## Mathematical and Computation Biology Archives

**November 14, Wednesday 1 – 2pm**.

Speaker: Michael Robinson, Department of Mathematics and Statistics, American University

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 CampaignsFriday, 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 Hopkins Applied Physics Laboratory.

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 90’s. He received his Ph.D. in mathematics from MIT and is a Phi Beta Kappa graduate from Duke University where he was a faculty scholar with a triple major in EE, computer science and mathematics.