SIAM Review, Volume 62, Issue 4, Page 779-780, January 2020.
We are fortunate to have three topically diverse papers featured in Research Spotlights in the current issue. The first of these, “Stochastic Sensitivity: A Computable Lagrangian Uncertainty Measure for Unsteady Flows," deals with modeling uncertainties in velocity data for the purpose of quantifying their influence when computing Lagrangian particle trajectories of fluids. One application that author Sanjeeva Balasuriya gives for pursuing this line of research is climate and environmental modeling: ocean and atmospheric models utilize velocity data to understand the movement of such quantities of interest as pollutants and plankton, and the trajectories of these quantities of interest have an impact on the environment and climate. This paper fills a gap in the current literature by addressing specifically the impact of velocity uncertainties---including those due to measurement error, turbulence at subgrid levels, or other effects uncaptured by the model---on trajectories. It offers the reader a “set of rigorous computational tools" to quantify the resulting Lagrangian uncertainties as a “physically interpretable field." The final section contains an extensive discussion in which the author considers connections of this work to uncertainty quantification and illuminates important remaining research directions. The second article, coauthored by Yuanzhao Zhang and Adilson E. Motter, is entitled “Symmetric-Independent Stability Analysis of Synchronization Patterns." The stability of synchronization patterns in complex networks is important to understand because of the “significant ramifications in various biological and technical systems" in the absence of such analysis. The key innovation in the present work is the introduction of a new algorithm to find the finest simultaneous block diagonalization (SBD) for any given set of self-adjoint matrices. This permits the extension of the master stability function (MSF) formalism since the proposed method now allows for the optimal separation of perturbation modes from which the stability of arbitrary synchronization patterns can then be undertaken. The authors provide a convincing demonstration of the strength of the new approach by applying their method to characterize permanently stable chimera-like states in multilayer networks. The paper includes a gentle introduction to matrix $*$-algebras and their relevance in developing the new algorithm; code for the latter is available on a GitHub repository, along with test problems. Importantly, the reader should note the potential for SBD in applications beyond the topic considered here---indeed, the authors suggest it may be relevant in other applications that involve many matrices such as control of network systems and semidefinite programming. The subject of the last of the three articles is extremely timely, as the title “Forecasting Elections Using Compartmental Models of Infection" itself suggests. Authors Alexandria Volkening, Daniel F. Linder, Mason A. Porter, and Grzegorz A. Rempala propose a data-driven mathematical model of the temporal evolution of political opinions during U.S. elections. Key features include the explicit modeling of how states influence each other through a compartmental model of disease dynamics, treating “voting intentions as contagions” that spread between states. Data fitting with polling data is used to specify the values of the parameters in the model, and the model predictions are compared to election outcomes from several recent U.S. elections. The initial model is expanded to a stochastic differential equations model in an effort to capture and quantify uncertainty in a given race. The authors are clear in describing their simplifications in modeling, yet the comparison reveals their forecasting method “performs as well as popular analysts." In the interest of transparency and in an effort to encourage more readers to become engaged in the remaining research questions, all codes and data associated with the article are available to the public. And yes, the authors also provide a link where the reader can find their model's forecast for the 2020 U.S. election!

中文翻译：

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研究热点

SIAM评论，第62卷，第4期，第779-780页，2020年1月。
我们很幸运地在本期的“研究热点”中发表了三篇主题各异的论文。其中第一个是“随机敏感度：一种用于计算非恒定流的拉格朗日不确定性度量”，目的是对速度数据中的不确定性进行建模，以便在计算流体的拉格朗日粒子轨迹时量化其影响。这方面的研究是气候和环境建模：海洋和大气模型利用速度数据来了解污染物和浮游生物等感兴趣量的运动，并且这些感兴趣量的轨迹对环境和气候有影响。本文通过专门解决速度不确定性对轨迹的影响（包括由于测量误差，子网格级别的湍流或模型未捕获的其他影响）而填补了当前文献中的空白。它为读者提供了“一组严格的计算工具”，以将由此产生的拉格朗日不确定性量化为“可物理解释的字段”。最后一部分包含一个广泛的讨论，作者在其中讨论了这项工作与不确定性量化之间的联系，并阐明了重要的剩余研究方向。第二篇文章由张元钊和Adilson E. Motter合着，标题为“同步模式的独立于对称性的稳定性分析”。本文对矩阵$ * $-代数及其在开发新算法中的相关性进行了简要介绍。后者的代码以及测试问题可在GitHub存储库上获得。重要的是，读者应该注意SBD在本主题之外的应用中的潜力-实际上，作者建议，它可能与涉及许多矩阵的其他应用（如网络系统控制和半定性编程）有关。这三篇文章的最后一部分的主题非常及时，正如标题“使用隔离感染模型进行预测选举”本身所暗示的那样，作者亚历山大·沃尔肯宁（Alexandria Volkening），丹尼尔·林德（Daniel F. Linder），梅森·阿·波特（Mason A.选举期间政治观点随时间变化的数学驱动模型。关键特征包括通过疾病动力学的隔间模型对状态如何相互影响的显式建模，将“投票意图作为传染病”在状态之间传播。使用具有轮询数据的数据拟合来指定模型中参数的值，并将模型预测与最近几次美国大选的选举结果进行比较。初始模型被扩展为随机微分方程模型，以捕获和量化给定种族中的不确定性。作者很清楚地描述了他们在建模方面的简化，但是比较结果表明他们的预测方法“表现出色，并且受欢迎的分析师也是如此。”为了透明起见，并且为了鼓励更多的读者参与其余的研究问题，与文章相关的所有代码和数据均可向公众公开。是的，作者还提供了一个链接，读者可以在其中找到其模型对2020年美国大选的预测！