Mathematics Commons^™

Why Some Powers Laws Are Possible And Some Are Not, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich, Olga Kosheleva, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

Many dependencies between quantities are described by power laws, in which y is proportional to x raised to some power a. In some application areas, in different situations, we observe all possible pairs (A,a) of the coefficient of proportionality A and of the exponent a. In other application areas, however, not all combinations (A,a) are possible: once we fix the coefficient A, it uniquely determines the exponent a. In such case, the dependence of a on A is usually described by an empirical logarithmic formula. In this paper, we show that natural scale-invariance ideas lead to a theoretical explanation for …

Using Robotics And Engineering Design Inquiries To Optimize Learning For Middle Level Teachers: A Case Study, Iman Chafik Chahine, Norman Robinson Iii, Kimbeni Mansion

Publications & Research

This exploratory case study reports findings on 20 middle-level science and mathematics teachers’ perceptions of the effectiveness of a one-year project in which teachers engaged in using robotics and engineering design inquiries in their classrooms. Principled by Bandura’s Social Learning Theory (SLT) and using mixed methods approaches, the study measured teachers' efficacy through the Mathematics Teaching Efficacy Belief Instrument (MTEBI) and observation logs before and after the program. The results of this study showed statistically significant differences between PRE MTEBI and POST MTEBI scores. Furthermore, five themes emerged that illuminated potential affordances and constraints that teachers perceive as opportunities and …

Absence Of Remotely Triggered Large Earthquakes: A Geometric Explanation, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that seismic waves from a large earthquake can trigger earthquakes in distant locations. Some of the triggered earthquakes are strong themselves. Interestingly, strong triggered earthquakes only happen within a reasonably small distance (less than 1000 km) from the original earthquake. Even catastrophic earthquakes do not trigger any strong earthquakes beyond this distance. In this paper, we provide a possible geometric explanation for this phenomenon.

Precision Medicine: Gene And Clinical Data Analysis Of Renal Cancer, Sumeyye Su

Mathematics Dissertations - Archive

Recent advances in biotechnology led to generation of large complex biological and clinical data sets that can be used to infer the underlying mechanism of many diseases and arrive at personalized treatments. One of these data sets are the whole genome profiles, including a good collection of publicly available human gene expression data sets. In the first part of this study, we analyzed gene expression profiles of patients with renal cell carcinoma (RCC). We found that the regulator of G-protein signaling 5 (RGS5) might play a crucial role in initiation and progression of RCC, and it might be prognostic. We …

Boolean Rank And Isolation Number Of N-Regular Tournaments, Matthew F. Deangelo

Undergraduate Honors Capstone Projects

We examine Boolean rank and isolation number of a class of matrices, the adjacency matrices of regular tournaments. Boolean rank is defined as the minimum k such that a m x n matrix can be factored into m x k and k x n matrices, using Boolean arithmetic. Isolation number is defined as the maximum number of 1’s that do not share a row, column, or 2 x 2 submatrix of 1’s. Linear programming can be applied by using the underlying structure of the tournament matrices to develop a relationship between Boolean rank and isolation number. We show possible methods …

The Two Types Of Society: Computationally Revealing Recurrent Social Formations And Their Evolutionary Trajectories, Lux Miranda

Undergraduate Honors Capstone Projects

Comparative social science has a long history of attempts to classify societies and cultures in terms of shared characteristics. However, only recently has it become feasible to conduct quantitative analysis of large historical datasets to mathematically approach the study of social complexity and classify shared societal characteristics. Such methods have the potential to identify recurrent social formations in human societies and contribute to social evolutionary theory. However, in order to achieve this potential, repeated studies are needed to assess the robustness of results to changing methods and data sets. Using an improved derivative of the Seshat: Global History Databank, we …

Demystification Of Graph And Information Entropy, Bryce Frederickson

Undergraduate Honors Capstone Projects

Shannon entropy is an information-theoretic measure of unpredictability in probabilistic models. Recently, it has been used to form a tool, called the von Neumann entropy, to study quantum mechanics and network flows by appealing to algebraic properties of graph matrices. But still, little is known about what the von Neumann entropy says about the combinatorial structure of the graphs themselves. This paper gives a new formulation of the von Neumann entropy that describes it as a rate at which random movement settles down in a graph. At the same time, this new perspective gives rise to a generalization of von …

Analysis Of Sat And Isat Scores For Madison School District In Rexburg, Idaho, Holly Dawn Palmer

Undergraduate Honors Capstone Projects

Testing is an integral part of measuring education. If used properly SAT scores can be compared across the nation, and statewide tests can compare different school districts to each other if done properly to avoid certain pitfalls (Fetler, 1991). However, if tests do not have a significant impact on a student, their motivation to take the test will be low and test quality cannot be assumed. When the state funds two separate tests for their students but only one has a significant impact on the student, how should the scores for each test be used, and is it okay to …

Semisimple Subalgebras Of Semisimple Lie Algebras, Mychelle Parker

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Let g be a Lie algebra. The subalgebra classification problem is to create a list of all subalgebras of g up to equivalence. The purpose of this thesis is to provide a software toolkit within the Differential Geometry package of Maple for classifying subalgebras of In particular the thesis will focus on classifying those subalgebras which are isomorphic to the Lie algebra sl(2) and those subalgebras of which have a basis aligned with the root space decomposition (regular subalgebras).

Novel Inference Methods For Generalized Linear Models Using Shrinkage Priors And Data Augmentation., Arinjita Bhattacharyya

Electronic Theses and Dissertations

Generalized linear models have broad applications in biostatistics and sociology. In a regression setup, the main target is to find a relevant set of predictors out of a large collection of covariates. Sparsity is the assumption that only a few of these covariates in a regression setup have a meaningful correlation with an outcome variate of interest. Sparsity is incorporated by regularizing the irrelevant slopes towards zero without changing the relevant predictors and keeping the resulting inferences intact. Frequentist variable selection and sparsity are addressed by popular techniques like Lasso, Elastic Net. Bayesian penalized regression can tackle the curse of …

Optimal Treatment Strategies For Cancer Patients In Terms Of Survival Months And Socio-Economic Factors, Omer Mogultay

Mathematics Dissertations - Archive

One of the main challenges of cancer patients and their healthcare providers is making decisions regarding choosing the best treatment option. In the first part of thesis, we analyze breast cancer patients’ data to discover characteristics of patients who would benefit from each breast cancer surgical procedure in terms of increasing survival months. Since the outcome of breast cancer treatments strongly depends on the tumor subtypes, several studies investigated the outcome of surgical procedures for each of these subtypes. On the other hand, it has been shown that the outcome of breast cancer treatments is significantly different between black and …

On The Zeta Kirchhoff Index Of Several Graph Transformations, Danny Cheuk

Dissertations and Theses @ UNI

In this paper, we first derived the Ihara zeta function, complexity and zeta Kirchhoff index of the k-th semitotal point graph (of regular graphs), a construction by Cui and Hou [5], where we create triangles for every edge in the original graph. Then, we extend the construction to the creation of equilaterals and polygons.

We also derived the zeta Kirchhoff indices for numerous graph transformations on regular graphs, and some selected families of graphs.

At the end, a data summary is provided for enumeration computed on simple connected md2 graphs up to degree 10.

An Exploration In Ramsey Theory, Jake Weber

Dissertations and Theses @ UNI

We present several introductory results in the realm of Ramsey Theory, a subfield of Combinatorics and Graph Theory. The proofs in this thesis revolve around identifying substructure amidst chaos. After showing the existence of Ramsey numbers of two types, we exhibit how these two numbers are related. Shifting our focus to one of the Ramsey number types, we provide an argument that establishes the exact Ramsey number for h(k, 3) for k ≥ 3; this result is the highlight of this thesis. We conclude with facts that begin to establish lower bounds on these types of Ramsey …

Semi-Automated Image Segmentation And Synthesis Of Virtual Samples Using Generative Adversarial Networks And Fuzzy Sets, Reza Vafaee

Theses, Dissertations and Culminating Projects

Data-driven modeling has gained a lot of attention over the past few years. In most cases, such models use a big collection of inputs and the corresponding outputs to find the pattern in data. Prerequisite for applying these models is the availability of a large collection of data. Data-driven modeling has been employed to accomplish many tasks over the years. However, due to the lack of clinical data, the advancement of data-driven modeling in medical imaging has been relatively limited, mainly due to challenges involved with medical data collection and analysis. This is particularly true in ultrasound imaging for assessing …

Design Of Strips With Geometry Shapes And Mathematical Analysis, Somia Benali

Theses, Dissertations and Culminating Projects

In this research, I investigate different methods to create geometric designs for textile strips and study the geometric properties of the involved shapes. I develop three designs that contain circles, squares, and golden spiral pieces with repeating patterns and certain tangencies. One interesting part of the work is to find the tangent points and to calculate the areas of the regions to which different colors maybe assigned. The main figure for Design I is a circle inscribed in a square and that for Design II is a circle inscribed in an isosceles triangle. The last design integrates Golden Spirals into …

A Network Thermodynamic Game-Theoretic Approach To Modeling Amyloid-Beta Aggregation Along Competing Pathways, Joseph Pateras

Theses, Dissertations and Culminating Projects

The formation of large AB fibril plaques in the human brain is considered important to the pathogenesis of Alzheimer's disease (AD), as protein aggregation elsewhere in the body underpins many human ailments. Now however, low-molecular weight intermediate AB oligomers, more than large fibrils, are thought to be a primary precursor in early AD etiology. The main obstacle in the study of AD is the lack of understanding we have pertaining to the evolution of the disease in a living brain. For this reason, a thorough study of AB aggregation begs exploration. Prior conjectures and new experiments emphasize the interaction between …

Valuation Of Variance Swaps In Volatile Markets With Regime Switching, Mariam Zuwaid Salem Khamis Alshamsi

Mathematical Sciences Theses

Stochastic differential equations (SDEs) are extensively used to model various financial quantities. In the last decades, financial modeling by SDEs under regime-switching have been utilized to allow moving from an economic state to another. The aim of this research work is to tackle the pricing of variance swaps in a volatile market under regime switching model. SDEs under regime-switching models are more realistic but the solution is more complicated and may not exist analytically. Therefore, numerical methods for finance are explored. The study proposes a new SDE under regime-switching with high volatility model for the prices of the underlying financial …

Examining The Concept Images Of Function Held By Preservice Secondary Mathematics Teachers With Varying Levels Of Prior Mathematical Experience, Janessa Michele Beach

Mathematics Dissertations - Archive

This multiple case study examines the function concept images of preservice secondary mathematics teachers (PSMTs) enrolled in a mathematics content course designed specifically for PSMTs at a large urban university in the southwestern United States. The primary research question explores the changes in PSMTs’ function concept images when they engage with research-based explorations designed to elicit function-related cognitive conflicts. Furthermore, this study explores the extent to which there are differences in the function concept images of advanced undergraduate mathematics majors and those with the minimum prerequisite knowledge. Thematic analysis is applied to identify PSMTs function-related associations and characterize their function …

Impact Of Domestic Animals On Prevalence Of Vector-Borne Diseases In Humans, Md Mondal Hasan Zahid

Mathematics Dissertations - Archive

Vector-borne infectious diseases are one of the leading problems for public health worldwide, particularly in underdeveloped and developing countries. These diseases infect humans through the bite of infected vectors. The effect of host diversity on disease persistence, well studied in ecological literature, is examined here in a domestic setting. Some additional hosts dilute infection, while others amplify certain disease infections. Domestic animals can play an important role, as an additional host, in the disease dynamics by affecting host-pathogen interactions. However, the effect of additional hosts is not always straightforward since their presence impacts negatively by helping the vector population grow …

The Game Of Cops And Robbers On Planar Graphs, Jordon S. Daugherty

Graduate Theses/Dissertations

In graph theory, the game of cops and robbers is played on a finite, connected graph. The players take turns moving along edges as the cops try to capture the robber and the robber tries to evade capture forever. This game has received quite a bit of recent attention including several conjectures that have yet to be proven. In this paper, we restricted our attention to planar graphs in order to try to prove the conjecture that the dodecahedron graph is the smallest planar graph, in terms of vertices, that has cop number three. Along the way we discuss several …