102 citations · 159 across the 33 of their papers we have counts for
35 papers
Homology of the Lie Algebra of Locally Generated Derivations of a Discrete and Proper Metric Space
Nigel Higson, Tsuyoshi Kato
We associate to each proper discrete metric space a Lie algebra that acts by locally generated derivations on an infinite tensor product of matrix algebras indexed by the point…
Vector fields on non-compact manifolds
Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya
Let be a non-compact connected manifold with a cocompact and properly discontinuous action of a discrete group . We establish a Poincaré-Hopf theorem for a bounded vector fi…
Seiberg-Witten theory on finite covering spaces of spin 4-manifolds
Tsuyoshi Kato, Doman Takata
We compute the equivariant Bauer-Furuta degree, when a finite group acts freely on a spin 4-manifold. In the case when the group is cyclic of order power of two, Bryan gave a formu…
Upper bounds for virtual dimensions of Seiberg-Witten moduli spaces
Tsuyoshi Kato, Daisuke Kishimoto, Nobuhiro Nakamura +1
Given a closed four-manifold with and a prime number , we prove that for any mod basic class, the virtual dimension of the Seiberg-Witten moduli space is bounded a…
Hilbert bundles with ends
Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya
Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and…
Homotopy type of the unitary group of the uniform Roe algebra on
Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya
We study the homotopy type of the space of the unitary group $\U_1(C^\ast_u(|\mathbb{Z}^n|))$ of the uniform Roe algebra of . We show that…
Learning Sign-Constrained Support Vector Machines
Kenya Tajima, Takahiko Henmi, Kohei Tsuchida +2
Domain knowledge is useful to improve the generalization performance of learning machines. Sign constraints are a handy representation to combine domain knowledge with learning mac…
A note on exotic families of 4-manifolds
Tsuyoshi Kato, Hokuto Konno, Nobuhiro Nakamura
We present a pair of smooth fiber bundles over the circle with a common -dimensional fiber with the following properties: (1) their total spaces are diffeomorphic to each other;…
The simple type conjecture for mod 2 Seiberg-Witten invariants
Tsuyoshi Kato, Nobuhiro Nakamura, Kouichi Yasui
We prove that, under a simple condition on the cohomology ring, every closed 4-manifold has mod 2 Seiberg-Witten simple type. This result shows that there exists a large class of t…
Adaptive Signal Variances: CNN Initialization Through Modern Architectures
Takahiko Henmi, Esmeraldo Ronnie Rey Zara, Yoshihiro Hirohashi +1
Deep convolutional neural networks (CNN) have achieved the unwavering confidence in its performance on image processing tasks. The CNN architecture constitutes a variety of differe…
Frank-Wolfe algorithm for learning SVM-type multi-category classifiers
Kenya Tajima, Yoshihiro Hirohashi, Esmeraldo Ronnie Rey Zara +1
Multi-category support vector machine (MC-SVM) is one of the most popular machine learning algorithms. There are lots of variants of MC-SVM, although different optimization algorit…
Homotopy type of the space of finite propagation unitary operators on
Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya
The index theory for the space of finite propagation unitary operators was developed by Gross, Nesme, Vogts and Werner from the viewpoint of quantum walks in mathematical physics.…
harmonic theory, Seiberg-Witten theory and asymptotics of differential forms
Tsuyoshi Kato
We present a pair of open smooth -manifolds that are mutually homeomorphic. One of them admits a Riemannian metric that possesses quasi-cylindricity, and positivity of scalar cu…
Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds
Tsuyoshi Kato, Hokuto Konno, Nobuhiro Nakamura
We show a rigidity theorem for the Seiberg-Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type i…
Higher Nahm transform in non commutative geometry
Tsuyoshi Kato, Hirofumi Sasahira, Hang Wang
Anti-self-dual (ASD) connections for a compact smooth four manifold arise as critical values for the Yang-Mills action functional. Nahm transform is a nice correspondence between a…
harmonic forms and the Seiberg-Witten map on non compact four manifolds
Tsuyoshi Kato
We explain a new phenomenon on non compact complete Riemannian four manifolds, where d^+ image of one forms can not exhaust densely on L^2 self dual forms on each compact subset, i…
Dynamics of the box-ball system with random initial conditions via Pitman's transformation
David A. Croydon, Tsuyoshi Kato, Makiko Sasada +1
The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour. In this article, we study the BBS when started fr…
Parametric Models for Mutual Kernel Matrix Completion
Rachelle Rivero, Tsuyoshi Kato
Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel m…
Threshold Auto-Tuning Metric Learning
Yuya Onuma, Rachelle Rivero, Tsuyoshi Kato
It has been reported repeatedly that discriminative learning of distance metric boosts the pattern recognition performance. A weak point of ITML-based methods is that the distance…
Induced map on K theory for certain Γ-equivariant maps between Hilbert spaces
Tsuyoshi Kato
Higson-Kapsparov-Trout introduced an infinite-dimensional Clifford algebra of a Hilbert space, and verified Bott periodicity on K-theory. To develop algebraic topology of maps betw…
Sign-Constrained Regularized Loss Minimization
Tsuyoshi Kato, Misato Kobayashi, Daisuke Sano
In practical analysis, domain knowledge about analysis target has often been accumulated, although, typically, such knowledge has been discarded in the statistical analysis stage,…
Twisted Donaldson invariants
Tsuyoshi Kato, Hirofumi Sasahira, Hang Wang
Fundamental group of a manifold gives a deep effect on its underlying smooth structure. In this paper we introduce a new variant of the Donaldson invariant in Yang-Mills gauge theo…
Mutual Kernel Matrix Completion
Tsuyoshi Kato, Rachelle Rivero
With the huge influx of various data nowadays, extracting knowledge from them has become an interesting but tedious task among data scientists, particularly when the data come in h…
Covering monopole map and higher degree in non commutative geometry
Tsuyoshi Kato
In this paper we develop analysis of the monopole maps over the universal covering space of a compact four manifold. We induce a property on local properness of the covering monopo…