Sensorimotor Transformations
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Transcript of Sensorimotor Transformations
Sensorimotor Transformations
Sensorimotor TransformationsMaurice J. Chacron and Kathleen E. CullenOutlineLecture 1: - Introduction to sensorimotor transformations - The case of linear sensorimotor transformations: refuge tracking in electric fish - introduction to linear systems identification techniques
- Example of sensorimotor transformations: Vestibular processing, the vestibulo-occular reflex (VOR). OutlineLecture 2: - Nonlinear sensorimotor transformations - Static nonlinearities - Dynamic nonlinearitiesLecture 1Sensorimotor transformation:
if we denote the sensory input as a vector S and the motor command as M, a sensorimotor transformation is a mapping from S to M : M =f(S)Where f is typically a nonlinear function
Examples of sensorimotor transformationsVestibulo-occular reflex
Reaching towards a visual target, etc
Example: Refuge tracking in weakly electric fish
Refuge tracking
Refuge tracking
Sensory inputMotor outputError8Results
(Cowan and Fortune, 2007)Tracking performance is best when the refuge moves slowly
Tracking performance degrades when the refuge moves at higher speeds
There is a linear relationship between sensory input and motor outputLinear systems identification techniquesLinear functionsWhat is a linear function?
So, a linear system must obey the following definition:
Linear functions (continued)This implies the following:
a stimulus at frequency f1 can only cause a response at frequency f1 Linear transformations
assume output is a convolutionof the input with a kernel T(t) withadditive noise. Well also assume that allterms are zero mean. Convolution is the most general linear transformation that can be done to a signal
An example of linear coding:Rate modulated Poisson processtime
time dependent firing rateLinear Coding:
Example:
Recording from a P-typeElectroreceptor afferent.
There is a linear relationship betweenInput and outputGussin et al. 2007 J. Neurophysiol.
Instantaneous input-output transfer function:Fourier decomposition and transfer functions- Fourier Theorem: Any smooth signal can be decomposed as a sum of sinewavesSince we are dealing with linear transformations, it is sufficient to understand the nature of linear transformations for a sinewaveLinear transformations of a sinewaveScaling (i.e. multiplying by a non-zero constant)
Shifting in time (i.e. adding a phase)
Cross-Correlation Function
For stationary processes:
In general,Cross-SpectrumFourier Transform of the Cross-correlation function
Complex number in general
a: real partb: imaginary partRepresenting the cross-spectrum:
: amplitude
: phaseTransfer functions (Linear Systems Identification)
assume output is a convolutionof the input with a kernel T(t) withadditive noise. Well also assume that allterms are zero mean.
Transfer functionCalculating the transfer function
multiply by:
and average over noise realizations
=0
Gain and phase:
Sinusoidal stimulationat different frequencies
StimulusResponse20 msec
GainCombining transfer functionsinput
output
Where transfer functions fail
Vestibular systemCullen and Sadeghi, 2008Example: vestibular afferents
CV=0.044CV=0.35
`Regular afferentFiring rate(spk/s)Head velocity(deg/s)120100806040200-20-40
`
Irregular afferentFiring rate(spk/s)Head velocity(deg/s)160140120100806040-20-40200Signal-to-noise Ratio:
Borst and Theunissen, 1999Using transfer functions to characterize and model refuge tracking in weakly electric fish
Sensory inputMotor outputErrorCharacterizing the sensorimotor transformation
1st order2nd orderModeling refuge tracking using transfer functionssensory input sensoryprocessing motor processing motor outputModeling refuge tracking using transfer functionssensory input sensoryprocessing motor output
NewtonSimulink demos
Mechanics constrain neural processing
SummarySome sensorimotor transformations can be described by linear systems identification techniques.These techniques have limits (i.e. they do not take variability into account) on top of assuming linearity.