Modeling The Spread And Prevention Of Malaria In Central America,
2019
Muhlenberg College
Modeling The Spread And Prevention Of Malaria In Central America, Michael Huber
CODEE Journal
In 2016, the World Health Organization (WHO) estimated that there were 216 million cases of Malaria reported in 91 countries around the world. The Central American country of Honduras has a high risk of malaria exposure, especially to United States soldiers deployed in the region. This article will discuss various aspects of the disease, its spread and its treatment and the development of models of some of these aspects with differential equations. Exercises are developed which involve, respectively, exponential growth, logistics growth, systems of first-order equations and Laplace transforms. Notes for instructors are included.
Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects,
2019
Frostburg State University
Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene
CODEE Journal
The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem highlights …
Consensus Building By Committed Agents,
2019
University of Alberta
Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang
CODEE Journal
One of the most striking features of our time is the polarization, nationally and globally, in politics and religion. How can a society achieve anything, let alone justice, when there are fundamental disagreements about what problems a society needs to address, about priorities among those problems, and no consensus on what constitutes justice itself? This paper explores a model for building social consensus in an ideologically divided community. Our model has three states: two of these represent ideological extremes while the third state designates a moderate position that blends aspects of the two extremes. Each individual in the community is …
The Ocean And Climate Change: Stommel's Conceptual Model,
2019
Oberlin College
The Ocean And Climate Change: Stommel's Conceptual Model, James Walsh
CODEE Journal
The ocean plays a major role in our climate system and in climate change. In this article we present a conceptual model of the Atlantic Meridional Overturning Circulation (AMOC), an important component of the ocean's global energy transport circulation that has, in recent times, been weakening anomalously. Introduced by Henry Stommel, the model results in a two-dimensional system of first order ODEs, which we explore via Mathematica. The model exhibits two stable regimes, one having an orientation aligned with today's AMOC, and the other corresponding to a reversal of the AMOC. This material is appropriate for a junior-level mathematical …
An Epidemiological Math Model Approach To A Political System With Three Parties,
2019
California State University, Channel Islands
An Epidemiological Math Model Approach To A Political System With Three Parties, Selenne Bañuelos, Ty Danet, Cynthia Flores, Angel Ramos
CODEE Journal
The United States has proven to be and remains a dual political party system. Each party is associated to its own ideologies, yet work by Baldassarri and Goldberg in Neither Ideologues Nor Agnostics show that many Americans have positions on economic and social issues that don't fall into one of the two mainstream party platforms. Our interest lies in studying how recruitment from one party into another impacts an election. In particular, there was a growing third party presence in the 2000 and 2016 elections. Motivated by previous work, an epidemiological approach is taken to treat the spread of ideologies …
Linking Differential Equations To Social Justice And Environmental Concerns,
2019
Claremont Colleges
Linking Differential Equations To Social Justice And Environmental Concerns
CODEE Journal
Special issue of the CODEE Journal in honor of its founder, Professor Robert Borrelli.
A Model Of The Transmission Of Cholera In A Population With Contaminated Water,
2019
Southwestern University
A Model Of The Transmission Of Cholera In A Population With Contaminated Water, Therese Shelton, Emma Kathryn Groves, Sherry Adrian
CODEE Journal
Cholera is an infectious disease that is a major concern in countries with inadequate access to clean water and proper sanitation. According to the World Health Organization (WHO), "cholera is a disease of inequity--an ancient illness that today sickens and kills only the poorest and most vulnerable people\dots The map of cholera is essentially the same as a map of poverty." We implement a published model (Fung, "Cholera Transmission Dynamic Models for Public Health Practitioners," Emerging Themes in Epidemiology, 2014) of a SIR model that includes a bacterial reservoir. Bacterial concentration in the water is modeled by the Monod …
Sir Models: Differential Equations That Support The Common Good,
2019
Dickinson College
Sir Models: Differential Equations That Support The Common Good, Lorelei Koss
CODEE Journal
This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns. We present models that have been used to study sustainable agriculture, drug and alcohol use, the spread of violent ideologies on the internet, criminal activity, and health issues such as bulimia and obesity.
Kremer's Model Relating Population Growth To Changes In Income And Technology,
2019
University of Arizona
Kremer's Model Relating Population Growth To Changes In Income And Technology, Dan Flath
CODEE Journal
For thousands of years the population of Earth increased slowly, while per capita income remained essentially constant, at subsistence level. At the beginning of the industrial revolution around 1800, population began to increase very rapidly and income started to climb. Then in the second half of the twentieth century as a demographic transition began, the birth and death rates, as well as the world population growth rate, began to decline. The reasons for these transitions are hotly debated with no expert consensus yet emerging. It's the problem of economic growth. In this document we investigate a mathematical model of economic …
A Note On Equity Within Differential Equations Education By Visualization,
2019
Islamic Azad University, Ahar Branch
A Note On Equity Within Differential Equations Education By Visualization, Younes Karimifardinpour
CODEE Journal
The growing importance of education equity is partly based on the premise that an individual's level of education directly correlates to future quality of life. Educational equity for differential equations (DEs) is related to achievement, fairness, and opportunity. Therefore, a pedagogy that practices DE educational equity gives a strong foundation of social justice. However, linguistic barriers pose a challenge to equity education in DEs. For example, I found myself teaching DEs either in classrooms with a low proficiency in the language of instruction or in multilingual classrooms. I grappled with a way to create an equity educational environment that supported …
Positivity, Rational Schur Functions, Blaschke Factors, And Other Related Results In The Grassmann Algebra,
2019
Chapman University
Positivity, Rational Schur Functions, Blaschke Factors, And Other Related Results In The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
We begin a study of Schur analysis in the setting of the Grassmann algebra when the latter is completed with respect to the 1-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra, and define a notion of positivity in this setting. We present a series of applications pertaining to Schur analysis, including a counterpart of the Schur algorithm, extension of matrices and rational functions. Other topics considered include Wiener algebra, reproducing kernels Banach modules, and Blaschke factors.
Mathematical Modeling Of Lung Cancer Screening Studies,
2019
Florida International University
Mathematical Modeling Of Lung Cancer Screening Studies, Deborah L. Goldwasser
Mathematics Colloquium Series
Lung cancer has the second highest cancer incidence, second only to prostate cancer in men and breast cancer in women. Furthermore, more cancer deaths are attributable to lung cancer than any other cancer for both genders. There is a high public health need for effective secondary prevention in the form of early detection and early treatment, complementary to smoking cessation efforts. The U.S. National Lung Screening Trial (NLST) demonstrated that non-small cell lung cancer (NSCLC) mortality can be reduced by 20% through a program of annual CT screening in high-risk individuals. However, CT screening regimens and adherence vary, potentially impacting …
On The Convergence Of Spectral Deferred Correction Methods,
2019
Kettering University
On The Convergence Of Spectral Deferred Correction Methods, Matthew F. Causley, David C. Seal
Mathematics Publications
In this work we analyze the convergence properties of the Spectral Deferred Correction (SDC) method originally proposed by Dutt et al. [BIT, 40 (2000), pp. 241--266]. The framework for this high-order ordinary differential equation (ODE) solver is typically described wherein a low-order approximation (such as forward or backward Euler) is lifted to higher order accuracy by applying the same low-order method to an error equation and then adding in the resulting defect to correct the solution. Our focus is not on solving the error equation to increase the order of accuracy, but on rewriting the solver as an iterative Picard …
Role Of Combinatorial Complexity In Genetic Networks,
2019
Southern Methodist University
Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang
SMU Journal of Undergraduate Research
A common motif found in genetic networks is the formation of large complexes. One difficulty in modeling this motif is the large number of possible intermediate complexes that can form. For instance, if a complex could contain up to 10 different proteins, 210 possible intermediate complexes can form. Keeping track of all complexes is difficult and often ignored in mathematical models. Here we present an algorithm to code ordinary differential equations (ODEs) to model genetic networks with combinatorial complexity. In these routines, the general binding rules, which counts for the majority of the reactions, are implemented automatically, thus the users …
Logics For Rough Concept Analysis,
2019
Utrecht University
Logics For Rough Concept Analysis, Giuseppe Greco, Peter Jipsen, Krishna Manoorkar, Alessandra Palmigiano, Apostolos Tzimoulis
Mathematics, Physics, and Computer Science Faculty Books and Book Chapters
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough algebra counterparts of certain subclasses of rough formal contexts, and introduce proper display calculi for the logics associated with these varieties which are sound, complete, conservative and with uniform cut elimination and subformula property. These calculi modularly extend the multi-type calculi for rough algebras to a ‘nondistributive’ (i.e. general lattice-based) setting.
Physics Beyond Catching A Mouse In The Dark: From Big Science To Deep Science,
2019
University of New Mexico
Physics Beyond Catching A Mouse In The Dark: From Big Science To Deep Science, Victor Christianto, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
The Higgs particle has been detected a few years ago, that is what newspapers tell us. For many physicists, the Standard Model of particle physics has accomplished all the jobs. Or to put it simply: The game is over. Is it true? Then some physicists began to ask: can go beyond the Standard Model? Because the supersymmetric extension of the Standard Model has failed. If you feel that theoretical physics is becoming boring, you are not alone. Fortunately, there is good news: a new generation of physicists are doing table-top experiments in their basements. Can we expect new results later?2 …
Singular Ramsey And Turán Numbers,
2019
University of Haifa-Oranim
Singular Ramsey And Turán Numbers, Yair Caro, Zsolt Tuza
Theory and Applications of Graphs
We say that a subgraph F of a graph G is singular if the degrees dG(v) are all equal or all distinct for the vertices v ∈ V (F). The singular Ramsey number Rs(F) is the smallest positive integer n such that, for every m at least n, in every edge 2-coloring of Km, at least one of the color classes contains F as a singular subgraph. In a similar flavor, the singular Turán number Ts(n,F) is defined as the maximum number of edges in a graph of order n, …
Hypersurfaces With Nonnegative Ricci Curvature In Hyperbolic Space,
2019
California Polytechnic State University - San Luis Obispo
Hypersurfaces With Nonnegative Ricci Curvature In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing
Mathematics
Based on properties of n-subharmonic functions we show that a complete, noncompact, properly embedded hypersurface with nonnegative Ricci curvature in hyperbolic space has an asymptotic boundary at infinity of at most two points. Moreover, the presence of two points in the asymptotic boundary is a rigidity condition that forces the hypersurface to be an equidistant hypersurface about a geodesic line in hyperbolic space. This gives an affirmative answer to the question raised by Alexander and Currier (Proc Symp Pure Math 54(3):37–44, 1993).
Estimating The Density Of The Abundant Numbers,
2019
Central Washington University
Estimating The Density Of The Abundant Numbers, Dominic Klyve, Melissa Pidde, Kathryn E. Temple
Mathematics Faculty Scholarship
Mathematicians have been interested in properties of abundant numbers – those which are smaller than the sum of their proper factors – for over 2,000 years. During the last century, one line of research has focused in particular on determining the density of abundant numbers in the integers. Current estimates have brought the upper and lower bounds on this density to within about 10−4, with a value of K ≈ 0.2476, but more precise values seem difficult to obtain. In this paper, we employ computational data and tools from inferential statistics to get more insight into this value. We also …
When Revolutions Happen: Algebraic Explanation,
2019
The University of Texas at El Paso
When Revolutions Happen: Algebraic Explanation, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, it may seem that revolutions happen when life becomes really intolerable. However, historical analysis shows a different story: that revolutions happen not when life becomes intolerable, but when a reasonably prosperous level of living suddenly worsens. This empirical observation seems to contradict traditional decision theory ideas, according to which, in general, people's happiness monotonically depends on their level of living. A more detailed model of human behavior, however, takes into account not only the current level of living, but also future expectations. In this paper, we show that if we properly take these future expectations into account, …
