EPaDel Speaker List

The Eastern Pennsylvania / Delaware (EPaDel) section of the Mathematical Association of America maintains this list as a courtesy to members and institutions in eastern Pennsylvania and Delaware. This list is open to anyone in the mathematics community, so presence on this list does not imply an endorsement of the speaker by the organization. Details such as availability, equipment needs, honoraria, and travel expenses should be sorted out directly with any potential speaker. If you would like to be included on this list, please fill out the form at https://forms.gle/nMraD1T2KESmWdSp6. For answers to questions or more information, please contact Michael Yatauro at mry3@psu.edu.

Craig Bauer (York College)

Topics: Combinatorics, Cryptography, Cryptology, History 

http://depts.ycp.edu/~cbauer/  
cbauer@ycp.edu 

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

Many colleges and universities were involved in offering cryptology classes in the 1940s. There was a tremendous amount of diversity in who delivered the classes. The professors were not all mathematicians, but rather came from departments that included Astronomy, Classics, English, Geology, Greek, Psychology, and Philosophy. Some of these classes were open to all students, while others were run with great secrecy and open only by invitation. These classes are detailed along with the backgrounds of the instructors and the role they played in the war. 

Dr. Donald H. Menzel is well known for his work in astronomy, but his cryptologic work (long secret) has attracted much less attention. This talk describes how his interest in this area was first sparked and provides the details of the secret class he led in "Naval Communications" (really cryptanalysis) at Radcliffe College during World War II. This class served as a prototype and was copied elsewhere. A sketch of some of the classified work he carried out during the war, and after, as a consultant, is also included, along with a brief over-view of Menzel’s personality and other interests. 

The Hill Cipher, also known as matrix encryption, uses matrices to encipher and decipher text. Various attacks, such as those found by Jack Levine, have been published for this system. This talk reviews a few previous results and presents a powerful new attack in which the rows of the matrix can be determined independent of one another, greatly reducing the amount of time needed for decipherment. 

An enumeration problem involving matrices is seen to give rise to Pascal's triangle, Stirling's triangle, and infinitely many other new triangles. Some special properties of the better known triangles are related and analogous results for the new triangles are investigated. This is an open problem with much work still to be done and best of all, it is appropriate for undergraduate contemplation! 

Ethan Berkove  (Lafayette College)

Topics: Geometry, Fractals, Origami and Mathematics 

https://sites.lafayette.edu/berkovee/   
berkovee@lafayette.edu  

☑︎ Face-to-face presentation
☒ No online presentations

Prepared Talks

Origami is the traditional Japanese art of paper folding. In the past 30 years investigations into folding properties have not only resulted in many stunning models, but also a surprising number of applications. In this talk we will provide an introduction to some of the interactions between mathematics of origami. We’ll describe what types of folds are mathematically possible, how "complicated" folding can be, and how mathematical ideas have helped further origami. We’ll also talk about a number of mathematical results inspired by origami.  

The Menger sponge is a 3-dimensional fractal that is formed from a unit cube by recursively removing collections of smaller and smaller subcubes. This talk’s title is literal: we will investigate what shadows are cast when you shine a light (at a point at infinity—it’s a bright light) on the Menger sponge from different angles. Along the way we’ll look at the Cantor set in a new light, and determine the structure of Menger sponge cross sections that are parallel to an outside face. These results were part of an REU project, and represent joint work with Max Auerbach, Adam Hodapp, Derek Smith, and Rebecca Whitman.

J. Robert Buchanan (Millersville University)

Topics: Financial Mathematics, Mathematical Biology 

https://sites.millersville.edu/rbuchanan/
Robert.Buchanan@millersville.edu

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

Marion Deutsche Cohen (Drexel University)

Topics: Mathematics in Communication/Arts/Literature, Associative Addition

marioncohen.net
mathwoman12@gmail.com 

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

In this talk I’ll discuss “mathLIKE”, a word I’ve coined (which means, roughly and predictably, "LIKE math") and how it pertains to a course I’ve developed, Mathematics in Literature, as well as to people, both mathematicians and not, and to events and impressions from everyday life. Two of the more obvious mathLIKE things are dreams and fears, both of which the students and I have discussed extensively in that course. Maybe everything is mathLIKE. At any rate, for math-anxious people, mathLIKE things can be helpful in dealing with (and teaching) actual math.  

A binary operation # on Z+ is said to be an associative arithmetic if both # and its iteration -- the binary operation * defined inductively by: x * 1 = x, 

x * y = [x * (y-1)] # x -- are associative. E. Rosinger showed that, under reasonable conditions, an associative arithmetic must be ordinary addition. However, in the general case, there are associative arithmetics that are not ordinary addition. This paper gives examples of these, as well as results towards a structure theorem for associative arithmetics. 

Annalisa Crannell (Franklin & Marshall College)

Topics: Geometry of perspective art: Portraying the 3-d world on a 2-d canvas. Euclidean and projective geometry

https://www.fandm.edu/annalisa-crannell
annalisa.crannell@fandm.edu 

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

The Renaissance famously brought us amazingly realistic perspective art. Creating that art was the spark from which projective geometry caught fire and grew. This talk looks directly at projective geometry as a tool to illuminate the way we see the world around us, whether we look with our eyes, with our cameras, or with the computer (via our favorite animated movies). One of the surprising results of projective geometry is that it implies that every quadrangle (whether convex or not) is the perspective image of a square. We will describe implications of this result for computer vision, for photogrammetry, for applications of piece-wise planar cones, and of course for perspective art and projective geometry.

What is the difference between Trompe L'Oeil and anamorphic art? One difference is that we think of the former as being surprisingly realistic, and as the latter as a distortion that can morph into being realistic if we stand in the "correct" spot. But both of these perspective art genres employ the same underlying mathematics, and in that sense, one might conclude they are both equally realistic. In this talk, we offer a measure of anamorphic distortion and describe its dependence on the standard measure of viewing distance. We conclude that Trompe L'Oeil and anamorphic art are not truly different in kind, but are rather variations along a spectrum, and that the spectrum varies with relative distances of the image to the viewing target of the particular piece. 

Those of us who teach projective geometry often nod to perspective art as the spark from which projective geometry caught fire and grew. This talk looks directly at projective geometry as a tool to illuminate the workings of perspective artists. We will particularly shine the light on Desargues' triangle theorem (which says that any pair of triangles that is perspective from a point is perspective from a line), together with an even simpler theorem (you have to see it to believe it!). Given any convoluted, complicated polygonal object, these theorems allow us to draw that object together with something that is related to it--- its shadow, reflection, or other rigid symmetries---and we'll show how this works. (If you enjoy doodling or sketching, bring your pencil, a good eraser, and a straightedge.) 

William Dunham (Bryn Mawr College)

Topics: History of Mathematics; Euler's works; Bryn Mawr College history

bdunham@brynmawr.edu
☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

The foundation of number theory lies among the primes. It thus seems fitting to examine three different proofs, from across history, of the infinitude of the prime numbers. We first look at Euclid’s argument from 300 BCE, which appears as Proposition 20 of Book IX of the Elements. Although "Euclid’s proof of the infinitude of primes" is a standard in every number theory textbook, some people might be surprised to see his argument in its original form. We next consider Euler’s analytic proof from 1737. Like so much of his work, this features a blizzard of formulas, manipulated with a maximum of agility and a minimum of rigor. But the outcome is spectacular. Finally, we examine Erdös’s combinatorial proof from the 20th century. This is an elementary argument, but it reminds us once again that "elementary" does not mean "trivial." Taken together, these proofs suggest that, to establish the infinitude of primes, it helps to have a two-syllable last name starting with "E." More to the point, they show mathematics as a subject whose creative variety knows no bounds.

This talk features some genuine Eulerian magic. In 1748, Leonhard Euler considered a modification of the harmonic series in which negative signs were attached to various terms by a rule that was far from self-evident. With his accustomed flair, he determined its sum, and the result was utterly improbable. There are a few occasions in mathematics when the term "breathtaking" is not too strong. This is one of them.

Over its first 50 years, Bryn Mawr College boasted three remarkable mathematicians who, one after the other, left deep footprints on the institution and on the U.S. mathematical community. They were Professors Charlotte Angas Scott (British), Anna Pell Wheeler (American), and Emmy Noether (German). In this lecture, we meet these women and flesh out their biographies with plenty of local color… not to mention a real-life assassin in a supporting role. From 1885 to 1935, they gave Bryn Mawr a record of women in mathematics unsurpassed by any college, anywhere.

Michael Ecker (Penn State Wilkes-Barre)

Topics: Analysis, Combinatorics, Recreational Mathematics

drmwecker@aol.com
☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

Many of the best recreations have a common theme. Start with a number, perform some process over and over, and always arrive at one particular number - the mathemagical black hole.  

How can you pass your body through a postcard? Can a surface really hold a finite volume of paint but not be painted? How does this last example relate to fractals, the von Koch snowflake, and the human intestines? What's the deal with time travel? How can removing balls from an urn lead to no balls or infinitely many? 


Timothy Feeman (Villanova University)

Topics: Modeling, Linear Algebra

https://www1.villanova.edu/university/liberal-arts-sciences/programs/mathematics-statistics/faculty.html
timothy.feeman@villanova.edu
☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talk

The ART of tomography. 

We will look at how an algorithm from linear algebra, called Kaczmarz's Method, can be used to create a CAT scan image from X-ray data. 

Darren Glass (Gettysburg College)

Topics: Number Theory, Algebraic Geometry, Cryptography, Graph Theory

https://www.gettysburg.edu/academic-programs/mathematics/faculty/
dglass@gettysburg.edu
☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

The goal of cryptography is to use mathematics to communicate secrets so that only the people you want to hear the information do in fact hear it. The goal of coding theory is to use mathematics to build redundancy into messages so that they can withstand errors that may occur in the transmission. While much of the mathematics used in these areas is extremely deep, major advancements in both of these areas have come from the simple fact that two points determine a unique line and some generalizations of this fact. In this talk, I will describe these applications of curve interpolation, and discuss broader ideas that come up in the modern theory of communications. 

Elliptic Curves have great interest to mathematicians for a variety of reasons, ranging from cryptography to the proof of Fermat's Last Theorem. In this talk, I will introduce the concept of elliptic curves, talk about some of their properties, and then show a modern proof of the classical result known as Poncelet's Porism, which uses Elliptic Curves in a surprising way. 

In this talk, we will introduce the notion of an arithmetical structure on a finite connected graph. These structures were defined by Dino Lorenzini in order to answer some questions in algebraic geometry and have deep structure, but in this talk we will discuss how they can be described only in terms of elementary number theory and linear algebra, and how new results can be obtained with only a little bit of elementary school arithmetic and a lot of doodling. One goal is to count how many different structures one can place on a given graph as well as discuss finite abelian groups that are associated to arithmetical structures. We will fully answer this question for some families of graphs, and discuss why it is a hard but interesting question for other families. 

Gary Gordon (Lafayette College)

Topics: Graph theory, card game SET, matroids, combinatorics

https://webbox.lafayette.edu/~gordong/
gordong@lafayette.edu   
☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

What is the probability that a randomly chosen subtree in a complete graph is a spanning tree? The surprising answer uses some standard counting and Taylor series. 

Suppose you roll a die twice. What is the probability that every face has moved to a new position? In this talk, we generalize ordinary derangements (a topic covered in combinatorics classes) to derangements of the hyper cube. Many familiar formulas for ordinary derangements can be generalized in a natural way. (Joint with Liz McMahon.) 

The card game SET has a deep connection to finite geometry and that connection can be used to analyze the game at a high level. We will examine some counting problems, probability, and geometry to answer natural questions that arise when playing the game. (Joint with Liz McMahon.)

Kira Hamman (Penn State Mont Alto)

Topics: Voting Theory & Districting, Philosophy of Mathematics

https://montalto.psu.edu/person/kira-hamman
khh11@psu.edu
☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

An overview of the mathematics behind districting and gerrymandering, voting methods, and/or apportionment. Appropriate for a general, non-mathematical audience.

A layperson's introduction to infinite numbers and different sizes of infinity. 

Well, maybe not murder. The story of the foundational crisis and the search for solid philosophical foundations for all of mathematics. Appropriate for any audience, although mathematical audiences who are not familiar with the story tend to enjoy it most.  

R. Andrew Hicks (Drexel University)

Topics: Mathematics of Optical Design

http://www.math.drexel.edu/~ahicks/
ahicks@math.drexel.edu 
☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talk

How does one design a driver side mirror without a blind spot that does not distort the image? This is essentially the fundamental problem of optical design, which is to guide a given collection of light rays to some prescribed target points on a surface via a family of optical components, such as mirrors and lenses. We consider the problem of performing this task for a single 2-parameter ray bundle as typically is generated by a single source, show that a single reflector is not adequate to solve the problem, and give estimates on how bad the situation can. We will describe applications, including a driver-side mirror with no the blind spot problem and mirrors designed for panoramic imaging. Prototypes will be available for inspection.

Vikram Kamat (Villanova University)

Topics: Combinatorics, Graph Theory, Algorithms 

https://www1.villanova.edu/university/liberal-arts-sciences/programs/mathematics-statistics/faculty/biodetail.html?mail=vikram.kamat@villanova.edu&xsl=bio_long  
vikram.kamat@villanova.edu
☑︎ Face-to-face presentation
☒ No online presentations

Prepared Talk

The Erdos--Ko--Rado (EKR) theorem, a foundational result in extremal finite set theory, states that any family of k-subsets of a finite set containing at least 2k elements that is intersecting, i.e. the family has the property that no two subsets in it are disjoint, can be no bigger than the family of all k-subsets containing a fixed element x. The latter family is trivially intersecting and is called a star centered at x. 

We discuss different proofs, new and old, of this classical result, uniqueness of the extremal star structures, and also recent work on a graph-theoretic generalization of the theorem that is partly inspired by a longstanding conjecture of Chvatal. We also consider a related problem of finding the optimal stars in this graph-theoretic setting, a problem that highlights some of the underlying challenges posed by Chvatal's conjecture. 

Alan Levine (Franklin & Marshall College)

Topics: History of Pi. Markov’s book on probability.


Alevine@fandm.edu 
☑︎ Face-to-face presentation

☒ No online presentations

Prepared Talks

During the past 4000 years or so, many mathematicians have derived a variety of methods for calculating Pi. We will look at several of these, including Archimedes, Euler, Gauss, Ramanujan, among others. 

In 1900, Markov wrote a book entitled “Calculus of Probabilities”. In this talk, we’ll explore some of the main concepts in this book, which has been translated into English by the speaker. In many ways, the book resembles modern probability texts. In other ways, it is very different. 

Liz McMahon (Lafayette College)

Topics: The Game of SET, Finite Geometry, Combinatorics

https://sites.lafayette.edu/mcmahone/
mcmahone@lafayette.edu
☑︎ Face-to-face presentation
☒ No online presentations

Prepared Talks

The card game SET is played with a special deck of 81 cards. There is quite a lot of mathematics that can be explored using the game; understanding that mathematics enhances our appreciation for the game, and the game enhances our appreciation for the mathematics!  We can look at questions in combinatorics, probability, linear algebra, and especially geometry.  The deck is an excellent model for the finite affine geometry AG(4,3) and provides an entry to surprisingly beautiful structure theorems for that geometry. If you’d like some practice before the talk, go to www.setgame.com for the rules and a Daily Puzzle.

The deck of cards for the game of SET is an excellent model for the finite affine geometry AG(4,3); the visualization that the game provides allows us to explore the structure of that geometry. In this talk, we’ll explore AG(4,3), focusing on the collections of cards that have no sets (called maximal caps). Contained within each maximal cap is a road map that leads us to surprisingly beautiful combinatorial structure theorems. There’s a wonderful connection to the outer automorphisms of S6 as well, but you don’t need to know what those are to follow the talk.

The SET Daily Puzzle appears on the SET website https://www.setgame.com/set/puzzle.  The puzzle consists of 12 cards that contain exactly six sets; the goal is to find all the sets (as quickly as possible). After playing the puzzle for a while, you may begin to notice some interesting things. Some cards may not appear in any of the sets. What is the largest number of cards that could never get used? What is the largest number of sets one card can be in? How many different card-set incidence structures are possible? Can we use the information we find to understand how the puzzle might be constructed? At present, many of our questions require computer simulations to answer, and the hope is to find direct proofs.

Marc Renault (Shippensburg University)

Topics: History, Recreational Mathematics

https://webspace.ship.edu/msrenault/
msrenault@ship.edu 

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talk

Infinity: It’s Really, Really Big. 

In this talk we’ll consider some common notions of infinity, and see how mathematicians and philosophers have attempted to understand it. We’ll look at some of the ideas of Georg Cantor (1845-1918), the first mathematician to put the infinite on a solid foundation, and we’ll see that there are in fact different “levels” of infinity! 

David Richeson (Dickinson College)

Topics: History, Recreational Mathematics

https://divisbyzero.com/
richesod@dickinson.edu 

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

"Nothing is impossible!" It is comforting to believe this greeting card sentiment; it is the American dream. Yet there are impossible things, and it is possible to prove that they are so. In this talk, we will look at some of the most famous impossibility theorems—the so-called "problems of antiquity." The ancient Greek geometers and future generations of mathematicians tried and failed to square circles, trisect angles, double cubes, and construct regular polygons using only a compass and straightedge. It took two thousand years to prove conclusively that all four of these are mathematically impossible. 

Dimension seems like an intuitive idea. We are all familiar with zero-dimensional points, one-dimensional curves, two-dimensional surfaces, and three-dimensional solids. Yet dimension is a slippery idea that took mathematicians many years to understand. We will use pictures, animations, and analogies to describe our three dimensions and help us visualize a fourth dimension. We will discuss the history of dimension, the public's and artistic community’s infatuation with the fourth dimension, time as an extra dimension, the meaning of non-integer dimensions, and the unexpected properties of high-dimensional spaces.

In 1751 Euler discovered that any polyhedron with V vertices, E edges, and F faces satisfies V-E+F=2, but the proof he gave was flawed.  Many rigorous proofs followed, but it took 150 years for mathematicians to fully understand this simple formula. Today Euler's formula is held aloft as one of the most beautiful theorems in all of mathematics and the first great theorem of topology.  In this talk, we will give the history of Euler's theorem and give a sampling of its many applications. 

Nathan Ryan (Bucknell University)

Topics: Number Theory, Computational Number Theory, Algorithmic Fairness, Data Science Applied to Social Justice, Equitable Access to Mathematics 

http://www.unix.bucknell.edu/~ncr006/
ncr006@bucknell.edu 

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

Ryan Savitz (Neumann University)

Topics: Mathematics Education, Data Analytics in Sports, Statistical Validation of Vaccination for Covid 

savitzr@neumann.edu 

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

This talk examines the effect of carbon plated “super shoes” on the performance of elite male marathoners. Prototypes of these carbon plated shoes with extraordinary cushioning were used beginning in 2016, and became widely available in 2017. In order to quantify the effect of these shoes on elite athletes, we analyzed data on the number of athletes who ran a marathon in under 2:08:00 each year from 1985 through 2021. A multiple linear regression model was constructed that controlled for the non-“super shoe” related upward time trend in the number of sub-2:08 times, utilizing a Cochrane-Orcutt transformation to correct for autocorrelation. This model shows that this new shoe technology is responsible for an additional roughly 24 additional sub-2:08 times per year. Estimated from this, we find a shoe-related time reduction of 1 minute and 31 seconds, or a 1.174% decrease in time. 

Introduction: In this talk, we examine the relationship between vaccination against COVID-19 and both the death rate from COVID-19 and the rate of COVID-19 spread. Our goal is determine if vaccination is associated with reduced death and/or spread of disease at the local level. Methods: This analysis was conducted at the county level in the state of Pennsylvania, United States of America, with data that were collected during the first half of 2022 from the state of Pennsylvania’s Covid Dashboard (COVID-19 Data for Pennsylvania (pa.gov). Results: This study finds the vaccines to be highly effective in preventing death from Corona virus, even at a time when there was a mismatch between the vaccines and the prevalent variants. Specifically, a 1% increase in vaccination rate was found to correspond to a 0.751% decrease in death rate (95% confidence interval (0.236%, 1.266%)). Given that, during this time period, the vaccines being used were not geared specifically toward the common variants at that time, we found no statistically significant relationship between disease spread and vaccination rate at the county level. Conclusions: These results support previous findings from across the world that Covid vaccination is highly efficacious in preventing death from the disease. Even during a time when vaccine design was not optimally matched with the prevailing strains, vaccination was found to reduce death rate. Hence, improving global vaccine availability is vitally important, in order to achieve necessary outcomes. 

This research project introduces a model that addresses the way competitors in Shotokan karate martial arts competitions are evaluated.  This new model is a combination of multiple variables that determine the winner of a sparring competition in Shotokan karate.  We constructed the model using the forward LR variety of logistic regression in order to predict the winner of these matches with a near 100% success rate.  Due to some issues of multicollinearity, this model was then refined using the author’s knowledge of karate. We also begin to investigate applications of artificial intelligence (AI) in predicting the outcome of Shotokan karate matches. 


Robert Styer (Villanova University)

Topics: Algebra, Recreational Mathematics

https://www1.villanova.edu/university/liberal-arts-sciences/programs/mathematics-statistics/faculty.html
robert.styer@villanova.edu 

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

If a ball bounces an infinite number of times, will it bounce an infinite amount of time?  We use some elementary physics of a bouncing ball to lead to geometric series.  Next, can you pile up Jenga blocks so the top one overhangs the bottom one?  Some elementary physics leads to the harmonic series.  Along the way we enjoy some paradoxes of calculating with infinite series.  

My seventh-grade math teacher introduced us to the abstract concepts of commutativity, associativity, and the like.  The ability to reduce previously arbitrary manipulations to a small list of fundamental principles excited me.  We will look at a hard problem, translate it to the geometric context of elliptic curves, then see how my seventh-grade introduction to commutativity applies to elliptic curves.  We conclude by briefly indicating why elliptic curves are useful in cryptography.  

Klaus Volpert (Villanova University)

Topics: Economics, Financial Mathematics

https://www1.villanova.edu/university/liberal-arts-sciences/programs/mathematics-statistics/faculty.html
klaus.volpert@villanova.edu 

☑︎ Face-to-face presentation
☑︎ Online presentation

Prepared Talks

Are Financial Derivatives the "Engine of the Economy," as declared by Alan Greenspan, or "Weapons of Mass Destruction," as Warren Buffett views them? Over the last 30 years, financial derivatives have overtaken stocks and bonds as the investment vehicle of choice for many large investors. Derivatives are often behind the spectacular profits of investment banks as well as the mind-boggling losses (e.g. at Citigroup) that we read about in the papers. While CEO’s and hedge fund managers profit handsomely when things are going well, the losses are mostly born by shareholders and small investors. Pension funds, even school districts and townships have suffered from disastrous deals in derivatives. It is therefore no exaggeration to say that taxpayers and investors can no longer afford to not understand derivatives. So what are derivatives? Simply put, they are contracts between two parties that stipulate some cash flow over a certain period of time. The size of that cash flow depends on what happens to some underlying asset, such as a stock prices, interest rates, currency exchange rates or commodity prices. The uncertainty in the development of the underlying creates the key difficulty, which is to properly evaluate the price and the risk inherent in a derivative. In this talk I will give an overview of the three main methods to price derivatives and  discuss the advantages and short-comings of each method:

The Gini-Index based on Lorenz Curves of income distributions has long been used to measure income inequality in societies. This single-valued index has the advantage of allowing comparisons among countries and within one country over time. However, being a summary measure, it does not distinguish between intersecting Lorenz curves, and may not detect certain sociological and economic trends over time. We will discuss a new two-parameter model for the Lorenz curves. We will present theoretical and empirical evidence for this model, discuss its mathematical properties, and its potential to discern hidden trends.