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IMA Newsletter #418

August 2011

IMA Events

PI Summer Graduate Program

Summer Program for Graduate Students: Topological Methods in Complex Systems

July 25 - August 12, 2011

Organizers: Robert Ghrist (University of Pennsylvania), Robert MacPherson (Institute for Advanced Study), Konstantin Mischaikow (Rutgers University)

Mathematical Modeling in Industry XV — A Workshop for Graduate Students

August 3-12, 2011

Organizers: Richard J. Braun (University of Delaware), Gilad Lerman (University of Minnesota Twin Cities)
Schedule

Wednesday, August 3

All Day Workshop Outline: Posing of problems by the 6 industry mentors. Half-hour introductory talks in the morning followed by a welcoming lunch. In the afternoon, the teams work with the mentors. The goal at the end of the day is to get the students to start working on the projects. MM8.3-12.11
9:00am-9:30am Coffee and RegistrationKeller Hall 3-176 MM8.3-12.11
9:30am-9:40am Welcome to the IMAFadil Santosa (University of Minnesota)Keller Hall 3-180 MM8.3-12.11
9:40am-10:00am Team 1: Geometric and appearance modeling of vascular structures in CT and MRStefan E. Atev (ViTAL Images, Inc.)Keller Hall 3-180 MM8.3-12.11
10:00am-10:20am Team 2: Modeling aircraft hoses and flexible conduitsThomas Grandine (Boeing)Keller Hall 3-180 MM8.3-12.11
10:20am-10:40am Team 3: Fast nearest neighbor search in massive high-dimensional sparse data setsSanjiv Kumar (Google Inc.)Keller Hall 3-180 MM8.3-12.11
10:40am-11:00am BreakKeller Hall 3-176 MM8.3-12.11
11:00am-11:20am Team 4: Diffraction by photomasksApo Sezginer (KLA - Tencor)Keller Hall 3-180 MM8.3-12.11
11:20am-11:40am Team 5: Optimizing power generation and delivery in smart electrical gridsChai Wah Wu (IBM)Keller Hall 3-180 MM8.3-12.11
11:45am-1:30pm LunchLind Hall 400 MM8.3-12.11
1:30pm-4:30pm
Afternoon - start work on projects
Team 1- 4-125A Mechanical Engineering
Team 2- 401 Lind Hall
Team 3- 305 Lind Hall
Team 4- 340 Lind Hall
Team 5- 321 Mechanical Engineering
MM8.3-12.11

Thursday, August 4

All Day
Students work on the projects. Mentors guide their groups through the modeling process, leading discussion sessions, suggesting references, and assigning work.
Team 1- 4-125A Mechanical Engineering
Team 2- 401 Lind Hall
Team 3- 305 Lind Hall
Team 4- 340 Lind Hall
Team 5- 321 Mechanical Engineering
MM8.3-12.11

Friday, August 5

All Day
Students work on the projects. Mentors available for consultation.
Team 1- 4-125A Mechanical Engineering
Team 2- 401 Lind Hall
Team 3- 305 Lind Hall
Team 4- 340 Lind Hall
Team 5- 321 Mechanical Engineering
MM8.3-12.11

Saturday, August 6

All Day
Students work on the projects.
Team 1- 4-125A Mechanical Engineering
Team 2- 401 Lind Hall
Team 3- 305 Lind Hall
Team 4- 340 Lind Hall
Team 5- 321 Mechanical Engineering
MM8.3-12.11

Sunday, August 7

All Day
Students work on the projects.
Team 1- 4-125A Mechanical Engineering
Team 2- 401 Lind Hall
Team 3- 305 Lind Hall
Team 4- 340 Lind Hall
Team 5- 321 Mechanical Engineering
MM8.3-12.11

Monday, August 8

9:00am-9:30am CoffeeKeller Hall 3-176 MM8.3-12.11
9:30am-9:50am Team 4 progress reportKeller Hall 3-180 MM8.3-12.11
9:50am-10:10am Team 2 progress reportKeller Hall 3-180 MM8.3-12.11
10:10am-10:30am Team 5 progress reportKeller Hall 3-180 MM8.3-12.11
10:30am-11:00am Break MM8.3-12.11
11:00am-11:20am Team 1 progress reportKeller Hall 3-180 MM8.3-12.11
11:20am-11:40am Team 3 progress reportKeller Hall 3-180 MM8.3-12.11
12:00pm-1:30pm Picnic at Lind Hall court yard area MM8.3-12.11
2:00pm-5:00pm
Students work on the projects. Mentors available for consultation.
Team 1- 4-125A Mechanical Engineering
Team 2- 401 Lind Hall
Team 3- 305 Lind Hall
Team 4- 340 Lind Hall
Team 5- 321 Mechanical Engineering
MM8.3-12.11

Tuesday, August 9

All Day
Students work on the projects. Mentors available for consultation.
Team 1- 4-125A Mechanical Engineering
Team 2- 401 Lind Hall
Team 3- 305 Lind Hall
Team 4- 340 Lind Hall
Team 5- 321 Mechanical Engineering
MM8.3-12.11

Wednesday, August 10

All Day
Students work on the projects. Mentors available for consultation.
Team 1- 4-125A Mechanical Engineering
Team 2- 401 Lind Hall
Team 3- 305 Lind Hall
Team 4- 340 Lind Hall
Team 5- 321 Mechanical Engineering
MM8.3-12.11

Thursday, August 11

All Day
Students work on the projects. Mentors available for consultation.
Team 1- 4-125A Mechanical Engineering
Team 2- 401 Lind Hall
Team 3- 305 Lind Hall
Team 4- 340 Lind Hall
Team 5- 321 Mechanical Engineering
MM8.3-12.11

Friday, August 12

8:30am-9:00am CoffeeKeller Hall 3-176 MM8.3-12.11
9:00am-9:30am Team 3 final reportKeller Hall 3-180 MM8.3-12.11
9:30am-10:00am Team 1 final reportKeller Hall 3-180 MM8.3-12.11
10:00am-10:30am Team 4 final reportKeller Hall 3-180 MM8.3-12.11
10:30am-11:00am Break MM8.3-12.11
11:00am-11:30am Team 5 final reportKeller Hall 3-180 MM8.3-12.11
11:30am-12:00pm Team 2 final reportKeller Hall 3-180 MM8.3-12.11
12:00pm-1:30pm Pizza party MM8.3-12.11
Abstracts
Stefan E. Atev (ViTAL Images, Inc.) Team 1: Geometric and appearance modeling of vascular structures in CT and MR
Abstract: Project Description:



Figure 1. Segmentation of the internal carotid artery (left). Vessel tree with the common, internal and external carotid arteries (right).


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.



Figure 2. Cross section of vessel segmentation from CT data, shown with straightened centerline.

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.


Figure 3. Vessel represented as a centerline with periodically sampled cross-sections in the planes orthogonal to the centerline. Note that some planes intersect, which makes this representation problematic. The in-plane cross-sections of the vessel are shown on the right.

The goal of this project is to design a method for refining a vessel segmentation based on the following general approach:
  1. Choose an appropriate geometric representations for vessel segmentation (e.g., generalized cylinders) and derive the equations and methods necessary to manipulate it as required and to convert to and from the representation. One common, but sometimes problematic representation is shown in Figure 3.

  2. Learn a geometric model for vessels based on the representation from a set of training data (for example segmentations obtained from low-noise clinical images). Example model parameters:

    • - Relative rate of vessel diameter change as a function of centerline curvature

      - Typical wall thickness as a function of lumen cross-section area

  3. Learn an appearance model for the vessels that captures details about how vessels appear in a clinical imaging modality such as CT. For example:

    • - Radial lumen intensity profile in Hounsfeld units

      - Rate of intensity change along the centerline

  4. Compute the most likely vessel representation given a starting segmentation and the learned geometric and appearance models.

The project will use real clinical data and many different types of vessels.

References:
  1. C. Kirbas and F. Quek. “A review of vessel extraction techniques and algorithms”. ACM Computing Surveys, vol. 36, pp. 81–121, 2000.

  2. T. McInerney and D. Terzopoulos. “Deformable models in medical image analysis: A survey”. Medical Image Analysis, vol. 1, pp. 91 – 108, 1996.
Prerequisites:
Optimization, Statistics and Estimation, Differential Equations and Geometry. MATLAB programming.

Keywords:
Vessel segmentation, shape statistics, appearance models
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):
  1. http://www.sanjivk.com/EECS6898/ApproxNearestNeighbors_1.pdf
  2. http://www.sanjivk.com/EECS6898/ApproxNearestNeighbors_2.pdf
Prerequisites:
- 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 year, that dimension will shrink to 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. An optical image of a photomask is projected on to a silicon wafer on which the integrated circuits will be formed. Presently, 193 nm wavelength deep UV light is used to project the image. Photomasks are inspected for defects by deep UV microscopy, which is subject to the same resolution limit as lithography. Manufacturing next generation integrated circuits and inspecting their photomasks require higher-resolution imaging. The leading candidate for next generation lithography, EUV (extreme ultraviolet) lithography uses 13.5 nm wavelength. At that wavelength, no material is highly reflective or transparent. The photomask and mirrors of the projector are coated with a multi-layer Bragg reflector to achieve sufficient reflectance. The photomask has a patterned absorber film over the Bragg reflector. The thickness of the absorber and the lateral dimensions of the mask pattern are on the order of four EUV wavelengths. Rapid yet accurate simulation of EUV image formation is essential to optimizing the photomask pattern and interpreting the images of an inspection microscope. This project concerns the key step of image simulation, which is calculating the diffracted near-field of the EUV photomask.

References:
  1. G. Kirchhoff, Vorlesungen uber Mathematiche Physik, Zweiter Band, Mathematiche Optik, Leipzig, Druck und Verlag, 1891, also books.google.com, p 80 states the Kirchhoff approximation.

  2. H. H. Hopkins, “On the diffraction theory of optical images,” Proc. Roy. SOC. London, Ser. A 217, pp. 408-432, 1953.

  3. C. A. Mack, Inside PROLITH: A Comprehensive Guide to Optical Lithography Simulation, FINLE Technologies (Austin, TX: 1997).

  4. K. Adam, A. R. Neureuther, “Domain decomposition methods for the rapid electromagnetic simulation of photomask scattering,” Journal of Micro/Nanolithography, MEMS, and MOEMS, Vol. 1, No. 3, p. 253-269, 2002, SPIE, Bellingham, WA.

  5. P. Evanschitzky, F. Shao, A. Erdmann, “Simulation of larger mask areas using the waveguide method with fast decomposition technique”, Proc. SPIE Vol. 6730, 2007, SPIE, Bellingham, WA.

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.
Visitors in Residence
Baha Alzalg Washington State University 8/2/2011 - 8/12/2011
Brendan P.W. Ames University of Minnesota 8/31/2011 - 8/30/2012
Catalina Anghel University of Toronto 8/2/2011 - 8/14/2011
Stefan E. Atev ViTAL Images, Inc. 8/3/2011 - 8/12/2011
Qichuan Bai Pennsylvania State University 8/2/2011 - 8/12/2011
Nusret Balci University of Minnesota 9/1/2009 - 8/31/2011
Jorge Humberto Banuelos Macalester College 8/2/2011 - 8/12/2011
Richard J. Braun University of Delaware 8/2/2011 - 8/8/2011
Luca Capogna University of Arkansas 8/15/2011 - 6/10/2012
Aycil Cesmelioglu University of Minnesota 9/30/2010 - 8/30/2012
Chi Hin Chan University of Minnesota 9/1/2009 - 8/31/2011
Weitao Chen Ohio State University 8/2/2011 - 8/12/2011
Paolo Codenotti University of Minnesota 8/31/2011 - 8/30/2012
Miles Crosskey Duke University 8/2/2011 - 8/13/2011
Jintao Cui University of Minnesota 8/31/2010 - 8/30/2012
Randy H. Ewoldt Massachusetts Institute of Technology 9/1/2009 - 8/15/2011
Brittan Farmer University of Michigan 8/2/2011 - 8/12/2011
Oscar E. Fernandez University of Michigan 8/31/2010 - 8/22/2011
Eric Thomas Foxall University of Victoria 8/2/2011 - 8/12/2011
Xing (Margaret) Fu Stanford University 8/2/2011 - 8/12/2011
Wenying Gan University of California, Los Angeles 8/2/2011 - 8/13/2011
Thomas Grandine Boeing 8/2/2011 - 8/13/2011
Ke Han Pennsylvania State University 8/2/2011 - 8/12/2011
Yulia Hristova University of Minnesota 9/1/2010 - 8/31/2012
Huiyi Hu University of California, Los Angeles 8/2/2011 - 8/13/2011
Boqiang Huang Universität Paderborn 8/24/2011 - 9/10/2011
Qing Huang Arizona State University 8/2/2011 - 8/12/2011
Jens Christian Jorgensen New York University 8/2/2011 - 8/12/2011
Sunnie Joshi Texas A & M University 8/2/2011 - 8/12/2011
Eunkyung Ko Mississippi State University 8/2/2011 - 8/12/2011
Pawel Konieczny University of Minnesota 9/1/2009 - 8/31/2011
Sanjiv Kumar Google Inc. 8/2/2011 - 8/12/2011
Angela Kunoth Universität Paderborn 7/23/2011 - 9/12/2011
Rosemonde Lareau-Dussault University of Sherbrooke 8/2/2011 - 8/12/2011
Gilad Lerman University of Minnesota 8/3/2011 - 8/12/2011
Hengguang Li Syracuse University 8/16/2010 - 8/16/2011
Zhi (George) Lin University of Minnesota 9/1/2009 - 8/31/2011
Xin Liu University of Minnesota 8/31/2011 - 8/30/2012
Shiqian Ma University of Minnesota 8/31/2011 - 8/30/2013
Kara Lee Maki University of Delaware 9/1/2009 - 8/19/2011
Yu (David) Mao University of Minnesota 8/31/2010 - 8/30/2012
Oumar Mbodji McMaster University 8/2/2011 - 8/13/2011
Dimitrios Mitsotakis University of Minnesota 10/27/2010 - 8/31/2012
Dennis Moore University of Kentucky 8/2/2011 - 8/12/2011
Cecilia Ortiz-Duenas University of Minnesota 9/1/2009 - 8/31/2011
Ahmet Ozkan Ozer Iowa State University 8/2/2011 - 8/12/2011
Mary Therese Padberg University of Iowa 8/1/2011 - 6/1/2012
Candice Renee Price University of Iowa 8/1/2011 - 7/31/2012
Weifeng (Frederick) Qiu University of Minnesota 8/31/2010 - 8/30/2012
Mustazee Rahman University of Toronto 8/2/2011 - 8/12/2011
Anton Sakovich McMaster University 8/2/2011 - 8/13/2011
Fadil Santosa University of Minnesota 7/1/2008 - 8/30/2011
Shirin Sardar Rice University 8/2/2011 - 8/13/2011
Apo Sezginer KLA - Tencor 8/2/2011 - 8/13/2011
Shuanglin Shao Institute for Advanced Study 9/1/2009 - 8/17/2011
Alex Shum University of Waterloo 8/2/2011 - 8/12/2011
Cory Simon University of British Columbia 8/2/2011 - 8/13/2011
Arthur Szlam University of Minnesota 8/31/2011 - 8/30/2012
Changhui Tan University of Maryland 8/2/2011 - 8/12/2011
Dimitar Trenev Texas A & M University 9/1/2009 - 8/4/2011
Hsiao-Chieh Tseng University of California, Davis 8/2/2011 - 8/12/2011
Caroline Uhler University of Minnesota 8/31/2011 - 10/30/2011
Divyanshu Vats University of Minnesota 8/31/2011 - 8/30/2012
Chai Wah Wu IBM 8/2/2011 - 8/13/2011
Haley Yaple Northwestern University 8/2/2011 - 8/12/2011
Kidist Zeleke University of Houston 8/2/2011 - 8/13/2011
Teng Zhang University of Minnesota 8/31/2011 - 8/30/2012
Zhou Zhou University of Michigan 8/2/2011 - 8/13/2011
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
Arizona State University, Boeing, Corning Incorporated, ExxonMobil, Ford, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Korea Advanced Institute of Science and Technology (KAIST), Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Mississippi State University, Northern Illinois University, Ohio State University, Pennsylvania State University, Portland State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger Cambridge Research, Schlumberger-Doll, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Central Florida, University of Chicago, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pennsylvania, University of Pittsburgh, University of Tennessee, University of Wisconsin-Madison, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute