## Seminars and Colloquia by Series

### Penalized orthogonal-components regression for large p small n data

Series
Stochastics Seminar
Time
Thursday, August 27, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dabao ZhangPurdue University
We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effectively identify sparse predictors of each component. POCRE is computationally efficient owing to its sequential construction of leading sparse principal components. In addition, such construction offers other properties such as grouping highly correlated predictors and allowing for collinear or nearly collinear predictors. With multivariate responses, POCRE can construct common components and thus build up latent-variable models for large p small n data. This is an joint work with Yanzhu Lin and Min Zhang

### Planar graphs and planar posets

Series
Graph Theory Seminar
Time
Thursday, August 27, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
William T. TrotterMath, GT
Slightly modifying a quote of Paul Erdos: The problem for graphs we solve this week. The corresponding problem for posets will take longer. As one example, testing a graph to determine if it is planar is linear in the number of edges. Testing an order (Hasse) diagram to determine if it is planar is NP-complete. As a second example, it is NP-complete to determine whether a graph is a cover graph. With these remarks in mind, we present some results, mostly new but some classic, regarding posets with planar cover graphs and planar diagrams. The most recent result is that for every h, there is a constant c_h so that if P is a poset of height h and the cover graph of P is planar, then the dimension of P is at most c_h.

### Big Bang and the Quantum

Series
School of Mathematics Colloquium
Time
Wednesday, August 26, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Chemistry and Biochemistry Boggs Building, Room B-6A
Speaker
Abhay AshtekarDepartment of Physics and Institute for Gravitational Physics and Geometry, Pennsylvania State University

Please Note: Pre-reception at 2:30 in Room N201.  If you would like to meet with Prof. Ashtekar while he is on campus (at the Center for Relativistic Astrophysics - Boggs building), please contact lori.federico@physics.gatech.edu.

General relativity is based on a deep interplay between physics and mathematics: Gravity is encoded in geometry. It has had spectacular observational success and has also pushed forward the frontier of geometric analysis. But the theory is incomplete because it ignores quantum physics. It predicts that the space-time ends at singularities such as the big-bang. Physics then comes to a halt. Recent developments in loop quantum gravity show that these predictions arise because the theory has been pushed beyond the domain of its validity. With new inputs from mathematics, one can extend cosmology beyond the big-bang. The talk will provide an overview of this new and rich interplay between physics and mathematics.

### On the interchange process on weighted graphs and other card shuffling models

Series
ACO Student Seminar
Time
Wednesday, August 26, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
SyE Executive Classroom
Speaker
Ton DiekerSchool of Industrial and Systems Engineering, Georgia Tech
A central question in the theory of card shuffling is how quickly a deck of cards becomes 'well-shuffled' given a shuffling rule. In this talk, I will discuss a probabilistic card shuffling model known as the 'interchange process'. A conjecture from 1992 about this model has recently been resolved and I will address how my work has been involved with this conjecture. I will also discuss other card shuffling models.

### Two weight inequalities for singular integrals

Series
Analysis Seminar
Time
Wednesday, August 26, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Michael LaceyGeorgia Institute of Technology
We will survey recent developments in the area of two weight inequalities, especially those relevant for singular integrals.  In the second lecture, we will go into some details of recent characterizations of maximal singular integrals of the speaker, Eric Sawyer, and Ignacio Uriate-Tuero.

### Analyticity in time and backward uniqueness of weak solutions of the Navier-Stokes equations of multidimensional, compressible flow

Series
PDE Seminar
Time
Tuesday, August 25, 2009 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
David HoffIndiana University, Bloomington
We prove that solutions of the Navier-Stokes equations of three-dimensional, compressible flow, restricted to fluid-particle trajectories, can be extended as analytic functions of complex time. One important corollary is backwards uniqueness: if two such solutions agree at a given time, then they must agree at all previous times. Additionally, analyticity yields sharp estimates for the time derivatives of arbitrary order of solutions along particle trajectories. I'm going to integrate into the talk something like a "pretalk" in an attempt to motivate the more technical material and to make things accessible to a general analysis audience.

### Bendixson conditions for differential equations in Banach spaces

Series
CDSNS Colloquium
Time
Monday, August 24, 2009 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Qian WangSchool of Mathematics, Georgia Tech
The Bendixson conditions for general nonlinear differential equations in Banach spaces are developed in terms of stability of associated compound differential equations. The generalized Bendixson criterion states that, if some measure of 2-dimensional surface area tends to zero with time, then there are no closed curves that are left invariant by the dynamics. In particular, there are no nontrivial periodic orbits, homoclinic loops or heteroclinic loops. Concrete conditions that preclude the existence of periodic solutions for a parabolic PDE will be given. This is joint work with Professor James S. Muldowney at University of Alberta.

### Submodular Function Approximation

Series
Combinatorics Seminar
Time
Friday, August 21, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Satoru IwataKyoto University
In this lecture, I will explain the greedy approximation algorithm on submodular function maximization due to Nemhauser, Wolsey, and Fisher. Then I will apply this algorithm to the problem of approximating an monotone submodular functions by another submodular function with succinct representation. This approximation method is based on the maximum volume ellipsoid inscribed in a centrally symmetric convex body. This is joint work with Michel Goemans, Nick Harvey, and Vahab Mirrokni.

### Submodular Function Minimization

Series
Combinatorics Seminar
Time
Wednesday, August 19, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Satoru IwataKyoto University
In this lecture, I will review combinatorial algorithms for minimizing submodular functions. In particular, I will present a new combinatorial algorithm obtained in my recent joint work with Jim Orlin.

### Rigid and Nonrigid Registration Models for Medical Images

Series
Applied and Computational Mathematics Seminar
Time
Tuesday, August 18, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Justin W. L. WanComputer Science, University of Waterloo
In image guided procedures such as radiation therapies and computer-assisted surgeries, physicians often need to align images that are taken at different times and by different modalities. Typically, a rigid registration is performed first, followed by a nonrigid registration. We are interested in efficient registrations methods which are robust (numerical solution procedure will not get stuck at local minima) and fast (ideally real time). We will present a robust continuous mutual information model for multimodality regisration and explore the new emerging parallel hardware for fast computation. Nonrigid registration is then applied afterwards to further enhance the results. Elastic and fluid models were usually used but edges and small details often appear smeared in the transformed templates. We will propose a new inviscid model formulated in a particle framework, and derive the corresponding nonlinear partial differential equations for computing the spatial transformation. The idea is to simulate the template image as a set of free particles moving toward the target positions under applied forces. Our model can accommodate both small and large deformations, with sharper edges and clear texture achieved at less computational cost. We demonstrate the performance of our model on a variety of images including 2D and 3D, mono-modal and multi-modal, synthetic and clinical data.