Brown Analysis Seminar
Abstract: Let L = div A Del be a second order elliptic operator, where A is a matrix of bounded measurable functions. For each point X in a domain Omega, the solution u(X) to Lu = 0 with u = f on the boundary of Omega is given by integration against "elliptic measure", d-omega^X, (the analog of harmonic measure). When Omega has a well defined surface measure d-sigma on its boundary, it is of interest to compare these two measures: A quantitative version of absolute continuity of d-omega^X with respect to d-sigma entails the solvability of a classical Dirichlet problem for L with data f in L^p(d-sigma). We discuss criteria for proving absolute continuity, a conjecture, and some consequences for non-divergence form operators as well.
Center for Computational Molecular Biology Seminar (***CANCELLED*** due to illness)
Abstract:
The evolutionary forces that establish and hone the network of target genes for
transcription factors are largely unknown. We report here new evidence that
mobile element mediated transcription regulation is an ongoing process.
Recent, species-specific mobile elements, in particular, endogenous
retroviruses (ERVs), can actively shape transcriptional networks in a
species-specific manner.
Using tumor suppressor and transcription factor p53 as an example, we show that
its binding sites are highly enriched in Long Terminal Repeats (LTRs) of a few
ERV subfamilies active only in primates. These p53 site-containing LTRs are
in vivo binding sites for p53 and account for more than 30% of p53 genomic
sites. Experimental validation confirmed that LTRs with a p53 site possess
p53-dependent regulatory potential and regulate nearby gene expression.
Similar phenomenon is observed for transcription factor Stat1.
Our study indicates that invaluable treasures are hidden in the "junk" DNA,
that these once foreign genetic materials are important evolutionary forces
that impact our genome in a systematic manner, and that the connections one
can make between mis-regulated mobile elements and human diseases provide a
new avenue for disease investigation.
The UCSC Cancer Genomics Browser
We describe the UCSC Cancer Genomics Browser, a suite of web-based tools to
integrate, visualize and analyze cancer genomics and clinical data. This
browser displays a whole-genome-oriented view of genome- wide experimental
measurements for individual and sets of samples alongside their associated
clinical information. The browser also enables investigators to order, filter,
aggregate, classify and display data interactively based on any given feature
set including clinical features, annotated biological pathways, and user-edited
collections of genes. Standard statistical tools are integrated to provide
quantitative analysis of whole genomic data or any of its subsets. We
demonstrate the capability of this browser with data from several published
large cancer genomics studies. The browser is also being used on confidential,
prepublication data by multiple groups.
This browser is an extension of the UCSC Genome Browser; thus it inherits and
integrates the Genome Browser's existing rich set of human biology and genetics
data to enhance the interpretability of the cancer genomics data.
Scientific Computing Seminar
Abstract:
In (1} we proposed a general numerical flux formula for the solution
derivative $u_x$, and developed the so-called direct discontinuous Gallerkin
(DDG) method. The DDG method has the drawback of obtaining its optimal
accuracy when k is even for $p^k$ polynomials. In this talk, we introduce a
refined DDG method such that optimal $(k+1)$th order of accuracy is obtained
for any $p^k$ polynomial approximations. Two types of admissible numerical
fluxes are studied. Admissibility and stability are discussed, and then the
DDG method with interface correction is extended to nonlinear convection
diffusion equations. Two dimensional extension is carried out also. A series
of numerical examples are presented to demonstrate the high order accuracy and
the capacity of the method.
Reference:
(1)Liu, H. and Yan, J.,The direct discontinuous {G}alerkin method for
diffusion problems, SIAM J. Numer. Anal.,VOLUME {47}, #1, January 16 2009,
available online.
PDE Seminar
Abstract: This talk is divided into two parts. In the first part, I will discuss how to construct a linear profile decomposition for the Airy equation; in the second part, I will discuss several applications.