Seminars and Colloquia by Series

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.

Submodular Functions in Graph Theory

Series
Combinatorics Seminar
Time
Friday, August 14, 2009 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Prof. Satoru IwataKyoto University
In this lecture, I will explain connections between graph theory and submodular optimization. The topics include theorems of Nash-Williams on orientation and detachment of graphs.

Parabolic systems and an underlying Lagrangian

Series
Dissertation Defense
Time
Thursday, July 2, 2009 - 13:30 for 2.5 hours
Location
Skiles 255
Speaker
Turkay YolcuSchool of Mathematics, Georgia Tech
In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite entropy, we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method reveals to be a powerful tool for proving convergence of our algorithm. Finally, we analyze uniqueness and stability of our solution in L^1.

Digital Chaotic Communications

Series
Dissertation Defense
Time
Wednesday, July 1, 2009 - 15:30 for 3 hours
Location
Skiles 255
Speaker
Alan J. MichaelsSchool of Electrical and Computer Engineering, Georgia Tech
This disseratation provides the conceptual development, modeling and simulation, physical implementation and measured hardware results for a procticable digital coherent chaotic communication system.

Brown bag seminar on mathematical challenges in astrophysics

Series
Other Talks
Time
Wednesday, July 1, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Pablo LagunaSchool of Physics, Georgia Tech
This will be an informal seminar with a discussion on some mathematical problems in relativistic astrophysics, and discuss plans for future joint seminars between the Schools of Mathematics and Physics.

Cubic graph with large girth

Series
Graph Theory Seminar
Time
Thursday, June 11, 2009 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Daniel KralITI, Charles University, Prague

We study several parameters of cubic graphs with large girth. In particular, we prove that every n-vertex cubic graph with sufficiently large girth satisfies the following:

  • has a dominating set of size at most 0.29987n (which improves the previous bound of 0.32122n of Rautenbach and Reed)
  • has fractional chromatic number at most 2.37547 (which improves the previous bound of 2.66881 of Hatami and Zhu)
  • has independent set of size at least 0.42097n (which improves the previous bound of 0.41391n of Shearer), and
  • has fractional total chromatic number arbitrarily close to 4 (which answers in the affirmative a conjecture of Reed). More strongly, there exists g such that the fractional total chromatic number of every bridgeless graph with girth at least g is equal to 4.
The presented bounds are based on a simple probabilistic argument.

The presentation is based on results obtained jointly with Tomas Kaiser, Andrew King, Petr Skoda and Jan Volec.

Crossing-critical graphs with large maximum degree

Series
Graph Theory Seminar
Time
Thursday, June 4, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Zdenek DvorakSimon Fraser University
Richter and Salazar conjectured that graphs that are critical for a fixed crossing number k have bounded bandwidth. A weaker well-known conjecture of Richter is that their maximum degree is bounded in terms of k. We disprove these conjectures for every k >170, by providing examples of k-crossing-critical graphs with arbitrarily large maximum degree, and explore the structure of such graphs.

Liar Games, Optimal Codes, and Deterministic Simulation of Random Walks

Series
Combinatorics Seminar
Time
Thursday, May 21, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Joshua CooperDepartment of Mathematics, University of South Carolina
We consider the Ulam "liar" and "pathological liar" games, natural and well-studied variants of "20 questions" in which the adversarial respondent is permitted to lie some fraction of the time. We give an improved upper bound for the optimal strategy (aka minimum-size covering code), coming within a triply iterated log factor of the so-called "sphere covering" lower bound. The approach is twofold: (1) use a greedy-type strategy until the game is nearly over, then (2) switch to applying the "liar machine" to the remaining Berlekamp position vector. The liar machine is a deterministic (countable) automaton which we show to be very close in behavior to a simple random walk, and this resemblance translates into a nearly optimal strategy for the pathological liar game.

Pages