Download presentation

Presentation is loading. Please wait.

Published byMohammad Bramlett Modified over 4 years ago

1
Sensorimotor Transformations Maurice J. Chacron and Kathleen E. Cullen

2
Outline Lecture 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).

3
Outline Lecture 2: - Nonlinear sensorimotor transformations - Static nonlinearities - Dynamic nonlinearities

4
Lecture 1 Sensorimotor 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

5
Examples of sensorimotor transformations -Vestibulo-occular reflex -Reaching towards a visual target, etc…

6
Example: Refuge tracking in weakly electric fish

7
Refuge tracking

8
Sensory input Motor output Error

9
Results (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 output

10
Linear systems identification techniques

11
Linear functions What is a linear function? So, a linear system must obey the following definition:

12
Linear functions (continued) This implies the following: a stimulus at frequency f 1 can only cause a response at frequency f 1

13
Linear transformations assume output is a convolution of the input with a kernel T(t) with additive noise. We’ll also assume that all terms are zero mean. -Convolution is the most general linear transformation that can be done to a signal

14
An example of linear coding: Rate modulated Poisson process time time dependent firing rate

15
Linear Coding: Example: Recording from a P-type Electroreceptor afferent. There is a linear relationship between Input and output Gussin et al. 2007 J. Neurophysiol.

16
Instantaneous input-output transfer function:

17
Fourier decomposition and transfer functions - Fourier Theorem: Any “smooth” signal can be decomposed as a sum of sinewaves -Since we are dealing with linear transformations, it is sufficient to understand the nature of linear transformations for a sinewave

18
Linear transformations of a sinewave Scaling (i.e. multiplying by a non-zero constant) Shifting in time (i.e. adding a phase)

19
Cross-Correlation Function For stationary processes: In general,

20
Cross-Spectrum Fourier Transform of the Cross-correlation function Complex number in general a: real part b: imaginary part

21
Representing the cross-spectrum: : amplitude : phase

22
Transfer functions (Linear Systems Identification) assume output is a convolution of the input with a kernel T(t) with additive noise. We’ll also assume that all terms are zero mean. Transfer function

23
Calculating the transfer function multiply by: and average over noise realizations =0

24
Gain and phase:

25
Sinusoidal stimulation at different frequencies Stimulus Response 20 msec

26
Gain

27
Combining transfer functions input output

28
Where transfer functions fail…

29
Vestibular system Cullen and Sadeghi, 2008

30
Example: vestibular afferents CV=0.044CV=0.35

31
` Regular afferent Firing rate (spk/s) Head velocity (deg/s) 120 100 80 60 40 20 0 -20 -40

32
` Irregular afferent Firing rate (spk/s) Head velocity (deg/s) 160 140 120 100 80 60 40 -20 -40 20 0

33
Signal-to-noise Ratio:

34
Borst and Theunissen, 1999

35
Using transfer functions to characterize and model refuge tracking in weakly electric fish Sensory input Motor output Error

36
Characterizing the sensorimotor transformation 1 st order 2 nd order

37
Modeling refuge tracking using transfer functions sensory input sensory processing motor processing motor output

38
Modeling refuge tracking using transfer functions sensory input sensory processing motor output Newton

39
Simulink demos

40
Mechanics constrain neural processing

41
Summary Some 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.

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google