Compatible Dynamical Models of Environmental,Sensory, and Perceptual Systems

ABSTRACT

One of the cornerstones of the ecological stance in psychology is the compatibility, or symmetry, between animal and environment. In this article, it is argued that a first principles reevaluation of the dynamical systems that structure the information signals animals live through is an important step in understanding how compatibility is possible. What is especially important is how environmental properties are encoded by dynamical laws into the information signals of the environment and how these signals can reveal environmental properties. It is argued that that compatibility is not just 2-way compatibility between animal and environment but also 3-way compatibility of environmental, sensory, and perceptual systems. The argument is illustrated using a conceptual exegesis of 2 dynamical systems, Newtonian mechanics and Webster's acoustic horn equation. The discussion of the latter equation is accompanied by the extraction of articulatory information from speech signals of 50 speakers. It is believed that the work presented here further develops the theory of ecological psychology as well as its specific application to speech perception pioneered by Carol Fowler.     

Extended Cognition & the Causal‐Constitutive Fallacy: In Search for a Diachronic and Dynamical Conception of Constitution

Philosophical accounts of the constitution relation have been explicated in terms of synchronic relations between higher‐ and lower‐level entities. Such accounts, I argue, are temporally austere or impoverished, and are consequently unable to make sense of the diachronic and dynamic character of constitution in dynamical systems generally and dynamically extended cognitive processes in particular. In this paper, my target domain is extended cognition based on insights from nonlinear dynamics. Contrariwise to the mainstream literature in both analytical metaphysics and extended cognition, I develop a nonstandard, alternative conception of constitution, which I call “diachronic process constitution”. It will be argued that only a diachronic and dynamical conception of constitution is consistent with the nature of constitution in distributed cognitive processes.     

Interference effects in bimanual coordination are independent of movement type

Simultaneously executed limb movements interfere with each other. Whereas the interference between discrete movements is examined mostly from a cognitive perspective, that between rhythmic movements is studied mainly from a dynamical systems perspective. As the tools and concepts developed by both communities are limited in their applicability to the other domain, it remains unclear if a common cause underlies motor interference in both domains. We investigated the interference between simultaneously executed discrete and rhythmic wrist movements. The discrete movements' reaction time and movement time decreased with increasing rhythmic movement frequency. The discrete movements accelerated or decelerated the rhythmic movements in a manner that depended on movement frequency and the discrete movement's initiation phase. The acceleration/deceleration profile was bimodal at low frequencies and unimodal at high frequencies, mimicking the hallmark feature of rhythmic-rhythmic coordination, thus suggesting that interference between movements may be invariant across different movement types.     

Coordination dynamics of rhythmical and discrete prehension movements: Implications of the scanning procedure and individual differences

The aim of this study was to compare the coordination dynamics of discrete and rhythmical reaching and grasping movements from a dynamical systems perspective. Previous research from this theoretical perspective had focused on rhythmical actions and it is unclear to what extent discrete movements are amenable to a similar dynamical systems analysis. Six adult subjects performed prehension in two conditions: a discrete, non-continuous mode and a rhythmical, continuous mode. A `scanning procedure' was implemented between pre- and post-tests in which the required time of final relative hand closure (T_rfc) was systematically varied. It was shown that the error in the reaching and grasping pattern was least at an attractor region and systematically increased with deviation from the attractor. Results also indicated that there were no differences between condition or trial block for the group. However, there were several within-subject effects of interest. The validity of the scanning procedure was found to be questionable in the discrete condition, where four subjects showed differences in T_rfc between pre- or post-test and the predicted T_rfc of the scanning procedure. Four out of six subjects also had different preferred T_rfc values for discrete and rhythmical movement, indicating that individual specific models might need to be constructed for future dynamical modelling of discrete movement.PsycINFO classification: 2330     

Fractal models for event-based and dynamical timers

Some recent papers proposed to distinguish between event-based and emergent timing. Event-based timing is conceived as prescribed by events produced by a central clock, and seems to be used in discrete tasks (e.g., finger tapping). Emergent or dynamical timing refers to the exploitation of the dynamical properties of effectors, and is typically used in continuous tasks (e.g., circle drawing). The analysis of period series suggested that both timing control processes possess fractal properties, characterized by self-similarity and long-range dependence. The aim of this article is to present two models that produce period series presenting the statistical properties previously evidenced in discrete and continuous rhythmic tasks. The first one is an adaptation of the classical activation/threshold models, including a plateau-like evolution of the threshold over time. The second one is a hybrid limit-cycle model, including a time-dependent linear stiffness parameter. Both models reproduced satisfactorily the spectral signatures of event-based and dynamical timing processes, respectively. The models also produced auto-correlation functions similar to those experimentally observed. Using ARFIMA modeling we show that these simulated series possess fractal properties. We suggest in conclusion some possible extensions of this modeling approach, to account for the effects of metronomic pacing, or to analyze bimanual coordination.     

Beyond curve fitting: a dynamical systems account of exponential learning in a discrete timing task

The authors examined the function for learning a discrete timing task from a dynamical systems perspective rather than solely the traditional curve-fitting viewpoint. Adult participants (N = 8) practiced a single-limb angular movement task of 125 ms over 20 degrees for 200 trials. There was no significant difference in percentage of variance accounted for in 3 parameter exponential and power-law nonlinear fits to the individual and averaged data. The percentage of variance increased in both exponential and power-law equations when the data were averaged over participants and trials. Drawing on a dynamical systems approach to time scales in motor learning and on analysis of the distinctive features of exponential and power-law functions, however, the authors conclude that the exponential is the learning function for that task and that level of practice.     

The Value of Symbolic Computation

Standard generative linguistic theory, which uses discrete symbolic models of cognition, has some strengths and weaknesses. It is strong on providing a network of outposts that make scientific travel in the jungles of natural language feasible. It is weak in that it currently depends on the elaborate and unformalized use of intuition to develop critical supporting assumptions about each data point. In this regard, it is not in a position to characterize natural language systems in the lawful terms that ecological psychologists strive for. Connectionist learning models offer some help: They define lawful relations between linguistic environments and language systems. But our understanding of them is currently weak, especially when it comes to natural language syntax. Fortunately, symbolic linguistic analysis can help connectionism if the two meet via dynamical systems theory. I discuss a case in point: Insights from linguistic explorations of natural language syntax appear to have identified information structures that are particularly relevant to understanding ecologically appealing but analytically mysterious connectionist learning models.     

Practical Tools and Guidelines for Exploring and Fitting Linear and Nonlinear Dynamical Systems Models

A dynamical system is a system of variables that show some regularity in how they evolve over time. Change concepts described in most dynamical systems models are by no means novel to social and behavioral scientists, but most applications of dynamic modeling techniques in these disciplines are grounded on a narrow subset of—typically linear—theories of change. I provide practical guidelines, recommendations, and software code for exploring and fitting dynamical systems models with linear and nonlinear change functions in the context of four illustrative examples. Cautionary notes, challenges, and unresolved issues in utilizing these techniques are discussed.     

Evaluation is a Dynamic Process: Moving Beyond Dual System Models

Over the past few decades, dual attitude/process/system models have emerged as the dominant framework for understanding a wide range of psychological phenomena. Most of these models characterize the unconscious and conscious mind as being built from discrete processes or systems: one that is reflexive, automatic, fast, affective, associative, and primitive, and a second that is deliberative, controlled, slow, cognitive, propositional, and more uniquely human. Although these models serve as a useful heuristic for characterizing the human mind, recent developments in social and cognitive neuroscience suggest that the human evaluative system, like most of cognition, is widely distributed and highly dynamic. Integrating these advances with current attitude theories, we review how the recently proposed Iterative Reprocessing Model can account for apparent dual systems as well as discrepancies between traditional dual system models and recent research revealing the dynamic nature of evaluation. Furthermore, we describe important implications this dynamical system approach has for various social psychological domains.     

From mutual manipulation to cognitive extension: challenges and implications

This paper examines the application of the mutual manipulability criterion as a way to demarcate constituents of cognitive systems from resources having a mere causal influence on cognitive systems. In particular, it is argued that on at least one interpretation of the mutual manipulability criterion, the criterion is inadequate because the criterion is conceptualized as identifying synchronic dependence between higher and lower ‘levels’ in mechanisms. It is argued that there is a second articulation of the mutual manipulability criterion available, and that it should be preferred for at least two reasons. The first is that the criterion of mutual manipulability is an instance of continuous reciprocal causation. The second is that it has implications for how to understand this distinction between causation and constitution. It is shown that when considering dynamic systems, continuous reciprocal causation - ubiquitous in dynamical systems - is a form of constitutive causality, which entails that causal factors may, in the right circumstances, by genuine constitutive factors of cognition. This notion of constitutive causality lends support to conceiving of the mutual manipulability criterion as a genuine demarcation principle in the debate over the boundaries of mind.     

Extracting Global and Local Dynamics From the Stochastics of Rhythmic Forearm Movements

The authors examined the dynamics governing rhythmic forearm movements that 9 participants performed under a variety of task constraints by using a generic, unbiased analysis technique for extracting the drift coefficients of Fokker-Planck equations from stochastic data. From those coefficients, they reconstructed and analyzed vector fields and phase portraits to identify characteristic, task-dependent kinematic and dynamical features. They first directly estimated the parameters of weakly nonlinear self-sustaining oscillators from the extracted drift coefficients. The estimated parameters that the authors had selected instinctively and then particularized by using averaging methods largely confirmed previously derived limit-cycle models. Next, they ventured beyond limit-cycle models to examine global and local dynamical features that those models cannot adequately address, particularly task-dependent changes in flow strength and curvature and distinct dynamical features associated with flexion and extension. The authors argue that those features should be focal points of researchers' future modeling efforts to formulate a more adequate and encompassing account of the dynamics of rhythmic movement.     

Extracting global and local dynamics from the stochastics of rhythmic forearm movements

The authors examined the dynamics governing rhythmic forearm movements that 9 participants performed under a variety of task constraints by using a generic, unbiased analysis technique for extracting the drift coefficients of Fokker-Planck equations from stochastic data. From those coefficients, they reconstructed and analyzed vector fields and phase portraits to identify characteristic, task-dependent kinematic and dynamical features. They first directly estimated the parameters of weakly nonlinear self-sustaining oscillators from the extracted drift coefficients. The estimated parameters that the authors had selected instinctively and then particularized by using averaging methods largely confirmed previously derived limit-cycle models. Next, they ventured beyond limit-cycle models to examine global and local dynamical features that those models cannot adequately address, particularly task-dependent changes in flow strength and curvature and distinct dynamical features associated with flexion and extension. The authors argue that those features should be focal points of researchers' future modeling efforts to formulate a more adequate and encompassing account of the dynamics of rhythmic movement.     

The undershoot bias: learning to act optimally under uncertainty

Abstract - Learning in stochastic environments is increasingly viewed as an important psychological ability. To extend these results from a perceptual to a motor domain, we tested whether participants could learn to solve a stochastic minimal-time task using exploratory learning. The task involved moving a cursor on a computer screen to a target. We systematically varied the degree of random error in movement in three different conditions; each condition had a distinct time-optimal solution. We found that participants approximated the optimal solutions with practice. The results show that adults are sensitive to the stochastic structure of a task and naturally adjust the magnitude of an undershoot bias to the particular movement error of a task.     

The Sequential Structure of Movement Outcome in Learning a Discrete Timing Task

The sequential structure of discrete movement outcomes in an elbow-flexion movement task was examined with a crossed design of 2 movement-time (125 and 500 ms) and 2 range-of-motion (5 degrees and 20 degrees ) conditions over sets of 200 trials of practice. Traditional analyses of error score. techniques, time-series analyses of the quantitative raw and differenced data, and a symbolic dynamic analysis of qualitative events arising from the data were conducted. The differenced data revealed a consistent order over 3-trial strings that was more apparent with larger steps in the data scores, but quantitative time-series and symbolic dynamic analyses of the raw movement-time data showed weaker relations. There were a few patterns of structure evident in the raw data time series that were a function of the movement condition and the skill level of the subject. The analyses of the movement-time scores revealed that, in learning the discrete timing task, there is more order apparent in the intrinsic frame of reference of the difference scores than in the extrinsic frame of reference.     

Multitimescale dynamical interactions between speech rhythm and gesture

Temporal patterns in human movement, and in speech in particular, occur on multiple timescales. Regularities in such patterns have been observed between speech gestures, which are relatively quick movements of articulators (e.g., tongue fronting and lip protrusion), and also between rhythmic units (e.g., syllables and metrical feet), which occur more slowly. Previous work has shown that patterns in both domains can be usefully modeled with oscillatory dynamical systems. To investigate how rhythmic and gestural domains interact, an experiment was conducted in which speakers performed a phrase repetition task, and gestural kinematics were recorded using electromagnetic articulometry. Variance in relative timing of gestural movements was correlated with variance in rhythmic timing, indicating that gestural and rhythmic systems interact in the process of planning and producing speech. A model of rhythmic and gestural planning oscillators with multifrequency coupling is presented, which can simulate the observed covariability between rhythmic and gestural timing.     

The Notion of Dynamic Unit: Conceptual Developments in Cognitive Science

We suggest a common ground for alternative proposals In different domains of cognitive science which have previously seemed to have little in common. The underlying common theme is associated with a redefinition of the basic unit of analysis in each domain of thought. Our framework suggests a definition of unity which is based not on inherent properties of the elements constituting the unit, but rather on dynamic patterns of correlation across the elements. We introduce a set of features that characterize the new dynamic units, and distinguish them from traditional units of analysis. A conceptual connection is made with the identification of elementary units in modern physics theories, as well as with concepts and structures in the study of complex dynamical systems and connectionism. The paper analyses the evolution of the concept of unit in different domains of thought in cognitive science, and examines the proposed framework of “dynamic unity” with regard to various theoretical problems within each domain. The particular cognitive science issues discussed in the paper include: (1) the binding problem in the brain; (2) the mental unit of conceptual organization; (3) defining ‘wordhood’ in linguistics; and (4) identifying the unit of cognition in the natural environment.     

On strong anticipation

We examine Dubois’s [Dubois, D., 2003. Mathematical foundations of discrete and functional systems with strong and weak anticipations. Lecture Notes in Computer Science 2684, 110–132.] distinction between weak anticipation and strong anticipation. Anticipation is weak if it arises from a model of the system via internal simulations. Anticipation is strong if it arises from the system itself via lawful regularities embedded in the system’s ordinary mode of functioning. The assumption of weak anticipation dominates cognitive science and neuroscience and in particular the study of perception and action. The assumption of strong anticipation, however, seems to be required by anticipation’s ubiquity. It is, for example, characteristic of homeostatic processes at the level of the organism, organs, and cells. We develop the formal distinction between strong and weak anticipation by elaboration of anticipating synchronization, a phenomenon arising from time delays in appropriately coupled dynamical systems. The elaboration is conducted in respect to (a) strictly physical systems, (b) the defining features of circadian rhythms, often viewed as paradigmatic of biological behavior based in internal models, (c) Pavlovian learning, and (d) forward models in motor control. We identify the common thread of strongly anticipatory systems and argue for its significance in furthering understanding of notions such as “internal”, “model” and “prediction”.     

Embodied task dynamics

Movement science faces the challenge of reconciling parallel sequences of discrete behavioral goals with observed fluid, context-sensitive motion. This challenge arises with a vengeance in the speech domain, in which gestural primitives play the role of discrete goals. The task dynamic framework has proved effective in modeling the manner in which the gestural primitives of articulatory phonology can result in smooth, biologically plausible, movement of model articulators. We present a variant of the task dynamic model with 1 significant innovation: Tasks are not abstract and context free but are embodied and tied to specific effectors. An advantage of this approach is that it allows the definition of a parametric cost function that can be optimized. Optimization generates gestural scores in which the relative timing of gestures is fully specified. We demonstrate that movements generated in an optimal manner are phonetically plausible. Highly nuanced movement trajectories are emergent based on relatively simple optimality criteria. This addresses a long-standing need within this theoretical framework and provides a rich modeling foundation for subsequent work.     

Coordination and movement pathology: models of structure and function

Here we consider the role of abstract models in advancing our understanding of movement pathology. Models of movement coordination and control provide the frameworks necessary for the design and interpretation of studies of acquired and developmental disorders. These models do not however provide the resolution necessary to reveal the nature of the functional impairments that characterise specific movement pathologies. In addition, they do not provide a mapping between the structural bases of various pathologies and the associated disorders of movement. Current and prospective approaches to the study and treatment of movement disorders are discussed. It is argued that the appreciation of structure–function relationships, to which these approaches give rise, represents a challenge to current models of interlimb coordination, and a stimulus for their continued development.     

The Dynamics of General Developmental Mechanisms: From Piaget and Vygotsky to Dynamic Systems Models

Dynamic systems theory conceives of development as a self-organizational process. Both complexity and order emerge as a product of elementary principles of interaction between components involved in the developmental process. This article presents a dynamic systems model based on a general dual developmental mechanism, adapted from Piaget and Vygotsky. The mechanism consists of a conservative force, further strengthening the already-consolidated level, and a progressive force, consolidating internal contents and procedures at more advanced levels. It is argued that this dual mechanism constitutes one of the few basic laws of learning and change, and is comparable to the laws of effect and of contiguity. Simulation studies suggest that this dual mechanism explains self-organization in developmental paths, including the emergence of discrete jumps from one equilibrium level to another, S-shaped growth, and the occurrence of co-existing levels.