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Author

Yasuaki Hiraoka

Other affiliations: Tohoku University, Osaka University, Kyushu University  ...read more
Bio: Yasuaki Hiraoka is an academic researcher from Kyoto University. The author has contributed to research in topics: Persistent homology & Topological data analysis. The author has an hindex of 21, co-authored 67 publications receiving 1494 citations. Previous affiliations of Yasuaki Hiraoka include Tohoku University & Osaka University.


Papers
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Journal ArticleDOI
TL;DR: A unified method using persistence diagrams for studying the geometry of atomic configurations in amorphous solids, which suggests that the PDs provide a unified method that extracts greater depth of geometric information in amortized solids than conventional methods.
Abstract: This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the PDs is given by an atomic configuration and the output is expressed as 2D histograms. Then, specific distributions such as curves and islands in the PDs identify meaningful shape characteristics of the atomic configuration. Although the method can be applied to a wide variety of disordered systems, it is applied here to silica glass, the Lennard-Jones system, and Cu-Zr metallic glass as standard examples of continuous random network and random packing structures. In silica glass, the method classified the atomic rings as short-range and medium-range orders and unveiled hierarchical ring structures among them. These detailed geometric characterizations clarified a real space origin of the first sharp diffraction peak and also indicated that PDs contain information on elastic response. Even in the Lennard-Jones system and Cu-Zr metallic glass, the hierarchical structures in the atomic configurations were derived in a similar way using PDs, although the glass structures and properties substantially differ from silica glass. These results suggest that the PDs provide a unified method that extracts greater depth of geometric information in amorphous solids than conventional methods.

276 citations

Journal ArticleDOI
TL;DR: In this paper, the authors partially clarify the relation between the compressibility of a protein and its molecular geometric structure by extracting a measure of compressibility derived from those topological features whose relevance is suggested by physical and chemical properties.
Abstract: In this paper we partially clarify the relation between the compressibility of a protein and its molecular geometric structure To identify and understand the relevant topological features within a given protein, we model its molecule as an alpha filtration and hence obtain multi-scale insight into the structure of its tunnels and cavities The persistence diagrams of this alpha filtration capture the sizes and robustness of such tunnels and cavities in a compact and meaningful manner From these persistence diagrams, we extract a measure of compressibility derived from those topological features whose relevance is suggested by physical and chemical properties Due to recent advances in combinatorial topology, this measure is efficiently and directly computable from information found in the Protein Data Bank (PDB) Our main result establishes a clear linear correlation between the topological measure and the experimentally-determined compressibility of most proteins for which both PDB information and experimental compressibility data are available Finally, we establish that both the topological measurement and the linear correlation are stable with respect to small perturbations in the input data, such as those arising from experimental errors in compressibility and X-ray crystallography experiments

143 citations

Proceedings Article
19 Jun 2016
TL;DR: In this article, a kernel method on persistence diagrams is proposed to develop a statistical framework in topological data analysis (TDA), which satisfies the stability property and provides explicit control on the effect of persistence.
Abstract: Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy topological properties. This paper proposes a kernel method on persistence diagrams to develop a statistical framework in TDA. The proposed kernel satisfies the stability property and provides explicit control on the effect of persistence. Furthermore, the method allows a fast approximation technique. The method is applied into practical data on proteins and oxide glasses, and the results show the advantage of our method compared to other relevant methods on persistence diagrams.

122 citations

Journal ArticleDOI
TL;DR: This map encodes new information on the formation process of tetrahedral and octahedral pores, the building blocks of perfect crystals, which reproduce the main changes of the map during crystallization and provide continuous deformation pathways representative of the crystallization dynamics.
Abstract: Uncovering grain-scale mechanisms that underlie the disorder–order transition in assemblies of dissipative, athermal particles is a fundamental problem with technological relevance. To date, the study of granular crystallization has mainly focussed on the symmetry of crystalline patterns while their emergence and growth from irregular clusters of grains remains largely unexplored. Here crystallization of three-dimensional packings of frictional spheres is studied at the grain-scale using X-ray tomography and persistent homology. The latter produces a map of the topological configurations of grains within static partially crystallized packings. Using numerical simulations, we show that similar maps are measured dynamically during the melting of a perfect crystal. This map encodes new information on the formation process of tetrahedral and octahedral pores, the building blocks of perfect crystals. Four key formation mechanisms of these pores reproduce the main changes of the map during crystallization and provide continuous deformation pathways representative of the crystallization dynamics. Emergence and growth of crystalline domains in granular media remains under-explored. Here, the authors analyse tomographic snapshots from partially recrystallized packings of spheres using persistent homology and find agreement with proposed transitions based on continuous deformation of octahedral and tetrahedral voids.

112 citations

Journal ArticleDOI
TL;DR: A new topological approach to extract a hierarchical structure of amorphous materials is presented, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations.
Abstract: The characterization of the medium-range (MRO) order in amorphous materials and its relation to the short-range order is discussed. A new topological approach to extract a hierarchical structure of amorphous materials is presented, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. This method is called the persistence diagram (PD) and introduces scales to many-body atomic structures to facilitate size and shape characterization. We first illustrate the representation of perfect crystalline and random structures in PDs. Then, the MRO in amorphous silica is characterized using the appropriate PD. The PD approach compresses the size of the data set significantly, to much smaller geometrical summaries, and has considerable potential for application to a wide range of materials, including complex molecular liquids, granular materials, and metallic glasses.

96 citations


Cited by
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01 May 1993
TL;DR: Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems.
Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

29,323 citations

Journal ArticleDOI
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations

Journal ArticleDOI
TL;DR: A friendly introduction to PH is given, the pipeline for the computation of PH is navigated with an eye towards applications, and a range of synthetic and real-world data sets are used to evaluate currently available open-source implementations for the computations of PH.
Abstract: Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input. The computation of PH is an open area with numerous important and fascinating challenges. The field of PH computation is evolving rapidly, and new algorithms and software implementations are being updated and released at a rapid pace. The purposes of our article are to (1) introduce theory and computational methods for PH to a broad range of computational scientists and (2) provide benchmarks of state-of-the-art implementations for the computation of PH. We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH. Based on our benchmarking, we indicate which algorithms and implementations are best suited to different types of data sets. In an accompanying tutorial, we provide guidelines for the computation of PH. We make publicly available all scripts that we wrote for the tutorial, and we make available the processed version of the data sets used in the benchmarking.

523 citations

Posted Content
TL;DR: This paper is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of TDA for non experts.
Abstract: Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of \tda\ for non experts.

324 citations