Topology in Biology

Ann Sizemore Blevins () and Danielle S. Bassett ()
Additional contact information
Ann Sizemore Blevins: University of Pennsylvania, Department of Bioengineering
Danielle S. Bassett: University of Pennsylvania, Department of Bioengineering

Chapter 80 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 2073-2095 from Springer

Abstract: Abstract Fueled by increasing computing power and ever-growing datasets, novel methods for complex systems analyses seem to emerge daily. With this whirlwind flows excitement and opportunity as new methods allow us to view our system of interest with a fresh perspective. One set of approaches that has offered particularly deep insights into complex systems is that of applied topology, also known as the field of topological data analysis (TDA). Topological data analysis specializes in representing and analyzing the entirety of the system and therefore can often remove the need for thresholds and filtering when selecting data, as is commonly done when studying biological systems. In this chapter we will briefly introduce the topological perspective that makes the above possible, and then we will dive into three methods within TDA through a biological lens. First, we cover persistent homology, which detects evolving topological cavities within data. Next, we join data to graphs in order to construct sheaves or structures that can help us understand systems with linear relations between adjacent nodes. We then describe path signatures, which allow us to detect lead-lag behavior in time series. While detailing each of these three main concepts, we note how we can view each as a perspective shift from an analysis we might already perform to a similar analysis using the topological language. As we discuss, this reframing into the language of topology can provide extensive additional insight into our system of interest, and at present, much of this added information remains ripe for interpretation and application.

Keywords: Applied topology; Computational biology; Computational neuroscience (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-57072-3_87

Ordering information: This item can be ordered from
http://www.springer.com/9783319570723

DOI: 10.1007/978-3-319-57072-3_87

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().