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Analytic materials.

ABSTRACT: The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer p. If p takes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rank p. For two-dimensional materials, further progress can be made in the identification of analytic materials by using the well-known fact that a 90° rotation applied to a divergence-free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.

SUBMITTER: Milton GW

PROVIDER: S-EPMC5134313 | biostudies-other | 2016 Nov

REPOSITORIES: biostudies-other

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Analytic materials.

Milton Graeme W GW

Proceedings. Mathematical, physical, and engineering sciences 20161101 2195

The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer p. If p takes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rank p. For two-dimensional materials, further progress can be made in the identification of analytic material ...[more]

PMID: 27956882

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Project description:BACKGROUND: Many computational methods are available for assembly and annotation of newly sequenced microbial genomes. However, when new genomes are reported in the literature, there is frequently very little critical analysis of choices made during the sequence assembly and gene annotation stages. These choices have a direct impact on the biologically relevant products of a genomic analysis--for instance identification of common and differentiating regions among genomes in a comparison, or identification of enriched gene functional categories in a specific strain. Here, we examine the outcomes of different assembly and analysis steps in typical workflows in a comparison among strains of Vibrio vulnificus. RESULTS: Using six recently sequenced strains of V. vulnificus, we demonstrate the "alternate realities" of comparative genomics, and how they depend on the choice of a robust assembly method and accurate ab initio annotation. We apply several popular assemblers for paired-end Illumina data, and three well-regarded ab initio genefinders. We demonstrate significant differences in detected gene overlap among comparative genomics workflows that depend on these two steps. The divergence between workflows, even those using widely adopted methods, is obvious both at the single genome level and when a comparison is performed. In a typical example where multiple workflows are applied to the strain V. vulnificus CECT 4606, a workflow that uses the Velvet assembler and Glimmer gene finder identifies 3275 gene features, while a workflow that uses the Velvet assembler and the RAST annotation system identifies 5011 gene features. Only 3171 genes are identical between both workflows. When we examine 9 assembly/annotation workflow scenarios as input to a three-way genome comparison, differentiating genes and even differentially represented functional categories change significantly from scenario to scenario. CONCLUSIONS: Inconsistencies in genomic analysis can arise depending on the choices that are made during the assembly and annotation stages. These inconsistencies can have a significant impact on the interpretation of an individual genome's content. The impact is multiplied when comparison of content and function among multiple genomes is the goal. Tracking the analysis history of the data--its analytic provenance--is critical for reproducible analysis of genome data.

Dataset Information

Analytic materials.

Publications

Analytic materials.

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