**Mathematical Application Seminar**

**Spring Fall 2012**

Monroe Hall, 2115 G Street, Room 267

**November 14, Wednesday 1 2pm.**

**Speaker:** Michael
Robinson, Department of Mathematics and
Statistics,

**Title: **Signal
processing with the Euler calculus

**Place**: Monroe 267, 2115 G Steet.

**Abstract: **It happens that many of
the transforms traditionally used in signal processing have natural analogs
under the Euler integral, popularized by Baryshnikov and Ghrist.
The properties of these transforms are sensitive to topological (as well as
certain geometric) features in the sensor field and allow signal processing to
be performed on structured, integer valued data, such as might be gathered from
ad hoc networks of inexpensive sensors. For instance, the analog of the Fourier
transform computes a measure of width of support for indicator functions. There
are some notable challenges in this theory, some of which are present in
traditional transform theory (such as the presence of sidelobes),
and some which are new (such as the nonlinearity of the transform when extended
to real-valued data). These challenges and some mitigation strategies will be
presented as well as a showcase of the transforms and their capabilities.

**SYMPOSIUM on Mathematics and Presidential Campaigns**

**Friday, October 19, 2012, 1:00 2:00 PM**

**Place: **Moot Courtroom, Law School,
2000 H St., NW, 1st floor (entrance also from Quad)

**Opening Remarks:** Leo Chalupa, Vice
President for Research.

**Keynote Speaker:** John Banzhaf, Law School, Inventor
of the "Banzhaf Index of Voting Power"

**Penelists****:** John Banzhaf, Law School, Inventor
of the "Banzhaf Index of Voting Power"

Danny
Hayes, Assistant Professor of Political Science

Edward
Turner, Dept. of Mathematics

Daniel Ullman, Co-Author, "A Mathematical Look at
Politics"

**Moderator:** Yongwu Rong, Dept.
of Mathematics and GWIMS.

Refreshments will be served
at the end

This symposium is sponsored
by the George Washington Institute for Mathematical Sciences (GWIMS), GW Economics Department,
and GW Mathematics
Department. Check http://home.gwu.edu/~rong/MathPolSymp.htm
for the latest update on the event.

**March 7, Wednesday 11:30 12:30 pm.**

**Speaker:** Sang (Peter)
Chin, Cyber Space Technology Branch, Johns

**Title: **Application
of Compressive Sensing to Cognitive Radio and Digital Holography

**Place**: Monroe 267, 2115 G Steet.

**Abstract: **One of the key aspects of
cognitive radio is the concept of dynamic spectrum access, where a radio
searches for a (temporarily) unused white space in order to transmit and
receive its data. To enable such dynamic spectrum utilization, it is
critical to detect the existence/absence of primary users, and furthermore
understand the spectrum usage pattern of primary users. Currently, this is done
by periodically switching the radio from the operation mode (transmit/receive)
to sensing mode, during which the radio tries to sense for the existence of
other (incumbent) signals. It is thus of utmost importance to make the sensing
period as small as possible, which can not only increase the operational
utilization, but also enable detection of more white spaces (including finer
ones that can't be otherwise detected). We show that the nascent theory of
compressive sensing, a revolutionary sampling paradigm which enables sampling
at a much lower rate than the Nyquist rate by
exploiting the sparsity of a given signal, can offer
new opportunities for DSA. In particular, we show that compressive sensing
theory is able to reduce significantly the amount of time and size of data that
a cognitive radio needs in order to sense the existence of incumbent signals.
Furthermore, We show that the recent progress on compressive sensing is also
applicable and useful in a digital hololographic
system, especially in that it greatly reduces the number of pixels (up to 80%)
in hologram that is necessary to reconstruct the image without losing essential
features of the image. This offers a path to sparsely sample the hologram and
produce images with resolution comparable to the fully populated array, which
in turn effects an holographic system to capture images at longer ranges using
an array of sparsely populated smaller CCD arrays.

**Biography:** Dr. Sang (Peter) Chin is currently a branch chief
scientist of CyberSpace Technology Branch at Johns
Hopkins Applied Physics Laboratory and a, where he is conducting research in
the area of compressive sensing, data fusion, game theory, MHT tracking,
quantum-game inspired cyber-security, and cognitive radio. Prior to joining
JHU/APL, he was a Division CTO at SAIC, and before that, he was a technology
manager for 90 nm technology at LSI Logic Corp., where he also helped to
develop its first Embedded DRAM technology jointly with Hitachi Semiconductor
in late 90s. He received his Ph.D. in mathematics from MIT and is a Phi Beta
Kappa graduate from

**The Mathematical
Application Seminar in Previous Years**

___________________________________

** The
Mathematical Application Seminar was sponsored by* *the George Washington University Seminars program
during 2008-2011**. *

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