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- All Subjects: Social networks
- All Subjects: Epidemics--Mathematical models.
- All Subjects: Mathematics Education
- Genre: Academic theses
- Creators: Castillo-Chavez, Carlos
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.
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.
Despite the success of these network embedding methods, the majority of them are dedicated to static plain networks, i.e., networks with fixed nodes and links only; while in social media, networks can present in various formats, such as attributed networks, signed networks, dynamic networks and heterogeneous networks. These social networks contain abundant rich information to alleviate the network sparsity problem and can help learn a better network representation; while plain network embedding approaches cannot tackle such networks. For example, signed social networks can have both positive and negative links. Recent study on signed networks shows that negative links have added value in addition to positive links for many tasks such as link prediction and node classification. However, the existence of negative links challenges the principles used for plain network embedding. Thus, it is important to study signed network embedding. Furthermore, social networks can be dynamic, where new nodes and links can be introduced anytime. Dynamic networks can reveal the concept drift of a user and require efficiently updating the representation when new links or users are introduced. However, static network embedding algorithms cannot deal with dynamic networks. Therefore, it is important and challenging to propose novel algorithms for tackling different types of social networks.
In this dissertation, we investigate network representation learning in social media. In particular, we study representative social networks, which includes attributed network, signed networks, dynamic networks and document networks. We propose novel frameworks to tackle the challenges of these networks and learn representations that not only capture the network structure but also the unique properties of these social networks.
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.
This thesis looks first at the impact that limited access to vaccine stockpiles may have on a single influenza outbreak. The purpose is to highlight the challenges faced by populations embedded in inadequate health systems and to identify and assess ways of ameliorating the impact of resource limitations on public health policy.
Age-specific per capita constraint rates play an important role on the dynamics of communicable diseases and, influenza is, of course, no exception. Yet the challenges associated with estimating age-specific contact rates have not been decisively met. And so, this thesis attempts to connect contact theory with age-specific contact data in the context of influenza outbreaks in practical ways. In mathematical epidemiology, proportionate mixing is used as the preferred theoretical mixing structure and so, the frame of discussion of this dissertation follows this specific theoretical framework. The questions that drive this dissertation, in the context of influenza dynamics, proportionate mixing, and control, are:
I. What is the role of age-aggregation on the dynamics of a single outbreak? Or simply speaking, does the number and length of the age-classes used to model a population make a significant difference on quantitative predictions?
II. What would the age-specific optimal influenza vaccination policies be? Or, what are the age-specific vaccination policies needed to control an outbreak in the presence of limited or unlimited vaccine stockpiles?
Intertwined with the above questions are issues of resilience and uncertainty including, whether or not data collected on mixing (by social scientists) can be used effectively to address both questions in the context of influenza and proportionate mixing. The objective is to provide answers to these questions by assessing the role of aggregation (number and length of age classes) and model robustness (does the aggregation scheme selected makes a difference on influenza dynamics and control) via comparisons between purely data-driven model and proportionate mixing models.
University researchers assume an important role in innovation, particularly as a result of the Bayh-Dole Act, which allowed universities to license inventions funded by federal research dollars, to private industry. Aligning the incentives to innovate at the university level with the incentives to adopt downstream, I show that non-exclusive licensing is preferred under both fixed fee and royalty licensing. Finding support for non-exclusive licensing is important as it provides evidence that the concept underlying the Bayh-Dole Act has economic merit, namely that the goals of university-based researchers are consistent with those of society, and taxpayers, in general.
After licensing, new products enter the diffusion process. Using a case study of small holders in Mozambique, I observe substantial geographic clustering of new-variety adoption decisions. Controlling for the other potential factors, I find that information diffusion through space is largely responsible for variation in adoption. As predicted by a social learning model, spatial effects are not based on geographic distance, but rather on neighbor-relationships that follow from information exchange. My findings are consistent with others who find information to be the primary barrier to adoption, and means that adoption can be accelerated by improving information exchange among farmers.
Ultimately, innovation is only useful when adopted by end consumers. Consumers’ choices of new products are determined by many factors such as personal preferences, the attributes of the products, and more importantly, peer recommendations. My experimental data shows that peers are indeed important, but “weak ties” or information from friends-of-friends is more important than close friends. Further, others regarded as experts in the subject matter exert the strongest influence on peer choices.