arXiv subjects
Publications and source records attributed to Kohei Tanaka.
In this paper, we establish a persistence version of the Quillen-McCord theorem for persistence finite posets. Given a map $f \colon P \rightarrow Q$ between persistence finite posets $P$ and $Q$ with weakly $\varepsilon$-contractible homotopy fibers, we provide an upper bound for the homotopy commutative interleaving distance between $P$ and $Q$.
In this paper, we propose a submission to the x-to-audio alignment (XACLE) challenge. The goal is to predict semantic alignment of a given general audio and text pair. The proposed system is based on a large audio language model (LALM) architecture. We employ a three-stage training pipeline: automated audio captioning pretraining, pretraining with CLAP pseudo-labels, and fine-tuning on the XACLE dataset. Our experiments show that pretraining with CLAP pseudo-labels is the primary performance driver. On the XACLE test set, our system reaches an SRCC of 0.632, significantly outperforming the baseline system (0.334) and securing third place in the challenge team ranking. Code and models can be found at https://github.com/shiotalab-tmu/tmu-xacle2026
Recently, opportunities to transmit speech data to deep learning models executed in the cloud have increased. This has led to growing concerns about speech privacy, including both speaker-specific information and the linguistic content of utterances. As an approach to preserving speech privacy, a speech privacy-preserving method based on encryption using a secret key with a random orthogonal matrix has been proposed. This method enables cloud-based model inference while concealing both the speech content and the speaker identity. However, the method has limited attack resistance and is constrained in terms of the deep learning models to which the encryption can be applied. In this work, we propose a method that enhances the attack resistance of the conventional speech privacy-preserving technique by employing multiple random orthogonal matrices as secret keys. We also introduce approaches to relax the model constraints, enabling the application of our method to a broader range of deep learning models. Furthermore, we investigate the robustness of the proposed method against attacks using extended attack scenarios based on the scenarios employed in the Voice Privacy Challenge. Our experimental results confirmed that the proposed method maintains privacy protection performance for speaker concealment, even under more powerful attack scenarios not considered in prior work.
Magnetic skyrmions in chiral-lattice ferromagnets are currently attracting enormous research interest because of their potential applications in spintronic devices. However, they emerge in bulk specimens only in a narrow window of temperature and magnetic field. This limited stability regime is recognized as an obstacle to technical applications. Recent experiments demonstrated that the thermodynamic stability of magnetic skyrmions is enhanced or suppressed by the application of a uniaxial strain depending on its axial direction in bulk chiral-lattice ferromagnets MnSi [Y. Nii et al., Nat. Commun. 6, 8539 (2015), A. Chacon et al., Phys. Rev. Lett. 115, 267202 (2015)] and Cu2OSeO3 [S. Seki et al., Phys. Rev. B 96, 220404(R) (2017)]. Motivated by these experimental discoveries, we theoretically investigated the effects of anisotropic Dzyaloshinskii--Moriya interactions on the stability of magnetic skyrmions caused by this uniaxial strain. We find that magnetic skyrmions are significantly stabilized (destabilized) in the presence of anisotropic DM interactions when an external magnetic field lies perpendicular (parallel) to the anisotropy axis, along which the DM coupling is strengthened. Our results account completely for the experimentally observed strain-induced stabilization and destabilization of magnetic skyrmions and provide a firm ground for possible strain engineering of skyrmion-based electronic devices.
Bloch lines are formed to reduce the magnetostatic energy generated by the Bloch walls in uniaxial magnets. Recently, it is reported that Bloch lines play important roles in the emergence and helicity reversal of magnetic bubbles in Sc-substitute M-type hexaferrites (BaFe$_{12-x-0.05}$Sc$_{x}$Mg$_{0.05}$O$_{19}$). Although Bloch lines have been discussed on the basis of micromagnetic simulations, the detailed structure was not observed directly. In this study, we investigated the microscopic structures of Bloch lines in BaFe$_{10.35}$Sc$_{1.6}$Mg$_{0.05}$O$_{19}$ uniaxial magnets. Differential-phase contrast scanning transmission microscopy (DPC-STEM) directly revealed that the edges of the Bloch walls were misaligned in the Bloch lines of BaFe$_{10.35}$Sc$_{1.6}$Mg$_{0.05}$O$_{19}$. From the micromagnetic simulations based on the Monte-Carlo technique, we showed that the misaligned Bloch walls were caused by the dipole-dipole interactions in the hexaferrite. Our results will help to understand the microstructures of Bloch lines at nanometer scale.
This paper proposes a method to reduce noise in acyclic sensor networks enumerating targets using the integral theory with respect to Euler characteristic. For an acyclic network (a partially ordered set) equipped with sensors detecting targets, we find reducible points for enumerating targets, as a generalization of weak beat points (homotopically reducible points). This theory is useful for improving the reliability and optimization of acyclic sensor networks.
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the topological complexity of its order complex.
The aim of this paper is to develop a refinement of Forman's discrete Morse theory. To an acyclic partial matching $μ$ on a finite regular CW complex $X$, Forman introduced a discrete analogue of gradient flows. Although Forman's gradient flow has been proved to be useful in practical computations of homology groups, it is not sufficient to recover the homotopy type of $X$. Forman also proved the existence of a CW complex which is homotopy equivalent to $X$ and whose cells are in one-to-one correspondence with the critical cells of $μ$, but the construction is ad hoc and does not have a combinatorial description. By relaxing the definition of Forman's gradient flows, we introduce the notion of flow paths, which contains enough information to reconstruct the homotopy type of $X$, while retaining a combinatorial description. The critical difference from Forman's gradient flows is the existence of a partial order on the set of flow paths, from which a $2$-category $C(μ)$ is constructed. It is shown that the classifying space of $C(μ)$ is homotopy equivalent to $X$ by using homotopy theory of $2$-categories. This result can be also regarded as a discrete analogue of the unpublished work of Cohen, Jones, and Segal on Morse theory in early 90's.
We extend the homotopy theories based on point reduction for finite spaces and simplicial complexes to finite acyclic categories and $Δ$-complexes, respectively. The functors of classifying spaces and face posets are compatible with these homotopy theories. In contrast with the classical settings of finite spaces and simplicial complexes, the universality of morphisms and simplices plays a central role in this paper.
This paper presents categorical structures on classical measure spaces and quantum measure spaces in order to deal with canonical maps associated with conditional measures as morphisms. We extend the Riesz-Markov-Kakutani representation theorem and the Gelfand duality theorem to an equivalence of categories between them. From this categorical viewpoint, we introduce a quantum version of conditional measures as a dual concept of the classical one.
This paper studies the Euler characteristic of a bicategory based on the concept of magnitudes introduced by Leinster. We focus on its invariance with respect to biequivalence and on the product formula for Buckley's fibered bicategories.
We present a combinatorial analogue of the nerve theorem for covers of small categories, using the Grothendieck construction. We apply our result to prove the inclusion-exclusion principle for the Euler characteristic of a finite category.
This paper provides the theory of integration with respect to Euler characteristics of finite categories. As an application, we use sensors to enumerate the targets lying on a poset. This is a discrete analogue to Baryshnikov and Ghrist's work on integral theory using topological Euler characteristics.
We define Euler characteristic of a category enriched by a monoidal model category. If a monoidal model category V is equipped with Euler characteristic that is compatible with weak equivalences and fibrations in V, then our Euler characteristic is also compatible with weak equivalences and fibrations in the model structure induced by that of V. In particular, we focus on the case of topological categories; that is, categories enriched by the category of topological spaces. As its application, we obtain the ordinary Euler characteristic of a cellular stratified space X by computing the Euler characteristic of the face category C(X) induced from X.
This paper describes how to recover the topology of a closed manifold $M$ from a good Morse function $f$ on $M$. The essential method was suggested by Cohen, Jones and Segal. They constructed a topological category $C_{f}$ and claimed that the classifying space $BC_{f}$ is homeomorphic to $M$. We prove it from a different viewpoint with them using a cell decomposition of $M$ associated to $f$. The cell complex $M_{f}$ equipped with the decomposition induces a topological category $C(M_{f})$ whose classifying space $BC(M_{f})$ is homeomorphic to $M$. We show that $C(M_{f})$ is isomorphic to $C_{f}$ as a topological category.
We define a new model structure on the category of small categories, which is intimately related to the notion of coverings and fundamental groups of small categories. Fibrant objects in the model structure coincide with groupoids, and the fibrant replacement is the groupoidification.