Seminars and Colloquia Schedule

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, February 20, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
TBA – Georgia Tech
A discussion of the paper "Algorithm independent properties of RNA secondary structure predictions" by Tacker et all (1996).

Non-­‐local models of anomalous transport

Series
CDSNS Colloquium
Time
Monday, February 20, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Diego Del Castillo-Negrete – Oak Ridge National Lab
The study of transport is an active area of applied mathematics of interest to fluid mechanics, plasma physics, geophysics, engineering, and biology among other areas. A considerable amount of work has been done in the context of diffusion models in which, according to the Fourier-­‐Fick’s prescription, the flux is assumed to depend on the instantaneous, local spatial gradient of the transported field. However, despiteits relative success, experimental, numerical, and theoretical results indicate that the diffusion paradigm fails to apply in the case of anomalous transport. Following an overview of anomalous transport we present an alternative(non-­‐diffusive) class of models in which the flux and the gradient are related non-­‐locally through integro-­differential operators, of which fractional Laplacians are a particularly important special case. We discuss the statistical foundations of these models in the context of generalized random walks with memory (modeling non-­‐locality in time) and jump statistics corresponding to general Levy processes (modeling non-­‐locality in space). We discuss several applications including: (i) Turbulent transport in the presence of coherent structures; (ii) chaotic transport in rapidly rotating fluids; (iii) non-­‐local fast heat transport in high temperature plasmas; (iv) front acceleration in the non-­‐local Fisher-­‐Kolmogorov equation, and (v) non-­‐Gaussian fluctuation-­‐driven transport in the non-­‐local Fokker-­‐Planck equation.

Variational Image Registration

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 20, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Benjamin Berkels – South Carolina University
Image registration is the task of transforming different images, or more general data sets, into a common coordinate system. In this talk, we employ a widely used general variational formulation for the registration of image pairs. We then discuss a general gradient flow based minimization framework suitable to numerically solve the arising minimization problems. The registration framework is next extended to handle the registration of hundreds of consecutive images to a single image. This registration approach allows us to average numerous noisy scanning transmission electron microscopy (STEM) images producing an improved image that surpasses the quality attainable by single shot STEM images.We extend these general ideas to develop a joint registration and denoising approach that allows to match the thorax surface extracted from 3D CT data and intra-fractionally recorded, noisy time-of-flight (ToF) range data. This model helps track intra-fractional respiratory motion with the aim of improving radiotherapy for patients with thoracic, abdominal and pelvic tumors.

The quantum content of the Neumann-Zagier equations

Series
Geometry Topology Seminar
Time
Monday, February 20, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Stavros Garoufalidis – Georgia Tech –
The Neumann-Zagier equations are well-understood objects of classical hyperbolic geometry. Our discovery is that they have a nontrivial quantum content, (that for instance captures the perturbation theory of the Kashaev invariant to all orders) expressed via universal combinatorial formulas. Joint work with Tudor Dimofte.

Remarks on the Theory of the Divergence-Measure Fields

Series
PDE Seminar
Time
Tuesday, February 21, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hermano Frid – IMPA, Brazil
We review the theory of the (extended) divergence-measure fields providing an up to date account of its basic results established by Chen and Frid (1999, 2002), as well as the more recent important contributions by Silhavy (2008, 2009). We include a discussion on some pairings that are important in connection with the definition of normal trace for divergence-measure fields. We also review its application to the uniqueness of Riemann solutions to the Euler equations in gas dynamics, as given by Chen and Frid (2002). While reviewing the theory, we simplify a number of proofs allowing an almost self-contained exposition.

Fish Robotics - Understanding the Diversity of Fish Locomotion Using Mechanical Devices

Series
Other Talks
Time
Tuesday, February 21, 2012 - 16:00 for 1 hour (actually 50 minutes)
Location
Klaus 1116
Speaker
George V. Lauder – Harvard University

Hosted by Dan Goldman, School of Physics

There are over 28,000 species of fishes, and a key feature of this remarkable evolutionary diversity is a great variety of propulsive systems used by fishes for maneuvering in the aquatic environment. Fishes have numerous control surfaces (fins) which act to transfer momentum to the surrounding fluid. In this presentation I will discuss the results of recent experimental kinematic and hydrodynamic studies of fish fin function, and their implications for the construction of robotic models of fishes. Recent high-resolution video analyses of fish fin movements during locomotion show that fins undergo much greater deformations than previously suspected and fish fins possess an clever active surface control mechanism. Fish fin motion results in the formation of vortex rings of various conformations, and quantification of vortex rings shed into the wake by freely-swimming fishes has proven to be useful for understanding the mechanisms of propulsion. Experimental analyses of propulsion in freely-swimming fishes have led to the development of a variety of self-propelling robotic models: pectoral fin and caudal fin (tail) robotic devices, and a flapping foil model fish of locomotion. Data from these devices will be presented and discussed in terms of the utility of using robotic models for understanding fish locomotor dynamics.

Minimax Rates of Estimation for Sparse PCA in High Dimensions

Series
High-Dimensional Phenomena in Statistics and Machine Learning Seminar
Time
Tuesday, February 21, 2012 - 16:00 for 1.5 hours (actually 80 minutes)
Location
Skyles 006
Speaker
Karim Lounici – Georgia Institute of Technology, School of Mathematics
This presentation is based on the papers by D. Paul and I. Johnstone (2007) and V.Q. Vu and J. Lei (2012). Here is the abstract of the second paper. We study the sparse principal components analysis in the high-dimensional setting, where $p$ (the number of variables) can be much larger than $n$ (the number of observations). We prove optimal, non-aymptotics lower bounds and upper bounds on the minimax estimation error for the leading eigenvector when it belongs to an $l_q$ ball for $q\in [0,1]$. Our bound are sharp in $p$ and $n$ for all $q\in[0,1]$ over a wide class of distributions. The upper bound is obtained by analyzing the performance of $l_q$-constrained PCA. In particular, our results provide convergence rates for $l_1$-constrained PCA.

Isoperimetric and Functional Inequalities on Discrete Spaces

Series
Research Horizons Seminar
Time
Wednesday, February 22, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prasad Tetali – Georgia Tech
Following exciting developments in the continuous setting of manifolds (and other geodesic spaces), in joint works with various collaborators, I have explored discrete analogs of the interconnection between several functional and isoperimetric inequalities in discrete spaces. Such inequalities include concentration, transportation, modified versions of the logarithmic Sobolev inequality, and (most recently) displacement convexity. I will attempt to motivate and review some of these connections and illustrate with examples. Time permitting, computational aspects of the underlying functional constants and other open problems will also be mentioned.

Recent asymptotic expansions related to numerical integration and orthogonal polynomial expansions

Series
Analysis Seminar
Time
Wednesday, February 22, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Avram Sidi – Tecnion-IIT, Haifa, Israel
We discuss some recent generalizations of Euler--Maclaurin expansions for the trapezoidal rule and of analogous asymptotic expansions for Gauss--Legendre quadrature, in the presence of arbitrary algebraic-logarithmic endpoint singularities. In addition of being of interest by themselves, these asymptotic expansions enable us to design appropriate variable transformations to improve the accuracies of these quadrature formulas arbitrarily. In general, these transformations are singular, and their singularities can be adjusted easily to achieve this improvement. We illustrate this issue with a numerical example involving Gauss--Legendre quadrature. We also discuss some recent asymptotic expansions of the coefficients of Legendre polynomial expansions of functions over a finite interval, assuming that the functions may have arbitrary algebraic-logarithmic interior and endpoint suingularities. These asymptotic expansions can be used to make definitive statements on the convergence acceleration rates of extrapolation methods as these are applied to the Legendre polynomial expansions.

Risk neutral and risk averse approaches to multistage stochastic programming

Series
School of Mathematics Colloquium
Time
Thursday, February 23, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexander Shapiro – ISyE, Georgia Tech
In many practical situations one has to make decisions sequentially based on data available at the time of the decision and facing uncertainty of the future. This leads to optimization problems which can be formulated in a framework of multistage stochastic programming. In this talk we consider risk neutral and risk averse approaches to multistage stochastic programming. We discuss conceptual and computational issues involved in formulation and solving such problems. As an example we give numerical results based on the Stochastic Dual Dynamic Programming method applied to planning of the Brazilian interconnected power system.

A stochastic approach to parabolicity and area growth of minimal ends

Series
Stochastics Seminar
Time
Thursday, February 23, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
006
Speaker
Robert W. Neel – Lehigh University –
We wish to understand ends of minimal surfaces contained in certain subsets of R^3. In particular, after explaining how the parabolicity and area growth of such minimal ends have been previously studied using universal superharmonic functions, we describe an alternative approach, yielding stronger results, based on studying Brownian motion on the surface. It turns out that the basic results also apply to a larger class of martingales than Brownian motion on a minimal surface, which both sheds light on the underlying geometry and potentially allows applications to other problems.

A Discrepancy based Approach to Integer Programming

Series
ACO Student Seminar
Time
Friday, February 24, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Klaus 1116W
Speaker
Karthekeyan Chandrasekaran – CoC, Georgia Tech
I will show a new approach based on the discrepancy of the constraint matrix to verify integer feasibility of polytopes. I will then use this method to show a threshold phenomenon for integer feasibility of random polytopes. The random polytope model that we consider is P(n,m,x0,R) - these are polytopes in n-dimensional space specified by m "random" tangential hyperplanes to a ball of radius R centered around the point x0. We show that there exist constants c_1 < c_2 such that with high probability, the random polytope P(n,m,x0=(0.5,...,0.5),R) is integer infeasible if R is less than c_1sqrt(log(2m/n)) and the random polytope P(n,m,x0,R) is integer feasible for every center x0 if the radius R is at least c_2sqrt(log(2m/n)). Thus, a transition from infeasibility to feasibility happens within a constant factor increase in the radius. Moreover, if the polytope contains a ball of radius Omega(log (2m/n)), then we can find an integer solution with high probability (over the input) in randomized polynomial time. This is joint work with Santosh Vempala.

4th Georgia Scientific Computing Symposium

Series
Other Talks
Time
Saturday, February 25, 2012 - 08:30 for 1 hour (actually 50 minutes)
Location
Room S175, Coverdell Center, University of Georgia
Speaker
Georgia Scientific Computing Symposium – University of Georgia
The purpose of the GSC Symposium is to provide an opportunity for professors, postdocs, and graduate students in the Atlanta area to meet in an informal setting, to exchange ideas, and to highlight local scientific computing research. Certainly, the symposium is open to whole mathematics and computer sciences communities. Three previous meetings were held at Emory University (2009), Georgia Institute of Technology (2010), and Emory University (2011). The 2012 GSC Symposium will be held at the University of Georgia campus and is organized by Dept. of Mathematics, University of Georgia. The following researchers have agreed to give invited plenary lectures: David Bader, College of Computing, Georgia Institute of Technology; Michele Benzi, Dept. of Mathematics and Computer Science, Emory University; Sung Ha Kang, School of Mathematics, Georgia Institute of Technology; Tianming Liu, Dept. of Computer Sciences, University of Georgia; Andrew Sornborger, Dept. of Mathematics, University of Georgia. There will be two poster sessions. Anyone attending this symposium may present a poster. We especially encourage graduate students and postdocs to use this opportunity displaying their research results. Please register at the  website.

Atlanta Lecture Series in Combinatorics and Graph Theory

Series
Other Talks
Time
Saturday, February 25, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Math and Science Center, Emory University
Speaker
Jacob Fox – Massachusetts Institute of Technology
The 5th in a series of 9 mini-conferences features Jacob Fox as the prominent researcher who will give 2 fifty-minute lectures and 4 other outstanding researchers each giving one fifty-minute lecture. There will also be several 25-minute lectures by young researchers and graduate students. The lectures will begin at 1 PM on Saturday, February 25 and conclude at at noon on Sunday, February 26.To register, please send an email to rg@mathcs.emory.edu and for complete details, see the website. Registration is free.