Applications of dynamical systems
The 2012 SIAM Conference on the Life Sciences was held in San Diego,
CA during the first week in August. Over the past two decades, the
application of mathematics to biological problems has seen significant
activity and rapid growth. More and more biologists are recognizing
that mathematicians can make significant contributions to problems in
the life sciences, and mathematicians are recognizing that biology
presents not only interesting scientific problems but exciting
mathematical challenges as well. This was reflected in the
demographics of the participants at the Life Sciences conference,
which included M.D.s, experimental biologists from academics,
representatives from the pharmaceutical industry, engineers, computer
modelers, and applied mathematicians. The applied mathematicians
included those from. In terms of mathematics, many areas of
traditionally applied mathematics and some areas of traditionally pure
mathematics were represented, but the conference was dominated by
dynamical systems theory.
In the opening plenary talk, Mike Reed (Duke University) gave several
examples that illustrated the difficulties and pleasures of
investigating biological systems in which (1) processes occur on
multiple space and time scales and (2) stochasticity is ubiquitous and
often fundamental to functionality. He asserted that only with
mathematics can we discover the mechanisms underlying the
bewilderingly complicated and complex behavior of these systems, and
he posed the question: What fields of mathematics are necessary and
useful for this endeavor, now and in the future? His answer was:
almost all, but progress in dynamical systems – both deterministic and
stochastic – will be central.
The plenary talks, mini-tutorials, mini-symposia talks and poster
presentations included a mix of new and now classical theories in
dynamical systems, and most presentations focused on the stochastic
and/or multi-scale nature of biological processes. Sam Isaacson
(Boston University) organized a mini-tutorial on numerical methods for
studying stochastic models, and Tim David (University of Canterbury)
organized another mini-tutorial on multi-scale modeling. In the
invited plenary talks: L. Mahadevan (Harvard University) used a
combination of physical experiments, mathematical models and numerical
computations to identify the bifurcations that lead to the morphology
of pollen tubes, algal blades and the looping pattern of the
vertebrate gut. Artie Sherman (NIH) described the bifurcation
structure associated with bursting electrical activity in neurons and
pancreatic beta-cells, referring to bifurcations as the dynamical
“atoms” upon which biological models are built. John Milton
(Claremont College) explained how time-delays and stochasticity make
neural systems sit on the edge of stability. He hypothesized that
this may be essential for neural systems to function but it also
predisposes them to certain pathological behaviors. Similarly, Ary
Goldberger (Harvard Medical School) argued that the multi-scale nature
of cardiac electrodynamics and cardiovascular control was necessary
for healthy cardiac function and that pathologies are often associated
with decreased complexity/dimensionality of cardiac dynamics. Charles
Taylor showed how his company HeartFlow Inc. is using computational
fluid dynamics as part of a safe, inexpensive diagnostic tool for
heart disease. Peter Hunter (University of Auckland) described the
efforts of the Virtual Physiological Human/Physiome Project to advance
multi-scale modeling of integrative physiological processes. Finally,
Mariel Vazquez (San Francisco State University) explained how she uses
topological methods and computational tools to understand DNA
unknotting and unlinking, and she described new work in which she is
modeling the dynamics of these processes. You can view all of the
invited plenary talks and the mini-tutorials on the SIAM website.
In his plenary talk, Mike Reed praised the efforts and accomplishments
of mathematical community in the Life Sciences and pointed out that
SIAM has vigorously supported these efforts. He concluded by saying,
“Hooray Life Sciences! Hooray SIAM!” … and we should add “Hooray for
Dynamical Systems”.
If you are a dynamical system theorist looking for interesting and
challenging mathematical problems with important applications, look to
the life sciences. If you aren’t already a member of the Life Science
SIAG, think about joining … and think about coming to the next SIAM
Conference on the Life Sciences in 2014.
As the departing co-chair of the SIAM Life Science Conferences, I
would like to take this opportunity to thank my co-chairs Jon Rubin
(2010) and Mette Olufsen (2012), the conference organizing committees,
the workshop and mini-tutorial organizers, the speakers, Lee Segel
Forum and Forward Looking Session panelists, poster presenters, and
the NSF for supporting the SIAM-LS conference. Finally, I would like
to thank the conference staff at SIAM, especially Nicole Erle – I
can’t imagine having had to organize the conferences without them.
Tim Lewis