Dept. of Mathematical and Statistical Sciences Fall 2021 Seminar Series Presents

Dr. Lutz Strüngmann
Mannheim University of Applied Sciences, Germany

WHEN: Thursday July 14th, 2022, from 5:00pm to 6:00pm

TITLE: Circular codes in genetic information

ABSTRACT: Circular codes originated in biology in the context of error detection and error correction during protein synthesis. A first example was discovered through an extensive statistical study of a large amount of genetic data by Arques and Michel in 1996. (Although the name circular code was coined already by Lassez in earlier works on coding theory). Roughly speaking, circular codes have the potential to ensure that genetic information encoded in deoxyribonucleic acid (DNA) is correctly translated during protein synthesis. A circular code X is a set of words such that each motif from X (a concatenation of words from X) enables the original (construction) frame to be retrieved, maintained and synchronised. A stronger version of circular codes are the comma-free codes that require frame shift detection to be instantaneous, i.e. it does not require a unique symbol to separate the code words. Unlike circular codes, comma-free codes have been studied extensively over the last sixty years from such diverse perspectives as biology, information theory and combinatorics (e.g. by Dellbrück, Golomb, Eastman, Scholz, Schützenberger and Luca-Restivo).

In this talk, we give an introduction to the theory of circular codes using approaches from graph theory, combinatorics, group theory and bioinformatics. However, due to the high complexity and diversity of circular codes, algorithmic computations easily reach their limits. In addition to classification theorems and construction principles, we will also discuss the possible feedback of the mathematical investigations on biology.

ATTENDING: Everyone is welcome to join the seminar. Seminar will be hydrid: in-person and virtual (zoom). The speaker will be remote. For in-person, please join us in Student Commons Building room #4017. For virtual attendance, please contact mathstaff@ucdenver.edu for Zoom information.