Dataset Information

Discovering multiscale and self-similar structure with data-driven wavelets.

ABSTRACT: Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting, describing, and defining such features are difficult tasks, at least in part because each system has a unique set of features. Here, we introduce an analysis method that, given a set of observations, discovers an energetic hierarchy of structures localized in scale and space. We call the resulting basis vectors a "data-driven wavelet decomposition." We show that this decomposition reflects the inherent structure of the dataset it acts on, whether it has no structure, structure dominated by a single scale, or structure on a hierarchy of scales. In particular, when applied to turbulence-a high-dimensional, nonlinear, multiscale process-the method reveals self-similar structure over a wide range of spatial scales, providing direct, model-free evidence for a century-old phenomenological picture of turbulence. This approach is a starting point for the characterization of localized hierarchical structures in multiscale systems, which we may think of as the building blocks of these systems.

SUBMITTER: Floryan D

PROVIDER: S-EPMC7817118 | biostudies-literature | 2021 Jan

REPOSITORIES: biostudies-literature

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Publications

Discovering multiscale and self-similar structure with data-driven wavelets.

Floryan Daniel D Graham Michael D MD

Proceedings of the National Academy of Sciences of the United States of America 20210101 1

Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting, describing, and defining such features are difficult tasks, at least in part because each system has a unique set of features. Here, we introduce an analysis method that, given a set of observations, discovers an energetic hierarchy of structures localized in s ...[more]

PMID: 33443189

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Project description:BackgroundMicroarray technology produces gene expression data on a genomic scale for an endless variety of organisms and conditions. However, this vast amount of information needs to be extracted in a reasonable way and funneled into manageable and functionally meaningful patterns. Genes may be reasonably combined using knowledge about their interaction behaviour. On a proteomic level, biochemical research has elucidated an increasingly complete image of the metabolic architecture, especially for less complex organisms like the well studied bacterium Escherichia coli.ResultsWe sought to discover central components of the metabolic network, regulated by the expression of associated genes under changing conditions. We mapped gene expression data from E. coli under aerobic and anaerobic conditions onto the enzymatic reaction nodes of its metabolic network. An adjacency matrix of the metabolites was created from this graph. A consecutive ones clustering method was used to obtain network clusters in the matrix. The wavelet method was applied on the adjacency matrices of these clusters to collect features for the classifier. With a feature extraction method the most discriminating features were selected. We yielded network sub-graphs from these top ranking features representing formate fermentation, in good agreement with the anaerobic response of hetero-fermentative bacteria. Furthermore, we found a switch in the starting point for NAD biosynthesis, and an adaptation of the l-aspartate metabolism, in accordance with its higher abundance under anaerobic conditions.ConclusionWe developed and tested a novel method, based on a combination of rationally chosen machine learning methods, to analyse gene expression data on the basis of interaction data, using a metabolic network of enzymes. As a case study, we applied our method to E. coli under oxygen deprived conditions and extracted physiologically relevant patterns that represent an adaptation of the cells to changing environmental conditions. In general, our concept may be transferred to network analyses on biological interaction data, when data for two comparable states of the associated nodes are made available.

Dataset Information

Discovering multiscale and self-similar structure with data-driven wavelets.

Publications

Discovering multiscale and self-similar structure with data-driven wavelets.

Similar Datasets

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