Related papers: Topological Data Analysis of Biological Aggregatio…
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…
We use topological data analysis as a tool to analyze the fit of mathematical models to experimental data. This study is built on data obtained from motion tracking groups of aphids in [Nilsen et al., PLOS One, 2013] and two random walk…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…
We consider the problem of learning the dynamics in the topology of time-evolving point clouds, the prevalent spatiotemporal model for systems exhibiting collective behavior, such as swarms of insects and birds or particles in physics. In…
Topological event detection allows for the distributed computation of homology by focusing on local changes occurring in a network over time. In this paper, a model for the monitoring of topological events in dynamically changing regions…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
The prediction of critical transitions, such as extinction events, is vitally important to preserving vulnerable populations in the face of a rapidly changing climate and continuously increasing human resource usage. Predicting such events…
Topological data analysis offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. Recently, an efficient quantum algorithm was proposed [Lloyd, Garnerone, Zanardi, Nat.…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of complex behavior which may be applied to high-throughput data.…
In this study, we present and analyze a framework for geometric and topological estimation for mapping of unknown environments. We consider agents mimicking motion behaviors of cyborg insects, known as biobots, and exploit coordinate-free…
Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges. The prevailing clustering algorithms widely depend on…
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…
We use the first Betti number of a complex to characterize the morphological structure of granular samples in mechanical equilibrium. We analyze two-dimensional granular packings after a tapping process by means of both simulations and…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…
Flocking phase transitions found in models of polar active matter are paradigmatic examples of active phase transitions in soft matter. An interesting specialization of flocking models concerns a ``topological'' vs ``metric'' choice by…
We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of…
There has been considerable recent interest, primarily motivated by problems in applied algebraic topology, in the homology of random simplicial complexes. We consider the scenario in which the vertices of the simplices are the points of a…