{"title":"多分形突发过程:乘法相互作用超越非线性成分特性","authors":"Madhur Mangalam, Damian G Kelty-Stephen","doi":"arxiv-2401.05105","DOIUrl":null,"url":null,"abstract":"Among the statistical models employed to approximate nonlinear interactions\nin biological and psychological processes, one prominent framework is that of\ncascades. Despite decades of empirical work using multifractal formalisms, a\nfundamental question has persisted: Do the observed nonlinear interactions\nacross scales owe their origin to multiplicative interactions, or do they\ninherently reside within the constituent processes? This study presents the\nresults of rigorous numerical simulations that demonstrate the supremacy of\nmultiplicative interactions over the intrinsic nonlinear properties of\ncomponent processes. To elucidate this point, we conducted simulations of\ncascade time series featuring component processes operating at distinct\ntimescales, each characterized by one of four properties: multifractal\nnonlinearity, multifractal linearity (obtained via the Iterative Amplitude\nAdjusted Wavelet Transform of multifractal nonlinearity), phase-randomized\nlinearity (obtained via the Iterative Amplitude Adjustment Fourier Transform),\nand phase- and amplitude-randomized (obtained via shuffling). Our findings\nunequivocally establish that the multiplicative interactions among components,\nrather than the inherent properties of the component processes themselves,\ndecisively dictate the multifractal emergent properties. Remarkably, even\ncomponent processes exhibiting purely linear traits can generate nonlinear\ninteractions across scales when these interactions assume a multiplicative\nnature. In stark contrast, additivity among component processes inevitably\nleads to a linear outcome. These outcomes provide a robust theoretical\nunderpinning for current interpretations of multifractal nonlinearity, firmly\nanchoring its roots in the domain of multiplicative interactions across scales\nwithin biological and psychological processes.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multifractal emergent processes: Multiplicative interactions override nonlinear component properties\",\"authors\":\"Madhur Mangalam, Damian G Kelty-Stephen\",\"doi\":\"arxiv-2401.05105\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Among the statistical models employed to approximate nonlinear interactions\\nin biological and psychological processes, one prominent framework is that of\\ncascades. Despite decades of empirical work using multifractal formalisms, a\\nfundamental question has persisted: Do the observed nonlinear interactions\\nacross scales owe their origin to multiplicative interactions, or do they\\ninherently reside within the constituent processes? This study presents the\\nresults of rigorous numerical simulations that demonstrate the supremacy of\\nmultiplicative interactions over the intrinsic nonlinear properties of\\ncomponent processes. To elucidate this point, we conducted simulations of\\ncascade time series featuring component processes operating at distinct\\ntimescales, each characterized by one of four properties: multifractal\\nnonlinearity, multifractal linearity (obtained via the Iterative Amplitude\\nAdjusted Wavelet Transform of multifractal nonlinearity), phase-randomized\\nlinearity (obtained via the Iterative Amplitude Adjustment Fourier Transform),\\nand phase- and amplitude-randomized (obtained via shuffling). Our findings\\nunequivocally establish that the multiplicative interactions among components,\\nrather than the inherent properties of the component processes themselves,\\ndecisively dictate the multifractal emergent properties. Remarkably, even\\ncomponent processes exhibiting purely linear traits can generate nonlinear\\ninteractions across scales when these interactions assume a multiplicative\\nnature. In stark contrast, additivity among component processes inevitably\\nleads to a linear outcome. These outcomes provide a robust theoretical\\nunderpinning for current interpretations of multifractal nonlinearity, firmly\\nanchoring its roots in the domain of multiplicative interactions across scales\\nwithin biological and psychological processes.\",\"PeriodicalId\":501305,\"journal\":{\"name\":\"arXiv - PHYS - Adaptation and Self-Organizing Systems\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Adaptation and Self-Organizing Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2401.05105\",\"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 - PHYS - Adaptation and Self-Organizing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2401.05105","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Among the statistical models employed to approximate nonlinear interactions
in biological and psychological processes, one prominent framework is that of
cascades. Despite decades of empirical work using multifractal formalisms, a
fundamental question has persisted: Do the observed nonlinear interactions
across scales owe their origin to multiplicative interactions, or do they
inherently reside within the constituent processes? This study presents the
results of rigorous numerical simulations that demonstrate the supremacy of
multiplicative interactions over the intrinsic nonlinear properties of
component processes. To elucidate this point, we conducted simulations of
cascade time series featuring component processes operating at distinct
timescales, each characterized by one of four properties: multifractal
nonlinearity, multifractal linearity (obtained via the Iterative Amplitude
Adjusted Wavelet Transform of multifractal nonlinearity), phase-randomized
linearity (obtained via the Iterative Amplitude Adjustment Fourier Transform),
and phase- and amplitude-randomized (obtained via shuffling). Our findings
unequivocally establish that the multiplicative interactions among components,
rather than the inherent properties of the component processes themselves,
decisively dictate the multifractal emergent properties. Remarkably, even
component processes exhibiting purely linear traits can generate nonlinear
interactions across scales when these interactions assume a multiplicative
nature. In stark contrast, additivity among component processes inevitably
leads to a linear outcome. These outcomes provide a robust theoretical
underpinning for current interpretations of multifractal nonlinearity, firmly
anchoring its roots in the domain of multiplicative interactions across scales
within biological and psychological processes.