Workshop 1: Dynamics in Networks with Special Properties

(January 25,2016 - January 29,2016 )

Organizers


Peter Ashwin
College of Engineering, Mathematics and Physical Sciences, University of Exeter
Gheorghe Craciun
Mathematics and Biomolecular Chemistry, University of Wisconsin-Madison
Tomas Gedeon
Department of Mathematical Sciences, Montana State University

Network structures underlie models for the dynamical descriptions and bifurcations in a wide range of biological phenomena. These include models for subcellular genomic and signaling processes, neural models at single-cell or multiple-cell level, high-level cognitive models, and many forms of chemically reacting systems. Naturally arising networks often have properties that make them especially pliant mathematically:

  1. Networks with special overall architectures (having, for example, special symmetries or special node-coupling rules) enable one to pose and answer questions about network dynamics by techniques that exploit those architectures.
  2. Networks often have natural and precise restrictions on the behavior of nodes or edges (for example, mass action kinetics, piecewise linear dynamics, or Boolean dynamics) that can lead to fairly deep and general theorems about network behavior.
  3. Small networks, quotient networks, factor networks, or network motifs can be used as building blocks to understand the dynamics of larger networks, allowing one to think of network structures in a constructive and synthetic way.

This workshop will explore the current state of affairs and ways of unifying emerging mathematical techniques by focusing on a variety of special biologically motivated structures. A few examples of applications with such structures include:

a. Chemical reaction network theory: In recent years separate theories have been developed for the dynamics of chemical reaction networks and for general networks with symmetry. Both theories have yielded interesting and nontrivial results. What has not been explored, however, are networks of identical and interconnected chemical cells. Although the dynamics within the cells themselves might exhibit a high degree of stability, there remain questions about the dynamics of the full multi-cell assembly that can exhibit important behavior through symmetry-breaking pattern formation.

b. Neuroscience: Classic central pattern generators and recent Wilson networks describing generalized rivalry have symmetries that dictate preferred kinds of patterned oscillation.

c. Gene expression networks: New technologies are providing massive data concerning the connectivity and functional control of these networks. Theoretical models based on these data typically incorporate combinatorial logical control of gene expression in dynamical models.

d. Epidemiology: Heterosexual contact networks are best explored by (quasi-) bipartite graphs, usually with fairly strong restrictions on degree distributions within each partition. Exploring sexually transmitted infection dynamics relies strongly on both this architecture (especially as the global description is preserved over time while local descriptions shift), but also on the time ordering of edge presence.

Development and analysis of models like these provide a rich source of new mathematical problems involving classification of dynamic states, bifurcations, and reverse engineering of complex networks based on observed dynamics.

Accepted Speakers

Murad Banaji
Madalena Chaves
Biocore, Inria
Stephen Coombes
Department of Mathematics, University of Nottingham
Roderick Edwards
Mathematics and Statistics, University of Victoria
Bard Ermentrout
Department of Mathematics, University of Pittsburgh
Viktor Jirsa
INS, AMU
Georgi Medvedev
Maya Mincheva
Mathematics, Northern Illinois University
Konstantin Mischaikow
Mathematics, Rutgers
Casian Pantea
Mathematics, West Virginia University
Linda Petzold
Mechanical Engineering, University of California, Santa Barbara
Arkady Pikovsky
Stephen Proulx
Anne Shiu
Mathematics, Texas A&M University
Krasimira Tsaneva-Atanasova
Department of Mathematics, University of Auckland
Pauline van den Driessche
Mathematics and Statistics, University of Victoria
Monday, January 25, 2016
Time Session
Tuesday, January 26, 2016
Time Session
Wednesday, January 27, 2016
Time Session
Thursday, January 28, 2016
Time Session
Friday, January 29, 2016
Time Session
Name Email Affiliation
Banaji, Murad murad.banaji@port.ac.uk
Chaves, Madalena madalena.chaves@inria.fr Biocore, Inria
Coombes, Stephen stephen.coombes@nottingham.ac.uk Department of Mathematics, University of Nottingham
Craciun, Gheorghe craciun@math.wisc.edu Mathematics and Biomolecular Chemistry, University of Wisconsin-Madison
Edwards, Roderick edwards@uvic.ca Mathematics and Statistics, University of Victoria
Ermentrout, Bard bard@pitt.edu Department of Mathematics, University of Pittsburgh
Gedeon, Tomas gedeon@math.montana.edu Department of Mathematical Sciences, Montana State University
Jirsa, Viktor viktor.jirsa@univ-amu.fr INS, AMU
Medvedev, Georgi medvedev@drexel.edu
Mincheva, Maya mincheva@math.niu.edu Mathematics, Northern Illinois University
Mischaikow, Konstantin mischaik@math.rutgers.edu Mathematics, Rutgers
Pantea, Casian cpantea@math.wvu.edu Mathematics, West Virginia University
Pikovsky, Arkady pikovsky@uni-potsdam.de
Proulx, Stephen proulx@lifesci.ucsb.edu
Shiu, Anne annejls@math.tamu.edu Mathematics, Texas A&M University
Tsaneva-Atanasova , Krasimira K.Tsaneva-Atanasova@exeter.ac.uk Department of Mathematics, University of Auckland
van den Driessche, Pauline pvdd@math.uvic.ca Mathematics and Statistics, University of Victoria