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Series: Math Physics Seminar

The McK--V system is a non--linear diffusion equation with a non--local
non--linearity provided by convolution. Recently popular in a variety
of applications, it enjoys an ancient heritage as a basis for
understanding equilibrium and near equilibrium fluids. The model is
discussed in finite volume where, on the basis of the physical
considerations, the correct scaling (for the model itself) is
identified. For dimension two and above and in large volume, the phase
structure of the model is completely elucidated in (somewhat
disturbing) contrast to dynamical results. This seminar represents
joint work with V. Panferov.

Series: Stochastics Seminar

The goal of this talk is to present a new method for sparse estimation
which does not use standard techniques such as $\ell_1$ penalization.
First, we introduce a new setup for aggregation which bears strong links
with generalized linear models and thus encompasses various response
models such as Gaussian regression and binary classification. Second, by
combining maximum likelihood estimators using exponential weights we
derive a new procedure for sparse estimations which satisfies exact
oracle inequalities with the desired remainder term. Even though the
procedure is simple, its implementation is not straightforward but it
can be approximated using the Metropolis algorithm which results in a
stochastic greedy algorithm and performs surprisingly well in a
simulated problem of sparse recovery.

Series: Graph Theory Seminar

We will discuss the classic theorem of Walter Schnyder: a graph G is planar if and only if the dimension of its incidence poset is at most 3. This result has been extended by Brightwell and Trotter to show that the dimension of the vertex-edge-face poset of a planar 3-connected graph is 4 and the removal of any vertex (or by duality, any face) reduces the dimension to 3. Recently, this result and its extension to planar multigraphs was key to resolving the question of the dimension of the adjacency poset of a planar bipartite graph. It also serves to motivate questions about the dimension of posets with planar cover graphs.

Series: Analysis Seminar

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.

Series: ACO Student Seminar

Sum-Product inequalities originated in the early 80's
with the work of Erdos and Szemeredi, who showed that there exists
a constant c such that if A is a set of n integers, n sufficiently
large, then either the sumset A+A = {a+b : a,b in A} or the product
set A.A = {ab : a,b in A}, must exceed n^(1+c) in size. Since that
time the subject has exploded with a vast number of generalizations
and extensions of the basic result, which has led to many
very interesting unsolved problems (that would make great thesis
topics). In this talk I will survey some of the developments in this
fast-growing area.

Series: Other Talks

In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

Series: PDE Seminar

This seminar concerns the analysis of a PDE, invented by J.M. Lasry
and P.L. Lions
whose applications need not concern us.
Notwithstanding, the focus of the application is the behavior of a
free boundary in a diffusion equation which has dynamically evolving,
non--standard sources. Global existence and uniqueness are
established for this system. The work to be discussed represents a
collaborative effort with
Maria del Mar Gonzalez, Maria Pia Gualdani and Inwon Kim.

Series: Geometry Topology Seminar

Not yet!

Monday, August 31, 2009 - 13:00 ,
Location: Skiles 255 ,
Nicola Guglielmi ,
Università di L'Aquila ,
guglielm@univaq.it ,
Organizer: Sung Ha Kang

In this talk I will address the problem of the computation of the jointspectral radius (j.s.r.) of a set of matrices.This tool is useful to determine uniform stability properties of non-autonomous discrete linear systems. After explaining how to extend the spectral radius from a single matrixto a set of matrices and illustrate some applications where such conceptplays an important role I will consider the problem of the computation ofthe j.s.r. and illustrate some possible strategies. A basic tool I willuse to this purpose consists of polytope norms, both real and complex.I will illustrate a possible algorithm for the computation of the j.s.r. ofa family of matrices which is based on the use of these classes of norms.Some examples will be shown to illustrate the behaviour of the algorithm.Finally I will address the problem of the finite computability of the j.s.r.and state some recent results, open problems and conjectures connected withthis issue.

Series: Stochastics Seminar

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