arXiv subjects

Takumi Watanabe

Publications and source records attributed to Takumi Watanabe.

5 recordsLinked to original sources

arXiv2026

On the $(φ,Γ)$-modules corresponding to crystalline representations

Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. We introduce the notion of crystalline $(φ,Γ)$-modules over $\widetilde{\mathbb{A}}_K^{+}$ and show that their category is equivalent to the category of crystalline $\mathbb{Z}_p$-representations of the absolute Galois group of $K$. In other words, we determine the $(φ,Γ)$-modules over $\widetilde{\mathbb{A}}_K$ that correspond to crystalline representations. This equivalence generalizes, in certain respects, that of L. Berger in the unramified case.

math.NT↗

arXiv2026

A remark on an integral structure of the imperfect coefficient ring of $(φ,Γ)$-modules

Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. Let $\mathbb{A}_K$ denote the imperfect coefficient ring of $(φ,Γ)$-modules defined by Jean-Marc Fontaine. We prove that the canonical map $W(k_{K_\infty})[[μ]]\rightarrow \mathbb{A}_K\cap A_{\mathrm{inf}}$ is an isomorphism, even when $K$ is ramified. This fact was remarked by Nathalie Wach without proof. In Appendix 2, we include a result of Dylan Pentland. Both results indicate the difficulty of constructing a coefficient ring of ``Wach modules'' in the ramified case.

math.NT↗

arXiv2022

Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures

Multinomial mixtures are widely used in the information engineering field, however, their mathematical properties are not yet clarified because they are singular learning models. In fact, the models are non-identifiable and their Fisher information matrices are not positive definite. In recent years, the mathematical foundation of singular statistical models are clarified by using algebraic geometric methods. In this paper, we clarify the real log canonical thresholds and multiplicities of the multinomial mixtures and elucidate their asymptotic behaviors of generalization error and free energy.

cs.LG↗

arXiv2021

Wheelchair Behavior Recognition for Visualizing Sidewalk Accessibility by Deep Neural Networks

This paper introduces our methodology to estimate sidewalk accessibilities from wheelchair behavior via a triaxial accelerometer in a smartphone installed under a wheelchair seat. Our method recognizes sidewalk accessibilities from environmental factors, e.g. gradient, curbs, and gaps, which influence wheelchair bodies and become a burden for people with mobility difficulties. This paper developed and evaluated a prototype system that visualizes sidewalk accessibility information by extracting knowledge from wheelchair acceleration using deep neural networks. Firstly, we created a supervised convolutional neural network model to classify road surface conditions using wheelchair acceleration data. Secondly, we applied a weakly supervised method to extract representations of road surface conditions without manual annotations. Finally, we developed a self-supervised variational autoencoder to assess sidewalk barriers for wheelchair users. The results show that the proposed method estimates sidewalk accessibilities from wheelchair accelerations and extracts knowledge of accessibilities by weakly supervised and self-supervised approaches.

cs.LG↗

arXiv2008

Nickel-based layered superconductor, LaNiOAs

Rietveld analysis of the powder X-ray diffraction of a new layered oxyarsenide, LaNiOAs, which was synthesized by solid-state reactions, revealed that LaNiOAs belongs to the tetragonal ZrCuSiAs-type structure (P4/nmm) and is composed of alternating stacks of La-O and Ni-As layers. The electrical and magnetic measurements demonstrated that LaNiOAs exhibits a superconducting transition at 2.4 K, and above this, LaNiOAs shows metallic conduction and Pauli paramagnetism. The diamagnetic susceptibility measured at 1.8 K corresponded to ~20% of perfect diamagnetic susceptibility, substantiating that LaNiOAs is a bulk superconductor.

cond-mat.supr-con↗