Multifractal test for nonlinearity of interactions across scales in time series

DG Kelty-Stephen, E Lane, L Bloomfield… - Behavior Research …, 2023 - Springer
The creativity and emergence of biological and psychological behavior tend to be nonlinear,
and correspondingly, biological and psychological measures contain degrees of irregularity …

Turing's cascade instability supports the coordination of the mind, brain, and behavior

DG Kelty-Stephen, M Mangalam - Neuroscience & Biobehavioral Reviews, 2022 - Elsevier
Turing inspired a computer metaphor of the mind and brain that has been handy and has
spawned decades of empirical investigation, but he did much more and offered behavioral …

[HTML][HTML] Multifractal foundations of biomarker discovery for heart disease and stroke

M Mangalam, A Sadri, J Hayano, E Watanabe… - Scientific reports, 2023 - nature.com
Any reliable biomarker has to be specific, generalizable, and reproducible across
individuals and contexts. The exact values of such a biomarker must represent similar health …

Multifractal descriptors ergodically characterize non-ergodic multiplicative cascade processes

DG Kelty-Stephen, M Mangalam - Physica A: Statistical Mechanics and its …, 2023 - Elsevier
Biological and psychological processes routinely break ergodicity, meaning they fail to have
stable means (M ean) and independent variation over time that we might find in additive …

Ergodic characterization of nonergodic anomalous diffusion processes

M Mangalam, R Metzler, DG Kelty-Stephen - Physical Review Research, 2023 - APS
Anomalous diffusion in various complex systems abounds in nature and spans multiple
space and time scales. Canonical characterization techniques that rely upon mean squared …

Fractal and multifractal descriptors restore ergodicity broken by non-Gaussianity in time series

DG Kelty-Stephen, M Mangalam - Chaos, Solitons & Fractals, 2022 - Elsevier
Ergodicity breaking is a challenge for biological and psychological sciences. Ergodicity is a
necessary condition for linear causal modeling. Long-range correlations and non …

Ergodic descriptors of non-ergodic stochastic processes

M Mangalam, DG Kelty-Stephen - Journal of the Royal …, 2022 - royalsocietypublishing.org
The stochastic processes underlying the growth and stability of biological and psychological
systems reveal themselves when far-from-equilibrium. Far-from-equilibrium, non-ergodicity …

Multifractal auditory stimulation promotes the effect of multifractal torso sway on spatial perception: Evidence from distance perception by blindwalking

D Kelty-Stephen, OD Similton, E Rabinowitz… - Ecological …, 2023 - Taylor & Francis
Stimulation and movement interact non-linearly across multiple scales—a point empirically
and quantitatively available through multifractal structure. Multifractal movements might …

Multifractal nonlinearity as a robust estimator of multiplicative cascade dynamics

M Mangalam, AD Likens, DG Kelty-Stephen - arXiv preprint arXiv …, 2023 - arxiv.org
Multifractal formalisms provide an apt framework to study random cascades in which
multifractal spectrum width $\Delta\alpha $ fluctuates depending on the number of estimable …

[HTML][HTML] Better than DFA? A Bayesian method for estimating the Hurst exponent in behavioral sciences

AD Likens, M Mangalam, AY Wong, AC Charles… - ArXiv, 2023 - ncbi.nlm.nih.gov
Abstract Detrended Fluctuation Analysis (DFA) is the most popular fractal analytical
technique used to evaluate the strength of long-range correlations in empirical time series in …