{"title":"A Bayesian Model for the Prediction of United States Presidential Elections","authors":"B. Alexander","doi":"10.1137/17S016166","DOIUrl":"https://doi.org/10.1137/17S016166","url":null,"abstract":"Using a combination of polling data and previous election results, FiveThirtyEight successfully predicted the Electoral College distribution in the presidential election in 2008 with 98% accuracy and in 2012 with 100% accuracy. This study applies a Bayesian analysis of polls, assuming a normal distribution of poll results using a normal conjugate prior. The data were taken from the Huffington Post’s Pollster. States were divided into categories based on past results and current demographics. Each category used a different poll source for the prior. This model was originally used to predict the 2016 election, but later it was applied to the poll data for 2008 and 2012. For 2016, the model had 88% accuracy for the 50 states. For 2008 and 2012, the model had the same Electoral College Prediction as FiveThirtyEight. The method of using state and national polls as a prior in election prediction seems promising and further study is needed.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Opinion Formation Dynamics with Contrarians and Zealots","authors":"Kaitlyn Eekhoff","doi":"10.1137/18S017314","DOIUrl":"https://doi.org/10.1137/18S017314","url":null,"abstract":"Mean-field type ODE models for opinion dynamics often assume that the entire population is comprised of congregators, who are agreeable. On the other hand, a contrarian opinion dynamics ODE model assumes the population has two personality types: congregators, and contrarians, who are disagreeable. In this paper we broadly study how contrarians influence the ability of the population to form a fixed and stable opinion. In particular, we re-examine the dynamics associated with the model introduced by Tanabe and Masuda [12] by looking at how the parameters effect the formation of stable periodic solutions (whose existence implies there is no fixed consensus opinion). Afterwards, we refine and analyze the model under two new hypotheses: (a) the contrarians bow to peer pressure and change their personality type to congregators if a large enough proportion of the entire population agrees on an opinion, and (b) there are zealots associated with one of the opinions. We conclude with a brief discussion on possible extensions of this work.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis of an Antimicrobial Resistance Transmission Model","authors":"John J. Kim","doi":"10.1137/19s1254805","DOIUrl":"https://doi.org/10.1137/19s1254805","url":null,"abstract":"We present an analysis of a system of differential equations that models the transmission dynamics of pathogens with antimicrobial resistance (AMR) in an intensive care unit (ICU) studied by Austin and Anderson (1999). In Austin and Anderson’s four–dimensional compartmental model, patients and health care workers are viewed as hosts and vectors of the pathogens, respectively, and subdivided into uncolonized and colonized populations. In the analysis, we reduce the model to a two–dimensional non–autonomous system. Noting that the reduced system has an autonomous limiting system, we then apply the theory of asymptotically autonomous differential equations systems in the plane developed by Markus (1956) and extended by Thieme (1992, 1994), and later by Castillo–Chavez and Thieme (1995). We first present a stability analysis of the limiting system and prove the existence of a locally asymptotically stable equilibrium point under a set of constraints expressed in terms of reproductive numbers. We then proceed to an asymptotic analysis of the non–autonomous, two–dimensional system by applying a Poincaré–Bendixson type trichotomy result proved by Thieme (1992, 1994). In particular, we establish that any forward bounded trajectory of the non–autonomous system that starts within a defined rectangular region will converge toward the equilibrium point of the limiting system, provided that certain conditions given in terms of the reproductive numbers are satisfied.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Using Mathematical Models to Rank the Members of Criminal Networks","authors":"Lucas Chirino","doi":"10.1137/17s016592","DOIUrl":"https://doi.org/10.1137/17s016592","url":null,"abstract":"Different mathematical approaches to ranking were used to determine the level of importance of every member in a criminal network. Two different data sets consisting of phone records provided by the FBI were analyzed. The first data set consisted of call logs over a three year span of members in a drug ring. The second data set consisted of the call logs of members in a gang. After analyzing the results of the rankings, properties of the two networks are discussed to provide further insight into why certain ranking algorithms performed well and others did not.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Lattice-Based Approach to the PSQ Smoking Model","authors":"Shengding Sun","doi":"10.1137/18S017077","DOIUrl":"https://doi.org/10.1137/18S017077","url":null,"abstract":"We study the dynamics of smoking behavior of agents with a stochastic lattice-based model, assuming that each agent occupies a node and is influenced by its neighbors. This mechanism is adapted from the PSQ smoking model, which is based on a system of ordinary differential equations. The difference in this model is that, more realistically, potential smokers are only influenced by nearby current smokers, instead of all smokers. In addition, the stochasticity of this model also accounts better for the randomness in real world smoking behavior. It is shown here that the quantitative estimates of this new lattice model are significantly different from the previous numerical results obtained in other works using the ODE model. This suggests that taking locality into account affects the model behavior. The critical exponents of this new lattice smoking model under von Neumann neighborhood condition are calculated and verified to be the same as the classic SIRS epidemic model, which classifies this model as belonging to the directed percolation class. We also consider the model in continuum setting, and solve the system numerically using a particular convolution kernel. To the author’s knowledge this is the first time where this widely used and discussed PSQ smoking model is incorporated into the lattice-based setting, and our results show that this changes the quantitative behavior of the PSQ model significantly.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Solving the Dirac Equation with the Unified Transform Method","authors":"Casey Garner","doi":"10.1137/19s1257925","DOIUrl":"https://doi.org/10.1137/19s1257925","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Comparison of Machine Learning Approaches to Housing Value Estimation","authors":"Orton Babb","doi":"10.1137/18s017296","DOIUrl":"https://doi.org/10.1137/18s017296","url":null,"abstract":"Housing value estimation relies on hedonic pricing models whereby price is determined by both internal characteristics (bedrooms, bathrooms, living area, etc.) as well as external characteristics (neighboring houses, ZIP code, etc.). While classical parametric models based on linear regression analysis have been well studied in this application, the theory of hedonic prices places no restrictions on the hedonic price functional form, and hence, more recent research has attempted to apply machine learning (ML) approaches such as K-Nearest Neighbors and Support Vector Machine Regression (SVR). Many of these ML methods are employed on the basis of their flexibility in terms of making less assumptions on the shape or distribution of the data. ML models are therefore used with the expectation of higher accuracy on predicting the final sale price of a house. In this study, we consider the combination of various pre-processing procedures and candidate models on a historical data set of house sales in King County, Washington. Different measures of accuracy are considered in interpreting model performance. The results suggest that while machine learning algorithms like SVR achieve top performance as measured by the adjusted R, classical parametric models can also achieve out-of-sample generalization nearing that of the more sophisticated ML models, with faster training times, no need for feature scaling and more easily interpreted parameters.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fast Implementation of mixed RT0 finite elements in MATLAB","authors":"Theodore Weinberg","doi":"10.1137/18S017430","DOIUrl":"https://doi.org/10.1137/18S017430","url":null,"abstract":"We develop a fast implementation of the mixed finite element method for the Darcy’s problem discretized by lowest-order Raviart-Thomas finite elements using Matlab. The implementation is based on the so-called vectorized approach applied to the computation of the finite element matrices and assembly of the global finite element matrix. The code supports both 2D and 3D domains, and the finite elements can be triangular, rectangular, tetrahedral or hexahedral. The code can also be easily modified to import user-provided meshes. We comment on our freely available code and present a performance comparison with the standard approach.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Survival Analysis of Young Leukemia Patients","authors":"T. Williams","doi":"10.1137/19S019085","DOIUrl":"https://doi.org/10.1137/19S019085","url":null,"abstract":"Faculty Advisors: Dr. Keshav P. Pokhrel 4, Dr. Taysseer Sharaf 5 ————————————————————————————— Abstract With cancer as a leading cause of death in the United States, the study of its related data is imperative due to the potential patient benefits. This paper examines the Surveillance, Epidemiology, and End Results program (SEER) research data of reported cancer diagnoses from 1973-2014 for the incidence of leukemia in young (019 years) patients in the United States. The aim is to identify variables, such as prior cancers and treatment, with a unique impact on survival time and five-year survival probabilities using visualizations and different machine learning techniques. This goal culminated in building multiple models to predict the patient's hazard. The two most insightful models constructed were both neural networks. One network used discrete survival time as a covariate to predict one conditional hazard per patient. The prediction rate is nearly 95% for testing datasets. The other network built hazards for discrete time intervals without survival time as a covariate and predicted with lower accuracy, but captured variable effects from initial testing better.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Substance Use and Abuse","authors":"Eric H. Chai","doi":"10.1137/19s1259870","DOIUrl":"https://doi.org/10.1137/19s1259870","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64310435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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