Audio
IAM-PIMS Joint Distinguished Colloquium
Dynamics of Abyssal Ocean Currents
Gordon E. Swaters
University of Alberta
Date: October 7, 2002
Location: UBC
Abstract
The ocean is the regulator of Earth's climate. The world's oceans store an enormous quantity of heat, which is redistributed throughout the world via the currents. Because the density of water is about a thousand times larger than the density of air, the ocean has a substantial inertia associated with it compared to the atmosphere. This implies that it takes an enormous quantity of energy to change an existing ocean circulatory pattern compared to the atmospheric winds. One can think of the ocean as the "memory" and "integrator" of past and evolving climate states.
One can characterize ocean currents into two broad groups. The first are the wind-driven currents. These currents are most intense near the surface of the ocean. Their principal role is to transport warm equatorial waters toward the polar regions. The second group of currents are those that are driven by density contrasts with the surrounding waters. Among these are the deep, or abyssal, currents flowing along or near the bottom of the oceans in narrow bands. Their principal role is to transport cold, dense waters produced in the polar regions toward the equator.
My research group is working toward understanding the dynamics of these abyssal currents. In particular, we have focused on developing innovative mathematical and computational models to describe the evolution, including the transition to instability and interaction with the surrounding ocean and bottom topography, of these currents. The goal of this research is to better understand the temporal variability in the planetary scale dynamics of the ocean climate system. Our work can be seen as "theoretical" in the sense that we attempt to develop new models to elucidate the most important dynamical balances at play and "process-oriented" in the sense that we attempt to use these models to make concrete predictions about the evolution of these flows. As such, our work is a blend of classical applied mathematics, high-performance computational science and physical oceanography.
In this talk, we will attempt to give an overview of our work in this area.
Transition pathways in complex systems: throwing ropes over rough mountain passes, in the dark
David Chandler
University of California
Date: October 28, 2002
Location: UBC
Abstract
This lecture describes the statistical mechanics of trajectory space and examples of what can be learned from it. These examples include numerical algorithms for studying rare but important events in complex systems -- systems where transition states are not initially known, where transition states need not coincide with saddles in a potential energy landscape, and where the number of saddles and other features are too numerous and complicated to enumerate explicitly. This methodology for studying trajectories is called "transition path sampling." Extensive material on this topic can be found at the web site: gold.cchem.berkeley.edu .
Spatial complexity in ecology and evolution
Ulf Dieckmann
The International Institute for Applied Systems Analysis
Date: December 2, 2002
Location: UBC
Abstract
The field of spatial ecology has expanded dramatically in the last few years. This talk gives an overview of the many intriguing phenomena arising from spatial structure in ecological and evolutionary models. While traditional ecological theory sadly fails to account for such phenomena, complex simulation studies offer but limited insight into the inner workings of spatially structured ecological interactions. The talk concludes with a survey of some novel methods for simplifying spatial complexity that offer a promising middle ground between spatially ignorant and spatially explicit approaches.
Turbulence and its Computation
Parviz Moin
Center for Turbulence Research, Stanford University and NASA Ames Research Center
Date: January 13, 2003
Location: UBC
Abstract
Turbulence is a common state of fluid motion in engineering applications and geophysical and astrophysical scales. Prediction of its statistical properties and the ability to control turbulence is of great practical significance. Progress toward a rigorous analytic theory has been prevented by the fact that turbulence is a mixture of high dimensional chaos and order, and turbulent flows possess a wide range of temporal and spatial scales with strong non-linear interactions. With the advent of supercomputers it has become possible to compute some turbulent flows from basic principles. The data generated from these calculations have helped to understand the nature and mechanics of turbulent flows in some detail. Recent examples from large scale computations of turbulent flows and novel numerical experiments used to study turbulence will be presented. These display a wide range in complexity from decaying turbulence in a box to turbulent combustion in a combustor of a real jet engine. The hierarchy of methods for computing turbulent flows and the problem of turbulence closure will be discussed. Recent applications of optimal control theory to turbulence control for drag and noise reduction will be presented.
Fast accurate solution of stiff PDE
Lloyd N. Trefethen
Oxford University Computing Laboratory
Date: March 17, 2003
Location: UBC
Abstract
Many partial differential equations combine higher-order linear terms with lower-order nonlinear terms. Examples include the KdV, Allen-Cahn, Burgers, and Kuramoto-Sivashinsky equations. High accuracy is typically needed because the solutions may be highly sensitive to small perturbations. For simulations in simple geometries, spectral discretization in space is excellent, but what about the time discretization? Too often, second-order methods are used because higher order seems impractical. In fact, fourth-order methods are entirely practical for such problems, and we present a comparison of the competing methods of linearly implicit schemes, split step schemes, integrating factors, "sliders", and ETD or exponential time differencing. In joint work with A-K Kassam we have found that a fourth-order Runge-Kutta scheme known as ETDRK4, developed by Cox and Matthews, performs impressively if its coefficients are stably computed by means of contour integrals in the complex plane. Online examples show that accurate solutions of challenging nonlinear PDE can be computed by a 30-line Matlab code in less than a second of laptop time.
Detached-Eddy Simulation
Philippe R. Spalart
Boeing Corp., Seattle
Date: October 1, 2001
Location: UBC
Abstract
DES is a recent technique, devised to predict separated flows at high Reynolds numbers with a manageable cost, for instance an airplane landing gear or a vehicle. The rationale is that on one hand, Large-Eddy Simulation (LES) is unaffordable in the thin regions of the boundary layer, and on the other hand, Reynolds-Averaged Navier-Stokes (RANS) models seem permanently unable to attain sufficient accuracy in regions of massive separation.
DES contains a single model, typically with one transport equation, which functions as a RANS model in the boundary layer and as a Sub-Grid-Scale model in separated regions, where the simulation becomes an LES. The approach has spread to a number of groups worldwide, and appears quite stable. A range of examples are presented, from flows as simple as a circular cylinder to flows as complex as a fighter airplane beyond stall. The promise and the limitations of the technique are discussed.
Numerical Simulation of Turbulence
Joel H. Ferziger
Stanford University
Date: November 26, 2001
Location: UBC
Abstract
Turbulence is a phenomenon (or rather a set of phenomena) that is difficult to deal with both mathematically and physically because it contains both deterministic and random elements. However, the equations governing its behavior are well known. After a short discussion of the physics of turbulence, we will give a discussion of the approaches used to deal with it and an example of the use of simulation techniques to learn about the physics of turbulence and the development of simple models for engineering use.
Approximation Algorithms and Games on Networks
Eva Tardos
Cornell University
Date: March 11, 2002
Location: UBC
Abstract
In this talk we discuss work at the intersection of algorithms design and game theory. Traditional algorithms design assumes that the problem is described by a single objective function. One of the main current trends of work focuses on approximation algorithm, where computing the exact optimum is too hard. However, there is an additional difficulty in a number of settings. It is natural to consider algorithmic questions where multiple agents each pursue their own selfish interests. We will discuss problems and results that arise from this perspective.
Algorithms and Software for Dynamic Optimization with Application to Chemical Vapor Deposition Processes
Linda Petzold
University of California at Santa Barbara
Date: November 1, 2000
Location: UBC
Abstract
In recent years, as computers and algorithms for simulation have become more efficient and reliable, an increasing amount of attention has focused on the more computationally intensive tasks of sensitivity analysis and optimal control. In this lecture we describe algorithms and software for sensitivity analysis and optimal control of large-scale differential-algebraic systems, focusing on the computational challenges. We introduce a new software package DASPK 3.0 for sensitivity analysis, and discuss our progress to date on the COOPT software and algorithms for optimal control. An application from the chemical vapor deposition growth of a thin film YBCO high-temperature superconductor will be described.
The Mathematics of Reflection Seismology
Gunther Uhlmann
University of Washington
Date: March 6, 2001
Location: UBC
Abstract
Reflection seismology is the principal exploration tool of the oil industry and has many other technical and scientific uses. Reflection seismograms contain enormous amounts of information about the Earth's structure, obscure by complex reflection and refraction effects. Modern mathematical understanding of wave propagation in heterogeneous materials has aided in the unraveling of this complexity. The speaker will outline some advances in the theory of oscillatory integrals which have had immediate practical application in seismology.
Radial Basis Functions - A future way to solve PDEs to spectral accuracy on irregular multidimensional domains?
Bengt Fornberg
University of Colorado
Date: March 27, 2001
Location: UBC
Abstract
It was discovered about 30 years ago that expansions in Radial Basis Functions (RBFs) provide very accurate interpolation of arbitrarily scattered data in any number of spatial dimensions. With both computational cost and coding effort for RBF approximations independent of the number of spatial dimensions, it is not surprising that RBFs have since found use in many applications. Their use as basis functions for the numerical solution of PDEs is however surprisingly novel. In this Colloquium, we will discuss RBF approximations from the perspective of someone interested in pseudospectral (spectral collocation) methods primarily for wave-type equations.
PIMS PDE/Geometry Seminar
Unusual comparison properties of capillary surfaces
Robert Finn
Stanford University
Date: This talk will address a question that was raised about 30 years ago by Mario Miranda, as to whether a given cylindrical capillary tube always raises liquid higher over its section than does a cylinder whose section strictly contains the given one. Depending on the specific shapes, the answer can take unanticipated forms exhibiting nonuniformity and discontinuous reversal in behavior, even in geometrically simple configurations. The presentation will be for the most part complete and self-contained, and is intended to be accessible for a broad mathematical audience.
Location:
Abstract
This talk will address a question that was raised about 30 years ago by Mario Miranda, as to whether a given cylindrical capillary tube always raises liquid higher over its section than does a cylinder whose section strictly contains the given one. Depending on the specific shapes, the answer can take unanticipated forms exhibiting nonuniformity and discontinuous reversal in behavior, even in geometrically simple configurations. The presentation will be for the most part complete and self-contained, and is intended to be accessible for a broad mathematical audience.
String Theory Seminar
D-particles with multipole moments of higher dimensional branes
Mark van Raamsdonk
Stanford University
Date: November 28, 2000
Location: UBC
Abstract
N/A
PIMS-MITACS Seminar on Computational Statistics and Data Mining
A Simple Model for a Complex System: Predicting Travel Times on Freeways
John A. Rice
UC Berkeley
Date: April 26, 2001
Location: UBC
Abstract
A group of researchers from the Departments of EECS, Statistics, and the Institute for Transportation Research at UC Berkeley has been collecting and studying data on traffic flow on freeways in California. I will describe the sources of data and give an overview of the problems being addressed. I will go into some detail on a particular problem-forecasting travel times over a network of freeways. Although the underlying system is very complex and tempting to model, a simple model is surprisingly effective at forecasting.
Some of the work the group is doing appears on these websites:
http://www.dailynews.com/news/articles/0201/20/new01.asp
http://oz.berkeley.edu/~fspe/
http://http.cs.berkeley.edu/~zephyr/freeway/
http://www.its.berkeley.edu/projects/freewaydata/
http://www.path.berkeley.edu/
http://http.cs.berkeley.edu/~pm/RoadWatch/index.html
http://www.path.berkeley.edu/~pettyk/rssearch.html
Robust Factor Model Fitting and Visualization of Stock Market Returns
R. Douglas Martin
University of Washington
Date: January 25, 2001
Location: UBC
Abstract
Stock market returns are often non-Gaussian by virtue of containing outliers. Modeling stock returns and calculating portfolio risk is almost invariably accomplished by fitting a linear model, called a "factor" model in the finance community, using the sanctified method of ordinary least squares (OLS). However, it is well-known that stock returns are often non-Gaussian by virtue of containing outliers, and that OLS estimates are not robust toward outliers. Modern robust regression methods are now available that are not for stock returns using firm size and book-to-market as the factors, where we show that OLS gives a misleading result. Then we show how Trellis graphics displays can be used to obtain quick, penetrating visualization of stock returns factor model data, and to obtain convenient comparisons of OLS and robust factor model fits. Last but not least, we point out that robust factor model fits and Trellis graphics displays are in effect powerful "data mining tools" for better understanding of financial data. Our examples are constructed using a new S-PLUS Robust Methods library and S-PLUS Trellis graphics displays.
PIMS-MITACS Financial Seminar Series
Levy Processes in Financial Modeling
Dilip Madan
University of Maryland
Date: March 9, 2001
Location: UBC
Abstract
We investigate the relative importance of diffusion and jumps in a new jump diffusion model for asset returns. In contrast to the standard modelling of jumps for asset returns, the jump component of our process can display finite or infinite activity, and finite or infinite variation. Empirical investigations of time series indicate that index dynamics are essentially devoid of a diffusion component, while this component may be present in the dynamics of individual stocks. This result leads to the conjecture that the risk-neutral process should be free of a diffusion component for both indices and individual stocks. Empirical investigation of options data tends to confirm this conjecture. We conclude that the statistical and risk-neutral processes for indices and stocks tend to be pure jump processes of infinite activity and finite variation.
PIMS Distinguished Lecture Series
Systems of Nonlinear PDEs arising in economic theory
Ivar Ekeland
Université Paris-Dauphine
Date: March 22, 2002
Location: UBC
Abstract
Testing the foundations of microeconomic theory leads us into a mathematical analysis of systems of nonlinear PDEs. Some of these can be solved in a C^\infty framework by using the classical Darboux theorem and its recent extensions, others require analysticity and more refined tools, such as the Cartan-Kahler theorem. Care will be taken to explain the economic framework and the tools of differential geometry.
Odd embeddings of lens spaces
David Gillman
UCLA
Date: May 31, 2001
Location: UBC
Abstract
N/A
Colliding Black Holes and Gravity Waves: A New Computational Challenge
Douglas N. Arnold
Institute for Mathematics and its Applications
Date: May 16, 2001
Location: UBC
Abstract
An ineluctable, though subtle, consequence of Einstein's theory of general relativity is that relatively accelerating masses generate tiny ripples on the curved surface of spacetime which propagate through the universe at the speed of light. Although such gravity waves have not yet been detected, it is believed that technology is reaching the point where detection is possible, and a massive effort to construct worldwide network of interferometer gravity wave observatories is well underway. They promise to be our first window to the universe outside the electromagnetic spectrum and so, to astrophysicists and others trying to fathom a universe composed primarily of electromagnetically dark matter, the potential payoff is enormous.
If gravitational wave detectors are to succeed as observatories, we must learn to interpret the wave forms which are detected. This requires the numerical simulation of the violent cosmic events, such as black hole collisions, which are the most likely sources of detectable radiation, via the numerical solution of the Einstein field equations. The Einstein equations form a system of ten second order nonlinear partial differential equations in four-dimensional spacetime which, while having a very elegant and fundamental geometric character, are extremely complex. Their numerical solution presents an enormous computational challenge which will require the application of state-of-the-art numerical methods from other areas of computational physics together with new ideas. This talk aims to introduce some of the scientific, mathematical, and computational problems involved in the burgeoning field of numerical relativity, discuss some recent progress, and suggest directions of future research.
Chow Forms and Resultants - old and new
David Eisenbud
Mathematical Science Research Institute (Berkeley)
Date: April 12, 2001
Location: UBC
Abstract
N/A
The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence
Robert L. Devaney
Boston University
Date: October 20, 2000
Location: UBC
Abstract
In this lecture several folk theorems concerning the Mandelbrot set will be described. It will be shown how one can determine the dynamics of the corresponding quadratic maps by visualizing tiny regions in the Mandelbrot set as well as how the size and location of the bulbs in the Mandelbrot set is governed by Farey arithmetic.
A Computational View of Randomness
Avi Wigderson
Hebrew University of Jerusalem
Date:
Location: UBC
Abstract
The current state of knowledge in Computational Complexity Theory suggests two strong empirical "facts" (whose truth are the two major open problems of this field).
1. Some natural computational tasks are infeasible (e.g. it seems so for computing the functions PERMANENT, FACTORING, CLIQUE, SATISFIABILITY ...)
2. Probabilistic algorithms can be much more efficient than deterministic ones. (e.g it seems so for PRIMALITY, VERIFYING IDENTITIES APPROXIMATING VOLUMES...).
As it does with other notions (e.g. knowledge, proof..), Complexity Theory attempts to understand the notion of randomness from a computational standpoint. One major achievement of this study is the following (surprising?) relation between these two "facts" above:
THEOREM: (1) contradicts (2) In words: If ANY "natural" problem is "infeasible", then EVERY probabilistic algorithm can be "efficiently" "derandomized".
I plan to explain the sequence of important ideas, definitions, and techniques developed in the last 20 years that enable a formal statement and proof of such theorems. Many of them, such as the formal notions of "pseudo-random generator", and "computational indistinguishability" are of fundamental interest beyond derandomization; they have far reaching implications on our ability to build efficient cryptographic systems, as well as our inability to efficiently learn natural concepts and effectively prove natural mathematical conjectures (such as (1) above).
Thematic Programme on Inverse Problems and Applications
Reconstructing the Location and Magnitude of Refractive Index Discontinuities from Truncated Phase-Contrast Tomographic Projections
Mark Anastasio
Illinois Institute of Technology
Date: August 4, 2003
Location: UBC
Abstract
Joint work with Daxin Shi, Yin Huang, and Francesco De Carlo. I. INTRODUCTION: In recent years, much effort has been devoted to developing imaging techniques that rely on contrast mechanisms other than absorption. Phase-contrast computed tomography (CT) is one such technique that exploits differences in the real part of the refractive index distribution of an object to form an image using a spatially coherent light source. Of particular interest is the ability of phase-contrast CT to produce useful images of objects that have very similar or identical absorption properties. In applications such as microtomography, it is imperative to reconstruct an image with high resolution. Experimentally, the demand of increased resolution can be achieved by highly collimating the incident light beam and using a microscope optic to focus the transmitted image, formed on a scintillator screen, onto the detector. When the object is larger than the field-of-view (FOV) of the imaging system, the measured phase-contrast projections are necessarily truncated and one is faced with the so-called local CT reconstruction problem. To circumvent the non-local nature of conventional CT, local CT algorithms have been developed that aim to to reconstruct a filtered image that contains detailed information regarding the location of discontinuities in the imaged object. Such information is sufficient for determining the structural composition of an object, which is the primary task in many biological and materials science imaging applications. II. METHODS A. Theory of Local Phase-Contrast Tomography: We have recently demonstrated that the mathematical theory of local CT, which was originally developed for absorption CT, can be applied naturally for understanding the problem of reconstructing the location of image boundaries (i.e., discontinuities) from truncated phase-contrast projections. Our analysis suggested the use of a simple backprojection-only algorithm for reconstructing object discontinuities from truncated phase-contrast projection data that is simpler and more theoretically appropriate than use of the FBP algorithm or use of the exact reconstruction algorithm for phase-contrast CT that was recently proposed by Bronnikov [1]. We demonstrated that the reason why this simple backprojection-only procedure represents an effective local reconstruction algorithm for phase-contrast CT is that the filtering operation that needs to be explicitly applied to the truncated projection data in conventional absorption CT is implicitly applied to the phase-contrast projection data (before they are measured) by the act of paraxial wavefield propagation in the near-field. In this talk, we review the application of local CT reconstruction theory to the phase-contrast imaging problem. Using concepts from microlocal analysis, we describe the features of an object that can be reliably reconstructed from incomplete phase-contrast projection data. In many applications, the magnitude of the refractive index jump across an interface may provide useful information about the object of interest. For the first time, we demonstrate that detailed information regarding the magnitude of refractive index discontinuities can be extracted from the phase-contrast projections. Moreover, we show that these magnitudes can be reliable reconstructed using adaptations of algorithms that were originally developed for absorption local CT. B. Numerical Results: We will present extensive numerical results to corroborate our theoretical assertions. Both simulation data and experimental coherent X-ray projection data acquired at the Advanced Photon Source (APS) at Argonne National Laboratory will be utilized. We will compare the ability of the available approximate and exact reconstruction algorithms to provide images that contain accurate information regarding the location and magnitude of refractive index discontinuities. The stability of the algorithms to data noise and inconsistencies will be reported. In Fig. 1, we show some examples of phase-contrast images reconstructed from noiseless simulation data. III. SUMMARY In this talk, we address the important problem of reconstructing the location and magnitude of refractive index discontinuities in phase-contrast tomography. We theoretically investigate existing and novel reconstruction algorithms for reconstructing such information from truncated phase-contrast tomographic projections and numerically corroborate our findings using simulation and experimental data. IV. REFERENCES [1] A. Bronnikov, "Theory of quantitative phase-contrast computed tomography," Journal of the Optical Society of America (A), vol. 19, pp. 472-480, 2002.
Anna Celler (Inverse Problems and Nuclear Medicine): Medical Imaging Research Group Division of Nuclear Medicine Vancouver Hospital and Health Sciences Centre Single Photon Emission Computed Tomography (SPECT) and Positron Emission Tomography (PET) are two nuclear medicine (NM) imaging techniques that visualize in 3D distributions of radiolabeled tracers inside the human body. Since concentration of the tracer in each location in the body reflects its physiology, these techniques constitute powerful diagnostic tools to investigate organ functions and changes in metabolism caused by disease processes. Currently however, clinical studies image only stationary activity distributions and the analysis of the results remains mainly qualitative. As it is believed that absolute quantitation of the data would greatly enhance diagnostic accuracy of the tests, a lot of research effort is directed towards this goal. Reconstructions that create 3D tomographic images from the data acquired around the patient represent an example of the inverse problem application. In the last years this area has undergone rapid development but still important questions persist. The data are incomplete, noisy and altered by physics phenomena and the acquisition process. This causes the problem to be illposed so that even small changes in the data can produce large effects in the solution. The talk will present basic principles of NM data acquisition and image creation and will relate them to the underlying physics effects. A discussionof the most important factors that limit quantitation and a short overview of the correction methods will follow. Different approaches to dynamic imaging will be presented.
Reconstruction Methods in Optical Tomography and Applications to Brain Imaging
Dr. Simon Arridge
University College London
Date: August 7, 2003
Location: UBC
Abstract
In the first part of this talk I will discuss methods for reconstruction of spatially-varying optical absorbtion and scattering images from measurements of transmitted light through highly scattering media. The problem is posed in terms of non-linear optimisation, based on a forward model of diffusive light propgation, and the principle method is linearisation using the adjoint field method. In the second part I will discuss the particular difficulties involved in imaing the brain. These include: - Accounting for non or weakly scattering regions that do not satisfy the diffusion approximation (the void problem) - Accounting for anisotropic scattering regions - Constructing realistic 3D models of the head shape - Dynamic imaging incorporating temporal regularisation
Fast Hierarchical Algorithms for Tomography
Yoram Bresler
University of Illinois at Urbana-Champaign
Date: August 8, 2003
Location: UBC
Abstract
The reconstruction problem in practical tomographic imaging systems is recovery from samples of either the x-ray transform (set of the line-integral projections) or the Radon transform (set of integrals on hyperplanes) of an unknown object density distribution. The method of choice for tomographic reconstruction is filtered backprojection (FBP), which uses a backprojection step. This step is the computational bottleneck in the technique, with computational requirements of O(N^3) for an NxN pixel image in two dimensions, and at least O(N^4) for an NxNxN voxel image in three dimensions. We present a family of fast hierarchical tomographic backprojection algorithms, which reduce the complexities to O(N^2 log N) and O(N^3 log N), respectively. These algorithms employ a divide-and-conquer strategy in the image domain, and rely on properties of the harmonic decomposition of the Radon transform. For image sizes typical in medical applications or airport baggage security, this results in speedups by a factor of 50 or greater. Such speedups are critical for next-generation real-time imaging systems.
How Medical Science will Benefit from Mathematics of the Inverse Problem
Thomas F. Budinger
Lawrence Berkeley National Laboratory and University of California Berkeley and San Francisco
Date: August 4, 2003
Location: UBC
Abstract
Selection of in-vivo imaging modalities (i.e x-ray, MRI, PET, SPECT, light absorption, fluorescence and luminescence, current source and electrical potential) can be logically approached by evaluating biological parameters relative to the biomedical objective (e.g. cardiac apoptosis vs cardiac stem cell trafficking and vs plaque composition vs plaque surface chemistry). For that evaluation, contrast resolution, of highest importance for modality selection in most cases, is defined as the signal to background for the desired biochemical or physiological parameter. But a particular modality which has exquisite biological potential (e.g. MRI and SPECT for atherosclerosis characterization) might not be deployed in medical science because appropriate algorithms are not available to deal with problems of blurring, variable point spread function, background scatter, detection sensitivity, attenuation and refraction. Trade-offs in technique selection frequently pit contrast resolution against intrinsic instrument resolution (temporal and spatial) and depth or size of the object. For example, imaging vulnerable carotid plaques using a molecular beacon with 5:1 signal to background and with 7 mm resolution in the human neck can be argued as superior to imaging tissue characteristics with 1:3:1 signal to background at 0.5 mm resolution with MRI. Another example is the use of the multidetector CT (helical) due to its relative speed instead of MRI to characterize coronary plaques even though MRI has much better intrinsic contrast mechanisms. The superior speed of modern CT argues for its preferred use. Some old examples of how mathematics of the inverse problem have enabled medical science advances include incorporation of attenuation compensation in SPECT imaging which brought SPECT to a quantitative technique, light transmission and fluorescence emission tomography, iterative reconstruction algorithm for all methods, and incorporation of phase encoding for MRI reconstruction. Current work on new mathematical approaches includes endeavors to improve resolution, improve sampling speed, decrease background and achieve reliable quantitation. Examples are rf exposure reduction in MRI by selective radio frequency pulses requiring low peak power, dose reduction by iterative reconstruction schemes in X-Ray CT, implementation of coded aperture models for emission tomography, 3D and time reversal ultrasound, a multitude of transmission and stimulated emission methods for light wavelength of 400nm to 3 cm, and electrical potential and electric source imaging. Many of these subjects will be discussed at this workshop and all rely on innovations in mathematics applied to the inverse problem.
New Multiscale Thoughts on Limited-Angle Tomography
Emmanuel Candes
California Institute of Technology
Date: August 4, 2003
Location: UBC
Abstract
This talk is concerned with the problem of reconstructing an object from noisy limited-angle tomographic data---a problem which arises in many important medical applications. Here, a central question is to describe which features can be reconstructed accurately from such data and how well, and which features cannot be recovered.
We argue that curvelets, a recently developed multiscale system, may have a great potential in this setting. Conceptually, curvelets are multiscale elements with a useful microlocal structure which makes them especially adapted to limited-angle tomography. We develop a theory of optimal rates of convergence which quantifies that features which are microlocally in the "good" direction can be recovered accurately and which shows that adapted curvelet-biorthogonal decompositions with thresholding can achieve quantitatively optimal rates of convergence. We hope to report on early numerical results.
Computed Imaging for Near-Field Microscopy
P. Scott Carney
University of Illinois at Urbana-Champaign
Date: August 7, 2003
Location: UBC
Abstract
Near-field optics provides a means to observe the electromagnetic field intensity in close proximity to a scattering of radiating sample. Modalities such as near-field scanning optical microscopy (NSOM) and photon scanning tunneling microscopy (PSTM) accomplish these measurements by placing a small probe close to the object (in the "near-zone") and then precision controlling the position. The data are usually plotted as a function probe position and the resulting figure is called an image. These modalities provide a means to circumvent the classical Rayleigh-Abbe resolution limits, providing resolution on scales of a small fraction of a wavelength.
There are a number of problems associated with the interpretation of near-field images. If the probe is slightly displaced from the surface of the object, the image quality degrades dramatically. If the sample is thick, the subsurface features are obscured. The quantitative connection between the measurements and the optical properties of the sample is unknown. To resolve all these problems it is desirable to solve the inverse scattering problem (ISP) for near-field optics. The solution of the ISP provides a means to tomographically image thick samples and assign quantitative meaning to the images. Furthermore, data taken at distances up to one wavelength from the sample may be processed to obtain a focused, or reconstructed image of the sample at subwavelength scales.
Preferred Pitches in Multislice Spiral CT from Periodic Sampling
Adel Faridani
Oregon State University
Date: August 4, 2003
Location: UBC
Abstract
Joint work with Larry Gratton. Applications of sampling theory in tomography include the identification of efficient sampling schemes; a qualitative understanding of some artifacts; numerical analysis of reconstruction methods; and efficient interpolation schemes for non-equidistant sampling. In this talk we present an application of periodic sampling theorems in three-dimensional multisclice helical tomography shedding light on the question of preferred pitches.
Spherical Means and Thermoacoustic Tomography
David Finch
Oregon Stage University
Date: August 6, 2003
Location: UBC
Abstract
In thermoacoustic tomography, impinging radiation causes local heating which generates sound waves. These are measured by transducers, and the problem is to recover the density of emitters. This may be modelled as the recovery of the initial value of the time derivative of the solution of the wave equation from knowledge of the solution on (part of) the boundary of the domain. This talk, in conjunction with the talk by Sarah Patch, will report on recent work by the author, S. Patch and Rakesh on uniqueness and stability and an inversion formula, in odd dimensions, for the special case when measurements are taken on an entire sphere surrounding the object. The well-known relation between spherical means and solutions of the wave equation then implies results on recovery of a function from its spherical means.
Transient Elastography and Supersonic Shear Imaging
Mathias Fink
Laboratoire Ondes et Acoustique ESPCI, Paris
Date: August 6, 2003
Location: UBC
Abstract
Palpation is a standard medical practice which relies on qualitative estimation of the tissue Young's modulus E. In soft tissues the Young's modulus is directly proportional to the shear modulus ó (E = 3ó). It explains the great interest for developing quantitative imaging of the shear modulus distribution map. This can be achieved by observing with NMR or with ultrasound the propagation of low frequency shear waves (between 50 Hz and 500 Hz) in the body. The celerity of these waves is relatively low (between 1 and 10 m/s) and these waves can be produced either by vibrators coupled to the body or by ultrasonic radiation pressure. We have developed an ultra high-rate ultrasonic scanner that can give 10.000 ultrasonic images per second of the body. With such a high frame-rate we can follow in real time the propagation of transient shear waves, and from the spatio-temporal evolution of the displacement fields, we can use inversion algorithm to recover the shear modulus map. New inversion algorithm can be used that are no more limited by diffraction limits. In order to obtain unbiased shear elasticity map, different configurations of shear sources induced by radiation pressure of focused transducer arrays are used. A very interesting configuration that induces quasi plane shear waves will be described. It used a sonic shear source that moves at supersonic velocities, and that is created by using a very peculiar beam forming in the transmit mode. In vitro and in vivo results will be presented that demonstrate the interest of this new transient elastographic technique.
Effects of Target Non-localization on the Contrast of Optical Images: Lessons for Inverse Reconstruction
Amir Gandjabkhche
NIH
Date: August 7, 2003
Location: UBC
Abstract
N/A
A general inversion formula for cone beam CT
Alexander Katsevich
University of Central Florida
Date: August 4, 2003
Location: UBC
Abstract
Given a rather general weight function n, we derive a new cone beam transform inversion formula. The derivation is explicitly based on Grangeat's formula and the classical 3D Radon transform inversion. The new formula is theoretically exact and is represented by a two-dimensional integral. We show that if the source trajectory C is complete (and satisfies two other very mild assumptions), then substituting the simplest uniform weight n gives a convolution-based filtered back-projection algorithm. However, this easy choice is not always optimal from the point of view of practical applications. Uniform weight works well for closed trajectories, but the resulting algorithm does not solve the long object problem if C is not closed. In the latter case one has to use the flexibility in choosing n and find the weight that gives an inversion formula with the desired properties. We show how this can be done for spiral CT. It turns out that the two inversion algorithms for spiral CT proposed earlier by the author are particular cases of the new formula. For general trajectories the choice of weight should be done on a case by case basis.
The Green's Function for the Radiative Transport Equation
Arnold Kim
Stanford University
Date: August 7, 2003
Location: UBC
Abstract
N/A
Reconstruction of conductivities in the plane
Kim Knudsen
Aalborg University
Date: August 5, 2003
Location: UBC
Abstract
Joint work with Jennifer Mueller, Samuli Siltanen and Alex Tamasan. In this talk I will consider the mathematical problem behind Electrical Impedance Tomography, the inverse conductivity problem. The problem is to reconstruct an isotropic conductivity distribution in a body from knowledge of the voltage-to-current map at the boundary of the body. I will discuss the two-dimensional problem and give a reconstruction algorithm, which is direct and mathematically exact. The method is based on the so-called dbar-method of inverse scattering. Both theoretical validation of the algorithm and numerical examples will be given.
Inverse scattering problem with a random potential
Matti Lassas
Rolf Nevanlinna Institute
Date: August 6, 2003
Location: UBC
Abstract
In these talk we consider scattering from random media and the inverse problem for it. As a stereotype of inverse scattering problems, we consider the SchrÎdinger equation $$ (\Delta+q+k^2)u(x,y,k)=\delta_y $$ with a random potential $q(x)$. Also, we discuss shortly the relation of this problem to medical imaging. The potential $q(x)$ is assumed to be a Gaussian random function which covariance function $E(q(x)q(y))$ is smooth outside the diagonal. We show how the realizations of the amplitude of the scattered field $|u_s(x,y,k)|$, averaged over frequency parameter $k>1$, can be used to determine stochastic properties of $q$, in particular the principal symbol of the covariance operator. This corresponds to finding the correlation length function of the random medium. In contrast to applied literature, we approach the problem with methods that do not require approximations. In technical point of view, we analyze the scattering from the random potential by combining methods of harmonic and microlocal analysis with stochastic, in particular with theory of ergodic processes.
Interior Elastodynamics Inverse Problems: Recovery of Shear Wavespeed in Transient Elastography
Dr. Joyce McLaughlin
RPI
Date: August 6, 2003
Location: UBC
Abstract
For this new inverse problem the data is the time and space dependent interior displacement measurements of a propagating elastic wave. The medium is initially at rest with a wave initiated at the boundary or at an interior point by a broad band source. A property of the wave is that it has a propagating front. For this new problem we present well posedness results and an algorithm that recovers shear wavespeed from the time and space dependent position of the propagating wavefront. We target the application from transient elastography where images are created of the shear wavespeed in biological tissue. The goal is to create a medical diagnostic tool where abnormal tissue is identified by its abnormal shear stiffness characteristics. Included in our presentation are images of stiffness changes recovered by our algorithms and using data measured in the laboratory of Mathias Fink.
Reconstructions of Chest Phantoms by the D-Bar Method for Electrical Impedance Tomography
Jennifer Mueller
Colorado State University
Date: August 5, 2003
Location: UBC
Abstract
In this talk a direct (noniterative) reconstruction algorithm for EIT in the two-dimensional geometry is presented. The algorithm is based on the mathematical uniqueness proof by A. Nachman [Ann. of Math. 143 (1996)] for the 2-D inverse conductivity problem. Reconstructions from experimental data collected on a saline-filled tank containing agar heart and lung phantoms are presented, and the results are compared to reconstructions by the NOSER algorithm on the same data.
3D Emission Tomography via Plane Integrals
Frank Natterer
University of Munster
Date: August 8, 2003
Location: UBC
Abstract
In emission tomography one reconstructs the activity distribution of a radioactive tracer in the human body by measuring the activity outside the body using collimated detectors. Usually the collimators single out lines along which the measurements are taken. In a novel design (Solstice camera) weighted plane integrals are measured instead. By a statistical error analysis it can be shown that the Solstice concept is superior to the classical line scan for high resolution, making Solstice attractive for small animal imaging. By a suitable approximation of the weight function we can reduce the reconstruction problem to Marr's two stage algorithm for the 3D Radon transform, leading to an efficient algorithm. In order to account for attenuation we approximate the 3D problem by the 2D attenuated Radon transform which can be inverted by Novikov's algorithm. We show reconstructions from simulated and measured data.
Information Geometry, Alternating Minimizations, and Transmission Tomography
Joseph A. O'Sullivan
Washington University in St. Louis
Date: August 8, 2003
Location: UBC
Abstract
Many medical imaging problems can be formulated as statistical inverse problems to which estimation theoretic methods can be applied. Statistical likelihood functions can be viewed in information-theoretic terms as well. Maximizations of statistical likelihood functions for several image estimation problems, including emission and transmission tomography, can be reformulated as double minimizations of information divergences. Properties of minimizations of I-divergences are studied in information geometry. This more general viewpoint yields new characterizations of algorithms and new algorithms for transmission tomography. These new algorithms are described in detail as are medical imaging applications of transmission tomography in the presence of metal.
Imaging in Clutter
George Papanicolau
Stanford University
Date: August 6, 2003
Location: UBC
Abstract
Array imaging, like synthetic aperture radar, does not produce good reflectivity images when there is clutter, or random scattering inhomogeneities, between the reflectors and the array. Can the blurring effects of clutter be controlled? I will discuss this issue in some detail and show that if bistatic array data is available and if the data is suitably preprocessed to stabilize clutter effects then a good deal can be done to minimize blurring.
Thermoacoustic Tomography - An Inherently 3D Generalized Radon Inversion Problem
Sarah Patch
GE Medical Systems
Date: August 6, 2003
Location: UBC
Abstract
Joint work with D. FINCH, RAKESH. A hybrid imaging technique using RF excitation measures ultrasound (US) data. Cancerous tissue is hypothesized to preferentially absorb RF energy, heating more and expanding faster than surrounding healthy tissue. Pressure waves therefore emanate from cancerous inclusions and are detected by US transducers located on the surface of a sphere surrounding the imaging object. A formula for the contrast function is derived in terms of data measured over the entire imaging surface. Existence and uniqueness for the inverse problem when transducers cover only a hemisphere also hold. However, explicit inversion for this clinically realizable case remains an open problem.
Limited Data Tomography in science and industry
Eric Todd Quinto
Tufts University
Date: August 7, 2003
Location: UBC
Abstract
Tomography has revolutionized diagnostic medicine, scientific testing, and industrial nondestructive evaluation, and some of the most difficult problems involve limited data, in which some data are missing. This talk will describe two practical problems and give the mathematical background. The first problem, in industrial nondestructive evaluation (joint with Perceptics, Inc.), uses limited-angle exterior CT to reconstruct a rocket mockup. The second, in electron microscopy (joint with Sidec Technologies), uses limited angle local CT to reconstruct RNA and a virus.
ECGI : A Noninvasive Imaging Modality for Cardiac Electrophysiology and Arrhythmias
Yoram Rudy
Case Western Reserve
Date: August 4, 2003
Location: UBC
Abstract
N/A
Nonlinear image reconstruction in optical tomography using an iterative Newton-Krylov method
Martin Schweiger
University College London
Date: August 7, 2003
Location: UBC
Abstract
Image reconstruction in optical tomography can be formulated as a nonlinear least squares optimisation problem. This paper describes an inexact regularised Gauss-Newton method to solve the normal equation, based on a projection onto the Krylov subspaces. The Krylov linear solver step addresses the Hessian only in the form of matrix-vector multiplications. We can therefore utilise an implicit definition of the Hessian, which only requires the computation of the Jacobian and the regularisation term. This method avoids the explicit formation of the Hessian matrix which is often intractable in large-scale three-dimensional reconstruction problems. We apply the method to the reconstructions of 3-D test problems in optical tomography, whereby we recover the volume distribution of absorption and scattering coefficients in a heterogeneous highly scattering medium from boundary measurements of infrared light transmission. We show that the Krylov method compares favourably to the explicit calculation of the Hessian both in terms of memory space and computational cost.
Inversion of the Bloch Equation
Meir Shinnar
Rutgers University of Medicine and Dentistry of New Jersey
Date: August 5, 2003
Location: UBC
Abstract
N/A
The Inverse Polynomial Reconstruction Method for Two Dimensional Image Reconstruction
Bernie Shizgal
University of British Columbia
Date: August 8, 2003
Location: UBC
Abstract
N/A
Three-dimensional X-ray imaging with few radiographs
Samuli Siltanen
Gunma University
Date: August 6, 2003
Location: UBC
Abstract
In medical X-ray tomography, three dimensional structure of tissue is reconstructed from a collection of projection images. In many practical imaging situations only a small number of truncated projections is available from a limited range of view. Traditional reconstruction algorithms, such as filtered backprojection (FBP), do not give satisfactory results when applied to such data. Instead of FBP, Bayesian inversion is suggested for reconstruction. In this approach, a priori information is used to compensate for the incomplete information of the measurement data. Examples with in vitro measurements from dental radiology and surgical imaging are presented.
Applications of Diffusion MRI to Electrical Impedance Tomography
David Tuch
MIT
Date: August 5, 2003
Location: UBC
Abstract
Diffusion MRI measures the molecular self-diffusion of the endogeneous water in tissue. In this talk, I will discuss various applications of diffusion MRI to electrical impedance tomography (EIT). In particular, I will discuss (i) how the anisotropy information from diffusion tensor imaging (DTI) can inform the EIT forward model, and (ii) how particular transport conservation principles measured with DTI can provide priors or hard constraints for the EIT inverse problem. I will also discuss some recent work on mapping non-tensorial diffusion using spherical tomographic inversions of the diffusion signal.
Cascade Topology Seminar
The best picture of Poincare's homology sphere
David Gillman
UCLA
Date: November 2, 2002
Location: UBC
Abstract
N/A
Homotopy self-equivalences of 4-manifolds
Ian Hambleton
McMaster University
Date: November 2, 2002
Location: UBC
Abstract
N/A
Skein theory in knot theory and beyond
Vaughan Jones
University of California, Berkeley
Date: November 3, 2002
Location: UBC
Abstract
N/A
New perspectives on self-linking
Dev Sinha
University of Oregon
Date: November 3, 2002
Location: UBC
Abstract
N/A
Topological robotics; topological complexity of projective spaces
Sergey Yuzvinsky
University of Oregon
Date: November 2, 2002
Location: UBC
Abstract
N/A
Thematic Programme on Asymptotic Geometric Analysis
Entropy increases at every step
Shiri Artstein
Tel Aviv University
Date: July 9, 2002
Location: UBC
Abstract
N/A
Convolution Inequalities in Convex Geometry
Keith Ball
University College London
Date: July 4, 2002
Location: UBC
Abstract
The talk presents a new an approach to entropy via a local reverse Brunn-Minkowski inequality. Applications will be presented by other speakers.
Optimal Measure Transportation
Franck Barthe
Université de Marne-la-Vallée
Date: July 9, 2002
Location: UBC
Abstract
N/A
Almost sure weak con- vergence and concentration for the circular ensembles of Dyson
Gordon Blower
Lancaster University
Date: July 12, 2002
Location: UBC
Abstract
N/A
On risk aversion and optimal terminal wealth
Christer Borell
Chalmers University
Date: July 11, 2002
Location: UBC
Abstract
N/A
Density and current interpolation
Yann Brenier
CNRS, Nice
Date: July 12, 2002
Location: UBC
Abstract
We discuss different way of interpolating densities, including the Moser lemma and the Monge-Kantorovich method. Natural extensions to currents interpolation will be addressed.
Asymptotic behaviour of fast diffusion equations
Jose A. Carrillo
Universidad de Granada
Date: July 11, 2002
Location: UBC
Abstract
N/A
Fast Diffusion to self-similarity: complete spectrum, long-time asymptotics and numerology
Jochen Denzler
University of Tennessee
Date: July 11, 2002
Location: UBC
Abstract
N/A
Measure Concentration, Transportation Cost, and Functional Inequalities
Michel Ledoux
University of Toulouse
Date: July 8, 2002
Location: UBC
Abstract
We present a triple description of the concentration of measure phenomenon, geometric (through Brunn-Minkoswki inequalities), measuretheoretic (through transportation cost inequalities) and functional (through logarithmic Sobolev inequalities), and investigate the relationships between these various viewpoints by means of hypercontractive bounds. This expository introduction directed at students and newcomers to the field has been already delivered at the Edinburgh ICMS meeting last April.
Nonlinear diffusion to self-similarity: spreading versus shape via gradient flow
Robert McCann
University of Toronto
Date: July 11, 2002
Location: UBC
Abstract
N/A
Geometric inequalities of hyperbolic type
Vitali Milman
Tel Aviv University
Date: July 10, 2002
Location: UBC
Abstract
N/A
Entropy jumps in the presence of a spectral gap
Assaf Naor
Microsoft Corporation
Date: July 9, 2002
Location: UBC
Abstract
N/A
Free probability and free diffusion
Roland Speicher
Queen's University
Date: July 12, 2002
Location: UBC
Abstract
N/A
Concentration of non-Lipschitz functions and combinatorial applications
Van Vu
University of California at San Diego
Date: July 11, 2002
Location: UBC
Abstract
We survey recent results concerning the concentration of functions with large Lipschitz coeffcients and their applications in combinatorial setting.
Optimal paths related to transport problems
Qinglan Xia
Rice University
Date: July 10, 2002
Location: UBC
Abstract
N/A
(n,d,lambda)-graphs in Extremal Combinatorics
Noga Alon
Tel Aviv University
Date: July 18, 2002
Location: UBC
Abstract
N/A
Sylvester's Question, Convex Bodies, Limit Shape
Imre Barany
University College London
Date: July 19, 2002
Location: UBC
Abstract
N/A
Transportation versus Rearrangement
Franck Barthe
Universite de Marne la Vallee
Date: July 15, 2002
Location: UBC
Abstract
N/A
How to Compute a Norm?
Alexander Barvinok
University of Michigan
Date: July 19, 2002
Location: UBC
Abstract
N/A
Phase Transition for the Biased Random Walk on Percolation Clusters
Noam Berger
University of California, Berkeley
Date: July 17, 2002
Location: UBC
Abstract
N/A
Phase Transition in the Random Partitioning Problem
Christian Borgs
Microsoft Research
Date: July 17, 2002
Location: UBC
Abstract
N/A
New Results on Green's Functions and Spectra for Discrete Schroedinger Operators
Jean Bourgain
Institute for Advanced Study
Date: July 22, 2002
Location: UBC
Abstract
N/A
On Optimal Transportation Theory
Yann Brenier
CNRS
Date: July 15, 2002
Location: UBC
Abstract
N/A
Recent Results in Combinatorial Number Theory
Mei-Chu Chang
University of California, Riverside
Date: July 17, 2002
Location: UBC
Abstract
N/A
Graphical Models of the Internet and the Web
Jennifer Chayes
Microsoft Research
Date: July 17, 2002
Location: UBC
Abstract
N/A
Random Sections and Random Rotations of High Dimensional Convex Bodies
Apostolos Giannopoulos
University of Crete
Date: July 19, 2002
Location: UBC
Abstract
N/A
On the Sections of Product Spaces and Related Topics
Efim Gluskin
Tel Aviv University
Date: July 15, 2002
Location: UBC
Abstract
N/A
The Poisson Cloning Model for Random Graphs with Applications to k-core Problems, Random 2-SAT, and Random Digraphs
Jeong Han Kim
Microsoft Research
Date: July 16, 2002
Location: UBC
Abstract
We will introduce a new model for random graphs, called the Poisson cloning model, in which all degrees are i.i.d. Poisson random variables. After showing how close this model is to the usual random graph model G(n; p), we will prove threshold phenomena of the k-core problem. The kcore problem is the question of when the random graph G(n; p) contains a k-core, where a k-core of a graph is a largest subgraph with minimum degree at least k. This, in particular, improves earlier bounds of Pittel, Spencer & Wormald. The method can be easily generalized to prove similar results for random hypergraphs. If time allows, we will also discuss the scaling window of random 2-SAT and/or the giant (strong) component of random digraphs.
Results and Problems around Borsuk's Conjecture
Gil Kalai
Hebrew University
Date: July 19, 2002
Location: UBC
Abstract
N/A
Random Submatrices of a Given Matrix
Ravindran Kannan
Yale University
Date: July 23, 2002
Location: UBC
Abstract
N/A
The Regularity Lemma for Sparse Graphs
Yoshiharu Kohyakawa
University of San Paulo
Date: July 18, 2002
Location: UBC
Abstract
One of the fundamental tools in asymptotic graph theory is the well-known regularity lemma of Szemereedi. In essence, the regularity lemma tells us that any large graph may be decomposed into a bounded number of quasi-random, induced bipartite graphs. Thus, this lemma is a powerful tool for detecting and making transparent the random-like behaviour of large deterministic graphs. Furthermore, in general, the quasi-random structure that the lemma provides is amenable to deep analysis, and this makes the lemma a very important tool.
The quasi-random bipartite graphs that Szemereedi's lemma uses in its decomposition are certain graphs in which the edges are uniformly distributed. The measure of uniformity is such that this concept becomes trivial for graphs of vanishing density. To manage sparse graphs, one may adjust this notion of uniform edge distribution in a natural way, and it is a routine matter to check that the original proof extends to this notion, provided we restrict ourselves to graphs of vanishing density that do not contain `dense patches'.
However, the quasi-random structure that the lemma reveals in this case is not too informative, and this puts into question the applicability of this variant of the lemma for `sparse graphs'. Nevertheless, there have been some successful applications of the lemma in this context. In this talk, we shall concentrate on the diffculties one faces and how one can overcome them in certain situations.
Algorithmic Applications of Graph Eigenvalues and Related Parameters
Michael Krivelevich
Tel Aviv University
Date: July 23, 2002
Location: UBC
Abstract
N/A
Tiling Problems and Spectral Sets
Izabella Laba
University of British Columbia
Date: July 22, 2002
Location: UBC
Abstract
N/A
Some Estimates of Norms of Random Matrices (non iid case)
Rafal Latala
Warsaw University
Date: July 22, 2002
Location: UBC
Abstract
N/A
Discrete Analytic Functions and Global Information from Local Observation
Laszlo Lovasz
Microsoft Research
Date: July 23, 2002
Location: UBC
Abstract
N/A
Concentration and Random Permutations
Colin McDiarmid
Oxford University
Date: July 15, 2002
Location: UBC
Abstract
N/A
Some phenomena of large dimension in Convex Geometric Analysis
Vitali Milman
Tel Aviv University
Date: July 16, 2002
Location: UBC
Abstract
N/A
Metric Ramsey-Type Phenomena
Assaf Naor
Microsoft Corporation
Date: July 19, 2002
Location: UBC
Abstract
In this talk we will discuss the problem of finding lower bounds for the distortion required to embed certain metric spaces in Hilbert space. We will show that these problems are intimately connected to certain Poincare type inequalities on graph metrics, and we will discuss recent developments which are based on the analysis of the behavior of Markov chains in metric spaces. These new methods allow us to strengthen known results by showing that large subsets of certain natural graphs must be significantly distorted if one wishes to embed them in Hilbert space.
On a Non-symmetric Version of the Khinchine-Kahane Inequality
Krzysztof Oleszkiewicz
Warsaw University
Date: July 16, 2002
Location: UBC
Abstract
N/A
Some Large Dimension Problems of Mathematical Physics
Leonid Pastur
Universitée Pierre & Marie Curie
Date: July 16, 2002
Location: UBC
Abstract
N/A
Crayola and Dice: Graph Colouring via the Probabilistic Method
Bruce Reed
McGill University
Date: July 18, 2002
Location: UBC
Abstract
We survey recent results on graph colouring via the probabilistic method. Tools used are the Local Lemma and Concentration inequalities.
Ramsey Properties of Random Structures
Andrzej Rucinski
Adam Mickiewicz University
Date: July 18, 2002
Location: UBC
Abstract
N/A
Distances between Sections of Convex Bodies
Mark Rudelson
University of Missouri
Date: July 19, 2002
Location: UBC
Abstract
N/A
Probabilistically Checkable Proofs (PCP) and Hardness of Approximation
Shmuel Safra
Tel Aviv University
Date: July 23, 2002
Location: UBC
Abstract
N/A
<2, well embed in l_1^{an}, for any a >1
Gideon Schechtman
The Weizmann Institute
Date: July 19, 2002
Location: UBC
Abstract
I'll discuss a recent result of Johnson and myself a particular case of which is the statement in the title.
Introduction to the Szemeredi Regularity Lemma
Miklos Simonovits
Hungarian Academy of Science
Date: July 18, 2002
Location: UBC
Abstract
N/A
The Percolation Phase Transition on the n-cube
Gordon Slade
University of British Columbia
Date: July 17, 2002
Location: UBC
Abstract
N/A
Zeroes of Random Analytic Functions
Mikhail Sodin
Tel Aviv University
Date: July 22, 2002
Location: UBC
Abstract
N/A
On the Largest Eigenvalue of a Random Subgraph of the Hypercube
Alexander Soshnikov
University of California at Davis
Date: July 22, 2002
Location: UBC
Abstract
N/A
On the Ramsey- and Turan-type Problems
Benjamin Sudakov
Princeton University
Date: July 18, 2002
Location: UBC
Abstract
N/A
On Pseudorandom Matrices
Stanislaw Szarek
Universitée Paris VI
Date: July 22, 2002
Location: UBC
Abstract
N/A
Families of Random Sections of Convex Bodies
Nicole Tomczak-Jaegermann
University of Alberta
Date: July 16, 2002
Location: UBC
Abstract
N/A
Expander Graphs - where Combinatorics and Algebra Compete and Cooperate
Avi Wigderson
Institute for Advanced Studies
Date: July 23, 2002
Location: UBC
Abstract
Expansion of graphs can be given equivalent deFInitions in combinatorial and algebraic terms. This is the most basic connection between combinatorics and algebra illuminated by expanders and the quest to construct them. The talk will survey how fertile this connection has been to both FIelds, focusing on recent results.
There are infinitely many irrational values of the zeta function at the odd integers
Keith Ball
University College London
Date: July 24, 2002
Location: UBC
Abstract
N/A
Applications of zonoids to Asymptotic Geometric Analysis
Yehoram Gordon
Haifa
Date: July 24, 2002
Location: UBC
Abstract
N/A
The Kakeya conjecture (Part 1)
Izabella Laba
University of Britich Columbia
Date: July 25, 2002
Location: UBC
Abstract
N/A
The Kakeya conjecture (Part 2)
Izabella Laba
University of British Columbia
Date: July 25, 2002
Location: UBC
Abstract
N/A
Stability of uniqueness results for convex bodies
Rolf Schneider
Freiburg
Date: July 25, 2002
Location: UBC
Abstract
N/A
Minkowski's existence theorem and some applications
Rolf Schneider
Freiburg
Date: July 24, 2002
Location: UBC
Abstract
N/A
Random Matrices: Gaussian Unitary Ensemble and Beyond (Part 1)
Alexander Soshnikov
Davis
Date: July 24, 2002
Location: UBC
Abstract
N/A
Random Matrices: Gaussian Unitary Ensemble and Beyond (Part 2)
Alexander Soshnikov
Davis
Date: July 25, 2002
Location: UBC
Abstract
N/A
Random Matrices: Gaussian Unitary Ensemble and Beyond (Part 3)
Alexander Soshnikov
Davis
Date: July 26, 2002
Location: UBC
Abstract
N/A
Noncommutative M-structure and the interplay of algebra and norm for operator algebras
David Blecher
Houston
Date: August 6, 2002
Location: UBC
Abstract
We report on a recent joint paper with Smith and Zarikian, following on from work of the author, Effros and Zarikian on noncommutative M-structure. Certain nonlinear but convex equations play a role. We discuss some extensions of these results, and some related ideas.
Operator spaces as `quantized' Banach spaces
Edward Effros
UCLA
Date: August 6, 2002
Location: UBC
Abstract
In the beginning it appeared that linear spaces of operators would have a theory much like that for Banach spaces. This misperception grew out of a series of remarkable discoveries, such as Arveson's version of the Hahn-Banach Theorem, Ruan's axiomatization of the operator spaces, and the theory of projective and injective tensor products. The problems of using Banach space theory as one's sole guide became apparent when one considered such classical notions as local relexivity. Owing to the availability of modern operator algebra theory, researchers have made great strides in understanding the beautiful and unexpected nature of these spaces.
Random Matrices and Magic Squares
Alexander Gamburd
Stanford
Date: August 6, 2002
Location: UBC
Abstract
Characteristic polynomials of random unitary matrices have been intensively studied in recent years: by number theorists in connection with Riemann zeta-function, and by theoretical physicists in connection with Quantum Chaos. In particular, Haake and collaborators have computed the variance of the coeficients of these polynomials and raised the question of computing the higher moments. The answer, obtained in recent joint work with Persi Diaconis, turns out to be intimately related to counting integer stochastic matrices (magic squares).
Free Entropy Dimension and Hyperfinite von Neumann algebras
Kenley Jung
Berkeley
Date: August 7, 2002
Location: UBC
Abstract
I will give a general introduction to Voiculescu's notions of free entropy and free entropy dimension and then discuss what they have in store for the most tractable of von Neumann algebras: those which are hyper nite and have a tracial state.
The central limit procedure for noncommuting random variables and applications
Marius Junge
Urbana
Date:
Location: UBC
Abstract
We investigated the algebra of central limits of a fixed set of random variables in the (commutative and) noncommutative context and matrix valued version thereof. In the noncommutative framework states instead of traces provide new examples of complex gaussian variables such that the real part does no longer commute with the imaginary part. Using this procedure, we may embed the operator Hilbert space (a central object in the theory of operator spaces introduced by Pisier) in a noncommutative L1 space and calculate the operator space analogue of the projection constant of the n-dimensional Hilbert space.
A Good formula for noncommutative cumulants
Franz Lehner
Graz
Date: August 7, 2002
Location: UBC
Abstract
Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants. It turns out that the essential property needed is exchangeability of random variables. This provides a simple unified method to derive the known examples of cumulants, like free cumulants and various q-cumulants, and will hopefully lead to interesting new examples.
Holomorphic functional calculus and square functions on non-commutative $L_p$-spaces
Christian Le Merdy
Besançon
Date: August 7, 2002
Location: UBC
Abstract
N/A
A2-point functions for multi-matrix models, and non-crossing partitions in an annulus
Alexandru Nica
University of Waterloo
Date: August 8, 2002
Location: UBC
Abstract
N/A
Hilbertian Operator spaces with few completely bounded maps
Eric Ricard
Paris 6
Date: August 6, 2002
Location: UBC
Abstract
N/A
Can non-commutative $L^p$ spaces be renormed to be stable?
Haskell Rosenthal
Austin
Date: August 6, 2002
Location: UBC
Abstract
N/A
On Real Operator Spaces
Zhong Jin Ruan
Urbana
Date: August 8, 2002
Location: UBC
Abstract
N/A
The Role of Maximal $L_p$ Bounds in Quantum Information Theory
Mary Beth Ruskai
Lowell
Date: August 7, 2002
Location: UBC
Abstract
N/A
Determinantal Random Point Fields
Alexander Soshnikov
University of California, Davis
Date: August 8, 2002
Location: UBC
Abstract
The purpose of the talk is to give an introduction to determinantal random point fields. Determinantal random point fields appear naturally in random matrix theory, probability theory, quantum mechanics, combinatorics, representation theory and some other areas of mathematics and physics. The first part of the talk will be devoted to some general results (i.e. existence and uniqueness theorem) and examples. In the second part we will concentrate on the CLT type results for the linear statistics and ergodic properties of the translation-invariant determinantal point fields.
Maximization of free entropy
Roland Speicher
Queen's University
Date: August 9, 2002
Location: UBC
Abstract
N/A
On the maximality of subdiagonal algebras
Quanhua Xu
Université de Franche-Comté
Date: August 9, 2002
Location: UBC
Abstract
We consider the open problem on the maximality of subdiagonal algebras posed by Arveson in 1967. We prove that a subdiagonal algebra is maximal if it is invariant under the modular automorphism group of a normal faithful state.
The method of minimal vectors
George Androulakis
University of South Carolina
Date: August 15, 2000
Location: UBC
Abstract
N/A
An introduction to the uniform classification of Banach spaces
Yoav Benyamini
Technion
Date: August 12, 2002
Location: UBC
Abstract
N/A
Baire-1 functions and spreading models
Vassiliki Farmaki
Athens University
Date: August 14, 2002
Location: UBC
Abstract
N/A
Selecting unconditional basic sequences
Tadek Figiel
Polish Academy of Sciences
Date: August 14, 2002
Location: UBC
Abstract
N/A
The Banach envelope of Paley-Wiener type spaces Ep for 0<p<1
Mark Hoffman
University of Missouri
Date: August 14, 2002
Location: UBC
Abstract
N/A
Weak topologies and properties that are fulfilled almost everywhere
Tamara Kuchurenko
University of Missouri
Date: August 12, 2002
Location: UBC
Abstract
N/A
On Frechet differentiability of Lipschitz functions, part I
Joram Lindenstrauss
The Hebrew University of Jerusalem
Date: August 12, 2002
Location: UBC
Abstract
N/A
On Frechet differentiability of Lipschitz functions, part II
Joram Lindenstrauss
The Hebrew University of Jerusalem
Date: August 12, 2002
Location: UBC
Abstract
N/A
The structure of level sets of Lipschitz quotients
Beata Randrianantoanina
Miami University
Date: August 12, 2002
Location: UBC
Abstract
N/A
How many operators do there exist on a Banach space?
Thomas Schlumprecht
Texas A & M University
Date: August 13, 2002
Location: UBC
Abstract
N/A
Lambda_p sets for some orthogonal systems
Lior Tzafriri
The Hebrew University
Date: August 15, 2002
Location: UBC
Abstract
N/A
Sigma shrinking Markushevich bases and Corson compacts
Vaclav Zizler
University of Alberta
Date: August 13, 2002
Location: UBC
Abstract
N/A
Frontiers of Mathematical Physics, Brane-World and Supersymmetry
Physics with Large Extra Dimensions (lecture 1)
Ignatios Antoniadis
CERN
Date: July 24, 2002
Location: UBC
Abstract
N/A
Physics with Large Extra Dimensions (lecture 2)
Ignatios Antoniadis
CERN
Date: July 25, 2002
Location: UBC
Abstract
N/A
Fixing Runaway Moduli
Cliff Burgess
McGill University
Date: July 22, 2002
Location: UBC
Abstract
N/A
Radius-dependent Gauge Coupling Renormalization in AdS5
Kiwoon Choi
KAIST
Date: July 24, 2002
Location: UBC
Abstract
N/A
Gauge Theories of the Symmetric Group in the large N Limit
Alessandro D'Adda
INFN, Torino
Date: July 22, 2002
Location: UBC
Abstract
N/A
Shape versus Volume: Rethinking the Properties of Large Extra Dimensions
Keith Dienes
University of Arizona
Date: August 1, 2002
Location: UBC
Abstract
N/A
Solving the Hierarchy Problem without SUSY or Extra Dimensions: An Alternative Approach
Keith Dienes
University of Arizona
Date: August 2, 2002
Location: UBC
Abstract
N/A
Universal Extra Dimensions
Bogdan Dobrescu
Yale University
Date: July 29, 2002
Location: UBC
Abstract
N/A
Deconstructing Warped Gauge Theory and Unification
Hyung Do Kim
KIAS
Date: July 29, 2002
Location: UBC
Abstract
N/A
Adding Flavour to ADS/CFT
Andreas Karch
University of Washington
Date: July 23, 2002
Location: UBC
Abstract
N/A
Little Higgses
Emanuel Katz
University of Washington
Date: August 2, 2002
Location: UBC
Abstract
N/A
Twisted superspace and Dirac-Kaehler Fermions
Noboru Kawamoto
Hokkaido University
Date: August 2, 2002
Location: UBC
Abstract
N/A
What can neutrino oscillation tell us about the possible existence of an extra dimension?
C.S. Lam
McGill University
Date: July 23, 2002
Location: UBC
Abstract
N/A
Limitation of Cardy-Verlinde Formula on the Holographic Description of Brane Cosmology
Y.S. Myung
Inje University
Date: July 31, 2002
Location: UBC
Abstract
N/A
Instanton effects in 5d Theories and Deconstruction
Erich Poppitz
University of Toronto
Date: July 31, 2002
Location: UBC
Abstract
N/A
A New Non-Commutative Field Theory
Konstantin Savvidis
Perimeter Institute
Date: July 26, 2002
Location: UBC
Abstract
N/A
Conformal Invariant String with Extrinsic Curvature Action
George Savvidy
National Research Center Demokritos
Date: July 31, 2002
Location: UBC
Abstract
N/A
Nonplanar Corrections to PP-wave Strings
Gordon Semenoff
University of British Columbia
Date: August 1, 2002
Location: UBC
Abstract
N/A
Cosmological Constant Problem in Infinite Volume Extra Dimensions: a Possible Solution
Mikhail Shifman
University of Minnesota
Date: July 25, 2002
Location: UBC
Abstract
N/A
Topological Effects in Our Brane World from Extra Dimensions
Mikhail Shifman
University of Minnesota
Date: July 26, 2002
Location: UBC
Abstract
N/A
Brane World Cosmology: From Superstring to Cosmic Strings
Henry Tye
Cornell University
Date: July 30, 2002
Location: UBC
Abstract
N/A
Supersoft Supersymmetry Breaking
Neal Weiner
University of Washington
Date: July 30, 2002
Location: UBC
Abstract
N/A
International Conference on Robust Statistics (ICORS 2002)
Dimension Reduction and Nonparametric Regression: A Robust Combination
Claudia Becker
University of Dortmund
Date: May 16, 2002
Location: UBC
Abstract
In modern statistical analysis, we often aim at determining a functional relationship between some response and a high-dimensional predictor variable. It is well-known that estimating this relationship from the data in a nonparametric setting can fail due to the curse of dimensionality. But a lower dimensional regressor space may be suffcient to describe the relationship of interest.
In the following, we consider the two main steps of a combined procedure in this setting: the dimension reduction step and the step of estimating the functional relation in the reduced space. The occurrence of outliers can disturb this process in several ways. When finding the reduced regressor space, the dimension may be wrongly determined. If the dimension is correctly estimated, the space itself may not be found correctly. As a consequence, it may happen that the functional relationship cannot be found, or an incorrect relation is determined. If both, dimension and space are correctly identified, outliers may still in uence the function estimation. Hence, we aim at constructing robust methods which are able to detect irregularities such as outliers in the data and at the same time can adjust the dimension and estimate the function without being affected by such phenomena.
Robust Inference for the Cox Model
Tadeusz Bednarski
University of Zielona Gora
Date: May 15, 2002
Location: UBC
Abstract
N/A
Robust Estimators in Partly Linear Models
Graciela Boente
University of Buenos Aires
Date: May 14, 2002
Location: UBC
Abstract
N/A
John Tukey and "Troubled" Time Series Data
David Brillinger
University of California, Berkeley
Date: May 13, 2002
Location: UBC
Abstract
On various occasions when discussing time series analysis John Tukey made reference to the use of robust methods. In this talk we will mention those remarks of his that we have found and discuss some other methods as well.
On the Bianco-Yohai Estimator for High Breakdown Logistic Regression
Christophe Croux
University of Leuven
Date:
Location: UBC
Abstract
Bianco and Yohai (1996) proposed a highly robust procedure for estimation of the logistic regression model. The results they obtain were very promising. We complement there study by providing a fast and stable algorithm to compute this estimator. Moreover, we discuss the problem of the existence of the estimator. We make a comparison with other robust estimators by means of a simulation study and examples. A discussion of the breakdown point of robust estimators for the logistic regression model will also be given.
Breakdown and groups
Laurie Davies
University of Essen
Date: May 14, 2002
Location: UBC
Abstract
The concept of breakdown point was introduced by Hodges (1967) and Hampel (1968, 1971) and still plays an important though at times a controversial role in robust statistics. In practice its use is confined to location, scale and linear regression problems and to functionals which have the appropriate equivariance structure. Attempts to extend the concept to other situations have not been successful. In this talk we clarify the role of the group structure in determining the maximal breakdown point of functionals which have the equivariance structure induced by the group. The analysis suggests that if a problem does not have a suficiently rich group of transformations under which it remains invariant then there is no canonical definition of breakdown and the highest possible breakdown point will be 1.
Robust Factor Analysis
Peter Filzmoser
Vienna University of Technology
Date: May 16, 2002
Location: UBC
Abstract
Two robust approaches to factor analysis are presented and compared. The first one uses a robust covariance matrix for estimating the factor loadings and the specific variances. The second one estimates factor loadings, scores and specific variances directly, using the alternating regression technique.
Straight Talks about Robust Methods
Xuming He
University of Illinois at Urbana-Champaign
Date: May 14, 2002
Location: UBC
Abstract
Instead of presenting another research result, I wish to use this opportunity to initiate some discussions on the views and uses of modern robust statistical methods. They will reflect some of the questions and concerns that have been nagging me for years, such as
1. Do we tend to be too demanding when we evaluate a robust procedure?
2. Is computational complexity a major hurdle or is there something more serious?
3. Do asymptotic properties matter?
4. Is the breakdown point a really pessimistic measure of robustness?
5. Should we promote the use of robust methods in exploratory or confirmatory data analysis?
6. Are robust methods needed to handle huge data sets with many variables?
I may argument the discussions with my own consulting experience where awareness of robustness often plays a very positive role. Please join me in examining those issues with an open mind and maybe we will agree to disagree.
Statistical Analysis of Microarray Data from Affymetrix Gene Chips
Karen Kafadar
University of Colorado
Date: May 16, 2002
Location: UBC
Abstract
Data obtained from experiments using Affymetrix gene chips are processed and analyzed using the statistical algorithms provided with the product. The details of the algorithms, including the calculations and parameters, are described in mechanical terms in the Appendices to their user's manual (Affymetrix Microarray Suite User Guide, Version 4.0, 2000). I will describe these details using a statistical framework, compare the algorithm with others that have been proposed (Li and Wong, 2002; Efron et al. 2001), and offer modifications that may provide more robust analyses and thus more insightful interpretations of the data.
Approaches to Robust Multivariate Estimation Based on Projections
Ricardo Maronna
Universidad Nacional de La Plata
Date: May 15, 2002
Location: UBC
Abstract
Projections are a useful tool to construct robust estimates of multivariate location and scatter with interesting theoretical and practical properties. In particular: the estimate proposed by Stahel (1981) and Donoho (1982), which was the first equivariant estimate with a high breakdown for all dimensions; Estimates with a maximum bias independent of the dimension, proposed by Maronna, Stahel and Yohai, (1992) for scatter and by Tyler (1994) for location, also studied by Adrover and Yohai (2002); and two recent fast proposals for high-dimensional data: one by Pea and Prieto (2001) based on the kurtosis of projections, and another by Maronna and Zamar (2002) based on pairwise robust covariances. Results and relatinships among these estimates will be reviewed.
Robust Statistics in Portfolio Optimization
Doug Martin
University of Washington and Insightful
Date: May 15, 2002
Location: UBC
Abstract
In this talk we discuss several applications of robust statistics in portfolio optimization, some of which have been only partially developed or are merely ideas of areas for future work. The primary focal points will be (a) The use of influence functions in connection with optimal portfolio quantities of interest, e.g., global minimum variance and associated mean return, tangency portfolio mean and variance, and Sharpe ratio, and (b) The use of robust covariance matrix and mean vector estimates in Markowitz optimal portfolios, and (c) Robustification of the new conditional valueat- risk (CVaR) portfolio theory due to Rockafellar and Uryasev. A brief tutorial on the CVaR optimality theory will be provided, along with discussion of critical questions related to robustifying this approach.
The Multihalver
Stephan Morgenthaler
École Polytechnique Fédérale de Lausanne
Date: May 13, 2002
Location: UBC
Abstract
N/A
Robust Space Transformations for Distance-based Outlier
Raymond Ng
University of British Columbia
Date: May 17, 2002
Location: UBC
Abstract
In the first part of this talk, we will present the notion of distance-based outliers. This is a nonparametric approach, and is particularly suitable for high dimensional data. We will show a case study based on video trajectory surveillance.
For distance-based outlier detection, there is an underlying multi-dimensional data space in which each tuple/object is represented as a point in the space. We observe that in the presence of variability, correlation, outliers and/or differing scales, we may get unintuitive results if an inappropriate space is used. The fundamental question addressed in the second half of this talk is: "What then is an appropriate space?". We propose using a robust space transformation called the Donoho-Stahel estimator. We will focus on the computation of the transformation.
Multivariate Outlier Detection and Cluster Identification
David Rocke
University of California, Davis
Date: May 13, 2002
Location: UBC
Abstract
We examine relationships between the problem of robust estimation of multivariate location and shape and the problem of maximum likelihood assignment of multivariate data to clusters. Recognition of the connections between estimators for clusters and outliers immediately yields one important result that we demonstrate in this paper; namely, outlier detection procedures can be improved by combining them with cluster identification techniques. Using this combined approach, one can achieve practical breakdown values that approach the theoretical limits. We report computational results that demonstrate the effectiveness of this approach. In addition, we provide a new robust clustering method.
Resistant Parametric and Nonparametric Modelling in Finance
Elvezio Ronchetti
University of Geneva
Date: May 16, 2002
Location: UBC
Abstract
We discuss how resistant parametric and nonparametric techniques can be used in the statistical analysis of financial models. As an illustration we re-examine the empirical evidence concerning one factor models for the short rate process and we focus on the estimation of the drift and the volatility.
Standard classical parametric procedures are highly unstable in this application. On the other hand, robust procedures deal with deviations from the assumptions on the model and are still reliable and reasonably efficient in a neighborhood of the model.
Finally, we show that resistant techniques are necessary also in the nonparametric framework, in particular for reliable bandwidth selection.
This is joint work with Rosario Dell'Aquila and Fabio Trojani, University of Southern Switzerland, Lugano.
Robustness Against Separation and Outliers in Binary Regression
Peter Rousseeuw
University of Antwerp
Date: May 14, 2002
Location: UBC
Abstract
The logistic regression model is commonly used to describe the effect of one or several explanatory variables on a binary response variable. Here we consider an alternative model under which the observed response is strongly related but not equal to the unobservable true response. We call this the hidden logistic regression (HLR) model because the unobservable true responses act as a hidden layer in a neural net. We propose the maximum estimated likelihood method in this model, which is robust against separation unlike all existing methods for logistic regression. We then construct an outlier-robust modification of this estimator, called the weighted maximum estimated likelihood (WEMEL) method, which is robust against both problems.
Estimating the p-values of Robust Tests for the Linear Model
Matias Salibian-Barrera
Carleton University
Date: May 17, 2002
Location: UBC
Abstract
There are several proposals of robust tests for the linear model in the literature (see, for example, Markatou, Stahel and Ronchetti, 1991). The finite-sample distributions of these test statistics are not known and their asymptotic distributions have been studied under the assumption that the scale of the errors is known, or that it can be estimated without affecting the asymptotic behaviour of the tests. This is in general true when the errors have a symmetric distribution.
Bootstrap methods can, in principle, be used to estimate the distribution of these test statistics under less restrictive assumptions. However, robust tests are typically based on robust regression estimates which are computationally demanding, specially with moderate- to high-dimensional data sets. Another problem when bootstrapping potentially contaminated data is that we cannot control the proportion of outliers that might enter the bootstrap samples. This could seriously affect the bootstrap estimates of the distribution of the test statistics, specially in their tails. Hence, the resulting p-value estimates may be critically affected by a relatively small amount of outliers in the original data.
In this paper we propose an extension of the Robust Bootstrap (Salibian-Barrera and Zamar, 2002) to obtain a fast and robust method to estimate p-values of robust tests for the linear model under less restrictive assumptions.
Computational Issues in Robust Statistics
Arnold J. Stromberg
University of Kentucky
Date: May 17, 2002
Location: UBC
Abstract
Hundreds, and perhaps thousands, of papers have been published in the area of robust statistics, yet robust methods are still not used routinely by most applied statisticians. An important reason for this is the many computational issues in robust statistics.
Most applied statisticians agree conceptually that robust methods are a good idea, but they fail to use them for a number of reasons. Often, software is not available. Other times, like in linear regression, there are so many choices, it is not clear which estimator to use. In still other situations, the data sets are too big for robust techniques to handle. This paper discusses these issues and others.
High Breakdown Point Multivariate M-Estimation
David Tyler
Rutgers University
Date: May 17, 2002
Location: UBC
Abstract
In this talk, a general study of the properties of the M-estimates of multivariate location and scatter with auxiliary scale proposed in Tatsuoka and Tyler (2000) is presented. This study provides a unifying treatment for some of the high breakdown point methods develop for multivariate statistics, as well as a unifying framework for comparing these methods. The multivariate M-estimates with auxiliary scale include as special cases the minimum volume ellipsoid estimates [Rousseeuw (1985)], the multivariate S-estimates [Davies (1987)], the multivariate constrained M-estimates [Kent and Tyler (1996)], and the recently introduced multivariate MM-estimates [Tatsuoka and Tyler (2000)]. The results obtained for the multivariate MM-estimates, such as its breakdown point, its influence function and its asymptotic distribution, are entirely new. The breakdown points of the M-estimates of multivariate location and scatter for fixed scale are also derived. This generalizes the results on the breakdown points of the univariate redescending M-estimates of location with fixed scale given by Huber (1984).
Semiparametric Random Effects Models for Longitudinal Data
Jane-Ling Wang
University of California, Davis
Date: May 13, 2002
Location: UBC
Abstract
A class of semiparametric regression models to describe the influence of covariates on a longitudinal (or functional) response is described. The model includes indices, which are linear functions of the covariates, unknown random functions of the indices, and unknown variance functions. They are thus semiparametric random effects models with many parsimonious submodels. The parametric components of the indices are estimated via quasi-score estimating equations, and the unknown smooth random and variance functions are estimated nonparametrically. Consistency of the procedures is obtained, and the procedure is illustrated with fecundity data for 1000 female Mediterranean fruit flies.
Robust, Sequential Design Strategies
Doug Wiens
University of Alberta
Date: May 16, 2002
Location: UBC
Abstract
N/A
High Breakdown Point Robust Regression with Censored Data
Victor Yohai
University of Buenos Aires
Date: May 13, 2002
Location: UBC
Abstract
N/A
Robustness Issues for Confidence Intervals
Julie Zhou
University of Victoria
Date: May 14, 2002
Location: UBC
Abstract
In many inference problems, it is of interest to compute confidence intervals or regions for the parameters of interest in the model under consideration. As with point estimation, it is important to know about the robustness of the confidence intervals. This involves evaluating the performance of the interval in terms of coverage and length in the face of small perturbations of the data or the model. Ideally we would like a procedure which gives efficient intervals and accurate coverage in the neighborhood of the model. In this talk, we will address the issues of robustness for confidence intervals and assess the robustness of some particular intervals. We will propose several measures including empirical influence function, gross-error sensitivity, and finite-sample breakdown point to study the robustness of confidence intervals. Those measures are applied to examine the robustness of unconditional intervals in the regression model for both the regression parameters and the scale and conditional intervals.
Pacific Northwest String Theory Seminar
Non-commutative Space And Chan-Paton Algebra in Open String Field Algebra
Kazuyuki Furuuchi
PIMS, University of British Columbia
Date: 2002
Location: UBC
Abstract
N/A
Adding Flavor to AdS/CFT
Andreas Karch
University of Washington
Date: 2002
Location: UBC
Abstract
N/A
Localized Closed String Tachyons
David Kutasov
University of Chicago
Date: 2002
Location: UBC
Abstract
N/A
Extension of Boundary String Field Theory on Disc and RP2 Worldsheet Geometries
Shin Nakamura
KEK
Date: 2002
Location: UBC
Abstract
N/A
Comments on Vacuum String Field Theory
Kazumi Okuyama
University of Chicago
Date: 2002
Location: UBC
Abstract
N/A
Wilson Loops in N=4 Super Yang-Mills Theory
Jan Plefka
AEI, Potsdam
Date: 2002
Location: UBC
Abstract
N/A
The Hierarchy Unification and the Entropy of de Sitter Space
Lisa Randall
Harvard University
Date: 2002
Location: UBC
Abstract
N/A
Nonperturbative Nonrenormalization in a Non-supersymmetric Nonlocal String Theory
Eva Silverstein
Stanford
Date: 2002
Location: UBC
Abstract
N/A
Index Puzzles in SUSY gauge mechanics
Matthias Staudacher
AEI, Potsdam
Date: 2002
Location: UBC
Abstract
N/A
Quantum Gravity in dS-Space?
Leonard Susskind
Stanford
Date: 2002
Location: UBC
Abstract
N/A
Thematic Programme on Nonlinear Partial Differential Equations
Recent Progress in Complex Geometry - Part 1 (unavailable),
Part 2,
Part 3,
Part 4
Gang Tian
Massachusetts Institute of Technology
Date: August 14-16, 2001
Location: UBC
Abstract
N/A
Geometric Variational Problems -
Part 1,
Part 2,
Part 3,
Part 4
Richard Schoen
Stanford University
Date: August 8-10, 2001
Location: UBC
Abstract
N/A
Variational problems in relativistic quantum mechanics: Dirac-Fock equations -
Part 1,
Part 2,
Part 3,
Part 4
Eric Séré
Université Paris IX
Date: August 2, 4, 7, 2001
Location: UBC
Abstract
N/A
Energy minimizers of the copolymer problem -
Part 1,
Part 2,
Part 3,
Part 4
Yann Brenier
CNRS Nice, on leave from Universite Paris 6
Date: July 30, 31, 2001
Location: UBC
Abstract
N/A
Variational problems related to operators with gaps and applications in relativistic quantum mechanics -
Part 1,
Part 2,
Part 3
Maria Esteban
Université Paris IX
Date: July 30,31 and August 1, 2001
Location: UBC
Abstract
N/A
On De Giorgi's conjecture in dimensions 4 and 5
Nassif Ghoussoub
Pacific Institute for the Mathematical Sciences
Date: August 1, 2001
Location: UBC
Abstract
N/A
Dynamics of Ginsburg-Landau and related equations -
Part 1,
Part 2,
Part 3,
Part 4
Fang Hua Lin
Courant Institute
Date: July 24-27, 2001
Location: UBC
Abstract
N/A
Diffusions, cross-diffusions, and their steady states -
Part 1,
Part 2
Changfeng Gui
University of British Columbia
Date: July 23 - 24, 2001
Location: UBC
Abstract
N/A
Diffusion & Cross Diffusion in Pattern Formation -
Part 1,
Part 2
Wei-Ming Ni
University of Minnesota
Date: July 20-21, 2001
Location: UBC
Abstract
N/A
About the De Giorgi conjecture in dimensions 4 and 5
Changfeng Gui
University of British Columbia
Date:
Location: UBC
Abstract
N/A
Propagation of fronts in excitable media -
Part 1,
Part 2,
Part 3,
Part 4
Henri Berestycki
Université Paris VI
Date: July 12-16, 2001
Location: UBC
Abstract
N/A
Ergodicity, singular perturbations, and homogenization in the HJB equations of stochastic control
Martino Bardi
University of Padua
Date: July 3, 2001
Location: UBC
Abstract
N/A
Fully nonlinear stochastic partial differential equations - Theory and Applications -
Part 1,
Part 2,
Part 3,
Part 4
Panagiotis Souganidis
University of Texas at Austin
Date: July 3 - 4, 2001
Location: UBC
Abstract
N/A
Frontiers of Mathematical Physics, Particles, Fields and Strings
Noncommutative Supersymmetric Tubes
Dongsu Bak
University of Seoul
Date: July 19, 2001
Location: SFU
Abstract
N/A
D-branes on Orbifolds: The Standard Model
Robert Leigh
University of Illinois
Date: July 16, 2001
Location: SFU
Abstract
N/A
Orientifolds, Conifolds and Quantum Deformations
Soonkeon Nam
Kyung Hee University
Date: July 16, 2001
Location: SFU
Abstract
N/A
PIMS-MITACS Workshop on Inverse Problems and Imaging
Sturm-Liouville problems with eigenvalue dependent and independent conditions
Paul Binding
University of Calgary
Date: June 10, 2001
Location: UBC
Abstract
We consider Sturm-Liouville problems with boundary conditions affinely dependent on the eigenvalue parameter. These are classified into three types, one being the standard case where the eigenvalue does not appear explicitly. We exhibit transformations between problems with these different types of boundary condition, preserving all eigenvalues and norming constants, except possibly two. In consequence, we extend some standard inverse Sturm-Liouville results to cases with eigenvalue dependent boundary conditions.
Wavetracing: Ray tracing for the propagation of band-limited signals for traveltime tomography
Kenneth P. Bube
University of Washington
Date:
Location: UBC
Abstract
Many seismic imaging techniques require computing traveltimesand travel paths. Methods to compute raypaths are usually based onhigh frequency approximations. In some situations like head waves,these raypaths minimize traveltime, but are not paths along whichmost of the energy travels. We present an approach to computingraypaths, using a modification of ray bending which we call"wavetracing," that computes raypaths and traveltimes that aremore consistent with the paths and times for the band-limited signalsin real seismic data. Wavetracing shortens the raypath, while stillkeeping the raypath within the Fresnel zone for a characteristicfrequency of the signal. This is joint work with John Washbourneof TomoSeis, Inc.
Synthetic Aperture Radar
Margaret Cheney
Department of Mathematical Sciences
Date: June 10, 2001
Location: UBC
Abstract
In Synthetic Aperture Radar (SAR) imaging, a plane or satellite carrying an antenna flies along a (usually straight) flight track. The antenna emits pulses of electromagnetic radiation; this radiation scatters off the terrain and is received back at the same antenna. These signals are used to produce an image of the terrain. The problem of producing a high-resolution image from SAR data is very similar to problems that arise in geophysics and tomography; techniques from seismology and X-ray tomography are now making their way into the SAR community. This talk will outline a mathematical model for the SAR imaging problem and discuss some of the associated problems.
Optimal Linear resolution and conservation of information
Keith S. Cover
University of British Columbia
Date: June 9, 2001
Location: UBC
Abstract
In linear inverse theory, when trying to estimate a model from data, it is widely advocated in the literature that finding an model which fits the data is the method of choice. However, several common algorithms yield estimates with optimal or near optimal linear resolution that do not fit the data. Prominent examples are the windowed discrete Fourier transform and algorithms following the Backus and Gilbert method. The Backus and Gilbert algorithms are often avoided because uncertainties of how to interpret estimates that do not fit the data. It is shown that algorithms with linear resolution, provided they can be expressed as a matrix multiplication which is invertible, produce an estimate which, along with its resolution functions and noise statistics, is a complete summary of all the models that fit the data. Such estimates also completely conserve the information provided by the data. If the resulting linear resolution of the algorithm is optimal or near optimal such estimates also effectively communicate the inherent nonuniqueness of the solution to an interpreter. This simple but novel theoretical finding will provide a valuable frame work in which to interpret the results of the linear inversion algorithms including those of the Backus and Gilbert type.
Microlocal Analysis and Seismic Inverse Scattering in Anisotropic Elastic Media
Maarten V. de Hoop
Colorado School of Mines
Date: June 9, 2001
Location: UBC
Abstract
N/A
A level set method for shape reconstruction in electromagnetic cross-borehole tomography
Oliver Dorn
UBC
Date: June 9, 2001
Location: UBC
Abstract
In geophysical applications, it is often the case that the shapes of some obstacles in the earth (e.g. pollutant plumes) have to be monitored from electromagnetic data. These problems can be considered as (ill-posed) nonlinear inverse problems, where typically iterative solution techniques and some regularization are required. Starting from some simple initial guess for the shapes, these shapes evolve during the reconstruction process in order to minimize a suitably chosen cost functional. Since the geometries of the hidden objects can be quite complicated and are not known a priori, a solution algorithm has to be able to model changes in the geometries and in the topologies of these objects during the reconstruction process reliably. We have developed a shape reconstruction algorithm which uses a level set representation for modelling the evolving shapes during the reconstructions. The algorithm, as well as the results of various numerical experiments, are discussed in the talk.
Applications of Sampling Theory in Tomography
Adel Faridani
Oregon State University
Date: June 9, 2001
Location: UBC
Abstract
Computed tomography produces images of opaque objects by reconstructing a density function f from measurements of its line integrals. We describe how Shannon Sampling Theory can be utilized to find the minimum number of measurements needed to achieve a desired resolution in the reconstructed image. An error analysis and numerical experiments are presented showing how to achieve high quality images from a minimal amount of data.
Geometric singularities in tomography
David Finch
Oregon State University
Date: June 9, 2001
Location: UBC
Abstract
N/A
Statistical Estimation of the Parameters of a PDE
Colin Fox
University of Auckland
Date: June 10, 2001
Location: UBC
Abstract
Non-invasive imaging remains a difficult problem in those cases where the forward map can only be adequately simulated by solving the appropriate partial-differential equation (PDE) subject to boundary conditions. However, in those problems, the inherent uncertainty in images recovered from actual measurements may be quantified using knowledge of the forward map and the mesurement process. We demonstrate image recovery for the problem of electrical conductivity imaging by sampling the distribution of all possible images and calculating summary statistics. This route to solving inverse problems has a number of advantageous points, including the ability to quantify accuracy of the recovered image, and a straightforward way to include model complexity such as complete descriptions of real electrodes.
Geophysical Inversion in the new millennium
Larry Lines
University of Calgary
Date: June 9, 2001
Location: UBC
Abstract
Geophysicists have been working on solutions to the inverse problem since the dawn of our profession. This presentation is an evaluation of inversion's present state and abbreviates an evaluation given by the authors in the January 2001 issue of Geophysics. Geophysical interpreters currently infer subsurface properties on the basis of observed data sets, such as seismograms or potential field recordings. A rough model of the process that produces the recorded data resides within the interpreter's brain; the interpreter then uses this rough mental model to reconstruct subsurface properties from the observed data. In modern parlance, the inference of subsurface properties from observed data is identified with the solution of a so-called "inverse problem". The currently used geophysical processing techniques can be viewed as attempts to solve the ubiquitous inverse problem: we have geophysical data, we have an abstract model of the process that produces the data, and we seek algorithms that allow us to invert for the model parameters. The theoretical and computational aspects of inverse theory will gain importance as geophysical processing technology continues to evolve. Iterative geophysical inversion is not yet in widespread use in the exploration industry today because the computing resources are barely adequate for the purpose. After all, it is only now that 3-D prestack depth migration has become economically feasible, and the day will surely not be far off when the inversion algorithms described above will come into their own, enabling the geophysicist to invert observations not only for a structure's subsurface geometry, but also for a growing number of detailed physical, chemical, and geological features. The day that such operations become routine will also be the day that geophysical inverse theory has come into its own in both mineral and petroleum exploration. coauthor: Sven Treitel
Approximate Fourier integral wavefield extrapolators for heterogeneous, anisotropic media
Gary Margrave
University of Calgary
Date: June 10, 2001
Location: UBC
Abstract
Seismic imaging uses wavefield data recorded on the earth's surface to construct images of the internal structure. A key part of this process is the extrapolation of wavefield data into the earth's interior. Most commonly, wavefield extrapolation is based on ray theory and incorporates a high-frequency approximation that allows the development of analytic expressions. This leads to computationally efficient imaging algorithms that incorporate both the advantages and the limitations of raytracing. An alternative approach is to perform a plane-wave decomposition of the recorded data and extrapolate each plane wave independently. For homogeneous media, the Fourier transform can be used for the plane-wave decomposition and phase shifts propagate the plane waves. We explore an approximate extension of this concept to heterogeneous media that uses pseudodifferential operator theory. In heterogeneous media, a plane wave does not remain planar as it propagates so there is not a one-to-one correspondence between plane-wave spectra at two different depth levels. A Fourier integral operator that performs the appropriate plane-wave mixing can be developed from pseudo-differential operator theory applied to the variable-coefficient scalar wave equation. We discuss the derivation of the operator and its basic properties. In particular, we demonstrate that the transpose of the operator is also a viable Fourier integral wavefield extrapolator with a first order error that opposes the original operator. Thus a simple symmetric operator, the average of our first extrapolator and its transpose, is more accurate. We show that that our first operator performs a spatially nonstationary phase shift that is simultaneous with the inverse Fourier transformation. The transpose operator also performs a nonstationary phase shift but simultaneously with the forward Fourier transform. We present both numerical experiments and theoretical arguments to characterize our results and discuss their possible extensions. coauthor: Michael LamoureuxDepartment of Mathematics and Statistics, University of Calgary
Simulation studies on Bioelectric and Biomagnetic Reconstruction of Currents on Curved surfaces and in Spherical Volume conductors
Ceon Ramon
University of Washington
Date: June 9, 2001
Location: UBC
Abstract
Reconstruction and resolution enhancement of the current distribution on curved surfaces and in volume conductors from the bioelectric or biomagnetic data is proposed. Applications will be in the reconstruction of current distribution in the heart wall or the localization of the sources in the brain. Our image reconstruction procedure is divided in two steps. First, the bioelectric or biomagnetic inverse problem is solved by use of the weighted pseudo-inverse techniques to reconstruct an initial image of the current distribution on a curved surface or in a volume conductor from a given electric potential or magnetic field profile. The current distribution thus obtained has poor resolution, it can barely resemble the original shape of the current distribution. The second step improves the resolution of the reconstructed image by using the method of alternating projections. The procedure assumes that images can be represented by line-like elements and involves finding the line-like elements based on the initial image and projecting back onto the original solution space. Simulation studies were performed on a set of parallel conductors on the curved surface modeled as set of multiple closely resemble the original shape of the conductors. Simulation studies were also performed for distributed dipolar sources in a spherical volume conductor. Resonation was performed with a 3-D alternating projection technique developed by us. Position of the reconstructed dipoles matched closely with the original dipoles. However, slight error was found in matching the dipolar intensity. Coauthors:Akira Ishimaru - Dept. of Electrical Engineering, University of WashingtonRobert Marks - Dept. of Electrical Engineering, University of WashingtonJoreg Schrieber - Biomagnetics Center, F. S. University, Jena, GermanyJens Haueisen - Biomagnetics Center, F. S. University, Jena, GermanyPaul Schimpf - Dept of Computer Science and Electrical Engineering, Washington State University
Wave equation least-squares Migration/Inversion
Mauricio D. Sacchi
University of Alberta
Date: June 10, 2001
Location: UBC
Abstract
coauthor: Henning KuehlDepartment of Physics, University of AlbertaLeast-squares (LS) migration based on Kirchhoff modeling/migration operators has been proposed in the literature to account for uneven subsurface illumination and to reduce imaging artifacts due to irregularly and/or coarsely sampled seismic wavefields (Nemeth et al., 1999; Duquet et al., 2000). In this presentation we show that least-squares migration can also be used to improve the performance of generalized phase-shift pre-stack Double-Square-Root (DSR) migration. Simulations with complete and incomplete data were used to test the feasibility of the proposed algorithm. In this case, rather than estimating an image of the subsurface by downward propagating wavefields measured at z=0, the image is estimated by solving a linear inverse problem. The solution of this problem requires the specification of two operators: a forward (modeling) operator and its adjoint (migration). The image can be retrieved using the method of conjugate gradients with different regularization schemes. In particular, we have developed a regularization strategy that operates on common angle images. Simulations with complete and incomplete data were used to test the feasibility of the proposed algorithm.
Duquet, B., Marfurt, J.K., and Dellinger, J.A., 2000, Kirchhoff modeling, inversion for reflectivity, and subsurface illumination, Geophysics, 65, 1195-1209. Nemeth, T., Wu, C., and Schuster, G.T., 1999, Least-squares migration of incomplete reflection data, Geophysics, 64, 208-221.
PIMS Pacific Northwest Seminar on String Theory
Tachyon condensation in open string field theory
Washington Taylor
MIT
Date: March 17, 2001
Location: UBC
Abstract
N/A
Holographic renormalization
Kostas Skenderis
Priceton University
Date: March 17, 2001
Location: UBC
Abstract
N/A
String theoretic mechanisms for spacetime singularity resolution
Amanda Peet
University of Toronto
Date: March 17, 2001
Location: UBC
Abstract
N/A
D-branes as noncommutative solitons: an algebraic approach
Emil Martinec
University of Chicago
Date: March 17, 2001
Location: UBC
Abstract
N/A
Strings in AdS_3 and the SL(2,R) WZW model
Hiroshi Ooguri
Caltech
Date: March 17, 2001
Location: UBC
Abstract
N/A
Thematic Programme on Graph Theory and Combinatorial Optimization
Random Homomorphisms
Peter Winkler
Bell Labs
Date: July 20, 2000
Location: SFU
Abstract
Let H be a fixed small graph, possibly with loops, and let G be a (possibly infinite) graph. Let f be chosen from the set Hom(G,H) of all homomorphisms from G to H.
If H is Kn, f is a proper coloring of G if H consists of two adjacent vertices one of which is looped, f is (in effect) an independent set in G These and other H give rise to "hard constraint" models of interest in statistical mechanics. One way to phrase the physicists' key question is: when G is infinite, is there a canonical way to pick f uniformly at random?
When G is a Cayley tree, f can be generated by a branching random walks on H and using this approach, we are able to characterize the H for which Hom(G,H) always has a unique "nice" probability distribution. We will sketch the proof but spend equal time illustrating the bizarre things that can happen when H is not so well behaved.
Reference: Graham R. Brightwell and Peter Winkler, Graph homomorphisms and phase transitions, J. Comb. Theory Series B (1999) 221--262.
Acyclic coloring, strong coloring, list coloring and graph embedding
Noga Alon
Tel Aviv University
Date: July 19, 2000
Location: SFU
Abstract
I will discuss various coloring problems and the relations among them. A representative example is the conjecture, studied in a joint paper with Sudakov and Zaks, that the edges of any simple graph with maximum degree d can be colored by at most d+2 colors with no pair of adjacent edges of the same color and no 2-colored cycle.
A three-color theorem for some graphs evenly embedded on orientable surfaces
Joan Hutchinson
Macalester College
Date: July 19, 2000
Location: SFU
Abstract
The easiest planar graph coloring theorem states that a graph in the plane can be 2-colored if and only if every face is bounded by an even number of edges; call such a graph "evenly embedded." What is the chromatic number of evenly embedded graphs on other surfaces? Three, provided the surface is orientable and the graph is embedded with all noncontractible cycles sufficiently long. We give a new proof of this result, using a theorem from Robertson-Seymour graph minors work and a technique of Hutchinson, Richter, and Seymour in a proof of a related 4-color theorem for Eulerian triangulations.
Colourings and orientations of graphs
Adrian Bondy
Université Claude Bernard
Date: July 18, 2000
Location: SFU
Abstract
To each proper colouring c:V -> {1,2,...,k} of the vertices of a graph G, there corresponds a canonical orientation of the edges of G, edge uv being oriented from u to v if and only if c(u) > c(v). This simple link between colourings and orientations is but the tip of the iceberg. The ties between the two notions are far more profound and remarkable than are suggested by the above observation. The aim of this talk is to describe some of these connections.
Integral polyhedra related to even-cycle and even-cut matroids
Bertrand Guenin
University of Waterloo
Date: July 11, 2000
Location: SFU
Abstract
N/A
Amalgamations of Graphs - Lecture 1, Part 1,
Part 2, Lecture 2,
Part 1,
Part 2
Chris Rodger
University of Auburn
Date: June 19 - June 30, 2000
Location: SFU
Abstract
N/A
TBA - Lecture 1 Part 1,
Part 2,
Lecture 2
Ron Gould
Emory University
Date: June 19 - June 30, 2000
Location: SFU
Abstract
N/A
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