Seminar Abstracts (fall 2010)
Donald Geman, Johns Hopkins University
Projects in Molecular Computational Biology
Abstract: I will talk about several projects in computational biology, including
cancer biomarker discovery and genetic network regulation. There are
two objectives in each case - biological understanding and
translational medicine, meaning bridging the gap between fundamental research and clinical practice. I will argue that rank-based statistics can account for combinatorial interactions among genes and gene products; accommodate variations in data normalization and limited sample sizes; and avoid the "black box" representations and decision rules generated by standard methods in computational learning. This is joint work with many indivduals both here
and at the University of Illinois.
Andrea Bertozzi, UCLA
Geometic Methods in Image Processing
Abstract: The talk will be an overview of geometric methods in image processing developed by my research group. Applications include hyperspectral imaging, image inpainting, pan sharpening, deblurring, and statistical density estimation. Mathematical methods include fast solution of higher order PDEs, methods that combine wavelet based methods with nonlinear geometric models, dictionary based methods, and graph based methods.
Carey Priebe, Johns Hopkins University
Manifold Matching: Joint Optimization of Fidelity and Commensurability
Chi-Kwong Li, College of William and Mary
Quantum operations and completely positive linear maps
Abstract: A brief introduction to quantum information science will be given. Recent results in matrix analysis connected to the subject will be described. Focus will be on the study of quantum operations using the theory of completely positive linear maps on matrix algebras.
Arthur T. Benjamin, Harvey Mudd University
Abstract: Many trigonometric identities, including the Pythagorean theorem, have
combinatorial proofs. Furthermore, some combinatorial problems have
trigonometric solutions. All of these problems can be reduced to
alternating sums, and are attacked by a technique we call D.I.E. (Description, Involution, Exception). This technique offers new insights to identities involving binomial coefficients, Fibonacci numbers, derangements, zig-zag permutations, and Chebyshev polynomials.
Laurent Younes, Johns Hopkins University
A comprehensive statistical model for cell signalling
Abstract: Protein signaling networks play a central role in transcriptional regulation and the etiology of many diseases. We propose a comprehensive statistical model that is anchored to a predefined core topology, has a limited complexity due to parameter sharing and uses micorarray data of mRNA transcripts as the only observable components of signaling. Specifically, we account for cell heterogeneity and a multi-level process, representing signaling as a Bayesian network at the cell level, modeling measurements as ensemble averages at the tissue level and incorporating patient-to-patient differences at the population level. Motivated by the goal of identifying individual protein abnormalities as potential therapeutical targets, we applied our method to the RAS-RAF network using a breast cancer study with 118 patients. We demonstrated rigorous statistical inference, established reproducibility through simulations and the ability to recover receptor status from available microarray data.
Stephan Huckeman, Institut fur Mathematische Stochastik, Gottingen
Shape Inference by Intrinsic Data Descriptors
This research is motivated by the question of understanding the temporal
evolution of leaf shape under growth arising in forest botany. To this
end we view not only Kendall's shape space as a manifold quotient due to
a Lie group action but also its space of geodesics. On that quotient we define a generalization of an extrinsic mean and derive two Central-Limit Theorems: one for the mean geodesic of shapes and one for the mean geodesic of geodesics. A test based on the latter applied to poplar leaf growth endorses the hypothesis of geodesic growth. This could not be found by a classical Procrustes scheme.
Ingo Ruczinski, Johns Hopkins University
Abstract: Logic regression is an adaptive regression methodology that attempts to construct predictors as Boolean combinations of binary covariates. In many regression problems a model is developed that relates the main effects (the predictors or transformations thereof) to the response, while interactions are usually kept simple (two- to three-way interactions at most). Often, especially when all predictors are binary, the interaction between many predictors may be what best explains the differences in response. This issue arises for example in the analysis of SNP data, and in various data mining problems. In the proposed methodology, given a set of binary predictors, we create new predictors such as “X1, X2, X3, and X4 are true,” or “X5 or X6 but not X7 are true”, and embed these Boolean terms into a regression framework. We present the methodology, show some case studies, and discuss statistical issues such as model selection, missing data, variable importance, and study design.
David Jacobs, The University of Maryland
Matching Images with Deformations for Recognition
Abstract: When we match images that come from the same object, we must often allow for 2D, non-linear deformations. I will focus on two pieces of work that address this problem, and briefly summarize other recent approaches that we have taken. First, I will present an approximation algorithm for computing the Earth Mover’s Distance (EMD), a metric for comparing probability distributions that can be used to match image descriptors, accounting for deformations. Using a wavelet-based representation, we construct an accurate, linear time algorithm for computing the EMD. Second, I will describe some preliminary work on building an image manifold that accounts for deformations and lighting variations. Our key novel contribution is to design a metric for intensity changes that assigns lower distances to variations that are typically produced by changes in lighting. I will describe an initial application of this metric to the problem of computing optical flow, and some theoretical results on geodesic paths on the Riemannian image manifold produced by this metric.
Joint work with Anne Jorstad, Sameer Sheorey, and Alain Trouvé
Minh Tang, Johns Hopkins University
Graph metrics and dimension reduction
Abstract: Since the introduction of Isomap and Locally Linear Embedding in 2000, there has been an explosion of interest in techniques for nonlinear dimension reduction. We present a framework that unifies several prominent techniques, notably diffusion maps and Laplacian eigenmaps. Our framework relies on the construction of various Euclidean distances on undirected graphs and the subsequent embedding of these distances in various Euclidean spaces. We also consider how to construct and embed Euclidean distances on directed graphs.
Nam Lee, Johns Hopkins University
Latent Process Models for Time Series of Attributed Random Graphs
Abstract: We introduce a latent process model for time series of attributed random graphs for characterizing multiple modes of association among a collection of actors over time. Two mathematically tractable approximations are derived, and we examine the performance of a class of test statistics for an illustrative change-point detection problem and demonstrate that analysis through approximation can provide valuable information regarding inference properties.
Bruno Jedynak, Johns Hopkins University
The Game of 20 Questions with Noisy Answers
Abstract: We will explore various instances of the game of 20 questions with special interest in the situations where the responses are noisy. After reviewing the potential applications, we will discuss several adaptive as well as non adaptive policies in the context of the method of Dynamic Programming.
This page uses Peter Jipsen and J. Knisley's implementation of LaTeXMathML.If you use Internet Explorer, you can either switch to Firefox, or install the mathPlayer plug-in to see nice mathematical expressions.