Self-Organization with Constraints—A Mathematical Model for Functional Differentiation

Tsuda, Ichiro; Yamaguti, Yutaka; Watanabe, Hiroshi

doi:10.3390/e18030074

Cited by 10 publications

(7 citation statements)

References 43 publications

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“…Haken ( 1983 ) associates intermittent synchronization with information transfer between levels of neurons. (Tsuda et al, 2016 ) identifies biological dynamics under constraints such as embryonic development and differentiation of cortical functions, as having dependencies on properties of non-equilibrium systems such as bifurcation and attractor formations such as those well-observed in Chua's circuit, and outlines a critical connection from chaotic dynamics to the capacity for macroscopic self-organization in biological systems, providing mathematical models. Although the Chua's circuit is a deterministic system, emergent oscillatory features cannot be predicted by the states of the individual Chua oscillator elements or from preceding states of the output signal.…”

Section: Results: Applying the Proposed Sonification Framework To Mulmentioning

confidence: 99%

Interactive Sonification Exploring Emergent Behavior Applying Models for Biological Information and Listening

Choi

2018

Front. Neurosci.

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Sonification is an open-ended design task to construct sound informing a listener of data. Understanding application context is critical for shaping design requirements for data translation into sound. Sonification requires methodology to maintain reproducibility when data sources exhibit non-linear properties of self-organization and emergent behavior. This research formalizes interactive sonification in an extensible model to support reproducibility when data exhibits emergent behavior. In the absence of sonification theory, extensibility demonstrates relevant methods across case studies. The interactive sonification framework foregrounds three factors: reproducible system implementation for generating sonification; interactive mechanisms enhancing a listener's multisensory observations; and reproducible data from models that characterize emergent behavior. Supramodal attention research suggests interactive exploration with auditory feedback can generate context for recognizing irregular patterns and transient dynamics. The sonification framework provides circular causality as a signal pathway for modeling a listener interacting with emergent behavior. The extensible sonification model adopts a data acquisition pathway to formalize functional symmetry across three subsystems: Experimental Data Source, Sound Generation, and Guided Exploration. To differentiate time criticality and dimensionality of emerging dynamics, tuning functions are applied between subsystems to maintain scale and symmetry of concurrent processes and temporal dynamics. Tuning functions accommodate sonification design strategies that yield order parameter values to render emerging patterns discoverable as well as rehearsable, to reproduce desired instances for clinical listeners. Case studies are implemented with two computational models, Chua's circuit and Swarm Chemistry social agent simulation, generating data in real-time that exhibits emergent behavior. Heuristic Listening is introduced as an informal model of a listener's clinical attention to data sonification through multisensory interaction in a context of structured inquiry. Three methods are introduced to assess the proposed sonification framework: Listening Scenario classification, data flow Attunement, and Sonification Design Patterns to classify sound control. Case study implementations are assessed against these methods comparing levels of abstraction between experimental data and sound generation. Outcomes demonstrate the framework performance as a reference model for representing experimental implementations, also for identifying common sonification structures having different experimental implementations, identifying common functions implemented in different subsystems, and comparing impact of affordances across multiple implementations of listening scenarios.

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Section: Results: Applying the Proposed Sonification Framework To Mulmentioning

confidence: 99%

Interactive Sonification Exploring Emergent Behavior Applying Models for Biological Information and Listening

Choi

2018

Front. Neurosci.

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“…From this informational aspect of the network values in McCulloch's sense, we investigated the change in the network structure (see Figure 3). For the first time, we constructed a randomly connected neural network that consisted of the elementary units described by Equation (1). We defined a layer of the network, according to the closeness to the unit 0, where closeness is defined as the least number of steps along the connected paths from unit 0 (Figure 3a).…”

Section: Dynamic Heterarchymentioning

confidence: 99%

“…As discussed previously [ 1 ], scientific (not philosophical) studies of self-organization started in accordance with the cybernetics movement, in which the theory of self-organization developed in the construction of control theory [ 5 ]. Thereafter, in physics and chemistry, Haken and Prigogine et al developed the concept of self-organization and formulated it as the emergence of macroscopic spatiotemporal patterns in far-from-equilibrium systems under stationary conditions.…”

Section: The Difference Between Self-organization and Self-organizati...mentioning

confidence: 99%

“…In this paper, we propose hypotheses concerning the neural mechanism of functional (including cell) differentiation. According to the research based on the framework of self-organization with constraints [ 1 ], we developed a constrained self-organization theory and applied it to the interacting systems with complex environments, which were realized by new artificial intelligence, such as evolutionary reservoir computers (ERC) [ 2 ] and evolutionary dynamical systems (EDS) [ 3 ]. With certain constraints, ERC and EDS revealed the emergence of the network function via an optimized evolutionary process, which was associated with the self-organization of neuronal components (i.e., elements), thus leading to the realization of functional differentiation.…”

Section: Introductionmentioning

confidence: 99%

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On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

Tsuda

Watanabe

Tsukada

et al. 2022

Entropy

Self Cite

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The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.

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“…Tsuda, Yamaguti, and Watanabe [16] deal with the development of the human brain as self-organizing process leading to functional differentiation of neurons and cortical modules. To this end they present numerical treatments of specific models such as one-dimensional maps, e.g., a time-discrete version of the well-known Kuramoto model.…”

Section: The Contributionsmentioning

confidence: 99%

Information and Self-Organization

Haken

Portugali

2016

Entropy

115

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The process of "self-organization" takes place in open and complex systems that acquire spatio-temporal or functional structures without specific ordering instructions from the outside. In domains such as physics, chemistry or biology, the phrase, "far from equilibrium", refers to systems that are "far from thermal equilibrium", while in other disciplines, the term refers to the property of being "away from the resting state". Such systems are "complex" in the sense that they are composed of many interacting components, parts, elements, etc., and "open" in the sense that they exchange with their environment matter, energy, and information. Here, "information" may imply Shannon information [1], as a measure of the capacity of a channel through which a message passes, pragmatic information, as the impact of a message on recipients, or semantic information, as the meaning conveyed by a message.An attempt to bring these lines of thought together was made by Hermann Haken in his 1988 book Information and Self-Organization [2]. In the meantime, a number of authors have studied the interplay between information and self-organization in a variety of fields. Though the selection of the relevant authors and topics is surely not complete, we believe that this special issue mirrors the state of these interdisciplinary approaches fairly well. In fact, the various papers of this Special Issue expose the different ways processes of self-organization are linked with the various forms of information. As will be seen below, a study of such links has consequences on a number of research domains, ranging from physics and chemistry, through the life sciences and cognitive science, including human behavior and action, to our understanding of society, economics, and the dynamics of cities and urbanization.As will be seen below, the contributions to this Special Issue shed light on the various facets of information and self-organization. And since these various facets do not lend themselves to a topic-oriented order, and since a reader may prefer one over another, we present the papers in an alphabetic order that follows the family name of the first author of each article. The ContributionsA central theme in the theories of complexity is the self-organized bottom-up transition from the local micro-scale of a system's elementary parts to the global macro-scale of the system as a whole. In a way, the various theories of complexity differ in their conceptualization of this scale-dependent transition. Harald Atmanspacher [3] approaches this issue from the perspective of his notions of contextual emergence and the associated process of partitioning; both notions are related to the property that complex systems are open in the sense that they exchange matter, energy and information with

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Self-Organization with Constraints—A Mathematical Model for Functional Differentiation

Cited by 10 publications

References 43 publications

Interactive Sonification Exploring Emergent Behavior Applying Models for Biological Information and Listening

Interactive Sonification Exploring Emergent Behavior Applying Models for Biological Information and Listening

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

Information and Self-Organization

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