Additivity suppresses multifractal nonlinearity due to multiplicative cascade dynamics

Kelty-Stephen, Damian G.; Mangalam, Madhur

doi:10.1016/j.physa.2024.129573

Cited by 4 publications

(1 citation statement)

References 121 publications

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“…Excitement over the innovation of new fractal methods notwithstanding, it is essential to learn how to probe for nuanced patterns within relatively short signals. The efficacy of such methods for the diagnosis will hinge on our ability, within short-term measurements, to distill short-term task effects from clinically relevant, chronic, or systematic group effects [61] . Task and context variations could result in false positives when diagnosing Parkinson’s disease using a biomarker derived from postural sway variability.…”

Section: Introductionmentioning

confidence: 99%

Spatial variability and directional shifts in postural control in Parkinson’s disease

Kelty-Stephen,

Kiyono,

Stergiou

et al. 2024

Clinical Parkinsonism & Related Disorders

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Section: Introductionmentioning

confidence: 99%

Spatial variability and directional shifts in postural control in Parkinson’s disease

Kelty-Stephen,

Kiyono,

Stergiou

et al. 2024

Clinical Parkinsonism & Related Disorders

Self Cite

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Multifractal perturbations to multiplicative cascades promote multifractal nonlinearity with asymmetric spectra

Mangalam,

Kelty-Stephen

2024

Phys. Rev. E

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Machine-learning classification with additivity and diverse multifractal pathways in multiplicativity

Mangalam,

Seckler,

Kelty-Stephen

2024

Phys. Rev. Research

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Evidence of multifractal structures has spread to a wider set of physiological time series supporting the intricate interplay of biological and psychological functioning. These dynamics manifest as random multiplicative cascades, embodying nonlinear relationships characterized by recurring division, branching, and aggregation processes implicating noise across successive generations. This investigation focuses on how well the diversity of multifractal properties can be specific to the type of cascade relationship between generation (i.e., multiplicative, additive, or a mixture) as well as to the type of noise (i.e., including additive white Gaussian noise, fractional Gaussian noise, and various amalgamations) among 15 distinct types of binomial cascade processes. Cross-correlation analysis of multifractal spectral features confirms that these features capture nuanced aspects of cascading processes with minimal redundancy. Principal component analysis using 13 distinct multifractal spectral features shows that different cascade processes can manifest multifractal evidence of nonlinearity for distinct reasons. This transparency of multifractal spectral features to underlying cascade dynamics becomes less amenable to machine-learning strategies. Fully connected neural networks struggled to classify the 15 distinct types of cascade processes based on the respective multifractal spectral features (45.5% accuracy) yet demonstrated improved accuracy when addressing single categories of cross-generation relationships, that is, additive (91.6%), multiplicative (75.4%), or additomultiplicative (70.6%). While traditional principal component analysis reveals distinct loadings attributed to individual noise processes, multiplicative relationships between generations effectively make the constituent noise processes less discernible to neural networks. Neural networks may lack sufficient hierarchical depth required to effectively distinguish among nonadditive cascading processes, recommending either elaborating multifractal geometry or using alternate architectures for machine-learning classification of cascades with multiplicative relationships. Published by the American Physical Society 2024

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Additivity suppresses multifractal nonlinearity due to multiplicative cascade dynamics

Cited by 4 publications

References 121 publications

Spatial variability and directional shifts in postural control in Parkinson’s disease

Spatial variability and directional shifts in postural control in Parkinson’s disease

Multifractal perturbations to multiplicative cascades promote multifractal nonlinearity with asymmetric spectra

Machine-learning classification with additivity and diverse multifractal pathways in multiplicativity

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