Download Two Views of Cortex

Two Views of Cortex
Lichtman & Sanes
S1
S2
V1
V2
A1
MT
Krubitzer & Kaas
More cortex = smarter?
Krubitzer & Kaas
S1
S2
V1
V2
A1
MT
Total surface area of the cerebral cortex (human) = 2,500 cm2 (“a large dinner napkin”, 20” x 20”)
(2.5 ft2; A. Peters, and E.G. Jones, Cerebral Cortex, 1984)
Total surface area of the cerebral cortex (lesser shrew) = 0.8 cm2
Total surface area of the cerebral cortex (rat) = 6 cm2 (“postage stamp”)
Total surface area of the cerebral cortex (cat) = 83 cm2
Total surface area of the cerebral cortex (monkey) = 225 cm2 (“two CDs”, ea. diam. 12 cm)
Total surface area of the cerebral cortex (African elephant) = 6,300 cm2
Total surface area of the cerebral cortex (Bottlenosed dolphin) = 3,745 cm2
(S.H. Ridgway, The Cetacean Central Nervous System, p. 221)
Total surface area of the cerebral cortex (pilot whale) = 5,800 cm2
Total surface area of the cerebral cortex (killer whale) = 7,400 cm2 (2.8x2.8 ft.)
(Reference for surface area figures: Nieuwenhuys, R., Ten Donkelaar, H.J. and Nicholson, C., The
Central nervous System of Vertebrates, Vol. 3, Berlin: Springer, 1998)
Total number of neurons in cerebral cortex = 10 billion (from G.M. Shepherd, The Synaptic
Organization of the Brain, 1998, p. 6). However, C. Koch lists the total number of neurons in the
cerebral cortex at 20 billion (Biophysics of Computation. Information Processing in Single Neurons,
New York: Oxford Univ. Press, 1999, page 87).
Total number of synapses in cerebral cortex = 60 trillion (yes, trillion) (from G.M. Shepherd, The
Synaptic Organization of the Brain, 1998, p. 6). However, C. Koch lists the total synapses in the
cerebral cortex at 240 trillion (Biophysics of Computation. Information Processing in Single Neurons,
New York: Oxford Univ. Press, 1999, page 87).
Uniformity of Cortex I: Numbers
30 μm
pia
white matter
Mouse
Rat
Cat
Monkey
Man
Motor
109.2 ± 6.7
108.2 ±5.8
103.9 ±7.6
110.2 ±9.4
102.3 ±9.5
mean ± s.d.
Somatosensory
111.9 ±6.9
107.0 ±6.7
106.6 ±7.2
109.4 ±9.4
103.7 ±5.8
Frontal
110.8 ±7.1
104.3 ±7.2
108.0 ±6.2
112.0 ±11.1
103.3 ±8.6
Temporal
110.5 ±6.5
107.7 ±9.2
113.8 ±7.3
109.8 ±10.3
107.7 ±7.5
Parietal
104.7 ±7.2
105.2 ±6.8
110.6 ±7.4
114.6 ±9.9
104.1 ±12.5
Visual
112.2 ±6.0
107.8 ±7.9
109.8 ±9.9
267.9 ±13.7
258.9 ±15.8
Mean of
means
109.9 ±6.8
106.7 ±7.4
108.8 ±7.7
-------
Rockel AJ, Hiorns RW & Powell TP (1980) “The basic uniformity in structure of
the neocortex,” Brain 103:221-44.
Uniformity of Cortex II: Modules
2
3
1
receptive fields
0
Hubel & Wiesel 1974
0
1
2
3 mm
cortex
visual field
45º
22º
.
0º
Hubel 1982
7º
10º
45º
Uniformity of Cortex II: Modules
Hubel & Wiesel
2 mm
Uniformity of Cortex II: Modules
“Thus the machinery may be roughly uniform over the
whole striate cortex, the differences being in the inputs. A
given region of cortex simply digests what is brought to it,
and the process is the same everywhere. . . . It may be that
there is a great developmental advantage in designing
such a machinery once only, and repeating it over and over
monotonously, like a crystal, for all parts of the visual field.”
Hubel & Wiesel (1974) “Uniformity of Monkey Striate
Cortex: A Parallel Relationship between Field Size,
Scatter, and Magnification Factor”, J. Comp. Neurol.
158:295-306.
“Hypercolumn”
~2 mm
~2 mm
~2 mm
Uniformity of Cortex III: Developmental multi-potentiality
Re-routing experiments (ferret)
visual
lab of Mriganka Sur
auditory
Uniformity of Cortex III: Developmental multi-potentiality
5 mm
1 mm
Roe et al. 1990
Uniformity of Cortex III: Developmental multi-potentiality
Sur et al. 1988
Scaling laws
10,000
porpoise
modern
human
Brain weight (grams)
1,000
blue
whale
elephant
E = 0.07 ∗ P2/3
100
crow
alligator
10
1 hummingbird
0.1
0.001
Primates
Bony Fish
Mammals
Reptiles
Birds
eel
goldfish
0.01
0.1
1
10
100
1,000
10,000
100,000
Body weight (Kilograms)
Crile & Quiring
What can you do with more cortex?
Van Essen et al. 1984
2º
1 cm
Tootell et al. 1982
Half of area V1 represents the central 10º (2% of the visual field)
See better?
Duncan & Boynton 2003
Two tests of visual actuity
low
grating acuity
vernier acuity
contrast
high
low
spatial frequency
high
Acuity scales with cortical magnification factor.
Duncan & Boynton 2003
Subjects with larger cortical
magnification factors have
better vernier acuity.
vernier acuity
grating acuity
Duncan & Boynton 2003
What can you do with more cortex?
?
Krubitzer & Kaas
S1
S2
V1
V2
A1
MT
More areas = more maps
Lateral view of monkey brain
Medial view of monkey brain
Felleman and Van Essen 1991
Cortex unfolded
What is the computational goal of the cortex?
"Thus the hypothesis is that the cerebral cortex confers skill in
deriving useful knowledge about the material and social world
from the uncertain evidence of our senses, it stores this
knowledge, and gives access to it when required."
Barlow 1994
What the cortex should do.
Finding New Associations in Sensory Data
1. Remove evidence of associations you
already know about . . .
. . . to facilitate detecting new ones.
(1/f2 and center-surround)
2. Make available the probabilities of the
features currently present . . .
. . . to determine chance expectations.
(-logp, adaptation)
3. Choose features that occur independently
of each other in the normal environment . . .
. . . to determine chance expectations
or combinations of them.
(lateral inhibition)
4. Choose “suspicious coincidences” as
features . . .
. . . to reduce redundancy and ensure
appropriate generalization.
(orientation selectivity)
Barlow 1994
What the cortex should do.
Context:
Stored knowledge
about environment
Previous sense data
Task priorities
Unsatisfied appetites
Model of
current scene
New associative
knowledge
What we
actually
see
Sensory
messages
Compare
and remove
matches
New information
about environment
This cycle can be repeated
Barlow 1994, fig. 1.3
Schematic of a Kalman Filter
Measurement Update (“Correct”)
Time Update (“Predict”)
(1)
(2)
)
and P
k −1
k −1
Initial estimates for x
Welch & Bishop, fig. 1.2
(3)
−1
Update estimate with measurement zk
)
)
)
x = x − + K ⎛⎜ z k − Hx − ⎞⎟
k
k
k⎝
k⎠
Project the error covariance ahead
P − = AP
AT + Q
k
k −1
Compute the Kalman gain
K = P − H T ⎛⎜ HP − H T + R ⎞⎟
k
k
⎝ k
⎠
Project the state ahead
)
)
+ Bu
x − = Ax
k
k −1
k −1
(2)
(1)
Update the error covariance
P = ⎛⎜1 − K H ⎞⎟ P −
k ⎝
k ⎠ k
Neighboring pixels tend to have similar values
Simoncelli & Olshausen 2001
Neighboring pixels tend to have similar values
natural image
1/f 2
Simoncelli & Olshausen 2001
“Whitened”: ∇2⋅G or what ctr-sur does
Sophie in the Arctic
8
3
10
10
2
6
10
Energy
Energy
10
4
0
2
10
10
-1
0
10 0
10
1
10
10
1
10
2
10
Spatial frequency (cycles/image)
3
10
10
0
10
1
10
2
10
3
10
Spatial frequency (cycles/image)
barlow_filt3.m
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
Reward?
Yes
Yes
Yellow
Volkswagen?
No
Harris 1980
No
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
sparse
“yellow
Volkswagen”
cell
dense
YV
“combinatorial explosion”
Harris 1980
“red
Ferrari”
cell
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
sparse
“yellow”
cell
dense
Y
V
Harris 1980
“Volkswagen”
cell
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
Yes
Yellow?
No
Harris 1980
Reward?
Reward?
Yes
Yes
No
Yes
Volkswagen?
No
No
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
sparse
dense
g
n
“y”
cell
k
e
s
y
“v”
cell
v
o
l
a
w
Harris 1980
How sparse?
Y
V
The curve shows how statistical efficiency for detecting associations with a feature X varies with the
value of a parameter defined as follows:
“sparseness”
Γx=αxpxZ / 〈α〉
where αx , 〈α〉 are the activity ratio for feature X and the average activity ratio, px is the probability of
X, and Z is the number of neurons in the subset under consideration. For instance, one could
identify an association with any one of the 45 possible pairs of active neurons in a subset of
10 with an efficiency of 50% provided that the neurons were active independently, the pair
caused two neurons to be active, the probability of the pair occurring was 0.1, and the
average fraction active was 0.2. (From Gardner-Medwin and Barlow 1994)
Gardner-Medwin & Barlow 2001
What are the desirable properties of
directly represented features?
“. . . primitive conjunctions of active elements that
actually occur often, but would be expected to occur
only infrequently by chance,” that is,
“suspicious coincidences”
Gardner-Medwin & Barlow 2001
“Whitened”: ∇2⋅G or what ctr-sur does
Sophie in the Arctic
Suspicious Coincidences
6
log10(#)
Random
4
2
0
2
3
4
5
6
7
8
log10(#)
6
Line
4
p < 0.0100
2
0
2
3
4
5
6
sum of 9 pixels
7
8
barlow_filt3.m
How do these areas consitute maps?
Intermission?
Lateral view of monkey brain
Medial view of monkey brain
Felleman and Van Essen 1991
Cortex unfolded
The perfect map?
A more useful map
11
12
13
K
L
T
T
M
Streets
Aberdeen Rd …….….C7
Academy St …….…...D9
Acorn Pk ……….…....F9
Acton St ……….…….C7
Adamian Pk …....……C9
Adams St ……….…...D9
Addison St ……..……D9
Aerial St ……….…....C8
Albermarle St ….……D8
Alfred Rd …………....E9
Allen St ……………...D9
Alpine St ………...…..C7
.
.
.
.
.
.
.
.
.
.
.
.
.
Longwood Ave …….L12
MBTA map
Linking Features: Orientation
Guzmann 1968
Striate cortex contains a map of
orientation.
“Hypercolumn”
after Hubel & Wiesel 1962
“Space”
Tootell et al. 1982
“Feature”
Intrinsic connectivity of V1 is not random.
Bosking et al. 1997
Mapping of visual space on to cortical space in V1
Tootell et al. 1982
Guzman’s linking via intrinsic connectivity in V1
Guzmann 1968
Efficient representations via hierarchical processing
gain adjustment
(1024 * 768)pixels * 24 bits/pixel = 18,874,368 bits
edge detection
invariance
a) position
b) sign of contrast
curvature
38 points * 2 words/point * 16 bits/word = 1,216 bits
compression ratio = 15,522
How do we build a bigger cortex?
Development of the mouse cortex: 11 cell cycles
Takahashi, Nowakowski & Caviness 1996
Development by the numbers
Q1
Q1
+
(P1∗2)∗Q2
+
(((P1∗2)∗P2)∗2)∗Q3
Q1
+
(P1∗2)∗Q2
Cumulative
Output
(((P1∗2)∗P2)∗2)∗Q3
(P1∗2)∗Q2
mitosis
Q1
PVE Size
1
P1
P1∗2
CC #1
Takahashi, Nowakowski & Caviness 1996
(P1∗2)∗P2
CC #2
((P1∗2)∗P2)∗2
(((P1∗2)∗P2)∗2)∗P3
CC #3
Q is a critical determinant of cortical size
150
1
PVE volume
#
0.8
Q
PVE output
Cumulative output
100
0.6
0.4
50
0.2
0
0
E11
1
2
3
4
5
6
7
8
Elapsed Cell Cycles
E12
E13
E14
E15
9
10 11
0
0
2
4
6
8
10
12
Elapsed Cell Cycles
E16
E17
Takahashi, Nowakowski & Caviness 1996
neuronogenetic.m
Experimental manipulation of Q
increased
mitotic rate?
NO
decreased
apoptosis?
NO
1 mm
decreased Q?
YES
2 mm
Chenn & Walsh 2002
Divvying up the cortical sheet and making “new” areas
Grove & Fukuchi-Shimogori 2001
Divvying up the cortical sheet: role of Emx2
gain of function
(S1 smaller and
shifted rostral and
lateral)
loss of function
(S1 larger and
shifted caudal and
medial)
Hamasaki et al. 2004