. We introduce and analyze a model for opinion dynamics comprised of nonlinear ODEs. The variables are the proportion of moderates in the population who hold opinion A, the proportion of zealots who hold opinion A, and the proportion of zealots who hold opinion B (not A). The zealots are willing to change their opinion at a much slower rate than the moderates. Our model takes into account such things as the inherent attractiveness of one opinion over the other, the indoctrination of moderates by the zealots, and deradicalization of the zealots by the moderates. A combination of theoretical and numerical analysis shows there are many different types of asymptotic configurations of the population. Many of these correspond to critical points of the system. The most intriguing finding is that if both A and B are roughly equally attractive, and the rate of indoctrination is roughly equal to the rate of deradicalization, then there will be a stable periodic orbit. The dynamics of this orbit show that a precursor to an opinion being dominant is that the proportion of zealots for the opinion must first grow to some critical value. Moreover, when the periodic orbit exists, there are no other solutions which allow for coexistence between the two opinions.
{"title":"Opinion Dynamics with Slowly Evolving Zealot Populations","authors":"Ashlyn DeGroot, E. Schmidt","doi":"10.1137/22s1515306","DOIUrl":"https://doi.org/10.1137/22s1515306","url":null,"abstract":". We introduce and analyze a model for opinion dynamics comprised of nonlinear ODEs. The variables are the proportion of moderates in the population who hold opinion A, the proportion of zealots who hold opinion A, and the proportion of zealots who hold opinion B (not A). The zealots are willing to change their opinion at a much slower rate than the moderates. Our model takes into account such things as the inherent attractiveness of one opinion over the other, the indoctrination of moderates by the zealots, and deradicalization of the zealots by the moderates. A combination of theoretical and numerical analysis shows there are many different types of asymptotic configurations of the population. Many of these correspond to critical points of the system. The most intriguing finding is that if both A and B are roughly equally attractive, and the rate of indoctrination is roughly equal to the rate of deradicalization, then there will be a stable periodic orbit. The dynamics of this orbit show that a precursor to an opinion being dominant is that the proportion of zealots for the opinion must first grow to some critical value. Moreover, when the periodic orbit exists, there are no other solutions which allow for coexistence between the two opinions.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317464","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}
As one of the oldest known diseases to inflict humanity (since the Agricultural Revolution about 12,000 years ago), malaria has proven to be a significant global challenge. Many intervention strategies have been undertaken in the last few decades such as widespread insecticide-treated bed nets (ITN), long-lasting insecticidal nets (LLIN) and indoor residual spraying (IRS). Yet even with great success, malaria continues to be a ravaging disease requiring inventive solutions. In this study, we develop a malaria early warning system, which utilizes an adapted Ross-MacDonald model to assess individual risk and disease epidemiology. Strategies for achieving a disease-free equilibrium state are also shown by performing local asymptotic stability analysis. It is important to note that the stages of the mosquito life-cycle are highly influenced by weather conditions, both in the aquatic and adult stages, as well as by the use of insecticides (either through ITN/LLIN use or via IRS). Therefore, we consider regional data parameters, such as weather conditions, parasite rate and resistance, to estimate deviated risk from the baseline, with the final product being a progressive web application (i.e. a web and mobile app). Such a product has widespread application primarily in holoendemic areas in Africa to inform both native and tourist populations of their relative risk of contracting malaria.
{"title":"Malaria Early Warning Application for Individual Risk Assessment","authors":"Janiah Kyle, Sagar Sadak, Cayden Goeringer","doi":"10.1137/23s154875x","DOIUrl":"https://doi.org/10.1137/23s154875x","url":null,"abstract":"As one of the oldest known diseases to inflict humanity (since the Agricultural Revolution about 12,000 years ago), malaria has proven to be a significant global challenge. Many intervention strategies have been undertaken in the last few decades such as widespread insecticide-treated bed nets (ITN), long-lasting insecticidal nets (LLIN) and indoor residual spraying (IRS). Yet even with great success, malaria continues to be a ravaging disease requiring inventive solutions. In this study, we develop a malaria early warning system, which utilizes an adapted Ross-MacDonald model to assess individual risk and disease epidemiology. Strategies for achieving a disease-free equilibrium state are also shown by performing local asymptotic stability analysis. It is important to note that the stages of the mosquito life-cycle are highly influenced by weather conditions, both in the aquatic and adult stages, as well as by the use of insecticides (either through ITN/LLIN use or via IRS). Therefore, we consider regional data parameters, such as weather conditions, parasite rate and resistance, to estimate deviated risk from the baseline, with the final product being a progressive web application (i.e. a web and mobile app). Such a product has widespread application primarily in holoendemic areas in Africa to inform both native and tourist populations of their relative risk of contracting malaria.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135507033","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}
Synchrony is an important feature of brain activities for the coordination of neural information and is also related to some neuronal disorders. Around 40 different measures have been proposed in literature for quantifying the synchrony of spike trains and the list is still growing. The main issue is that it is not clear to users which one to use and how measurements correspond to different features of synchrony. In this work, instead of looking at all methods at once, we focus on investigating one of the popular measures in the field of neuroscience: Spike Time Tiling Coefficient (STTC) proposed by Cutts and Eglen in 2014. We simulate three scenarios of neural spike trains and study how STTC values depend on distributions and phase shifts of spike trains. Firstly, we study pairs of simple periodic binary time series. We derive an analytical formula showing that the dependence of the STTC value on the phase shift is symmetric and has a general trend where the maximum value of STTC occurs when the phase shift is zero and the minimum value occurs when the phase shift is half of the period. Secondly, we investigate pairs of “periodic” normally distributed spike trains. While we observe the similar trends shown in the first scenario, we notice an exception. We also observe a general trend where the STTC value decreases as the standard deviation of the normal distribution increases. Thirdly, we study pairs of Poisson distributed spike trains. Using properties of the Poisson distribution, we generate pairs of Poisson distributed spike trains with certain overlap ratios and study the relationship between STTC and the overlap ratio. In general, this relationship is nonlinear. We observe that as the synchronicity window decreases towards zero, this nonlinear relationship tends toward a linear relationship. We derive analytical formulas to describe this nonlinear relationship and quantitatively evaluate its closeness to a linear relationship as the syn-chronicity window decreases towards zero. Through studying STTC, we notice that when the synchronicity window is too large, the problem of dividing by zero occurs in the calculation of STTC. To avoid such a problem, we derive an upper bound for the synchronicity window. We also argue that STTC can only approach − 1, and show a case to demonstrate this argument
{"title":"Understanding a Measure for Synchrony: Spike Time Tiling Coefficient Method","authors":"Kevin Li, Evan Huang, Bill Sun","doi":"10.1137/23s1576104","DOIUrl":"https://doi.org/10.1137/23s1576104","url":null,"abstract":"Synchrony is an important feature of brain activities for the coordination of neural information and is also related to some neuronal disorders. Around 40 different measures have been proposed in literature for quantifying the synchrony of spike trains and the list is still growing. The main issue is that it is not clear to users which one to use and how measurements correspond to different features of synchrony. In this work, instead of looking at all methods at once, we focus on investigating one of the popular measures in the field of neuroscience: Spike Time Tiling Coefficient (STTC) proposed by Cutts and Eglen in 2014. We simulate three scenarios of neural spike trains and study how STTC values depend on distributions and phase shifts of spike trains. Firstly, we study pairs of simple periodic binary time series. We derive an analytical formula showing that the dependence of the STTC value on the phase shift is symmetric and has a general trend where the maximum value of STTC occurs when the phase shift is zero and the minimum value occurs when the phase shift is half of the period. Secondly, we investigate pairs of “periodic” normally distributed spike trains. While we observe the similar trends shown in the first scenario, we notice an exception. We also observe a general trend where the STTC value decreases as the standard deviation of the normal distribution increases. Thirdly, we study pairs of Poisson distributed spike trains. Using properties of the Poisson distribution, we generate pairs of Poisson distributed spike trains with certain overlap ratios and study the relationship between STTC and the overlap ratio. In general, this relationship is nonlinear. We observe that as the synchronicity window decreases towards zero, this nonlinear relationship tends toward a linear relationship. We derive analytical formulas to describe this nonlinear relationship and quantitatively evaluate its closeness to a linear relationship as the syn-chronicity window decreases towards zero. Through studying STTC, we notice that when the synchronicity window is too large, the problem of dividing by zero occurs in the calculation of STTC. To avoid such a problem, we derive an upper bound for the synchronicity window. We also argue that STTC can only approach − 1, and show a case to demonstrate this argument","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135310699","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}
F. Jiang, Zhengyang Guo, Dong'ang Liu, Yanghao Wang
Project
项目
{"title":"Symmetry and Free Boundary Points in a Class of Linear Ordinary Differential Equations","authors":"F. Jiang, Zhengyang Guo, Dong'ang Liu, Yanghao Wang","doi":"10.1137/21s1454110","DOIUrl":"https://doi.org/10.1137/21s1454110","url":null,"abstract":"Project","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315921","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}
. In recent decades, scientists have observed that the mortality rate of some competing species increases superlinearly as populations grow to unsustainable levels. This is modeled by terms representing crowding effects in a system of nonlinear differential equations that describes population growth of two species competing for resources under the effects of crowding. After applying nondimensionalization to reduce parameters in the system, the stability of the steady state solutions of the system is examined. A semi-implicit numerical scheme is proposed which guarantees the positivity of the solutions. The long term behavior of the numerical solutions is studied. The error estimate between the numerical solution and the true solution is given.
{"title":"Numerical Analysis of Crowding Effects in Competing Species","authors":"B. Carlson","doi":"10.1137/22s151042x","DOIUrl":"https://doi.org/10.1137/22s151042x","url":null,"abstract":". In recent decades, scientists have observed that the mortality rate of some competing species increases superlinearly as populations grow to unsustainable levels. This is modeled by terms representing crowding effects in a system of nonlinear differential equations that describes population growth of two species competing for resources under the effects of crowding. After applying nondimensionalization to reduce parameters in the system, the stability of the steady state solutions of the system is examined. A semi-implicit numerical scheme is proposed which guarantees the positivity of the solutions. The long term behavior of the numerical solutions is studied. The error estimate between the numerical solution and the true solution is given.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317385","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}
In this paper and accompanying software, we give a fully functional implementation of the Boneh-Franklin Identity-Based Encryption (IBE) scheme using the Weil pairing, which runs efficiently even with primes of cryptographic size. We describe the conceptual framework of the IBE, give background on the Weil pairing. Further, we discuss the challenges in the process of creating a functional implementation, and how we overcame them. The reader is encouraged to experiment with the accompanying software, which is written in SageMath.
{"title":"Implementation of the Boneh-Franklin IBE Scheme","authors":"Florence Lam","doi":"10.1137/22s1532901","DOIUrl":"https://doi.org/10.1137/22s1532901","url":null,"abstract":"In this paper and accompanying software, we give a fully functional implementation of the Boneh-Franklin Identity-Based Encryption (IBE) scheme using the Weil pairing, which runs efficiently even with primes of cryptographic size. We describe the conceptual framework of the IBE, give background on the Weil pairing. Further, we discuss the challenges in the process of creating a functional implementation, and how we overcame them. The reader is encouraged to experiment with the accompanying software, which is written in SageMath.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"121 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317903","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":"Modelling the Evolutionary Dynamics of an Infectious Disease with an Initial Asymptomatic Infection Stage with Recovery","authors":"S. Manivannan","doi":"10.1137/22s151755x","DOIUrl":"https://doi.org/10.1137/22s151755x","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317922","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}
We study an efficient time-stepping scheme for the 1D Fujita equation that is implicit for the linear terms but explicit for the nonlinear terms. We analyze the long-time stability of the scheme for varying parameter values, which reveal parameter value regimes in which the method is stable. We provide numerical results that illustrate the theory and show the analytically derived stability conditions are sufficient to achieve long-time stability results
{"title":"Long-time L2 Stability for an IMEX Discretization of the 1D Fujita Equation","authors":"Victoria Luongo","doi":"10.1137/23s1556940","DOIUrl":"https://doi.org/10.1137/23s1556940","url":null,"abstract":"We study an efficient time-stepping scheme for the 1D Fujita equation that is implicit for the linear terms but explicit for the nonlinear terms. We analyze the long-time stability of the scheme for varying parameter values, which reveal parameter value regimes in which the method is stable. We provide numerical results that illustrate the theory and show the analytically derived stability conditions are sufficient to achieve long-time stability results","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135403480","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}
. With the prevalence of big data in recent years, the importance of modeling high dimensional data and selecting important features has increased greatly. High dimensional data is common in many fields such as genome decoding, rare disease identification, and environmental modeling. However, most traditional regression machine learning models are not designed to handle high dimensional data or conduct variable selection. In this paper, we investigate the use of penalized regression meth-ods such as ridge, least absolute shrinkage and selection operation, elastic net, smoothly clipped absolute deviation, and minimax concave penalty compared to traditional machine learning models such as random forest, XGBoost, and support vector machines. We compare these models using factorial design methods for Monte Carlo simulations in 540 environments, with factors being the response variable, number of predictors, number of samples, signal to noise ratio, covariance matrix, and correlation strength. We also compare different models using empirical data to evaluate their viability in real-world scenarios. We evaluate the models using the training and test mean squared error, variable selection accuracy, β -sensitivity, and β -specificity. We found that the performance of penalized regression models is comparable with traditional machine learning algorithms in most high-dimensional situations. The analysis helps to create a greater understanding of the strengths and weaknesses of each model type and provide a reference for other researchers on which machine learning techniques they should use, depending on a range of factors and data environments. Our study shows that penalized regression techniques should be included in predictive modelers’ toolbox.
{"title":"A Comparative Study of Penalized Regression and Machine Learning Algorithms in High Dimensional Scenarios","authors":"Connor Shrader, Gabriel Ackall","doi":"10.1137/22s1538302","DOIUrl":"https://doi.org/10.1137/22s1538302","url":null,"abstract":". With the prevalence of big data in recent years, the importance of modeling high dimensional data and selecting important features has increased greatly. High dimensional data is common in many fields such as genome decoding, rare disease identification, and environmental modeling. However, most traditional regression machine learning models are not designed to handle high dimensional data or conduct variable selection. In this paper, we investigate the use of penalized regression meth-ods such as ridge, least absolute shrinkage and selection operation, elastic net, smoothly clipped absolute deviation, and minimax concave penalty compared to traditional machine learning models such as random forest, XGBoost, and support vector machines. We compare these models using factorial design methods for Monte Carlo simulations in 540 environments, with factors being the response variable, number of predictors, number of samples, signal to noise ratio, covariance matrix, and correlation strength. We also compare different models using empirical data to evaluate their viability in real-world scenarios. We evaluate the models using the training and test mean squared error, variable selection accuracy, β -sensitivity, and β -specificity. We found that the performance of penalized regression models is comparable with traditional machine learning algorithms in most high-dimensional situations. The analysis helps to create a greater understanding of the strengths and weaknesses of each model type and provide a reference for other researchers on which machine learning techniques they should use, depending on a range of factors and data environments. Our study shows that penalized regression techniques should be included in predictive modelers’ toolbox.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317667","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}
. Univariate regression models are commonly used in statistics and machine learning to examine the relationship between an outcome variable and a set of explanatory variables, and possibly use this relationship to predict the unknown values of the outcome variable. However, when dealing with multiple outcome variables that are interrelated, multivariate regression models are preferred. These models simultaneously capture the dependencies between outcome variables and their collective relationships with explanatory variables. While multivariate regression models provide a rigorous and comprehensive understanding of factors associated with outcomes of interest, they have several limitations including: increased model complexity, larger sample size requirements, and lack of interpretability. To address these issues, we propose an alternative approach, called Integrated Multivariate Regression (IMR) that reduces the dimensionality of the outcome variables by transforming them into one or more derived outcome variables that retain important information. Using simulated and real data, we demonstrate that IMR simplifies the analysis and increases statistical power by reducing the number of parameters, while simultaneously maintaining interpretability and accounting for interdependencies among the outcome variables.
{"title":"In Pursuit of Higher Power Through Integrated Multivariate Regression","authors":"Ryan Shahbaba","doi":"10.1137/23s1584344","DOIUrl":"https://doi.org/10.1137/23s1584344","url":null,"abstract":". Univariate regression models are commonly used in statistics and machine learning to examine the relationship between an outcome variable and a set of explanatory variables, and possibly use this relationship to predict the unknown values of the outcome variable. However, when dealing with multiple outcome variables that are interrelated, multivariate regression models are preferred. These models simultaneously capture the dependencies between outcome variables and their collective relationships with explanatory variables. While multivariate regression models provide a rigorous and comprehensive understanding of factors associated with outcomes of interest, they have several limitations including: increased model complexity, larger sample size requirements, and lack of interpretability. To address these issues, we propose an alternative approach, called Integrated Multivariate Regression (IMR) that reduces the dimensionality of the outcome variables by transforming them into one or more derived outcome variables that retain important information. Using simulated and real data, we demonstrate that IMR simplifies the analysis and increases statistical power by reducing the number of parameters, while simultaneously maintaining interpretability and accounting for interdependencies among the outcome variables.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135056966","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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