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Higher Order Fourier Finite Element Methods for Hodge Laplacian Problems on Axisymmetric Domains 轴对称区域上Hodge Laplacian问题的高阶傅里叶有限元方法
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/21s1416813
Nicole Stock
{"title":"Higher Order Fourier Finite Element Methods for Hodge Laplacian Problems on Axisymmetric Domains","authors":"Nicole Stock","doi":"10.1137/21s1416813","DOIUrl":"https://doi.org/10.1137/21s1416813","url":null,"abstract":"In this paper, we construct a new family of higher order Fourier finite element spaces to discretize the axisymmetric Hodge Laplacian problems. We demonstrate that these new higher order Fourier finite element methods provide improved computational efficiency as well as increased accuracy.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315106","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}
引用次数: 0
Urban City: Crime Attractors and Offender Mobility 城市:犯罪吸引因素和罪犯流动
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/21s1420551
V. Nguyen
{"title":"Urban City: Crime Attractors and Offender Mobility","authors":"V. Nguyen","doi":"10.1137/21s1420551","DOIUrl":"https://doi.org/10.1137/21s1420551","url":null,"abstract":"This article develops a generalizable agent-based simulation model of crime. This model is a direct application of a diffusion model of residential burglary and offender mobility by Short et al. [31] to real world crime. Offender mobility is modeled through biased random movement and crime attractiveness of a location is derived from past crimes, diffusion of information and memory decay of past events. Simulations use realistic spatial and crime data for Vancouver, Canada with an error analysis performed at the macro, meso, and micro level. The experimental results are convincing, achieving Pearson Correlation values of 0.988, 0.909, and 0.732 for each level respectively using a Truncated Levy Flight mobility framework. Without a mobility framework, we were able to achieve 0.997, 0.954, and 0.645 for these same levels.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315261","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}
引用次数: 0
Defeating the Digital Divide 消除数字鸿沟
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/21s1417922
Edward Q. Wang
{"title":"Defeating the Digital Divide","authors":"Edward Q. Wang","doi":"10.1137/21s1417922","DOIUrl":"https://doi.org/10.1137/21s1417922","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315155","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}
引用次数: 0
The HyperType Model for Clustering in Networks 网络中聚类的HyperType模型
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/20s1369142
Huandong Chang
{"title":"The HyperType Model for Clustering in Networks","authors":"Huandong Chang","doi":"10.1137/20s1369142","DOIUrl":"https://doi.org/10.1137/20s1369142","url":null,"abstract":"In the field of network analysis, incorporating higher-order features into network models has become increasingly routine. In this paper we introduce the HyperType network model: an extension of a simple typing model with better clustering due to the focus on triangles instead of single edges. In addition to more realistic clustering, we empirically show HyperType retains many features from the original typing model. We empirically fit HyperType to real data, and show an interesting relationship to a recursive Kronecker product.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64313473","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}
引用次数: 0
The Evolution of the Identifiable Analysis of the COVID-19 Virus COVID-19病毒可识别分析的演变
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/21s1422847
Vivek Sreejithkumar
{"title":"The Evolution of the Identifiable Analysis of the COVID-19 Virus","authors":"Vivek Sreejithkumar","doi":"10.1137/21s1422847","DOIUrl":"https://doi.org/10.1137/21s1422847","url":null,"abstract":"It is important to accurately forecast a new infection such as COVID-19 in order to effectively 4 implement control measures. For this purpose, we study whether the epidemiological parameters 5 such as the rate of infection, incubation period, and rate of recovery for the COVID-19 disease 6 can be identified from daily incidences and death data. The data are obtained from the Florida 7 Department of Health, which reports the numbers of daily COVID-19 cases and disease-induced 8 casualties. Two mathematical models that consist of a system of ordinary differential equations are 9 used to simulate the spread of the coronavirus in the Florida population. Structural identifiability 10 analysis is conducted on the models to determine whether the models are well-structured to forecast 11 the outbreak. Analysis revealed that the SEIR model is structurally identifiable, while the social 12 distancing model is not structurally identifiable. If the model is structurally unidentifiable, it may 13 not accurately forecast the pandemic, and in turn, may lead to inaccurate control measures. Then, 14 the practical identifiability of parameter estimates that provide the best fit was investigated using 15 Monte Carlo simulations. The practical identifiability analysis revealed that all of the parameters 16 in the SEIR model are practically identifiable, but the parameters δ, δE , and ρ were found to be 17 unidentifiable in the social distancing model. By comparing two models in this project, we were able 18 to determine the effectiveness of social distancing in preventing incidences and saving lives from the 19 disease in Florida. Furthermore, we consider how people’s behavior changes over time, and how this 20 may affect the rate of disease spread in the population. To represent this, we develop a recipe to 21 determine the time-dependent transmission rate, β(t), from the data and introduce a methodology 22 of how to accomplish this. 23","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315337","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}
引用次数: 0
Analytical Solution of the T, T*, VI, VNI Model for HIV-1 Dynamics HIV-1动力学T, T*， VI, VNI模型的解析解
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/20s133467x
A. Creel
{"title":"Analytical Solution of the T, T*, VI, VNI Model for HIV-1 Dynamics","authors":"A. Creel","doi":"10.1137/20s133467x","DOIUrl":"https://doi.org/10.1137/20s133467x","url":null,"abstract":"This paper investigates a model for cellular and viral interactions following Human Immunodeficiency Virus Type 1 (HIV-1) infection. A simplified version of this model, which considers interactions between the populations of susceptible CD4+ T cells, infected CD4+ T cells, infectious virus, and non-infectious virus, under the effects of reverse transcriptase and protease inhibitors, is presented and solved analytically. The solution is obtained through an iterative method after isolating one dependent variable and performing various substitutions. Although an analytical solution is more difficult to obtain than numerical approximations, it produces exact results to the system of equations. As such, the analytical solution can be used to study the behavior of HIV-1 and its interactions with various treatment methods in an infected patient.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64313161","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}
引用次数: 0
Keep On Trucking 继续运输
SIAM undergraduate research online Pub Date : 2020-01-01 DOI: 10.1137/20s1335091
C. Guan
{"title":"Keep On Trucking","authors":"C. Guan","doi":"10.1137/20s1335091","DOIUrl":"https://doi.org/10.1137/20s1335091","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64313226","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}
引用次数: 0
An Integro-Differential Model of Language Competition 语言竞争的积分-微分模型
SIAM undergraduate research online Pub Date : 2019-01-01 DOI: 10.1137/18s017363
Mallory Gaspard
{"title":"An Integro-Differential Model of Language Competition","authors":"Mallory Gaspard","doi":"10.1137/18s017363","DOIUrl":"https://doi.org/10.1137/18s017363","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":"64310392","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}
引用次数: 1
An Adaptive, Highly Accurate and Efficient, Parker-Sochacki Algorithm for Numerical Solutions to Initial Value Ordinary Differential Equation Systems 初值常微分方程数值解的自适应、高精度、高效的Parker-Sochacki算法
SIAM undergraduate research online Pub Date : 2019-01-01 DOI: 10.1137/19S019115
Jenna Guenther
{"title":"An Adaptive, Highly Accurate and Efficient, Parker-Sochacki Algorithm for Numerical Solutions to Initial Value Ordinary Differential Equation Systems","authors":"Jenna Guenther","doi":"10.1137/19S019115","DOIUrl":"https://doi.org/10.1137/19S019115","url":null,"abstract":"6 The Parker-Sochacki Method (PSM) allows the numerical approximation of solutions to a polynomial 7 initial value ordinary differential equation or system (IVODE) using an algebraic power series method. PSM 8 is equivalent to a modified Picard iteration and provides an efficient, recursive computation of the coefficients 9 of the Taylor polynomial at each step. To date, PSM has largely concentrated on fixed step methods. We 10 develop and test an adaptive stepping scheme that, for many IVODEs, enhances the accuracy and efficiency of 11 PSM. PSM Adaptive (PSMA) is compared to its fixed step counterpart and to standard Runge-Kutta (RK) 12 foundation algorithms using three example IVODEs. In comparison, PSMA is shown to be competitive, often 13 outperforming these methods in terms of accuracy, number of steps, and execution time. A library of functions 14 is also presented that allows access to PSM techniques for many non-polynomial IVODEs without having to 15 first rewrite these in the necessary polynomial form, making PSM a more practical tool. 16","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":"64310230","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}
引用次数: 2
Analytical Solutions of the Susceptible-Infected-Virus (SIV) Model 易感感染病毒(SIV)模型的解析解
SIAM undergraduate research online Pub Date : 2019-01-01 DOI: 10.1137/18S017545
Emily MacIndoe
{"title":"Analytical Solutions of the Susceptible-Infected-Virus (SIV) Model","authors":"Emily MacIndoe","doi":"10.1137/18S017545","DOIUrl":"https://doi.org/10.1137/18S017545","url":null,"abstract":"The Susceptible-Infected-Virus (SIV) model is a compartmental model to describe within-host dynamics of a viral infection. We apply the SIV model to the human immunodeficiency virus (HIV); in particular, we present analytical solutions to two versions of the model. The first version includes only terms related to the susceptible cell-virus particle interaction and virus production, while the second includes those terms in addition to the infected cell death rate. An analytical solution, although more challenging and time-consuming than numerical methods, has the advantage of giving exact, rather than approximate, results. These results contribute to our understanding of virus dynamics and could be used to develop better treatment options. The approach used to solve each model involved first isolating one of the dependent variables, that is, deriving an equation that involves only one of the variables and its derivatives. Next, various substitutions were used to bring the equation to a more easily solvable form. For the first model, an exact solution is obtained in the form of an implicit equation. For the second model, we give an analytical solution generated by an iterative method.","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":"64310454","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}
引用次数: 2
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