functors among categories O of rational Cherednik algebras for the complex reflection group of type G(r, 1, n) and their parabolic subgroups.

math.RT↗
arXiv2017

Self-injective cellular algebras of polynomial growth representation type

We classify Morita equivalence classes of indecomposable self-injective cellular algebras which have polynomial growth representation type, assuming that the base field has an odd characteristic. This assumption on the characteristic is for the cellularity to be a Morita invariant property.

math.RT↗
arXiv2017

Stellar Abundances for Galactic Archaeology Database IV - Compilation of Stars in Dwarf Galaxies

We have constructed the database of stars in the local group using the extended version of the SAGA (Stellar Abundances for Galactic Archaeology) database that contains stars in 24 dwarf spheroidal galaxies and ultra faint dwarfs. The new version of the database includes more than 4500 stars in the Milky Way, by removing the previous metallicity criterion of [Fe/H] <= -2.5, and more than 6000 stars in the local group galaxies. We examined a validity of using a combined data set for elemental abundances. We also checked a consistency between the derived distances to individual stars and those to galaxies in the literature values. Using the updated database, the characteristics of stars in dwarf galaxies are discussed. Our statistical analyses of alpha-element abundances show that the change of the slope of the [alpha/Fe] relative to [Fe/H] (so-called "knee") occurs at [Fe/H] = -1.0+-0.1 for the Milky Way. The knee positions for selected galaxies are derived by applying the same method. Star formation history of individual galaxies are explored using the slope of the cumulative metallicity distribution function. Radial gradients along the four directions are inspected in six galaxies where we find no direction dependence of metallicity gradients along the major and minor axes. The compilation of all the available data shows a lack of CEMP-s population in dwarf galaxies, while there may be some CEMP-no stars at [Fe/H] <~ -3 even in the very small sample. The inspection of the relationship between Eu and Ba abundances confirms an anomalously Ba-rich population in Fornax, which indicates a pre-enrichment of interstellar gas with r-process elements. We do not find any evidence of anti-correlations in O-Na and Mg-Al abundances, which characterises the abundance trends in the Galactic globular clusters.

astro-ph.GA↗
arXiv2015

New realization of cyclotomic $q$-Schur algebras I

We introduce a Lie algebra $\mathfrak{g}_{\mathbf{Q}}(\mathbf{m})$ and an associative algebra $\mathcal{U}_{q,\mathbf{Q}}(\mathbf{m})$ associated with the Cartan data of $\mathfrak{gl}_m$ which is separated into $r$ parts with respect to $\mathbf{m}=(m_1, \dots, m_r)$ such that $m_1+ \dots + m_r =m$. We show that the Lie algebra $\mathfrak{g}_{\mathbf{Q}} (\mathbf{m})$ is a filtered deformation of the current Lie algebra of $\mathfrak{gl}_m$, and we can regard the algebra $\mathcal{U}_{q, \mathbf{Q}}(\mathbf{m})$ as a "$q$-analogue" of $U(\mathfrak{g}_{\mathbf{Q}}(\mathbf{m}))$. Then, we realize a cyclotomic $q$-Schur algebra as a quotient algebra of $\mathcal{U}_{q, \mathbf{Q}}(\mathbf{m})$ under a certain mild condition. We also study the representation theory for $\mathfrak{g}_{\mathbf{Q}}(\mathbf{m})$ and $\mathcal{U}_{q,\mathbf{Q}}(\mathbf{m})$, and we apply them to the representations of the cyclotomic $q$-Schur algebras.

math.RT↗
arXiv2014

On Weyl Groups and Artin Groups Associated to Orbifold Projective Lines

We associate a generalized root system in the sense of Kyoji Saito to an orbifold projective line via the derived category of finite dimensional representations of a certain bound quiver algebra. We generalize results by Saito--Takebayshi and Yamada for elliptic Weyl groups and elliptic Artin groups to the Weyl groups and the fundamental groups of the regular orbit spaces associated to the generalized root systems. Moreover we study the relation between this fundamental group and a certain subgroup of the autoequivalence group of a triangulated subcategory of the derived category of $2$-Calabi--Yau completion of the bound quiver algebra.

math.AG↗
arXiv2011

On Weyl modules of cyclotomic $q$-Schur algebras

We study on Weyl modules of cyclotomic $q$-Schur algebras. In particular, we give the character formula of the Weyl modules by using the Kostka numbers and some numbers which are computed by a generalization of Littlewood-Richardson rule. We also study corresponding symmetric functions. Finally, we give some simple applications to modular representations of cyclotomic $q$-Schur algebras.

math.RT↗
arXiv2009

Presenting cyclotomic q-Schur algebras

We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras.

math.RT↗
arXiv2008

A cellular algebra with certain idempotent decomposition

For a cellular algebra $\A$ with a cellular basis $\ZC$, we consider a decomposition of the unit element $1_\A$ into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular basis $\ZC$ can be partitioned into some pieces with good properties. Then by using a certain map $\a$, we give a coarse partition of $\ZC$ whose refinement is the original partition. We construct a Levi type subalgebra $\aA$ of $\A$ and its quotient algebra $\oA$, and also construct a parabolic type subalgebra $\tA$ of $\A$, which contains $\aA$ with respect to the map $\a$. Then, we study the relation of standard modules, simple modules and decomposition numbers among these algebras. Finally, we study the relationship of blocks among these algebras.

math.RT↗
arXiv2007

Product formulas for the cyclotomic v-Schur algebra and for the canonical bases of the Fock space

In our earlier work, we have proved a product formula for certain decomposition numbers of the cyclotomic v-Schur algebra associated to the Ariki-Koike algebra. It is conjectured by Yvonne that the decomposition numbers of this algebra can be described in terms of the canonical basis of the higher level Fock space studied by Uglov. In this paper we prove a product formula related to the canonical basis of the Fock space. In view of Yvonne's conjecture, this formula is regarded as a counter-part for the Fock space of our previous formula.

math.RT↗
arXiv2007

Cyclotomic $q$-Schur algebras associated to the Ariki-Koike algebra

Let $S$ be the cyclotomic $q$-Schur algebra associated to the Ariki-Koike algebra $H_{n,r}$ of rank $n$, introduced by Dipper-James-Mathas. For each $p = (r_1, ..., r_g)$ such that $r_1 + ... + r_g = r$, we define a subalgebra $S^p$ of $S$ and its quotient algebra $\bar S^p$. It is shown that $S^p$ is a standardly based algebra and $\bar S^p$ is a cellular algebra. By making use of these algebras, we show that certain decomposition numbers for $S$ can be expressed as a product of decomposition numbers for cyclotomic $q$-Schur algebras associated to smaller Ariki_koike algebras $H_{n_k,r_k}$.

math.RT↗
arXiv2007

On decomposition numbers with Jantzen filtration of cyclotomic $q$-Schur algebras

Let $\Sc(\vL)$ be the cyclotomic $q$-Schur algebra associated to the Ariki-Koike algebra $\He_{n,r}$, introduced by Dipper-James-Mathas. In this paper, we consider $v$-decomposition numbers of $\Sc(\vL)$, namely decomposition numbers with respect to the Jantzen filtrations of Weyl modules. We prove, as a $v$-analogue of the result obtained by Shoji-Wada, a product formula for $v$-decomposition numbers of $\Sc(\vL)$, which asserts that certain $v$-decomposition numbers are expressed as a product of $v$-decomposition numbers for various cyclotomic $q$-Schur algebras associated to Ariki-koike algebras $\He_{n_i,r_i}$ of smaller rank. Moreover we prove a similar formula for $v$-decomposition numbers of $\He_{n,r}$ by using a Schur functor.

math.RT↗