On the dynamical foundation of multifractality

Mahmoodi, Korosh; West, Bruce J.; Grigolini, Paolo

doi:10.1016/j.physa.2019.124038

Cited by 10 publications

(17 citation statements)

References 54 publications

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“…We align the present work with a growing body of evidence and theory suggesting that the absorption of multifractal fluctuations by the movement system is a generic case of complexity matching in which the coupling of two systems occasions a sharing of multifractal fluctuations (Delignières et al, 2016 ; Almurad et al, 2017 ; Mahmoodi et al, 2017 ). Neither would it be the first time that speech perception has been understood as a sort of complexity matching.…”

Section: Discussionsupporting

confidence: 82%

Bringing the Nonlinearity of the Movement System to Gestural Theories of Language Use: Multifractal Structure of Spoken English Supports the Compensation for Coarticulation in Human Speech Perception

Ward

Kelty-Stephen

2018

Front. Physiol.

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Coarticulation is the tendency for speech vocalization and articulation even at the phonemic level to change with context, and compensation for coarticulation (CfC) reflects the striking human ability to perceive phonemic stability despite this variability. A current controversy centers on whether CfC depends on contrast between formants of a speech-signal spectrogram—specifically, contrast between offset formants concluding context stimuli and onset formants opening the target sound—or on speech-sound variability specific to the coordinative movement of speech articulators (e.g., vocal folds, postural muscles, lips, tongues). This manuscript aims to encode that coordinative-movement context in terms of speech-signal multifractal structure and to determine whether speech's multifractal structure might explain the crucial gestural support for any proposed spectral contrast. We asked human participants to categorize individual target stimuli drawn from an 11-step [ga]-to-[da] continuum as either phonemes “GA” or “DA.” Three groups each heard a specific-type context stimulus preceding target stimuli: either real-speech [al] or [a], sine-wave tones at the third-formant offset frequency of either [al] or [aɹ], and either simulated-speech contexts [al] or [aɹ]. Here, simulating speech contexts involved randomizing the sequence of relatively homogeneous pitch periods within vowel-sound [a] of each [al] and [aɹ]. Crucially, simulated-speech contexts had the same offset and extremely similar vowel formants as and, to additional naïve participants, sounded identical to real-speech contexts. However, randomization distorted original speech-context multifractality, and effects of spectral contrast following speech only appeared after regression modeling of trial-by-trial “GA” judgments controlled for context-stimulus multifractality. Furthermore, simulated-speech contexts elicited faster responses (like tone contexts do) and weakened known biases in CfC, suggesting that spectral contrast depends on the nonlinear interactions across multiple scales that articulatory gestures express through the speech signal. Traditional mouse-tracking behaviors measured as participants moved their computer-mouse cursor to register their “GA”-or-“DA” decisions with mouse-clicks suggest that listening to speech leads the movement system to resonate with the multifractality of context stimuli. We interpret these results as shedding light on a new multifractal terrain upon which to found a better understanding in which movement systems play an important role in shaping how speech perception makes use of acoustic information.

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Section: Discussionsupporting

confidence: 82%

Bringing the Nonlinearity of the Movement System to Gestural Theories of Language Use: Multifractal Structure of Spoken English Supports the Compensation for Coarticulation in Human Speech Perception

Ward

Kelty-Stephen

2018

Front. Physiol.

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“…Our theoretical approach is based on the essential role of crucial events. The crucial events with µ becoming closer to µ = 2 are generators of multifractality, as pointed out in the work of Bohara et al (2017) and Mahmoodi et al (1990). Thus, our prediction that the walker with µ close to 2 attracts the µ of the walker close to the Gaussian region µ = 3 can be interpreted as transmission of multifractality from the healthy to the pathological walker in a surprising agreement with the recent experimental result of Almurad et al (2018).…”

Section: Lack Of Difficult Task Perceptionsupporting

confidence: 91%

“…They also conjectured that self-organization generating crucial events may also be the generator of multifractality. This last conjecture has been fully confirmed in the recent work of Bohara et al (2017) and Mahmoodi et al (1990).…”

Section: Information Reductionsupporting

confidence: 62%

“…In line with the theory of Mahmoodi et al (1990) showing that multifractality is generated by crucial events at criticality, the main goal of the present manuscript is to prove that the complexity index µ is the proper measure of complexity. To make the significance of achieving this goal more apparent, we supplement this result with a proper revision of the connection between complexity matching and complexity management.…”

Section: Introduction: Walking Together As a Form Of Therapeutic Syncmentioning

confidence: 89%

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Complex Periodicity and Synchronization

2020

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A recent experiment proves the therapeutic effect of arm-in-arm walking, showing that if an aged participant walks in close synchrony with a young companion, the complexity matching effect results in the restoration of complexity in the former. A clear manifestation of complexity restoration is a perfect synchronization. The authors of this interesting experiment leave open two important problems. The first is the measure of complexity that is interpreted as a degree of multifractality. The second problem is the lack of a theoretical derivation of synchronization, which is experimentally observed with no theoretical derivation. The main goal of this paper is to establish a physiological foundation of these important results based on the recent advances on the dynamics of the brain, interpreted as a system at criticality. Criticality is a phenomenon requiring the cooperative interaction of units, the neurons of the brain, and is hypothesized as the main source of cognition. Using the criticality-induced intelligence, we define complexity as a property of crucial events, a form of temporal complexity, and we prove that the perfect synchronization is due to the interaction between the two systems, with the more complex system restoring the temporal complexity of the less complex system. The phenomenon of temporal complexity is characterized by ergodicity breaking that has made it difficult in the past to derive the perfect synchronization generated by complexity matching. For this reason, we supplement the main result of this paper with a comparison between complexity matching and complexity management.

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“…We focus on the important role of crucial events , advocated in 2002 by Allegrini et al ( 2002 ). More recently the authors of Bohara et al ( 2017 ) and Mahmoodi et al ( 2017a ) proved that the occurrence of crucial events activates multifractal fluctuations, thereby raising the question of what is the origin of crucial events. Herein we rely on the validity of the hypothesis that crucial events are generated by the phenomenon of Self-Organized Temporal Criticality (SOTC) (Mahmoodi et al, 2017b ).…”

Section: Future Directionsmentioning

confidence: 99%

Meditation-Induced Coherence and Crucial Events

et al. 2018

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In this paper we emphasize that 1/f noise has two different origins, one compatible with Laplace determinism and one determined by unpredictable crucial events. The dynamics of heartbeats, manifest as heart rate variability (HRV) time series, are determined by the joint action of these different memory sources with meditation turning the Laplace memory into a strongly coherent process while exerting an action on the crucial events favoring the transition from the condition of ideal 1/f noise to the Gaussian basin of attraction. This theoretical development affords a method of statistical analysis that establishes a quantitative approach to the evaluation of the stress reduction realized by the practice of Chi meditation and Kundalini Yoga.

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On the dynamical foundation of multifractality

Cited by 10 publications

References 54 publications

Bringing the Nonlinearity of the Movement System to Gestural Theories of Language Use: Multifractal Structure of Spoken English Supports the Compensation for Coarticulation in Human Speech Perception

Bringing the Nonlinearity of the Movement System to Gestural Theories of Language Use: Multifractal Structure of Spoken English Supports the Compensation for Coarticulation in Human Speech Perception

Complex Periodicity and Synchronization

Meditation-Induced Coherence and Crucial Events

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