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Topological properties of a bipartite lattice of domain wall states.

ABSTRACT: We propose a generalization of the Su-Schrieffer-Heeger (SSH) model of the bipartite lattice, consisting of a periodic array of domain walls. The low-energy description is governed by the superposition of localized states at each domain wall, forming an effective mono-atomic chain at a larger scale. When the domain walls are dimerized, topologically protected edge states can appear, just like in the original SSH model. These new edge states are formed exclusively by soliton-like states and therefore, the new topological states are qualitatively different from the regular SSH edge states. They posses a much longer localization length and are more resistant to on-site disorder, in marked contrast to the standard SSH case.

SUBMITTER: Munoz F

PROVIDER: S-EPMC6255788 | biostudies-other | 2018 Nov

REPOSITORIES: biostudies-other

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Topological properties of a bipartite lattice of domain wall states.

Munoz F F Pinilla Fernanda F Mella J J Molina Mario I MI

Scientific reports 20181126 1

We propose a generalization of the Su-Schrieffer-Heeger (SSH) model of the bipartite lattice, consisting of a periodic array of domain walls. The low-energy description is governed by the superposition of localized states at each domain wall, forming an effective mono-atomic chain at a larger scale. When the domain walls are dimerized, topologically protected edge states can appear, just like in the original SSH model. These new edge states are formed exclusively by soliton-like states and there ...[more]

PMID: 30478353

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Project description:BackgroundHigh throughput gene expression experiments yield large amounts of data that can augment our understanding of disease processes, in addition to classifying samples. Here we present new paradigms of data Separation based on construction of transcriptional regulatory networks for normal and abnormal cells using sequence predictions, literature based data and gene expression studies. We analyzed expression datasets from a number of diseased and normal cells, including different types of acute leukemia, and breast cancer with variable clinical outcome.ResultsWe constructed sample-specific regulatory networks to identify links between transcription factors (TFs) and regulated genes that differentiate between healthy and diseased states. This approach carries the advantage of identifying key transcription factor-gene pairs with differential activity between healthy and diseased states rather than merely using gene expression profiles, thus alluding to processes that may be involved in gene deregulation. We then generalized this approach by studying simultaneous changes in functionality of multiple regulatory links pointing to a regulated gene or emanating from one TF (or changes in gene centrality defined by its in-degree or out-degree measures, respectively). We found that samples can often be separated based on these measures of gene centrality more robustly than using individual links. We examined distributions of distances (the number of links needed to traverse the path between each pair of genes) in the transcriptional networks for gene subsets whose collective expression profiles could best separate each dataset into predefined groups. We found that genes that optimally classify samples are concentrated in neighborhoods in the gene regulatory networks. This suggests that genes that are deregulated in diseased states exhibit a remarkable degree of connectivity.ConclusionTranscription factor-regulated gene links and centrality of genes on transcriptional networks can be used to differentiate between cell types. Transcriptional network blueprints can be used as a basis for further research into gene deregulation in diseased states.

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Topological properties of a bipartite lattice of domain wall states.

Publications

Topological properties of a bipartite lattice of domain wall states.

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