Random dynamics and the research programme of classical mechanics

The modern mathematical theory of dynamical systems proposes a new model of mechanical motion. In this model the deterministic unstable systems can behave in a statistical manner. Both kinds of motion are inseparably connected, they depend on the point of view and researcher's approach to the system. This mathematical fact solves in a new way the old problem of statistical laws in the world which is essentially deterministic. The classical opposition: deterministic‐statistical, disappears in random dynamics. The main thesis of the paper is that the new theory of motion is a revolution in the research programme of classical mechanics. It is the revolution brought about by the development of mathematics.     

Three Dimensional Image Reconstruction of Neuroanatomical Structures: Methods for Isolation of the Cortex, Ventricular System, Hippocampus, and Fornix

Magnetic Resonance (MR) imaging allows volumetric quantification of a variety of neuroanatomical structures using two dimensional (2D) images as well as three-dimensional (3D) reconstruction of the brain and any of its constituent parts. Three-dimensional analysis permits integration of the neuroanatomical changes which occur in pathologic states, with the cognitive and behavioral changes elucidated through neuropsychological assessment. This paper describes uniform methods for 3D neuroanatomical isolation of the neocortex, ventricular system, and hippocampus in both normal and pathologic states. The 3D methods are described in detail using two different software programs, ANALYZE and IMAGE. Three-dimensional neuroanatomical reconstructions were carried out on a patient who sustained a very severe traumatic brain injury. The 3D image analysis in the patient with traumatic brain injury, revealed structural changes in frontal and temporal cortex, ventricular dilation, and hippocampal atropy. The neuropsychological impairments in this patient, were consistent with the observed neuroanatomical changes revealed on 3D image reconstruction. This technology permits precise determinations of the extent and severity of the neuroanatomical changes which follow neurological injury disease.     

Equilibria in Personality States: A Conceptual Primer for Dynamics in Personality States

We provide a basic, step-by-step introduction to the core concepts and mathematical fundamentals of dynamic systems modelling through applying the Change as Outcome model, a simple dynamical systems model, to personality state data. This model characterizes changes in personality states with respect to equilibrium points, estimating attractors and their strength in time series data. Using data from the Personality and Interpersonal Roles study, we find that mean state is highly correlated with attractor position but weakly correlated with attractor strength, suggesting strength provides added information not captured by summaries of the distribution. We then discuss how taking a dynamic systems approach to personality states also entails a theoretical shift. Instead of emphasizing partitioning trait and state variance, dynamic systems analyses of personality states emphasize characterizing patterns generated by mutual, ongoing interactions. Change as Outcome modelling also allows for estimating nuanced effects of personality development after significant life changes, separating effects on characteristic states after the significant change and how strongly she or he is drawn towards those states (an aspect of resiliency). Estimating this model demonstrates core dynamics principles and provides quantitative grounding for measures of ‘repulsive’ personality states and ‘ambivert’ personality structures. © 2020 European Association of Personality Psychology     

A Trajectory Approach to Causality

In this paper we propose a new approach to address the ramification problem in common-sense reasoning about action and change. We contrast the methods of McCain and Turner, Thielscher and Sandewall and, based on some of the limitations they encounter, we introduce a trajectory-based approach which keeps a history of the states through which a system evolves to characterise its dynamical state. We furnish an underlying state-transition semantics and a logic that admits an expressive, dynamical account of some typical scenarios which encounter modelling difficulties in the other approaches mentioned.     

On the dynamics and adaptivity of mental processes: Relating adaptive dynamical systems and self-modeling network models by mathematical analysis

In this paper, it is addressed by mathematical analysis how network-oriented modeling relates to the dynamical systems perspective on mental processes. It has been mathematically proven that any dynamical system can be modeled as a temporal-causal network model and that any adaptive dynamical system (of any order) can be modeled by a self-modeling network (of the same order).     

Tools for connectionist modeling: The dynamical systems methodology

Some understanding of dynamical systems is essential to achieving competency in connectionist models. This mathematical background can be acquired either through a rigorous set of upper undergraduate and/or graduate formal courses or via disciplined self-teaching. As part of developing a course in connectionism, we feel that although certain very basic mathematical tools are most appropriately learned in their “pure” form (i.e., from mathematics textbooks and courses), more advanced exposure to dynamical systems theory can be given in the context of an introduction to connectionism. Students thus learn to write connectionist simulations by first writing programs for simulating arbitrary dynamical systems, then using them to learn some aspects of dynamical systems in general by simulating some special cases, and finally applying this technique to connectionist models of increasing complexity.     

Extending Dynamical Systems Theory to Model Embodied Cognition

We define a mathematical formalism based on the concept of an ‘‘open dynamical system” and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ‘‘total system’’ (which models an agent in an environment) and an ‘‘agent system’’ (which models an agent by itself), and it includes tools for analyzing the collections of overlapping paths that occur in an embedded agent's state space. To illustrate the way this formalism can be applied, several neural network models are embedded in a simple model environment. Such phenomena as masking, perceptual ambiguity, and priming are then observed. We also use this formalism to reinterpret examples from the embodiment literature, arguing that it provides for a more thorough analysis of the relevant phenomena.     

Multiattribute Decision Making in Context: A Dynamic Neural Network Methodology

A theoretical structure for multiattribute decision making is presented, based on a dynamical system for interactions in a neural network incorporating affective and rational variables. This enables modeling of problems that elude two prevailing economic decision theories: subjective expected utility theory and prospect theory. The network is unlike some that fit economic data by choosing optimal weights or coefficients within a predetermined mathematical framework. Rather, the framework itself is based on principles used elsewhere to model many other cognitive and behavioral data, in a manner approximating how humans perform behavioral functions. Different, interconnected modules within the network encode (a) attributes of objects among which choices are made, (b) object categories, (c) and goals of the decision maker. An example is utilized to simulate the actual consumer choice between old and new versions of Coca-Cola. Potential applications are also discussed to market decisions involving negotiations between participants, such as international petroleum traders.     

动力学与吸引子理论在冲突研究中的应用

用动力学的观点来看待冲突是近年来关于冲突研究的一个新发展。与传统的研究概念和方法不同的是,动力学的观点将冲突及与冲突相关的过程作为一个复杂系统,冲突各方的思想、情感和行为的相互关系构成了冲突内在的动力学机制。系统内各要素的相互关系可以用吸引子来反映,冲突的发展和结束取决于引发冲突的吸引子的性质。所谓成功的干预则意味着冲突各方形成了新的心理和行为模式和不同于以往的心理和社会环境。     

基于鼠标追踪技术的个体建构过程实时测量

个体建构研究探讨分类的低水平知觉过程及其机制, 涉及诸多自动化加工。基于手的运动可以实时地反映大脑内的信息加工过程这一原理, 鼠标追踪技术通过对被试移动电脑鼠标反应时鼠标运动轨迹的跟踪记录与分析, 对心理加工过程进行实时测量, 是实时测量心理加工过程的新技术。基于鼠标追踪技术的最新操作软件—— MouseTracker的个体建构过程实时测量研究发现, 社会类别和刻板印象遵循动态连续激活原则; 动态激活过程中, 基于面孔肤色的分类加工优先于基于面部轮廓的分类加工; 不同通道间的社会类别遵循动态整合激活原则; 个体建构过程是一个对他人的动态知觉系统, 该系统中社会类别、刻板印象、高水平认知状态以及对面孔、声音等的低水平加工之间可连续、动态地相互作用。     

Awareness is relative: dissociation as the organisation of meaning

This essay discusses how the organisation of mental material within the cognitive system can influence consciousness and awareness, and presents a theory of dissociation based on the premise that awareness is relative, contingent on the activated representation of the ongoing event being linked to the activated self-representation. It allows four possible variations of integration: (i) non-integrated experience--perceptions about an object/event are either not perceived or they remain at the sensory level: traditional dissociative states, amnesia, depersonalisation etc; (ii) variably integrated experience--activation of information of a specific valence about an object blocks activation of information of contrasting valence: splitting; (iii) alternatively integrated experience--experience is integrated into a specific, limited active self-representation: fugue and multiple identity states; (iv) dis-integrated experience-the ongoing experience of innate drives and needs is no longer consistently activated in the core self-representation: repression and isolation.     

Information integration based predictions about the conscious states of a spiking neural network

This paper describes how Tononi’s information integration theory of consciousness was used to make detailed predictions about the distribution of phenomenal states in a spiking neural network. This network had approximately 18,000 neurons and 700,000 connections and it used models of emotion and imagination to control the eye movements of a virtual robot and avoid ‘negative’ stimuli. The first stage in the analysis was the development of a formal definition of Tononi’s theory of consciousness. The network was then analysed for information integration and detailed predictions were made about the distribution of consciousness for each time step of recorded activity. This work demonstrates how an artificial system can be analysed for consciousness using a particular theory and in the future this approach could be used to make predictions about the phenomenal states associated with biological systems.     

Information Processing and Dynamics in Minimally Cognitive Agents

There has been considerable debate in the literature about the relative merits of information processing versus dynamical approaches to understanding cognitive processes. In this article, we explore the relationship between these two styles of explanation using a model agent evolved to solve a relational categorization task. Specifically, we separately analyze the operation of this agent using the mathematical tools of information theory and dynamical systems theory. Information‐theoretic analysis reveals how task‐relevant information flows through the system to be combined into a categorization decision. Dynamical analysis reveals the key geometrical and temporal interrelationships underlying the categorization decision. Finally, we propose a framework for directly relating these two different styles of explanation and discuss the possible implications of our analysis for some of the ongoing debates in cognitive science.     

Differences in dimensionality of electroencephalogram during awake and deeper sleep stages

The nonlinear dynamical systems theory provides some tools for the analysis of electroencephalogram (EEG) at different sleep stages. Its use could allow the automatic monitoring of the states of the sleep and it would also contribute an explanatory level of the differences between stages. The goal of the present paper is to address this type of analysis, focusing on the most different stages. Estimations of dimensionality were compared when six subjects were awake and in a deep sleep stage. Greater dimensionality involves more complexity because the system receives more external influences. If this dimensionality is maximum, we can consider that the time series is a noisy one. A smaller dimensionality involves lower complexity because the system receives fewer inputs. We hypothesized that we would find greater dimensionality when subjects were awake than in a deep sleep stage. Results show a noisy time series during the awake stage, whereas in the sleep stage, dimensionality is smaller, confirming our hypothesis. This result is similar to the findings reached previously by other authors.     

Two Strands of Scholarship on Language Comprehension: Phoneme Monitoring and Discourse Context

This paper briefly reviews two areas of work on language comprehension and gives an informal assessment of each. One area discussed is phoneme monitoring, a method for measuring on-line spoken language comprehension. The origins of this method are sketched, as are some of the ways in which it has been used and the assumptions behind its use. The second area is substantive rather than methodological, being concerned with discourse context and its effect upon word and sentence processing. The hypothesis of interest states that discourse context has its effects on subsequent word processing primarily by affecting the ease of integrating new information into the ongoing discourse representation. This organizationally based view is distinct from a more elementaristic one which states that context operates by items priming other individual items. Some work consistent with the integration perspective is noted.     

A dynamic interactive theory of person construal

A dynamic interactive theory of person construal is proposed. It assumes that the perception of other people is accomplished by a dynamical system involving continuous interaction between social categories, stereotypes, high-level cognitive states, and the low-level processing of facial, vocal, and bodily cues. This system permits lower-level sensory perception and higher-order social cognition to dynamically coordinate across multiple interactive levels of processing to give rise to stable person construals. A recurrent connectionist model of this system is described, which accounts for major findings on (a) partial parallel activation and dynamic competition in categorization and stereotyping, (b) top-down influences of high-level cognitive states and stereotype activations on categorization, (c) bottom-up category interactions due to shared perceptual features, and (d) contextual and cross-modal effects on categorization. The system's probabilistic and continuously evolving activation states permit multiple construals to be flexibly active in parallel. These activation states are also able to be tightly yoked to ongoing changes in external perceptual cues and to ongoing changes in high-level cognitive states. The implications of a rapidly adaptive, dynamic, and interactive person construal system are discussed.     

Modeling the Dynamics of Risky Choice

Individuals make decisions under uncertainty every day. Decisions are based on incomplete information concerning the potential outcome or the predicted likelihood with which events occur. In addition, individuals' choices often deviate from the rational or mathematically objective solution. Accordingly, the dynamics of human decision making are difficult to capture using conventional, linear mathematical models. Here, we present data from a 2-choice task with variable risk between sure loss and risky loss to illustrate how a simple nonlinear dynamical system can be employed to capture the dynamics of human decision making under uncertainty (i.e., multistability, bifurcations). We test the feasibility of this model quantitatively and demonstrate how the model can account for up to 86% of the observed choice behavior. The implications of using dynamical models for explaining the nonlinear complexities of human decision making are discussed as well as the degree to which the theory of nonlinear dynamical systems might offer an alternative framework for understanding human decision making processes.