Digital Commons Network^™

An Innovative Approach On Yao’S Three-Way Decision Model Using Intuitionistic Fuzzy Sets For Medical Diagnosis, Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Florentin Smarandache, Hamza Ghazanfar Toor, Faiza Asif

Branch Mathematics and Statistics Faculty and Staff Publications

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a …

A New Mood’S Median Test For Imprecise Data, Abdulrahman Alaita, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The existing Mood’s median test is a non-parametric test used to compare two or more sample data sets whether they are from the same population or not. There can be no application of this test to uncertain and indeterminate data. Therefore, it is necessary to find a generalization of this test that will enable us to apply it in uncertain environments. This study will present a new approach that utilizes neutrosophic statistics to apply Mood’s median test. The approach involves defining hypotheses, determining a decision rule, and performing the test in an uncertain environment. An evaluation of the performance of …

A Comprehensive Study On Decision-Making Algorithms In Retail And Project Management Using Double Framed Hypersoft Sets, Ajoy Kanti Das, Florentin Smarandache, Rakhal Das, Suman Das

Branch Mathematics and Statistics Faculty and Staff Publications

In today's dynamic business environment, effective decision-making plays a crucial role in the success of retail businesses and project management endeavors. This paper presents a comprehensive study of decision-making algorithms, focusing on the utilization of Double Framed Hypersoft Sets (DFHS) in retail and project management contexts. The study explores the theoretical foundations of DFHS and its practical applications in customer segmentation, personalized marketing, project selection, and resource allocation. Various algorithms and methodologies incorporating DFHS are discussed and analyzed, highlighting their advantages, limitations, and real-world implications. Through a series of numerical examples, case studies, and comparative analyses, this study provides valuable …

Row-Column Designs: A Novel Approach For Analyzing Imprecise And Uncertain Observations, Abdulrahman Alaita, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Classical row-column designs cannot be applied when the underlying data set contains some imprecise, uncertain, or undetermined observations. In this paper, we discuss row-column design under a neutrosophic statistical framework. A significant contribution of our study is to propose a novel approach to analyzing row-column designs using neutrosophic data. This approach involves calculating the neutrosophic analysis of variance (NANOVA) table for the proposed design and using it to derive the FN -test in an uncertain environment. Two numerical examples have been used to assess the proposed design’s performance. Results from the study indicated that a row column design under …

Modeling Inflation Using A Fast Fourier Transform (Fft), Blake Smith

Williams Honors College, Honors Research Projects

This paper utilizes a Fast Fourier Transform (FFT) algorithm to construct a trigonometric interpolant for the Consumer Price Index (CPI), which is then differentiated and used to obtain a continuous function for “instantaneous” (i.e., month-wise) inflation, as opposed to a 12-month percent-change. Fourier coefficients are analyzed to investigate underlying periodicities in the newly constructed function. This metric does not hold significant predictive value but it may prove helpful in retroactive analysis of inflation trends.

Multiple Imputation For Robust Cluster Analysis To Address Missingness In Medical Data, Arnold Harder, Gayla R. Olbricht, Godwin Ekuma, Daniel B. Hier, Tayo Obafemi-Ajayi

Mathematics and Statistics Faculty Research & Creative Works

Cluster Analysis Has Been Applied To A Wide Range Of Problems As An Exploratory Tool To Enhance Knowledge Discovery. Clustering Aids Disease Subtyping, I.e. Identifying Homogeneous Patient Subgroups, In Medical Data. Missing Data Is A Common Problem In Medical Research And Could Bias Clustering Results If Not Properly Handled. Yet, Multiple Imputation Has Been Under-Utilized To Address Missingness, When Clustering Medical Data. Its Limited Integration In Clustering Of Medical Data, Despite The Known Advantages And Benefits Of Multiple Imputation, Could Be Attributed To Many Factors. This Includes Methodological Complexity, Difficulties In Pooling Results To Obtain A Consensus Clustering, Uncertainty Regarding …

Estimated Glomerular Filtration Rate Slope And Risk Of Primary And Secondary Major Adverse Cardiovascular Events And Heart Failure Hospitalization In People With Type 2 Diabetes: An Analysis Of The Exscel Trial, Abderrahim Oulhaj, Faisal Aziz, Abubaker Suliman, Kathrin Eller, Rachid Bentoumi, John B. Buse, Wael Al Mahmeed, Dirk Von Lewinski, Ruth L. Coleman, Rury R. Holman, Harald Sourij

All Works

Aim: The decline in estimated glomerular filtration rate (eGFR), a significant predictor of cardiovascular disease (CVD), occurs heterogeneously in people with diabetes because of various risk factors. We investigated the role of eGFR decline in predicting CVD events in people with type 2 diabetes in both primary and secondary CVD prevention settings. Materials and Methods: Bayesian joint modelling of repeated measures of eGFR and time to CVD event was applied to the Exenatide Study of Cardiovascular Event Lowering (EXSCEL) trial to examine the association between the eGFR slope and the incidence of major adverse CV event/hospitalization for heart failure (MACE/hHF) …

Refining The Inverse Lipschitz Constant For Injective Relu Networks, Cole Rausch

Electronic Theses and Dissertations

In this thesis, we study the Inverse Lipschitz Constant (ILC) of injective ReLU layers. We study the tightness of the ILC lower bound established in Puthawala et al. Our approach has three components. First, we find that the conditions for injectivity on lines yield a weaker condition than the general condition given in Puthawala et al. Second, we perform numerical experiments to judge the tightness of the existing ILC lower bound and find that bound is overly conservative. Third, we identify the source of the potential slack in the proof of the existing ILC bound, and perform further numerical experiments …

Decompositions Of Nonlinear Input-Output Systems To Zero The Output, W. Steven Gray, Kurusch Ebrahimi-Fard, Alexander Schmeding

Electrical & Computer Engineering Faculty Publications

Consider an input–output system where the output is the tracking error given some desired reference signal. It is natural to consider under what conditions the problem has an exact solution, that is, the tracking error is exactly the zero function. If the system has a well defined relative degree and the zero function is in the range of the input–output map, then it is well known that the system is locally left invertible, and thus, the problem has a unique exact solution. A system will fail to have relative degree when more than one exact solution exists. The general goal …

Id Numbers Of Lobster Graphs, Mark Anthony C. Tolentino, Luis Silvestre Jr, Richwell T. Chan Sim, Amir Jann Erikson Diga, Althea Julia R. Loyola

Mathematics Faculty Publications

No abstract provided.

Can't We Just Use Computers? Initial Efforts On Technology-Enhanced Learning Of Operations Research In A Philippine University, Lester Hao, Jeric C. Briones, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Operations Research (OR) is a required course in any applied math program in the Philippines. It involves complex and computation-heavy algorithms to guide and improve decision-making in organizations and relevant contexts. Despite the advent of software that have automated the computations or the implementation of algorithms, the teaching and learning of OR may still be rife with procedures being performed manually by hand. In this paper, we report on our initial progress on a research project that aims to revise the OR syllabi in one Philippine university, by integrating more technological tools in the teaching and learning of OR for …

Adjusting For Participation Bias In Case-Control Genetic Association Studies For Rare Diseases, Le Wang, Ben Fitzpatrick, Zhengbang Li, Clarice Weinberg, Jinbo Chen

Mathematics, Statistics and Data Science Faculty Works

Collection of genotype data in case-control genetic association studies may often be incomplete for reasons related to genes themselves. This non-ignorable missingness structure, if not appropriately accounted for, can result in participation bias in association analyses. To deal with this issue, Chen et al. [7] proposed to collect additional genetic information from family members of individuals whose genotype data were not available, and developed a maximum likelihood method for bias correction. In this study, we develop an estimating equation approach to analyzing data collected from this design that allows adjustment of covariates. It jointly estimates odds ratio parameters for genetic …

Rising Plant Demand Strengthens Nitrogen Limitation In Tidal Marsh, Le Wang, Adam Langley, Bella Yedman, Patrick Megonigal

Mathematics, Statistics and Data Science Faculty Works

Nitrogen (N) is a limiting nutrient for primary productivity in most terrestrial ecosystems, but whether N limitation is strengthening or weakening remains controversial because both N sources and sinks are increasing in magnitude globally. Temperate marshes are exposed to greater amounts of external N inputs than most terrestrial ecosystems and more than in preindustrial times owing to their position downstream of major sources of human-derived N runoff along river mouths and estuaries. Simultaneously, ecosystem N demand may also be increasing owing to other global changes such as rising atmospheric [CO2]. Here, we used interannual variability in external drivers and variables …

Persistent Relative Homology For Topological Data Analysis, Christian J. Lentz

Mathematics, Statistics, and Computer Science Honors Projects

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via the language of persistent homology, which encodes features of interest as holes within a filtration of the data. The recently presented U-Match Decomposition places the standard persistence computation in a flexible form, allowing for straight-forward extensions of the algorithm to variations of persistent homology. We describe U-Match Decomposition in the context of persistent homology, and extend it to an algorithm for persistent relative homology, providing proofs for the correctness and stability of the presented algorithm.

An Investigation Of Students' Modes Of Thinking Concerning Linearity In Linear Algebra, Noa Levy

Honors Undergraduate Theses

The intent of this thesis is to investigate student approaches to linearity within a linear algebra context, focusing on definitional, computational, and theoretical skills. Linear algebra’s abstract nature constitutes a major challenge for a significant sector of STEM students, with the course often serving as undergraduates’ first encounter with mathematical proofs and extrapolations. The current student struggle is reflected through the prominent gap in knowledge derived from a lack of a concrete understanding of rudimentary concepts (like linearity), pivotal to student success. As such, this investigation aimed to bridge this gap by considering students’ modes of thinking regarding the elementary …

Frieze And Tiling Groups In The Lorentz-Minkowski Plane, Michael O. Lynch

Honors Undergraduate Theses

In this thesis, there is a presentation of the isometries from the Lorentz-Minkowski Plane and a solution to the Frieze Patterns. There is a suggestion for a solution for the Tiling Patterns. Since the construction of these mathematical structures is well understood in the Euclidean plane, one can follow a similar approach to the construction of such objects to find the unique number of groups that describe all possible frieze patterns while there is a suggestion of the number for the tiling case. There is a reflection of these results in a computational and cosmological context.

The Atiyah-Hitchin-Singer Theorem And An 8-Dimensional Generalization, Timothy Ponepal

Theses and Dissertations (Comprehensive)

The Atiyah-Hitchin-Singer theorem states that the twistor almost complex structure on a certain S² bundle over an oriented Riemannian 4-manifold (M, g) is integrable if and only if the Weyl curvature tensor of g is self-dual. These ideas were developed by Roger Penrose connecting 4-dimensional Riemannian geometry with complex geometry. We present a new approach to the Atiyah-Hitchin-Singer theorem using horizontal lifts and their respective flows, cross products and the quaternions to show that the Nijenhuis tensor vanishes if and only if the Weyl curvature tensor of g is anti-self-dual. An eight dimensional generalization is presented when the …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

A Spiral Workbook For Discrete Mathematics 2nd Edition, Harris Kwong

Milne Open Textbooks

This updated text covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is …

Torricelli's Law And The Turn-Up Number, Bianca K. Hampel

Theses and Dissertations

We investigate Torricelli's differential law for solids of revolution. Computing the ratio of times of drainage under the same circumstances (same existing requirements) but rotating the solids 180 degrees allows us to define a "Torricelli turn-up number" associated with the solid. For various solids, we calculate this turn-up number and construct solids that are not symmetric under the 180-degree rotation but with a turn-up number of 1. That allows us to construct nonsymmetric clepsydra.

GröBner Bases With An Application To Tame Functions, Jessica D. Marconi

UNF Graduate Theses and Dissertations

Grobner bases are essential tools in algebraic geometry, used to simplify and solve systems of polynomial equations. These bases revolutionized computational methods in various branches of mathematics after being introduced in 1965 by Bruno Buchberger. This thesis explores the foundational concepts of Grobner bases, including their formation and properties. It also demonstrates their use in solving mathematical problems in algebraic geometry, including the ideal membership problem. As an application, we show how Grobner bases can be used to determine whether a polynomial mapping is tame. This concept is crucial for analyzing the topology near singular points and establishing whether a …

Leveraging Redundancy As A Link Between Spreading Dynamics On And Of Networks, Felipe Xavier Costa

Electronic Theses & Dissertations (2024 - present)

A constant quest in network science has been in the development of methods to identify the most relevant components in a dynamical system solely via the interaction structure amongst its subsystems. This information allows the development of control and intervention strategies in biochemical signaling and epidemic spreading. We highlight the relevant components in heterogeneous dynamical system by their patterns of redundancy, which can connect how dynamics affect network topology and which pathways are necessary to spreading phenomena on networks. In order to measure the redundancies in a large class of empirical systems, we develop the backbone of directed networks methodology, …

Bayesian Analyses For Time-Varying Data And Opinion Dynamics, Torin Quinlivan

Graduate Research Theses & Dissertations

We consider Bayesian analyses for time-varying data from the opinion dynamics in social networks and the processes of sensorimotor learning. Firstly, understanding the underlying opinions of social media users is a difficult process, as they must be understood filtered through the messages sent. To understand how to best estimate the latent opinions, we use a Bayesian approach to estimate various characteristics of the users and the network. We present a model for using Bayesian methods for this problem, along with a simulation study to demonstrate effectiveness. Secondly, incentivization with punishments or rewards may affect human skill learning. To investigate the …

Volume 15, Connor Thompson, Emily Steffenhagen, Emily Robertson, Luis Fernando Dos Reis, Emily Farmer, Samuel Villa, Robert Allison, Zachary Chessor, Megan Borden, Austin Burnett, Larry W. Grant Jr., Tristan Marowski, Emma Moore, Pearl Siff

Incite: The Journal of Undergraduate Scholarship

Introduction Dr. Amorette Barber, Director, Office of Student Research

From the Editor Dr. Hannah Dudley-Shotwell

Artist’s Statement Connor Thompson

On Mentorship Dr. John Miller

The Meat of the Matter: Alien, Human, and Animal in Terry Bisson’s “They’re Made Out of Meat” by Emily Steffenhagen

“Please REBLOG!”: An Ethical Analysis of Doxxing, Internet Vigilantism and Racists Getting Fired by Emily Robertson

Journaling: Paper Has More Patience Than People by Luis Fernando Dos Reis

The Effects of Climate Change on the Archaeological World by Emily Farmer

Lowered Seat Height Does Not Impair Wingate Performance in Untrained Cyclists by Samuel Villa, Robert Allison, …

Prospective Teachers' Conceptions Of Area, Betsy Mcneal, Sayonita Ghosh Hajra, Michael Battista, Ayse Ozturk

Teaching & Learning Faculty Publications

This study explored 10 prospective teachers’ (PTs’) understanding of the area of a rectangular region using square and non-square rectangular area-units. In an hour-long interview, each PT was first asked to explain how they would find the area of a given rectangular region in terms of a non-square notecard. For several PTs, this task prompted discussion of a square unit defined by the edge of the notecard. In a second task, PTs were presented with a rectangular array of squares and were asked to explain to a fictional child why multiplying length times width does not count the top left …

On The Structure Of Repeated-Root Polycyclic Codes Over Local Rings, Maryam Bajalan, Edgar Martinez-Moro, Reza Sobhani, Steve Szabo, Guelsuem Goezde Yilmazguc

EKU Faculty and Staff Scholarship

This paper provides the Generalized Mattson Solomon polynomial for repeated-root polycyclic codes over local rings that gives an explicit decomposition of them in terms of idempotents. It also states some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes. Both approaches provide a description of the perpendicular to 0-dual code for a given polycyclic code. (c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Paley Graphs, Prime Graphs, And Crossword Puzzles, Robert D. Jacobs Jr.

Theses and Dissertations

In this paper, we will talk about many different mathematical concepts. We will prove theorems about Paley graphs, prime graphs, and crossword puzzles. It will be very fun.

The results in the section about Paley graphs include structure theorems about the subgraph induced by the quadratic residues, the subgraph induced by the non-residues and a few related subgraphs. The main is to better understand the “independence structure” of the Paley graph itself. No good upper bound on the independence number of Paley graphs is known. Theorems about these subgraphs, and various counts aim at future improvement of upper bounds for …

Problems In Graph Theory With Applications To Topology And Modeling Rna, Rayan K. Ibrahim

Theses and Dissertations

In this thesis, we explore four projects. In the first project, we explore $r$-neighbor bootstrap percolation on a graph $G$. We establish upper bounds for the number of vertices required to percolate in the case that $r=2$ for particular classes of graphs. In the second project, we study the structure of graphs with independence number two. We prove a lower bound on the number of edges of such graphs, related to an upper bound on the number of edges in a triangle-saturated graph, and give a sufficient forbidden induced subgraph condition for independence number two graphs. In the third project, …

Graph Coloring Reconfiguration, Reem Mahmoud

Theses and Dissertations

Reconfiguration is the concept of moving between different solutions to a problem by transforming one solution into another using some prescribed transformation rule (move). Given two solutions s₁ and s₂ of a problem, reconfiguration asks whether there exists a sequence of moves which transforms s₁ into s₂. Reconfiguration is an area of research with many contributions towards various fields such as mathematics and computer science.
The k-coloring reconfiguration problem asks whether there exists a sequence of moves which transforms one k-coloring of a graph G into another. A move in this case is a type …

Mixed Mechanisms Of Multi-Site Phosphorylation, Suha Jayyousi Dajani

Graduate Research Theses & Dissertations

Multi-site phosphorylation is an important mechanism in cell biology that regulates protein function and activity. It also plays a critical role in a wide variety of cellular processes that control intra-cellular signaling. Studies on mono- and dual-site phosphorylation have been conducted theoretically and experimentally by researchers. However, there is little research on triple-site and multi-site mixed mechanism phosphorylation.

The aim of this research is to study and identify the number of positive steady states (multistationarity) in a mathematical model of a triple-site mixed mechanism, processive and distributive, phosphorylation network. This research is accomplished by means of ordinary differential equations, Jacobian …