Seminars and Colloquia by Series

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.

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.

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.

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

Please Note: 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.

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.

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.

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.

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.

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