Annual Report 2008.pdf - SAMSI

Michael Reed (Mathematics, Duke), Greg Forest (Mathematics, UNC), Alun Lloyd (Math, NC
State), H.T. Banks (Math, NC State), Giles Hooker (Bio. Stat. and Comp. Biology, Cornell),
George Oster (Bio., U. C. Berkeley) , Hans Othmer (Math, Minnesota), Sunney Xie,
(Chemistry, Harvard), Jianhua Xing, (Bio., Virginia, Tech), Charles Peskin, (Math, NYU),
Natalia Komarova (Math, U. C. Irvine), Michael Reed (Mathematics, Duke)
2.2.3 Stochastic Analysis and Numerical Methods
In recent years it has become increasingly clear that to effectively understand complex
stochastic systems, a combination of modern numerical analysis, estimation and sampling
techniques, and rigorous analysis of stochastic dynamics is required. Whether one speaks of path
sampling techniques, estimation in complex non-linear dynamics, or simulation of rare-events it
is important to bring both sophisticated analytic tools and an understanding of what one can
compute efficiently.
A working group in stochastic analysis and numerical methods is partially inspired by a
recent workshop, sponsored by AIM and the NSF, concerning approaches for the numerical
integration of stochastic systems which span many temporal-scales. This subject would fit well
with other potential working group topics of multi-scale computing and/or biological
applications. Important issues such as the erogodicity of numerical methods for SDEs, the
construction of higher order methods for SDEs and SPDEs, the role of holonomic constraints and
how to enforce them in numerical methods, or ways to efficiently compute quantities like free
energies in chemical kinetic simulations would provide very fertile ground for productive
collaboration between mathematicians, statisticians, and computational scientists under the
stochastic dynamics banner.
Possible working group leaders:
Martin Hairer (Math, Warwick), Jonathan Mattingly (Math, Duke)
Possible Participants:
Andrew Stuart (Mathematics, Warwick), Garreth Roberts (Math and Stat, Lancaster), Terry
Lyons (Math, Oxford), Eric Vanden-Eijnden (Math, NYU), Alina Chertock (Math, NC State)
2.2.4 Modeling of Dynamic Network
Network data, unlike some other examples of large scale data are distinguished by the
inherent dependencies among units. Indeed these dependencies, usually represented by (binary
or more general) links are a primary focus of analysis. Among a multitude of examples are social
networks, organization theory, homeland security, public health, E-mail networks, Internet links
and protein-protein interactions.
Many existing models for inference about networks are descriptive rather than
generative--that is, they do not attempt to explain the "physics" of the network, but only to
describe the data. Virtually none of them models the dynamics of networks: the appearance or
disappearance of nodes, the evolution of link existence or strength, or the characteristics of
nodes. Indeed, at an NSF workshop in October 2007 on "Discovery in Complex or Massive
Data: Common Statistical Themes," there was consensus about an urgent need for models of the
dynamics of networks and associated tools for inference.
Particular issues include: