Equation of motion and general solution for the one-dimensional complex cell response in the signal-tuned approach
A signal-tuned approach has been recently introduced for modeling stimulus-dependent cortical receptive fields. The approach is based on signal-tuned Gabor functions, which are Gaussian-modulated sinusoids whose parameters are obtained from a "tuning" signal. Given a stimulus to a cell, it is taken as the tuning signal for the Gabor function modeling the cell's receptive field, and the inner product of the stimulus and the stimulus-dependent field produces the cell's response. Here, we derive and solve the equation of motion for the signal-tuned complex cell response r(x,τ), where x and τ are receptive-field parameters: its center, and the delay with which it adapts to a change in input. The motion equation can be mapped onto the Schrödinger equation for a system with time-dependent imaginary mass and time-dependent complex potential, and yields a plane-wave solution and an Airy-packet solution. The plane-wave solution replicates responses previously obtained for temporally modulated and translating signals, and yields responses which seem compatible with apparent-motion effects, when the stimulus is a pair of alternating pulses. The Airy-packet solution can lead to long-range propagating responses.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2015 |
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| Erschienen: |
2015 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:109 |
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| Enthalten in: |
Biological cybernetics - 109(2015), 4-5 vom: 17. Okt., Seite 435-52 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Torreão, José R A [VerfasserIn] |
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| Links: |
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| Themen: |
Apparent motion |
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| Anmerkungen: |
Date Completed 15.06.2016 Date Revised 17.09.2015 published: Print-Electronic Citation Status MEDLINE |
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| doi: |
10.1007/s00422-015-0653-7 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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| PPN (Katalog-ID): |
NLM250034557 |
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| 245 | 1 | 0 | |a Equation of motion and general solution for the one-dimensional complex cell response in the signal-tuned approach |
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| 500 | |a Date Completed 15.06.2016 | ||
| 500 | |a Date Revised 17.09.2015 | ||
| 500 | |a published: Print-Electronic | ||
| 500 | |a Citation Status MEDLINE | ||
| 520 | |a A signal-tuned approach has been recently introduced for modeling stimulus-dependent cortical receptive fields. The approach is based on signal-tuned Gabor functions, which are Gaussian-modulated sinusoids whose parameters are obtained from a "tuning" signal. Given a stimulus to a cell, it is taken as the tuning signal for the Gabor function modeling the cell's receptive field, and the inner product of the stimulus and the stimulus-dependent field produces the cell's response. Here, we derive and solve the equation of motion for the signal-tuned complex cell response r(x,τ), where x and τ are receptive-field parameters: its center, and the delay with which it adapts to a change in input. The motion equation can be mapped onto the Schrödinger equation for a system with time-dependent imaginary mass and time-dependent complex potential, and yields a plane-wave solution and an Airy-packet solution. The plane-wave solution replicates responses previously obtained for temporally modulated and translating signals, and yields responses which seem compatible with apparent-motion effects, when the stimulus is a pair of alternating pulses. The Airy-packet solution can lead to long-range propagating responses | ||
| 650 | 4 | |a Journal Article | |
| 650 | 4 | |a Research Support, Non-U.S. Gov't | |
| 650 | 4 | |a Apparent motion | |
| 650 | 4 | |a Complex cells | |
| 650 | 4 | |a Schrödinger equation | |
| 650 | 4 | |a Signal-tuned Gabor approach | |
| 650 | 4 | |a Visual cortex | |
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