Digital Commons Network^™

Low Shear In Short-Term Impacts Endothelial Cell Traction And Alignment In Long-Term, Mohanish K. Chandurkar, Nikhil Mittal, Shaina P. Royer-Weeden, Steven D. Lehmann, Yeonwoo Rho, Sangyoon J. Han

Michigan Tech Publications

Within the vascular system, endothelial cells (ECs) are exposed to fluid shear stress (FSS), a mechanical force exerted by blood flow that is critical for regulating cellular tension and maintaining vascular homeostasis. The way ECs react to FSS varies significantly; while high, laminar FSS supports vasodilation and suppresses inflammation, low or disturbed FSS can lead to endothelial dysfunction and increase the risk of cardiovascular diseases. Yet, the adaptation of ECs to dynamically varying FSS remains poorly understood. This study focuses on the dynamic responses of ECs to brief periods of low FSS, examining its impact on endothelial traction—a measure of …

A Causal Inference Approach For Spike Train Interactions, Zach Saccomano

Dissertations, Theses, and Capstone Projects

Since the 1960s, neuroscientists have worked on the problem of estimating synaptic properties, such as connectivity and strength, from simultaneously recorded spike trains. Recent years have seen renewed interest in the problem coinciding with rapid advances in experimental technologies, including an approximate exponential increase in the number of neurons that can be recorded in parallel and perturbation techniques such as optogenetics that can be used to calibrate and validate causal hypotheses about functional connectivity. This thesis presents a mathematical examination of synaptic inference from two perspectives: (1) using in vivo data and biophysical models, we ask in what cases the …

An Overview Of The Second-Previous Memory Effect In The Strictlyalternating Donation Game, Mohamed Zayet, Essam El-Seidy, Amira Abdel-Malek, Aya Rabie

Basic Science Engineering

Game theory delves into the examination of strategic behaviour across diverse domains such as insurance, business, military, biology, andmore,with the aim of deriving optimal decisions. Recent research focusing on the alteration of memory in the donation game with simultaneous iterated rounds has spurred our interest in investigating this phenomenon within the realm of the strictly alternating donation game. This study proposes a novel decision-making approach, utilising the previous unit instead of the most recent one. Thescopenarrowsdownto16employedstrategies,each definedbyfinitetwo-stateautomata,whileaccountingforpotentialimplementationerrorsinthe computationofstrategypayoffs.Dominant strategies are determined by assessing the interaction payoffs among strategy pairs. This article centres on the calculation of equilibrium points among heteroclinic …

Modifed Playfair For Text File Encryption And Meticulous Decryption With Arbitrary Fillers By Septenary Quadrate Pattern, N. Sugirtham, R. Sherine Jenny, B. Thiyaneswaran, S. Kumarganesh, C. Venkatesan, K. Martin Sagayam, Lam Dang, Linh Dinh, Helen Dang

Mathematics and Computer Studies: Faculty Publications

Cryptography secures data and serves to ensure the confidentiality of records. Playfair is a cryptographic symmetrical algorithm that encrypts statistics based on key costs. This secret is shared with an authorized person to retrieve data. In the conventional pattern, there is an area complexity and deficiency in letters, numbers, and special characters. This hassle has been overcome in previous studies by editing pattern dimensions. The fillers used throughout the enciphering were not eliminated during the retrieval process, which resulted in the indiscrimination of the retrieved statistics. The proposed method uses a separate quadrate pattern that strengthens the Playfair cipher and …

A Finite Element Model For Hydro-Thermal Convective Flow In A Porous Medium: Effects Of Hydraulic Resistivity And Thermal Diffusivity, S. M. Mallikarjunaiah, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

In this article, a finite element model is implemented to analyze hydro-thermal convective flow in a porous medium. The mathematical model encompasses Darcy’s law for incompressible fluid behavior, which is coupled with a convection-diffusion-type energy equation to characterize the temperature in the porous medium. The current investigation presents an efficient, stable, and accurate finite element discretization for the hydro-thermal convective flow model. The well-posedness of the proposed discrete Galerkin finite element formulation is guaranteed due to the decoupling property and the linearity of the numerical method. Computational experiments confirm the optimal convergence rates for a manufactured solution. Several numerical results …

Conditional Optimal Sets And The Quantization Coefficients For Some Uniform Distributions, Evans Nyanney, Megha Pandey, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists as a finite positive number. By giving different examples, in this paper, we have shown that the quantization coefficients for absolutely continuous probability measures defined on the same Euclidean space can be different. We have taken uniform distribution as a prototype of an absolutely continuous probability measure. In addition, we have also calculated the conditional optimal sets of n-points and the nth conditional quantization errors …

Automorphisms: New Cars For 2024, Jane P. Sheldon

Journal of Humanistic Mathematics

This review of new cars for 2024 demonstrates total variation.

Mathematical Relationships, David Sheskin

Journal of Humanistic Mathematics

A digital collage depicting the mathematics of interpersonal relationships.

Hypatia's Math: A Play, Daniel S. Helman

Journal of Humanistic Mathematics

Hypatia of Alexandria was the most famous woman mathematician of antiquity, and her story is as relevant now as it was in her day. This play tells her story. While the events in the play are based closely on extant historical texts, inspiring excerpts from classical works by Porphyry, Plotinus, Aristotle and Plato are woven into the action to further the plot and add to the classical mood. Dance and music, including an Homeric hymn, add to the artistic texture.

The Free Numbers, Jessica Greenbaum

Journal of Humanistic Mathematics

No abstract provided.

Persistence: A Romance In Many Dimensions, Tony Bedenikovic

Journal of Humanistic Mathematics

This is a short poem which is inspired by Edwin Abbott's Flatland. The poem follows the narrator through a typical day with a focus on the individual's persistence in the face of nature's brawn and magnitude.

The Point At Infinity, Josh Hiller

Journal of Humanistic Mathematics

A poem about the longing for parallel lines to meet.

The Conviction Of Miss Prediction, Dane C. Joseph

Journal of Humanistic Mathematics

Miss Prediction is questioned in a court of law over her involvement in the mischaracterization of linear models when they were inappropriate.

Pied Beauty, Pamela Vale

Journal of Humanistic Mathematics

This is a shape poem about the beauty of mathematics formed with the lines containing the number of words corresponding to the digits in pi (to 26 places).

Variations On A Meme: Thoughts And Responses To Isaac Elishakoff’S “Differential Equations Of Love And Love Of Differential Equations", Jonathan Kinsman

Journal of Humanistic Mathematics

This folder contains reflections and three poems written in response to Isaac Elishakoff’s JHM article “Differential Equations of Love and Love of Differential Equations" (July 2019).

A Personal And Multicultural Journey Through The World Of Games (With A Little Math) Or Book Review: Around The World In Eighty Games, By Marcus Du Sautoy, Karl-Dieter Crisman

Journal of Humanistic Mathematics

Author and number theorist Marcus Du Sautoy has written a book about games, including a light dose of mathematics. In it, he journeys through far more than (his choice of) eighty of “the world’s greatest games”, laying out a charming voyage through many lands. Despite some reservations, this reviewer finds that Around the World in Eighty Games is well-written and quite fascinating, largely due to its idiosyncratic, personal nature.

Quik Church, Route 3.141592, Sarah Voss

Journal of Humanistic Mathematics

The following set of poems are from one of ten sections in a collection of poetry called Quik Church: Short Poems that Travel Far. Each section illustrates one of many “streets” which individuals often take on their spiritual journey through life, e.g., the Old Gods Path, Nature Trail, Memory Skyway, Mystic Avenue, Pastoral Lane, and so on. This one, Route 3.141592, is the route of mathematics and the science that depends on mathematics.

Hockey Card Statistics Are Stagnant And Stale, Egan J. Chernoff

Journal of Humanistic Mathematics

The purchase of a coffee at a Canadian institution, Tim Hortons, turned into an informal investigation into hockey card statistics. Turns out, hockey card statistics are stagnant and stale. This was disappointing to see because the game of hockey has changed, the statistics used to keep track of the game have changed. Even the cards have changed. Well, not the back of the cards, which do not well enough paint a statistical picture of the hockey player photographed on the front of the card.

The Limits Of Data Science, David E. Drew

Journal of Humanistic Mathematics

Data science can contribute valuable predictions in diverse fields. But I write to express some concerns and red flags. I suggest that data science is being oversold. This article contains three questions that I believe data science must address as this new discipline matures. Is data science significantly different from statistics? This is a question that has haunted the field since the term first was introduced. By creating algorithms based on current societal decision rules that may be biased, even bigoted, does data science lock in and exacerbate inequality? Scholars have identified a continuum from data to information to knowledge …

Reflections On Teaching Mathematics In Prisons, Matthew Junge

Journal of Humanistic Mathematics

I started teaching math in prison ten years ago during my PhD studies. Since then, I have taught for three different college-in-prison programs across the country. The goal of this piece is to communicate my experiences with the hopes of encouraging more mathematicians to get involved.

Polygon Quadrature And Dodecagonal Tessellation With Pattern Blocks, Gunhan Caglayan, Ben Kamau

Journal of Humanistic Mathematics

The age-old challenge of polygon quadrature involves converting a polygon into a square of equal area. In this educational resource, we utilize pattern blocks, commonly employed instructional aids in K-12 education across the United States, to visually demonstrate the transformation of different equilateral and regular pattern block polygons into squares. This is achieved through the application of the area conservation principle and geometric congruence/similarity reasoning.

Benefits Of Risk-Taking In Teaching Mathematics, Mehmet Kirmizi, Abigail Quansah, Zafer Buber

Journal of Humanistic Mathematics

In this paper, we, a group of graduate students in mathematics education, discuss some of the metacognitive benefits of the non-traditional teaching methods we observed employed by one of our professors. This professor’s methods challenge the common belief that well-managed class time is key for positive learning outcomes. Instead, he orients his teaching to share the exploration and sense-making phases of doing mathematics. The goal of his teaching is to share the idea that learning mathematics is a process of “refining our mathematical thinking”. We argue that this approach to teaching helps students see that mathematics is a human endeavor, …

Does Chatgpt Know Calculus?, Kris H. Green

Journal of Humanistic Mathematics

Academics and educators across the world are grappling with how OpenAI’s new software, ChatGPT, will impact teaching and learning. This essay explores ChatGPT’s response to a typical calculus problem as a way of illustrating its functionality and limitations.

The Frankensteinian Nature Of Mathematics, Ali Barahmand

Journal of Humanistic Mathematics

Frankenstein is a story about a scientist who creates a sapient creature that gets out of control and horrifies its creator by its unexpected behavior. In this note, we show that this type of undesirable behavior can reflect a part of the nature of mathematics, and that its origin is related to the ontological question of whether mathematics is invented or discovered. Based on a review of the relationship be- tween discovery and invention, we demonstrate that mathematics has similarities and differences with both discovery and invention. In the natural sciences, new instruments have to be invented to discover new …

Seating Groups And 'What A Coincidence!': Mathematics In The Making And How It Gets Presented, Peter J. Rowlett

Journal of Humanistic Mathematics

Mathematics is often presented as a neatly polished finished product, yet its development is messy and often full of mis-steps that could have been avoided with hindsight. An experience with a puzzle illustrates this conflict. The puzzle asks for the probability that a group of four and a group of two are seated adjacently within a hundred seats, and is solved using combinatorics techniques.

Logical Or Epistemological? A Study On Kepler’S 3m Cosmological Model, Po-Hung Liu

Journal of Humanistic Mathematics

Kepler published Mysterium Cosmographicum in 1597 constructing his cosmo- logical model based on the five regular polyhedra. Such a creative but weird idea was almost consistent with empirical evidence. Furthermore, following the Pythagorean belief about the connection between music and astronomy, Kepler delved into looking for what things having to do with the planetary movements have the harmonic consonances. This article claims that Kepler’s model is a 3M (mathematical, musical, and metaphysical) model and demonstrates how it had been constructed. Furthermore, I explore the reasons behind Kepler’s departure from the 3M model and his subsequent consideration of a non-circular orbit, …

On Parallels Between Words And Music, Will Turner

Journal of Humanistic Mathematics

A generalised song is a means of drawing parallels between words and music. The parallels are encoded in a mathematical structure, which is interpreted in a verbal structure and a musical structure. Here we develop a number of new techniques for drawing such parallels, in giving two examples of generalised songs, `Relation', and `Merge/Split'.

The first five partials of a note played on a piano are roughly 0,12,19,24,28 semitones above the fundamental.`Relation' is a generalised song, whose musical part is played on a piano, constructed from the mathematical relation 4.28 = 3.12 + 4.19.

`Merge/Split' is a generalised song whose …

Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett

Journal of Humanistic Mathematics

Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both …

Aesthetic Approaches To Symmetric Functions, John M. Campbell

Journal of Humanistic Mathematics

Symmetry is often regarded as an integral aspect about aesthetics. This motivates the pursuit of interdisciplinary studies based on the use of subjects in mathematics concerned with symmetry in conjunction with aesthetics. What is referred to as a symmetric function in the field of algebraic combinatorics is an abstraction based on polynomials that exhibit a symmetric property, and this leads us to pursue an algebraic combinatorics-inspired exploration based on aesthetics. In particular, we use different bases and transitions between them to create aesthetically pleasing visualizations of symmetric functions. We see that these visualizations in turn raise new and interesting questions.

Mathematicians Going East, Pasha Zusmanovich

Journal of Humanistic Mathematics

I survey emigration of mathematicians from Europe, before and during WWII, to Russia. The emigration started at the end of 1920s, the time of “Great Break”, and accelerated in 1930s, after the introduction in Germany of the “non-Aryan laws”. Not everyone who wanted to emigrate managed to do so, and most of those who did spent a relatively short time in Russia, being murdered or deported, or fleeing the Russian regime. After 1937, the year of “Great Purge”, only a handful of emigrant mathematicians remained, and even fewer managed to leave a trace in the scientific milieu of their new …