{"title":"缺陷网络上基于广义特征向量的模式重构","authors":"Marie Dorchain, Riccardo Muolo, Timoteo Carletti","doi":"10.1209/0295-5075/acfbad","DOIUrl":null,"url":null,"abstract":"Abstract Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In the presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous domains obtained from a diffusion-driven instability mechanism. The theory was later extended to networked systems, where the reaction processes occur locally (in the nodes), while diffusion takes place through the networks links. The condition for the instability onset relies on the spectral property of the Laplace matrix, i.e. , the diffusive operator, and in particular on the existence of an eigenbasis. In this work, we make one step forward and we prove the validity of Turing idea also in the case of a network with a defective Laplace matrix. Moreover, by using both eigenvectors and generalized eigenvectors we show that we can reconstruct the asymptotic pattern with a relatively small discrepancy. Because a large majority of empirical networks is non-normal and often defective, our results pave the way for a thorough understanding of self-organization in real-world systems.","PeriodicalId":11738,"journal":{"name":"EPL","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pattern reconstruction through generalized eigenvectors on defective networks\",\"authors\":\"Marie Dorchain, Riccardo Muolo, Timoteo Carletti\",\"doi\":\"10.1209/0295-5075/acfbad\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In the presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous domains obtained from a diffusion-driven instability mechanism. The theory was later extended to networked systems, where the reaction processes occur locally (in the nodes), while diffusion takes place through the networks links. The condition for the instability onset relies on the spectral property of the Laplace matrix, i.e. , the diffusive operator, and in particular on the existence of an eigenbasis. In this work, we make one step forward and we prove the validity of Turing idea also in the case of a network with a defective Laplace matrix. Moreover, by using both eigenvectors and generalized eigenvectors we show that we can reconstruct the asymptotic pattern with a relatively small discrepancy. Because a large majority of empirical networks is non-normal and often defective, our results pave the way for a thorough understanding of self-organization in real-world systems.\",\"PeriodicalId\":11738,\"journal\":{\"name\":\"EPL\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EPL\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1209/0295-5075/acfbad\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPL","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1209/0295-5075/acfbad","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Pattern reconstruction through generalized eigenvectors on defective networks
Abstract Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In the presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous domains obtained from a diffusion-driven instability mechanism. The theory was later extended to networked systems, where the reaction processes occur locally (in the nodes), while diffusion takes place through the networks links. The condition for the instability onset relies on the spectral property of the Laplace matrix, i.e. , the diffusive operator, and in particular on the existence of an eigenbasis. In this work, we make one step forward and we prove the validity of Turing idea also in the case of a network with a defective Laplace matrix. Moreover, by using both eigenvectors and generalized eigenvectors we show that we can reconstruct the asymptotic pattern with a relatively small discrepancy. Because a large majority of empirical networks is non-normal and often defective, our results pave the way for a thorough understanding of self-organization in real-world systems.
期刊介绍:
General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology.
Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate).
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