🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.001205s)

  1. Computing Robustness and Persistence for Images (2010)

    P. Bendich, H. Edelsbrunner, M. Kerber
    Abstract We are interested in 3-dimensional images given as arrays of voxels with intensity values. Extending these values to a continuous function, we study the robustness of homology classes in its level and interlevel sets, that is, the amount of perturbation needed to destroy these classes. The structure of the homology classes and their robustness, over all level and interlevel sets, can be visualized by a triangular diagram of dots obtained by computing the extended persistence of the function. We give a fast hierarchical algorithm using the dual complexes of oct-tree approximations of the function. In addition, we show that for balanced oct-trees, the dual complexes are geometrically realized in R3 and can thus be used to construct level and interlevel sets. We apply these tools to study 3-dimensional images of plant root systems.

  2. The Persistent Homology Mathematical Framework Provides Enhanced Genotype-to-Phenotype Associations for Plant Morphology (2018)

    Mao Li, Margaret H. Frank, Viktoriya Coneva, Washington Mio, Daniel H. Chitwood, Christopher N. Topp
    Abstract Efforts to understand the genetic and environmental conditioning of plant morphology are hindered by the lack of flexible and effective tools for quantifying morphology. Here, we demonstrate that persistent-homology-based topological methods can improve measurement of variation in leaf shape, serrations, and root architecture. We apply these methods to 2D images of leaves and root systems in field-grown plants of a domesticated introgression line population of tomato (Solanum pennellii). We find that compared with some commonly used conventional traits, (1) persistent-homology-based methods can more comprehensively capture morphological variation; (2) these techniques discriminate between genotypes with a larger normalized effect size and detect a greater number of unique quantitative trait loci (QTLs); (3) multivariate traits, whether statistically derived from univariate or persistent-homology-based traits, improve our ability to understand the genetic basis of phenotype; and (4) persistent-homology-based techniques detect unique QTLs compared to conventional traits or their multivariate derivatives, indicating that previously unmeasured aspects of morphology are now detectable. The QTL results further imply that genetic contributions to morphology can affect both the shoot and root, revealing a pleiotropic basis to natural variation in tomato. Persistent homology is a versatile framework to quantify plant morphology and developmental processes that complements and extends existing methods.

  3. Rootstock Effects on Scion Phenotypes in a ‘Chambourcin’ Experimental Vineyard (2019)

    Zoë Migicovsky, Zachary N Harris, Laura L Klein, Mao Li, Adam McDermaid, Daniel H Chitwood, Anne Fennell, Laszlo G Kovacs, Misha Kwasniewski, Jason P Londo, Qin Ma, Allison J Miller
    Abstract Understanding how root systems modulate shoot system phenotypes is a fundamental question in plant biology and will be useful in developing resilient agricultural crops. Grafting is a common horticultural practice that joins the roots (rootstock) of one plant to the shoot (scion) of another, providing an excellent method for investigating how these two organ systems affect each other. In this study, we used the French-American hybrid grapevine ‘Chambourcin’ (Vitis L.) as a model to explore the rootstock–scion relationship. We examined leaf shape, ion concentrations, and gene expression in ‘Chambourcin’ grown ungrafted as well as grafted to three different rootstocks (‘SO4’, ‘1103P’ and ‘3309C’) across 2 years and three different irrigation treatments. We found that a significant amount of the variation in leaf shape could be explained by the interaction between rootstock and irrigation. For ion concentrations, the primary source of variation identified was the position of a leaf in a shoot, although rootstock and rootstock by irrigation interaction also explained a significant amount of variation for most ions. Lastly, we found rootstock-specific patterns of gene expression in grafted plants when compared to ungrafted vines. Thus, our work reveals the subtle and complex effect of grafting on ‘Chambourcin’ leaf morphology, ionomics, and gene expression.