今日论文合集：cs.SD语音1篇，eess.AS音频处理1篇。
【1】 Topological data analysis hearing the shapes of drums and bells
标题：听到鼓声和铃声形状的拓扑数据分析
链接：https://arxiv.org/abs/2301.05025
摘要：马克·卡茨在1966年提出了一个著名的问题，题目是“人们能听到鼓的形状吗？”一个频谱几何问题，在过去的60年里一直吸引着数学家的兴趣，并且对许多其他领域也很重要，例如建筑声学、音频取证、模式识别、放射学和成像科学。一个相关的问题是如何听到鼓的形状。我们证明答案是在65个曾侯乙编钟设置追溯到公元前475-433年在中国。编钟的大小和重量逐渐变化，以适应旋律、音程和音律。同样的设计原理也应用于许多其他乐器，如木琴、排箫、钢琴等。我们揭示了许多乐器的行进模式与拓扑数据分析（TDA）中的滤波（或谱序列）之间存在着迷人的联系。我们认为，过滤诱导的进化de Rham-Hodge理论为乐器提供了一个新的数学基础。简要讨论了它的离散形式--持久拉普拉斯算子和其它持久拓扑拉普拉斯算子，包括持久层拉普拉斯算子和持久路径拉普拉斯算子。 摘要：Mark Kac asked a famous question in 1966 entitled Can one hear the shape of a drum?, a spectral geometry problem that has intrigued mathematicians for the last six decades and is important to many other fields, such as architectural acoustics, audio forensics, pattern recognition, radiology, and imaging science. A related question is how to hear the shape of a drum. We show that the answer was given in the set of 65 Zenghouyi chime bells dated back to 475-433 B.C. in China. The set of chime bells gradually varies their sizes and weights to enable melodies, intervals, and temperaments. The same design principle was used in many other musical instruments, such as xylophones, pan flutes, pianos, etc. We reveal that there is a fascinating connection between the progression pattern of many musical instruments and filtration (or spectral sequence) in topological data analysis (TDA). We argue that filtration-induced evolutionary de Rham-Hodge theory provides a new mathematical foundation for musical instruments. Its discrete counterpart, persistent Laplacians and many other persistent topological Laplacians, including persistent sheaf Laplacians and persistent path Laplacians are briefly discussed.【1】 Topological data analysis hearing the shapes of drums and bells
标题：听到鼓声和铃声形状的拓扑数据分析
链接：https://arxiv.org/abs/2301.05025
*与cs.SD语音【1】为同一篇
摘要：马克·卡茨在1966年提出了一个著名的问题，题目是“人们能听到鼓的形状吗？”一个频谱几何问题，在过去的60年里一直吸引着数学家的兴趣，并且对许多其他领域也很重要，例如建筑声学、音频取证、模式识别、放射学和成像科学。一个相关的问题是如何听到鼓的形状。我们证明答案是在65个曾侯乙编钟设置追溯到公元前475-433年在中国。编钟的大小和重量逐渐变化，以适应旋律、音程和音律。同样的设计原理也应用于许多其他乐器，如木琴、排箫、钢琴等。我们揭示了许多乐器的行进模式与拓扑数据分析（TDA）中的滤波（或谱序列）之间存在着迷人的联系。我们认为，过滤诱导的进化de Rham-Hodge理论为乐器提供了一个新的数学基础。简要讨论了它的离散形式--持久拉普拉斯算子和其它持久拓扑拉普拉斯算子，包括持久层拉普拉斯算子和持久路径拉普拉斯算子。摘要：Mark Kac asked a famous question in 1966 entitled Can one hear the shape of a drum?, a spectral geometry problem that has intrigued mathematicians for the last six decades and is important to many other fields, such as architectural acoustics, audio forensics, pattern recognition, radiology, and imaging science. A related question is how to hear the shape of a drum. We show that the answer was given in the set of 65 Zenghouyi chime bells dated back to 475-433 B.C. in China. The set of chime bells gradually varies their sizes and weights to enable melodies, intervals, and temperaments. The same design principle was used in many other musical instruments, such as xylophones, pan flutes, pianos, etc. We reveal that there is a fascinating connection between the progression pattern of many musical instruments and filtration (or spectral sequence) in topological data analysis (TDA). We argue that filtration-induced evolutionary de Rham-Hodge theory provides a new mathematical foundation for musical instruments. Its discrete counterpart, persistent Laplacians and many other persistent topological Laplacians, including persistent sheaf Laplacians and persistent path Laplacians are briefly discussed.机器翻译，仅供参考
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