Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input. Despite recent progress, the… (More)
We discuss our outreach efforts to introduce school students to network science and explain why networks researchers should be involved in such outreach activities. We provide overviews of modules that we have designed for these efforts, comment on our successes and failures, and illustrate the potentially enormous impact of such outreach efforts.
Persistent homology is a method from computational algebraic topology that can be used to study the " shape " of data. We illustrate two filtrations — the weight rank clique filtration and the Vietoris–Rips (VR) filtration — that are commonly used in persistent homology, and we apply these filtrations to a pair of data sets that are both related to the 2016… (More)
A hybrid model for tumor-induced angiogenesis in the cornea in the presence of inhibitors Abstract The present work formulates and analyzes, by means of numerical experiments, a model for tumor-induced angiogenesis in the presence of inhibitors in the cornea. Our model is a generalization of the earlier work of Tong and Yuan [S. Tong, F. Yuan, Numerical… (More)