Lecture 1: Neurons Lecture 2: Coding with spikes Lecture 3: Tuning - - PowerPoint PPT Presentation

Lecture 1: Neurons Lecture 2: Coding with spikes Lecture 3: Tuning curves and receptive fields Lecture 4: Population vectors To gain a basic understanding of how population vectors are constructed

4 credit students: First assignment is posted. You have one week to work on

• it. You can work in groups as long as all contribute and each

student submits its own write up. There will be a doodle-poll link posted to schedule meetings to talk about the assignment. Please fill in your available times as soon as possible.

180o right 90o up 0o left 

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Firing frequency Movement angle “Best” angle for a given cell (angle smax that elicits maximal response rmax)

Vectors

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Firing frequency Movement angle 20 15 10 5 s0 s1 s2 s3 s4 smax = 135o 90o x y 0o 180o 10 Hz 135o

s3

90o x y 0o 180o 10 Hz 135o

s2

90o x y 0o 180o 10 Hz 135o

s4

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Firing frequency

N1 N2 N3 N4 N5 smax(N1) = 40o smax(N2) = 110o smax(N3) = 135o smax(N4) = 180o smax(N5) = 230o s1 s3 s2 10 90o x y 0o 180o N1 N2 N3 N4 N5 90o x y 0o 180o N2 N3 90o x y 0o 180o N2 N3 N2+N3

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Firing frequency

N1 N2 N3 N4 N5 smax(N1) = 40o smax(N2) = 110o smax(N3) = 135o smax(N4) = 180o smax(N5) = 230o s1 s3 s2 10 90o x y 0o 180o N2 N3 90o x y 0o 180o N2

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Firing frequency

N1 N2 N3 N4 N5 s1 s3 s2 10

Exercise: You recorded from three neurons during a monkey’s movement. You have approximated each response curve with a cosine function. Each neuron’s response is normalized to its OWN maximal response.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

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Movement angle Normalized firing rate A B C

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

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Movement angle Normalized firing rate A B C

You now use your recordings to predict what the monkey is going to do. The numbers I will give you will be in normalized firing rate. You record the following: A = 1.0, B = 0.0, C = 0.0. What is the best estimate for the angle of movement?

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

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Movement angle Normalized firing rate A B C

You record A = 0.9, B = 0.6. Use three different methods to estimate the angle of the movement from these numbers. Discuss which is best and why.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

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Movement angle Normalized firing rate A B C

You record A=0, B = 0.6 and C = 0. What is your best estimate? How accurate do you think this could be?

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 20 40 60 80 100 120 140

Movement angle Normalized firing rate A B C

You notice that all your predictions are off by several degrees. State several reasons why this could be the case. How well would a labeled line vs population code decoding strategy work in this case? What would happen if you could increase the number of neurons by 100 fold?

R G B Yellow light ~ 590 nm nm

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Deuteranomaly, caused by a similar shift in the green retinal receptors, is by far the most common type of color vision deficiency, mildly affecting red–green hue discrimination in 5% of males. It is hereditary and sex-linked.

R G B Yellow light ~ 590 nm nm

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nm

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R G B

angle is close

R G B Red light ~ 625 nm nm

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nm

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R G B

Angle is changed, color perception changes

• J. E. Lewis

Sensory processing and the network mechanisms for reading neuronal population codes

a, Schematic of the local bend network that processes the location S of a touch stimulus to produce a bend directed away from the touch. The network is contained in a single segmental ganglion of the leech nervous system. There are three layers of neurons in the network. The number of neurons at sensory and motor levels is indicated by the number of circles. The exact number of interneurons is not known, although 17 have been identified so far8. b, The tuning properties of the mechanosensory P neurons to stimulus location. Shown are curves fitted to data described in Lewis9 and given by Pi(S) = F(cos(S - Pi

*)) where S is the stimulus location, Pi(S) is the

normalized spike count, F(x) = 0 for x 0 and F(x) = x for x >

• 0. The perimeter of the cross-sectional body wall is roughly
• circular. We define a location = 0° as the dorsal midline, =

180° = -180° as the ventral midline and = -90° and = 90° as the left and right lateral midlines, respectively. c, To emphasize the directionality of the neural responses and to allow comparison with the behavioural responses discussed later, the same P neuron tuning curves are expressed in a polar coordinate system. The Pi

*are the stimulus locations where the

peak response occurs (that is, preferred locations). Pi

* =

(45°,135°,-135°,-45°) for i = (1,...,4).

In all panels, solid lines drawn in the polar coordinate system are unit vectors (directed toward the

• rigin) corresponding to the bend direction. Dotted lines correspond to the mean bend direction. a,

The responses to a touch stimulus at S = 45° (denoted by the arrow). b, The responses to intracellular current injection in the P2 neuron (denoted by the icon). c, The responses elicited by simultaneous delivery of both stimuli. The data shown are from 15–16 trials in four animals.

a, Summary of the errors produced by the model for different numbers of interneurons (NI) and noise levels, k. Also shown for reference are the experimentally measured behavioural error (dotted line) and the P neuron decoding error (solid line). The filled circles show the results for zero noise level (k = 0). b, The minimum number of interneurons (NI) required so that the model is more accurate than the experimentally observed

• behaviour. Minimum NI increases

almost linearly with the noise level. c, The responses of the model (NI = 16) for 20 trials at a stimulus location

• f S = 90° (compare with Fig. 2c).