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University of Calgary | |
University of Calgary | |
University of Minnesota, Twin Cities | |
University of Calgary |
The IMA, in collaboration with PIMS, is holding a 10-day workshop on Mathematical Modeling in Industry in Calgary, Canada. 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.
Touch interfaces for small-size consumer devices are becoming ubiquitous, and are now penetrating into new areas like large display-walls, collaborative surfaces, and more. However, different methods of sensing are called for in order to deal with the economics of touch-interface for a very large surface. One such method uses small number of cameras and multiple light sources, as depicted in the example in Fig 1 below. When an object is placed on the surface, it blocks the line of sight between a few of the light sources and various cameras, and thus creates silhouette images. Using the input from all cameras, one can try and reconstruct the shape and location of the object touching the screen.
Of course, one can use more cameras, and various light/camera arrangements, to get different performances. Things get a little more complicated when we consider non-Euclidean surfaces (tracking on a ball?).
There is plenty of current research into Shape From Silhouettes (SFS), especially in order to reconstruct a 3D shape. Our case might seem simpler, as it is 2D only, but it has many practical requirements to address: Limited number of camera-views, minimization of light-sources, and so on. Moreover, the specifications we have for the system consider (for example) resolution, minimum detectable object, and how close two-objects can be together and still detected.
In this work we will build the tools to analyze, using analytic-geometry, various combinations of surface-shapes, cameras, light sources, and objects touching the surface. We will then venture into related aspects, depending on the inclination and composition of the team:
Figure 1: Sample system for touch sensing (see details in the abstract), and a finger (object) on the surface.
Prerequisites:
From all members: - Analytic geometry - Some familiarity with computer graphics will help as well. Many similarities exist.
At least from some of the group members: - Ability to simulate using Matlab, Mathematica, or any similar tool.
Bibliography: A basic reference:
Some more recent works:
Significant uncertainty and risk is associated with operation and maintenance costs for oil drilling. The requirement for service concepts is to guarantee high availability and productivity at low service costs during the service period. Failures of the oil rigs, the number of service technicians, the position of the home base and the availability of spare parts are the relevant parameters influencing the service costs. In addition various strategies combining scheduled and unscheduled maintenance can be considered. To support this process, simulation methods can be used to establish and optimize operation and maintenance strategies. From the simulation of operation the outcome must be optimum transport logistic set-up, the optimum number of technicians to cover the service and warranty work in order to get the highest production output with the lowest costs.
The goal of the project is to develop a simulation software that determines service concepts for oil drilling that are optimal with respect to high availability and low costs. The following aspects will be modeled for this project:
References: G.L. Nemhauser, L.A. Wolsey, Integer and Combinatorial Optimization, John Wiley & Sons, 1988
An increasing amount of the oil and gas produced in North America and the world is from unconventional reservoirs. Understanding the fractures within the reservoir plays an important role in developing this resource. The objective of this project is to infer from P-wave seismic amplitude variations with offset and azimuth (AVAz) the elastic parameters of the earth and then from these elastic parameters characterize the fractures (Figure 1). The forward model is primarily described by two key models, the first describes the functional relationship between the anisotropic elastic parameters and the fractures, and the second describes the AVAz. One possible way of modeling this is to use linear slip theory [7,8] to characterize the fractures and then use a linearized approximation of the Zoeppritz equations [5] to describe the AVAz. It is then possible to estimate the fractures by inverting the nonlinear forward problem using simulated annealing [2].
Figure 1: Fracture direction and magnitude displayed for a carbonate reservoir
The inversion problem is nonlinear, under-resolved and ill-conditioned. In order to make the problem better posed and resolved, assumptions are typically made about the type and complexity of the fractures [4,6]. One of the goals of this project is to understand the resolvability of these models and their parameterizations under different noise conditions. Another goal is to explore different methods to solve this nonlinear problem. Under certain data and parameter transformations [3] it is possible to linearize certain aspects of this problem. For this portion of the problem it is possible to perform a traditional parameter and data resolution analysis [1,4]. In this workshop we would like to explore techniques to understand the resolvability of the parameters for the full nonlinear problem.
Prerequisites:
We expect students with a strong background in optimization, numerical analysis, and good computing skills (MatLab or C/C++). Knowledge of statistical methods and stochastic analysis would be an asset.
References:
Sugars, the collection of all naturally-occurring monosaccharides and disaccharides, are small molecules belonging to the class of carbohydrates. Examples of sugars are glucose, fructose, and sucrose. Essentially all sugars have the same chemical formula but different molecular structures. Virtually all metabolites found in bodily fluids (primarily blood, urine, and saliva) can be identified and quantified using gas chromatography – mass spectrometry (See Figure 1). However, sugars cannot; they must be identified using techniques other than mass spectrometry. This is because, even under ideal conditions, the mass spectra of sugars are very similar, though not identical. (See Figure 2.) In a real world laboratory setting lack of sufficient sample and interferences from other molecules in the bodily fluid create noise and uncertainty in the mass spectra. This makes identifying sugars in real samples difficult. A positive advancement in the field of clinical analysis would be the ability to identify sugars in bodily fluids by GC-MS. This would avoid the need to perform completely separate experiments to determine sugar content.
GC-MS identifies components of complex mixtures such as bodily fluids by vaporizing the sample and forcing the vapor through a capillary column having an absorptive inner lining. As the substance passes through the column different molecules elute at different times due to differences in each molecule’s thermodynamic gas/liquid partition function. The molecules are then sent to the mass spectrometer. Here they are ionized by electron impact. The high energy electron beam breaks the molecules apart and their characteristic mass spectrum is measured. Thus, a mass spectrum is a collection of mass and intensity pairs which can be plotted. This plot (or spectrum as in Figure 1) is then compared to a database of existing spectra and the compound is identified. Identifying sugars however, is a notoriously difficult problem.
Given the spectra of an unknown sugar, can a searching function be constructed that successfully identifies the sugar from a collection of known sugar spectra? Given a known sugar with known chemical structure and given a collection of mass spectra collected on different instruments and with varying degrees of accuracy, can one model the noise or error associated with an instrument? Can one derive necessary or sufficient conditions for an unknown sugar to be identifiable (or not identifiable)? Finally, can one select instrument settings that produce spectra that, when compared to library spectra, minimize the maximum likelihood of a incorrectly identifying an unknown?
This project will involve investigating the mathematical and statistical techniques for estimating the distance between chemical spectra of varying degrees of accuracy and searching functions designed to identify sugars. Other classes of substances may also be considered (pesticides, pollutants, methamphetamines).
Prerequisites:
Interest in computing (Matlab or C/C++). Background in optimization or statistics; some linear algebra. Special interest in things like regression, machine learning, filtering methods...etc would be beneficial but not necessary.
References:
W. Demuth, M. Karlovits, K. Varmuza. ``Spectral similarity versus structural similarity: mass spectrometry’’, Analytica Chimica Acta, 2004. pp 75—85.
NIST, Mass Spectral Database 2011, National Institute of Standards and Technology, http://www.nist.gov/srd/nist1a.htm, Gaithersburg, MD, 1998
S. Stein. ``Chemical substructure identification by mass spectral library searching’’, Journal of the American Society for Mass Spectrometry’’, 1995. pp 644-655.
Algorithms for design optimization are increasingly able to handle complex problem formulations. We will consider the design of a fuel tank consisting of four different disciplinary sub-system components- structures, aerodynamics, cost, and systems. This is a multi-disciplinary, design problem with multiple competing objectives. We will examine several formulations and how to best match the problem formulation with the choice of optimizer. As the complexity of the problem grows, so does the amount of data generated during an optimization. This adds on the challenge of interpreting the data. We will investigate different methods for representing the data. Visualization methods will be considered in two groups- those suited to developing a greater understanding of the problem (for team members) and those suited to presenting results (for customers).
This project is intended to give a flavor of what an industrial mathematician does throughout the lifecycle of a given project. This project has 3 steps:
References: Schuman, T., De Weck, O., Sobieski, J. (2005) Integrated System-Level Optimization for Concurrent Engineering with Parametric Subsystem Modeling AIAA 2005-2199.
De Weck, O. (2004), Multidisciplinary System Design Optimization (MSDO): Decomposition and Coupling, Module 6 Notes, MIT OpenCourseWare 16.888 / ESD.77, Massachusetts Institute of Technology.
Cramer, E. J., J. E. Dennis, Jr., P. D. Frank, R. M. Lewis, G. R. Shubin (1994), Problem formulation for multidisciplinary optimization, SIAM Journal of Optimization 4 (4): 754-776.
Cancer is the second cause of death in USA with estimated deaths of 570,000 in 2010. In USA, about 2/3 of cancer patients are treated with radiotherapy since it has proven a particularly effective treatment for many cancer types. Radiation is generated by a medical linear accelerator mounted on a gantry that can deliver the radiation to the patient’s body from various orientations with optimized intensity profiles of the x-ray beams (Fig-1). The main objective of radiotherapy is to deliver a lethal dose of radiation to the tumor to kill cancerous cells while sparing surrounding healthy organs and normal tissues. The treatment is complex and very patient specific. The radiation beam parameters have to be tailored to each patient's case, through a process called treatment planning, where an optimal treatment plan is designed for a particular patient based on the patient's CT image data and the physician's prescription.
Fig-1: A Medical Linear Accelerator
Fig-2: DVH Curves
(Cumulative) Dose Volume Histogram (DVH) is the most common tool employed by physicians to evaluate the quality of the plan (Fig-2). Point (D, V) on a DVH curve means for this organ, V (%) of the volume receives radiation dose more than D (Gy). Treatment planning is an multiple objective optimization problem, - delivering the desired radiation dose to the target (PTV) while minimizing dose to each healthy organ. We propose to use an interactive planning method to solve this problem. The physician will adjust the tradeoff among the target and the organs from an initial treatment plan. When the physician is satisfied with the DVH curves for some organs, s/he will "lock" these curves and keep looking to improve/modify the others. In this project we aim to develop a mathematically innovative and computationally efficient method to solve this important clinical problem.
Prerequisites:
Strong background in optimization, Good computing skills (MatLab or C/C++).
References:
More and more over-the-counter (OTC) derivatives traded post-crisis are collateralized in order to reduce counterparty’s credit risk or to be required in clearing houses according to new regulation. In this case, financial institutions need to incorporate the cost to raise capital for funding the collateral request into the traditional (uncollateralized) valuation models to find the fair value of the derivatives, which attracts large amount of attention and interest in funding value adjustment (FVA). If the OTC derivatives are perfectly collateralized, an OIS discounting is sufficient for the correct valuation methodology as pointed out in [5]. However, in practice, collateralization under the credit support annex (CSA) may be imperfect, such that OIS discounting is not necessarily a suitable valuation method any more.
We are planning to perform some quantitative impact study on valuation OTC derivatives with imperfect collateralization. In particular, an interesting topic is the cross currency collateralization, which is widely applied in practice. In the simplest case, the collateral may be posted in a pre-determined currency different from the derivative itself, this may lead to certain quanto effect in valuation [3]. A further study will be for the case that collateral can be chosen among a set of currencies such that the party to post collateral will choose the one with minimum funding cost, which leads to the complexity of the cheapest-to-deliver option similar to bond futures [2]. It is worth noting that this is an American or Bermudan style option, such that one may need to apply the valuation approaches in [1,4]. We will attempt to model these problems, develop valuation methodologies, and obtain some numerical results for the problems during this workshop.
Prerequisites:
Stochastic analysis, financial modelling, derivative pricing, computer coding (C++ or Matlab) Desired: numerical optimization
References:
More and more over-the-counter (OTC) derivatives traded post-crisis are collateralized in order to reduce counterparty’s credit risk or to be required in clearing houses according to new regulation. In this case, financial institutions need to incorporate the cost to raise capital for funding the collateral request into the traditional (uncollateralized) valuation models to find the fair value of the derivatives, which attracts large amount of attention and interest in funding value adjustment (FVA). If the OTC derivatives are perfectly collateralized, an OIS discounting is sufficient for the correct valuation methodology as pointed out in [5]. However, in practice, collateralization under the credit support annex (CSA) may be imperfect, such that OIS discounting is not necessarily a suitable valuation method any more.
We are planning to perform some quantitative impact study on valuation OTC derivatives with imperfect collateralization. In particular, an interesting topic is the cross currency collateralization, which is widely applied in practice. In the simplest case, the collateral may be posted in a pre-determined currency different from the derivative itself, this may lead to certain quanto effect in valuation [3]. A further study will be for the case that collateral can be chosen among a set of currencies such that the party to post collateral will choose the one with minimum funding cost, which leads to the complexity of the cheapest-to-deliver option similar to bond futures [2]. It is worth noting that this is an American or Bermudan style option, such that one may need to apply the valuation approaches in [1,4]. We will attempt to model these problems, develop valuation methodologies, and obtain some numerical results for the problems during this workshop.
Prerequisites:
Stochastic analysis, financial modelling, derivative pricing, computer coding (C++ or Matlab) Desired: numerical optimization
References:
Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday Monday | Tuesday | Wednesday | | |||
---|---|---|---|
Monday June 18, 2012 | |||
9:00am-9:20am | Team 1: Touch sensing, Silhouettes, and “Polygons-of-Uncertainty” | Izhak (Zachi) Baharav (Corning Incorporated) | Taylor Digital Family Library - Gallery Hall Main Floor |
9:20am-9:40am | Team 2: Validation of Service Concepts for Oil Drilling by Simulation | Efrossini Tsouchnika (Siemens) | Taylor Digital Family Library - Gallery Hall Main Floor |
9:40am-10:00am | Team 3: Azimuthal elastic inversion for fracture characterization | Jon Downton (CGGVeritas) | Taylor Digital Family Library - Gallery Hall Main Floor |
10:00am-10:20am | Break | ||
10:20am-10:40am | Team 4: Identifying sugars | Anthony Kearsley (National Institute of Standards and Technology) | Taylor Digital Family Library - Gallery Hall Main Floor |
10:40am-11:00am | Team 5: Multi-objective design of a fuel tank | Laura Lurati (The Boeing Company) | Taylor Digital Family Library - Gallery Hall Main Floor |
11:00am-11:20am | Team 6: Interactive Treatment Planning in Cancer Radiotherapy | Masoud Zaripisheh (University of California, San Diego) | Taylor Digital Family Library - Gallery Hall Main Floor |
11:20am-11:40am | Team 7: Valuation of Over-the-Counter Derivatives with Collateralization | Ritchie He (Royal Bank of Canada) | Taylor Digital Family Library - Gallery Hall Main Floor |
11:40am-1:30pm | Lunch | ||
1:30pm-5:00pm | Start work on projects | ||
Tuesday June 19, 2012 | |||
Work on projects | |||
Wednesday June 20, 2012 | |||
Work on Projects | |||
12:00pm-1:15pm | Lunch and Learn | Nexen Technology Centre 5th floor, University of Calgary downtown campus 906-8th Avenue | |
Thursday June 21, 2012 | |||
Work on Projects | |||
Friday June 22, 2012 | |||
9:00am-9:15am | Team 5 progress report | Information and Communications Technologies Building ICT 102 | |
9:15am-9:30am | Team 2 progress report | Information and Communications Technologies Building ICT 102 | |
9:30am-9:45am | Team 5 progress report | Information and Communications Technologies Building ICT 102 | |
9:45am-10:15am | Break | ||
10:15am-10:30am | Team 7 progress report | Information and Communications Technologies Building ICT 102 | |
10:30am-10:45am | Team 4 progress report | Information and Communications Technologies Building ICT 102 | |
10:45am-11:00am | Team 1 progress report | Information and Communications Technologies Building ICT 102 | |
11:00am-11:15am | Team 3 progress report | Information and Communications Technologies Building ICT 102 | |
11:30am-12:30pm | Lunch (food will be provided) | ||
12:30pm-2:00pm | Getting Started with Networking: Practical Tips for Growing Your Personal Network | ||
Sunday June 24, 2012 | |||
9:00am-6:30pm | Kananaskis Hike and Picnic Lunch | Rawson Lake Trail | |
Monday June 25, 2012 | |||
Work on Projects | |||
Tuesday June 26, 2012 | |||
Work on Projects | |||
4:00pm-5:00pm | Employability and Careers in Math | Information and Communications Technologies Building ICT 102 | |
5:00pm-6:00pm | Pizza Dinner | Math Lounge- Math Sciences Building MS 461 | |
Wednesday June 27, 2012 | |||
9:00am-9:20am | Team 3 progress report | Energy, Environment, Experiential Learning Building EEEL 161 | |
9:20am-9:40am | Team 6 progress report | Energy, Environment, Experiential Learning Building EEEL 161 | |
9:40am-10:00am | Team 7 progress report | Energy, Environment, Experiential Learning Building EEEL 161 | |
10:00am-10:20am | Break | ||
10:20am-10:40am | Team 5 progress report | Energy, Environment, Experiential Learning Building EEEL 161 | |
10:40am-11:00am | Team 1 progress report | Energy, Environment, Experiential Learning Building EEEL 161 | |
11:00am-11:20am | Team 2 progress report | Energy, Environment, Experiential Learning Building EEEL 161 | |
11:20am-11:40am | Team 4 progress report | Energy, Environment, Experiential Learning Building EEEL 161 | |
11:40am-12:00pm | Concluding remarks |
NAME | DEPARTMENT | AFFILIATION |
---|---|---|
Abraham Abebe | Department of Mathematics | University of North Carolina, Greensboro |
Salam Alanabulsi | Department of Mathematics | University of Calgary |
Izhak (Zachi) Baharav | Corning Incorporated | |
Kristine Bauer | Department of Mathematics and Statistics | University of Calgary |
Alexander Blaessle | IK Barber School | University of British Columbia Okanagan |
Dagny Butler | Mathematics and Statistics Department | Mississippi State University |
Allison Cullen | Mathematics Department | Wayne State University |
Clifton Cunningham | Department of Mathematics | University of Calgary |
Jon Downton | CGGVeritas | |
Peng Du | Department of Mathematics | University of Alberta |
Aditi Ghosh | Department of Mathematics | Texas A & M University |
Anna Glazyrina | Department of Mathematical and Statistical Sciences | University of Alberta |
Leon Guerrero | Department of Mathematics | University of Central Florida |
Omar Gutierrez Navarro | Facultad de Ciencias | Universidad Autonoma de San Luis Potosi |
Ritchie He | Royal Bank of Canada | |
Bamdad Hosseini | Department of Mathematics | Simon Fraser University |
Alexander Howse | Department of Mathematics | Memorial University of Newfoundland |
Bebart Janbek | Department of Mathematics | Simon Fraser University |
Shi Jin | Department of Mathematical Sciences | University of Delaware |
Ehsan Kamalinejad | Department of Mathematics | University of Toronto |
Anthony Kearsley | Mathematical and Computational Sciences Division | National Institute of Standards and Technology |
Henrike Koepke | Department of Mathematics | University of Victoria |
Guoqing Liu | Department of Mathematics | University of Pittsburgh |
Lifeng Liu | Department of Mathematics | University of Pittsburgh |
Laura Lurati | Department of Applied Mathematics | The Boeing Company |
Justin Meskas | Department of Mathematics | Simon Fraser University |
Arun Moorthy | Department of Mathematics | University of Guelph |
Kanna Nakamura | Department of Mathematics | University of Maryland |
Elham Negahdary | Department of Mathematics | University of Calgary |
Kimberly Nolan | Department of Mathematics | Drexel University |
Laura Norena | Department of Mathematics | University of Central Florida |
Mololaji Ogunsolu | Department of Mathematics | University of Calgary |
Victor Paraschiv | Mathematics and Statistics Department | University of Victoria |
Charles Puelz | Department of Computational and Applied Mathematics | Rice University |
Cristian Rios | Department of Mathematics and Statistics | University of Calgary |
Fadil Santosa | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |
Madeline Schrier | Department of Mathematics | University of Minnesota, Twin Cities |
Mohammad Shakourifar | Department of Computer Science | University of Toronto |
Wenling Shang | Department of Mathematics | University of Michigan |
Pooyan Shirvani Ghomi | Department of Mathematics | University of Calgary |
Mikhail Smilovic | Department of Mathematics | McGill University |
Samantha Tracht | Department of Mathematics | University of Tennessee |
Giulio Trigila | Courant Institute | New York University |
Efrossini Tsouchnika | Siemens | |
Iva Vukicevic | Department of Applied Physics and Applied Mathematics | Columbia University |
Binbin Wang | Department of Mathematics | University of Calgary |
Jing Wang | Department of Mathematical and Statistical Sciences | University of Alberta |
Ke Yin | Mathematics Department | Georgia Institute of Technology |
Yun Zeng | Mathematical Sciences | University of Delaware |
Tong Zhao | Department of Mathematics | Iowa State University |
Yuriy Zinchenko | University of Calgary |
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