当前位置: X-MOL 学术SIAM Rev. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Research Spotlights
SIAM Review ( IF 10.8 ) Pub Date : 2021-02-04 , DOI: 10.1137/21n975175
Misha E. Kilmer

SIAM Review, Volume 63, Issue 1, Page 65-65, January 2021.
We have two Research Spotlights papers in the lineup this issue. The first of these, “Persistent Homology of Geospatial Data: A Case Study with Voting," written by Michelle Feng and Mason Porter, is quite timely. The article begins with a gentle introduction into the what and why of persistent homology (PH): after converting the point cloud of data into a series of simplicial complexes at different scales, the homology groups are computed at each scale, with homological features tracked across scales. It is generally assumed that persistence of features can then be used to distinguish signal (important patterns) from noise. Of concern is the method of converting the data into the simplicial complexes. The authors argue that PH using the simplicial complexes computed via the distance-based approach can lead to erroneous assumptions or missed characteristics about the voting data they consider. They propose to counter these deficiencies by developing two new methods, one based on adjacency networks and one that utilizes level sets to capture the manifold nature of the data, for building a filtered simplicial complex. The dramatic differences achieved by varying the complexes on the resulting PH are colorfully illustrated and interpreted for real voter data. Readers may appreciate not only the tools used and results obtained, but also the broad range of problems---transportation networks, spatial demography, granular materials, biological structures---identified by the authors for which the new approaches may prove relevant. An animal's ability to localize odor sources and follow trails of odor is key to many aspects of its survival. Authors Nour Riman, Jonathan D. Victor, Sebastian D. Boie, and Bard Ermentrout focus their article, “The Dynamics of Bilateral Olfactory Search and Navigation," on providing a comprehensive mathematical analysis of the dynamics of the differential equations that model the way that animals use bilateral information to navigate odor sources. When odor sensors are located at two different positions of the body, it enables comparison of odor concentrations and thus allows the animal to determine whether to move toward or away from the stimulus. Tropotaxis in the present context refers to the movement of the animal in response to an odor directly toward or away from the source of the odor. The sensor angles, which the animal can control, play an important role in enabling the animal to find and follow a trail. The other model parameters include sensor length and sensitivity to concentration change. The authors investigate tropotaxis as functions of the model parameters under varying conditions for the odor sources and trails. In some cases, the authors are able to reduce the dynamics to a planar system. Graphical illustrations compliment the discussion of the behavior. The paper concludes with a discussion of future research, particularly with respect to exploring the effects of noise on the models. It is the hope that this new “understanding [of] the underlying dynamics of the bilateral model will help in building models that use bilateral information together with other strategies."


中文翻译:

研究焦点

SIAM 评论,第 63 卷,第 1 期,第 65-65 页,2021 年 1 月。
本期我们有两篇 Research Spotlights 论文。其中第一篇文章“地理空间数据的持久同源性:投票案例研究”由 Michelle Feng 和 Mason Porter 撰写,非常及时。文章首先温和地介绍了持久同源性 (PH) 的含义和原因:将数据的点云转换成一系列不同尺度的单纯复形后,在每个尺度计算同源群,跨尺度跟踪同源特征。通常假设特征的持久性可以用来区分信号(重要模式)来自噪声。值得关注的是将数据转换为单纯复形的方法。作者认为,使用通过基于距离的方法计算的单纯复形的 PH 可能会导致错误的假设或丢失关于他们考虑的投票数据的特征。他们建议通过开发两种新方法来解决这些缺陷,一种基于邻接网络,另一种利用水平集来捕获数据的多种性质,以构建过滤的单纯复形。通过改变最终 PH 上的复合物所实现的显着差异针对真实选民数据进行了丰富多彩的说明和解释。读者可能不仅会欣赏所使用的工具和所获得的结果,还会欣赏作者确定的广泛问题——交通网络、空间人口学、颗粒材料、生物结构——这些新方法可能证明是相关的。一只动物' 定位气味来源和追踪气味踪迹的能力是其生存的许多方面的关键。作者 Nour Riman、Jonathan D. Victor、Sebastian D. Boie 和 Bard Ermentrout 在他们的文章“双边嗅觉搜索和导航的动力学”中重点介绍了对微分方程的动力学进行全面的数学分析,这些微分方程建模的方式动物使用双边信息来导航气味来源。当气味传感器位于身体的两个不同位置时,它可以比较气味浓度,从而允许动物确定是靠近还是远离刺激。是指动物响应气味直接朝向或远离气味源的运动。动物可以控制的传感器角度,在使动物找到并跟随踪迹方面发挥重要作用。其他模型参数包括传感器长度和对浓度变化的敏感性。作者研究了在气味来源和踪迹的不同条件下作为模型参数的函数的趋向性。在某些情况下,作者能够将动力学简化为平面系统。图形插图补充了对行为的讨论。本文最后讨论了未来的研究,特别是在探索噪声对模型的影响方面。希望这种新的“对双边模型潜在动态的理解将有助于构建将双边信息与其他策略结合使用的模型。” 其他模型参数包括传感器长度和对浓度变化的敏感性。作者研究了在气味来源和踪迹的不同条件下作为模型参数的函数的趋向性。在某些情况下,作者能够将动力学简化为平面系统。图形插图补充了对行为的讨论。本文最后讨论了未来的研究,特别是在探索噪声对模型的影响方面。希望这种新的“对双边模型潜在动态的理解将有助于构建将双边信息与其他策略结合使用的模型。” 其他模型参数包括传感器长度和对浓度变化的敏感性。作者研究了在气味来源和踪迹的不同条件下作为模型参数的函数的趋向性。在某些情况下,作者能够将动力学简化为平面系统。图形插图补充了对行为的讨论。本文最后讨论了未来的研究,特别是在探索噪声对模型的影响方面。希望这种新的“对双边模型潜在动态的理解将有助于构建将双边信息与其他策略结合使用的模型”。作者研究了在气味来源和踪迹的不同条件下作为模型参数的函数的趋向性。在某些情况下,作者能够将动力学简化为平面系统。图形插图补充了对行为的讨论。本文最后讨论了未来的研究,特别是在探索噪声对模型的影响方面。希望这种新的“对双边模型潜在动态的理解将有助于构建将双边信息与其他策略结合使用的模型。” 作者研究了在气味来源和踪迹的不同条件下作为模型参数的函数的趋向性。在某些情况下,作者能够将动力学简化为平面系统。图形插图补充了对行为的讨论。本文最后讨论了未来的研究,特别是在探索噪声对模型的影响方面。希望这种新的“对双边模型潜在动态的理解将有助于构建将双边信息与其他策略结合使用的模型。” 特别是在探索噪声对模型的影响方面。希望这种新的“对双边模型潜在动态的理解将有助于构建将双边信息与其他策略结合使用的模型。” 特别是在探索噪声对模型的影响方面。希望这种新的“对双边模型潜在动态的理解将有助于构建将双边信息与其他策略结合使用的模型。”
更新日期:2021-02-04
down
wechat
bug