Brown University Center for Statistical Sciences Seminar
Abstract:
Data arising from networks can be rich and complex. For example, the "header"
information in email messages specifies a sender, recipient(s) and transaction
time. Each email address can be viewed as a node in a graph, and email as
transactions along the edges. The availability of large databases of such
transactional network data presents challenging opportunities for the
development of new models.
The usual "statistical learning" (supervised or unsupervised) can only be
attempted after developing novel techniques to deal with this complex structure,
or after manipulating the data so that more conventional methods can be
brought to bear. In this talk I will outline models and methods for both
supervised and unsupervised learning on transactional data of this form, and
also for other kinds of social network data.
Brown Analysis Seminar
Boston University/Brown University PDE Seminar
Abstract:
We report on an experimental and theoretical study of Langmuir layers, defined
as a molecularly thin polymer layer on the surface of a subfluid. Langmuir
layers can have multiple phases (e.g. fluid, gas, liquid crystal, isotropic
or anisotropic solid); at phase boundaries a line tension force (the
two-dimensional analogue of surface tension) is observed. We first consider
two co-existing fluid phases; specifically a localized phase embedded in an
infinite secondary phase. When the localized phase is stretched (by a transient
stagnation flow), it takes the form of a bola consisting of two roughly
circular reservoirs connected by a thin tether. This shape then relaxes to
the minimum energy configuration of a circular domain. The tether is never
observed to rupture, even when it is more than a hundred times as long as it
is thin. We model these experiments by taking previous descriptions of the
full hydrodynamics (primarily those of Stone & McConnell and Lubensky &
Goldstein), identifying the dominant effects via dimensional analysis, and
reducing the system to a more tractable form. The result is a free boundary
problem where motion is driven by the line tension of the domain and damped
by the viscosity of the subfluid. The problem has a boundary integral
formulation that allows us to numerically simulate the tether relaxation;
comparison with the experiments allows us to estimate the line tension in the
system, often to within 1%. As time allows we will also report on some other
phenomena observed in Langmuir systems, including collapse of gas phase
bubbles, co-existence of three or more fluid phases, elastic buckling of
surface layers, and formation of dogbone and labyrinth patterns due to dipolar
repulsion in the layer.
This work is collaborative with Jacob Wintersmith (HMC 2006), George Tucker
(HMC 2008), Elizabeth Mann (Kent State), Lu Zou (Kent State), J. Adin Mann,
Jr. (CWRU) and James Alexander (CWRU).
Boston University/Brown University PDE Seminar
Abstract: Burgers equation arises in several surprising contexts. In this talk I will show how Burgers equation arises in the theory of random matrices. Dyson showed that the eigenvalues of random matrices from Gaussian ensembles satisfy a simple SDE. In a scaling limit, as the size of the matrices goes to infinity, we obtain a kinetic equation (first derived by Kerov) for the spectral measure whose Cauchy transform satisfies Burgers equation. No knowledge of random matrices will be presumed, and the talk will be largely self-contained.
Applied Mathematics Colloquium
Abstract: The speaker will describe a number of unusual letters that he has received over the years and the consequences that ensued.
Scientific Computing Seminar
Abstract: The purpose of this project is to reconstruct the shape of mountains millions or ten millions of years ago from the history temperature data at several points. Two main models will be involved: one is Heat Transport Process Model, which is used to explain how the temperature of rocks change, and another is Surface Process Model, which is used to explain the change of surface of mountains. These two models are coupled with each other. I will talk about the formulation and the inverse problems in this model. I will also present some preliminary numerical result.
PDE Seminar
Abstract: From the H.Lewy theorem and Gleason-Wolff counterexample, we know the three dimension harmonic function has very special geometry properties. In this talk, we give the sharp Gaussian curvature and principal curvature estimates of the level sets of three harmonic function and minimal graph on convex ring. In the end, we also state a constant rank theorem on the second fundamental form of the convex level sets for a class fully nonlinear elliptic equations.