Atomic and Electronic Structure in MgO-SiO2.

Understanding disordered structure is difficult due to insufficient information in experimental data. Here, we overcome this issue by using a combination of diffraction and simulation to investigate oxygen packing and network topology in glassy (g-) and liquid (l-) MgO-SiO2 based on a comparison with the crystalline topology. We find that packing of oxygen atoms in Mg2SiO4 is larger than that in MgSiO3, and that of the glasses is larger than that of the liquids. Moreover, topological analysis suggests that topological similarity between crystalline (c)- and g-(l-) Mg2SiO4 is the signature of low glass-forming ability (GFA), and high GFA g-(l-) MgSiO3 shows a unique glass topology, which is different from c-MgSiO3. We also find that the lowest unoccupied molecular orbital (LUMO) is a free electron-like state at a void site of magnesium atom arising from decreased oxygen coordination, which is far away from crystalline oxides in which LUMO is occupied by oxygen's 3s orbital state in g- and l-MgO-SiO2, suggesting that electronic structure does not play an important role to determine GFA. We finally concluded the GFA of MgO-SiO2 binary is dominated by the atomic structure in terms of network topology.

Resolution of the curse of dimensionality in single-cell RNA sequencing data analysis.

Single-cell RNA sequencing (scRNA-seq) can determine gene expression in numerous individual cells simultaneously, promoting progress in the biomedical sciences. However, scRNA-seq data are high-dimensional with substantial technical noise, including dropouts. During analysis of scRNA-seq data, such noise engenders a statistical problem known as the curse of dimensionality (COD). Based on high-dimensional statistics, we herein formulate a noise reduction method, RECODE (resolution of the curse of dimensionality), for high-dimensional data with random sampling noise. We show that RECODE consistently resolves COD in relevant scRNA-seq data with unique molecular identifiers. RECODE does not involve dimension reduction and recovers expression values for all genes, including lowly expressed genes, realizing precise delineation of cell fate transitions and identification of rare cells with all gene information. Compared with representative imputation methods, RECODE employs different principles and exhibits superior overall performance in cell-clustering, expression value recovery, and single-cell-level analysis. The RECODE algorithm is parameter-free, data-driven, deterministic, and high-speed, and its applicability can be predicted based on the variance normalization performance. We propose RECODE as a powerful strategy for preprocessing noisy high-dimensional data.

Nucleome programming is required for the foundation of totipotency in mammalian germline development.

Germ cells are unique in engendering totipotency, yet the mechanisms underlying this capacity remain elusive. Here, we perform comprehensive and in-depth nucleome analysis of mouse germ-cell development in vitro, encompassing pluripotent precursors, primordial germ cells (PGCs) before and after epigenetic reprogramming, and spermatogonia/spermatogonial stem cells (SSCs). Although epigenetic reprogramming, including genome-wide DNA de-methylation, creates broadly open chromatin with abundant enhancer-like signatures, the augmented chromatin insulation safeguards transcriptional fidelity. These insulatory constraints are then erased en masse for spermatogonial development. Notably, despite distinguishing epigenetic programming, including global DNA re-methylation, the PGCs-to-spermatogonia/SSCs development entails further euchromatization. This accompanies substantial erasure of lamina-associated domains, generating spermatogonia/SSCs with a minimal peripheral attachment of chromatin except for pericentromeres-an architecture conserved in primates. Accordingly, faulty nucleome maturation, including persistent insulation and improper euchromatization, leads to impaired spermatogenic potential. Given that PGCs after epigenetic reprogramming serve as oogenic progenitors as well, our findings elucidate a principle for the nucleome programming that creates gametogenic progenitors in both sexes, defining a basis for nuclear totipotency.

Flow estimation solely from image data through persistent homology analysis.

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.

Protein-Folding Analysis Using Features Obtained by Persistent Homology.

Understanding the protein-folding process is an outstanding issue in biophysics; recent developments in molecular dynamics simulation have provided insights into this phenomenon. However, the large freedom of atomic motion hinders the understanding of this process. In this study, we applied persistent homology, an emerging method to analyze topological features in a data set, to reveal protein-folding dynamics. We developed a new, to our knowledge, method to characterize the protein structure based on persistent homology and applied this method to molecular dynamics simulations of chignolin. Using principle component analysis or nonnegative matrix factorization, our analysis method revealed two stable states and one saddle state, corresponding to the native, misfolded, and transition states, respectively. We also identified an unfolded state with slow dynamics in the reduced space. Our method serves as a promising tool to understand the protein-folding process.

Hepatic tumor classification using texture and topology analysis of non-contrast-enhanced three-dimensional T1-weighted MR images with a radiomics approach.

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.

Non-empirical identification of trigger sites in heterogeneous processes using persistent homology.

Macroscopic phenomena, such as fracture, corrosion, and degradation of materials, are associated with various reactions which progress heterogeneously. Thus, material properties are generally determined not by their averaged characteristics but by specific features in heterogeneity (or 'trigger sites') of phases, chemical states, etc., where the key reactions that dictate macroscopic properties initiate and propagate. Therefore, the identification of trigger sites is crucial for controlling macroscopic properties. However, this is a challenging task. Previous studies have attempted to identify trigger sites based on the knowledge of materials science derived from experimental data ('empirical approach'). However, this approach becomes impractical when little is known about the reaction or when large multi-dimensional datasets, such as those with multiscale heterogeneities in time and/or space, are considered. Here, we introduce a new persistent homology approach for identifying trigger sites and apply it to the heterogeneous reduction of iron ore sinters. Four types of trigger sites, 'hourglass'-shaped calcium ferrites and 'island'- shaped iron oxides, were determined to initiate crack formation using only mapping data depicting the heterogeneities of phases and cracks without prior mechanistic information. The identification of these trigger sites can provide a design rule for reducing mechanical degradation during reduction.

Persistent homology analysis of craze formation.

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.

Hierarchical structures of amorphous solids characterized by persistent homology.

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.

Persistent homology and many-body atomic structure for medium-range order in the glass.

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.