Previous Mathematics Clinic Projects

The Clinic program at 91探花 Mudd has a rich history. Past project descriptions for math Clinics are available here. Please note that ongoing projects may be governed by confidentiality agreements. You can also view the projects by sponsor and projects by advisor.

Ashley Kim
Shreya Reddi
Caroline Sorrells
Terence Chen
Kenji Horigome

Leslie Garay Belmontes
Lucas Lang
Luis Beltran
Nico Monsalve
Eric Zhang

Georgia Klein
Mo Kyn
Ryder Mitchell
Allyson Yao

Amber Means
Julianna Schalkwyk
Katie Wu
Qing Yang
Justin Yeh

Jack Ontiveros
Michael Giordano
Shanni Lam
Shaurya Pednekar
Vibha Rohilla

Mary Anderson
Hannah Davalos
Chaitanya Karamchedu
Sam Ness
Eric Thompson-Martin

Jeremy Jess
T.Y. Lim
Cat Ngo
Anna Serbent
Mingyu Zheng

Jonathan Hayase
Jason Ma
Joe Nunez (Project Manager)
Adelaide Punt
Pedro Sandoval Segura
Ricky Shapley

Porter Adams
Ryan Haughton (spring)
Cade Hulse (Project Manager)
Shreyas Kadaba
Anji Malpani
Laurel Schy (fall)

Stetson Bost
Max Howard
Yichen Lu (Project Manager)
Noah Marcus

Jessica de la Fuente (fall)
Kanak Singh (fall)
Aleina Wachtel (fall) (Project Manager)
Allison Barry (spring) (Project Manager)
Rachel O鈥橬eill (spring)
Stephen Schein

Arianna Perkins (fall) (Project Manager)
Xinlei (Mimee) Xu (spring) (Project Manager)
Will Clausen
Abhishek Goenka
Huameng (Michael) Jiang

Travis Athougies
Ben Corr (Project Manager)
Michael Fox
David Scott

Ben Gross
Katarina Hoeger (Project Manager)
Kevin Varela O鈥橦ara
Tim Yee

Emil Guliyev
Lindsay Hall (Project Manager)
Brandon Wei
Rebecca Young

Jacob Bouricius (Project Manager)
Maxwell Lee
Andrea Levy
Margaret Rogers

Jeffrey Burkert
Bryce Lampe
Taiki Sakai (Project Manager)
Jason Wyman

Aaron Abromowitz
Richard Bowen (Project Manager)
Donavion Huskey
Brett McLarnon

Greg Borish
Jason Christiansen (Project Manager)
Alex Korn
Minal Shankar

Nate Chenette
James Egan
Herbie Huff
William Warriner

Para Thomas (fall)
Aaron Becker
Daniel Cicio
Katherine Todd-Brown
Lisa Wice

This project will build on previous Math Clinic projects on Web search, with the goal of improving techniques for topic-dependent relevance ordering. Of the different approaches to ranking Web search results, some are static and global, using the Web as a whole to vote on the relative importance of pages, while others are more dynamic and local, ranking pages only within a search result set or a topic cluster. In a purely static and global approach, if page A appears before page B when a user enters a search query Q, then A will appear before B for all other queries Q鈥�. An example of a local technique is Kleinberg鈥檚 HITS technique for link analysis; Brin and Page鈥檚 PageRank is global. In a Summer 2002 Math Clinic, a specific approach was proposed for focusing link analysis, effectively making it more local. This 2002-2003 Math Clinic project will begin by evaluating that approach against some competing baseline approaches, then look at ways to blend local and global relevance scores, and compare local analysis within a topic cluster to local analysis within a search result set.

Advisor

Lesley Ward

Team

Erin Bodine
David Gleich
Cathy Kurata
Jordon Kwan

Colin Little
Cameron McLeman
Braden Pellett
Simon Tse

2000 鈥� 2001

Applied Biosystems: Modeling of TaqMan Reactions for DNA/RNA Quantifications Using PCR (polymerase chain reaction)

Polymerase chain reaction amplification, or PCR, is a powerful and widely used technique for producing large quantities of a given DNA (or RNA) species from a small initial amount in a biological sample. The initial sample could contain as little as a single copy of the DNA molecule. Roughly speaking, PCR works by separating the two strands of the double helix, and using each strand as the template for a new double helix. So each cycle of PCR doubles the quantity of the given DNA species present (the PCR product).

A recent application is quantitative PCR: the use of PCR to determine how much of a given DNA species there was in the initial sample. The underlying idea is that because of the exponential increase of the PCR product, there is a linear relationship between (i) the time (number of PCR cycles) taken to accumulate a certain fixed threshold quantity of PCR product, and (ii) the logarithm of the initial amount of DNA present.

In practice, the accumulation of PCR product is monitored using fluorescent probe molecules called TaqMan molecules. The TaqMan molecule alternatively binds to and is cleaved from the DNA when PCR amplification is occurring. It fluoresces (under ultraviolet light) when it cleaves from the DNA. As more DNA molecules are produced, the fluorescence increases.

Natan Bershtel
John Chou
Claire Launay
John Lu

Space Systems/Loral: Optimization of Orbit-Raising Using Ion Propulsion

Space Systems/Loral is one of the world leaders in the design, building, launching, and management of weather and communications satellite. Because the cost of raising propellant into orbit is roughly $10,000 per kilogram, determining the optimal launch parameters for getting a satellite into orbit efficiently may ultimately save millions of dollars.

At present Space Systems/Loral鈥檚 electric orbit raising (EOR) algorithm which is used to determine trajectories for optimal propellant usage is, unwieldy, unreliable, and difficult to use. It consists of numerical routines that arrive at a solution, but does so in a ponderous fashion. It may also produce solutions that are local minimum but not globally optimal.

This clinic would concentrate on improving the efficiency and reliability of the EOR, goals include 1. Reduce processing time; 2. Implement a more efficient ODE solver (at present the routine uses fourth-order Runge Kutta); 3. Improve the optimization routine; and 4. Develop methods for accessing if a locally optimal solution is globally optimal.

Advisor

Andrew J. Bernoff

Team

Kylie Bryant
Matt Gedigian
Tyson MacDonald
Jay Trautman
Alex Wilkins

1999 鈥� 2000

Fair, Isaac, and Company, Inc.: Preemptive Offers for Portfolio Defense

The purpose of the project is to study the mathematical risk structure of preemptive offers, the effect these have on the likelihood of acceptance and thereby develop insights for the design of decision models that characterize successful preemptive offer strategies. The team鈥檚 goal will be to assess the expected costs and benefits accruing from one or more decision models for preemptive offers. A simulation of the decision process will be demonstrated, using a range of realistic parameters and account data supplied by the sponsor. An analysis of model behaviors will be distilled into a recommended strategy for the sponsor.

Advisor

Andrew J. Bernoff

Team

Otto Cortez
Jeffrey Hartline
Philip Martin (Team Leader)
Helen Munroe

HNC Software, Inc.: Link Analysis

This clinic project will explore the application of 鈥榣ink analysis鈥� to large datasets representing these networks. Link analysis attempts to improve on basic search techniques by analyzing both the properties of the nodes and the properties of its linkage to the network. This project will produce a written survey of the literature of link analysis, with a focus on techniques and models that appear to be useful for detecting group behaviors of interest to HNC. New models and techniques may be proposed by the team. If feasible, the team will implement and evaluate one or more of these models on a small-scale HNC data collection or simulated data and make recommendations for applying the techniques to full-scale data collections.

Advisor

Lesley Ward

Team

Gregory Mae (Team Leader)
Joel Miller
Fred Schaefer

Space Systems/Loral: Advanced Propellant Dispersion Analysis for Orbit-Raising and Maintenance of Geosynchronous Satellites

This project involves the extension of an analysis tool that was developed by last year鈥檚 SS/Loral Math Clinic team. The purposes of this year鈥檚 project are:

1. To incorporate an improved mathematical model of the orbital mechanics, both for the launch phase and the on-orbit phase of the mission. In particular, perturbation analysis of the exact orbit changes produced by each thruster firing will be considered a better model for the thruster firing than the instantaneous impulse model assumed last year.

2. To analyze empirical data provided by the project sponsor and its suppliers in order to better model the distributions of the various dispersions involved.

3. To review the existing software code in order to look for possible inefficiencies and discrepancies from sponsor expected results and to provide user documentation for the software.

Advisor

Henry Krieger

Team

Mark Amasuga
Christopher Sherwin
Kate Sims
Jennifer Voelmeck (Team Leader)

Belinda Fischer (Team Leader)
Tyson Kackley
Naveen Matthew
Scott Robertson
Tara Salamone

1997 鈥� 1998

1996 鈥� 1997

Jet Propulsion Laboratory: Formal Methods Applied to Spacecraft Subsystems

Formal verification is an alternative family of methods that use techniques based on mathematical logic to insure the quality of hardware and software systems. Systems are being designed and built with ever-increasing complexity. At the same time, the testing and validation costs of these systems is growing exponentially. Because of this, many systems are fielded today with a profound lack of proper validation. Formal methods are one of the few techniques with the potential to both cap testing costs and deliver the required reliability/safety in areas such as transportation, spaceflight, telecommunications, banking, etc.

Verification takes two approaches. Design verification uses formal logic in the design and specification of a system, providing a structured framework for translating top-level design specifications into a collection of concrete tasks describable by algorithms which can be realized by programmers. Program verification involves proofs of correctness of the programs themselves. A wide variety of tools, such as automated theorem provers and proof checkers, have been constructed to assist in design and program verification, and some of them have been implemented into integrated systems. The Clinic team will survey existing verification systems and techniques during the first semester. Guided by the sponsor鈥檚 expertise and interest, the team will identify an application area and appropriate tools, and during the second semester pursue this application in depth.

Advisor

Everett Bull

1995 鈥� 1996

David Bosley

1993 鈥� 1994

AlliedSignal Automotive: Radial Wheel Thickness Optimization

Turbine and compressor wheels for automotive turbochargers must be designed to withstand the centrifugal stress caused by high speed rotation and to avoid destructive vibrational resonances. This is accomplished by adjusting the thickness of the blade at all locations to meet maximum stress and minimum resonant frequency limits, subject to the side condition that the blade satisfy certain conditions of smoothness.

This design process is tedious and time-consuming. In principle it could be automated using one of various optimization routines which have been developed recently. To do this, both the condition mathematically, and software must be written to make changes in blade thickness, check for (or impose) smoothness, execute the code for calculating stress and vibrational frequency using one of several existing finite element routines, check the results against preset limits, and repeat the process until the limits are satisfied.

Advisor

David Bosley

Naval Health Research Center: Sizing An Artificial Neural Network

Unavailable

Advisor

John Angus 鈥� CGU

Northrop Corporation: Maximizing Energy Attenuation in Coated WaveGuides

This project will combine modelling, analysis of special cases and the development of a numerical method for designing the coating of a waveguide in order to maximize the attenuation of electromagnetic energy impinging on it. The derivation of the impedance that would achieve the desired attenuation for a simplified scalar one dimensional system will be used to gain intuition into the more complicated multidimensional vector problem of primary interest. Analytical expressions for the attenuation will also be sought for cylindrical waveguides with coatings of various electrical properties. These will be used to design coatings for a waveguide to attenuate electromagnetic energy by a prescribed amount over a given band of frequencies.

The second phase of this project will concentrate on refining previous clinic work on numerical algorithms for designing optimal waveguide coatings. One goal is to redesign these programs so as not to use proprietary general purpose software and to increase their portability and efficiency. The team will also investigate the possibility of extending the code to include variable material properties, anisotropic materials, coupling of energy, different boundary conditions, and other effects that will make the program more realistic.

Advisor

David Bosley

USC Information Sciences Institute: Modeling of Short Channel MOSFET Devices for Use in VLSI Simulations

Unavailable

Advisor

Jerome Spanier 鈥� CGU

1990 鈥� 1991

Teledyne Microelectronics: Statistical Process Control In Microelectronics

In the machine bonding of wire to semiconductors there are several measurable parameters (the 鈥渟econdary parameters鈥�) which are used to evaluate the overall quality of the process, and there is another set of machine specific parameters (the 鈥減rimary parameters鈥�) which can be set in order to control the bonding process. In this project a sensitivity analysis is performed on the main wire bonding secondary parameters in order to determine their interaction with the primary parameters controlling the performance of this process.

The project centered around the study of the effects of variations in each secondary parameter, and in the interaction between the secondary and the primary control parameters. Moreover, the secondary parameters were grouped using different permutations and the interaction of simultaneous variations in such groupings with the primary parameters were studied. The aim was to develop a control envelope which described the processes鈥� preset tolerance limits, and which could form the basis for a computer control system of the wire bonding machine.

McDonnell Douglas: Density and Energy Distribution of Electrons in the Lower Van Allen Belts

Accurate specification of natural radiation environments have an impact on the design of space electronics. Poor specification of the environment and its effects can cause serious system anomalies and loss of mission capability. The radiation belt environments have not been updated in 20 years.

The objective of this study is to use newer satellite data to upgrade and update Van Allen belt inner zone electron radiation models at low altitude. The low altitude radiation belt models are based upon early satellite results. The more recent satellite data have not been organized into model form and compared with the accepted models. This task will do this comparison.

Advisor

Mario Martelli

Northrop B2 Division: An Investigation of Reflection, Transmission, and Absorption of Electromagnetic Energy Interacting With Waveguides

Inlet and exhaust cavities can be important sources of scattering for low observable 鈥渟tealthy鈥� vehicles. Analyzing these cavities considered as waveguides may provide a simple characterization of the cavities鈥� radar backscatter.

Task I. Consider a rectangular and circular waveguide coated with a lossy (complex permittivity and/or permeability) isotropic material. Develop a computer code to calculate the energy transmission and attenuation per wavelength of the waveguide for the lowest modes of propagation. Extend this method to high model scattering. Perform optimization studies of attenuation for specific classes of materials.

Task II. Generalize Task I to consider a coated waveguide with N-Layers of isotropic material (cf. 鈥淎n Investigation of Reflection, Transmission and Absorption of Electromagnetic Energy,鈥� 1988/1989 Mathematics Clinic Final Report to B-2 Division).

Task III. Time permitting, generalize Task II to consider anisotropic material (cf. op. cit.).

Advisor

Robert Borrelli

Rand Corporation: Theory of Chaos Applied to Combat Models

The objective of this project is to investigate the possibility that competitive populations that model attrition and reinforcement exhibit chaos, and, if so, to investigate ways to ameliorate the effects of that chaos.

Advisor

Stavros Busenberg

Teledyne Microelectronics: Establishment of Statistical Process Control Program

This project is a follow-on to the work already started by 91探花 in developing statistical process control systems for hybrid lead bond operations. With 91探花 Mudd鈥檚 assistance Teledyne wishes to review, study and implement a direct linkage between the testing/evaluation system and the automated wire bonding process. What is envisioned is a data linkage between two test systems and a computer/controller which will take precalculated statistical parameters from the two machines and calculate and continually monitor this statistical data. The controller/computer will also monitor the auto bond machine, and with these inputs send out updated optimized parameters (power, time and pressure) to the auto bonder.

Teledyne is looking to 91探花 Mudd for not only proof of concept, but to presenting a full-up working model.

Northrop B2 Division: An Investigation of Reflection, Transmission and Absorption of Electromagnetic Energy

The propagation, reflection and refraction of electromagnetic energy is easily computed for non-conducting and very conducting media. In order to solve electromagnetic problems encountered in aircraft design, the general case of arbitrary conductivity must be considered.

Jet Propulsion Laboratory: Optimal Data Collection for MOSFET Modeling

Problem 1. Physical and geometrical parameters used in modeling the flow of current were not known and were hard to measure. They were inferred (鈥減arameter extraction鈥�) from current measurements. The clinic addressed how the latter can be reduced, retaining good accuracy on the extracted values.

Jet Propulsion Laboratory: Prediction of Contact Yields for MOSFET鈥檚

Problem 1. A JPL Scientist had invented a device to measure the resistance of a single contact on a chip. Statistical extrapolation from data of 1,000 measurements did not give good results for the whole chip (15 million contacts). The clinic investigated more appropriate probability distributions, taking into account the fabrication process.

System Development Corporation: Multispectral Classifier

鈥淩emote sensing systems routinely provide multi-spectral information and digital image processing provides qualitative tools for visual interpretation as well as quantitative tools for categorizing this information. Multispectral classification, a common approach to computer-aided mapping, was used to reduce the large, apparently unrelated, amounts of information to a set of features with similar reflective or emissive properties. A classifier algorithm must first compute the statistics which describe these features and then attempt to isolate unknown spectral signatures into the appropriate class using the predetermined statistics to define the decision boundary between each category.

The clinic project was to design, implement and test an unsupervised classifier on a VAX under VMS. Imagery, processed or unprocessed, would be provided by SDC. The design included (1) investigation of known algorithms with implementation and test of the most promising; (2) any other algorithms proposed by the Clinic team; (3) suggested preprocessing options; (4) design of a user interface; and (5) validation of an imagery set that was separate, but similar to that used for development. SDC provided the necessary components of their SDCIPS software package to HMC so that HMC could accomplish this task and have a product compatible with IPS.鈥�

Advisor

Henry Krieger

1984 鈥� 1985

1983 鈥� 1984

1982 鈥� 1983

1981 鈥� 1982

This project was concerned with a stability analysis of a passive communication satellite concept known as PACSAT. This device consists of 1.5m sections of steel wire of diameter about 1mm which are hinged together with friction joints to form a one-dimensional diffraction grating of total length 1.5km. A typical orbital altitude is about one earth radius, and when irradiated from the earth, PACSAT acts essentially as a one-dimensional diffraction grating producing a high gain cone whose cone angle is frequency-dependent. The concern of this project was focused on the adequacy of gravity gradient forces to keep the orbiting PACSAT in a stable configuration of a nearly straight line directed toward the earth鈥檚 center in spite of expected perturbing forces (e.g., solar heating, eclipsing, non-sphericity of the earth, etc.). Small deviations from this nominal configuration above narrow tolerances would severely diminish PACSAT鈥檚 usefulness as a communications satellite.

Advisor

Stavros Busenberg

1979 鈥� 1980

This project identified probability distributions for frequency of fire ignitions and for frequency of different fire sizes. The most usable output was the mean and distribution of simple relative frequency or rate of occurrence of fires by fuel, cause, weather and quarter of the year. Another result was the distribution of different fire sizes stratified by fuel, cause, fire danger and quarter of the year, using forests and years as replications. To make the output more usable, the time unit was quarter of the year and area 鈥渕illions of acres.鈥�

Advisors

Robert Borrelli
Robert Mifflin

Greg Pierce 鈥� CGU

This project developed a mathematical model for the concentration of certain pollutants in underground water. A computer program based on this model was also produced by the project. This program can be used to determine nitrate concentrations in the groundwater and to produce graphical displays of such levels.

Advisor

Stavros Busenberg