Department of Biostatistics, The University of Texas, MD Anderson Cancer Center | |
Abstract: Many studies yield functional data, with the ideal units of observation curves and observed data sampled on a fine grid. These curves frequently have irregular features requiring spatially adaptive nonparametric representations. We discuss new methods for modeling these data using functional mixed models, which treat the curves as responses and relate them to covariates using nonparametric fixed and random effect functions. This Bayesian wavelet-based approach yields adaptively regularized posterior samples for all model parameters that can be used for any desired Bayesian estimation, inference or prediction. We illustrate this method on 4 applications yielding spiky functional data, and describe how it can be extended to deal with incomplete functional data for which some regions of some of the functions are missing, and to model higher dimensional functional data, e.g. images.
Brown University
The Department of Computer Science Seminar
Tel-Aviv University | |
Refreshments will be served at 1:45 p.m. |
Abstract: Challenging object detection and segmentation tasks can be facilitated by the availability of a reference object. However, accounting for possible transformations between the different object views, as part of the segmentation process, remains difficult. Recent statistical methods address this problem by using comprehensive training data. Other techniques can only accommodate similarity transformations. We suggest a variational approach to prior-based segmentation, using a single reference object, in the presence of planar projective transformations. The proposed algorithm detects the object of interest, extracts its boundaries, and concurrently carries out the registration to the prior shape.
Explicit prior shape information is not always available. Consider the simultaneous segmentation of two object views. When neither of the images contains sufficient information for correct object extraction - none of them can be used as a reliable prior for the other image. We therefore suggest an alternate minimization framework in which the evolving segmentation of each image provides a dynamic prior for the other. We call this process ``mutual segmentation''.
When only a single image is given, but the object taken is known to be symmetrical, the symmetry property forms a significant shape constraint and thus can be used to facilitate segmentation. This task becomes nontrivial when the object undergoes a projective transformation. We introduce a novel method for the extraction of symmetrical object distorted by perspectivity. Information on the symmetry axis of the object and the distorting transformation is recovered, up to well-defined limits, as part of the segmentation process.
Host: Professor Michael Black
Brown Analysis Seminar
Abstract: Random Matrix Theory was developed by physicists to model the energy levels of heavy nuclei. We discuss some of the classical results, and consider an interesting new ensemble, that of Real Symmetric Toeplitz Matrices. Such matrices have far fewer degrees of freedom than the ensemble of all real symmetric matrices, and new behavior is seen: the density of eigenvalues of normalized Real Symmetric matrices is a semi-circle; Real Symmetric Toeplitz matrices are almost a Gaussian. The deviations can be interpreted in terms of obstructions to Diophantine equations. We show that the obstructions vanish if we consider Palindromic Toeplitz matrices (ie, matrices where the first row is also a palindrome). If time permits we will discuss some open problems for related ensembles.
Applied Mathematics Colloquium
ETHZ, Zurich, Switzerland | |
Abstract: We consider the Finite Element (FE) Solution of elliptic problems with spatially inhomogeneous random coefficients of finite second moments.
We address fast, FMM-based computation of a Wiener Chaos expansion of Karhunen Loeve (KL) type in infinitely many random variables for given two-point correlation functions of the data in general domains.
Decay estimates for KL Eigenvalues and for the pointwise convergence of the KL expansions are presented.
We present convergence rates and complexity estimates for a sparse, ANOVA-type discretization of the random solution, parametrized in the first M KL-Variables of the input data, as the number M of stochastic variables tends to infinity as well as the mesh width in the stochastic variable tends to zero respectively the polynomial degree in the stochastic variable tends to \infty.
Numerical experiments in physical dimension 2 and 3 with stochastic dimension M up to 80 are shown.
Joint work with R.A. Todor , P. Frauenfelder and M. Bieri.
Department of Mathematics Special Colloquium
Please Note Change of Day and Time for This Week only |
Abstract: A branched polymer is a connected set of unit balls with nonoverlapping interiors. In 2002, Brydges and Imbrie computed the volume of the space of branched polymers with n balls, in 2 and 3 dimensions. We give a combinatorial proof of their results, and use it to get a finer description of the space of polymers. In particular we show that the diameter of a 3D branched polymer on n disks is of order n^1/2, and give some exact simulations.
<--- 2007 Index