Monday, Februray 20 - Thursday, February 23, 2012 1:30 - 2:30 p.m. Room 305 Lind Hall
Wenbo Li, University of Delaware and IMA
Metric Entropy and Applications
Abstract
Poster
Metric entropy is defined as the logarithm of
the minimum covering number of a compact set by balls of very small radius.
In this series of lectures, we will provide an overview of various available
techniques and significant applications to theory of approximation, machine learning,
data compression,probability and statistics.
All talks are accessible to graduate students in any areas of mathematics.
Monday, March 5 - Wednesday 7, 2012 1:30 - 2:30 p.m., Room 305 Lind Hall
Vladimir Temlyakov, University of South Carolina
Greedy Approximations
Abstract
This lecture series is a survey of greedy approximation methods for nonlinear sparse approximation of functions.
Thursday, March 8, 3:30 p.m., Room 16, Vincent Hall and Friday, March 9, 1:30 p.m., Room 305, Lind Hall
Holger Rauhut, University of Bonn
Two Lectures on Compressive Sensing
Abstract
Lecture 1: Structured Random Matrices in Compressive Sensing (School of Mathematics Colloquium)
Thursday, March 8, 3:30 p.m., Room 16, Vincent Hall
Compressive sensing is concerned with the recovery of sparse vectors from incomplete linear information via efficient algorithms. It is
well-known that Gaussian random matrices provide optimal measurement matrices in this context. From an application point of view such completely
unstructured matrices are, however, of limited use. Indeed, structure allows to model physically meaningful information acquisition processes,
and also allows fast matrix-vector multiplication which helps in speeding up recovery algorithms such as l1-minimization. In this talk I will
report on two types of structured random matrices. Partial random circulant matrices describe subsampled random convolutions. I will present
sparse recovery results for these, and in particular, recent estimates for their restricted isometry constants. The corresponding analysis uses
a new generic chaining type bound for chaos processes. Furthermore, I will discuss a structured random matrix arising in radar imaging. The
randomness comes from placing antenna elements at random locations on a square aperture. The difficulty in the corresponding analysis lies in
the fact that neither the columns nor the rows of this matrix are independent.
Lecture 2: Restricted Isometry Properties of Random Matrices
Friday, March 9, 1:30 p.m., Room 305, Lind Hall
I will discuss techniques for proving the restricted isometry property for certain classes of random matrices, including Gaussian and Bernoulli matrices. Depending on interest, I will also cover random partial Fourier matrices and/or partial random circulant matrices.
Tuesday, March 13, 3:00 - 4:00 p.m., Room 305, Lind Hall
Mark Iwen, Duke University
Compressed Sensing for Manifold Data
Abstract
We will discuss techniques for approximating a point in
high-dimensional Euclidean space which is close to a known
low-dimensional compact submanifold when only a compressed linear
sketch of the point is available. More specifically, given a point,
x, in R^D we will consider linear measurement operators, M: R^D ->
R^m, which have associated nonlinear inverses, A: R^m -> R^D, so that
|| x - A(Mx) || is small even when m << D. Both the design of good
linear operators, M, and the design of stable nonlinear inverses, A,
will be discussed. More specifically, an algorithmic implementation a
particular nonlinear inverse will be presented, along with related
stability bounds for the approximation of manifold data.
Tuesday, March 20th and Thursday, March 22nd, 2012 1:30 - 2:30 p.m. Room 305 Lind Hall
Arindam Banerjee, University of Minnesota
Two Tutorial Lectures on Machine Learning
Abstract
Lecture 1, Tuesday, March 20, 2012, 1:30-2:30pm, Room 305 Lind Hall
The lecture will have two parts. The first part will give a brief overview of machine learning (ML),
including a discussion on some of the key problems the community focuses on solving. In this
context, we will briefly discuss support vector machine (SVMs) and kernel methods. The second part
will focus on probabilistic graphical models with a brief discussion of the progress so far, some
applications, and some key themes currently being explored by the community.
The lecture provides background material to the IMA workshop talks by Alex Smola (Yahoo) on Monday,
3/26, and by Corinna Cortes (Google) on Thursday, 3/29 .
Lecture 2, Thursday, March 22, 2012, 1:30-2:30pm, Room 305 Lind Hall
The primary theme of the lecture will be high-dimensional problems. The lecture will have two parts. The first part will focus
on consistency of high-dimensional modeling, with focus on regression especially when the number of
samples is smaller than the number of dimensions, which is the case for several modern problems. The
analysis will be connected to structure learning problems in graphical models (lecture 1). The second
ill focus on large scale optimization, which emphasis on non-smooth and online optimization problems.
Such optimization methods form a key part of learning in a wide variety of models.
The lecture will provide background material to the IMA workshop talks, including the one given by
Steven Wright on Tuesday, 3/27.
(RESCHEDULED from 3/14) Wednesday, March 21, 1:30 p.m., Room 305, Lind Hall
Lan Wang, University of Minnesota
An overview of current trends in high-dimensional statistical data analysis
Abstract
The talk will provide a survey of recent developments in statistical analysis of high-dimensional data, where the number of parameters is much
larger than the number of experimental units. Areas of application include image analysis, microarray analysis, finance, document classification,
astronomy, atmospheric science, among others. The talk will be accessible for graduate students with background in mathematics or statistics.
Friday, March 30, 1:30 p.m., Room 305, Lind Hall
Felix Krahmer, Georg-August-Universität Göttingen
Suprema of Chaos Processes and the Restricted Isometry Property
Abstract
The theory of compressed sensing considers the following problem: Let A ∈ C
^{mxn} and let x ∈ C^{n} be s-sparse, i.e.,
x_{i} = 0 for all but s indices i. One seeks to recover
x uniquely and effciently from linear measurements y = Ax, although
m ‹‹ n. A sufficient condition to ensure that this is possible is the Restricted
Isometry Property (RIP). A is said to have the RIP, if its restriction to any small subset
of the columns acts almost like an isometry.
In this talk, we study two classes of matrices with respect to the RIP: First, we consider
matrices A which represent the convolution with a random vector followed by a restriction to
an arbitrary fixed set of entries. We focus on the scenario that ∈is a Rademacher vector, i.e.,
a vector whose entries are independent random signs. Second, we study Gabor synthesis
matrices, that is, matrices consisting of time-frequency shifts of a Rademacher vector.
This is joint work with Shahar Mendelson and Holger Rauhut.
The Fall semester seminars were organized by
Luke Olson
The intent of this seminar series is to expose the research activities and expertise of long term visitors in the program in order to facilitate
discussion and integrate different areas of research surrounding the Mathematics of Information.
September 16, 2011 9:30 am, Room 305 Lind Hall
Candice Price, University of Iowa
Oriented skein relation for knot Floer homology and a biological application
Abstract
Candice studies protein-DNA interactions using a particular invariant known as knot Floer Homology. In this talk Candice will give some mathematical and biological background and discuss some results.
September 23, 2011 9:30 am, Room 3-180 Keller Hall
Carsten Schuett, Christian-Albrechts Universität Kiel,
An excursion into Banach space theory
September 23, 2011 - December 22, 2011 (except during IMA workshops), 1:25pm to 2:15pm, Room 401 Lind Hall
Topics in High Dimensional Phenomena
October 5, 2011 11:00 am, Room 3-180 Keller Hall
Leonardo Espin
Solute uptake in vessels with oscillatory walls
Abstract
We study computationally the absorption of a passive solute through the walls of an oscillating channel of finite length. The channel is filled with an incompressible fluid which carries the solute. The channel walls pulsate in a prescribed manner and these pulsations generate a fluid flow that modifies the solute transference to the medium that surrounds the channel, and consumes solute at a constant rate. The fluid motion is governed by the incompressible Navier-Stokes equations and no-slip conditions at the solid-liquid interface. We apply our numerical results to a two dimensional model of a surgical technique used for treating patients with coronary artery disease.
October 12, 2011 11:00 am, Room 3-180 Keller Hall
Lars Eldén, Department of Mathematics, Linköping University, Sweden
Computing Semantic Clusters by Semantic Mirroring and
Spectral Graph Partitioning
Abstract
A great deal of linguistic knowledge is encoded implicitly in bilingual
resources such as parallel texts and dictionaries. Semantic
mirroring is a linguistic technique, where one performs two-way
translations using a bilingual lexicon. The translations involving a set of
words in a source language can be seen to constitute an undirected graph,
where the vertices are words in the source language and the edges the
translations via words in the target language. The connectedness of the
graph holds information about the different meanings of words that occur in
the translations. Spectral graph partitioning is used to cluster the words
according to different senses. Results using a lexicon of Swedish and
English adjectives are reported.
Tuesday, Oct 11, 2:30 to 3:30, Room 305 Lind
Information passing and collective animal behavior
Naomi Ehrich Leonard (Mechanical and Aerospace Engineering, Princeton University)
Abstract
Information passing through social interactions in moving animal groups, such as bird flocks and fish schools, is credited both with improving group responsiveness to external environmental stimuli and with maintaining group cohesiveness in the presence of uncertainty. Agent-based dynamical models with interaction terms that enable information diffusion have been used successfully to reproduce a range of observed collective motions. I will discuss analytic approaches for examining group decision making and exploring group robustness to uncertainty. Of particular interest is the role of the topology of the interconnections among individuals on the emergent outcomes and performance at the level of the group.
Dr. Ehrich Leonard will also be delivering the IMA Public Lecture in the evening.
October 19, 2011 11:00 am, Room 3-180 Keller Hall
Isabel Darcy, Department of Mathematics, University of Iowa
Topology, Graphs, and Data
Abstract
I will give two short introductory talks.
First, I will describe a graph where the vertices represent knots and
the knots are connected by an edge if one can be converted to the
other via an operation such as changing one crossing. These graphs
were developed to better understand the action of proteins which can
knot circular DNA. Some proteins will cut DNA and change the DNA
configuration before resealing the DNA. Thus, if the DNA is circular,
the DNA can become knotted.
Second, I will give a very elementary introduction to algebraic
topology and how it can be used in a variety of applications.
Thursday, November 3, 2:30 to 3:30, Room 305 Lind
"P vs. NP" problem: Efficient computation, internet security, and the limits to human knowledge
Avi Wigderson (Institute for Advanced Study, Princeton)
Abstract
November 9, 2011 11:00 am, Room 3-180 Keller Hall
Luke Olson, Department of Computer Science, University of Illinois at Urbana-Champaign
An algebraic view of topological problems: solvers and graphs
Abstract
We take a look at a class of problems called k-form or de Rham Laplacians. These operators give us certain properties in a graph, but are a challenge computationally. In this talk we'll take a look at algebraic multigrid solvers and specifically a solver that conforms to the topology or calculus of the problem.
November 29, 2011 3:00 p.m., Room 401 Lind Hall
Dainius Dzindzalieta, Institute of Mathematics and Informatics, Vilnius State University
Extremal Lipschitz functions on isoperimetric spaces
Abstract
We consider Lipschitz functions on probability metric spaces. We provide an explicit description of Lipchitz functions which are deviated from it's mean by some number $x$ with a largest possible probability. It turns out that negative distance functions are the extremal ones.