{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T12:56:26Z","timestamp":1774270586338,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T00:00:00Z","timestamp":1774137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The generative mechanisms underlying multifractal scaling in complex systems remain a fundamental unsolved problem, limiting our ability to distinguish healthy from pathological dynamics, predict system failures, or understand how scale-invariant organization emerges across vastly different physical domains. We resolve this challenge by introducing threshold sensitivity analysis\u2014an extension of Chhabra\u2013Jensen\u2019s direct method\u2014as a framework that classifies cascade types by examining how scaling reliability varies across moment orders q. Different q values systematically probe weak fluctuations (negative q) versus strong fluctuations (positive q), and the coefficient of determination (r2) of partition function regressions quantifies scaling reliability at each q. Analyzing r2(q) patterns in 280 cardiac recordings (healthy controls through fatal heart failure), 200 financial time series (global equity markets and currencies, 2000\u20132025), and 80 climate stations (tropical to continental zones, 2000\u20132025), we discover a universal diagnostic signature: symmetric expansion of valid scaling behavior under relaxed r2 thresholds, spanning both weak and strong fluctuations. This threshold sensitivity fingerprint\u2014predicted by synthetic cascade simulations but never before validated empirically\u2014uniquely identifies additomultiplicative cascades, hybrid processes that randomly alternate between additive stabilization and multiplicative amplification. Critically, this symmetric signature persists universally across domains: cardiac dynamics maintain consistent patterns across health and disease states, financial markets show varying robustness across asset classes (currencies more variable than US equities) while preserving a hybrid structure, and climate systems exhibit geographical variations (subtropical\/continental stronger than tropical) without altering fundamental cascade type. These findings suggest that additomultiplicative organization is a unifying feature of complex adaptive systems, offering a resolution to decades of debate between additive and multiplicative models. The r2(q) profiling provides a mechanistic diagnostic capable of detecting early dysfunction, assessing system resilience, and revealing how environmental constraints shape\u2014but do not determine\u2014the fundamental principles governing multifractal complexity.<\/jats:p>","DOI":"10.3390\/e28030359","type":"journal-article","created":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T11:59:36Z","timestamp":1774267176000},"page":"359","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Additomultiplicative Cascades Govern Multifractal Scaling Reliability Across Cardiac, Financial, and Climate Systems"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6369-0414","authenticated-orcid":false,"given":"Madhur","family":"Mangalam","sequence":"first","affiliation":[{"name":"Department of Biomechanics, University of Nebraska at Omaha, Omaha, NE 68182, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2375-2323","authenticated-orcid":false,"given":"Eiichi","family":"Watanabe","sequence":"additional","affiliation":[{"name":"Department of Cardiology, Fujita Health University School of Medicine, Toyoake 470-1192, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5433-7002","authenticated-orcid":false,"given":"Ken","family":"Kiyono","sequence":"additional","affiliation":[{"name":"Graduate School of Engineering Science, University of Osaka, Toyonaka 560-8531, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ashkenazy, Y., Baker, D.R., Gildor, H., and Havlin, S. (2003). Nonlinearity and multifractality of climate change in the past 420,000 years. arXiv.","DOI":"10.1029\/2003GL018099"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1162\/003465302320259420","article-title":"Multifractality in asset returns: Theory and evidence","volume":"84","author":"Calvet","year":"2002","journal-title":"Rev. Econ. Stat."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2466","DOI":"10.1073\/pnas.012579499","article-title":"Fractal dynamics in physiology: Alterations with disease and aging","volume":"99","author":"Goldberger","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1038\/20924","article-title":"Multifractality in human heartbeat dynamics","volume":"399","author":"Ivanov","year":"1999","journal-title":"Nature"},{"key":"ref_5","unstructured":"Mandelbrot, B.B. (1982). The Fractal Geometry of Nature, WH Freeman."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S0378-4371(99)00230-7","article-title":"Statistical physics and physiology: Monofractal and multifractal approaches","volume":"270","author":"Stanley","year":"1999","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2463","DOI":"10.1029\/96WR01099","article-title":"Multifractal properties of daily rainfall in two different climates","volume":"32","author":"Svensson","year":"1996","journal-title":"Water Resour. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"129573","DOI":"10.1016\/j.physa.2024.129573","article-title":"Additivity suppresses multifractal nonlinearity due to multiplicative cascade dynamics","volume":"637","author":"Mangalam","year":"2024","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"033276","DOI":"10.1103\/PhysRevResearch.6.033276","article-title":"Machine-learning classification with additivity and diverse multifractal pathways in multiplicativity","volume":"6","author":"Mangalam","year":"2024","journal-title":"Phys. Rev. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"064212","DOI":"10.1103\/PhysRevE.109.064212","article-title":"Multifractal perturbations to multiplicative cascades promote multifractal nonlinearity with asymmetric spectra","volume":"109","author":"Mangalam","year":"2024","journal-title":"Phys. Rev. E"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"034126","DOI":"10.1103\/PhysRevE.111.034126","article-title":"Multifractal nonlinearity as a robust estimator of multiplicative cascade dynamics","volume":"111","author":"Mangalam","year":"2025","journal-title":"Phys. Rev. E"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"131260","DOI":"10.1016\/j.physa.2025.131260","article-title":"Additomultiplicative cascades sustain multifractal reliability across fluctuation intensities","volume":"684","author":"Mangalam","year":"2026","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1103\/PhysRevLett.62.1327","article-title":"Direct determination of the f(\u03b1) singularity spectrum","volume":"62","author":"Chhabra","year":"1989","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","first-page":"2249","article-title":"Multifractal test for nonlinearity of interactions across scales in time series","volume":"55","author":"Lane","year":"2023","journal-title":"Behav. Res. Methods"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1080\/10407413.2017.1368355","article-title":"Multifractality versus (mono-) fractality as evidence of nonlinear interactions across timescales: Disentangling the belief in nonlinearity from the diagnosis of nonlinearity in empirical data","volume":"29","author":"Wallot","year":"2017","journal-title":"Ecol. Psychol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6026","DOI":"10.1103\/PhysRevLett.86.6026","article-title":"Behavioral-independent features of complex heartbeat dynamics","volume":"86","author":"Amaral","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0197-4580(01)00266-4","article-title":"What is physiologic complexity and how does it change with aging and disease?","volume":"23","author":"Goldberger","year":"2002","journal-title":"Neurobiol. Aging"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"e13174","DOI":"10.1111\/eci.13174","article-title":"Heart rate variability in atrial fibrillation: The balance between sympathetic and parasympathetic nervous system","volume":"49","author":"Khan","year":"2019","journal-title":"Eur. J. Clin. Investig."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1161\/01.CIR.84.2.482","article-title":"Cardiovascular neural regulation explored in the frequency domain","volume":"84","author":"Malliani","year":"1991","journal-title":"Circulation"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5305","DOI":"10.1103\/PhysRevE.60.5305","article-title":"Scaling of the distribution of fluctuations of financial market indices","volume":"60","author":"Gopikrishnan","year":"1999","journal-title":"Phys. Rev. E"},{"key":"ref_21","unstructured":"Mandelbrot, B.B. (2013). Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, Springer."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1088\/1469-7688\/1\/4\/701","article-title":"An introduction to econophysics: Correlations and complexity in finance","volume":"1","author":"Shalizi","year":"2001","journal-title":"Quant. Financ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1038\/nclimate2245","article-title":"Nonlinear climate change","volume":"4","author":"Franzke","year":"2014","journal-title":"Nat. Clim. Change"},{"key":"ref_24","unstructured":"Lovejoy, S., and Schertzer, D. (2018). The Weather and Climate: Emergent Laws and Multifractal Cascades, Cambridge University Press."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Pietronero, L. (1989). Nonlinear variability in geophysics: Multifractal simulations and analysis. Fractals\u2019 Physical Origin and Properties, Springer.","DOI":"10.1007\/978-1-4899-3499-4"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Schertzer, D., and Lovejoy, S. (1991). Nonlinear geodynamical variability: Multiple singularities, universality and observables. Non-linear Variability in Geophysics: Scaling and Fractals, Springer.","DOI":"10.1007\/978-94-009-2147-4_4"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1175\/1520-0450(1993)032<0223:UMTAOF>2.0.CO;2","article-title":"Universal multifractals: Theory and observations for rain and clouds","volume":"32","author":"Tessier","year":"1993","journal-title":"J. Appl. Meteorol. Climatol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.hrthm.2007.10.030","article-title":"Non-Gaussian heart rate as an independent predictor of mortality in patients with chronic heart failure","volume":"5","author":"Kiyono","year":"2008","journal-title":"Heart Rhythm"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"18316","DOI":"10.1038\/s41598-023-45184-2","article-title":"Multifractal foundations of biomarker discovery for heart disease and stroke","volume":"13","author":"Mangalam","year":"2023","journal-title":"Sci. Rep."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ihlen, E.A.F. (2012). Introduction to multifractal detrended fluctuation analysis in Matlab. Front. Physiol., 3.","DOI":"10.3389\/fphys.2012.00141"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0378-4371(02)01383-3","article-title":"Multifractal detrended fluctuation analysis of nonstationary time series","volume":"316","author":"Kantelhardt","year":"2002","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3515","DOI":"10.1103\/PhysRevLett.67.3515","article-title":"Wavelets and multifractal formalism for singular signals: Application to turbulence data","volume":"67","author":"Muzy","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Gen\u00e7ay, R., Dacorogna, M., Muller, U.A., Pictet, O., and Olsen, R. (2001). An Introduction to High-Frequency Finance, Elsevier.","DOI":"10.1016\/B978-012279671-5.50004-6"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1198\/073500106000000044","article-title":"Properties of realized variance under alternative sampling schemes","volume":"24","author":"Oomen","year":"2006","journal-title":"J. Bus. Econ. Stat."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1257\/000282803321455151","article-title":"Micro effects of macro announcements: Real-time price discovery in foreign exchange","volume":"93","author":"Anderson","year":"2003","journal-title":"Am. Econ. Rev."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1086\/324391","article-title":"Order flow and exchange rate dynamics","volume":"110","author":"Evans","year":"2002","journal-title":"J. Political Econ."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1086\/429137","article-title":"Exchange rates and fundamentals","volume":"113","author":"Engel","year":"2005","journal-title":"J. Political Econ."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0167-2789(90)90035-N","article-title":"Velocity probability density functions of high Reynolds number turbulence","volume":"46","author":"Castaing","year":"1990","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1086\/511515","article-title":"Density fluctuations in MHD turbulence: Spectra, intermittency, and topology","volume":"658","author":"Kowal","year":"2007","journal-title":"Astrophys. J."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"056121","DOI":"10.1103\/PhysRevE.66.056121","article-title":"Multifractal stationary random measures and multifractal random walks with log infinitely divisible scaling laws","volume":"66","author":"Muzy","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"9693","DOI":"10.1029\/JD092iD08p09693","article-title":"Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes","volume":"92","author":"Schertzer","year":"1987","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1103\/PhysRevLett.59.381","article-title":"Self-organized criticality: An explanation of the 1\/f noise","volume":"59","author":"Bak","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1103\/PhysRevA.38.364","article-title":"Self-organized criticality","volume":"38","author":"Bak","year":"1988","journal-title":"Phys. Rev. A"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Jensen, H.J. (1998). Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems, Cambridge University Press.","DOI":"10.1017\/CBO9780511622717"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"11167","DOI":"10.1523\/JNEUROSCI.23-35-11167.2003","article-title":"Neuronal avalanches in neocortical circuits","volume":"23","author":"Beggs","year":"2003","journal-title":"J. Neurosci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1007\/s10955-011-0229-4","article-title":"Are biological systems poised at criticality?","volume":"144","author":"Mora","year":"2011","journal-title":"J. Stat. Phys."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"15595","DOI":"10.1523\/JNEUROSCI.3864-09.2009","article-title":"Neuronal avalanches imply maximum dynamic range in cortical networks at criticality","volume":"29","author":"Shew","year":"2009","journal-title":"J. Neurosci."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"034139","DOI":"10.1103\/PhysRevE.107.034139","article-title":"Genuine multifractality in time series is due to temporal correlations","volume":"107","author":"Blasiak","year":"2023","journal-title":"Phys. Rev. E"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/359\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T12:04:45Z","timestamp":1774267485000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/359"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,22]]},"references-count":48,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["e28030359"],"URL":"https:\/\/doi.org\/10.3390\/e28030359","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,22]]}}}