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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