- Title Information
- Title
- Topological Data Analysis of Collective Motion
- Name:
Personal
- Name Part
- Bhaskar, Dhananjay
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Wong, Ian
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Crawford, Lorin
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Darling, Eric
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Sandstede, Bjorn
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Zenit, Roberto
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Ziegelmeier, Lori
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Biology and Medicine: Biomedical Engineering
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2021
- Physical Description
- Extent
- xiv, 169 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2021
- Genre (aat)
- theses
- Abstract
- Coordinated migration patterns emerge from the interactions of discrete individuals, ranging from self-propelled particles and mammalian cells at the microscopic scale to robots and animals at the macroscale, representing a fundamental problem that bridges quantitative biology, statistical physics, and data science. Historically, these rich behaviors of self-organization, phase transitions, and pattern formation have been analyzed in a problem-specific manner, which may not be widely applicable. Here, I develop an approach based on topological data analysis to visualize the spatial organization of discrete particles that migrate and proliferate in a biologically-inspired manner. Using persistent homology, the number of connected components, loops, voids, and higher dimensional holes are tracked at multiple spatial scales, thus quantifying the 'shape' of point-cloud data consisting of particle positions at each time point. This information may be represented interchangeably as a topological barcode, persistence diagram, a matrix of Betti numbers, or persistence image. Furthermore, distinct particle configurations are compared by defining a metric to compute the distance between their corresponding topological representations. Using this methodology, phase transitions experimentally observed in proliferating mammary epithelial cells (subject to various culture media and drug treatments), can be automatically classified, revealing distinct regimes of individual motility, formation of branched networks, and compact clusters, are automatically identified. In another case study, rules of interaction are inferred from simulated trajectories of collective motion in animals, including swarming, flocking and milling patterns, using a combination of topological data analysis and machine learning. Overall, the findings indicate that unsupervised topological classification can outperform unsupervised classification based on order parameters, and offers a unique insight into the multiscale dynamics that drive phase transitions in these systems. Broadly, I envision this approach can be applied to elucidate emergent behaviors arising from interacting individuals in a wide variety of biological and physical phenomena.
- Subject
- Topic
- Machine Learning
- Subject
- Topic
- agent-based models
- Subject
- Topic
- topological data analysis
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00867354")
- Topic
- Collective behavior
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20210607
- Type of Resource (primo)
- dissertations