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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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Space Trusses: Problem Solving01:29

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A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
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Transfer Function to State Space01:23

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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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State Space to Transfer Function01:21

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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
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Dynamics and development in number-to-space mapping.

Dan Kim1, John E Opfer1

  • 1The Ohio State University, 255 Psychology Building, Columbus, OH 43210, USA.

Cognitive Psychology
|November 16, 2018
PubMed
Summary
This summary is machine-generated.

Children’s number estimates are often logarithmic. This study suggests number estimation relies on a dynamic mechanism, not solely innate logarithmic encoding, with sequential effects influencing linearity in adults.

Keywords:
Cognitive developmentLogarithmic compressionNumber-line estimationNumber-to-space mapping

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Area of Science:

  • Cognitive psychology
  • Developmental psychology
  • Numerical cognition

Background:

  • Young children's numerical magnitude estimates approximate a logarithmic function.
  • This logarithmic scaling is conventionally attributed to an innate number representation.
  • Recent research suggests dynamic encoding, influenced by prior stimuli, may explain these estimates.

Purpose of the Study:

  • To test a dynamic model of numerical magnitude estimation (D-MLLM).
  • To investigate the role of sequential effects in number-line estimation.
  • To differentiate between innate logarithmic encoding and dynamic encoding mechanisms.

Main Methods:

  • Examined trial-to-trial changes in the logarithmicity of numerosity estimates.
  • Tested the D-MLLM model in adults across four studies and in children in one study.
  • Analyzed the influence of previous numerical stimuli on current estimates.

Main Results:

  • First-trial numerosity estimates in both adults and children were strongly logarithmic, independent of prior stimuli.
  • Previous trial magnitudes influenced adult estimates, but this effect aligned with the D-MLLM's predicted logarithmic-to-linear shift.
  • Evidence supports a dynamic encoding mechanism sensitive to sequential effects.

Conclusions:

  • A dynamic encoding mechanism is not essential for compressive numerical mapping.
  • Sequential effects on response scaling can contribute to linearity in adult numerosity estimation.
  • The findings challenge the interpretation of innate logarithmic number encoding.