Developed at unprecedented speeds, vaccines have thus far played a crucial role in slowing down the COVID-19 pandemic around the world. Therefore, it is an absolute necessity for countries to be able to accu-rately forecast the distribution of vaccines. This paper uses an Auto-Regressive Integrated Moving Average (ARIMA) model to analyze and forecast 30 days of COVID-19 vaccine distribution for the United States, Japan, Taiwan, and China. Specifically, for the United States and Japan, the predicted variable was the percent of the population that was fully vaccinated while the predicted variable for Taiwan and China was the total number of doses administered. The data used to fit our model was pulled from a publicly available dataset compiled from various sources around the world. For each country, the training data consisted of that country’s vaccination data from whenever they first administered vaccines until July 19, 2021. After fitting the model on the training data, the model was then tested against 30 days of data from July 20, 2021 to August 18, 2021. The paper found that the univariate ARIMA model was able to, on average, forecast the distribution of COVID-19 vaccines within 5% of the actual value for each country.
{"title":"Forecasting COVID-19 Vaccine Distribution in the United States, Japan, Taiwan, and China using the Auto-Regressive Integrated Moving Average (ARIMA) model","authors":"Kefei Chen","doi":"10.1137/21s145584x","DOIUrl":"https://doi.org/10.1137/21s145584x","url":null,"abstract":"Developed at unprecedented speeds, vaccines have thus far played a crucial role in slowing down the COVID-19 pandemic around the world. Therefore, it is an absolute necessity for countries to be able to accu-rately forecast the distribution of vaccines. This paper uses an Auto-Regressive Integrated Moving Average (ARIMA) model to analyze and forecast 30 days of COVID-19 vaccine distribution for the United States, Japan, Taiwan, and China. Specifically, for the United States and Japan, the predicted variable was the percent of the population that was fully vaccinated while the predicted variable for Taiwan and China was the total number of doses administered. The data used to fit our model was pulled from a publicly available dataset compiled from various sources around the world. For each country, the training data consisted of that country’s vaccination data from whenever they first administered vaccines until July 19, 2021. After fitting the model on the training data, the model was then tested against 30 days of data from July 20, 2021 to August 18, 2021. The paper found that the univariate ARIMA model was able to, on average, forecast the distribution of COVID-19 vaccines within 5% of the actual value for each country.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315575","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":"Discretized Migration Flow: A Vector Field Based Tool for Avian Mobility in Patchy Mechanistic Models of Early Pathogenic Spread","authors":"Raphael Kelly","doi":"10.1137/21s1461381","DOIUrl":"https://doi.org/10.1137/21s1461381","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315753","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":"Introduction for M3 Winning Paper Remote Work: Fad or Future","authors":"Michelle Montgomery","doi":"10.1137/22s1493136","DOIUrl":"https://doi.org/10.1137/22s1493136","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317069","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 artificial neural networks to classify optimal microswimmers based on their shapes","authors":"Niyizhen Jin, Xinyue Qi, Nicole Surgent, Wanting Huang","doi":"10.1137/22s1479816","DOIUrl":"https://doi.org/10.1137/22s1479816","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317413","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}
Highly accurate numerical approximations of analytic Caputo fractional derivatives are dif-ficult to compute due to the upper bound singularity in its integral definition. However, it has been recently demonstrated that Caputo fractional derivatives of analytic functions can be numerically evaluated to double-precision accuracy by utilizing only function values in a grid. This is done by considering a modified Trapezoidal Rule (TR) and placing equispaced finite difference (FD) correction stencils at both endpoints. In terms of complex-valued analytic functions f ( z ), these fractional derivatives are multi-valued. In this paper, we provide several test functions for this numerical method of evaluating Caputo fractional derivatives. We produce figures of the principal branch of the functions’ approximated fractional derivatives, and include error plots of these approximations.
{"title":"Numerical Computation of Fractional Derivatives of Complex-Valued Analytic Functions","authors":"A. Higgins","doi":"10.1137/22s1520566","DOIUrl":"https://doi.org/10.1137/22s1520566","url":null,"abstract":"Highly accurate numerical approximations of analytic Caputo fractional derivatives are dif-ficult to compute due to the upper bound singularity in its integral definition. However, it has been recently demonstrated that Caputo fractional derivatives of analytic functions can be numerically evaluated to double-precision accuracy by utilizing only function values in a grid. This is done by considering a modified Trapezoidal Rule (TR) and placing equispaced finite difference (FD) correction stencils at both endpoints. In terms of complex-valued analytic functions f ( z ), these fractional derivatives are multi-valued. In this paper, we provide several test functions for this numerical method of evaluating Caputo fractional derivatives. We produce figures of the principal branch of the functions’ approximated fractional derivatives, and include error plots of these approximations.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317481","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":"Finding the optimum times to flip a beefsteak using a genetic algorithm","authors":"Rebekah Chin","doi":"10.1137/21s1414917","DOIUrl":"https://doi.org/10.1137/21s1414917","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315042","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}
A two-dimensional (2D) material is a crystalline material consisting of a single layer of atoms. These materials are used in many applications including photovoltaics, semiconductors, electrodes, and water purification. These materials’ atomic structures can be represented as a discrete infinite periodic graph. Using Floquet-Bloch theory, the spectrum of the Schrödinger operator can be calculated on these infinite graphical representations by computing the eigenvalues of the magnetic flux Schrödinger operator on a fundamental domain for every possible value of magnetic flux. Previous researchers have conjectured a relationship between the special physical properties of one 2D material, graphene, and the Dirac conical points which appear in the spectrum of its Schrödinger operator. However, graphene was the only material studied with respect to these Dirac conical points. The existence of spectral touching points in different two-dimensional materials is proved, including muscovite, quartz, and transition metal oxides, under certain conditions on electric potential. The spectral touching points found in transition metal oxides are not the Dirac conical points found in graphene, but rather a previously unknown type of spectral touching point, named the mesa touching point, which appears in the Schrödinger operator for transition metal oxides under certain conditions.
{"title":"Spectral Touching Points in Two-Dimensional Materials","authors":"Andrea R. Wynn","doi":"10.1137/21s143889x","DOIUrl":"https://doi.org/10.1137/21s143889x","url":null,"abstract":"A two-dimensional (2D) material is a crystalline material consisting of a single layer of atoms. These materials are used in many applications including photovoltaics, semiconductors, electrodes, and water purification. These materials’ atomic structures can be represented as a discrete infinite periodic graph. Using Floquet-Bloch theory, the spectrum of the Schrödinger operator can be calculated on these infinite graphical representations by computing the eigenvalues of the magnetic flux Schrödinger operator on a fundamental domain for every possible value of magnetic flux. Previous researchers have conjectured a relationship between the special physical properties of one 2D material, graphene, and the Dirac conical points which appear in the spectrum of its Schrödinger operator. However, graphene was the only material studied with respect to these Dirac conical points. The existence of spectral touching points in different two-dimensional materials is proved, including muscovite, quartz, and transition metal oxides, under certain conditions on electric potential. The spectral touching points found in transition metal oxides are not the Dirac conical points found in graphene, but rather a previously unknown type of spectral touching point, named the mesa touching point, which appears in the Schrödinger operator for transition metal oxides under certain conditions.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315165","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}
This work is a simple example of the quantum dynamics of a particle in a disordered system in one dimension. In particular, we illustrate numerically the phenomenon of Anderson localisation of a wave packet using a basic model constructed with small random rectangular potential barriers. Also, we study the dynamics of a quantum particle in a disordered potential formed by an harmonic oscillator perturbed by random rectangular barriers. To show the effects of disorder on the dynamics of the system, we compare the time evolution of the wave function of the unperturbed harmonic oscillator with the wave function of the disordered system. We do this by taking the scalar product between the unperturbed and perturbed wave functions at each timestep for different values of the perturbation parameters affecting the disordered wave packet.
{"title":"Quantum Evolution in One Dimensional Disordered Systems: Localisation and Oscillations","authors":"E. Sharp","doi":"10.1137/22s1516373","DOIUrl":"https://doi.org/10.1137/22s1516373","url":null,"abstract":"This work is a simple example of the quantum dynamics of a particle in a disordered system in one dimension. In particular, we illustrate numerically the phenomenon of Anderson localisation of a wave packet using a basic model constructed with small random rectangular potential barriers. Also, we study the dynamics of a quantum particle in a disordered potential formed by an harmonic oscillator perturbed by random rectangular barriers. To show the effects of disorder on the dynamics of the system, we compare the time evolution of the wave function of the unperturbed harmonic oscillator with the wave function of the disordered system. We do this by taking the scalar product between the unperturbed and perturbed wave functions at each timestep for different values of the perturbation parameters affecting the disordered wave packet.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317634","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}
After each census, researchers analyze election data to provide information relevant to the redistricting process. South Carolina is among a collection of states which face certain issues regarding election analysis of fairness due to the presence of a large percentage of uncontested races. Although uncontested results are known to create analysis challenges, there is not a universal consensus on how to best handle these situations. Here we explore quantification of partisan fairness and the impact of using statewide election county-level data as a proxy for estimating uncontested results. We develop a district approximation method using statewide elections at the county scale and use known metrics to qualitatively and quantitatively evaluate resulting election characteristics in historical and simulated election contexts. The same metrics were then used to perform a thorough comparative analysis of other common approximation methods. We find county-level election data to be an effective tool in approximating uncontested elections by providing evidence to support the notion that county-level data is effective under multiple election conditions. Furthermore, analysis of different approximation methods show how measures of partisan fairness for a particular election can change based upon a particular approximation method, potentially affecting future interpretations of uncontested election results.
{"title":"Implementation of Statewide Election Data to Examine Fairness of South Carolina District Maps: A Comparative Analysis of Approaches for Approximating Results in Uncontested Races","authors":"Alfie-Louise Brownless","doi":"10.1137/21s1437342","DOIUrl":"https://doi.org/10.1137/21s1437342","url":null,"abstract":"After each census, researchers analyze election data to provide information relevant to the redistricting process. South Carolina is among a collection of states which face certain issues regarding election analysis of fairness due to the presence of a large percentage of uncontested races. Although uncontested results are known to create analysis challenges, there is not a universal consensus on how to best handle these situations. Here we explore quantification of partisan fairness and the impact of using statewide election county-level data as a proxy for estimating uncontested results. We develop a district approximation method using statewide elections at the county scale and use known metrics to qualitatively and quantitatively evaluate resulting election characteristics in historical and simulated election contexts. The same metrics were then used to perform a thorough comparative analysis of other common approximation methods. We find county-level election data to be an effective tool in approximating uncontested elections by providing evidence to support the notion that county-level data is effective under multiple election conditions. Furthermore, analysis of different approximation methods show how measures of partisan fairness for a particular election can change based upon a particular approximation method, potentially affecting future interpretations of uncontested election results.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315016","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}
: The COIVD pandemic has swept the globe since 2019, posing a grave threat to human life. There are multiple ways for the government to control the pandemic, including promoting the vaccination, limiting the number of people in public places, requiring people to wear masks in public places, and suggesting infected people isolate themselves. In this paper, we used a compartmental model to analyze the spread of COVID-19 under the promotion of rapid tests. The result shows that popularization of rapid tests may have a significant impact on controlling the pandemic. With an estimated minimum requirement for the use of rapid tests, we are able to put forward suggestions on reasonable ways to curtail the pandemic.
{"title":"Rapid Testing in COVID and Modified SIR Model","authors":"Jiawei Chen, Ran Li, Junru Lin","doi":"10.1137/21s1460399","DOIUrl":"https://doi.org/10.1137/21s1460399","url":null,"abstract":": The COIVD pandemic has swept the globe since 2019, posing a grave threat to human life. There are multiple ways for the government to control the pandemic, including promoting the vaccination, limiting the number of people in public places, requiring people to wear masks in public places, and suggesting infected people isolate themselves. In this paper, we used a compartmental model to analyze the spread of COVID-19 under the promotion of rapid tests. The result shows that popularization of rapid tests may have a significant impact on controlling the pandemic. With an estimated minimum requirement for the use of rapid tests, we are able to put forward suggestions on reasonable ways to curtail the pandemic.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315695","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：