Workshop 2: The Interplay of Stochastic and Deterministic Dynamics in Networks

(February 22,2016 - February 26,2016 )

Organizers


James Keener
Dept of Math, University of Utah
Ruth Williams
Mathematics, University of California, San Diego
Lai-Sang Young
Courant Institute of Mathematical Sciences, New York University

Many advances in modern biosciences will depend on our ability to harness the vast amounts of data coming from increasingly more complicated experimental techniques by using sophisticated methods of mathematical analysis. The modeling challenges include the ability to abstract common concepts across various mathematical sub-fields and to develop methods that are robust in the presence of noise, variations in model assumptions, uncertainty about models dynamics and parameter values.

This workshop will focus on dynamic models of biological networks that involve both deterministic and stochastic aspects. An important aim of the workshop is to bring together mathematical researchers in dynamical systems, probability, and statistics, together with biologists, to share their expertise towards analyzing dynamic biological network problems. Network structure can constrain and thereby impact the behavior of dynamic systems in various ways. Examples of such constraints are topological constraints, limitations on the size of quantities, limitations on resources, and delays in propagation of signals. Particular emphasis will be placed on how network structure can be exploited and how it impacts dynamic behavior.

The interplay of deterministic and stochastic dynamics can occur in a variety of different forms in biological dynamical models. In some biological systems such as gene regulatory networks, some species need to be modeled stochastically while other species can be modeled using deterministic dynamical systems. Analyzing the interactions between these different types of species on behavior presents challenging mathematical problems. Neuronal dynamics is another arena where dynamical behavior, stochastic influences, and network structure affect behavior and require innovative analysis. Some biological systems, from subcellullar to whole organisms switch stochastically from one dynamics to another. For, example, insect trachea are large collections of tubes that connect the cells of insects to the outside atmosphere. Insects open and close the networks stochastically in order to gain oxygen and lose carbon dioxide. The analysis of such biological systems requires understanding how system behavior changes when important properties of the network (like the existence of edges or the existence of inputs) change stochastically. Analyzing the relationship between stochastic changes, network structure, and network dynamics poses difficult, new, analytical questions.

There are many statistical issues associated with modeling such networks. Over the last two decades many sophisticated experimental methods have been developed that allow for the partial observation of a time trajectory of a biological network (for instance a gene regulatory network). The natural question of interest is how such longitudinal data may be used for the inference about various network characteristics, both quantitative and qualitative, as well as for predicting network behavior. In particular, the issue of proper quantification of the inference uncertainty must be addressed.

Monday, February 22, 2016
Time Session
Tuesday, February 23, 2016
Time Session
Wednesday, February 24, 2016
Time Session
Thursday, February 25, 2016
Time Session
Friday, February 26, 2016
Time Session
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