Nonlinear Dynamics Psychology and Life Sciences最新文献

This year's cover artist, Clinton Marstall, creates fractal imagery by photographing natural patterns. He then uses a pen to highlight the patterns and projects them on to a canvas for painting. Using this precision technique, he integrates a number of biomorphic images into a unique amalgum of multi-scaled complexity.

Mathematical modeling and computer simulations are important means to understand the mechanisms of psychotherapy. The challenge is to design models which not only predict outcome, but simulate the nonlinear trajectories of change. Another challenge is to validate them with empirical data. We proposed a model on change dynamics which integrates five variables (order parameters) (therapeutic progress or success, motivation for change, problem severity, emotions, and insight) and four control parameters (capacity to enter a trustful cooperation and working alliance, cognitive competencies and mindfulness, hopefulness, behavioral resources). The control parameters modulate the nonlinear functions interrelating the variables. The evolution dynamics of the system is determined by a set of nine nonlinear difference equations, one for each variable and parameter. Here we outline how the model can be tested and validated by empirical time series data of the variables, by time series of the therapeutic alliance, and by assessing the input onto the system as it is perceived by the client. The parameters are measured by questionnaires at the beginning and at the end of the treatment. A key element of the validation algorithm is the adjustment of the parameter values as assessed by the questionnaires to model-specific parameter values by which the dynamics can be reproduced (calibration). The validation steps are illustrated by the data of a client who used an internet-based tool for high-frequency therapy monitoring (daily self-ratings). Especially after applying the input vector (interventions as experienced by the client) the similarity between the empirical and the model dynamics becomes evident. The averaged correlation between the empirical and the simulated dynamics across all variables is .41, after applying a short averaging mean window and eliminating an initial transient period, it is .62, varying between .47 and .81, depending on the variable. The discussion opens perspectives on the combination of mathematical modeling with real-time monitoring in order to realize data-driven simulations for short-term predictions and to estimate the effects of interventions before real interventions are applied.

In this article we study the application of nonlinear indices (sometimes called complexity indices) to univariate time series data arising from studies of schizophrenia and bipolar disorder. Specifically, we consider time series arising from EEG studies, ECG studies, and self-report mood data. As part of our analysis, we empirically examine the claim in the literature that complexity tends to be higher in the EEG of schizophrenia patients than controls and that this tendency is dampened or even inverted by medication, increasing age, and reduced symptomatology. Our conclusion is that this claim is only partially supported and propose that symptomatology, specifically the presence or absence of schizophrenia 'deficit syndrome,' may be the most important factor. Results are more consistent in ECG studies in which reduced heart rate complexity is observed in both schizophrenia and bipolar disorder. The applications of nonlinear indices to the effects of antipsychotic medication and the discrimination of mood states are also examined. It is concluded that the monitoring of nonlinear indices may be useful in predicting response to medication and predicting onset of specific mood states.

Since the mid 1980's, mainstream social psychology investigations of self-complexity and psychopathology have produced contradictory results. These results are likely the result of a lack of theoretical and methodological grounding in complexity theory. The current study proposes that the self has an interconnected fractal structure, and that this structure may be reflected within inverse-power law (IPL) distributions of response times to self-related questions. MMPI-2 item response sets (N = 300) were selected from a larger pool of 1,881 forensic administrations. Self-complexity was operationalized as the inverse of the shape parameter (?) of the frequency distribution of reaction times to MMPI-2 items (n = 567) for each participant. It was predicted that: (a) these distributions would generally have strong fits with IPL distributions; and (b) that ? would tend to be correlated with pathology among the MMPI-2 scale scores. The results confirmed that the response-time distributions tended to fit IPLs (mean R2 = .94; range: .64 to .99). Furthermore, 18 of 45 correlations between ? and MMPI-2 scale scores associated with pathology were statistically significant, suggesting that rigidity in fractal self-structure is associated with broadband psychopathology. A follow up principal components analysis of the 45 individual scale scores across the participants confirmed this conclusion, producing three latent components, each of which was significantly correlated with ?, and each of which had a broad variety of scales with factor loadings > |.5|. These results may provide a first step toward a practical complexity-science approach to measuring the structural resilience of the self, and viewing the self as a complex self-organizing system.

This study analyzed Maternal Sensitivity in the interaction of mother-infant dyads to distinguish different dynamics associated with their attachment group membership - Insecure-Avoidant (A), Secure (B), or Insecure-Resistant (C), with no Disorganized traits - that they developed at 15 months. Participants were 26 eight-month old infants interacting with their mothers in a free-play setting. The analyses used sequential streams of infant actions and maternal responses, and state-space grids to study the temporal organization of the sequences. We examined appropriateness and promptness of the maternal response to infant behavior and a dynamic analysis of the interactive process. In Group B, when the antecedent behavior was infant social approach, the appropriateness of the maternal profile (sensitive vs. intrusive responses) was related to their children's subsequent security. However, how promptly mothers responded was not predictive. Conversely, when the antecedent behavior was infant play, how promptly the mothers responded was associated with securely attached children while mothers' profile of appropriate responses did not distinguish the subsequent quality of attachment. The indices derived from state-space grids were associated with attachment type and distinguished Group C from Groups B and A. However, results from analysis of a specific region of states, 'maternal interfering response to infant social approach,' showed significant discriminant function that correctly classified 78% of Group B, 73% of Group A, and 83% of Group C. Group B infants received less intrusive behavior than their counterparts, and when they did, it involved positive affection or playfulness. Finally, regarding attractors, although more Group B dyads showed multi-stability of coexisting attractors, than Groups A or C, the differences were not statistically significant.

A systematic single case study with a mixed quantitative and qualitative methodology was conducted to investigate the nonlinear dynamics of change in play profiles of a child in psychodynamic play therapy. The first aim of the study was to cluster the different features of play characteristics (i.e., descriptive, cognitive, affective, and social characteristics of play, and the defensive strategies used in play) in order to construct the different play profiles of this child, and secondly to assess the transitions between profiles over the course of treatment. It was expected that there would be an increase in critical fluctuations during the transitions between the profiles and an increase in the variability of play profiles. Results showed that the child's play characteristics clustered into eight states and three attractors. The Markov Transition Matrix showed how play profiles evolved over time. Entropy analyses comparing the first and the second half of therapy showed an increase in variability. Qualitative analyses indicated the importance of expression of the child's underlying fear, and its integration with overt anger in the generation of the new play profiles. The results indicate an increase in variability, and a destabilization of old play profiles that were used towards generating new play profiles.

Time series analysis, nonlinear or otherwise, requires an appropriate lag length between observations. The choice of lag length is contingent to some extent on whether the source data are under- or over-sampled. For neuro-cognitive data, the time granularity should represent psychologically meaningful units. Automatic methods for determining optimal lag length are not readily available, particularly for potentially oversampled data and if the eventual goal is to compare linear versus nonlinear models in large quantities across experimental conditions. The present study examined the interacting roles of down-sampling rate, natural lag rates, task types, real-time lapse, and lag units on the accuracy of linear and nonlinear (exponential structures) autocor-relational models, starting with electrodermal data sampled at 200 obs/sec. Participants were 197 undergraduates organized into groups of 3-7 people in three sequential task conditions: watching a video that explained the problem situation, an individual mental task, and a group problem-solving task. Results showed that the optimal lag structures came from natural rates of 2 obs/sec at 1 sec lag or 3 obs/sec at 1 lag unit. Results varied modestly across the subtasks such that greater stability occurred when participants watched the video, followed by the group task, followed by the individual task. Nonlinear models were more accurate than ARMA generally, although there were specific experimental conditions in which the reverse was true. Future research across disciplines should investigate optimal lags from a perspective of naturally occurring change processes rate rather than rely on automatic computations.

The prey-predator model in the form of Lotka-Volterra equation represents a nonlinear description of the dynamics of two or more interacting populations. In this article, several versions of the Lotka-Volterra model are analyzed from the point of view of parameter uncertainty. The uncertainty treatment is quite different from the common approach. We do not treat uncertain parameters as random. Instead, we analyze the behavior of the models supposing that the uncertain parameters may change in time within given limits. The simulation tool used in this paper is based on the differential inclusions, instead of the ordinary differential equations. This permits us to determine the attainable sets in the state space, due to the parameter uncertainty.

The present study explored the potential growth pattern of reading development from kindergarten to high school using the publicly available dataset from the Early Childhood Longitudinal Study-Kindergarten cohort (ECLS-K). We extended the piecewise growth mixture model (PGMM) with a single unknown knot into the situation with more than one knot. The results showed that the PGMM with more than one knot could be used to study reading development. Students' reading development had fast growth before entering elementary school, but development slowed after. The turning point appears differently for a heterogeneous population. For the normal group, the knot was at Grade 2 (y =2.01), while the faster group transferred into the second period much earlier than the normal group around Grade 1 (y = 0.87). However, both groups reached similar ability levels in later school years. Moreover, teachers should pay special attention to the slower group, which had not only slower growth (y = 2.69) than but also difficulty catching up with the normal-level children.