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Full-Text Articles in Physical Sciences and Mathematics
The Commutant Of The Fourier–Plancherel Transform, Brianna Cantrall
The Commutant Of The Fourier–Plancherel Transform, Brianna Cantrall
Honors Theses
One can see that this matrix is unitary and has eigenvalues {1,−i,−1, I}, each of infinite multiplicity. Throughout the remainder of this thesis, we will convince the reader that the above linear transformation is actually the Fourier transform. We will compute the commutant, as well as its invariant subspaces. The key to do this relies on the Hermite polynomials. Why do we recast the Fourier transform from its well-known and well studied integral form to the matrix form shown above? As we will see, the matrix form allows us to efficiently discover the operator theory of the Fourier transform obfuscated …
Dictionary-Based Data Generation For Fine-Tuning Bert For Adverbial Paraphrasing Tasks, Mark Anthony Carthon
Dictionary-Based Data Generation For Fine-Tuning Bert For Adverbial Paraphrasing Tasks, Mark Anthony Carthon
Theses and Dissertations
Recent advances in natural language processing technology have led to the emergence of
large and deep pre-trained neural networks. The use and focus of these networks are on transfer
learning. More specifically, retraining or fine-tuning such pre-trained networks to achieve state
of the art performance in a variety of challenging natural language processing/understanding
(NLP/NLU) tasks. In this thesis, we focus on identifying paraphrases at the sentence level using
the network Bidirectional Encoder Representations from Transformers (BERT). It is well
understood that in deep learning the volume and quality of training data is a determining factor
of performance. The objective of …
The Use Of Digital Applications And Websites In Completing Math Assignments, Ronna Williams
The Use Of Digital Applications And Websites In Completing Math Assignments, Ronna Williams
CUP Ed.D. Dissertations
There is a large assortment of digital applications and websites available for students to use in completing their math assignments. The problem is how and why they are using these applications. This study looked at the different applications and websites used by students, including Slader, Wolfram Alpha, Symbolab, Desmos, and Photomath. The study then explored why students used these applications and websites. The idea of plagiarism in mathematics was presented to the students in this study. The review of the literature included the concepts of plagiarism and cheating and illustrated that students have a history of using tools for accomplishing …
Predicting How People Vote From How They Tweet, Rao B. Vinnakota
Predicting How People Vote From How They Tweet, Rao B. Vinnakota
Senior Projects Spring 2019
In 2016 Donald Trump stunned the nation and not a single pollster predicted the outcome. For the last few decades, pollsters have relied on phone banking as their main source of information. There is reason to believe that this method does not present the complete picture it once did due to several factors--less landline usage, a younger and more active electorate, and the rise of social media. Social media specifically has grown in prominence and become a forum for political debate. This project quantitatively analyzes political twitter data and leverages machine learning techniques such as Naive-Bayes to model election results. …
An Overview Of Computational Mathematical Physics: A Deep Dive On Gauge Theories, Andre Simoneau
An Overview Of Computational Mathematical Physics: A Deep Dive On Gauge Theories, Andre Simoneau
CMC Senior Theses
Over the course of a college mathematics degree, students are inevitably exposed to elementary physics. The derivation of the equations of motion are the classic examples of applications of derivatives and integrals. These equations of motion are easy to understand, however they can be expressed in other ways that students aren't often exposed to. Using the Lagrangian and the Hamiltonian, we can capture the same governing dynamics of Newtonian mechanics with equations that emphasize physical quantities other than position, velocity, and acceleration like Newton's equations do. Building o of these alternate interpretations of mechanics and understanding gauge transformations, we begin …
The Expectation For The Center Of Mass Of Finite Integer Grids, Finnegan Maximilan Muller Hardy
The Expectation For The Center Of Mass Of Finite Integer Grids, Finnegan Maximilan Muller Hardy
Senior Projects Spring 2017
Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.
The Facilitation Of Sound Waves Using Mathematical And Scientific Methods Of Digital Signal Processing, Benjamin Rocco Moss
The Facilitation Of Sound Waves Using Mathematical And Scientific Methods Of Digital Signal Processing, Benjamin Rocco Moss
Senior Projects Spring 2016
Mathematics and music have been lifelong partners since the beginning of time. Rhythm and time are two fundamental aspects of music which rely solely on counting, an under-appreciated skill in mathematics, yet recognized by all mathematically-minded people as the foundation of some of the most important mathematical findings; as John B. Fraleigh would say, “Never underestimate a theorem that counts something!” However, music recordings have evolved through the use of technology further than merely possessing the capabilities to quantify and archive the notes that were played in the recording. In the days before digital recordings, the only way to ensure …
An Elliptic Exploration, David Curtis Swart
An Elliptic Exploration, David Curtis Swart
Online Theses and Dissertations
In this paper I will be giving an introduction to an interesting kind of equation called elliptic curves, and how they can be used to protect our national security through Cryptology. We will explore the unique operation for adding points on elliptic curves and the group structure that it creates, as well as the ECC method, which stands among the RSA and AES methods as one of the modern day's most secure systems of cryptography. In addition, I will also introduce several algorithms and methods that are useful for working with ECC such as Schoof's Algorithm, and I will also …
Tournament Matrices An Overview, Russel O. Carlson
Tournament Matrices An Overview, Russel O. Carlson
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The results of a round robin tournament can be represented as a matrix of zeros and ones, by ordering the players and placing a one in the (i,j) position if player i beat player j, and zeros otherwise. These matrices, called tournament matrices, can be represented by graphs, called tournament graphs. They have been the subject of much research and study, yet there have been few attempts to give a wide exposition on the subject. Those that have been done tend to focus on the graph theoretical aspects of tournaments. S. Ree and Y. Koh did write a brief …