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Network topological model of reconstructive solid-state transformations.

ABSTRACT: Reconstructive solid-state transformations are followed by significant changes in the system of chemical bonds, i.e. in the topology of the substance. Understanding these mechanisms at the atomic level is crucial for proper explanation and prediction of chemical reactions and phase transitions in solids and, ultimately, for the design of new materials. Modeling of solid-state transitions by geometrical, molecular dynamics or quantum-mechanical methods does not account for topological transformations. As a result, the chemical nature of the transformation processes are overlooked, which limits the predictive power of the models. We propose a universal model based on network representation of extended structures, which treats any reorganization in the solid state as a network transformation. We demonstrate this approach rationalizes the configuration space of the solid system and enables prediction of new phases that are closely related to already known phases. Some new phases and unclear transition pathways are discovered in example systems including elementary substances, ionic compounds and molecular crystals.

SUBMITTER: Blatov VA

PROVIDER: S-EPMC6461690 | biostudies-literature | 2019 Apr

REPOSITORIES: biostudies-literature

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Network topological model of reconstructive solid-state transformations.

Blatov Vladislav A VA Golov Andrey A AA Yang Changhao C Zeng Qingfeng Q Kabanov Artem A AA

Scientific reports 20190412 1

Reconstructive solid-state transformations are followed by significant changes in the system of chemical bonds, i.e. in the topology of the substance. Understanding these mechanisms at the atomic level is crucial for proper explanation and prediction of chemical reactions and phase transitions in solids and, ultimately, for the design of new materials. Modeling of solid-state transitions by geometrical, molecular dynamics or quantum-mechanical methods does not account for topological transformat ...[more]

PMID: 30979949

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Project description:In this paper, we propose a graphlet-based topological algorithm for the investigation of the brain network at resting state (RS). To this aim, we model the brain as a graph, where (labeled) nodes correspond to specific cerebral areas and links are weighted connections determined by the intensity of the functional magnetic resonance imaging (fMRI). Then, we select a number of working graphlets, namely, connected and non-isomorphic induced subgraphs. We compute, for each labeled node, its Graphlet Degree Vector (GDV), which allows us to associate a GDV matrix to each one of the 133 subjects of the considered sample, reporting how many times each node of the atlas "touches" the independent orbits defined by the graphlet set. We focus on the 56 independent columns (i.e., non-redundant orbits) of the GDV matrices. By aggregating their count all over the 133 subjects and then by sorting each column independently, we obtain a sorted node table, whose top-level entries highlight the nodes (i.e., brain regions) most frequently touching each of the 56 independent graphlet orbits. Then, by pairwise comparing the columns of the sorted node table in the top-k entries for various values of k, we identify sets of nodes that are consistently involved with high frequency in the 56 independent graphlet orbits all over the 133 subjects. It turns out that these sets consist of labeled nodes directly belonging to the default mode network (DMN) or strongly interacting with it at the RS, indicating that graphlet analysis provides a viable tool for the topological characterization of such brain regions. We finally provide a validation of the graphlet approach by testing its power in catching network differences. To this aim, we encode in a Graphlet Correlation Matrix (GCM) the network information associated with each subject then construct a subject-to-subject Graphlet Correlation Distance (GCD) matrix based on the Euclidean distances between all possible pairs of GCM. The analysis of the clusters induced by the GCD matrix shows a clear separation of the subjects in two groups, whose relationship with the subject characteristics is investigated.

Dataset Information

Network topological model of reconstructive solid-state transformations.

Publications

Network topological model of reconstructive solid-state transformations.

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