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Articles 1 - 6 of 6
Full-Text Articles in Other Applied Mathematics
Weathering And Beyond: Leveraging Mathematical Modeling To Simulate Erosion In Digital Media, Fiona Irving-Beck
Weathering And Beyond: Leveraging Mathematical Modeling To Simulate Erosion In Digital Media, Fiona Irving-Beck
Scripps Senior Theses
How might we bring an idea to life from both a mathematical and an artistic perspective? Within Weathering, I use imagery of environmental erosion to explore the differences between physical and digital forms of representation. I created a physical painting of an abandoned copper mine, digitized the work, and then used a mathematical model to digitally “erode” it, which I re-translated into paintings. While the explicit texture present in physical work speaks best to my practice/intent, the mathematical framework that is the basis for my digital work affords a powerful mode of temporal flexibility. Used in conjunction, these two …
Correlation Does Not Imply Correlation: A Thesis On Causal Influence And Simpson’S Paradox, Emily Naitoh
Correlation Does Not Imply Correlation: A Thesis On Causal Influence And Simpson’S Paradox, Emily Naitoh
Scripps Senior Theses
In our data-driven world, it has become commonplace to attempt to find
causal relationships. One of the themes of this thesis is to show methods of
determining causation. The second theme follows a saying in mathematics,
"correlation does not imply causation". We will also discuss situations where
correlation does not even imply correlation itself. These cases are described
by Simpson’s paradox in an exploration of different areas of mathematics
and computer coding.
A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, Jordan Wellington
A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, Jordan Wellington
Scripps Senior Theses
On May 6th, 2020, after extensive public comment and review, the Department of Education published the final rule for the new Title IX regulations, which took effect in schools on August 14th. Title IX is the nearly fifty year old piece of the Education Amendments that prohibits sexual discrimination in federally funded schools. Several of these changes, such as the inclusion of live hearings and cross examination of witnesses, have been widely criticized by victims’ rights advocates for potentially retraumatizing victims of sexual assault and discouraging students from pursuing a Title IX claim. While the impact of the new regulations …
Eradicating Malaria: Improving A Multiple-Timestep Optimization Model Of Malarial Intervention Policy, Taryn M. Ohashi
Eradicating Malaria: Improving A Multiple-Timestep Optimization Model Of Malarial Intervention Policy, Taryn M. Ohashi
Scripps Senior Theses
Malaria is a preventable and treatable blood-borne disease whose complications can be fatal. Although many interventions exist in order to reduce the impacts of malaria, the optimal method of distributing these interventions in a geographical area with limited resources must be determined. This thesis refines a model that uses an integer linear program and a compartmental model of epidemiology called an SIR model of ordinary differential equations. The objective of the model is to find an intervention strategy over multiple time steps and multiple geographic regions that minimizes the number of days people spend infected with malaria. In this paper, …
Clustering Methods And Their Applications To Adolescent Healthcare Data, Morgan Mayer-Jochimsen
Clustering Methods And Their Applications To Adolescent Healthcare Data, Morgan Mayer-Jochimsen
Scripps Senior Theses
Clustering is a mathematical method of data analysis which identifies trends in data by efficiently separating data into a specified number of clusters so is incredibly useful and widely applicable for questions of interrelatedness of data. Two methods of clustering are considered here. K-means clustering defines clusters in relation to the centroid, or center, of a cluster. Spectral clustering establishes connections between all of the data points to be clustered, then eliminates those connections that link dissimilar points. This is represented as an eigenvector problem where the solution is given by the eigenvectors of the Normalized Graph Laplacian. Spectral clustering …
Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho
Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho
Scripps Senior Theses
Maximum likelihood methods are used to estimate the phylogenetic trees for a set of species. The probabilities of DNA base substitutions are modeled by continuous-time Markov chains. We use these probabilities to estimate which DNA bases would produce the data that we observe. The topology of the tree is also determined using base substitution probabilities and conditional likelihoods. Felsenstein [2] introduced this method of finding an estimate for the maximum likelihood phylogenetic tree. We will explore this method in detail in this paper.