Organizing Committee

Konstantin Mischaikow
Mathematics, Rutgers
Qing Nie
Biomedical Engineering & Mathematics, University of California, Irvine
Horacio Rotstein
Department of Mathematical Sciences, New Jersey Institute of Technology
Terence Speed
Bioinformatics, Walter & Eliza Hall Institute of Medical Research
Vladimir Vacic
Computer Science, University of California, Riverside
Michael Waterman
Biological Sciences, Mathematics, and Computer Science, University of Southern California

Within the next few years all fields of mathematical biology will be impacted by large amounts of complex data. Because of this, there are many new mathematical questions to be addressed. Should old simple models be thrown out and should we begin again with newer complex models? Or are there mathematical ways to use the new data to determine parameters in the old models more accurately and thus allow their parameters to be updated automatically in real time as the data stream in. These questions are fundamental to medical practice in acute crises, to the dynamical behavior of cells, to policy decisions about vaccination and epidemic spread, to the effects of climate change on ecological niches, and to our understanding of brain function.

Scientists now have huge amounts of data about processes that are only partially known or unknown. The question is: How can we use the data to gain new mechanistic understanding about how biological systems work? Some examples are:

  • New techniques in imaging allow the collection of large amounts of patient data. Monitors give huge amounts of data on real time about organ and whole body physiology, as well as microbiomes. We can now understand better how we are different as well as how we are similar, and what consequences these differences have.
  • Sensors can track individual animals and reveal complicated changes in ecological environments due to climate change. Cell phones can record geospatial information that can be useful when trying to understand the spread of diseases.
  • New techniques allow biologists to observe subcellular behavior in real time.
  • Moreover, these data can be connected in important ways. The evolution over relatively short times of pathogens within individuals affects the spread of disease in populations. So population dynamics is related to immune system dynamics.

This MBI emphasis program will explore new mathematical techniques that can be used in the analysis of complex data in a variety of biological systems and settings. Fields that can be expected to contribute to the understanding of complex data are combinatorics, probability theory, statistics, geometry, algebraic topology, control theory, and ordinary and partial differential equations.

The program will consist of four workshops. Workshop 1 will focus on geometric and topological methods of data analysis. Workshop 2 will focus on mathematical methods for analyzing data sets in cancer biology. Workshop 3 will discuss the ways of linking complex data with dynamical systems models in neuroscience. Workshop 4 will be devoted to the impact of new streaming data collection techniques on population biology from the cellular, the organismal, to the ecological level, with special emphasis on the dynamics of disease spread in real time.