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Ryo Takahashi

Publications and source records attributed to Ryo Takahashi.

At least 73 records · Page 4Linked to original sources
arXiv2022

When is a subcategory Serre or torsionfree?

Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated R-modules. In the present paper, we first provide various sufficient (and necessary) conditions for a full subcategory of mod R to be a Serre subcategory, which include several refinements of theorems of Stanley and Wang and of Takahashi with simpler proofs. Next we consider when an IKE-closed subcategory of mod R is a torsionfree class. We investigate certain modules out of which all modules of finite length can be built by taking direct summands and extensions, and then we apply it to show that the IKE-closed subcategories of mod R are torsionfree classes in the case where R is a certain numerical semigroup ring.

math.AC↗
arXiv2022

Fractional hinge and corner charges in various crystal shapes with cubic symmetry

Higher-order topological insulators host gapless states on hinges or corners of three-dimensional crystals. Recent studies suggested that even topologically trivial insulators may exhibit fractionally quantized charges localized at hinges or corners. Although most of the previous studies focused on two-dimensional systems, in this work, we take the initial step toward the systematic understanding of hinge and corner charges in three-dimensional insulators. We consider five crystal shapes of vertex-transitive polyhedra with the cubic symmetry such as a cube, an octahedron and a cuboctahedron. We derive real-space formulas for the hinge and corner charges in terms of the electric charges associated with bulk Wyckoff positions. We find that both the hinge and corner charges can be predicted from the bulk perspective only modulo certain fractions depending on the crystal shape, because the relaxation near boundaries of the crystal may affect the fractional parts. In particular, we show that a fractionally quantized charge $1/24$ mod $1/12$ in the unit of elementary charge can appear in a crystal with a shape of a truncated cube or a truncated octahedron. We also investigate momentum-space formulas for the hinge and corner charges. It turns out that the irreducible representations of filled bands at high-symmetry momenta are not sufficient to determine the corner charge. We introduce an additional Wilson-loop invariant to resolve this issue.

cond-mat.mes-hall↗
arXiv2021

NeurIPS 2020 EfficientQA Competition: Systems, Analyses and Lessons Learned

We review the EfficientQA competition from NeurIPS 2020. The competition focused on open-domain question answering (QA), where systems take natural language questions as input and return natural language answers. The aim of the competition was to build systems that can predict correct answers while also satisfying strict on-disk memory budgets. These memory budgets were designed to encourage contestants to explore the trade-off between storing retrieval corpora or the parameters of learned models. In this report, we describe the motivation and organization of the competition, review the best submissions, and analyze system predictions to inform a discussion of evaluation for open-domain QA.

cs.CL↗
arXiv2021

Comparisons between Annihilators of Tor and Ext

In this paper, we compare annihilators of Tor and Ext modules of finitely generated modules over a commutative noetherian ring. For local Cohen--Macaulay rings, one of our results refines a theorem of Dao and Takahashi.

math.AC↗
arXiv2021

Non-Hermitian band topology with generalized inversion symmetry

Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. In this study, we give methods to theoretically detect skin effects and exceptional points by generalizing inversion symmetry. The generalization of inversion symmetry is unique to non-Hermitian systems. We show that parities of the winding numbers can be determined from energy eigenvalues on the inversion-invariant momenta when generalized inversion symmetry is present. The simple expressions for the winding numbers allow us to easily analyze skin effects and exceptional points in non-Hermitian bands. We also demonstrate the methods for (second-order) skin effects and exceptional points by using lattice models.

cond-mat.mes-hall↗
arXiv2021

Two Training Strategies for Improving Relation Extraction over Universal Graph

This paper explores how the Distantly Supervised Relation Extraction (DS-RE) can benefit from the use of a Universal Graph (UG), the combination of a Knowledge Graph (KG) and a large-scale text collection. A straightforward extension of a current state-of-the-art neural model for DS-RE with a UG may lead to degradation in performance. We first report that this degradation is associated with the difficulty in learning a UG and then propose two training strategies: (1) Path Type Adaptive Pretraining, which sequentially trains the model with different types of UG paths so as to prevent the reliance on a single type of UG path; and (2) Complexity Ranking Guided Attention mechanism, which restricts the attention span according to the complexity of a UG path so as to force the model to extract features not only from simple UG paths but also from complex ones. Experimental results on both biomedical and NYT10 datasets prove the robustness of our methods and achieve a new state-of-the-art result on the NYT10 dataset. The code and datasets used in this paper are available at https://github.com/baodaiqin/UGDSRE.

cs.CL↗
arXiv2021

General corner charge formula in two-dimensional C_n-symmetric higher-order topological insulators

In this paper, we derive a general formula for the quantized fractional corner charge in two-dimensional C_n-symmetric higher-order topological insulators. We assume that the electronic states can be described by the Wannier functions and that the edges are charge neutral, but we do not assume vanishing bulk electric polarization. We expand the scope of the corner charge formula obtained in previous works by considering more general surface conditions, such as surfaces with higher Miller index and surfaces with surface reconstruction. Our theory is applicable even when the electronic states are largely modulated near system boundaries. It also applies to insulators with non-vanishing bulk polarization, and we find that in such cases the value of the corner charge depends on the surface termination even for the same bulk crystal with C_3 or C_4 symmetry, via a difference in the Wyckoff position of the center of the C_n-symmetric crystal.

cond-mat.mes-hall↗
arXiv2021

Quasi-projective dimension

In this paper, we introduce a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. We discuss various properties of quasi-projective dimension. Among other things, we prove the following. (1) Over a quotient of a regular local ring by a regular sequence, every finitely generated module has finite quasi-projective dimension. (2) The Auslander--Buchsbaum formula and the depth formula for modules of finite projective dimension remain valid for modules of finite quasi-projective dimension. (3) Several results on vanishing of Tor and Ext hold for modules of finite quasi-projective dimension.

math.AC↗
arXiv2021

On the Subcategories of n-Torsionfree Modules and Related Modules

Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated R-modules. In this paper, we study n-torsionfree modules in the sense of Auslander and Bridger, by comparing them with n-syzygy modules, and modules satisfying Serre's condition (S_n). We mainly investigate closedness properties of the full subcategories of mod R consisting of those modules.

math.AC↗
arXiv2020

Second-order topological non-Hermitian skin effects

Higher-order topology realizes topologically robust corner modes as a manifestation of nontriviality. We theoretically propose non-Hermitian skin effects which stem from second-order topology of chiral-symmetric Hermitian systems. It is found that the skin modes are localized at the corners. We demonstrate two types of second-order topological skin effects by two-dimensional intrinsic and extrinsic second-order topology. The intrinsic second-order topological skin effect is characterized topologically by bulk inversion symmetry as well as chiral symmetry. Meanwhile, the extrinsic second-order topological skin effect occurs from the topological correspondence between the edges and corners. We show that the non-Hermitian skin modes emerge by using a relationship between second-order and conventional first-order topology.

cond-mat.mes-hall↗
arXiv2020

Grothendieck groups, convex cones and maximal Cohen-Macaulay points

Let A be a commutative noetherian ring. Let H(A) be the quotient of the Grothendieck group of finitely generated A-modules by the subgroup generated by pseudo-zero modules. Suppose that the real vector space H(A)_R = H(A) \otimes_Z R has finite dimension. Let C(A) (resp. C_r(A)) be the convex cone in H(A)_R spanned by maximal Cohen-Macaulay A-modules (resp. maximal Cohen-Macaulay A-modules of rank r). We explore the interior, closure and boundary, and convex polyhedral subcones of C(A). We provide various equivalent conditions for A to have only finitely many rank r maximal Cohen-Macaulay points in C_r(A) in terms of topological properties of C_r(A). Finally, we consider maximal Cohen-Macaulay modules of rank one as elements of the divisor class group Cl(A).

math.AC↗
arXiv2020

Word Rotator's Distance

A key principle in assessing textual similarity is measuring the degree of semantic overlap between two texts by considering the word alignment. Such alignment-based approaches are intuitive and interpretable; however, they are empirically inferior to the simple cosine similarity between general-purpose sentence vectors. To address this issue, we focus on and demonstrate the fact that the norm of word vectors is a good proxy for word importance, and their angle is a good proxy for word similarity. Alignment-based approaches do not distinguish them, whereas sentence-vector approaches automatically use the norm as the word importance. Accordingly, we propose a method that first decouples word vectors into their norm and direction, and then computes alignment-based similarity using earth mover's distance (i.e., optimal transport cost), which we refer to as word rotator's distance. Besides, we find how to grow the norm and direction of word vectors (vector converter), which is a new systematic approach derived from sentence-vector estimation methods. On several textual similarity datasets, the combination of these simple proposed methods outperformed not only alignment-based approaches but also strong baselines. The source code is available at https://github.com/eumesy/wrd

cs.CL↗
arXiv2020

Trace of canonical modules, annihilator of Ext, and classes of rings close to being Gorenstein

In this note we study trace ideals of canonical modules. Characterizations of the trace ideals in terms of annihilators of certain Ext modules are given. We apply our results to study many classes of rings close to being Gorenstein that appear in recent literature. We discuss the behavior of nearly Gorensteinness, introduced by Herzog-Hibi-Stamate, under reductions by regular sequences. A nearly Gorenstein version of the Tachikawa conjecture is posed, and an affirmative answer given for type 2 rings. We also introduce the class of weakly almost Gorenstein rings using the canonical module, and show that they are almost Gorenstein rings in dimension one, and are closely related to Teter rings in the artinian case. We explain their basic properties and give some examples.

math.AC↗
arXiv2020

Theory of inversion-$\mathbb{Z}_{4}$ protected topological chiral hinge states and its applications to layered antiferromagnets

We study positions of chiral hinge states in higher-order topological insulators (HOTIs) with inversion symmetry. First, we exhaust all possible configurations of the hinge states in the HOTIs in all type-I magnetic space groups with inversion symmetry by studying dependence of the sign of the surface Dirac mass on surface orientations. In particular, in the presence of glide symmetry, for particular surface orientations, the surface Dirac mass changes sign by changing the surface terminations. By applying this result to a layered antiferromagnet (AFM), we find a difference in the hinge states between the cases with an even and odd number of layers. In the case of an even number of layers, which does not preserve inversion symmetry, positions of hinge states are not inversion symmetric. Nonetheless, these inversion-asymmetric hinge states result from the bulk topology. We show that their inversion-asymmetric configurations are uniquely determined from the symmetries and the topological invariant.

cond-mat.mes-hall↗
arXiv2020

An Empirical Study of Contextual Data Augmentation for Japanese Zero Anaphora Resolution

One critical issue of zero anaphora resolution (ZAR) is the scarcity of labeled data. This study explores how effectively this problem can be alleviated by data augmentation. We adopt a state-of-the-art data augmentation method, called the contextual data augmentation (CDA), that generates labeled training instances using a pretrained language model. The CDA has been reported to work well for several other natural language processing tasks, including text classification and machine translation. This study addresses two underexplored issues on CDA, that is, how to reduce the computational cost of data augmentation and how to ensure the quality of the generated data. We also propose two methods to adapt CDA to ZAR: [MASK]-based augmentation and linguistically-controlled masking. Consequently, the experimental results on Japanese ZAR show that our methods contribute to both the accuracy gain and the computation cost reduction. Our closer analysis reveals that the proposed method can improve the quality of the augmented training data when compared to the conventional CDA.

cs.CL↗
arXiv2020

Modeling Event Salience in Narratives via Barthes' Cardinal Functions

Events in a narrative differ in salience: some are more important to the story than others. Estimating event salience is useful for tasks such as story generation, and as a tool for text analysis in narratology and folkloristics. To compute event salience without any annotations, we adopt Barthes' definition of event salience and propose several unsupervised methods that require only a pre-trained language model. Evaluating the proposed methods on folktales with event salience annotation, we show that the proposed methods outperform baseline methods and find fine-tuning a language model on narrative texts is a key factor in improving the proposed methods.

cs.CL↗
arXiv2020

On reducing homological dimensions over noetherian rings

Let $Λ$ be a left and right noetherian ring. First, for $m,n\in\mathbb{N}\cup\{\infty\}$, we give equivalent conditions for a given $Λ$-module to be $n$-torsionfree and have $m$-torsionfree transpose. Using them, we investigate totally reflexive modules and reducing Gorenstein dimension. Next, we introduce homological invariants for $Λ$-modules which we call upper reducing projective and Gorenstein dimensions. We provide an inequality of upper reducing projective dimension and complexity when $Λ$ is commutative and local. Using it, we consider how upper reducing projective dimension relates to reducing projective dimension, and the complete intersection and AB properties of a commutative noetherian local ring.

math.AC↗