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Full-Text Articles in Mathematics
Topological Data Analysis And Ant Interaction Networks, Adam Banatwala, Esther Rønn
Topological Data Analysis And Ant Interaction Networks, Adam Banatwala, Esther Rønn
Mathematics & Computer Science Student Scholarship
Adam Banatwala ’22, Majors: Mathematics and Finance
Esther Rønn ’23, Majors: Physics and Mathematics
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science
Our research group used topological data analysis (TDA) to quantify the movement and behavior of ants in a colony.
We extracted higher dimensional networks from point cloud data collected from Dr. James Waters’ lab. Varying the proximity parameter in this construction gives a sequence of networks. We analyzed the enduring topological features of these networks, and how these features evolve over time as the ants move in the colony. Both the experimental and null model simulation data …
Classifications Of Transformations Of Km#Tn And Pm#Tn Via Symmetry Groups, Adam Banatwala, Jensen Barry, Mackenzie Maude
Classifications Of Transformations Of Km#Tn And Pm#Tn Via Symmetry Groups, Adam Banatwala, Jensen Barry, Mackenzie Maude
Mathematics & Computer Science Student Scholarship
Adam Banatwala ’22, Majors: Mathematics and Finance
Jensen Barry ’22, Majors: Biology and Mathematics
Mackenzie Maude ’22, Majors: Mathematics and Art History
Faculty Mentor: Dr. C. Joanna Su, Mathematics and Computer Science
One of the main topics in topology is the classification and comparison of shapes and surfaces. Since Spring 2020, our research group has been using symmetry groups to classify the 1- and 2-dimensional orientable and non-orientable closed surfaces.
First, the group worked on the symmetry groups of the 1- and 2-dimensional orientable closed surfaces; namely, the classification on V?? 1 (the one-point adjoint of n circles) …
Lines On A Smooth Projective Surface, Jordan Demoura
Lines On A Smooth Projective Surface, Jordan Demoura
Mathematics & Computer Science Student Scholarship
Jordan DeMoura ’22
Major: Mathematics
Faculty Mentor: Dr. Su-Jeong Kang, Math
This research is to investigate lines on a smooth projective surface. A quadric surface contains two families of planes that provide a ruling of the surface. A cubic surface contains twenty-seven lines, and we provide a complete description of these lines for a Fermat cubic surface. Furthermore, under the Plucker embedding, we show that each family of the lines on a quadric surface corresponds to plane conic curves lying on complementary planes in the projective space of dimension five.
The Impact Of Decriminalizing Marijuana In Rhode Island On The Number Of Narcotic Related Arrests And Quantities Seized, Abigail Kojoian
The Impact Of Decriminalizing Marijuana In Rhode Island On The Number Of Narcotic Related Arrests And Quantities Seized, Abigail Kojoian
Mathematics & Computer Science Student Scholarship
Major: Mathematics
Minor: Classics
Faculty Mentor: Dr. Asta Shomberg, Mathematics
Self-Supervised Learning For Single-Molecule Localization Microscopy, Clare Minnerath
Self-Supervised Learning For Single-Molecule Localization Microscopy, Clare Minnerath
Mathematics & Computer Science Student Scholarship
Major: Mathematics and Computer Science
Faculty Mentor: Dr. Lynette Boos, Mathematics
We evaluate the ability of self-supervised deep learning for Poisson denoising of Single-Molecule Localization Microscopy (SMLM) in addition to the impact denoising can have on the ability to locate molecules within the Single-Molecule Localization Microscopy images. SMLM images are predominantly corrupted with Poisson noise. There is a need for a superior technique to provide accurate SMLM images in order for scientists to gain a better understanding of the functions of live cells at the nanoscale. By denoising SMLM images prior to the images undergoing the current state- of-the-art super-resolution …
Research In Sabermetrics: The Cape Cod Baseball League, Thomas Zinzarella
Research In Sabermetrics: The Cape Cod Baseball League, Thomas Zinzarella
Mathematics & Computer Science Student Scholarship
Major: Sports Media
Faculty Mentor: Fr. Humbert Kilanowski O.P, Mathematics and Computer Science
We analyzed data from the Cape Cod Baseball League, a prestigious summer baseball league, where we looked at sabermetric statistics such as WAR (Wins above replacement). Stats like these can help evaluate a player and project whether they are a future MLB player or not. Especially on the Cape, where 1 in 7 current Major League Baseball players have played in the league.
Simplexity Of The N-Cube, Peter Graziano
Simplexity Of The N-Cube, Peter Graziano
Mathematics & Computer Science Student Scholarship
Major: Mathematics and Classics
Faculty Mentor: Dr. Su-Jeong Kang, Mathematics
The process of dividing shapes into triangles is called triangulation, and it is possible to abstract the idea of a triangle to higher dimensions, where it will be called a simplex in n-dimensions, or an n-simplex. I studied this process of generalized triangulation, or decomposition, in order to find an optimal decomposition of a 5-cube to help improve the bounds on the general case of an n-cube.
Application Of Black-Scholes-Merton Model In Option Pricing And Intangibles Assets, Giang Nguyen-Hoang
Application Of Black-Scholes-Merton Model In Option Pricing And Intangibles Assets, Giang Nguyen-Hoang
Mathematics & Computer Science Student Scholarship
Major: Finance and Mathematics
Faculty Mentor: Dr. Joseph Shomberg, Mathematics
The Black-Scholes model was developed by Fisher Black and Myron Scholes in the 1970s to price stock options. Since then the model has been suited to price so-called intangible assets such as trademarks and patents. In this paper, we investigate the related Black-Scholes-Merton model and the relevant characteristics of patents in order to associate patents as real options. After describing patents as options, we apply the Black-Scholes-Merton model to the valuation of the intangible assets. Special attention is given to modeling volatility and the cost of delay in order to …
Using Neural Networks To Classify Pdes, Julia Balukonis, Sabrina Fuller, Haley Rosso
Using Neural Networks To Classify Pdes, Julia Balukonis, Sabrina Fuller, Haley Rosso
Mathematics & Computer Science Student Scholarship
Major: Mathematics
Minor: Computer Science and Film
Faculty Mentor: Dr. Lynette Boos, Mathematics and Computer Science
We designed two neural networks that can learn how to classify three different types of partial differential equations (PDEs). Our data consists of numerical solutions to three categories of PDEs: Burger’s, Diffusion, and Transport equations. Using TensorFlow and the Keras library, we performed two tasks – the first a binary classification of Burger’s and Diffusion equation data, and the second a multi-label classification incorporating the Transport Equations as well. Our binary classification network requires vector labels to perform efficiently. Furthermore, our tertiary classification network …