PSB2016 Workshop on Abstract
Algebra and Algebraic Topology in Biomedicine
Organizers:Eric Neumann (Foundation
Medicine), Svetlana Lockwood (WSU), David Spivak (MIT), Bala
The Problem: The use of large-scale data analytics is becoming prevalent for the life and health sciences. The complexity of the data structure associated with such data sets is one of the aspects that is not so readily overcome using existing technological solutions. The relevance of finding structure in rich data has been underscored by the increasing efforts to combine clinical data with genomic analyses. Understanding the structure of the data is crucial for data analysis and hypothesis generation.
The Solution: Abstract algebra and algebraic topology (AAAT) provides powerful tools for analysis of biomedical data. The key benefits of using AAAT to describe data include coordinate-free description of shape, robustness in the presence of noise and invariance under many trans formations, as well as highly compressed representations of structures. The potential of such analysis is just beginning to emerge from limited cross-pollination between AAAT and the life and health sciences.
This Workshop: This workshop will address several emerging trends from life and health sciences research that apply topological and algebraic forms to genomic and complex data problems. In the first part of the workshop we review the basics of Categorical Theory (CT), functors, bundles, and (pre)sheaves. CT originates from abstract algebra and has several powerful features for organizing concepts and the inherent logic of a system. In the second part of the workshop we will review basic notion of simplicial complexes, formal models, and application of algebraic topology to analysis of complex biological data. We also review software available for research.
Handouts on category theory
Handouts for the talks on Topology and Data (I and II)
Slides for the talks on Topology and Data (I and II)