Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

Abstract

A passive dynamic walker is a mechanical system that walks down a slope without any control, and gives useful insights into the dynamic mechanism of stable walking. This system shows specific attractor characteristics depending on the slope angle due to nonlinear dynamics, such as period-doubling to chaos and its disappearance by a boundary crisis. However, it remains unclear what happens to the basin of attraction. In our previous studies, we showed that a fractal basin of attraction is generated using a simple model over a critical slope angle by iteratively applying the inverse image of the Poincaré map, which has stretching and bending effects. In the present study, we show that the size and fractality of the basin of attraction sharply change many times by changing the slope angle. Furthermore, we improved our previous analysis to clarify the mechanisms for these changes and the disappearance of the basin of attraction based on the stretching and bending deformation in the basin formation process. These findings will improve our understanding of the governing dynamics to generate the basin of attraction in walking.

DOI： 10.1007/s11071-023-08913-w

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Other Link： https://link.springer.com/article/10.1007/s11071-023-08913-w/fulltext.html

Language：English   Publishing type：Part of collection (book)   Publisher：Springer Nature Singapore  

DOI： 10.1007/978-981-99-5235-9_11

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Michiki Taniwaki Tokyo Univ. of Sci. Foggiatto Lira Alexandre Tokyo Univ. of Sci. Chiharu Mitsumata Tokyo Univ. of Sci. Takahiro Yamazaki Tokyo Univ. of Sci. Ippei Obayashi Okayama Univ. Yasuaki Hiraoka Kyoto Univ. Yasuhiko Igarashi Tsukuba Univ. Yuta Mizutori Tsukuba Univ. Sepehri Amin Hossein NIMS Tadakatsu Ohkubo NIMS Masato Kotsugi Tokyo Univ. of Sci.  

We analyzed the magnetization reversal process of non-oriented electromagnetic steel sheets using the extended Landau free energy model (eX-GL). The model is a new analysis approach that can connect the macroscopic function and the microscopic structure beyond the hierarchy by using data science technique. It can treat grain boundaries and defects, which frequently occur in actual magnetic materials, furthermore it can visualize the inhibiting factors of magnetization reversal back to the original image. As a result, we could draw the experimental energy landscape of an electromagnetic steel sheet for the first time, and the magnetic domain walls that contribute to magnetization reversal was selectively visualized.

DOI： 10.1109/INTERMAGShortPapers58606.2023.10228817

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AIP Publishing  

High-accuracy prediction of the physical properties of amorphous materials is challenging in condensed-matter physics. A promising method to achieve this is machine-learning potentials, which is an alternative to computationally demanding ab initio calculations. When applying machine-learning potentials, the construction of descriptors to represent atomic configurations is crucial. These descriptors should be invariant to symmetry operations. Handcrafted representations using a smooth overlap of atomic positions and graph neural networks (GNN) are examples of methods used for constructing symmetry-invariant descriptors. In this study, we propose a novel descriptor based on a persistence diagram (PD), a two-dimensional representation of persistent homology (PH). First, we demonstrated that the normalized two-dimensional histogram obtained from PD could predict the average energy per atom of amorphous carbon at various densities, even when using a simple model. Second, an analysis of the dimensional reduction results of the descriptor spaces revealed that PH can be used to construct descriptors with characteristics similar to those of a latent space in a GNN. These results indicate that PH is a promising method for constructing descriptors suitable for machine-learning potentials without hyperparameter tuning and deep-learning techniques.

DOI： 10.1063/5.0159349

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

Abstract

This paper tackles the problem of coefficient field choice in persistent homology. When we compute a persistence diagram, we need to select a coefficient field before computation. We should understand the dependence of the diagram on the coefficient field to facilitate computation and interpretation of the diagram. We clarify that the dependence is strongly related to the torsion part of $$\mathbb {Z}$$ relative homology in the filtration. We show the sufficient and necessary conditions of the independence of coefficient field choice. An efficient algorithm is proposed to verify the independence. A slight modification of the standard persistence algorithm gives the verification algorithm. In a numerical experiment with the algorithm, a persistence diagram rarely changes even when the coefficient field changes if we consider a filtration in $$\mathbb {R}^3$$. The experiment suggests that, in practical terms, changes in the field coefficient will not change persistence diagrams when the data are in $$\mathbb {R}^3$$.

DOI： 10.1007/s00454-023-00544-7

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Other Link： https://link.springer.com/article/10.1007/s00454-023-00544-7/fulltext.html

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

Abstract

This paper proposes a stable volume and a stable volume variant, referred to as a stable sub-volume, for more reliable data analysis using persistent homology. In prior research, an optimal cycle and similar ideas have been proposed to identify the homological structure corresponding to each birth-death pair in a persistence diagram. While this is helpful for data analysis using persistent homology, the results are sensitive to noise. The sensitivity affects the reliability and interpretability of the analysis. In this paper, stable volumes and stable sub-volumes are proposed to solve this problem. For a special case, we prove that a stable volume is the robust part of an optimal volume against noise. We implemented stable volumes and sub-volumes on HomCloud, a data analysis software package based on persistent homology, and show examples of stable volumes and sub-volumes.

DOI： 10.1007/s41468-023-00119-8

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Other Link： https://link.springer.com/article/10.1007/s41468-023-00119-8/fulltext.html

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：The Japan Society for Industrial and Applied Mathematics  

DOI： 10.14495/jsiaml.14.151

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Publishing type：Research paper (scientific journal)   Publisher：Physical Society of Japan  

DOI： 10.7566/JPSJ.91.091013

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AIP Publishing  

Quantifying the correlation between the complex structures of amorphous materials and their physical properties has been a longstanding problem in materials science. In amorphous Si, a representative covalent amorphous solid, the presence of a medium-range order (MRO) has been intensively discussed. However, the specific atomic arrangement corresponding to the MRO and its relationship with physical properties, such as thermal conductivity, remains elusive. We solved this problem by combining topological data analysis, machine learning, and molecular dynamics simulations. Using persistent homology, we constructed a topological descriptor that can predict thermal conductivity. Moreover, from the inverse analysis of the descriptor, we determined the typical ring features correlated with both the thermal conductivity and MRO. The results could provide an avenue for controlling material characteristics through the topology of the nanostructures.

DOI： 10.1063/5.0093441

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Publishing type：Research paper (scientific journal)   Publisher：Frontiers Media SA  

Stride intervals in human walking fluctuate from one stride to the next, exhibiting statistical persistence. This statistical property is changed by aging, neural disorders, and experimental interventions. It has been hypothesized that the central nervous system is responsible for the statistical persistence. Human walking is a complex phenomenon generated through the dynamic interactions between the central nervous system and the biomechanical system. It has also been hypothesized that the statistical persistence emerges through the dynamic interactions during walking. In particular, a previous study integrated a biomechanical model composed of seven rigid links with a central pattern generator (CPG) model, which incorporated a phase resetting mechanism as sensory feedback as well as feedforward, trajectory tracking, and intermittent feedback controllers, and suggested that phase resetting contributes to the statistical persistence in stride intervals. However, the essential mechanisms remain largely unclear due to the complexity of the neuromechanical model. In this study, we reproduced the statistical persistence in stride intervals using a simplified neuromechanical model composed of a simple compass-type biomechanical model and a simple CPG model that incorporates only phase resetting and a feedforward controller. A lack of phase resetting induced a loss of statistical persistence, as observed for aging, neural disorders, and experimental interventions. These mechanisms were clarified based on the phase response characteristics of our model. These findings provide useful insight into the mechanisms responsible for the statistical persistence of stride intervals in human walking.

DOI： 10.3389/fncir.2022.836121

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Publishing type：Research paper (scientific journal)   Publisher：American Vacuum Society  

To determine the correlation between local structure and thermal conductivity of amorphous carbon, we investigated heat conduction in 216-atom systems with different densities (2.0–3.4 g/cm³) using the ab initio molecular dynamics approach. By applying the Allen–Feldman theory with interatomic force constants from ab initio calculations, we report a significant correlation between the thermal conductivity and the density. To clarify which structural characteristics in the high- and low-density cases determine the magnitude of thermal conductivity, we performed geometrical and topological analyses. Coordination number analysis and ring statistics revealed that the sp/sp²/sp³ bond ratios and topological characteristics correlate with density. We also demonstrated that these structural characteristics can be quantified using persistent homology analysis, providing a predictive model of thermal conductivity.

DOI： 10.1116/6.0001744

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Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

<title>Abstract</title>Topological data analysis is an emerging concept of data analysis for characterizing shapes. A state-of-the-art tool in topological data analysis is persistent homology, which is expected to summarize quantified topological and geometric features. Although persistent homology is useful for revealing the topological and geometric information, it is difficult to interpret the parameters of persistent homology themselves and difficult to directly relate the parameters to physical properties. In this study, we focus on connectivity and apertures of flow channels detected from persistent homology analysis. We propose a method to estimate permeability in fracture networks from parameters of persistent homology. Synthetic 3D fracture network patterns and their direct flow simulations are used for the validation. The results suggest that the persistent homology can estimate fluid flow in fracture network based on the image data. This method can easily derive the flow phenomena based on the information of the structure.

DOI： 10.1038/s41598-021-97222-6

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Other Link： https://www.nature.com/articles/s41598-021-97222-6

Language：English   Publishing type：Research paper (scientific journal)   Publisher：NATURE RESEARCH  

The broken symmetry in the atomic-scale ordering of glassy versus crystalline solids leads to a daunting challenge to provide suitable metrics for describing the order within disorder, especially on length scales beyond the nearest neighbor that are characterized by rich structural complexity. Here, we address this challenge for silica, a canonical network-forming glass, by using hot versus cold compression to (i) systematically increase the structural ordering after densification and (ii) prepare two glasses with the same high-density but contrasting structures. The structure was measured by high-energy X-ray and neutron diffraction, and atomistic models were generated that reproduce the experimental results. The vibrational and thermodynamic properties of the glasses were probed by using inelastic neutron scattering and calorimetry, respectively. Traditional measures of amorphous structures show relatively subtle changes upon compacting the glass. The method of persistent homology identifies, however, distinct features in the network topology that change as the initially open structure of the glass is collapsed. The results for the same high-density glasses show that the nature of structural disorder does impact the heat capacity and boson peak in the low-frequency dynamical spectra. Densification is discussed in terms of the loss of locally favored tetrahedral structures comprising oxygen-decorated SiSi4 tetrahedra.

DOI： 10.1038/s41427-020-00262-z

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media {LLC}  

<title>Abstract</title>The structural origin of the slow dynamics in glass formation remains to be understood owing to the subtle structural differences between the liquid and glass states. Even from simulations, where the positions of all atoms are deterministic, it is difficult to extract significant structural components for glass formation. In this study, we have extracted significant local atomic structures from a large number of metallic glass models with different cooling rates by utilising a computational persistent homology method combined with linear machine learning techniques. A drastic change in the extended range atomic structure consisting of 3–9 prism-type atomic clusters, rather than a change in individual atomic clusters, was found during the glass formation. The present method would be helpful towards understanding the hierarchical features of the unique static structure of the glass states.

DOI： 10.1038/s43246-020-00100-3

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Other Link： http://www.nature.com/articles/s43246-020-00100-3

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

DOI： 10.1109/iros45743.2020.9341800

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Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

© 2020 The Author(s) Persistent homology is a mathematical method to quantify topological features of shapes, such as connectivity. This study applied persistent homology to analyze fracture network patterns in rocks. We show that persistent homology can detect paths connecting from one boundary to the other boundary constituting fractures, which is useful for understanding relationships between fracture patterns and flow phenomena. In addition, complex fracture network patterns so-called mesh textures in serpentine were analyzed by persistent homology. In previous studies, fracture network patterns for different flow conditions were generated by a hydraulic–chemical–mechanical simulation and classified based on additional data and on expert's experience and knowledge. In this study, image analysis based on persistent homology alone was able to characterize fracture patterns. Similarities and differences of fracture network patterns between natural serpentinite and simulation were quantified and discussed. The data-driven approach combining with the persistent homology analysis helps to infer fracture forming processes in rocks. The results of persistent homology analysis provide critical topological information that cannot be obtained by geometric analysis of image data only.

DOI： 10.1016/j.cageo.2020.104550

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

Abstract

Passive dynamic walking is a model that walks down a shallow slope without any control or input. This model has been widely used to investigate how humans walk with low energy consumption and provides design principles for energy-efficient biped robots. However, the basin of attraction is very small and thin and has a fractal-like complicated shape, which makes producing stable walking difficult. In our previous study, we used the simplest walking model and investigated the fractal-like basin of attraction based on dynamical systems theory by focusing on the hybrid dynamics of the model composed of the continuous dynamics with saddle hyperbolicity and the discontinuous dynamics caused by the impact upon foot contact. We clarified that the fractal-like basin of attraction is generated through iterative stretching and bending deformations of the domain of the Poincaré map by sequential inverse images. However, whether the fractal-like basin of attraction is actually fractal, i.e., whether infinitely many self-similar patterns are embedded in the basin of attraction, is dependent on the slope angle, and the mechanism remains unclear. In the present study, we improved our previous analysis in order to clarify this mechanism. In particular, we newly focused on the range of the Poincaré map and specified the regions that are stretched and bent by the sequential inverse images of the Poincaré map. Through the analysis of the specified regions, we clarified the conditions and mechanism required for the basin of attraction to be fractal.

DOI： 10.1088/1748-3190/ab9283

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Other Link： https://iopscience.iop.org/article/10.1088/1748-3190/ab9283/pdf

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.bpj.2020.04.032

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：NATURE PUBLISHING GROUP  

Understanding the liquid structure provides information that is crucial to uncovering the nature of the glass-liquid transition. We apply an aerodynamic levitation technique and high-energy X-rays to liquid (l)-Er(2)O(3)to discover its structure. The sample densities are measured by electrostatic levitation at the International Space Station. Liquid Er(2)O(3)displays a very sharp diffraction peak (principal peak). Applying a combined reverse Monte Carlo - molecular dynamics approach, the simulations produce an Er-O coordination number of 6.1, which is comparable to that of another nonglass-forming liquid,l-ZrO2. The atomic structure ofl-Er(2)O(3)comprises distorted OEr4 tetraclusters in nearly linear arrangements, as manifested by a prominent peak observed at similar to 180 degrees in the Er-O-Er bond angle distribution. This structural feature gives rise to long periodicity corresponding to the sharp principal peak in the X-ray diffraction data. A persistent homology analysis suggests thatl-Er(2)O(3)is homologically similar to the crystalline phase. Moreover, electronic structure calculations show thatl-Er(2)O(3)has a modest band gap of 0.6 eV that is significantly reduced from the crystalline phase due to the tetracluster distortions. The estimated viscosity is very low above the melting point forl-ZrO2, and the material can be described as an extremely fragile liquid.

DOI： 10.1038/s41427-020-0220-0

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：CERAMIC SOC JAPAN-NIPPON SERAMIKKUSU KYOKAI  

The structure of glassy, liquid, and amorphous materials is still not well understood, due to the insufficient structural information from diffraction data. In this article, attempts are made to understand the origin of diffraction peaks, particularly of the first sharp diffraction peak (FSDP, Q(1)), the principal peak (PP, Q(2)), and the third peak (Q(3)), observed in the measured diffraction patterns of disordered materials whose structure contains tetrahedral motifs. It is confirmed that the FSDP (Q(1)) is not a signature of the formation of a network, because an FSDP is observed in tetrahedral molecular liquids. It is found that the PP (Q(2)) reflects orientational correlations of tetrahedra. Q(3), that can be observed in all disordered materials, even in common liquid metals, stems from simple pair correlations. Moreover, information on the topology of disordered materials was revealed by utilizing persistent homology analyses. The persistence diagram of silica (SiO2) glass suggests that the shape of rings in the glass is similar not only to those in the crystalline phase with comparable density (alpha-cristobalite), but also to rings present in crystalline phases with higher density (alpha-quartz and coesite); this is thought to be the signature of disorder. Furthermore, we have succeeded in revealing the differences, in terms of persistent homology, between tetrahedral networks and tetrahedral molecular liquids, and the difference/similarity between liquid and amorphous (glassy) states. Our series of analyses demonstrated that a combination of diffraction data and persistent homology analyses is a useful tool for allowing us to uncover structural features hidden in halo pattern of disordered materials. (C) 2019 The Ceramic Society of Japan. All rights reserved.

DOI： 10.2109/jcersj2.19143

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media {LLC}  

DOI： 10.1038/s41427-019-0180-4

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Language：Japanese   Publishing type：Research paper (scientific journal)  

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Language：Japanese   Publisher：Surface Science Society Japan  

<p>We executed the topological data analysis of labyrinth magnetic domain structure to visualize pinning site during the magnetization reversal process. We utilized persistent homology to extract the topological feature of the magnetic domain structure, and principal component analysis was used to construct the correlation between persistence diagram and magnetic hysteresis loop. As a result, we could automatically visualize the pinning site as topological defect on the original magnetic domain structure.</p>

DOI： 10.1380/vss.62.153

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Language：Japanese   Publisher：The Japan Society of Vacuum and Surface Science  

<p>We executed the topological data analysis of labyrinth magnetic domain structure to visualize pinning site during the magnetization reversal process. We utilized persistent homology to extract the topological feature of the magnetic domain structure, and principal component analysis was used to construct the correlation between persistence diagram and magnetic hysteresis loop. As a result, we could automatically visualize the pinning site as topological defect on the original magnetic domain structure.</p>

DOI： 10.1380/vss.62.153

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Publishing type：Research paper (scientific journal)   Publisher：Japan Institute of Metals  

DOI： 10.2320/materia.58.17

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Publishing type：Research paper (scientific journal)   Publisher：American Physical Society ({APS})  

DOI： 10.1103/physrevb.99.045153

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Language：English   Publishing type：Research paper (scientific journal)  

The purpose of this study is to evaluate the accuracy for classification of hepatic tumors by characterization of T1-weighted magnetic resonance (MR) images using two radiomics approaches with machine learning models: texture analysis and topological data analysis using persistent homology. This study assessed non-contrast-enhanced fat-suppressed three-dimensional (3D) T1-weighted images of 150 hepatic tumors. The lesions included 50 hepatocellular carcinomas (HCCs), 50 metastatic tumors (MTs), and 50 hepatic hemangiomas (HHs) found respectively in 37, 23, and 33 patients. For classification, texture features were calculated, and also persistence images of three types (degree 0, degree 1 and degree 2) were obtained for each lesion from the 3D MR imaging data. We used three classification models. In the classification of HCC and MT (resp. HCC and HH, HH and MT), we obtained accuracy of 92% (resp. 90%, 73%) by texture analysis, and the highest accuracy of 85% (resp. 84%, 74%) when degree 1 (resp. degree 1, degree 2) persistence images were used. Our methods using texture analysis or topological data analysis allow for classification of the three hepatic tumors with considerable accuracy, and thus might be useful when applied for computer-aided diagnosis with MR images.

DOI： 10.1038/s41598-019-45283-z

PubMed

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Language：Japanese   Publishing type：Research paper (scientific journal)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Society for Industrial {\&} Applied Mathematics ({SIAM})  

DOI： 10.1137/17M1159439

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Cambridge University Press ({CUP})  

DOI： 10.1017/s1431927618014897

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Nature  

DOI： 10.1007/s41468-018-0013-5

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Nature  

DOI： 10.1038/s41598-018-21867-z

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We apply a persistent homology analysis to investigate the behavior of nanovoids during the crazing process of glassy polymers. We carry out a coarse-grained molecular dynamics simulation of the uniaxial deformation of an amorphous polymer and analyze the results with persistent homology. Persistent homology reveals the void coalescence during craze formation, and the results suggest that the yielding process is regarded as the percolation of nanovoids created by deformation.

DOI： 10.1103/PhysRevE.95.012504

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Language：Japanese   Publishing type：Research paper (scientific journal)  

DOI： 10.11540/bjsiam.26.4_7

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

Iron ore sinter constitutes the major component of the iron-bearing burden in blast furnaces, and its reduction mechanism is one of the keys to improving the productivity of ironmaking. Iron ore sinter is composed of multiple iron oxide phases and calcium ferrites (CFs), and their heterogeneous reduction was investigated in terms of changes in iron chemical state: Fe-III, Fe-II, and Fe-0 were examined macroscopically by 2D X-ray absorption and microscopically by 3D transmission X-ray microscopy (TXM). It was shown that the reduction starts at iron oxide grains rather than at calcium ferrite (CF) grains, especially those located near micropores. The heterogeneous reduction causes crack formation and deteriorates the mechanical strength of the sinter. These results help us to understand the fundamental aspects of heterogeneous reduction schemes in iron ore sinter.

DOI： 10.1088/1742-6596/849/1/012015

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Meteorological Society of Japan  

<p>This paper addresses a cyclone identification algorithm with the superlevel set filtration of the persistent homology together with the merge-tree reconstruction of data. Based on the information of peaks and saddles of the scaler field, the newly developed algorithm divides the analysis area into several homology classes, each of which satisfies the peak-to-saddle difference larger than a criterion that should be set in advance. Applied to the 850-hPa relative vorticity in the western North Pacific at 1200 UTC on 2 March 2013, 3 homology classes were found with the criterion of 100 × 10⁻⁶ s⁻¹ and 17 homology classes were found with the criterion of 50 × 10⁻⁶ s⁻¹. The merge-tree restructuring clarified the neighbour relation among homology classes. The result suggests that the weak criterion detected too much homology classes, some of which are small peaks inside of a single cyclone. The climatology feature density provides the Pacific storm track with the strict criterion. Finally, a possible way to extend toward cyclone tracking with the persistent homology is discussed.</p>

DOI： 10.2151/sola.2017-039

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton-Raphson continuation method in this setting. Given an original point cloud P, its persistence diagram D, and a target persistence diagram D', we gradually move from D to D', by successively computing intermediate point clouds until we finally find a point cloud P' having D' as its persistence diagram. Our method can be applied to a wide variety of situations in topological data analysis where it is necessary to solve an inverse problem, from persistence diagrams to point cloud data. (C) 2015 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physd.2015.11.011

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ROYAL SOC  

Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking.

DOI： 10.1098/rspa.2016.0028

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER JAPAN KK  

In this paper, we investigate the mathematical structures and mechanisms of bipedal walking from a dynamical viewpoint. Especially, we focus on the basin of attraction since it determines the stability of bipedal walking. We treat two similar but different bipedal walking models (passive and active dynamic walking models) and examine common mathematical structure between these models. We find that the saddle hyperbolicity and hybrid system play important roles for the shape of the basin of attraction in both models, which are quite common for more general bipedal models and important for understanding the stability mechanism of bipedal walking.

DOI： 10.1007/s13160-015-0181-9

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Netherlands  

DOI： 10.1007/978-94-007-4792-0_89

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER INST PHYSICS  

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

DOI： 10.1063/1.4767672

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SIAM PUBLICATIONS  

A new computer-assisted verification method for invariant densities and decay rates of correlations is proposed. This new method is based on the Hilbert cone technique.

DOI： 10.1137/09077864X

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

Dolgopyat [4] showed that a class of Axiom A flows has exponential decay of correlations for smooth observables, and Baladi-Vallee [2] gave a nice interpretation of it on suspension semiflows of one-dimensional expanding countable Markov maps. Avila-Gouezel-Yoccoz [1] extends the result of Baladi-Vallee to higher dimensional systems.
In this paper we show that a class of non-Markov semiflows also has exponential decay of correlations.
We prove that such exponential decay can be shown on an open dense condition for the suspensions of piecewise expanding maps.

DOI： 10.1215/kjm/1256219166

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (bulletin of university, research institution)  

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Language：Abkhazian   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)   Publisher：The Crystallographic Society of Japan  

DOI： 10.5940/jcrsj.62.43

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (other)  

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Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

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Language：Japanese   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：Japan Institute of Metals  

DOI： 10.2320/materia.57.595

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Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

J-GLOBAL

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Language：English   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)   Publisher：Springer Singapore  

This paper provides an introduction to persistent homology and a survey of its applications to materials science. Mathematical prerequisites are limited to elementary linear algebra. Important concepts in topological data analysis such as persistent homology and persistence diagram are explained in a selfcontained manner with several examples. These tools are applied to glass structural analysis, crystallization of granular systems, and craze formation of polymers.

DOI： 10.1007/978-981-10-7617-6_5

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)   Publisher：Japanese Neural Network Society  

DOI： 10.3902/jnns.22.68

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)  

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Other Link： http://orcid.org/0000-0002-7207-7280

Language：Japanese   Presentation type：Poster presentation  

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Venue：札幌  

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Venue：Online  

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Venue：Online  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Oral presentation (general)  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Ohio State University, Columbus, Ohio, USA  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

Venue：JST東京本部, 東京  

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Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Meiji Univ., Tokyo  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

Venue：明治大学駿河台キャンパス, 東京  

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Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Shibaura Institute of technology, Tokyo  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：東京理科大学  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Language：English   Presentation type：Oral presentation (invited, special)  

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Award type：Award from international society, conference, symposium, etc. 

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