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The dot product is an essential concept in mathematics and physics.
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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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The filled-space illusion induced by a single-dot distractor.

Aleksandr Bulatov1, Vilius Marma2, Natalija Bulatova3

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Our computational model accurately predicts the filled-space illusion magnitude with single-dot distractors. The model

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Area of Science:

  • Visual perception
  • Computational modeling
  • Psychophysics

Background:

  • The filled-space illusion, where a line segment appears longer when filled with elements, is a well-documented phenomenon.
  • Understanding the underlying mechanisms of this illusion is crucial for visual science.

Purpose of the Study:

  • To validate a computational model of the filled-space illusion using experimental data.
  • To investigate the influence of distractor dot placement on the filled-space illusion.

Main Methods:

  • Experimental manipulation of distractor dot positions relative to a spatial interval.
  • Psychophysical testing of the Oppel-Kundt stimulus with varying numbers of dots.
  • Comparison of computational model predictions with empirical data.

Main Results:

  • The computational model successfully predicted the magnitude of the filled-space illusion across various distractor configurations.
  • Model predictions aligned with experimental findings for single and multiple distractor dots.
  • Adequate correspondence was found between computational and experimental data for the Oppel-Kundt stimulus.

Conclusions:

  • The study supports the proposed assumptions regarding the origin of the filled-space illusion.
  • The validated computational model provides a robust framework for understanding this visual illusion.