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 …
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 …
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 …
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 …
stable means (M ean) and independent variation over time that we might find in additive …
Ergodic characterization of nonergodic anomalous diffusion processes
Anomalous diffusion in various complex systems abounds in nature and spans multiple
space and time scales. Canonical characterization techniques that rely upon mean squared …
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 …
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 …
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 …
and quantitatively available through multifractal structure. Multifractal movements might …
Multifractal nonlinearity as a robust estimator of multiplicative cascade dynamics
Multifractal formalisms provide an apt framework to study random cascades in which
multifractal spectrum width $\Delta\alpha $ fluctuates depending on the number of estimable …
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 …
technique used to evaluate the strength of long-range correlations in empirical time series in …