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Hierarchical structures of amorphous solids characterized by persistent homology

- Y. Hiraoka, T. Nakamura, A. Hirata, Emerson G. Escolar, K. Matsue, Y. Nishiura
- Materials Science, Physics
- Proceedings of the National Academy of Sciences
- 15 January 2015

Significance Persistent homology is an emerging mathematical concept for characterizing shapes of data. In particular, it provides a tool called the persistence diagram that extracts multiscale… Expand

Geometric Frustration of Icosahedron in Metallic Glasses

- A. Hirata, L. J. Kang, +5 authors M. Chen
- Medicine
- Science
- 26 July 2013

Order, Order The structure of glassy materials, which are known to have short-range order but no long-range pattern, continues to be a puzzle. One current theory is that some glassy materials possess… Expand

Numerical validation of blow-up solutions of ordinary differential equations

- Akitoshi Takayasu, K. Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, S. Oishi
- Mathematics, Computer Science
- J. Comput. Appl. Math.
- 9 June 2016

TLDR

A note on the spectral mapping theorem of quantum walk models

- K. Matsue, O. Ogurisu, E. Segawa
- Mathematics, Physics
- 3 April 2016

We discuss the description of eigenspace of a quantum walk model $U$ with an associating linear operator $T$ in abstract settings of quantum walk including the Szegedy walk on graphs. In particular,… Expand

Rigorous numerics for fast-slow systems with one-dimensional slow variable: topological shadowing approach

- K. Matsue
- Mathematics
- 6 July 2015

We provide a rigorous numerical computation method to validate periodic, homoclinic and heteroclinic orbits as the continuation of singular limit orbits for the fast-slow system $x' =… Expand

On Blow-Up Solutions of Differential Equations with Poincaré-Type Compactifications

- K. Matsue
- Computer Science, Mathematics
- SIAM J. Appl. Dyn. Syst.
- 11 September 2018

TLDR

Quantum walks on simplicial complexes

- K. Matsue, O. Ogurisu, E. Segawa
- Physics, Computer Science
- Quantum Inf. Process.
- 5 July 2015

TLDR

Quaternionic quantum walks of Szegedy type and zeta functions of graphs

- N. Konno, K. Matsue, H. Mitsuhashi, I. Sato
- Physics, Mathematics
- Quantum Inf. Comput.
- 15 March 2017

TLDR

On the construction of Lyapunov functions with computer assistance

- K. Matsue, Tomohiro Hiwaki, N. Yamamoto
- Mathematics, Computer Science
- J. Comput. Appl. Math.
- 20 April 2016

TLDR

Description of Medium-Range Order in Amorphous Structures by Persistent Homology

- T. Nakamura, Y. Hiraoka, A. Hirata, Emerson G. Escolar, K. Matsue, Y. Nishiura
- Materials Science
- 15 January 2015

The description of amorphous structures has been a long-standing problem, and conventional methods are insufficient for revealing intrinsic structures. In this Letter, we propose a computational… Expand

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