- Title Information
- Title
- Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Santorella, Rebecca
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Sandstede, Bjorn
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Singh, Ritambhara
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Harrison, Matthew
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2022
- Physical Description
- Extent
- xii, 199 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2022
- Genre (aat)
- theses
- Abstract
- Abstract of Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice, by Rebecca Santorella Ph.D., Brown University, May 2022.
As data becomes more abundant, we need more data-driven mathematical methods to offer insights into a broad range of applications. This thesis explores data-driven techniques in various settings. First, we present a framework to conduct equation-free modeling via diffusion maps, which allows us to study macro-level dynamics in slow-fast systems. Second, we construct the first public dataset connecting federal criminal cases with their sentencing judge and use this data to expose racial disparities in sentencing. Finally, we apply optimal transport in two very different settings: First, we audit automated decision-making systems by quantifying bias. Second, we use Gromov-Wasserstein optimal transport to align and integrate single-cell multi-omics data. Through all of these applications, we demonstrate the need for more data-driven mathematical techniques.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01400410")
- Topic
- Applied mathematics
- Subject
- Topic
- dynamical systems
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00871990")
- Topic
- Computational biology
- Subject
- Topic
- Fair Machine Learning
- Subject
- Topic
- federal sentencing
- Subject
- Topic
- data science
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20220706