**Mathematical Application Seminar **

**Spring 2008**

Mondays 11:10 – 12:10pm.

Monroe Hall,

**_________________________________________________________________________**

**February 4, 2008, Monday 11:10
– 12:10pm**

**Speaker:** Xianfeng David Gu (CS dept,

**Title:** Computational Conformal Geometry, Algorithms and
Applications

**Place**: Monroe Hall,

**Abstract:** Computational conformal geometry is an
interdisciplinary field,

combining modern
geometry theories from pure mathematics with computational

algorithms from
computer science. Computational conformal geometry offers

many powerful tools to
handle a broad range of geometric problems in

engineering fields.
This work summarizes our research results in the past

years. We have
introduced efficient and robust algorithms for computing

conformal structures
of surfaces acquired from the real life, which are

based on harmonic
maps, holomorphic differential forms and surface
Ricci

flow. We have applied
conformal geometric algorithms in computer graphics,

computer vision,
geometric modeling and medical imaging.

**February 11, 2008, Monday
11:10 – 12:10pm**

**Speaker:** E. Arthur Robinson (Math Dept, GWU)

**Title:** An introduction to the use of algebraic statistics
in modeling

biological sequence data.

**Place:** Monroe Hall,

**Abstract:** We discuss the method of algebraic statistics, which
uses computational

algebraic geometry (e.g., Groebner bases) to model DNA and RNA sequences.

This idea was pioneered by Lior Pachter and Bernd Sturmfels. The talk is expository.

It will cover the basic
ideas behind this method and consider some simple examples.

**February 18, 2008, ** **President’s Day. GWU is closed.**

**No talk scheduled.**

(A previously scheduled talk
by Teresa Przytycka is rescheduled to be on March 3).

**February 25, 2008, Monday
11:10 – 12:10pm**

**Speaker**: Li Chen (UDC, CS Dept)

**Title:** Connectedness in digital space

**Place**: Monroe Hall,

**Abstract: ** This talk will begin with an overview on
digital geometry, digital space connectivity,

and digital objects such as
digital curves and surfaces. Then we will focus on digital

functions and connectedness.
In addition, the necessary and sufficient condition for

the existing measure
regarding to connectedness will be presented. We will also explore

related topics including the
digitally "continuous" parts, graph-based spanning trees,

and the maximum
connectedness. Finally, we will discuss some applications of

connectedness to image
segmentation.

**March 3, 2008, Monday
11:10 – 12:10pm**

**Speaker: **Teresa Przytycka, NIH | NLM
| NCBI

**Title**: Towards uncovering connections between
graph-theoretical properties of nodes in

protein interaction network and their biological essentiality.

**Place**: Monroe Hall,

**Abstract: **An intriguing question in the analysis of biological
networks is whether biological

characteristics of a
protein, such as essentiality, can be explained by its placement in the
network,

i.e., whether topological
prominence implies biological importance. One of the first connections

between the two in the
context of a protein interaction network, the so-called centrality-lethality
rule,

was observed by Jeong and colleagues (Jeong et
al. 2001) who demonstrated that high-degree nodes

or hubs in a protein
interaction network of Saccharomyces cerevisiae contain more essential proteins

than would be expected by
chance. Even though the correlation between degree and essentiality was

confirmed by many
independent studies, the reason for this correlation remains illusive.

I will discus several
hypotheses about putative connections between essentiality of hubs and the

topology of protein-protein
interaction network that have been proposed recently and demonstrate

that these explanations are
not always supported by the properties of protein interaction networks.

I will also discuss an
alternative explanation.

**March 10, 2008, Monday
11:10 – 12:10pm**

**Speaker: **Sudip Bose (GWU, Statistics Department)

** Title**: Methods of algebraic geometry in biology and
statistics

**Place**: Monroe Hall,

**Abstract:** This is an expository talk about the uses of
computational commutative algebra (CCA)

in biology, statistics and
related fields. As a simple example, one may note that

the probability distribution
from the Hardy-Weinberg principle in genetics can be viewed

as an algebraic
variety. The work of Diaconis and Sturmfels in the early 90s applied

Buchberger's methods to contingency tables. Pistone and Wynn demonstrated the use

of CCA in design of
experiments. The study of Boolean algebras leads to

applications in modeling
biological systems, and in reliability. In fact, rings and ideals

arise naturally in the study
of probability distributions and standard statistical models.

The focus of the talk will
be on the connections rather than specific details of the

application of, say, Grobner bases, to the solution of optimization problems in
statistics and biology.

**March 17, 2008. GWU pring break**.**
No seminar.**

**March 24, 2008, Monday
11:10 – 12:10pm**

**Speaker:** Ken Shaw (ONR)

**Topic:** Compressive Sampling

**Reference: **http://www.dsp.ece.rice.edu/cs/

**Place**: Monroe Hall,

**Abstract:** This is an expository lecture on the subject of
compressive sampling (CS),

also known as compressive
sensing, sparse sensing or sparse sampling. CS is a priority

research area for
surveillance and homeland security purposes because of its potential to

help cope with large streams
of data. Indeed, the real promise of CS lies not in data

reduction but sparse signal
construction through adroit under-sampling.

The field is an attractive
combination of mathematical optimization and probability.

Typical results involve
convex minimization problems whose solutions are exact –

with "high probability."
The talk intends to survey the field and point out some prospective

research problems. It will
be accessible to a general mathematical audience.

**Brief biographical
sketch:** Ken Shaw is an emeritus
professor of mathematics at

Virginia Tech and until
March 1, 2008, was a program officer at the Office of Naval Research.

He was a program officer in
applied mathematics at the National Science Foundation

between 2002 and 2005.
During the academic years 2005-2007 he served as director

of operations for the
graduate program in mathematics and statistics at

and is currently an
Affiliated Faculty member in mathematics at

**April 14, 2008.**

**No talk scheduled.**

(A previously scheduled talk
by Susan Cheng (CS Dept, GWU) will be rescheduled in Fall 2008)

**April 21, 2008**

**No talk scheduled due to
a thesis defense**

**April 28, 2008****, Monday 11:10
– 12:10pm**

**Speaker:** Hosam Mahmoud
(GWU, Statistics Department)

**Title**: Algorithmic and mathematical issues in pattern
matching

**Place**: Monroe Hall,

**Abstract:** The speaker will present some of his own results in
pattern matching

in strings, and more complex
combinatorial structures such as random trees. The

intent is to give the
audience an idea about the algorithmic and combinatorial

issues involved, and
the flavor of the associated results (such as approximating

exact discrete distributions
by continuous limits like the Gaussian and mixed normal

distributions). The talk is
intended to a broad audience of scientists, specially

biologists interested in
mathematical models, and the speaker will try to sketch the results

while staying away from
technically involved proofs.

**_________________________________________________________________________**

**Some future speakers
(subject to confirmation)**

Christian Laing (NYU)

Rahul Simha (GWU, CS)

Chen Zeng
(GWU, bio-physics)

**Speaker:** Xiuzhen (Susan) Cheng (CS
Dept, GWU) http://www.seas.gwu.edu/~cheng

**Topic**: Connected dominating set and its applications in
wireless networks.

**Place**: Monroe Hall,

**_________________________________________________________________________**