{"title":"通过持久同源性从局部结构推断超均匀性","authors":"Abel H. G. Milor, Marco Salvalaglio","doi":"arxiv-2409.08899","DOIUrl":null,"url":null,"abstract":"Hyperuniformity refers to the suppression of density fluctuations at large\nscales. Typical for ordered systems, this property also emerges in several\ndisordered physical and biological systems, where it is particularly relevant\nto understand mechanisms of pattern formation and to exploit peculiar\nattributes, e.g., interaction with light and transport phenomena. While\nhyperuniformity is a global property, it has been shown in [Phys. Rev. Research\n6, 023107 (2024)] that global hyperuniform characteristics systematically\ncorrelate with topological properties representative of local arrangements. In\nthis work, building on this information, we explore and assess the inverse\nrelationship between hyperuniformity and local structures in point\ndistributions as described by persistent homology. Standard machine learning\nalgorithms trained on persistence diagrams are shown to detect hyperuniformity\nwith high accuracy. Therefore, we demonstrate that the information on patterns'\nlocal structure allows for inferring hyperuniformity. Then, addressing more\nquantitative aspects, we show that parameters defining hyperuniformity\nglobally, for instance entering the structure factor, can be reconstructed by\ncomparing persistence diagrams of targeted patterns with reference ones. We\nalso explore the generation of patterns entailing given topological properties.\nThe results of this study pave the way for advanced analysis of hyperuniform\npatterns including local information, and introduce basic concepts for their\ninverse design.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"206 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inferring hyperuniformity from local structures via persistent homology\",\"authors\":\"Abel H. G. Milor, Marco Salvalaglio\",\"doi\":\"arxiv-2409.08899\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Hyperuniformity refers to the suppression of density fluctuations at large\\nscales. Typical for ordered systems, this property also emerges in several\\ndisordered physical and biological systems, where it is particularly relevant\\nto understand mechanisms of pattern formation and to exploit peculiar\\nattributes, e.g., interaction with light and transport phenomena. While\\nhyperuniformity is a global property, it has been shown in [Phys. Rev. Research\\n6, 023107 (2024)] that global hyperuniform characteristics systematically\\ncorrelate with topological properties representative of local arrangements. In\\nthis work, building on this information, we explore and assess the inverse\\nrelationship between hyperuniformity and local structures in point\\ndistributions as described by persistent homology. Standard machine learning\\nalgorithms trained on persistence diagrams are shown to detect hyperuniformity\\nwith high accuracy. Therefore, we demonstrate that the information on patterns'\\nlocal structure allows for inferring hyperuniformity. Then, addressing more\\nquantitative aspects, we show that parameters defining hyperuniformity\\nglobally, for instance entering the structure factor, can be reconstructed by\\ncomparing persistence diagrams of targeted patterns with reference ones. We\\nalso explore the generation of patterns entailing given topological properties.\\nThe results of this study pave the way for advanced analysis of hyperuniform\\npatterns including local information, and introduce basic concepts for their\\ninverse design.\",\"PeriodicalId\":501119,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Topology\",\"volume\":\"206 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Algebraic Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.08899\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08899","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Inferring hyperuniformity from local structures via persistent homology
Hyperuniformity refers to the suppression of density fluctuations at large
scales. Typical for ordered systems, this property also emerges in several
disordered physical and biological systems, where it is particularly relevant
to understand mechanisms of pattern formation and to exploit peculiar
attributes, e.g., interaction with light and transport phenomena. While
hyperuniformity is a global property, it has been shown in [Phys. Rev. Research
6, 023107 (2024)] that global hyperuniform characteristics systematically
correlate with topological properties representative of local arrangements. In
this work, building on this information, we explore and assess the inverse
relationship between hyperuniformity and local structures in point
distributions as described by persistent homology. Standard machine learning
algorithms trained on persistence diagrams are shown to detect hyperuniformity
with high accuracy. Therefore, we demonstrate that the information on patterns'
local structure allows for inferring hyperuniformity. Then, addressing more
quantitative aspects, we show that parameters defining hyperuniformity
globally, for instance entering the structure factor, can be reconstructed by
comparing persistence diagrams of targeted patterns with reference ones. We
also explore the generation of patterns entailing given topological properties.
The results of this study pave the way for advanced analysis of hyperuniform
patterns including local information, and introduce basic concepts for their
inverse design.