Multifractal formalisms of human behavior

With the mounting realization that variability is an inevitable part of human behavior comes the need to integrate this phenomenon in concomitant models and theories of motor control. Among other things, this has resulted in a debate throughout the last decades about the origin of variability in behavior, the outcome of which has important implications for motor control theories. To date, a monofractal formalism of variability has been used as the basis for arguing for component- versus interaction-oriented theories of motor control. However, monofractal formalism alone cannot decide between the opposing sides of the debate. The present theoretical overview introduces multifractal formalisms as a necessary extension of the conventional monofractal formalism. In multifractal formalisms, the scale invariance of behavior is numerically defined as a spectrum of scaling exponents, rather than a single average exponent as in the monofractal formalism. Several methods to estimate the multifractal spectrum of scaling exponents – all within two multifractal formalisms called large deviation and Legendre formalism – are introduced and briefly discussed. Furthermore, the multifractal analyses within these two formalisms are applied to several performance tasks to illustrate how explanations of motor control vary with the methods used. The main section of the theoretical overview discusses the implications of multifractal extensions of the component- and interaction-oriented models for existing theories of motor control.     

Does the transtheoretical model need an attitude adjustment?: Integrating attitude with decisional balance as predictors of stage of change for exercise

Objectives. To compare conceptually similar decision-making components from the theory of planned behavior (attitude) and the transtheoretical model (pros and cons) to determine the extent to which attitude towards exercise adds to the prediction of stage of exercise behavior beyond that of pros and cons.Method. A sample of college undergraduates (N=223) were given stage of change, attitude and decisional balance measures regarding their exercise behavior. Structural equation modeling (SEM) was used to test the underlying measurement structure of the decision-making components, while a series of discriminant function analyses (DFAs) was performed using a combination of pros, cons, and cognitive and affective attitudes as predictors of membership in one of the five stages of change.Results. SEM determined that a correlated four-factor model, which included pros and cons and two attitude subscales, provided the best fit to the data. The DFAs revealed that the addition of attitude components to pros and cons significantly increased the overall explained variance across the stages of change from 32% to 56%, and improved the predictive ability of pros and cons from 31.2% to 48.2%.Conclusions. Although conceptually related, pros, cons and attitude were not closely linked at a construct-measurement level. Furthermore, the addition of attitude to pros and cons increased the overall explained variance across stages of change and improved the predictive ability of pros and cons alone. The measurement model and DFA results taken in combination strongly suggest that the addition of cognitive and affective attitudes may strengthen the decision-making aspect of the transtheoretical model.     

Multifractality of Unperturbed and Asymmetric Locomotion

The purpose of this study was to explore the extent of multifractality in unperturbed and constrained locomotion, and to determine if multifractality predicted gait adaptability. Young, healthy participants (n?=?15) walked at preferred and slow speeds, as well as asymmetrically (one leg at half speed) on a split-belt treadmill. Stride time multifractality was assessed via local detrended fluctuation analysis, which evaluates the evolution of fluctuations both spatially and temporally. Unperturbed walking exhibited monofractal behavior. Asymmetric walking displayed greater multifractality in the faster moving limb, indicating more intermittent periods of extreme high or low variance. Multifractality was not associated with adaptation to asymmetric walking. These findings further suggest that unperturbed locomotion is monofractal and establish that perturbed walking yields multifractal behavior.     

Contemporary theories of 1/f noise in motor control

1/f noise has been discovered in a number of time series collected in psychological and behavioral experiments. This ubiquitous phenomenon has been ignored for a long time and classical models were not designed for accounting for these long-range correlations. The aim of this paper is to present and discuss contrasted theoretical perspectives on 1/f noise, in order to provide a comprehensive overview of current debates in this domain. In a first part, we propose a formal definition of the phenomenon of 1/f noise, and we present some commonly used methods for measuring long-range correlations in time series. In a second part, we develop a theoretical position that considers 1/f noise as the hallmark of system complexity. From this point of view, 1/f noise emerges from the coordination of the many elements that compose the system. In a third part, we present a theoretical counterpoint suggesting that 1/f noise could emerge from localized sources within the system. In conclusion, we try to draw some lines of reasoning for going beyond the opposition between these two approaches.     

Is the heart preadapted to hypoxia? Evidence from fractal dynamics of heartbeat interval fluctuations at high altitude (5,050 m)

The dynamics of heartbeat interval time series over large time scales were studied by a modifed random walk analysis introduced recently asDetrended Fluctuation Analysis. In this analysis, the intrinsic fractal long-range power-law correlation properties of beat-to-beat fluctuations generated by the dynamical system (i.e., cardiac rhythm generator), after decomposition from extrinsic uncorrelated sources, can be quantified by the scaling exponent (α) which, in healthy subjects, for time scales of ∼10⁴ beats is ∼1.0. The effects of chronic hypoxia were determined from serial heartbeat interval time series of digitized twenty-four-hour ambulatory ECGs recorded in nine healthy subjects (mean age thirty-four years old) at sea level and during a sojourn at 5,050 m for thirty-four days (Ev-K2-CNR Pyramid Laboratory, Sagarmatha National Park, Nepal). The group averaged α exponent (±SD) was 0.99±0.04 (range 0.93–1.04). Longitudinal assessment of α in individual subjects did not reveal any effect of exposure to chronic high altitude hypoxia. The finding of α∼1 indicating scale-invariant long-range power-law correlations (1/f noise) of heartbeat fluctuations would reflect a genuinely self-similar fractal process that typically generates fluctuations on a wide range of time scales. Lack of a characteristic time scale along with the absence of any effect from exposure to chronic hypoxia on scaling properties suggests that the neuroautonomic cardiac control system is preadapted to hypoxia which helps prevent excessive mode-locking (error tolerance) that would restrict its functional responsiveness (plasticity) to hypoxic or other physiological stimuli. Editorial Note: A philosopher is, by definition, a lover of wisdom. In the following article, Dr. Dimitrov, as a philosopher, examines the principles that underlie being and thinking as performed by the structures of the brain. He reports his thoughts in a “virtual context.” Virtual, a word enjoying great popularity today, is derived from the Latin word for man; it describes manliness and implies apparent, but not actual, power. In his analysis of how information is dealt with by the human being, the author uses theoretical physics and mathematics that may seem arcane to some readers. A major aspect of his thesis declares that the effective performance of information systems relies not on the structures involved, but on the way they interact.     

Pink Noise in Language Production: A Nonlinear Approach to the Multilingual Lexicon

Most theories of (second) language processing are based on component-dominant models that assume linear relationships between linguistic factors affecting language production and language comprehension. In this contribution we argue that in the wake of current nonlinear approaches to cognition, language processing must be seen in terms of interaction-dominant dynamics manifested in 1/f scaling relations. Our study showed that increased experience in second language use leads to scaling relations that more and more tend toward pink noise. Moreover, our data tentatively show that intensive immersion in a second-language context leads to steeper spectral slopes in response time series of that same language. These findings demonstrate the significant contribution of nonlinear analyses to the study of real-time language processing in multilinguals.     

Stability of heartbeat interval distributions in chronic high altitude hypoxia.

Recent studies of nonlinear dynamics of the long-term variability of heart rate have identified nontrivial long-range correlations and scale-invariant power-law characteristics (l/f noise) that were remarkably consistent between individuals and were unrelated to external or environmental stimuli (Meyer et al., 1998a). The present analysis of complex nonstationary heartbeat patterns is based on the sequential application of the wavelet transform for elimination of local polynomial nonstationary behavior and an analytic signal approach by use of the Hilbert transform (Cumulative Variation Amplitude Analysis). The effects of chronic high altitude hypoxia on the distributions and scaling functions of cardiac intervals over 24 hr epochs and 4 hr day/nighttime subepochs were determined from serial heartbeat interval time series of digitized 24 hr ambulatory ECGs recorded in 9 healthy subjects (mean age 34 yrs) at sea level and during a sojourn at high altitude (5,050 m) for 34 days (Ev-K2-CNR Pyramid Laboratory, Sagarmatha National Park, Nepal). The results suggest that there exists a hidden, potentially universal, common structure in the heterogeneous time series. A common scaling function with a stable Gamma distribution defines the probability density of the amplitudes of the fluctuations in the heartbeat interval time series of individual subjects. The appropriately rescaled distributions of normal subjects at sea level demonstrated stable Gamma scaling consistent with a single scaled plot (data collapse). Longitudinal assessment of the rescaled distributions of the 24 hr recordings of individual subjects showed that the stability of the distributions was unaffected by the subject's exposure to a hypobaric (hypoxic) environment. The rescaled distributions of 4 hr subepochs showed similar scaling behavior with a stable Gamma distribution indicating that the common structure was unequivocally applicable to both day and night phases and, furthermore, did not undergo systematic changes in response to high altitude. In contrast, a single function stable over a wide range of time scales was not observed in patients with congestive heart failure or patients after cardiac transplantation. The functional form of the scaling in normal subjects would seem to be attributable to the underlying nonlinear dynamics of cardiac control. The results suggest that the observed Gamma scaling of the distributions in healthy subjects constitutes an intrinsic dynamical property of normal heart function that would not undergo early readjustment or late acclimatization to extrinsic environmental physiological stress, e.g., chronic hypoxia.     

Stability of heartbeat interval distributions in chronic high altitude hypoxia

Recent studies of nonlinear dynamics of the long-term variability of heart rate have identified nontrivial long-range correlations and scale-invariant power-law characteristics (1/f noise) that were remarkably consistent between individuals and were unrelated to external or environmental stimuli (Meyer et al., 1998a). The present analysis of complex nonstationary heartbeat patterns is based on the sequential application of the wavelet transform for elimination of local polynomial nonstationary behavior and an analytic signal approach by use of the Hilbert transform (Cumulative Variation Amplitude Analysis). The effects of chronic high altitude hypoxia on the distributions and scaling functions of cardiac intervals over 24 hr epochs and 4 hr day/nighttime subepochs were determined from serial heartbeat interval time series of digitized 24 hr ambulatory ECGs recorded in 9 healthy subjects (mean age 34 yrs) at sea level and during a sojourn at high altitude (5,050 m) for 34 days (Ev-K2-CNR Pyramid Laboratory, Sagarmatha National Park, Nepal). The results suggest that there exists a hidden, potentially universal, common structure in the heterogeneous time series. A common scaling function with a stable Gamma distribution defines the probability density of the amplitudes of the fluctuations in the heartbeat interval time series of individual subjects. The appropriately rescaled distributions of normal subjects at sea level demonstrated stable Gamma scaling consistent with a single scaled plot (data collapse). Longitudinal assessment of the rescaled distributions of the 24 hr recordings of individual subjects showed that the stability of the distributions was unaffected by the subject’s exposure to a hypobaric (hypoxic) environment. The rescaled distributions of 4 hr subepochs showed similar scaling behavior with a stable Gamma distribution indicating that the common structure was unequivocally applicable to both day and night phases and, furthermore, did not undergo systematic changes in response to high altitude. In contrast, a single function stable over a wide range of time scales was not observed in patients with congestive heart failure or patients after cardiac transplantation. The functional form of the scaling in normal subjects would seem to be attributable to the underlying nonlinear dynamics of cardiac control. The results suggest that the observed Gamma scaling of the distributions in healthy subjects constitutes an intrinsic dynamical property of normal heart function that would not undergo early readjustment or late acclimatization to extrinsic environmental physiological stress, e.g., chronic hypoxia.     

Multifractal roots of suprapostural dexterity

Visually guided postural control emerges in response to task constraints. Task constraints generate physiological fluctuations that foster the exploration of available sensory information at many scales. Temporally correlated fluctuations quantified using fractal and multifractal metrics have been shown to carry perceptual information across the body. The risk of temporally correlated fluctuations is that stable sway appears to depend on a healthy balance of standard deviation (SD): too much or too little SD entails destabilization of posture. This study presses on the visual guidance of posture by prompting participants to quietly stand and fixate at distances within, less than, and beyond comfortable viewing distance. Manipulations of the visual precision demands associated with fixating nearer and farther than comfortable viewing distance reveals an adaptive relationship between SD and temporal correlations in postural fluctuations. Changing the viewing distance of the fixation target shows that increases in temporal correlations and SD predict subsequent reductions in each other. These findings indicate that the balance of SD within stable bounds may depend on a tendency for temporal correlations to self-correct across time. Notably, these relationships became stronger with greater distance from the most comfortable viewing and reaching distance, suggesting that this self-correcting relationship allows the visual layout to press the postural system into a poise for engaging with objects and events. Incorporating multifractal analysis showed that all effects attributable to monofractal evidence were better attributed to multifractal evidence of nonlinear interactions across scales. These results offer a glimpse of how current nonlinear dynamical models of self-correction may play out in biological goal-oriented behavior. We interpret these findings as part of the growing evidence that multifractal nonlinearity is a modeling strategy that resonates strongly with ecological-psychological approaches to perception and action.     

The pros and cons of temporally near and distant action

The present research demonstrated that in considering an action, considerations against (con) the action tend to be subordinate to considerations in favor of (pro) the action in that cons are considered only if the level of pros is sufficient, whereas pros are considered independent of the level of cons (Studies 1A and IB). The authors therefore concluded that pros constitute a higher construal level than cons and predict, on the basis of temporal construal processes (Y. Trope & N. Liberman. 2003). that pros would be more salient in making decisions for the more distant future, whereas the reverse should hold for cons. As predicted, participants generated more pros and fewer cons toward new exam procedures (Study 2), public policies (Study 3), and personal and interpersonal behaviors (Studies 4-6) that were expected to take place in the more distant future. This research also examined the limiting conditions and the evaluative consequences of these shifts.     

Perceived Pros and Cons of Condom Use as Predictors of its Consistent Use with a Heterosexual Romantic Partner Among Young Adults

The present research examines the pros and cons of condom use as predictors of consistent condom use with a heterosexual romantic partner. Data from 619 undergraduate students (35.1 % males; mean of age?=?20.31) were collected using a voluntary and anonymous self-report survey. The pros and cons predicted consistent condom use during the last month among females, whereas only the pros were predictive of consistent condom use in men. Similarly, only the feelings of safety predicted consistent condom use among men. However, the reduction of pleasure for women, the side-effects of other contraceptive methods, the difficulty in asking for condom use when they were also using the pill and the fact that condom use interrupts and cools off foreplay were also predictors among women. Besides the superiority of the pros over the cons, in general, the present research identifies a number of important pros and cons that should be used to encourage condom use.     

GPS analysis of human locomotion: further evidence for long-range correlations in stride-to-stride fluctuations of gait parameters

During free walking, gait is automatically adjusted to provide optimal mechanical output and minimal energy expenditure; gait parameters, such as cadence, fluctuate from one stride to the next around average values. It was described that this fluctuation exhibited long-range correlations and fractal-like patterns. In addition, it was suggested that these long-range correlations disappeared if the participant followed the beep of metronome to regulate his or her pace. Until now, these fractal fluctuations were only observed for stride interval, because no technique existed to adequately analyze an extended time of free walking. The aim of the present study was to measure walking speed (WS), step frequency (SF) and step length (SL) with high accuracy (<1 cm) satellite positioning method (global positioning system or GPS) in order to detect long-range correlations in the stride-to-stride fluctuations. Eight participants walked 30 min under free and constrained (metronome) conditions. Under free walking conditions, DFA (detrended fluctuation analysis) and surrogate data tests showed that the fluctuation of WS, SL and SF exhibited a fractal pattern (i.e., scaling exponent alpha: 0.5 < alpha < 1) in a large majority of participants (7/8). Under constrained conditions (metronome), SF fluctuations became significantly anti-correlated (alpha < 0.5) in all participants. However, the scaling exponent of SL and WS was not modified. We conclude that, when the walking pace is controlled by an auditory signal, the feedback loop between the planned movement (at supraspinal level) and the sensory inputs induces a continual shifting of SF around the mean (persistent anti-correlation), but with no effect on the fluctuation dynamics of the other parameters (SL, WS).     

Effect of the SNS-Based Physical Activity-Related Psychological Intervention on Physical Activity and Psychological Constructs among Inactive University Students

Background/ObjectiveThe current study investigated the effects of the physical activity-related psychological intervention via social network service (SNS) on physical activity and psychological constructs in inactive university students.MethodThirty inactive university students participated in the 12-week intervention and received the physical activity-related psychological strategy via SNS. The physical activity levels, stages of physical activity, self-efficacy, pros, and cons were measured at the three time points (baseline, after 6 weeks, and after 12 weeks). Data analyses included frequency analysis, McNemar chi-square (χ²) test, and a repeated measures ANOVA were conducted.ResultsResults indicated that the number of inactive university students gradually decreased across the three different time points, and that a total physical activity of inactive university students significantly increased over the 12-week intervention. In addition, pros and self-efficacy significantly increased but cons gradually decreased over the intervention.ConclusionsThe current study suggests that the SNS-based physical activity-related psychological strategies have positive effects on promoting physical activity and its related psychological constructs for inactive university students.     

Cluster subtypes within the precontemplation stage of change for sun protection behavior

The aim of this study is to identify replicable cluster subtypes within the precontemplation stage of change for sun protection. Secondary data analysis of baseline data from a sample of participants in a home-based expert system intervention was performed. Three random samples were selected from participants in the precontemplation stage (N = 570). Cluster analyses were performed using the scales of pros, cons, and self-efficacy. Interpretability of pattern, pseudo F-test, and dendograms were used to determine the number of clusters. A four-cluster solution replicated across subsamples. Significant differences between clusters on the nine processes of change and on behavioral measures were found. Cluster solutions were robust, interpretable and with good initial external validity. They replicated patterns found for other behaviors, demonstrating long-term predictability and providing basis for tailored interventions.     

Predicting increases in readiness to quit smoking: A prospective analysis using the contemplation ladder

Abstract

Most smokers are not motivated to quit. The transtheoretical model posits mechanisms (processes of change and pros and cons) by which smokers might increase their stage of readiness to quit. While cross-sectional relationships among the stages of change, processes of change, and pros and cons are well established, there is little evidence that processes of change and pros and cons predict progressive stage movements. This study uses data from a large worksite-based cancer prevention study (the Working Well Trial) to test the hypothesis that processes of change and the pros and cons of smoking predict progressive movement up the contemplation ladder, which is an alternative measure of motivation to quit smoking based on social cognitive theory. The results indicate that experiential processes of change promote increases in readiness to quit smoking. This study provides further evidence for the predictive validity of the contemplation ladder and sheds light on how unmotivated, nonvolunteer smokers can be motivated to consider cessation.     

Long-range correlation properties in motor timing are individual and task specific

1/f (β) noise represents a specific form of (long-range) correlations in a time series that is pervasive across many sensorimotor variables. Recent studies have shown that the precise properties of the correlations demonstrated by a group of test participants may vary as a function of experimental conditions or factors characterizing the group. Our purpose in the present study was to clarify whether long-range correlations affect sensorimotor performance generally or in a task-specific manner and whether each individual produces characteristic long-range correlations that are reliable across several runs of the same task. We analyzed the series of time intervals produced by 43 participants in two timing tasks: unimanual rhythmic tapping and circle drawing. We found that a participant's 1/f (β) properties in tapping were not related to the 1/f (β) properties in circle drawing. However, within each task, individual differences were reliable, and a Cronbach's alpha of .59 showed a high degree of within-subjects reproducibility of the long-range correlations. Thus, long-range correlations represent a consistent and distinctive characteristic of individuals performing a particular task, rather than a ubiquitous generic property of sensorimotor time series. The implications of these results are discussed from both a theoretical and a methodological perspective.     

Inverse attribute functions and the proposed modifications of the power law

Three prominent modifications of Stevens’ power law, designed to account for the curvature at low stimulus intensities, were examined in the light of previously reported inverse attribute functions and five new experiments scaling loudness and softness by magnitude estimation. One hundred and seven students served as observers in the five experiments. Lack of curvature in the inverse functions at low stimulus intensities, plus the lack of parameter invariance, pointed to the inadequacy of the effective threshold and physiological noise modifications. The additive constant model of zero-point response bias, previously advanced by Irwin and Corballis (1968)and McGill (1960)was found more satisfactory. A discussion of the implications of the research findings for subsequent formulations of the modified power law was included.     

Wishful information preference: positive fantasies mimic the effects of intentions

When pursuing set goals or intentions, people prefer to acquire information about the pros rather than the cons of their goal pursuit. Little is known about information preferences at earlier stages, when people are not yet serious about pursuing a given future. In the present three studies, positive fantasies that depicted an idealized desired future--compared with fantasies that questioned whether the future would be so ideal--created a preference for pros over cons, just like set goals or intentions have been shown to do. Positive fantasies created a stronger preference for pros versus cons when people were not serious about pursuing an imagined future or had just foregone an opportunity to do so. Results suggest that before people are engaged in serious pursuits, positive fantasies spur the selective acquisition of pro information, which may lead to poor decisions even if the acquired information is carefully deliberated on later.     

The Pervasiveness of 1/f Scaling in Speech Reflects the Metastable Basis of Cognition

Human neural and behavioral activities have been reported to exhibit fractal dynamics known as 1/f noise , which is more aptly named 1/f scaling . Some argue that 1/f scaling is a general and pervasive property of the dynamical substrate from which cognitive functions are formed. Others argue that it is an idiosyncratic property of domain-specific processes. An experiment was conducted to investigate whether 1/f scaling pervades the intrinsic fluctuations of a spoken word. Ten participants each repeated the word bucket over 1,000 times, and fluctuations in acoustic measurements across repetitions generally followed the 1/f scaling relation, including numerous parallel yet distinct series of 1/f fluctuations. On the basis of work showing that 1/f scaling is a universal earmark of metastability, it is proposed that the observed pervasiveness of 1/f fluctuations in speech reflects the fact that cognitive functions are formed as metastable patterns of activity in brain, body, and environment.     

Fractal properties and short-term correlations in motor control in cycling: influence of a cognitive challenge

Fluctuations in cyclic tasks periods is a known characteristic of human motor control. Specifically, long-range fractal fluctuations have been evidenced in the temporal structure of these variations in human locomotion and thought to be the outcome of a multicomponent physiologic system in which control is distributed across intricate cortical, spinal and neuromuscular regulation loops.Combined with long-range correlation analyses, short-range autocorrelations have proven their use to describe control distribution across central and motor components.We used relevant tools to characterize long- and short-range correlations in revolution time series during cycling on an ergometer in 19 healthy young adults. We evaluated the impact of introducing a cognitive task (PASAT) to assess the role of central structures in control organization.Autocorrelation function and detrending fluctuation analysis (DFA) demonstrated the presence of fractal scaling. PSD in the short range revealed a singular behavior which cannot be explained by the usual models of even-based and emergent timing.The main outcomes are that (1) timing in cycling is a fractal process, (2) this long-range fractal behavior increases in persistence with dual-task condition, which has not been previously observed, (3) short-range behavior is highly persistent and unaffected by dual-task.Relying on the inertia of the oscillator may be a way to distribute more control to the periphery, thereby allocating less resources to central process and better managing additional cognitive demands. This original behavior in cycling may explain the high short-range persistence unaffected by dual-task, and the increase in long-range persistence with dual-task.