Pub Date : 2020-10-06DOI: 10.1365/s13291-020-00221-1
Angeliki Koutsoukou-Argyraki
{"title":"Formalising Mathematics – in Praxis; A Mathematician’s First Experiences with Isabelle/HOL and the Why and How of Getting Started","authors":"Angeliki Koutsoukou-Argyraki","doi":"10.1365/s13291-020-00221-1","DOIUrl":"https://doi.org/10.1365/s13291-020-00221-1","url":null,"abstract":"","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83097508","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}
Pub Date : 2020-06-23DOI: 10.1365/s13291-020-00218-w
P. Kügler
{"title":"Modelling and Simulation for Preclinical Cardiac Safety Assessment of Drugs with Human iPSC-Derived Cardiomyocytes","authors":"P. Kügler","doi":"10.1365/s13291-020-00218-w","DOIUrl":"https://doi.org/10.1365/s13291-020-00218-w","url":null,"abstract":"","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86539729","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}
Pub Date : 2020-05-07DOI: 10.1365/s13291-020-00216-y
F. Hettlich
{"title":"H. Isozaki: “Maxwell Equation—Inverse Scattering in Electromagnetism”","authors":"F. Hettlich","doi":"10.1365/s13291-020-00216-y","DOIUrl":"https://doi.org/10.1365/s13291-020-00216-y","url":null,"abstract":"","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72662270","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}
Pub Date : 2020-03-18DOI: 10.1365/s13291-020-00215-z
H. Markwig
{"title":"Tropical Curves and Covers and Their Moduli Spaces","authors":"H. Markwig","doi":"10.1365/s13291-020-00215-z","DOIUrl":"https://doi.org/10.1365/s13291-020-00215-z","url":null,"abstract":"","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91395435","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}
Pub Date : 2020-03-05DOI: 10.1365/s13291-020-00214-0
U. Felgner
{"title":"Die Begriffe der Äquivalenz, der Gleichheit und der Identität","authors":"U. Felgner","doi":"10.1365/s13291-020-00214-0","DOIUrl":"https://doi.org/10.1365/s13291-020-00214-0","url":null,"abstract":"","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81737720","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}
Pub Date : 2020-01-01Epub Date: 2020-06-29DOI: 10.1365/s13291-020-00219-9
Robert Schaback
This is an analysis of the COVID-19 pandemic by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country with a reliable technique. The difference to other modelling approaches is to stay extremely close to the available data, using as few hypotheses and parameters as possible. For the convenience of readers, the basic notions of modelling epidemics are collected first, focusing on the standard SIR model. Proofs of various properties of the model are included. But such models are not directly compatible with available data. Therefore a special variation of a SIR model is presented that directly works with the data provided by the Johns Hopkins University. It allows to monitor the registered part of the pandemic, but is unable to deal with the hidden part. To reconstruct data for the unregistered Infected, a second model uses current experimental values of the infection fatality rate and a data-driven estimation of a specific form of the recovery rate. All other ingredients are data-driven as well. This model allows predictions of infection peaks. Various examples of predictions are provided for illustration. They show what countries have to face that are still expecting their infection peak. Running the model on earlier data shows how closely the predictions follow the transition from an uncontrolled outbreak to the mitigation situation by non-pharmaceutical interventions like contact restrictions.
Supplementary information: The online version of this article (10.1365/s13291-020-00219-9) contains supplementary material, which is available to authorized users.
这是用比较简单的数学和数值方法对 COVID-19 大流行进行的分析。最终目标是以可靠的技术预测每个国家的疫情爆发高峰。与其他建模方法不同的是，该方法极为贴近现有数据，使用尽可能少的假设和参数。为方便读者，本文首先收集了流行病建模的基本概念，重点介绍标准 SIR 模型。书中还包括该模型各种属性的证明。但这种模型与现有数据并不直接兼容。因此，本文介绍了 SIR 模型的一个特殊变体，它可直接与约翰霍普金斯大学提供的数据配合使用。该模型可以监测大流行的登记部分，但无法处理隐藏部分。为了重建未登记感染者的数据，第二个模型使用了当前感染致死率的实验值和数据驱动的特定形式的恢复率估计值。所有其他成分也都是数据驱动的。该模型可以预测感染峰值。为说明问题，我们提供了各种预测实例。它们显示了仍在期待感染高峰的国家所面临的问题。在早期数据的基础上运行该模型，可以看出预测结果与疫情从失控到通过非药物干预措施（如接触限制）缓解疫情的过渡非常吻合：本文在线版（10.1365/s13291-020-00219-9）包含补充材料，授权用户可查阅。
{"title":"On COVID-19 Modelling.","authors":"Robert Schaback","doi":"10.1365/s13291-020-00219-9","DOIUrl":"10.1365/s13291-020-00219-9","url":null,"abstract":"<p><p>This is an analysis of the COVID-19 pandemic by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country with a reliable technique. The difference to other modelling approaches is to stay extremely close to the available data, using as few hypotheses and parameters as possible. For the convenience of readers, the basic notions of modelling epidemics are collected first, focusing on the standard SIR model. Proofs of various properties of the model are included. But such models are not directly compatible with available data. Therefore a special variation of a SIR model is presented that directly works with the data provided by the Johns Hopkins University. It allows to monitor the registered part of the pandemic, but is unable to deal with the hidden part. To reconstruct data for the unregistered Infected, a second model uses current experimental values of the infection fatality rate and a data-driven estimation of a specific form of the recovery rate. All other ingredients are data-driven as well. This model allows predictions of infection peaks. Various examples of predictions are provided for illustration. They show what countries have to face that are still expecting their infection peak. Running the model on earlier data shows how closely the predictions follow the transition from an uncontrolled outbreak to the mitigation situation by non-pharmaceutical interventions like contact restrictions.</p><p><strong>Supplementary information: </strong>The online version of this article (10.1365/s13291-020-00219-9) contains supplementary material, which is available to authorized users.</p>","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7322402/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84310139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-10-08DOI: 10.1365/s13291-019-00210-z
J. Lankeit, M. Winkler
{"title":"Facing Low Regularity in Chemotaxis Systems","authors":"J. Lankeit, M. Winkler","doi":"10.1365/s13291-019-00210-z","DOIUrl":"https://doi.org/10.1365/s13291-019-00210-z","url":null,"abstract":"","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84535595","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}
Pub Date : 2019-09-25DOI: 10.1365/s13291-019-00211-y
T. Wedhorn
{"title":"On the Work of Peter Scholze","authors":"T. Wedhorn","doi":"10.1365/s13291-019-00211-y","DOIUrl":"https://doi.org/10.1365/s13291-019-00211-y","url":null,"abstract":"","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81800320","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}
Pub Date : 2019-09-16DOI: 10.1365/s13291-019-00209-6
Fr'ed'eric Naud
{"title":"Hyperbolic Dynamics Meet Fourier Analysis, an Invitation to the Book by V. Baladi: “Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps”","authors":"Fr'ed'eric Naud","doi":"10.1365/s13291-019-00209-6","DOIUrl":"https://doi.org/10.1365/s13291-019-00209-6","url":null,"abstract":"","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81519721","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}
Pub Date : 2019-09-10DOI: 10.1365/s13291-019-00208-7
K. Neeb
{"title":"A. Kosyak: “Regular, Quasi-regular and Induced Representations of Infinite-dimensional Groups”","authors":"K. Neeb","doi":"10.1365/s13291-019-00208-7","DOIUrl":"https://doi.org/10.1365/s13291-019-00208-7","url":null,"abstract":"","PeriodicalId":73532,"journal":{"name":"Jahresbericht der Deutschen Mathematiker-Vereinigung. Deutsche Mathematiker-Vereinigung","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78934224","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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