Impact of Teaching an Interdisciplinary Course Introduction of Applied Mathematics for the Life and Social Sciences on High School Students' Skills and Attitudes Towards Mathematics in a JBMSHP Summer Program

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Description

Research shows that the subject of mathematics, although revered, remains a source of trepidation for many individuals, as they find it difficult to form a connection between the work they do on paper and their work's practical applications. This research…

Research shows that the subject of mathematics, although revered, remains a source of trepidation for many individuals, as they find it difficult to form a connection between the work they do on paper and their work's practical applications. This research study describes the impact of teaching a challenging introductive applied mathematics course on high school students' skills and attitudes towards mathematics in a college Summer Program. In the analysis of my research data, I identified several emerging changes in skills and attitudes towards mathematics, skills that high-school students needed or developed when taking the mathematical modeling course. Results indicated that the applied mathematics course had a positive impact on several students' attitudes, in general, such as, self-confidence, meanings of what mathematics is, and their perceptions of what solutions are. It also had a positive impact on several skills, such as translating real-life situations to mathematics via flow diagrams, translating the models' solutions back from mathematics to the real world, and interpreting graphs. Students showed positive results when the context of their problems was applied or graphical, and fewer improvement on problems that were not. Research also indicated some negatives outcomes, a decrease in confidence for certain students, and persistent negative ways of thinking about graphs. Based on these findings, I make recommendations for teaching similar mathematical modeling at the pre-university level, to encourage the development of young students through educational, research and similar mentorship activities, to increase their inspiration and interest in mathematics, and possibly consider a variety of sciences, technology, engineering and mathematics-related (STEM) fields and careers.

Date Created
2020
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The Influence of Class Nonlinear Dynamics and Education on Socio-Economic Mobility

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The dissertation addresses questions tied in to the challenges posed by the impact of environmental factors on the nonlinear dynamics of social upward mobility. The proportion of educated individuals from various socio-economic backgrounds is used as a proxy for…

The dissertation addresses questions tied in to the challenges posed by the impact of environmental factors on the nonlinear dynamics of social upward mobility. The proportion of educated individuals from various socio-economic backgrounds is used as a proxy for the environmental impact on the status quo state.

Chapter 1 carries out a review of the mobility models found in the literature and sets the economic context of this dissertation. Chapter 2 explores a simple model that considers poor and rich classes and the impact that educational success may have on altering mobility patterns. The role of the environment is modeled through the use of a modified version of the invasion/extinction model of Richard Levins. Chapter 3 expands the socio-economic classes to include a large middle class to study the role of social mobility in the presence of higher heterogeneity. Chapter 4 includes demographic growth and explores what would be the time scales needed to accelerate mobility. The dissertation asked how long it will take to increase by 22% the proportion of educated from the poor classes under demographic versus non-demographic growth conditions. Chapter 5 summarizes results and includes a discussion of results. It also explores ways of modeling the influence of nonlinear dynamics of mobility, via exogenous factors. Finally, Chapter 6 presents economic perspectives about the role of environmental influence on college success. The framework can be used to incorporate the impact of economic factors and social changes, such as unemployment, or gap between the haves and have nots. The dissertation shows that peer influence (poor influencing the poor) has a larger effect than class influence (rich influencing the poor). Additionally, more heterogeneity may ease mobility of groups but results depend on initial conditions. Finally, average well-being of the community and income disparities may improve over time. Finally, population growth may extend time scales needed to achieve a specific goal of educated poor.
Date Created
2020
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Lifelong Adaptive Neuronal Learning for Autonomous Multi-Robot Demining in Colombia, and Enhancing the Science, Technology and Innovation Capacity of the Ejército Nacional de Colombia

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Description
In order to deploy autonomous multi-robot teams for humanitarian demining in Colombia, two key problems need to be addressed. First, a robotic controller with limited power that can completely cover a dynamic search area is needed. Second, the Colombian National…

In order to deploy autonomous multi-robot teams for humanitarian demining in Colombia, two key problems need to be addressed. First, a robotic controller with limited power that can completely cover a dynamic search area is needed. Second, the Colombian National Army (COLAR) needs to increase its science, technology and innovation (STI) capacity to help develop, build and maintain such robots. Using Thangavelautham's (2012, 2017) Artificial Neural Tissue (ANT) control algorithm, a robotic controller for an autonomous multi-robot team was developed. Trained by a simple genetic algorithm, ANT is an artificial neural network (ANN) controller with a sparse, coarse coding network architecture and adaptive activation functions. Starting from the exterior of open, basic geometric grid areas, computer simulations of an ANT multi-robot team with limited time steps, no central controller and limited a priori information, covered some areas completely in linear time, and other areas near completely in quasi-linear time, comparable to the theoretical cover time bounds of grid-based, ant pheromone, area coverage algorithms. To mitigate catastrophic forgetting, a new learning method for ANT, Lifelong Adaptive Neuronal Learning (LANL) was developed, where neural network weight parameters for a specific coverage task were frozen, and only the activation function and output behavior parameters were re-trained for a new coverage task. The performance of the LANL controllers were comparable to training all parameters ab initio, for a new ANT controller for the new coverage task.

To increase COLAR's STI capacity, a proposal for a new STI officer corps, Project ÉLITE (Equipo de Líderes en Investigación y Tecnología del Ejército) was developed, where officers enroll in a research intensive, master of science program in applied mathematics or physics in Colombia, and conduct research in the US during their final year. ÉLITE is inspired by the Israel Defense Forces Talpiot program.
Date Created
2019
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Attention harvesting for knowledge production

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Description
This dissertation seeks to understand and study the process of attention harvesting and knowledge production on typical online Q&A communities. Goals of this study include quantifying the attention harvesting and online knowledge, damping the effect of competition for attention on…

This dissertation seeks to understand and study the process of attention harvesting and knowledge production on typical online Q&A communities. Goals of this study include quantifying the attention harvesting and online knowledge, damping the effect of competition for attention on knowledge production, and examining the diversity of user behaviors on question answering. Project 1 starts with a simplistic discrete time model on a scale-free network and provides the method to measure the attention harvested. Further, project 1 highlights the effect of distractions on harvesting productive attention and in the end concludes which factors are influential and sensitive to the attention harvesting. The main finding is the critical condition to optimize the attention harvesting on the network by reducing network connection. Project 2 extends the scope of the study to quantify the value and quality of knowledge, focusing on the question answering dynamics. This part of research models how attention was distributed under typical answering strategies on a virtual online Q&A community. The final result provides an approach to measure the efficiency of attention transferred into value production and observes the contribution of different scenarios under various computed metrics. Project 3 is an advanced study on the foundation of the virtual question answering community from project 2. With highlights of different user behavioral preferences, algorithm stochastically simulates individual decisions and behavior. Results from sensitivity analysis on different mixtures of user groups gives insight of nonlinear dynamics for the objectives of success. Simulation finding shows reputation rewarding mechanism on Stack Overflow shapes the crowd mixture of behavior to be successful. In addition, project proposed an attention allocation scenario of question answering to improve the success metrics when coupling with a particular selection strategy.
Date Created
2019
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The Impact of Anthropologically Motivated Human Social Networks on the Transmission Dynamics of Infectious Disease

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Description
Understanding the consequences of changes in social networks is an important an-

thropological research goal. This dissertation looks at the role of data-driven social

networks on infectious disease transmission and evolution. The dissertation has two

projects. The first project is an examination of…

Understanding the consequences of changes in social networks is an important an-

thropological research goal. This dissertation looks at the role of data-driven social

networks on infectious disease transmission and evolution. The dissertation has two

projects. The first project is an examination of the effects of the superspreading

phenomenon, wherein a relatively few individuals are responsible for a dispropor-

tionate number of secondary cases, on the patterns of an infectious disease. The

second project examines the timing of the initial introduction of tuberculosis (TB) to

the human population. The results suggest that TB has a long evolutionary history

with hunter-gatherers. Both of these projects demonstrate the consequences of social

networks for infectious disease transmission and evolution.

The introductory chapter provides a review of social network-based studies in an-

thropology and epidemiology. Particular emphasis is paid to the concept and models

of superspreading and why to consider it, as this is central to the discussion in chapter

2. The introductory chapter also reviews relevant epidemic mathematical modeling

studies.

In chapter 2, social networks are connected with superspreading events, followed

by an investigation of how social networks can provide greater understanding of in-

fectious disease transmission through mathematical models. Using the example of

SARS, the research shows how heterogeneity in transmission rate impacts super-

spreading which, in turn, can change epidemiological inference on model parameters

for an epidemic.

Chapter 3 uses a different mathematical model to investigate the evolution of TB

in hunter-gatherers. The underlying question is the timing of the introduction of TB

to the human population. Chapter 3 finds that TB’s long latent period is consistent

with the evolutionary pressure which would be exerted by transmission on a hunter-

igatherer social network. Evidence of a long coevolution with humans indicates an

early introduction of TB to the human population.

Both of the projects in this dissertation are demonstrations of the impact of var-

ious characteristics and types of social networks on infectious disease transmission

dynamics. The projects together force epidemiologists to think about networks and

their context in nontraditional ways.
Date Created
2019
Agent

Understanding the emerging behaviors and demands for the colony success of social insects: a mathematical approach

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Description
The most advanced social insects, the eusocial insects, form often large societies in which there is reproductive division of labor, queens and workers, have overlapping generations, and cooperative brood care where daughter workers remain in the nest with their queen…

The most advanced social insects, the eusocial insects, form often large societies in which there is reproductive division of labor, queens and workers, have overlapping generations, and cooperative brood care where daughter workers remain in the nest with their queen mother and care for their siblings. The eusocial insects are composed of representative species of bees and wasps, and all species of ants and termites. Much is known about their organizational structure, but remains to be discovered.

The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
Date Created
2018
Agent

Understanding the impact of social factors on the transmission dynamics of infectious diseases across highly heterogeneous risk environments

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Description
This dissertation explores the impact of environmental dependent risk on disease dynamics within a Lagrangian modeling perspective; where the identity (defined by place of residency) of individuals is preserved throughout the epidemic process. In Chapter Three, the impact of individuals…

This dissertation explores the impact of environmental dependent risk on disease dynamics within a Lagrangian modeling perspective; where the identity (defined by place of residency) of individuals is preserved throughout the epidemic process. In Chapter Three, the impact of individuals who refuse to be vaccinated is explored. MMR vaccination and birth rate data from the State of California are used to determine the impact of the anti-vaccine movement on the dynamics of growth of the anti-vaccine sub-population. Dissertation results suggest that under realistic California social dynamics scenarios, it is not possible to revert the influence of anti-vaccine

contagion. In Chapter Four, the dynamics of Zika virus are explored in two highly distinct idealized environments defined by a parameter that models highly distinctive levels of risk, the result of vector and host density and vector control measures. The underlying assumption is that these two communities are intimately connected due to economics with the impact of various patterns of mobility being incorporated via

the use of residency times. In short, a highly heterogeneous community is defined by its risk of acquiring a Zika infection within one of two "spaces," one lacking access to health services or effective vector control policies (lack of resources or ignored due to high levels of crime, or poverty, or both). Low risk regions are defined as those with access to solid health facilities and where vector control measures are implemented routinely. It was found that the better connected these communities are, the existence of communities where mobility between risk regions is not hampered, lower the overall, two patch Zika prevalence. Chapter Five focuses on the dynamics of tuberculosis (TB), a communicable disease, also on an idealized high-low risk set up. The impact of mobility within these two highly distinct TB-risk environments on the dynamics and control of this disease is systematically explored. It is found that collaboration and mobility, under some circumstances, can reduce the overall TB burden.
Date Created
2018
Agent

Consequences of short term mobility across heterogeneous risk environments: the 2014 west African Ebola outbreak

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Description
In this dissertation the potential impact of some social, cultural and economic factors on

Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability

to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is

addressed.…

In this dissertation the potential impact of some social, cultural and economic factors on

Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability

to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is

addressed. A mathematical model, calibrated with data from the 2014 West African outbreak,

is used to show the dynamics of EVD control under various quarantine and isolation

effectiveness regimes. It is shown that in order to make a difference it must reach a high

proportion of the infected population. The effect of EVD-dead bodies has been incorporated

in the quarantine effectiveness. In Chapter four, the potential impact of differential

risk is assessed. A two-patch model without explicitly incorporate quarantine is used to

assess the impact of mobility on communities at risk of EVD. It is shown that the

overall EVD burden may lessen when mobility in this artificial high-low risk society is allowed.

The cost that individuals in the low-risk patch must pay, as measured by secondary

cases is highlighted. In Chapter five a model explicitly incorporating patch-specific quarantine

levels is used to show that quarantine a large enough proportion of the population

under effective isolation leads to a measurable reduction of secondary cases in the presence

of mobility. It is shown that sharing limited resources can improve the effectiveness of

EVD effective control in the two-patch high-low risk system. Identifying the conditions

under which the low-risk community would be willing to accept the increases in EVD risk,

needed to reduce the total number of secondary cases in a community composed of two

patches with highly differentiated risks has not been addressed. In summary, this dissertation

looks at EVD dynamics within an idealized highly polarized world where resources

are primarily in the hands of a low-risk community – a community of lower density, higher

levels of education and reasonable health services – that shares a “border” with a high-risk

community that lacks minimal resources to survive an EVD outbreak.
Date Created
2018
Agent

Estimate of the reproduction number of the 2015 Zika virus outbreak in Barranquilla, Colombia, and estimation of the relative role of sexual transmission

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Description

Background
In 2015, the Zika arbovirus (ZIKV) began circulating in the Americas, rapidly expanding its global geographic range in explosive outbreaks. Unusual among mosquito-borne diseases, ZIKV has been shown to also be sexually transmitted, although sustained autochthonous transmission due to sexual…

Background
In 2015, the Zika arbovirus (ZIKV) began circulating in the Americas, rapidly expanding its global geographic range in explosive outbreaks. Unusual among mosquito-borne diseases, ZIKV has been shown to also be sexually transmitted, although sustained autochthonous transmission due to sexual transmission alone has not been observed, indicating the reproduction number (R0) for sexual transmission alone is less than 1. Critical to the assessment of outbreak risk, estimation of the potential attack rates, and assessment of control measures, are estimates of the basic reproduction number, R0.
Methods
We estimated the R0 of the 2015 ZIKV outbreak in Barranquilla, Colombia, through an analysis of the exponential rise in clinically identified ZIKV cases (n = 359 to the end of November, 2015).
Findings
The rate of exponential rise in cases was ρ = 0.076 days[superscript −1], with 95% CI [0.066,0.087] days[superscript −1]. We used a vector-borne disease model with additional direct transmission to estimate the R0; assuming the R0 of sexual transmission alone is less than 1, we estimated the total R0 = 3.8 [2.4,5.6], and that the fraction of cases due to sexual transmission was 0.23 [0.01,0.47] with 95% confidence.
Interpretation
This is among the first estimates of R0 for a ZIKV outbreak in the Americas, and also among the first quantifications of the relative impact of sexual transmission.

Date Created
2016-10-17
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Intramyocellular Lipids and the Progression of Muscular Insulin Resistance

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Description
Diabetes is a disease characterized by reduced insulin action and secretion, leading to elevated blood glucose. In the 1990s, studies showed that intravenous injection of fatty acids led to a sharp negative response in insulin action that subsided hours after…

Diabetes is a disease characterized by reduced insulin action and secretion, leading to elevated blood glucose. In the 1990s, studies showed that intravenous injection of fatty acids led to a sharp negative response in insulin action that subsided hours after the injection. The molecule associated with diminished insulin signalling response was a byproduct of fatty acids, diacylglycerol. This dissertation is focused on the formulation of a model built around the known mechanisms of glucose and fatty acid storage and metabolism within myocytes, as well as downstream effects of diacylglycerol on insulin action. Data from euglycemic-hyperinsulinemic clamp with fatty acid infusion studies are used to validate the qualitative behavior of the model and estimate parameters. The model closely matches clinical data and suggests a new metric to determine quantitative measurements of insulin action downregulation. Analysis and numerical simulation of the long term, piecewise smooth system of ordinary differential equations demonstrates a discontinuous bifurcation implicating nutrient excess as a driver of muscular insulin resistance.
Date Created
2017
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