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Description
The Mathematical and Theoretical Biology Institute (MTBI) is a summer research program for undergraduate students, largely from underrepresented minority groups. Founded in 1996, it serves as a 'life-long' mentorship program, providing continuous support for its students and alumni. This study investigates how MTBI supports student development in applied mathematical research. This includes identifying of motivational factors to pursue and develop capacity to complete higher education.
The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to the collaborative and creative way students co-create the process of becoming scientists. This results in building a continuing network of academic and professional relationships among peers and mentors, in which around three quarters of MTBI PhD graduates come from underrepresented groups.
The extent to which MTBI creates a Vygotskian learning environment is explored from the perspectives of participants who earned doctoral degrees. Previously hypothesized factors (Castillo-Garsow, Castillo-Chavez and Woodley, 2013) that affect participants’ educational and professional development are expanded on.
Factors identified by participants are a passion for the mathematical sciences; desire to grow; enriching collaborative and peer-like interactions; and discovering career options. The self-recognition that they had the ability to be successful, key element of the Vygotskian-Holzman theoretical framework, was a commonly identified theme for their educational development and professional growth.
Participants characterize the collaborative and creative aspects of MTBI. They reported that collaborative dynamics with peers were strengthened as they co-created a learning environment that facilitated and accelerated their understanding of the mathematics needed to address their research. The dynamics of collaboration allowed them to complete complex homework assignments, and helped them formulate and complete their projects. Participants identified the creative environments of their research projects as where creativity emerged in the dynamics of the program.
These data-driven findings characterize for the first time a summer program in the mathematical sciences as a Vygotskian-Holzman environment, that is, a `place’ where participants are seen as capable applied mathematicians, where the dynamics of collaboration and creativity are fundamental components.
The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to the collaborative and creative way students co-create the process of becoming scientists. This results in building a continuing network of academic and professional relationships among peers and mentors, in which around three quarters of MTBI PhD graduates come from underrepresented groups.
The extent to which MTBI creates a Vygotskian learning environment is explored from the perspectives of participants who earned doctoral degrees. Previously hypothesized factors (Castillo-Garsow, Castillo-Chavez and Woodley, 2013) that affect participants’ educational and professional development are expanded on.
Factors identified by participants are a passion for the mathematical sciences; desire to grow; enriching collaborative and peer-like interactions; and discovering career options. The self-recognition that they had the ability to be successful, key element of the Vygotskian-Holzman theoretical framework, was a commonly identified theme for their educational development and professional growth.
Participants characterize the collaborative and creative aspects of MTBI. They reported that collaborative dynamics with peers were strengthened as they co-created a learning environment that facilitated and accelerated their understanding of the mathematics needed to address their research. The dynamics of collaboration allowed them to complete complex homework assignments, and helped them formulate and complete their projects. Participants identified the creative environments of their research projects as where creativity emerged in the dynamics of the program.
These data-driven findings characterize for the first time a summer program in the mathematical sciences as a Vygotskian-Holzman environment, that is, a `place’ where participants are seen as capable applied mathematicians, where the dynamics of collaboration and creativity are fundamental components.
ContributorsEvangelista, Arlene Morales (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Holmes, Raquell M. (Committee member) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2015
Description
Sense of Community is related to numerous positive outcomes for university students. The purpose of this study was to explore sense of community amongst low income students who received a last dollar scholarship. This study also sought to understand how students define community and how they interact with communities from their past (before university), present (since they started college), and how they envision their future community involvement after graduation. Through purposive sampling, six low income Arizona State University students were selected based on similar characteristics. The scholarship that they belong to selects them based on financial need, integrity, and prolonged commitment to community service. Using a qualitative narrative inquiry, I interviewed participants about their understanding and experiences with communities. Interviews were audio recorded and transcribed verbatim for analysis. Based on the analysis, I identified three major themes: community as construction, community as nonlinear, and community as intersectional. Drawing from participants' definitions and experiences of community, I argue that community is a construction. In other words, individuals create their own constructions of community, and their actions vary based on that construction. Participants also experience their communities intersectionally, that is individual's experience their communities as coexisting and through multiple community perspectives, rather than as a single stand-alone entity. Finally, community does not exist as part of a linear time paradigm. Instead community is experienced in terms of relevance to the individual in creating meaning from that community. In addition to the above themes, I also examined participant perspectives of ASU as a community. Based on this research, I recommend that a platform be provided for students to engage in a dialogue about their understanding of community and interactions with communities. Moreover, I suggest researchers utilize intersectionality, constructionism, and non-linear time to frame future research on sense of community. This research is significant because it helps us understand student engagement, and offers a framework through which universities can provide students an opportunity to better understand their own sense of community.
ContributorsWhite, Misha Alexsandra (Author) / Foroughi-Mobarakeh, Behrang (Thesis director) / Legg, Walter Eric (Committee member) / School of Community Resources and Development (Contributor) / School of Social Transformation (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
The Visceral Leishmaniasis (VL) is primarily endemic in five countries, with India and Sudan having the highest burden. The risk factors associated with VL are either unknown in some regions or vary drastically among empirical studies. Here, a dynamical model, motivated and informed by field data from the literature, is analyzed and employed to identify and quantify the impact of region dependent risks on the VL transmission dynamics. Parameter estimation procedures were developed using model-derived quantities and empirical data from multiple resources. The dynamics of VL depend on the estimates of the control reproductive number, RC, interpreted as the average number of secondary infections generated by a single infectious individual during the infectious period. The distribution of RC was estimated for both India (with mean 2.1 ± 1.1) and Sudan (with mean 1.45 ± 0.57). This suggests that VL can be established in naive regions of India more easily than in naive regions of Sudan. The parameter sensitivity analysis on RC suggests that the average biting rate and transmission probabilities between host and vector are among the most sensitive parameters for both countries. The comparative assessment of VL transmission dynamics in both India and Sudan was carried out by parameter sensitivity analysis on VL-related prevalences (such as prevalences of asymptomatic hosts, symptomatic hosts, and infected vectors). The results identify that the treatment and symptoms’ developmental rates are parameters that are highly sensitive to VL symptomatic and asymptomatic host prevalence, respectively, for both countries. It is found that the estimates of transmission probability are significantly different between India (from human to sandflies with mean of 0.39 ± 0.12; from sandflies to human with mean 0.0005 ± 0.0002) and Sudan (from human to sandflies with mean 0.26 ± 0.07; from sandflies to human with mean 0.0002 ± 0.0001). The results have significant implications for elimination. An increasing focus on elimination requires a review of priorities within the VL control agenda. The development of systematic implementation of control programs based on identified risk factors (such as monitoring of asymptomatically infected individuals) has a high transmission-blocking potential.
ContributorsBarley, Kamal K (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Safan, Muntaser (Committee member) / Arizona State University (Publisher)
Created2016
Description
Statistical Methods have been widely used in understanding factors for clinical and public health data. Statistical hypotheses are procedures for testing pre-stated hypotheses. The development and properties of these procedures as well as their performance are based upon certain assumptions. Desirable properties of statistical tests are to maintain validity and to perform well even if these assumptions are not met. A statistical test that maintains such desirable properties is called robust. Mathematical models are typically mechanistic framework, used to study dynamic interactions between components (mechanisms) of a system, and how these interactions give rise to the changes in behavior (patterns) of the system as a whole over time.
In this thesis, I have developed a study that uses novel techniques to link robust statistical tests and mathematical modeling methods guided by limited data from developed and developing regions in order to address pressing clinical and epidemiological questions of interest. The procedure in this study consists of three primary steps, namely, data collection, uncertainty quantification in data, and linking dynamic model to collected data.
The first part of the study focuses on designing, collecting, and summarizing empirical data from the only national survey of hospitals ever conducted regarding patient controlled analgesia (PCA) practices among 168 hospitals across 40 states, in order to assess risks before putting patients on PCA. I used statistical relational models and exploratory data analysis to address the question. Risk factors assessed indicate a great concern for the safety of patients from one healthcare institution to other.
In the second part, I quantify uncertainty associated with data obtained from James A Lovell Federal Healthcare Center to primarily study the effect of Benign Prostatic Hypertrophy (BPH) on sleep architecture in patients with Obstructive Sleep Apnea (OSA). Patients with OSA and BPH demonstrated significant difference in their sleep architecture in comparison to patients without BPH. One of the ways to validate these differences in sleep architecture between the two groups may be to carry out a similar study that evaluates the effect of some other chronic disease on sleep architecture in patients with OSA.
Additionally, I also address theoretical statistical questions such as (1) how to estimate the distribution of a variable in order to retest null hypothesis when the sample size is limited, and (2) how changes on assumptions (like monotonicity and nonlinearity) translate into the effect of the independent variable on the outcome variable. To address these questions we use multiple techniques such as Partial Rank Correlation Coefficients (PRCC) based sensitivity analysis, Fractional Polynomials, and statistical relational models.
In the third part, my goal was to identify socio-economic-environment-related risk factors for Visceral Leishmaniasis (VL) and use the identified critical factors to develop a mathematical model to understand VL transmission dynamics when data is highly underreported. I primarily studied the role of age-specific- susceptibility and epidemiological quantities on the dynamics of VL in the Indian state of Bihar. Statistical results provided ideas on the choice of the modeling framework and estimates of model parameters.
In the conclusion, this study addressed three primary theoretical modeling-related questions (1) how to analyze collected data when sample size limited, and how modeling assumptions varies results of data analysis? (2) Is it possible to identify hidden associations and nonlinearity of these associations using such underpowered data and (3) how statistical models provide more reasonable structure to mathematical modeling framework that can be used in turn to understand dynamics of the system.
In this thesis, I have developed a study that uses novel techniques to link robust statistical tests and mathematical modeling methods guided by limited data from developed and developing regions in order to address pressing clinical and epidemiological questions of interest. The procedure in this study consists of three primary steps, namely, data collection, uncertainty quantification in data, and linking dynamic model to collected data.
The first part of the study focuses on designing, collecting, and summarizing empirical data from the only national survey of hospitals ever conducted regarding patient controlled analgesia (PCA) practices among 168 hospitals across 40 states, in order to assess risks before putting patients on PCA. I used statistical relational models and exploratory data analysis to address the question. Risk factors assessed indicate a great concern for the safety of patients from one healthcare institution to other.
In the second part, I quantify uncertainty associated with data obtained from James A Lovell Federal Healthcare Center to primarily study the effect of Benign Prostatic Hypertrophy (BPH) on sleep architecture in patients with Obstructive Sleep Apnea (OSA). Patients with OSA and BPH demonstrated significant difference in their sleep architecture in comparison to patients without BPH. One of the ways to validate these differences in sleep architecture between the two groups may be to carry out a similar study that evaluates the effect of some other chronic disease on sleep architecture in patients with OSA.
Additionally, I also address theoretical statistical questions such as (1) how to estimate the distribution of a variable in order to retest null hypothesis when the sample size is limited, and (2) how changes on assumptions (like monotonicity and nonlinearity) translate into the effect of the independent variable on the outcome variable. To address these questions we use multiple techniques such as Partial Rank Correlation Coefficients (PRCC) based sensitivity analysis, Fractional Polynomials, and statistical relational models.
In the third part, my goal was to identify socio-economic-environment-related risk factors for Visceral Leishmaniasis (VL) and use the identified critical factors to develop a mathematical model to understand VL transmission dynamics when data is highly underreported. I primarily studied the role of age-specific- susceptibility and epidemiological quantities on the dynamics of VL in the Indian state of Bihar. Statistical results provided ideas on the choice of the modeling framework and estimates of model parameters.
In the conclusion, this study addressed three primary theoretical modeling-related questions (1) how to analyze collected data when sample size limited, and how modeling assumptions varies results of data analysis? (2) Is it possible to identify hidden associations and nonlinearity of these associations using such underpowered data and (3) how statistical models provide more reasonable structure to mathematical modeling framework that can be used in turn to understand dynamics of the system.
ContributorsGonzalez, Beverly, 1980- (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Nuno, Miriam (Committee member) / Arizona State University (Publisher)
Created2015
Description
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.
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.
ContributorsMontalvo, Cesar Paul (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Perrings, Charles (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2020