| Institute for Mathematics and its Applications University of Minnesota 400 Lind Hall 207 Church Street SE Minneapolis, MN 55455 |
| 9:00am-10:30am | Other attendees speak | Lind Hall 305 | ND6.20-7.1.11 | |
| 10:30am-11:00am | Break | 4th floor Lind | ND6.20-7.1.11 | |
| 11:00am-12:30pm | Plus open problems | Lind Hall 305 | ND6.20-7.1.11 | |
| 2:30pm-3:00pm | Coffee break | Lind Hall 400 |
| All Day | Independence Day. The IMA is closed. |
| 8:30am-9:00am | Registration and coffee | Keller Hall 3-176 | SW7.13-16.11 | |
| 8:30am-9:00am | Registration and coffee | Keller Hall 3-176 | SWb7.13-16.11 | |
| 9:00am-9:15am | Welcome; Introductions | Fadil Santosa (University of Minnesota) | Keller Hall 3-176 | SW7.13-16.11 |
| 9:00am-9:15am | Welcome; Introductions | Fadil Santosa (University of Minnesota) | Keller Hall 3-176 | SWb7.13-16.11 |
| 9:15am-10:30am | Project Descriptions/Formation of Breakout Groups | Keller Hall 2-172 | SWb7.13-16.11 | |
| 9:15am-10:15am | Why Wavelets? | Keller Hall 2-170 | SW7.13-16.11 | |
| 10:15am-10:30am | Break | Keller Hall 3-176 | SW7.13-16.11 | |
| 10:30am-11:45am | Individual Group Work | Keller Hall 2-172 | SWb7.13-16.11 | |
| 10:30am-11:45am | Digital Images | Keller Hall 2-170 | SW7.13-16.11 | |
| 11:45am-1:30pm | Lunch | SW7.13-16.11 | ||
| 11:45am-1:30pm | Lunch | SWb7.13-16.11 | ||
| 1:30pm-2:45pm | Individual Group Work | Keller Hall 2-172 | SWb7.13-16.11 | |
| 1:30pm-2:45pm | The Haar Wavelet Transformation (HWT) | Keller Hall 2-170 | SW7.13-16.11 | |
| 2:45pm-3:00pm | Break | Keller Hall 3-176 | SW7.13-16.11 | |
| 2:45pm-3:00pm | Break | Keller Hall 3-176 | SWb7.13-16.11 | |
| 3:00pm-4:15pm | Individual Group Work | Keller Hall 2-172 | SWb7.13-16.11 | |
| 3:00pm-4:15pm | Coding the HWT, Edge Detection Application | Keller Hall 2-170 | SW7.13-16.11 | |
| 4:15pm-4:30pm | Group photo | SW7.13-16.11 | ||
| 4:15pm-4:30pm | Group photo | SWb7.13-16.11 |
| 8:30am-9:00am | Coffee | Keller Hall 3-176 | SW7.13-16.11 | |
| 8:30am-9:00am | Coffee | Keller Hall 3-176 | SWb7.13-16.11 | |
| 9:00am-10:15am | Individual Group Work | Keller Hall 2-172 | SWb7.13-16.11 | |
| 9:00am-10:15am | Cumulative Energy, Entropy, and PSNR | Keller Hall 2-170 | SW7.13-16.11 | |
| 10:15am-10:30am | Break | Keller Hall 3-176 | SW7.13-16.11 | |
| 10:15am-10:30am | Break | Keller Hall 3-176 | SWb7.13-16.11 | |
| 10:30am-11:45am | Individual Group Work | Keller Hall 2-172 | SWb7.13-16.11 | |
| 10:30am-11:45am | Huffman Coding | Keller Hall 2-170 | SW7.13-16.11 | |
| 11:45am-1:15pm | Lunch | SW7.13-16.11 | ||
| 11:45am-1:15pm | Lunch | SWb7.13-16.11 | ||
| 1:15pm-2:30pm | Status Report from All Groups | Keller Hall 2-172 | SWb7.13-16.11 | |
| 1:15pm-2:30pm | Putting It All Together: Image Compression | Keller Hall 2-170 | SW7.13-16.11 | |
| 2:30pm-2:45pm | Break | Keller Hall 3-176 | SW7.13-16.11 | |
| 2:30pm-2:45pm | Break | Keller Hall 3-176 | SWb7.13-16.11 | |
| 2:45pm-4:00pm | Individual Group Work | Keller Hall 2-172 | SWb7.13-16.11 | |
| 2:45pm-4:00pm | Daubechies Wavelet Transformations | Keller Hall 2-170 | SW7.13-16.11 | |
| 5:00pm-10:30pm | Dinner Excursion | SWb7.13-16.11 | ||
| 5:00pm-10:30pm | Dinner Excursion | TBA | SW7.13-16.11 |
| 8:30am-9:00am | Coffee | Keller Hall 3-176 | SW7.13-16.11 | |
| 8:30am-9:00am | Coffee | Keller Hall 3-176 | SWb7.13-16.11 | |
| 9:00am-10:15am | Individual Group Work | Keller Hall 2-172 | SWb7.13-16.11 | |
| 9:00am-10:15am | Fourier Series and Filter Construction | Keller Hall 2-170 | SW7.13-16.11 | |
| 10:15am-10:30am | Break | Keller Hall 3-176 | SW7.13-16.11 | |
| 10:15am-10:30am | Break | Keller Hall 3-176 | SWb7.13-16.11 | |
| 10:30am-11:45am | Individual Group Work | Keller Hall 2-172 | SWb7.13-16.11 | |
| 10:30am-11:45am | Biorthogonal Wavelet Filters | Keller Hall 2-170 | SW7.13-16.11 | |
| 11:45am-1:30pm | Lunch | SW7.13-16.11 | ||
| 11:45am-1:30pm | Lunch | SWb7.13-16.11 | ||
| 1:30pm-5:00pm | Excursion: TBA | TBA | SW7.13-16.11 | |
| 1:30pm-5:00pm | Excursion: TBA | SWb7.13-16.11 |
| 8:30am-9:00am | Coffee | Keller Hall 3-176 | SW7.13-16.11 | |
| 8:30am-9:00am | Coffee | Keller Hall 3-176 | SWb7.13-16.11 | |
| 9:00am-10:15am | Presentations to Introductory Workshop Participants | Keller Hall 3-180 | SWb7.13-16.11 | |
| 9:00am-10:15am | Presentations from Projects Workshop Participants | Keller Hall 3-180 | SW7.13-16.11 | |
| 10:15am-10:30am | Break | Keller Hall 3-176 | SW7.13-16.11 | |
| 10:15am-11:30am | Break | Keller Hall 3-176 | SWb7.13-16.11 | |
| 10:30am-11:45am | Presentations to Introductory Workshop Participants | Keller Hall 3-180 | SWb7.13-16.11 | |
| 10:30am-11:45am | Presentations from Projects Workshop Participants | Keller Hall 3-180 | SW7.13-16.11 |
| Why Wavelets? | |
| Abstract: TBA | |
| Stefan E. Atev (ViTAL Images, Inc.) | Team 1: Geometric and appearance modeling of vascular structures in CT and MR |
Abstract: Project Description:
Accurate vessel segmentation is required in many clinical applications, such as identifying the degree of stenosis (narrowing) of a vessel to assess if blood flow to an organ is sufficient, quantification of plaque buildup (to determine the risk of stroke, for example), and in detecting aneurisms which pose severe risks if ruptured. Proximity to bone can pose segmentation challenges due to the similar appearance of bone and contrasted vessels in CT (Figure 1 – the internal carotid has to cross the skull base); other challenges are posed by low X-ray dose images, and pathology such as stenosis and calcifications.
A typical segmentation consists of a centerline that tracks the length of the vessel, lumen surface and vessel wall surface. Since for performance reasons most clinical applications use only local vessel models for detection, tracking and segmentation, in the presence of noise the results can become physiologically unrealistic – for example in the figure above, the diameter of the lumen and wall cross-sections vary too rapidly.
The goal of this project is to design a method for refining a vessel segmentation based on the following general approach:
The project will use real clinical data and many different types of vessels. References:
Optimization, Statistics and Estimation, Differential Equations and Geometry. MATLAB programming. Keywords: Vessel segmentation, shape statistics, appearance models |
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| Thomas Grandine (Boeing) | Team 2: Modeling aircraft hoses and flexible conduits |
Abstract: Project Description:
Modern commercial airplanes are assembled out of millions of different parts. While many of these parts are rigid, many of them are not. For example, the hydraulic lines and flexible electrical conduits that supply an airplane's landing gear change their shape as the landing gear goes through its motion (you can see some of these lines in the accompanying photograph). These shapes can be modeled by minimizing the potential energy of the rest state of one of these flexible lines as the ends of the lines are moved by the landing gear. While this problem is amenable to solution through direct optimization of individual finite elements, the method often proves to be slow and unreliable. In this investigation, we will explore the use of variational methods (i.e. the calculus of variations) in an attempt to discover a more elegant and robust approach to modeling these flexible airplane parts. Reference: Any textbook on the calculus of variations. My favorite is The Variational Principles of Mechanics, by Cornelius Lanczos. Keywords: Geometrical modeling, calculus of variations, boundary value problems Prerequisites: Calculus of variations, optimization, numerical methods for ODEs and 2-point boundary value problems, Matlab |
|
| Sanjiv Kumar (Google Inc.) | Team 3: Fast nearest neighbor search in massive high-dimensional sparse data sets |
Abstract: Project Description:
Driven by rapid advances in many fields including Biology, Finance and Web Services, applications involving millions or even billions of data items such as documents, user records, reviews, images or videos are not that uncommon. Given a query from a user, fast and accurate retrieval of relevant items from such massive data sets is of critical importance. Each item in a data set is typically represented by a feature vector, possibly in a very high dimensional space. Moreover, such a vector tends to be sparse for many applications. For instance, text documents are encoded as a word frequency vector. Similarly, images and videos are commonly represented as sparse histograms of a large number of visual features. Many techniques have been proposed in the past for fast nearest neighbor search. Most of these can be divided in two paradigms: Specialized data structures (e.g., trees), and hashing (representing each item as a compact code). Tree-based methods scale poorly with dimensionality, typically reducing to worst case linear search. Hashing based methods are popular for large-scale search but learning accurate and fast hashes for high-dimensional sparse data is still an open question. In this project, we aim to focus on fast approximate nearest neighbor search in massive databases by converting each item as a binary code. Locality Sensitive Hashing (LSH) is one of the most prominent methods that uses randomized projections to generate simple hash functions. However, LSH usually requires long codes for good performance. The main challenge of this project is how to learn appropriate hash functions that take input data distribution into consideration. This will lead to more compact codes, thus reducing the storage and computational needs significantly. The project will focus on understanding and implementing a few state-of-the-art hashing methods, developing the formulation for learning data-dependent hash functions assuming a known data density, and experimenting with medium to large scale datasets. Keywords: Approximate Nearest Neighbor (ANN) search, Hashing, LSH, Sparse data, High-dimensional hashing References: For a quick overview of ANN search, review the following tutorials (more references are given at the end of the tutorials):
- Good computing skills (Matlab or C/C++) - Strong background in optimization, linear algebra and calculus - Machine learning and computational geometry background preferred but not necessary |
|
| Apo Sezginer (KLA - Tencor) | Team 4: Diffraction by photomasks |
Abstract: Project Description:
A PC sold in 2010 had billions of transistors with 32 nm gate-length. In a few years, that dimension will become 22 nm. Light is essential to fabrication and quality control of such small semiconductor devices. Integrated circuits are manufactured by repeatedly depositing a film of material and etching a pattern in the deposited film. The pattern is formed by a process called photo lithography, Greek for writing on stone with light. Lithography optically projects a pattern that is present on a photomask, a master copy, using light of 193 nm wavelength, on to a silicon wafer on which the integrated circuits will be formed. Writing 22 nm patterns using 193 nm wavelength is challenging and takes massive amount of calculation. The pattern on the photomask is different from the pattern printed on the wafer, and it is obtained by solving an inverse problem. Reducing the wavelength simplifies the mathematical problem but introduces physical challenges. Extreme ultraviolet light (close to soft x-rays, 13.5 nm wavelength) lithography is being developed but 193 nm light will remain the work horse for many years. A photomask is manufactured by electron-beam lithography and optically inspected, again using a wavelength that is larger than the features that are inspected. The image of the photomask formed in the inspection microscope can be significantly different from the pattern on the photomask. Determining whether the photomask is correctly written requires calculating the expected inspection image in real-time. Both lithography and inspection use partial coherence imaging, which means the photomask is illuminated from many directions by spatially coherent time-harmonic plane-waves that are temporally incoherent with each other. Accurately simulating partial coherent imaging requires solving Maxwell’s equations for many plane-waves incident from different directions. Approximate methods such as Born approximation are not applicable because photomask materials are strong scatterers. Rigorous lithography simulators comprising Mawell’s Equations solvers3 are used to study at most a micron-by-micron portion of a circuit. Simulating an entire photomask in that manner would take millions of years using a supercomputer. Fast approximations due to Kirchhoff1 and Hopkins2 are used to handle an entire chip or photomask. These approximations have been extended to include edge diffraction4. An approach called domain decomposition (different than the domain decomposition method in PDEs) estimates the diffracted near-field as a collage of easier-to-solve diffracted fields5. Kirchhoff+Hopkins approximation and some of its extensions provide an estimate of the diffracted near-field in O(n) operations for n field points at the exit plane of the photomask. O(n) methods ignore multiple scattering which leads to waveguide effects, and Wood’s anomalies. As we move deeper into the sub-wavelength domain, no O(n) method remains accurate, and no method that is more rigorous moves into the reach of computers as the computation complexity grows in proportion to the speed of computers. The goal of this project is to improve the accuracy of fast partial coherence image computation. References:
Keywords: Diffraction, Computational Lithography, Partial Coherence Imaging Prerequisites: Basic optics, electromagnetics, computational methods for wave equations |
|
| Chai Wah Wu (IBM) | Team 5: Optimizing power generation and delivery in smart electrical grids |
Abstract: Project Description:
In the next generation electrical grid, or "smart grid", there will be many heterogeneous power generators, power storage devices and power consumers. This will include residential customers who traditionally are only part of the ecosystem as consumers, but will in the foreseeable future increasingly provide renewable energy generation through photovoltaics and wind energy and provide energy storage through plug-in hybrid vehicles. What makes this electrical grid "smart" is the capability to insert a vast number of sensors and actuators into the system. This allows a wide variety of information about all the constituents to be collected and various aspects of the electrical grid to be controlled via advanced electric meters, smart appliances, etc. Information gathered consists of e.g. amount of energy use, planned energy consumption, efficiency and status of equipment, energy generation costs, etc and this information is then used by all constituents to optimize certain objectives. This necessitates communication and information technology to transmit and process this information. The goal of this project is to focus on the optimization of local objectives in a smart grid. In particular, we study various centralized and decentralized optimization algorithms to determine the optimal matching and maintain stability between energy producers, energy storage, and energy consumers all connected in a complex and dynamic network. Technical prerequisites: scripting languages (Matlab, python), optimization, linear and nonlinear programming. Preferred but not necessary: graph theory, combinatorics, computer programming, experience with CPLEX, R. |
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| Bruce Atwood | Beloit College | 7/12/2011 - 7/16/2011 |
| Nusret Balci | University of Minnesota | 9/1/2009 - 8/31/2011 |
| Brett Barwick | University of South Carolina | 7/24/2011 - 7/30/2011 |
| Daniel J. Bates | Colorado State University | 7/24/2011 - 7/30/2011 |
| Peter W. Bates | Michigan State University | 6/19/2011 - 7/1/2011 |
| Catherine Beneteau | University of South Florida | 7/12/2011 - 7/16/2011 |
| John Burke | Boston University | 6/19/2011 - 7/1/2011 |
| Marta Canadell Cano | University of Barcelona | 6/18/2011 - 7/1/2011 |
| Fatih Celiker | Wayne State University | 7/24/2011 - 7/31/2011 |
| Aycil Cesmelioglu | University of Minnesota | 9/30/2010 - 8/30/2012 |
| Chi Hin Chan | University of Minnesota | 9/1/2009 - 8/31/2011 |
| Soumyadeep Chatterjee | University of Minnesota | 7/13/2011 - 7/16/2011 |
| David Cook II | University of Kentucky | 7/24/2011 - 7/30/2011 |
| Jintao Cui | University of Minnesota | 8/31/2010 - 8/30/2012 |
| Rafael de la Llave | University of Texas at Austin | 6/19/2011 - 7/3/2011 |
| Adrian Delgado | University of Texas | 7/12/2011 - 7/16/2011 |
| Oliver R. Diaz-Espinosa | Duke University | 6/19/2011 - 7/1/2011 |
| David Eisenbud | Mathematical Sciences Research Institute | 7/24/2011 - 7/30/2011 |
| Mohamed Sami ElBialy | University of Toledo | 6/19/2011 - 7/2/2011 |
| Daniel Erman | University of Michigan | 7/24/2011 - 7/30/2011 |
| Randy H. Ewoldt | University of Minnesota | 9/1/2009 - 8/31/2011 |
| Oscar E. Fernandez | University of Michigan | 8/31/2010 - 8/30/2011 |
| Florian Geiß | Universität des Saarlandes | 7/24/2011 - 7/30/2011 |
| Daniel R. Grayson | University of Illinois at Urbana-Champaign | 7/24/2011 - 7/30/2011 |
| Alexander Grigo | University of Toronto | 6/19/2011 - 7/1/2011 |
| Elizabeth Gross | University of Illinois | 7/24/2011 - 7/30/2011 |
| Caroline Haddad | College at Geneseo, SUNY | 7/12/2011 - 7/16/2011 |
| Àlex Haro Provinciale | University of Barcelona | 6/18/2011 - 7/1/2011 |
| Gurgen (Greg) Hayrapetyan | Michigan State University | 6/19/2011 - 7/1/2011 |
| Franziska Babette Hinkelmann | Virginia Polytechnic Institute and State University | 7/24/2011 - 7/30/2011 |
| Yulia Hristova | University of Minnesota | 9/1/2010 - 8/31/2012 |
| Gemma Huguet | Centre de Recerca Matemàtica | 6/19/2011 - 7/1/2011 |
| Anders Nedergaard Jensen | Aarhus University | 7/24/2011 - 7/30/2011 |
| Christine Jost | University of Stockholm | 7/24/2011 - 7/30/2011 |
| Vishesh Karwa | Pennsylvania State University | 7/24/2011 - 7/30/2011 |
| Changho Keem | Seoul National University | 7/24/2011 - 7/30/2011 |
| Kimberly D. Kendricks | Central State University | 6/5/2011 - 7/6/2011 |
| Gabor Kiss | University of Exeter | 6/19/2011 - 7/1/2011 |
| Helmut Knaust | University of Texas | 7/12/2011 - 7/16/2011 |
| Pawel Konieczny | University of Minnesota | 9/1/2009 - 8/31/2011 |
| Robert Krone | Georgia Institute of Technology | 7/24/2011 - 7/30/2011 |
| Angela Kunoth | Universität Paderborn | 7/23/2011 - 9/12/2011 |
| Guang-Tsai Lei | GTG Research | 6/19/2011 - 7/1/2011 |
| Anton Leykin | Georgia Institute of Technology | 7/24/2011 - 7/30/2011 |
| Hengguang Li | University of Minnesota | 8/16/2010 - 8/15/2011 |
| Ji Li | Brigham Young University | 6/19/2011 - 7/1/2011 |
| Zeng Lian | New York University | 6/19/2011 - 7/2/2011 |
| Yu Liang | Michigan State University | 6/19/2011 - 7/2/2011 |
| Zhi (George) Lin | University of Minnesota | 9/1/2009 - 8/31/2011 |
| Zhiwu Lin | Georgia Institute of Technology | 6/19/2011 - 7/1/2011 |
| Martin Wen-Yu Lo | National Aeronautics and Space Administration (NASA) | 6/19/2011 - 7/1/2011 |
| Nan Lu | Georgia Institute of Technology | 6/19/2011 - 7/1/2011 |
| Kara Lee Maki | University of Minnesota | 9/1/2009 - 8/31/2011 |
| Yu (David) Mao | University of Minnesota | 8/31/2010 - 8/30/2012 |
| Abraham Martin del Campo | Texas A & M University | 7/24/2011 - 7/30/2011 |
| John Conrad Merkel III | Oglethorpe University | 7/12/2011 - 7/17/2011 |
| Dimitrios Mitsotakis | University of Minnesota | 10/27/2010 - 8/31/2012 |
| Jose-Maria Mondelo | Autonomous University of Barcelona | 6/18/2011 - 7/1/2011 |
| W. Frank Moore | Cornell University | 7/24/2011 - 7/30/2011 |
| Charles Howard Morgan Jr. | Lock Haven University | 6/19/2011 - 7/1/2011 |
| Benson Muite | University of Michigan | 6/19/2011 - 7/1/2011 |
| David Murrugarra Tomairo | Virginia Polytechnic Institute and State University | 7/24/2011 - 7/30/2011 |
| Zubin Olikara | University of Colorado | 6/19/2011 - 7/1/2011 |
| Eduardo Ortiz | University of Puerto Rico | 7/12/2011 - 7/16/2011 |
| Cecilia Ortiz-Duenas | University of Minnesota | 9/1/2009 - 8/31/2011 |
| Bruce B. Peckham | University of Minnesota | 6/19/2011 - 7/1/2011 |
| Nikola Petrov | University of Oklahoma | 6/20/2011 - 7/2/2011 |
| Sonja Petrović | University of Illinois | 7/24/2011 - 7/30/2011 |
| Tuoc Van Phan | University of Tennessee | 6/19/2011 - 7/1/2011 |
| Weifeng (Frederick) Qiu | University of Minnesota | 8/31/2010 - 8/30/2012 |
| Claudiu Raicu | University of California, Berkeley | 7/24/2011 - 7/30/2011 |
| Ajaykumar Rajasekharan | Seagate Technology | 7/13/2011 - 7/16/2011 |
| Narayanan Ramakrishnan | Seagate Technology | 7/13/2011 - 7/16/2011 |
| David Ruch | Metropolitan State College of Denver | 7/12/2011 - 7/17/2011 |
| Julio Cesar Salazar Ospina | École Polytechnique de Montréal | 6/19/2011 - 7/2/2011 |
| Fadil Santosa | University of Minnesota | 7/1/2008 - 8/30/2011 |
| Stephen Schecter | North Carolina State University | 6/28/2011 - 7/1/2011 |
| George R Sell | University of Minnesota | 6/20/2011 - 7/1/2011 |
| Shuanglin Shao | University of Minnesota | 9/1/2009 - 8/31/2011 |
| Gregory G. Smith | Queen's University | 7/24/2011 - 7/30/2011 |
| Bart Snapp | Ohio State University | 7/24/2011 - 7/30/2011 |
| Dumitru Stamate | University of Bucharest | 7/24/2011 - 7/30/2011 |
| Milena Stanislavova | University of Kansas | 6/19/2011 - 7/1/2011 |
| Michael E. Stillman | Cornell University | 7/24/2011 - 7/30/2011 |
| Stephen Sturgeon | University of Kentucky | 7/24/2011 - 7/30/2011 |
| Seth Sullivant | Harvard University | 7/24/2011 - 7/29/2011 |
| Kaisa Taipale | St. Olaf College | 7/25/2011 - 7/29/2011 |
| Zach Teitler | Boise State University | 7/24/2011 - 7/30/2011 |
| Dimitar Trenev | University of Minnesota | 9/1/2009 - 8/31/2011 |
| Patrick Van Fleet | University of St. Thomas | 7/13/2011 - 7/16/2011 |
| Jan Verschelde | University of Illinois | 7/24/2011 - 7/30/2011 |
| Rachel Weir | Allegheny College | 7/12/2011 - 7/17/2011 |
| Gwyneth Whieldon | Cornell University | 7/24/2011 - 7/30/2011 |
| Alexander Wurm | Western New England College | 6/19/2011 - 7/1/2011 |
| Zhifu Xie | Virginia State University | 6/19/2011 - 7/1/2011 |
| Josephine Yu | Massachusetts Institute of Technology | 7/24/2011 - 7/30/2011 |
| Ganghua Yuan | Northeast (Dongbei) Normal University | 4/27/2011 - 7/27/2011 |
| YI Zhang | University of Minnesota | 7/25/2011 - 7/29/2011 |