Special Analysis Seminar
Abstract: Given a finite positive measure on the real line we would like to know how many exponential functions (say with exponents from -a to a) do we need to be able to approximate every function square summable with respect to this measure. More precisely, we discuss what perturbations of the measure preserve the critical value of a.
Analysis Seminar
Abstract: The harmonic measure distribution function h(r) of a planar domain D specifies the harmonic measure of the part of the boundary of D that lies within distance r of a fixed basepoint in D. It thus relates the geometry of the domain to the behavior of Brownian motion in the domain. We establish sufficient conditions under which these functions h_n for a sequence of domains D_n converge pointwise to the function h for a limiting domain D, at all points of continuity of h. We establish this convergence for a model example. This is joint work with M. Snipes.
Brown University Center for Statistical Sciences Seminar
Refreshments beginning at 3:15pm |
Abstract: Neuroimaging studies often aim to analyze imaging data with complex spatial correlation structures and activation patterns on a two-dimensional (2D) surface or in a 3D volume. The goal of this presentation is to develop a multiscale adaptive regression model (MARM) for spatial and adaptive analysis of neuroimaging data. Compared with the existing voxel-wise approach, MARM has three unique features: being spatial, being hierarchical and being adaptive. MARM creates a small sphere with a given radius at each location (called voxel), analyzes all observations in the sphere of each voxel, and then uses these consecutively-connected spheres across all voxels to capture spatial dependence among imaging observations. MARM builds hierarchically nested spheres by increasing the radius of a spherical neighborhood around each voxel and utilizes information in each of the nested spheres at each voxel. Finally, MARM combines imaging observations with adaptive weights in the voxels within the sphere of the current voxel to adaptively calculate parameter estimates and test statistics. Theoretically, we establish consistency and asymptotic normality of the adaptive estimates and the asymptotic distributions of the adaptive test statistics under some mild conditions. Three sets of simulation studies are used to demonstrate the methodology and examine the finite sample performance of the adaptive estimates and test statistics in MARM. We apply MARM to quantify spatiotemporal white matter maturation patterns in early postnatal populations using diffusion tensor imaging. Our simulation studies and real data analysis confirm that MARM significantly outperforms voxel-wise methods.
Probability Seminar
Abstract: We discuss collateralized debt obligations and tranched pools of credit assets through the lens of large deviations theory. We find that this provides a convenient set of tools for understanding some of the complexities involved in structured financial products.
Center for Vision Research Seminar
Abstract: In an attempt to quell rumors regarding the health of North Korea'sleader Kim Jong-Il, the North Korean government released a series of photographs showing a healthy and active Kim Jong-Il. Shortly after their release the BBC claimed that the photographs were doctored. The article pointed to purported visual incongruities, which were claimed to be the result of photo tampering. The BBC was wrong. Because judgments of photo authenticity are often made by eye, we wondered how reliable the human visual system is in detecting discrepancies that might arise from photo tampering. We describe three experiments that show that the human visual is remarkably inept at detecting simple geometric inconsistencies in shadows, reflections, and planar perspective distortions. We also describe computational methods that can be applied to detect the inconsistencies that seem to elude the human visual system. ____ Hany Farid received his undergraduate degree in Computer Science and Applied Mathematics from the University of Rochester in 1989. He received his Ph.D. in Computer Science from the University of Pennsylvania in 1997. Following a two year post-doctoral position in Brain and Cognitive Sciences at MIT, he joined the Computer Science Department at Dartmouth in 1999. Hany is the William H. Neukom 1964 Distinguished Professor of Computational Science, and the Director of the Neukom Institute for Computational Science. Hany is the recipient of an NSF CAREER award, a Sloan Fellowship and a Guggenheim Fellowship. From working with federal law enforcement agencies on digital forensics, to the digital reconstruction of Ancient Egyptian tombs, Hany works and plays with digital media at the crossroads of computer science, engineering, mathematics, optics, and psychology. http://www.cs.dartmouth.edu/farid/
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract:
Functional approaches to modeling dynamics of biological systems, trends in financial cycle, seasonal measurements of spectral bands in remote sensing, are becoming increasingly popular as a data analysis tool.Clustering and classification is often an important final objective of functional data analysis. But most model based clustering techniques rely on the assumptions of normal or T distributions and as such are not appropriate for clustering functional data, which often lie on non-linear manifolds. In this talk we will present a novel model based clustering techniques for analyzing functional data. Our method is based on the modal clustering methodology developed by Li, Ray and Lindsay (2007), but new visualization, computational and inferential techniques need to be designed especially for functional data. The talk will also focus on parallelization of modal clustering. Application of functional clustering to remote sensing data will also be discussed.
[pizza will be provided]
Joint Lefschetz Center for Dynamical Systems/Mathematics Colloquium
Abstract: The speaker will discuss recent work with A.Its and I.Krasovsky] on the asymptotics of Toeplitz determinants with Fisher hartwig singularities.
Department of Mathematics Colloquium
Abstract: The speaker will discuss recent work with A.Its and I.Krasovsky on the asymptotics of Toeplitz determinants with Fisher hartwig singularities.
Center for Computational Molecular Biology Seminar
Abstract:
Results and current progress of a large-scale case-control genome-wide association study (GWAS) of rheumatoid arthritis (RA) shed further light on this autoimmune disease, and help to frame a broad perspective on mapping complex traits. Genotypes at over 2.5 million common single nucleotide polymorphisms (SNPs) were tested for association with RA in 5539 cases and 20169 controls of European descent. Eleven new RA risk alleles replicate in additional samples. Conditional and haplotype analyses refine the association signal in several loci with evidence for multiple independent effects in autoimmunity. Still, all common variant associations validated to date together explain relatively little of the additive genetic variance for RA, and suggest major contributions of (1) many more common variants of very small effect, (2) copy number or other kinds of variants, (3) rare variants, and/or (4) non-additive genetic, epigenetic or non-genetic effects. A polygenic risk score analysis can allow inference of the remaining effect due to common variants en masse (scenario 1, with some implications for scenarios 2 and 3). The direct benefit of current and future common-variant GWAS is limited under all of these scenarios, but GWAS certainly inform complimentary approaches including deep re-sequencing in case-control cohorts, and integrated clinical/functional and genetic analyses.
Hosted by: Daniel Weinreich
Refreshments will be served at 3:45pm
PDE Seminar
Abstract: In the study of the qualitative aspects of the solutions of the Boltzmann equation in kinetic theory, an invariable step is the use of weighted L^p (convolution) estimates for the collision operator. This applied analysis talk is intended to revisit this topic and show how an essential tool in harmonic analysis, namely, a radial symmetrization lemma, can be used to simplify the existent proofs and provide new results in this direction, giving a better understanding of the constants governing these inequalities. Despite the technicalities of the subject I intent to keep the presentation as simple and accessible as possible. This is a joint program with R. J. Alonso (Rice) and I. M. Gamba (Texas - Austin).