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Schemas01:42

Schemas

A schema is a mental construct consisting of a cluster or collection of related concepts (Bartlett, 1932). There are many different types of schemata, and they all have one thing in common: schemata are a method of organizing information that allows the brain to work more efficiently. When a schema is activated, the brain makes immediate assumptions about the person or object being observed.
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Related Experiment Video

Updated: Jul 11, 2026

Rodent Brain Microinjection to Study Molecular Substrates of Motivated Behavior
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Rodent Brain Microinjection to Study Molecular Substrates of Motivated Behavior

Published on: September 16, 2015

Abstract heterarchy: time/state-scale re-entrant form.

Yukio-Pegio Gunji1, Kazauto Sasai, Sohei Wakisaka

  • 1Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada Kobe 657-8501, Japan. yukio@kobe-u.ac.jp

Bio Systems
|September 28, 2007
PubMed
Summary

This study defines heterarchies as dynamical systems with self-reference and frame problems. Coupling these properties reveals a discontinuous, self-similar map exhibiting robust and emergent behaviors.

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Area of Science:

  • Complex Systems
  • Dynamical Systems Theory
  • Theoretical Computer Science

Background:

  • Heterarchies are dynamical hierarchical systems with inherent logical inconsistencies.
  • Formalizing heterarchies as dynamical systems is challenging due to these inconsistencies.

Purpose of the Study:

  • To propose a formal definition for the essence of a heterarchy.
  • To model the interaction between self-reference and the frame problem in dynamical systems.

Main Methods:

  • Defined self-reference and frame problem using logical operations.
  • Replaced these properties with temporal dynamics and state-scale dynamics derived from a "liar statement".
  • Coupled a modified tent map (temporal dynamics) with a tent map (state-scale dynamics).

Main Results:

  • Developed a discontinuous, self-similar map representing the coupled dynamical system.
  • Demonstrated that both state-scale and temporal dynamics contribute to the system's behavior.
  • Observed both robust and emergent behaviors within the modeled heterarchy.

Conclusions:

  • The proposed model successfully captures the essence of heterarchy.
  • The interaction of self-reference and frame problem leads to complex dynamical behaviors.
  • This framework provides a new perspective on understanding and formalizing heterarchical systems.