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A Numerical Study on Sparse Learning of Interaction Laws in Homogeneous Multiparticle Systems 均匀多粒子系统相互作用规律稀疏学习的数值研究
SIAM undergraduate research online Pub Date : 2022-01-01 DOI: 10.1137/22s1469341
Ritwik Trehan
{"title":"A Numerical Study on Sparse Learning of Interaction Laws in Homogeneous Multiparticle Systems","authors":"Ritwik Trehan","doi":"10.1137/22s1469341","DOIUrl":"https://doi.org/10.1137/22s1469341","url":null,"abstract":". Multi-agent systems have found wide applications in science and engineering ranging from opinion dynamics to predator-prey systems. A grand challenge encountered in these areas is to reveal the interaction laws between individual agents leading to collective behaviors. In this article, we consider a system of ODEs that is often used in modeling opinion dynamics, where the laws of the interaction are dependent on pairwise distances. We leverage recent advancements in sparsity-promoted algo-rithms and propose a new approach to learning the interaction laws from a small amount of data. Numerical experiments demonstrate the effectiveness and robustness of the proposed approach in a small, noisy data regime and show the superiority of the proposed approach.","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":"64316909","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
A numerical investigation of Rayleigh-Benard convection with an obstruction 有障碍物的瑞利-贝纳德对流的数值研究
SIAM undergraduate research online Pub Date : 2021-10-21 DOI: 10.1137/21s1454535
Harieth Mhina, Samira Souley Hassane, M. McCurdy
{"title":"A numerical investigation of Rayleigh-Benard convection with an obstruction","authors":"Harieth Mhina, Samira Souley Hassane, M. McCurdy","doi":"10.1137/21s1454535","DOIUrl":"https://doi.org/10.1137/21s1454535","url":null,"abstract":". The phenomenon of convection is found in a wide variety of settings on different scales– from applications in the cooling technology of laptops to heating water on a stove, and from the movement of ocean currents to describing astrophysical events with the convective zones of stars. Given its importance in these diverse areas, the process of convection has been the focus of many research studies over the past two centuries. However, much less research has been conducted on how the presence of an obstruction in the flow can impact convection. In this work, we find that the presence of an obstruction can greatly affect convection. We note occurrences where the presence of an obstruction yields similar behavior to flow without an obstruction. Additionally, we find cases with markedly different features in comparison to their counterpart without an obstruction– notably, exhibiting long-term periodic behavior instead of achieving a constant steady-state, or the formation of convection cells versus an absence of them.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46373015","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
Statistical Learning for Best Practices in Tattoo Removal 纹身去除最佳实践的统计学习
SIAM undergraduate research online Pub Date : 2021-05-19 DOI: 10.1137/21s1421325
Richard Yim, Jamie Haddock, D. Needell
{"title":"Statistical Learning for Best Practices in Tattoo Removal","authors":"Richard Yim, Jamie Haddock, D. Needell","doi":"10.1137/21s1421325","DOIUrl":"https://doi.org/10.1137/21s1421325","url":null,"abstract":"The causes behind complications in laser-assisted tattoo removal are currently not well understood, and in the literature relating to tattoo removal the emphasis on removal treatment is on removal technologies and tools, not best parameters involved in the treatment process. Additionally, the very challenge of determining best practices is difficult given the complexity of interactions between factors that may correlate to these complications. In this paper we apply a battery of classical statistical methods and techniques to identify features that may be closely correlated to causes of complication during the tattoo removal process, and report quantitative evidence for potential best practices. We develop elementary statistical descriptions of tattoo data collected by the largest gang rehabilitation and reentry organization in the world, Homeboy Industries; perform parametric and nonparametric tests of significance; and finally, produce a statistical model explaining treatment parameter interactions, as well as develop a ranking system for treatment parameters utilizing bootstrapping and gradient boosting.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45788827","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
Comparing Finite-Time Lyapunov Exponents and Lagrangian Descriptors for identifying phase space structures in a simple two-dimensional, time-periodic double-gyre model 比较有限时间李雅普诺夫指数和拉格朗日描述符识别简单二维时间周期双环流模型中的相空间结构
SIAM undergraduate research online Pub Date : 2021-03-23 DOI: 10.1137/20S137208110.1137/20S1372081
Timothy R. Getscher
{"title":"Comparing Finite-Time Lyapunov Exponents and Lagrangian Descriptors for identifying phase space structures in a simple two-dimensional, time-periodic double-gyre model","authors":"Timothy R. Getscher","doi":"10.1137/20S137208110.1137/20S1372081","DOIUrl":"https://doi.org/10.1137/20S137208110.1137/20S1372081","url":null,"abstract":"This paper compares the advantages, limitations, and computational considerations of using Finite-Time Lyapunov Exponents (FTLEs) and Lagrangian Descriptors (LDs) as tools for identifying barriers and mechanisms of fluid transport in two-dimensional time-periodic flows. These barriers and mechanisms of transport are often referred to as \"Lagrangian Coherent Structures,\" though this term often changes meaning depending on the author or context. This paper will specifically focus on using FTLEs and LDs to identify stable and unstable manifolds of hyperbolic stagnation points, and the Kolmogorov-Arnold-Moser (KAM) tori associated with elliptic stagnation points. The background and theory behind both methods and their associated phase space structures will be presented, and then examples of FTLEs and LDs will be shown based on a simple, periodic, time-dependent double-gyre toy model with varying parameters.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47320780","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
Antibiotics Resistance Forecasting: A Comparison of Two Time Series Forecast Models 抗生素耐药性预测:两种时间序列预测模型的比较
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/20s1365284
Darja Strahlberg
{"title":"Antibiotics Resistance Forecasting: A Comparison of Two Time Series Forecast Models","authors":"Darja Strahlberg","doi":"10.1137/20s1365284","DOIUrl":"https://doi.org/10.1137/20s1365284","url":null,"abstract":"The rise of antibiotic resistance is a growing challenge for global health. Antibiotics are used for disease treatment, as well as for medical procedures, for instance, operations and transplants. The aim of this work is to compare auto-regressive integrated moving average (ARIMA) and recurrent neural networks (RNN) to forecast the spread of drug-resistant bacterial infections at the community level. The comparison of two algorithms is performed for a multistep time series univariate dataset. Five distinct time series were modelled, each one representing the number of episodes per single ESKAPE infecting pathogen, that has occurred quarterly between 2008 and 2018 calendar years in Germany. The forecast quality is evaluated by the root mean squared error between the forecasted values and the test data set. The experimental results show that multi-neural network forecasting RNN is significantly poorer than ARIMA for multi-step forecasting on univariate datasets. Finally, the paper provides a conclusion, that machine learning complexity is not always adding skill to the forecast. The forthcoming challenges are setting conditions when machine learning models can perform well for the real-world applications. The code used to evaluate the concept is available.","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":"64313253","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
Media Processing and A Modified Watermarking Scheme Based on the Singular Value Decomposition 基于奇异值分解的媒体处理和改进的水印方案
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/21s1411664
Jennifer Zheng
{"title":"Media Processing and A Modified Watermarking Scheme Based on the Singular Value Decomposition","authors":"Jennifer Zheng","doi":"10.1137/21s1411664","DOIUrl":"https://doi.org/10.1137/21s1411664","url":null,"abstract":"We introduce the singular value decomposition (SVD) along with some of its key properties, illustrate its utility in image processing and audio processing, and show how this relates to watermarking and digital ownership protection. After establishing experimental results regarding image processing, we propose a modified version of a watermarking scheme introduced in Jain, Arora, and Panigrahi, A reliable SVD based watermarking scheme, CoRR abs/0808.0309 (2008) which offers improved robustness and imperceptibility properties.","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":"64315320","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
Deterministic walks in a random cylinder 确定性在随机圆柱体中行走
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/20s1380612
Tanav Choudhary
{"title":"Deterministic walks in a random cylinder","authors":"Tanav Choudhary","doi":"10.1137/20s1380612","DOIUrl":"https://doi.org/10.1137/20s1380612","url":null,"abstract":"In this paper, we consider the deterministic paths traversed by a particle in a randomly configured infinite cylinder. We derive a formula for the expected value of the number of loops that a particle takes around the cylinder in one period of the path given that the path is periodic.","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":"64313512","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
Clinical Data Validated Mathematical Model for Intermittent Abiraterone Response in Castration-Resistant Prostate Cancer Patients 临床数据验证了去势抵抗性前列腺癌患者间歇性阿比特龙反应的数学模型
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/19S1300571
J. Bennett
{"title":"Clinical Data Validated Mathematical Model for Intermittent Abiraterone Response in Castration-Resistant Prostate Cancer Patients","authors":"J. Bennett","doi":"10.1137/19S1300571","DOIUrl":"https://doi.org/10.1137/19S1300571","url":null,"abstract":"Over time, tumor treatment resistance inadvertently develops when androgen deprivation therapy (ADT) is applied to metastasized prostate cancer (PCa). To combat tumor resistance, while reducing the harsh side effects o f h ormone t herapy, t he clinician may opt to cyclically alternates the patient’s treatment on and off. This method, known as intermittent ADT, is an alternative to continuous ADT that improves the patient’s quality of life while testosterone levels recover between cycles. In this paper, we explore the response of intermittent ADT to metastasized prostate cancer by em-ploying a previously clinical data validated mathematical model to new clinical data from patients undergoing Abiraterone therapy. This cell quota model, a system of ordinary differential equations constructed using Droop’s nutrient limiting theory, as-sumes the tumor comprises of castration-sensitive (CS) and castration-resistant (CR) cancer sub-populations. The two sub-populations rely on varying levels of intracellular androgen for growth, death and transformation. Due to the complexity of the model, we carry out sensitivity analyses to study the effect o f c ertain p arameters o n their outputs, and to increase the identifiability of each patient’s unique parameter s et. The model’s forecasting results show consistent accuracy for patients with sufficient data, which means the model could give useful information in practice, especially to decide","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":"64310634","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
Surfactant Dynamics from the Arnold Perspective 阿诺德视角下的表面活性剂动力学
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/20s1378144
E. Lu
{"title":"Surfactant Dynamics from the Arnold Perspective","authors":"E. Lu","doi":"10.1137/20s1378144","DOIUrl":"https://doi.org/10.1137/20s1378144","url":null,"abstract":"Abstract. In 1966, V. Arnold established an important connection between the incompressible Euler equations and a particular set of geodesic flows, using variational techniques to characterize the latter as solutions to the former. Motivated by his results, we investigate a series of similar PDEs characterizing constrained critical points of action functionals, paying particular interest to those associated with surfactant dynamics. Starting with the Arnold functional, we introduce various complications, adding terms associated to potential energies, surface tension, and surfactant momentum to derive different PDEs.","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":"64313788","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
Symmetric Random Walks on Wheel-and-Spokes Graphs 轮辐图上的对称随机漫步
SIAM undergraduate research online Pub Date : 2021-01-01 DOI: 10.1137/21s1423531
Collin Tully
{"title":"Symmetric Random Walks on Wheel-and-Spokes Graphs","authors":"Collin Tully","doi":"10.1137/21s1423531","DOIUrl":"https://doi.org/10.1137/21s1423531","url":null,"abstract":"We study symmetric random walks on the vertices of a wheel-and-spokes graph. We consider the following questions. How long does it take for the walk to go from one vertex to another? Starting from one vertex, how long does it take to visit all vertices? Having visited all vertices, how much additional time does it take to return to the starting vertex? The answers to these questions are random variables for which we desire the exact probability distributions, if possible; otherwise, we seek at least their means and standard deviations. We compare our results to those of symmetric random walks on the vertices of polygons.","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":"64315395","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
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