Physical Sciences and Mathematics Commons^™

Using Particle Swarm Optimization To Generate Optimal Experimental Designs With Replication Structures, Thomsen Bolton

Student Research Symposium

The modern dominant approach to planning experiments in industrial engineering and manufacturing is optimal design. This is a popular design paradigm because it 1) requires specification of an optimality criterion which incorporates practical objectives as definition of a design with high quality and 2) yields a design via high-dimensional optimization that gives the researcher ‘the most bang for the buck’ for a fixed sample/experimental run size. We aim to adapt the state-of-the-art meta-heuristic optimization algorithm, the Particle Swarm Optimization (PSO), to generating optimal designs with user-specified replication structure. Recently, PSO has been demonstrated to be highly effective at generating candidate …

Generating Optimal Space-Filling Designs With Particle Swarm Optimization, Rebekah Scott

Student Research Symposium

In 1935, Ronald Fisher published The Design of Experiments, establishing classical designs for various types of experiments. With the rise of computing power came optimal design, where statisticians can better customize designs according to the needs of the researchers running the experiment. This research focuses on generating optimal MaxMin space-filling designs with particle swarm optimization using various distance metrics (Manhattan, Euclidean, etc). Interestingly, changing the distance metric in the objective function had a minimal effect on the design, except for Aitchison geometry on the simplex. Space-filling designs are optimal for supporting high-order models with only a small sacrifice in prediction …

Fast Computation Of Friction Stir Welding Process With Model Order Reduction And Machine Learning, Joshua Kay

Student Research Symposium

Joining aluminum alloys and other metal workpieces is a typical manufacturing process, which can be accomplished by various welding techniques. Friction stir welding (FSW), a relatively new technology patented in 1991, has many advantages over conventional welding processes. For the FSW process, it is desirable to determine an optimal set of parameters to avoid product defects in the joints. Modeling and simulating the FSW process is computationally expensive which creates a bottleneck in searching for optimal operating parameters. Reduced order modeling techniques will be used to significantly reduce computation time for FSW models while maintaining accuracy. In addition, machine learning …

Manifold Alignment With Inter-Domain Diffusion, Andres Duque

Student Research Symposium

The integration of multimodal data presents a challenge in cases when the study of a given phenomena by different instruments or conditions generates distinct but related domains. In this paper, we propose Diffusion Transport Alignment (DTA) a semi-supervised manifold alignment method that exploits prior correspondence knowledge between distinct data views. DTA finds a bijection between two domains, which by assumption, share a similar geometrical structure coming from the same underlying data generating process. We empirically demonstrate the effectiveness of our method to integrate multimodal data, as well as how it can improve the performance of machine learning tasks, otherwise less …

Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton

Student Research Symposium

Using Natural Language Processing (NLP), we are able to analyze text from suicidal individuals. This can be done using a variety of methods. I analyzed a dataset of a girl named Victoria that died by suicide. I used a machine learning method to train a different dataset and tested it on her diary entries to classify her text into two categories: suicidal vs non-suicidal. I used topic modeling to find out unique topics in each subset. I also found a pattern in her diary entries. NLP allows us to help individuals that are suicidal and their family members and close …

Modeling The Spread Of Curly Top Disease In Tomato Crops, Rachel Frantz

Student Research Symposium

Curly Top disease (CT), caused by a family of curtoviruses, infects a wide variety of agricultural crops. Historically, CT has caused extensive damage in tomato crops resulting in substantial economic loss for the tomato industry. Control methods for CT are scarce, and methods for predicting and assessing the scope of CT outbreaks are limited. In this paper, we formulate two theoretical models, a deterministic model and a stochastic model, for the spread of CT in a heterogeneous environment consisting of beets (preferred host) and tomatoes. The models are composed of two susceptible classes and two infected classes (infectious beets and …

The Outdoor Fashion Industry Is Not Sustainable, Joshua Hillam

Student Research Symposium

Outdoor fashion companies are responsible for a large amount of waste and pollution worldwide. I believe they are ethically bound to make changes in their manufacturing process to decrease their footprint because their products are used in outdoor environments that are impacted negatively by waste and pollution. The fashion industry as a whole is responsible for 10% of the carbon emissions worldwide. Research was conducted by first understanding what being sustainable means from the EPA, from individuals who work in the fashion industry, and from companies that advocate for more sustainable clothing. I then investigated what materials are the most …

Finding Higher Order Interactions Using Local Corex, Thomas Kerby

Student Research Symposium

In applications such as financial markets, social networks, and gene expression data, the variables often interact in complex ways. Yet accurately characterizing pairwise variable interactions can be a difficult task, let alone efficiently characterizing complex higher-order interactions, which is an unsolved problem. This difficulty is exacerbated when variable interactions change across the data. For example, gene interactions in single-cell RNA-sequencing (scRNA-seq) data will typically differ from one cell type to another. To solve these problems, we propose a new method called Local Correlation Explanation (CorEx). Local CorEx captures higher-order variable interactions at a local scale by first clustering data points …

Modeling The Extended Low And Sudden High Periods Of Activity In Infectious Diseases, Dana Strong

Student Research Symposium

This research explores how the aggregation of individuals during disease spread may, in conjunction with noise, explain how some diseases’ trajectories spend some time at low numbers after which there is a sudden outbreak.

Ensemble Kernel Density Estimation, Ethan Ancell

Student Research Symposium

The problem of estimating a probability density function from data has many applications in machine learning and data science. Nonparametric estimators are useful in this context as they require relatively few assumptions on the densities. Unfortunately, standard nonparametric methods such as kernel density estimationtend to converge slowly to the true value in high dimensions as a function of the data sample size. Recent work has shown that optimally weighted ensembles of nonparametric estimators can be used to achieve a fast convergence rate when estimating information theoretic functionals such as information divergence. We explore the extension of this theory to density …

Development Of Particle Image Velocimetry Learning Tool: Learnpiv.Org, Kevin Roberts

Student Research Symposium

Particle Image Velocimetry (PIV) is an experimental measurement technique used for quantitative and visual analysis of the velocity distribution in a flow field. Researchers conduct PIV by using lasers to illuminate particles in a flow field of interest, digital cameras to record images of these illuminated particles, and PIV software to analyze the recorded images, producing a velocity vector field. Applying proper techniques to gather useful images and identifying PIV processing algorithm parameters to the collected images is a challenging task for novice PIV users who are unaware of the inner workings of PIV algorithms. Recognizing this problem, we created …

An Operational Drought Prediction Framework With Application Of Vine Copula Functions, Mahkameh Zarekarizi

Student Research Symposium

Early and accurate drought predictions can benefit water resources and emergency managers by enhancing drought preparedness. Soil moisture memory is shown to contain helpful information for prediction of future values. This study uses the soil moisture memory to predict their future states via multivariate statistical modeling. We present a drought forecasting framework which issues monthly and seasonal drought forecasts. This framework estimates droughts with different lead times and updates the forecasts when more data become available. Forecasts are generated by conditioning future soil moisture values on antecedent drought status. The statistical model is initialized by soil moisture simulations retrieved from …

Cox Processes For Visual Object Counting, Yongming Ma

Student Research Symposium

We present a model that utilizes Cox processes and CNN classifiers in order to count the number of instances of an object in an image. Poisson processes are well suited to events that occur randomly in space, like the location of objects in an image, as well as to the task of counting. Mixed Poisson processes also offer increased flexibility, however they do not easily scale with image size: they typically require O(n3) computation time and O(n2) storage, where n is the number of pixels. To mitigate this problem, we employ Kronecker algebra which takes advantage of the direct product …

Math And Sudoku: Exploring Sudoku Boards Through Graph Theory, Group Theory, And Combinatorics, Kyle Oddson

Student Research Symposium

Encoding Sudoku puzzles as partially colored graphs, we state and prove Akman’s theorem [1] regarding the associated partial chromatic polynomial [5]; we count the 4x4 sudoku boards, in total and fundamentally distinct; we count the diagonally distinct 4x4 sudoku boards; and we classify and enumerate the different structure types of 4x4 boards.

The Smallest Intersecting Ball Problem, Daniel J. Giles, Mau Nam Nguyen

Student Research Symposium

The smallest intersecting ball problem involves finding the minimal radius necessary to intersect a collection of closed convex sets. This poster discusses relevant tools of convex optimization and explores three methods of finding the optimal solution: the subgradient method, log-exponential smoothing, and an original approach using target set expansion. A fourth algorithm based on weighted projections is given, but its convergence is yet unproven. Numerical tests and comparison between methods are also presented.

Non-Orientable Objects As Gaming Surfaces, Haley P. Bourke, Paul Latiolais

Student Research Symposium

Developed in Python, Klein Space Fighter is an interactive learning tool and mathematically themed arcade game that allows the player to combat on different mathematical surfaces including a 2D Klein bottle. The app is available for Android and desktop devices, and will be made available for iOS in the future.

To receive an invitation to download the app through Google Play, contact me at HaleyoBourke@yahoo.com