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The IMA is holding a 10-day workshop on Mathematical Modeling in Industry. The workshop is designed to provide graduate students and qualified advanced undergraduates with first hand experience in industrial research.
Format
Students will work in teams of up to 6 students under the guidance of a mentor from industry. The mentor will help guide the students in the modeling process, analysis and computational work associated with a real-world industrial problem. A progress report from each team will be scheduled during the period. In addition, each team will be expected to make an oral final presentation and submit a written report at the end of the 10-day period.
Application Procedure
Graduate students and advanced undergraduates are invited to apply. An application form must be submitted to the IMA. In addition, two letters of recommendation are required; one must be from the student's advisor, director of graduate studies, or department chair. Prerequisites vary and depend on the project, but computational skills are important.
The IMA will cover local living expenses and will offer to pay airfare for the math modeling participants. Selection criteria will be based on background and statement of interest, as well as geographic and institutional diversity. Women and minorities are especially encouraged to apply. Applications must be completed by April 28, 2008 for full consideration. Early submissions are encouraged. Successful applicants will be notified by May 5, 2008.
Project Description:
Due to the complexity of financial markets, financial derivative modeling requires both an ability to understand and implement theoretical mathematical objects as well as a reliance on simulation techniques. A well known economist, Eugene Fama, once said, “We know all models are false.” This notwithstanding, an approximate model allows the practitioner to understand her position in terms of widely used market parameters such as volatility or correlation. Additionally, insight may be gained into the approximate distribution of payoffs as a function of such parameters once a model has been designated.
This project will present and model a financial instrument dubbed a ‘dispersion option’. Such an option has a payoff structure contingent on how much individual stock returns within a basket diverge from the average return of the basket. As a first step, we will simulate such an option with a variety of real market data, and examine the distribution of payoffs, thereby gaining insight into the historical behavior of such instruments. We will then attempt to examine the distribution of payoffs of such an option based on multiple models of the underlying names. This may be done using simulation techniques or via a mathematical proof depending on the complexity of the model assumed. Of primary interest would be to understand the payoff structure of the option as a function of easily identifiable parameters.
Reference:
Options, Futures, and Other Derivatives, J. C. Hull, Prentice Hall. Especially chapters titled "Numerical Procedures", and "More on Models and Numerical Procedures" in the sixth edition.
Prerequisites:
Knowledge of options pricing theory (especially Risk-Neutral Valuation), statistics, some numerical analysis, and ability to write simulation code. Desired: Coursework in mathematical finance and statistics, Matlab programming, and a familiarity with model selection techniques and evaluation.
Project Description:
The goal of this research is to revisit the stability results of Yeow (1974) on extending flows with free surfaces. The eigenvalue problem will be formulated and solved for the flow of a Newtonian film such as the one encountered in film casting. The stable and unstable region boundaries will be obtained. The analysis will be extended to a non-isothermal case similar to the work by Shah and Pearson (1972). Stability boundaries for different draw velocity (at the inlet and the exit of the process), and viscosity ratios will be sought. For the solutions which are unstable (or marginally unstable), time-dependent solutions (oscillating or growing in time) describing the free surface motion will be obtained.
References:
Y. L., Yeow: On the stability of extending films: a model for the film casting process (J. Fluid Mech. 1974 v66 (3) 613-622.
Y. T. Shah & J. R. A. Pearson: On the stability of non-isothermal fiber spinning - general case. Industrial & Engineering Chemistry Fundamentals. 1972 v11 (2) 150-153.
Additional References: D. Silagy, Y. Demay, J-F. Agassant: Study of Stability of the Film Casting Process. Polymer Engineering and Science, 1996 V36 (21) 2614-2625.
Y. Shah & J.R. Pearson: Stability of Fiber Spinning of Power-law fluids. Ind. Eng. Chem. Fundam. 1972 v11 (2)
G. Lamberti, G. Titomanlio, V. Brucato: Measurement and modeling of the film casting process 1. Width distribution along draw direction. Chemical Engineering Science 2002, v56, 5749-5761
G. Lamberti, G. Titomanlio, V. Brucato: Measurement and modelling of the $lm casting process 2. Temperature distribution along draw direction. Chemical Engineering Science 2002, v57, 1993-1996.
Prerequisites:
Computing skills, asymptotic analysis, numerical methods, familiarity with conservation laws in particular Navier-Stokes system of Newtonian fluids. Matlab, Maple and Comsol knowledge could be beneficial but not required.
Project Description:
ome electrical interconnections in medical devices are made by forming and welding piece of thin flat ribbon (or wire) between two electrical terminals. Current equipment for forming the ribbon allows for a virtually an infinite set of motions between the two terminals to be programmed. Currently the only method for determining what the resulting shape of the ribbon will be from a set of machine motions is to program the machine, form a ribbon, visually observe the resultant shape, and iterate until the "desired shape" is obtained. The problems proposed are 1) Given some data regarding the ribbon shapes that result from a very limited set of tool motions, can a more general model be developed that can predict the shape of the loop based on the machine motions, 2) Can this model be improved by incorporating the material response behavior of the ribbon or other physical relationships that govern ribbon formation, 3) Can this model be inverted so that if a particular ribbon shape is desired, a corresponding set of machine parameters can be identified, and 4) If only the spacing, positioning, and clearance around two terminals are known, can an optimal shape be identified that minimizes the stress induced in the ribbon from relative motion between the terminals while avoiding interference with any of the surrounding geometric constraints.
References:
1. "Wire-Bonding Loop Profiles" http://www.siliconfareast.com/wirebond-loop-profiles.htm
2. "Apparatus and method for laser welding of ribbons" US Patent 6,717,100
Prerequisites:
Familiarity with mechanics of materials, plastic deformation of thin metal, curve fitting, data analysis, optimization, & machine control would all be helpful.
Project Description:
The process of laying out the curves and surfaces needed to describe free form shapes in mechanical design is called lofting. Examples of lofting include shapes such as ship hulls, airplane wings and bodies, automobile exteriors, and so on. The best lofting procedures take a vector of inputs, which can contain items like wing span, wing sweep angle, aspect ratios, wing leading edge curvatures, etc., and produce a mathematical model of the geometric shape. Good lofting procedures necessarily have to process the input data nonlinearly in order to produce acceptable shapes.
Additionally, it is frequently important to solve the inverse problem. Specifically, one is given a mathematical model of a geometric shape and, with any luck, a lofting code and wants to know what vector of inputs to the lofting code will produce the given shape. This problem has been called the unlofting problem, and it can usually be solved with with standard techniques in non-linear least squares and non-linear parameter estimation. Just as frequently, though, the unlofting problem arises in contexts where no lofting code exists, requiring such a code to be produced as part of the solution. So far, the requirement to produce a lofting code as part of the solution to the unlofting problem has ruined all attempts to produce a fully automatic solution.
This project will attempt to construct a prototype unlofting code given only a final geometric shape with no accompanying lofting code. Some recent developments in multiresolution modeling have suggested a promising approach to this problem that we will explore during the workshop, focusing initially on 2D curves and then migrating to simple 3D shapes if time permits.
References:
"Multiresolution morphing for planar curves," by S. Hahmann, G.-P. Bonneau, M. Cornillac, and B. Caramiaux. Computing 79 (2-4), pp. 197-209 (2007)
Prerequisites:
Required: 1 semester of numerical analysis and computing skills. Desired: Knowledge of non-linear least squares, splines, and Python programming.
Project Description:
Instruments for chemical spectroscopy are finding key application in fields of homeland security, healthcare and manufacturing of chemicals and machine parts [1]. The need to automatically analyze large amounts of data quickly and to calibrate these instruments in an unbiased way is thus becoming ever more important. In many applications, for example healthcare and law enforcement, both calibration [2] and data analysis ([3,4]) should be performed with as little operator input as possible.
One of the most important chemical spectroscopy instruments is the Matrix Assisted Laser Desorption Absorption Time of Flight (MALDI-TOF) mass spectrometer. A schematic of the instrument is shown above, and sample data output is shown below. The MALDI-TOF produces a collection of 2-tuples (usually between 50,000-100,000 pairs of data points), from which one should identify peaks and then integrate the area underneath each peak. A major challenge is the development of an automated peak peaking and peak integration algorithm requiring no operator input. A second and closely related challenge is the development of an operator independent calibration scheme.
I will outline an approach to the data analysis problem and present some very precursory work involving Standard Reference Materials (SRM). I will also present a first attempt at automatic instrument calibration. Data from larger molecules will be used as a litmus test. If time permits, I will will present at least one other spectroscopy instrument.
References:
[1] Introduction to Mass Spectrometry, J. T. Watson, Lippencott-Raven, 1997.
[2] Wallace, W. E., Guttman, C. M., Flynn, K. M., Kearsley, A. J., `Numerical optimization of matrix-assisted laser desorption/ionization time-of-flight mass spectrometry: Application to synthetic polymer molecular mass distribution measurement’ ANALYTICA CHIMICA ACTA Volume: 604 Issue: 1 Special Issue: Pages: 62-68 NOV 26 2007
[3] Wallace, W. E., Kearsley, A. J., Guttman, C. M., `An operator-independent approach to mass spectral peak identification and integration’ ANALYTICAL CHEMISTRY. Volume: 76 Issue: 9 Pages: 2446-2452. MAY 1 2004
[4] Wallace, W. E., Kearsley, A. J., Guttman, C. M., `MassSpectator: Fully automated peak picking and integration - A Web-based tool for locating mass spectral peaks and calculating their areas without user input. ‘ ANALYTICAL CHEMISTRY Volume: 76 Issue: 9 Pages: 183A-184A MAY 1 2004
Prerequisites:
A programming language, (Fortran 90, C, C++, or Matlab); a course in optimization or signal processing is helpful but not necessary.
Project description:
Peer-to-peer networks are decentralized computing architectures that promise to deliver scalability in data sharing and streaming applications under dynamic network conditions. In these architectures peers are connected to the network and contribute resources in return for some useful services delivered by the network. Some questions that determine the performance and robustness of the peer-to-peer network are: what is the capacity of the network? How robust is the network behavior with respect to flashcrowds and random peer failures and departures? In this project we study the performance and robustness of various peer-to-peer networks by studying various algorithms for constructing the overlay network and for determining the data packets that are transmitted . We study the properties of the complex network resulting from these algorithms in order to identify peer-to-peer networks which are both robust and efficient.
Prerequisites:
Computer programming (C, Matlab or Python), discrete mathematics. Desired: computer networks, graph theory, probability.
Wednesday | Thursday | Friday | Saturday | Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | | |||||
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Wednesday August 06, 2008 | |||||
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. | |||||
9:00am-9:30am | Coffee and Registration | EE/CS 3-176 | |||
9:30am-9:40am | Welcome and Introduction | Richard Braun (University of Delaware) Fadil Santosa (University of Minnesota, Twin Cities) | EE/CS 3-180 | ||
9:40am-10:00am | Team 1: Modeling, simulation, and the analysis of a financial derivative | Christopher Bemis (Whitebox Advisors) | EE/CS 3-180 | ||
10:00am-10:20am | Team 2: Stability of extending films | Olus Boratav (Corning Incorporated) | EE/CS 3-180 | ||
10:20am-10:40am | Team 3: Ribbon formation for electrical interconnection | J. Michael Gray (Medtronic) Robert Shimpa (Medtronic) | EE/CS 3-180 | ||
10:40am-11:00am | Break | EE/CS 3-176 | |||
11:00am-11:20am | Team 4: Loft-free unlofting methods for geometric design | Thomas Grandine (The Boeing Company) | EE/CS 3-180 | ||
11:20am-11:40am | Team 5: Optimal calibration in chemical spectroscopy | Anthony Kearsley (National Institute of Standards and Technology) | EE/CS 3-180 | ||
11:40am-12:00pm | Team 6: Performance and robustness study of peer-to-peer networks | Chai Wah Wu (IBM) | EE/CS 3-180 | ||
12:00pm-1:30pm | Lunch | ||||
1:30pm-4:30pm | Afternoon - start work on projectsBreak-out Rooms
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Thursday August 07, 2008 | |||||
Students work on the projects. Mentors guide their groups through the modeling process, leading discussion sessions, suggesting references, and assigning work.
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Friday August 08, 2008 | |||||
Students work on the projects. Mentors available for consultation.
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Saturday August 09, 2008 | |||||
Students work on the projects.
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Sunday August 10, 2008 | |||||
Students work on the projects.
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Monday August 11, 2008 | |||||
9:00am-9:30am | Coffee | EE/CS 3-176 | |||
9:30am-9:50am | Team 4 progress report | EE/CS 3-180 | |||
9:50am-10:10am | Team 2 progress report | EE/CS 3-180 | |||
10:10am-10:30am | Team 5 progress report | EE/CS 3-180 | |||
10:30am-11:00am | Break | EE/CS 3-176 | |||
11:00am-11:20am | Team 1 progress report | EE/CS 3-180 | |||
11:20am-11:40am | Team 6 progress report | EE/CS 3-180 | |||
11:40am-12:00pm | Team 3 progress report | EE/CS 3-180 | |||
12:00pm-1:30pm | Picnic at Cooke Hall Fields Picnic area map | Cooke Hall Fields Picnic area | |||
2:00pm-5:00pm | Remainder of the day
| Breakout Rooms | |||
Tuesday August 12, 2008 | |||||
Students work on the projects. Mentors available for consultation.
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Wednesday August 13, 2008 | |||||
Students work on the projects. Mentors available for consultation.
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Thursday August 14, 2008 | |||||
Students work on the projects. Mentors available for consultation.
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Friday August 15, 2008 | |||||
8:30am-9:00am | Coffee | EE/CS 3-176 | |||
9:00am-9:30am | Team 3 final report | EE/CS 3-180 | |||
9:30am-10:00am | Team 6 final report | EE/CS 3-180 | |||
10:00am-10:30am | Team 1 final report | EE/CS 3-180 | |||
10:30am-11:00am | Break | EE/CS 3-176 | |||
11:00am-11:30am | Team 5 final report | EE/CS 3-180 | |||
11:30am-12:00pm | Team 2 final report | EE/CS 3-180 | |||
12:00pm-12:30pm | Team 4 final report | EE/CS 3-180 | |||
12:30pm-2:00pm | Pizza party | Lind Hall 400 |
NAME | DEPARTMENT | AFFILIATION |
---|---|---|
Kapil Ahuja | Department of Mathematics | Virginia Polytechnic Institute and State University |
Richard Barnard | Department of Mathematics | Louisiana State University |
Christopher Bemis | Whitebox Advisors | |
Olus Boratav | Science and Technology Department | Corning Incorporated |
Richard Braun | Department of Mathematical Sciences | University of Delaware |
Lyrial Chism | Department of Mathematics | University of Mississippi |
Sohhyun (Holly) Chung | Department of Mathematics | University of Michigan |
Holly Clark | Department of Mathematics | University of Tennessee |
Yilin Dai | Department of Mathematical Sciences | Michigan Technological University |
Christina Dekany | Department of Computational and Applied Mathematics | Southern Methodist University |
Yuan Dong | Department of Mathematical Sciences | Northern Illinois University |
Yutheeka Gadhyan | Department of Mathematics | University of Houston |
Simon Gemmrich | Department of Mathematics & Statistics | McGill University |
Jerome Goddard | Department of Mathematics & Statistics | Mississippi State University |
Thomas Grandine | Department of Applied Mathematics | The Boeing Company |
J. Michael Gray | Medtronic | |
Huaiying Gu | Department of Mathematics | University of Michigan |
Shiyuan Gu | Department of Mathematics | Louisiana State University |
Xiaoqing He | School of Mathematics | University of Minnesota, Twin Cities |
Junming Huang | Department of Mathematics | University of Pittsburgh |
Liquan Huang | Department of Mathematical Sciences | University of Delaware |
Ashraf Ibrahim | Department of Mathematics | Texas A & M University |
Christopher Jones | Department of Mathematics | University of Pittsburgh |
Anthony Kearsley | Mathematical and Computational Sciences Division | National Institute of Standards and Technology |
Taebeom Kim | Department of Mathematics | University of Houston |
Jill Klentzman | Department of Mathematics | Southern Methodist University |
Dias Kurmashev | Department of Mathematics | University of Memphis |
Jiyung Lois Kwon | Department of Mathematics | Washington State University |
Xingjie Li | Department of Mathematics | University of Minnesota, Twin Cities |
Youzuo Lin | Department of Mathematics & Statistics | Arizona State University |
Zhongyi Nie | Department of Mathematics | University of Kentucky |
Mauricio Osorio | Department of Mathematical Sciences | University of Cincinnati |
Gregory Richards | Kent State University | |
Fadil Santosa | School of Mathematics | University of Minnesota, Twin Cities |
Qiling Shi | Department of Mathematics | University of Central Florida |
Robert Shimpa | Medtronic | |
Yan Shu | School of Mathematics | Georgia Institute of Technology |
Lin Tong | Department of Mathematics | Iowa State University |
Jon Van Laarhoven | Department of Applied Mathematical and Computational Sciences | The University of Iowa |
Jiabin Wang | Department of Statistics | Rutgers, The State University Of New Jersey |
Jia Wei | Department of Mathematics | Texas A & M University |
Chai Wah Wu | Thomas J. Watson Research Center | IBM |
Mohammad Zaki | Department of Mathematics | University of Illinois at Urbana-Champaign |
Guangjin Zhong | Department of Mathematical Sciences | Michigan Technological University |
Qinghua Zhu | Department of Mathematical Sciences | University of Delaware |
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