🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.001028s)

  2. Topological Descriptors for Coral Reef Resilience Using a Stochastic Spatial Model (2022)

    Robert A. McDonald, Rosanna Neuhausler, Martin Robinson, Laurel G. Larsen, Heather A. Harrington, Maria Bruna
    Abstract A complex interplay between species governs the evolution of spatial patterns in ecology. An open problem in the biological sciences is characterizing spatio-temporal data and understanding how changes at the local scale affect global dynamics/behavior. We present a toolkit of multiscale methods and use them to analyze coral reef resilience and dynamics.Here, we extend a well-studied temporal mathematical model of coral reef dynamics to include stochastic and spatial interactions and then generate data to study different ecological scenarios. We present descriptors to characterize patterns in heterogeneous spatio-temporal data surpassing spatially averaged measures. We apply these descriptors to simulated coral data and demonstrate the utility of two topological data analysis techniques--persistent homology and zigzag persistence--for characterizing the spatiotemporal evolution of reefs and generating insight into mechanisms of reef resilience. We show that the introduction of local competition between species leads to the appearance of coral clusters in the reef. Furthermore, we use our analyses to distinguish the temporal dynamics that stem from different initial configurations of coral, showing that the neighborhood composition of coral sites determines their long-term survival. Finally, we use zigzag persistence to quantify spatial behavior in the metastable regime as the level of fish grazing on algae varies and determine which spatial configurations protect coral from extinction in different environments.

  3. Tracking Resilience to Infections by Mapping Disease Space (2016)

    Brenda Y. Torres, Jose Henrique M. Oliveira, Ann Thomas Tate, Poonam Rath, Katherine Cumnock, David S. Schneider
    Abstract Infected hosts differ in their responses to pathogens; some hosts are resilient and recover their original health, whereas others follow a divergent path and die. To quantitate these differences, we propose mapping the routes infected individuals take through “disease space.” We find that when plotting physiological parameters against each other, many pairs have hysteretic relationships that identify the current location of the host and predict the future route of the infection. These maps can readily be constructed from experimental longitudinal data, and we provide two methods to generate the maps from the cross-sectional data that is commonly gathered in field trials. We hypothesize that resilient hosts tend to take small loops through disease space, whereas nonresilient individuals take large loops. We support this hypothesis with experimental data in mice infected with Plasmodium chabaudi, finding that dying mice trace a large arc in red blood cells (RBCs) by reticulocyte space as compared to surviving mice. We find that human malaria patients who are heterozygous for sickle cell hemoglobin occupy a small area of RBCs by reticulocyte space, suggesting this approach can be used to distinguish resilience in human populations. This technique should be broadly useful in describing the in-host dynamics of infections in both model hosts and patients at both population and individual levels.