Physical Sciences and Mathematics Commons^™

Improving Accessibility And Understanding: Studying The Impact Of Human Activities And Dam Removals On Anadromous Fish Species In The Pacific Northwest, Adia F. Bennett

Scripps Senior Theses

Human activities in North American watersheds have significantly impacted anadromous fish, causing some species of salmon and steelhead to become threatened and endangered. These fish hold ecological, cultural, and economic importance, yet factors such as habitat destruction, overfishing, pollution, climate change, and hydroelectric dams continue to degrade populations. Dams are particularly harmful to anadromous fish, sparking a recent movement advocating for dam removals. This study uses NOAA’s 2022 Biological Viability Assessment to examine the response of anadromous fish to recent dam removals in the Pacific Northwest. Four populations were selected to analyze due to their interaction with sites that had …

Bayesian Inference In Reinforcement Learning Neural Networks During A Markov Decision Processes?, Katherine Graham

Scripps Senior Theses

The predictive mind theory proposes that brains work in a way that makes predictions about future stimuli to process information efficiently and accurately. Bayesian brain theory suggests that the brain utilizes Bayesian probability models to make predictions, while the free-energy minimization hypothesis proposes that these predictions are made to minimize energy or uncertainty, ensuring accurate perceptions. Vertechi et al. (2020) explored animal participants’ utilization of stimulus-bound strategy versus inference-based strategy to solve a Markov decision process with a 2-state environment, one of which is always active. These sites have a certain probability of switching to a different site and the …

A Petrographic And Geochemical Study Of The Rangataua Lava Flows, Mount Ruapehu, Aotearoa New Zealand, Lucy Smith

Scripps Senior Theses

Mount Ruapehu is a large stratovolcano on the North Island of Aotearoa New Zealand. The Rangataua lava flow is situated on the southern flanks of Ruapehu, and extends for 15-16 km. The flow is of andesite composition and comprised of three units: proximal, medial and distal. Mount Ruapehu is both scientifically and culturally significant.

Geochemical analyses of 13 whole rock samples, Electron Microprobe analyses of three polished thin sections, and geothermobarometry calculations were conducted to obtain data on pre-eruptive intensive parameters. Petrographic observations were used to investigate disequilibrium textures and shed light on magma chamber processes.

Results of this study …

Geographically Dependent Thermodynamic And Geochemical Evolution In The Post-Batholith Upper Mantle Beneath The Sierra Nevada: Analysis Of The Blue Knob Xenoliths, Eleanor Ruos

Scripps Senior Theses

Xenoliths entrained in recent (Miocene) volcanics from the Sierra Nevada provide insights into a continuously evolving upper mantle during post-batholith generation periods (early Cenozoic–present). Hypothesized mantle refertilization followed by subsequent delamination of the lithospheric root beneath the Sierra provides a contextual framework for analyzing how the upper mantle responds to such events. This study contributes new geochemical data from the ultramafic xenoliths of Blue Knob, including bulk-rock major and trace element data, thin-section petrography, mineral chemistry and thermobarometry, and oxygen isotopes (delta¹⁸O). Blue knob (Eastern Sierra) data are compared to previous works on xenoliths from Chinese Peak and …

Synergetic Effects Of Democracy And Economic Development On Income Inequality And The Role Of Relative Political Capacity, Nazif Sali

CGU Theses & Dissertations

Diving into the complex dynamics of income inequality, this dissertation studies the multifaceted relationships between democracy, economic development, and inequality, placing a spotlight on the mediating influence of Relative Political Capacity (RPC). Uncovering the pivotal role of RPC as democracies advance and economies progress, this research navigates the contours of income inequality. By dissecting distinct sub-samples of OECD and non-OECD countries, nuanced insights surface. Employing robust methodologies such as ordinary least squares regressions and fixed effects analysis, I argue that targeted policies addressing inequality can not only foster inclusive economic growth but also fortify the foundations of democratic institutions. As …

Applications And Analysis Of Nlp Deep Learning Models For Antibiotic's Side Effects Classifications, An Ly

CGU Theses & Dissertations

I introduce a novel recursive modification to the classical Goemans-Williamson MaxCut algorithm, offering improved performance in vectorized data clustering tasks. Focusing on the clustering of medical publications, I suggest to employ recursive iterations in conjunction with a dimension relaxation method to enhance density of clustering results. Furthermore, I propose a new vectorization technique for articles, leveraging conditional probabilities for more effective clustering. I believe that these methods will provide advantages in both computational efficiency and clustering accuracy. I will analyze the effectiveness of recursive iterations and higher-dimensional generalizations of the GWA in the hopes of achieving more accurate dissimilarity-based clustering. …

Nitrate Contamination In Two California Groundwater Basins: What Creates Disparities?, Catherine Protiva

Scripps Senior Theses

Nitrate contamination is a major problem within California groundwater basins. A form of nitrogen, nitrates leach into groundwater aquifers from the surface where they remain for many decades. The most common source for the contaminant is agricultural sources like nitrogen fertilizer. Consequently, the problem is concentrated in regions of the state with a history of large-scale agricultural production. When water is pulled from contaminated basins and used as drinking water, the nitrates can cause serious negative health consequences, most commonly methemoglobinemia, also known as blue baby syndrome. In this thesis, I will examine what factors contribute to a region’s ability …

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

How To Intercept A High-Speed Rocket With A Pair Of Compasses And A Straightedge?, Yagub N. Aliyev

CODEE Journal

In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are …

Population Growth Models: Relationship Between Sustainable Fishing And Making A Profit, James Sandefur

CODEE Journal

In this paper, we develop differential equations that model the sustainable harvesting of species having different characteristics. Specifically, we assume the species satisfies one of two different types of density dependence. From these equations, we consider maximizing sustainable harvests. We then introduce a cost function for fishing and study how maximizing profit affects the harvesting strategy. We finally introduce the concept of open access which helps explain the collapse of many fish stocks.

The equations studied involve relatively simple rational and exponential functions. We analyze the differential equations using phase-line analysis as well as graphing approximate solutions using Euler's method, …

Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli

CODEE Journal

The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.

Exploring Parameter Sensitivity Analysis In Mathematical Modeling With Ordinary Differential Equations, Viktoria Savatorova

CODEE Journal

This paper presents an exploration into parameter sensitivity analysis in mathematical modeling using ordinary differential equations (ODEs). Taking the first steps in understanding local sensitivity analysis through the direct differential method and global sensitivity analysis using metrics like Pearson, Spearman, PRCC, and Sobol’, we provide readers with a basic understanding of parameter sensitivity analysis for mathematical modeling using ODEs. As an illustrative application, the system of differential equations modeling population dynamics of several fish species with harvest considerations is utilized. The results of employing local and global sensitivity analysis are compared, shedding light on the strengths and limitations of each …

A Generalized Solution Method To Undamped Constant-Coefficient Second-Order Odes Using Laplace Transforms And Fourier Series, Laurie A. Florio, Ryan D. Hanc

CODEE Journal

A generalized method for solving an undamped second order, linear ordinary differential equation with constant coefficients is presented where the non-homogeneous term of the differential equation is represented by Fourier series and a solution is found through Laplace transforms. This method makes use of a particular partial fraction expansion form for finding the inverse Laplace transform. If a non-homogeneous function meets certain criteria for a Fourier series representation, then this technique can be used as a more automated means to solve the differential equation as transforms for specific functions need not be determined. The combined use of the Fourier series …

Synthesis Of 2-Arylpyridines By The Suzuki–Miyaura Cross-Coupling Of Pyfluor With Hetero (Aryl) Boronic Acids And Esters, Juan Rueda-Espinosa, Dewni Ramanayake, Nicholas Ball, Jennifer A. Love

Pomona Faculty Publications and Research

The Suzuki–Miyaura cross-coupling of pyridine-2-sulfonyl fluoride (PyFluor) with hetero(aryl) boronic acids and pinacol boronic esters is reported. The reactions can be performed using Pd(dppf)Cl2 as the catalyst, at temperatures between 65 and 100 °C and in the presence of water and oxygen. This transformation generates 2-arylpyridines in modest to good yields (5%–89%).

Undetermined Coefficients With Hyperbolic Sines And Cosines, Laurie A. Florio, George L. Fischer

CODEE Journal

The method of undetermined coefficients is commonly applied to solve linear, constant coefficient, non-homogeneous ordinary differential equations when the forcing function is from a selected class of functions. Often the hyperbolic sine and cosine functions are not explicitly included in this list of functions. Through a set of guided examples, this work argues that the hyperbolic sine and cosine ought to be included in the select class of functions. Careful explanation is provided for the necessary treatment of the cases where the argument of the hyperbolic sine and/or cosine functions matches one or both of the roots of the characteristic …

Cookie(X) = 1/2, Lawrence M. Lesser

Journal of Humanistic Mathematics

This poem applies the concept of expected value, denoted E(X), to the context of any limited resources two parties desire. Usually, "you divide, I choose" keeps pieces equal enough to preempt charges of unfairness. But if one piece is much larger, many distrust the unbiased (in expected value) process of a coin flip giving each person the same chance at the bigger piece and the same cookie amount on average: E(X) = (1/2)p + (1/2)(1-p) = 1/2

Ahab's Mercy, David Sheskin

Journal of Humanistic Mathematics

A tale in which Captain Ahab and his chief mate Starbuck confront a classic problem in probability theory: the Monty Hall Problem.

Zeno Of Elea: A Dichotomy, Joseph Chaney

Journal of Humanistic Mathematics

This two-part poem interprets Zeno's paradoxes as dimensions of a paradoxical view of reality.

I Am A Math Professor, Cacey L. Wells

Journal of Humanistic Mathematics

Original poem depicting the life of a math professor.

Elephant In The Room, Sabrina Sixta

Journal of Humanistic Mathematics

This poem tries to express the difficulty of staying focused on one's research when there is so much turmoil in the world.

Infinity, Holly Wilson

Journal of Humanistic Mathematics

No abstract provided.

Ultrafilters, Klaas Pieter Hart

Journal of Humanistic Mathematics

5-7-5 musings on ultrafilters.

Her X'S And Y'S: Limericks About Women Mathematicians, Marion D. Cohen

Journal of Humanistic Mathematics

This poetry folder is just what its title says, limericks about women mathematicians. A few of them I’ve known personally, most not. There are, of course, many many many other women mathematicians; even though I write limericks prolifically, I could never finish writing about them all!

May Graduation, Samuel Coskey

Journal of Humanistic Mathematics

Here I narrate the story of the last few days of my graduate program in mathematics. After the completion of the thesis and the delivery of the defense, several twists and turns await in the hours and even minutes before the last deadline.

Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. Monte-Serrat, Carlo Cattani

Journal of Humanistic Mathematics

Mathematics plays an important role in the linguistic structure of artificial in- telligence (AI). We describe the linguistic process as a unique structure present both in human cognition and in cognitive computing. The close relationship with both AI and human cognition is due to this unique structure, which paves the way for AI to interfere with the behavior of those who interact with it. We highlight the role of mathematicians in designing algorithms—the core of the AI linguistic process—and in defining steps and instructions for AI. Because al- gorithms, through AI, interfere with the thought of those who interact with …

Beauty Of Life In Dynamical Systems: Philosophical Musings And Resources For Students, Soumya Banerjee, Joyeeta Ghose, Tarakeswar Banerjee, Kalyani Banerjee

Journal of Humanistic Mathematics

Information plays a key role in life and in complex biological systems, and dynamical systems underlie and can be used to represent many complex systems. Indeed, dynamical systems and information processing capabilities may be the hallmarks of life-like systems. In this paper we combine dynamical systems with a computational framework to generate art. The framework can be used to generate aesthetically appealing forms of life-like systems. Our work suggests that we may need an ``aesthetic sense'' to recognize life that we have not seen before. We also provide teaching resources for students in schools and undergraduate institutions.

The Number Systems Tower, Bill Bauldry, Michael J. Bossé, William J. Cook, Trina Palmer, Jaehee K. Post

Journal of Humanistic Mathematics

For high school and college instructors and students, this paper connects number systems, field axioms, and polynomials. It also considers other properties such as cardinality, density, subset, and superset relationships. Additional aspects of this paper include gains and losses through sequences of number systems. The paper ends with a great number of activities for classroom use.

The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson

Journal of Humanistic Mathematics

In this paper we analyze the distribution of musical note frequencies in Hertz to see whether they follow the logarithmic Benford distribution. Our results show that the music of Johann Sebastian Bach and Johann Christian Bach is Benford distributed while the computer-generated music is not. We also find that computer-generated music is statistically less Benford distributed than human- composed music.

Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers

Journal of Humanistic Mathematics

In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for their students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia “superpower”, describes how it impacted her learning. We collected data for this case study through an audio-recorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as …

“I Got You”: Centering Identities And Humanness In Collaborations Between Mathematics Educators And Mathematicians, Anne M. Marshall, Sarah Sword, Mollie Applegate, Steven Greenstein, Terrance Pendleton, Kamuela E. Yong, Michael Young, Jennifer A. Wolfe, Theodore Chao, Pamela E. Harris

Journal of Humanistic Mathematics

Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations – one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration – and a look at how collaborations built with …