Brown University
  1. Top
  2. ...
  3. Theses and Dissertations
  4. bdr:t8a6cvbu

Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice

Full Metadata

Overview

Year:
2022
Contributor:
Santorella, Rebecca (creator)
Sandstede, Bjorn (Advisor)
Singh, Ritambhara (Reader)
Harrison, Matthew (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
dynamical systems
Computational biology
Fair Machine Learning
federal sentencing
data science
Extent:
xii, 199 p.

Files

Description

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.
Notes:
Thesis (Ph. D.)--Brown University, 2022

Content

Citation

Santorella, Rebecca, "Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice" (2022). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://repository.library.brown.edu/studio/item/bdr:t8a6cvbu/

Relations

Collection: