The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

__Bubacarr Bah, Jesse Holzer__, *Graduate student in University of Edinburgh and graduate student in Math respectively*

** Date and Time: **Nov 30, 2011 (12:30 PM)

**Location: **
Orchard room (3280) at the Wisconsin Institute for Discovery Building

Bubacarr's talk:

ABSTRACT:

Restricted Isometry Constants (RICs) of a matrix are a popular tool in the analysis of compressed sensing algorithms. The best known bounds will be presented for Gaussian matrices as well as expander graphs. In the former case we will also present explicit formulae for the bounds in three extreme asymptotic limits. Implications for compressed sensing will be discussed.

Jesse's talk

ABSTRACT:

Given distances between nodes in Euclidean space, the network

localization problem is to estimate the positions of the nodes.

In other words, given a weighted graph G = (N,E,D),

find x_n in R^K, n in N, minimizing

sum_{n1n2 = e in E} (|x_n1 - x_n2| - d_e)^2. This is an

unconstrained minimization problem with a highly nonconvex

objective.

Network localization was the subject of the AIMMS/MOPTA modeling

competition this year, which I took part in together with UW-Madison

teammates Lisa Tang and Aditya Gore. In the competition, it was

given that node pairs (n1,n2) not in E are far apart. This

additional information should be used.

In this talk I'll discuss the difficult nonconvexity of the

network localization NLP, SDP relaxations for this problem,

our approach inspired by low-rank methods for SDP,

and how we dealt with node pairs not in E. As befits a talk of a

geometric nature, there will be lots of pretty pictures.