Mathematics Commons^™

Lasso: Listing All Subset Sums Obediently For Evaluating Unbounded Subset Sums, Christopher N. Burgoyne, Travis J. Wheeler

Graduate Student Theses, Dissertations, & Professional Papers

In this study we present a novel algorithm, LASSO, for solving the unbounded and bounded subset sum problem. The LASSO algorithm was designed to solve the unbounded SSP quickly and to return all subsets summing to a target sum. As speed was the highest priority, we benchmarked the run time performance of LASSO against implementations of some common approaches to the bounded SSP, as well as the only comparable implementation for solving the unbounded SSP that we could find. In solving the bounded SSP, our algorithm had a significantly faster run time than the competing algorithms when the target sum …

Global Existence And Blow-Up Phenomena For A Periodic Modified Camassa–Holm Equation (Moch), Zhaonan Luo, Zhijun Qiao, Zhaoyang Yin

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study global existence and blow-up for a periodic modified Camassa–Holm equation in nonhomogeneous Sobolev spaces. Also, we provide a key blow-up criteria to investigate norm inflation and ill-posedness problem for the equation in the critical Sobolev space.

On The Frequency Module Of The Hull Of A Primitive Substitution Tiling, April Lynne D. Say-Awen, Dirk Frettlöh, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

Understanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitution. A method is presented on how to arrive at the frequency module of the hull of a primitive substitution tiling (the minimal -module, where is the set of integers) containing the absolute frequency of each of its patches. The method involves deriving the tiling's edge types and vertex stars; in the process, a …

On Twin Edge Colorings In M-Ary Trees, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from ℤ_k and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in ℤ_k) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by χ′_t(G …

Deployment Of Mathematical Resources To A Philippine High School Through A Community Lte Network, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Verzosa

Mathematics Faculty Publications

In the Philippines, one challenge that continues to be faced by the Department of Education in bringing educational content in a blended learning modality is the lack of internet access of the learners. This paper discusses the distribution, through a community LTE network, of mathematical resources for Grades 7 to 10 to teachers and students of a particular high school in the Philippines. It also gives details on particular technological tools (mathematical applications) that were created to help the mathematical learning of students in a remote setting.

Sigma Chromatic Numbers Of The Middle Graph Of Some Families Of Graphs, Jay-R Manamtam, Agnes Garciano, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Let G be a nontrivial connected graph and let c : V (G) → be a vertex coloring of G, where adjacent vertices may have the same color. For a vertex υ of G, the color sum σ(υ) of υ is the sum of the colors of the vertices adjacent to υ. The coloring c is said to be a sigma coloring of G if σ(u) ≠ σ(υ) whenever u and υ are adjacent vertices in G. The minimum number of colors that can be …

Development Of An App And Videos To Support The Fraction Learning Trajectory From Grades 1-7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Juan Carlo F. Mallari, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Lack of procedural fluency in fractions impedes access to advanced mathematical courses and limits opportunities for entry into STEM-related fields. This paper describes the design and pedagogical basis of the Moving Fractions app and supplementary fraction videos for promoting fraction learning. Moving Fractions utilizes game-design factors to draw students through a trajectory of fraction learning from part-whole comparisons to a more robust understanding of the measurement concept of fractions. The supplementary video immerses students in a broad range of fraction representations. The app and video are intended to form a fraction learning package for distribution in Philippine schools. Future work …

Benchmarking Graph Neural Networks, Thomas Laurent, Vijay Prakash Dwivedi, Chaitanya K. Joshi, Anh Tuan Luu, Yoshua Bengio, Xavier Bresson

Mathematics, Statistics and Data Science Faculty Works

In the last few years, graph neural networks (GNNs) have become the standard toolkit for analyzing and learning from data on graphs. This emerging field has witnessed an extensive growth of promising techniques that have been applied with success to computer science, mathematics, biology, physics and chemistry. But for any successful field to become mainstream and reliable, benchmarks must be developed to quantify progress. This led us in March 2020 to release a benchmark framework that i) comprises of a diverse collection of mathematical and real-world graphs, ii) enables fair model comparison with the same parameter budget to identify key …

Online Algorithms With Advice For The 𝒌-Search Problem, Jhoirene B. Clemente, Henry N. Adorna, Proceso L. Fernandez Jr

Department of Information Systems & Computer Science Faculty Publications

In the online search problem, a seller seeks to find the maximum price from a sequence of prices p1, p2,…, pn that is revealed in a piece-wise manner. The bound for all prices is well known in advance with m ≤ pί ≤ M. In the online k-search problem, the seller seeks to find the k maximum out of the n prices. In this paper, we present a tight bound of [Formula Presented] on the advice complexity of optimal online algorithms for online k-search. We also provide online algorithms with advice that use less than the required number of bits …

An Introduction To Pascal’S Triangle, Daniel Chenoweth

Masters Essays

No abstract provided.

Exploration Of Triangles In Euclidean, Spherical, And Hyperbolic Spaces For The High School Geometry Classroom, John Rowell

Masters Essays

No abstract provided.

Estimating The Statistics Of Operational Loss Through The Analyzation Of A Time Series, Maurice L. Brown

Theses and Dissertations

In the world of finance, appropriately understanding risk is key to success or failure because it is a fundamental driver for institutional behavior. Here we focus on risk as it relates to the operations of financial institutions, namely operational risk. Quantifying operational risk begins with data in the form of a time series of realized losses, which can occur for a number of reasons, can vary over different time intervals, and can pose a challenge that is exacerbated by having to account for both frequency and severity of losses. We introduce a stochastic point process model for the frequency distribution …

A Comparison Of Stacking Methods To Estimate Survival Using Residual Lifetime Data From Prevalent Cohort Studies, Zhaoheng Li

Mathematics, Statistics, and Computer Science Honors Projects

Prevalent cohort studies are widely used for their cost-efficiency and convenience. However, in such studies, only the residual lifetime can be observed. Traditionally, researchers rely on self-reported onset times to infer the underlying survival distribution, which may introduce additional bias that confounds downstream analysis. This study compares two stacking procedures and one mixture model approach that uses only residual lifetime data while leveraging the strengths of different estimators. Our simulation results show that the two stacked estimators outperform the nonparametric maximum likelihood estimator (NPMLE) and the mixture model, allowing robust and accurate estimations for underlying survival distributions.

Spin(7) Orientifolds And 2d N = (0, 1) Triality, Sebastían Franco, Alessandro Mininno, Ángel M. Uranga, Xingyang Yu

Publications and Research

We present a new, geometric perspective on the recently proposed triality of 2d N = (0, 1) gauge theories, based on its engineering in terms of D1-branes probing Spin(7) orientifolds. In this context, triality translates into the fact that multiple gauge theories correspond to the same underlying orientifold. We show how Spin(7) orientifolds based on a particular involution, which we call the universal involution, give rise to precisely the original version of N = (0, 1) triality. Interestingly, our work also shows that the space of possibilities is significantly richer. Indeed, general Spin(7) orientifolds extend triality to theories that can …

Fano 3-Folds, Reflexive Polytopes And Brane Brick Models, Sebastían Franco, Rak-Kyeong Seong

Publications and Research

Reflexive polytopes in n dimensions have attracted much attention both in mathematics and theoretical physics due to their connection to Fano n-folds and mirror symmetry. This work focuses on the 18 regular reflexive polytopes corresponding to smooth Fano 3-folds. For the first time, we show that all 18 regular reflexive polytopes have corresponding 2d (0, 2) gauge theories realized by brane brick models. These 2d gauge theories can be considered as the worldvolume theories of D1-branes probing the toric Calabi-Yau 4-singularities whose toric diagrams are given by the associated regular reflexive polytopes. The generators of the mesonic moduli …

Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, Landon Gauthier

Theses and Dissertations--Mathematics

We consider inverse boundary problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.

An Integrated Computational Pipeline To Construct Patient-Specific Cancer Models, Daniel Plaugher

Theses and Dissertations--Mathematics

Precision oncology largely involves tumor genomics to guide therapy protocols. Yet, it is well known that many commonly mutated genes cannot be easily targeted. Even when genes can be targeted, resistance to therapy is quite common. A rising field with promising results is that of mathematical biology, where in silico models are often used for the discovery of general principles and novel hypotheses that can guide the development of new treatments. A major goal is that eventually in silico models will accurately predict clinically relevant endpoints and find optimal control interventions to stop (or reverse) disease progression. Thus, it is …

The Infinity Conundrum: Understanding Topics In Set Theory And The Continuum Hypothesis, Sabrina Grace Helck

Senior Independent Study Theses

This project is concerned with articulating the necessary background in order to understand the famous result of the undecidability of the continuum hypothesis. The first chapter of this independent study discusses the foundations of set theory, stating fundamental definitions and theorems that will be used throughout the remainder of the project. The second chapter focuses on ordinal and cardinal numbers which will directly relate to the final chapter. First, there is a clear explanation of the notion of order and what it means for a set to be well-ordered. Then ordinal numbers are defined and some properties are listed and …

Highlights Generation For Tennis Matches Using Computer Vision, Natural Language Processing And Audio Analysis, Alon Liberman

Senior Independent Study Theses

This project uses computer vision, natural language processing and audio analysis to automatize the highlights generation task for tennis matches. Computer vision techniques such as camera shot detection, hough transform and neural networks are used to extract the time intervals of the points. To detect the best points, three approaches are used. Point length suggests which points correspond to rallies and aces. The audio waves are analyzed to search for the highest audio peaks, which indicate the moments where the crowd cheers the most. Sentiment analysis, a natural language processing technique, is used to look for points where the commentators …

Wildfire Simulation Using Agent Based Modeling: Expanding Controlled Burn Season, Morgan C. Kromer

Senior Independent Study Theses

The United States is home to many different and unique forests. Prior to the 21st century, the United States Forests Service assumed that the best way to protect these forests was to put all efforts to keeping them alive. An enemy to these efforts were wildfires, thus the US adopted a complete fire suppression approach. At the turn of the century, the US realized that wildfires are a necessary part of a forest ecosystem, as they help return nutrients to the soil and reduce ground fuels. However, after suppressing all fires for over 100 years, the forests evolved into a …

Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft

Theses and Dissertations

Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

Function Approximation Guarantees For A Shallow Neural Network Trained By Gradient Flow, Russell Gentile

Electronic Theses and Dissertations, 2020-2023

This work features an original result linking approximation and optimization theory for deep learning. Several examples from recent literature show that, given the same number of learnable parameters, deep neural networks can approximate richer classes of functions, with better accuracy than classical methods. The bulk of approximation theory results though, are only concerned with the infimum error for all possible parameterizations of a given network size. Their proofs often rely on hand-crafted networks, where the weights and biases are carefully selected. Optimization theory indicates that such models would be difficult or impossible to realize with standard gradient-based training methods. The …

Mathematical Reasoning: Writing And Proof (Pretext Edition), Ted Sundstrom

Open Textbooks

Mathematical Reasoning: Writing and Proof is a text for the first college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.

Mathematical Reasoning: Writing and Proof (PreTeXt Edition) was developed as part of the Accelerating Open Educational Resources Initiative at Grand Valley State University, with support from the University Libraries and the President's Innovation Fund.

Mathematical Reasoning: Writing and Proof was written by Ted Sundstrom, Professor Emeritus of Mathematics at Grand Valley State University. This textbook was converted into PreTeXt by Ian Curtis, Editorial Assistant for the …

Finite Integration Method Using Chebyshev Expansion For Solving Heat Equation With Non-Local Boundary Conditions, Thanakorn Prasansri

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Eigenvalues Of Unitary Cayley Graph Of Matrix Algebras And Its Subconstituents, Jitsupat Rattanakangwanwong

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Cryptography Through The Lens Of Group Theory, Dawson M. Shores

College of Graduate Studies: Theses & Dissertations

Cryptography has been around for many years, and mathematics has been around even longer. When the two subjects were combined, however, both the improvements and attacks on cryptography were prevalent. This paper introduces and performs a comparative analysis of two versions of the ElGamal cryptosystem, both of which use the specific field of mathematics known as group theory.

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

College of Graduate Studies: Theses & Dissertations

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.

On The Geometry Of The Multiplier Space Of ℓPA, Christopher Felder, Raymond Cheng

Mathematics & Statistics Faculty Publications

For p ∊ (1, ∞)\ {2}, some properties of the space M_p of multipliers on ℓ^p_A are derived. In particular, the failure of the weak parallelogram laws and the Pythagorean inequalities is demonstrated for M_p. It is also shown that extremal multipliers on the ℓ^p_A spaces are exactly the monomials, in stark contrast to the p = 2 case.

A Drop In The Bucket?: Solutions For Fermi Questions, December 2022, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.