Statistical Physics and Theoretical Biophysics Group: Computational Biophysics

Master Seminar: Topological Methods in Biophysics

Venue: Philosophenweg 12, Seminar Room

Time: Tuesdays, 15:15 - 17:00

PLEASE NOTE: The first meeting will be April 16th 2019!
We will discuss topic assignments and dates for the presentations.

Topology enters more and more the field of physics and biology. Whereas geometric methods have had a dominating presence in the past, due to new measurement methods that yield topological information and the emergence of big data topological ideas, methods and algorithms from topology are gaining fast track. The seminar explores some these new developments.

This seminar touches upon some of the topics that are currently being actively worked on. Most of these can be expanded to at least two talks. Interested students should contact with me via email.

Objectives:

Familiarity with basics in topology for physics and biology

Prerequisites:

Willingness to engage with mathematical concepts, big data methods openness to biology

Topics:

Some basics
- Topological spaces, metric space topology Simplices, simplicial complexes, Chech complexes, Vietoris-Rips complexes,homology
  Computational topology, Herbert Edelsbrunner and John L. Harer
Persistent homology
- Persistent homology: theory and practice. 2014
  Edelsbrunner H.
  http://pub.ist.ac.at/~edels/Papers/2012-P-11-PHTheoryPractice.pdf
Persistent homology: algorithms
- Persistent Homology — a Survey
  Herbert Edelsbrunner and John Harer
  http://www.maths.ed.ac.uk/~aar/papers/edelhare.pdf
  
  Computing Persistent Homology
  Afra Zomorodian and Gunnar Carlsson
  https://geometry.stanford.edu/papers/zc-cph-05/zc-cph-05.pdf
Topological data analysis
- An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists
  Frédéric Chazal and Bertrand Michel
  https://arxiv.org/pdf/1710.04019.pdf
  
  Topological data analysis: A promising big data exploration tool in biology, analytical
  chemistry and physical chemistry
  Marc Offroy, Ludovic Duponchel
  Analytica Chimica Acta 910 (2016) 1e11
Topological data analysis: algorithms
- Illustrations of Data Analysis Using the Mapper Algorithm and Persistent Homology
  Rami Kraft
  http://www.diva-portal.org/smash/get/diva2:900997/FULLTEXT01.pdf
Topological Data Analysis of Biological Aggregation Models
- Chad M. Topaz and Lori Ziegelmeier, Tom Halverson
  https://doi.org/10.1371/journal.pone.0126383
Topology and prediction of RNA pseudoknots
- Christian M. Reidys, Fenix W.D. Huang, Jørgen E. Andersen, Robert C. Penner, Peter F. Stadler, and Markus E. Nebel
  Bioinformatics 2011
Applications of topology to DNA
- Isabel K. Darcy and De Witt Sumners
  KNOT THEORY, BANACH CENTER PUBLICATIONS, VOLUME 42 INSTITUTE OF MATHEMATICS
  POLISH ACADEMY OF SCIENCES WARSZAWA 1998
Persistent Homolgy and Protein Binding
- Using persistent homology and dynamical distances to analyze protein binding
  Kovacev-Nikolic, Peter Bubenik, Dragan Nikolic and Giseon Heo arxiv 2015
Neural Networks and Persistent Homology
- Deep Learning with Topological Signatures
  Christoph Hofer, Roland Kwitt, Marc Niethammer and Andreas Uhl
  arxiv 2017