Track: Applied Systems Engineering
Project: Nonnegative Matrix Factorization for Community Detection in Medical Images
Advisor(s): Akwum Onwunta
Student(s): Aditi Sathe
Student Prerequisites: 3rd or 4th year; coursework in ISE, Math, Finance/ Economics, or CSE preferred; interested students are required to have basic programming experience in either MATLAB, python, or R; deterministic optimization background (such as ISE 240) strongly preferred.
Description: Medical image datasets can have a prohibitively large number of images representing patients with different health conditions and various disease severity. When dealing with raw unlabeled image datasets, the large number of samples often makes it hard for experts and non-experts to understand the variety of images present in a dataset.
This project aims to develop efficient community detection algorithms based on nonnegative matrix factorization (NMF). NMF is an unsupervised machine learning technique for dimensionality reduction that can reveal hidden patterns and important relationships in the data without requiring labels. Furthermore, it exhibits good mathematical interpretability and natural applicability to detecting overlapping communities. In particular, the algorithms developed in the project will be used to identify and analyze the similarities of communities in unlabeled medical image datasets. Analyzing the similarities may be used to infer the severity and recommend appropriate treatment of the disease.
Project: Challenges in Privacy and Security of Health Data
Advisor(s): Ana Alexandrescu
Student(s): Marina Falzone
Student Prerequisites: 3rd or 4th year; coursework in ISE, Math, Finance/ Economics, or CSE preferred; interested students are required to have basic programming experience in either MATLAB, python, or R; deterministic optimization background (such as ISE 240) strongly preferred.
Description: Medical image datasets can have a prohibitively large number of images representing patients with different health conditions and various disease severity. When dealing with raw unlabeled image datasets, the large number of samples often makes it hard for experts and non-experts to understand the variety of images present in a dataset.
This project aims to develop efficient community detection algorithms based on nonnegative matrix factorization (NMF). NMF is an unsupervised machine learning technique for dimensionality reduction that can reveal hidden patterns and important relationships in the data without requiring labels. Furthermore, it exhibits good mathematical interpretability and natural applicability to detecting overlapping communities. In particular, the algorithms developed in the project will be used to identify and analyze the similarities of communities in unlabeled medical image datasets. Analyzing the similarities may be used to infer the severity and recommend appropriate treatment of the disease.
Track: Mathematics and Statistics in ISE
Project : Is soccer so popular because it is the most random ball sport?
Advisor(s): Luis Nunes Vicente
Student(s): Thaksheel Alleck, Roman Mitchell, Ori Remen, Claire Samson
Student Prerequisites: interest in soccer; 2nd, 3rd, or 4th year; coursework in engineering, math, with particular emphasis on probability and statistics.
Description: In this project we will try to explain the popularity of soccer through a study of randomness in ball sports. A hypothesis to be validated is that popularity, when expressed by the likelihood of weaker teams beating stronger ones, is highly correlated with chance. We will derive a model of randomness for ball sports and validate it with historical data.
Project : Electric Grid Interdiction
Advisor(s): Luis Zuluaga
Student(s): Melissa Caracciolo
Student Prerequisites: discrete optimization, linear algebra.
Description: In this project we will try to build models for analyzing and supporting decision-making regarding the structure of power grids, with a focus on resilience and protection from targeted attacks.
Project : Math Modeling Contest
Advisor(s): Jiayuan Wang, Ana Alexandrescu
Student(s) – non-credit: Jason Ye, Jon Klein, Tommy Parisi
Student Prerequisites: all majors welcome; background and interest in math & modeling (various topics) needed.
Description: The math modeling contest is an online competition over the span of four days (February 1 – February 5, 2024). You will form teams of up to three to work on a real-world application problem. During the four days, you will do research/literature review, gather/clean data, build models to analyze the data and produce a final report of at most 25 pages. One exciting feature about this contest is the variety of problem choices, especially the interdisciplinary one: data insights, operation research/network science, sustainability (environmental science) and policy. This contest provides an excellent opportunity for you to gain research/modeling experience, apply your knowledge and skills from multiple disciplines, and learn to work as a team. More importantly, this gives you an impressive resume credential for when you apply for internships in industry or graduate schools.Click here to see more problems and winning papers.
Track: Software & Computing in ISE
Project: Developing a User-Friendly Hospital Call Scheduling Tool
Advisor(s): Frank Curtis, Karmel Shehadeh
Student(s): Josie Charles, Connor McDowell
Student Prerequisites: 3rd, 4th, or 5th year; programming experience necessary; coursework in ISE (ISE 240 and ISE 230), Math, or CSE preferred.
Description: The goal of this on-going project is to develop a user-friendly tool for optimizing the call schedule for a set of residents in a large academic hospital. This is a complex scheduling problem and suboptimal rotation scheduling can lead to burnout, unfair distribution of workload, and uneven coverage of needed medical areas. The tool should be understandable and usable by chief residents who are responsible for constructing the call schedules. It is expected that real data from a large academic hospital can be obtained.
Project: Quantum Computing for Optimization
Advisor(s): Mohammadhossein Mohammadisiahroudi, Tamas Terlaky
Student(s): Kate Saltovets
Student Prerequisites: Basic knowledge of Python. Familiarity with linear algebra is preferable.
Description: Quantum computing has attracted significant interest in many fields like optimization because it potentially can solve classes of hard problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially one approach is using quantum linear algebra to speed up Interior Point Method which is one of the most powerful algorithms in optimization. In QCOL Lab, we are developing such hybrid quantum-classical algorithms to solve optimization problem.
Goals:
- Learning about linear and conic optimization problem and interior point method, which is the most
popular algorithm to solve such problem. - Learning about some quantum algorithms such as Quantum Linear System Algorithms (QLSAs)
which can solve linear systems faster than classical counterparts, and Quantum Interior Point Methods
(QIPMs). - Coding Quantum Algorithm using IBM QISKIT package and do some experiment to evaluate the
performance of quantum algorithm on quantum simulator and real quantum computers of IBM.
Project: Treatment Planning for Proton Therapy
Advisor(s): Mohammadhossein Mohammadisiahroudi, Tamas Terlaky
Student(s): Rodrigo Gonzalez Masselli
Student Prerequisites: Basic knowledge of Python. Familiarity with linear algebra is preferable.
Description: Radiation therapy (RT) has been well established as an essential tool to treat cancers. In radiotherapy, radiation treatment planning is the process in which a team consisting of radiation oncologists, radiation therapist, and medical physicists plan the appropriate external beam intensity and other factors to get the best result. In radiation treatment planning, the problem of finding appropriate machine configurations to get maximal coverage of tumor and limited damage to health organs is an important optimization problem. In this project, we try different formulations of radiotherapy optimization model for proton therapy and evaluate their performance.
Goals:
- Learning about optimization models for radiation therapy planing.
- Coding and solving optimization models with optimization solvers.