Download - THE MANDALA OF THE MIND
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Network Architecture of the Long-Distance Pathways in the Macaque Brain
Modha, D. S. & Singh, R. (July 12, 2010) Proc. Natl. Acad. Sci. USA, 10.1073/pnas.1008054107
Dharmendra S ModhaIBM Research – Almaden
Raghavendra Singh IBM Research – India
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Consensus dendrogram of a network of speciesClauset, Moore, Newman, Nature, 2008
Topological modules in E. coli metabolismRavasz, Somera, Mongru, Oltvai, Barabasi
Science, 2002
Cartographic representation of the metabolic network of E. Coli
Guimera, Amaral, Nature 2005Map of protein–protein interactions
Jeong, Mason, Barabasi, Oltvai, Nature 2001
Networks are Everywhere
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The human brain is the most complex mass of protoplasm on earth-perhaps even in our galaxy.
Marian C. Diamond, Arnold B. Scheibel
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Gray and White Matter
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Multiple Scales of The Brain Network Brainbow
Livet et al, Nature 2007 Denk, Seung, et al, 2007
Hagman et al, PLoS Biology 2008
Binzeggar, Douglas, Martin, J. Neurosci. 2004
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Nicolaus Steno, 1669
“white matter is nature’s finest masterpiece”
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CoCoMac
413 literature reports
7007 brain sites
8003 mapping details
2508 tracer injections
39748 connection details
Rolf Kotter, Klass Stephen, 2000
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Divergent Nomenclature and Abundant Conflicts
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Occipital Lobe: 23 Brain Regions
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Temporal Lobe: 88 Brain Regions
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Insula & Cingulate Cortex: 12 & 18 Brain Regions
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Parietal Lobe: 41 Brain Regions
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Frontal Lobe: 81 Brain Regions
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Thalamus: 75 Brain Regions
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Basal Ganglia: 41 Brain Regions
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383 Brain Regions
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1 connection
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6,602 Connections
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Bundling Algorithm by Holten, 2006
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Species Study Brain Regions
Connections
Monkey Felleman, Van Essen, 91 32 305
Young, 93 70 700
Kaiser, Hilgetag, 06 95 2,402
Cat Scannell et al., 95 65 1,139
Scannell et al., 99 95 1,500
Notable Collations
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Species Study Brain Regions
Connections
Monkey Felleman, Van Essen, 91 32 305
Young, 93 70 700
Kaiser, Hilgetag, 06 95 2,402
Cat Scannell et al., 95 65 1,139
Scannell et al., 99 95 1,500
Monkey This Collection 383 6,602
Notable Collations
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Kaiser, Hilgetag, 2006
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Felleman, Van Essen, 1991
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Ungerleider, Mishkin, 1982
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Arcuate Fasciculus
Schmahmann & Pandya, 2006
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Cingulum BundleSchmahmann & Pandya, 2006
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Extreme CapsuleSchmahmann & Pandya, 2006
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Fronto-occipital Fasciculus
Schmahmann & Pandya, 2006
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Inferior Longitudinal Fasciculus
Schmahmann & Pandya, 2006
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Middle Longitudinal Fasciculus
Schmahmann & Pandya, 2006
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Superior Longitudinal FasciculusSchmahmann & Pandya, 2006
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Uncinate Fasciculus
Schmahmann & Pandya, 2006
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Connectivity between Cortex and Thalamus
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Connectivity between Cortex and Amygdala
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Connectivity between Cortex and Striatum/Claustrum
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Connectivity between Amygdala and Diencephalon
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Comprehensive Includes every study in CoCoMac
Consistent Every connection can be tracked back
Concise 6,877 areas to 383
Coherent Unified hierarchical parcellation
Colossal 3 times larger than previous network
C, C, C, C, and C
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Brain is small-world
Brain Random(100 trials)
Diameter 6 3.93
Characteristic Path Length 2.62 2.30
Average Clustering Coefficient 0.33 0.0528
Reciprocity 42% 5.34%
SCC: 351 brain regions, 6,491 projections; Sparse: 4.5%
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DiE BG OC#2 Pl#6 TL#2 FL#2 CgG#2 InsulaDiE 10 10 37 160 105 600 25 26BG 37 186 8 8 140 95 14 24OC#2 61 16 77 53 77 46 6 0Pl#6 103 47 38 178 83 251 55 21TL#2 92 172 60 99 684 388 70 28FL#2 197 145 12 178 238 695 151 32CgG#2 37 22 0 48 63 202 39 10Insula 15 44 0 41 78 101 13 14#Areas 75 41 23 41 88 81 18 12In-Degree (avg) 8.5 15.83 11.09 20.67 17.67 30.16 21.94 14.27Out-Degree (avg) 14.16 14.25 15.85 20.45 19.16 20.71 24.64 27.45
“Organized Complexity” – Weaver, 1948
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Degree Distribution Consistent with Exponential
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302 Neuron Network in C. Elegans is Exponential
Watts and Strogatz; Amaral et al, 2000
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Characteristic Rank 1 2 3 4 5 6 7 8 9 10
Integrator In-Degree 32 46 12o 12l 11 24 F7 14 8A LIP
In-Closeness 46 12o 32,11 24 12l MD 8A 23c 8B LIP,F7
Authorities 32 12o 46 11 12l 24 14 F7 MD 9
Distributor Out-Degree 46 24 TF 9 13 13a TH TE,LIP PGm V2
Out-Closeness 46 24 TF TE 9 TH LIP PGm 45,23 12
Hubs 46 24 9 TF TE TH 13 32 23 PM#3
Intermediary Betweeness 24 46 LIP 13a MD 32 TF PIT 13 PS
PageRank 32 MD 46 36r PIT 12o 24 23c 12l 11
Metrics for Topologically Centrality
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Characteristic Rank 1 2 3 4 5 6 7 8 9 10
Integrator In-Degree 32 46 12o 12l 11 24 F7 14 8A LIP
In-Closeness 46 12o 32,11 24 12l MD 8A 23c 8B LIP,F7
Authorities 32 12o 46 11 12l 24 14 F7 MD 9
Distributor Out-Degree 46 24 TF 9 13 13a TH TE,LIP PGm V2
Out-Closeness 46 24 TF TE 9 TH LIP PGm 45,23 12
Hubs 46 24 9 TF TE TH 13 32 23 PM#3
Intermediary Betweeness 24 46 LIP 13a MD 32 TF PIT 13 PS
PageRank 32 MD 46 36r PIT 12o 24 23c 12l 11
Prefrontal Cortex is Topologically Central
Yellow = PfC
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Brain is small-world, Core is “tiny”-world!
Brain Core
Diameter 6 4
Characteristic Path Lengh 2.62 1.95
Average Clustering Coefficient 0.33 0.39
Core contains only 32% of vertices yet 88% of all edges originate or terminate in the core
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Core contains correlated-anti-correlated networksand may be a key to higher cognition & consciousness
Fox, Snyder, Vincent, Corbetta, Van Essen, and Raichle, 2005
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Rachel Jones, Nature Rev. Neurosci., 2002
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Sherbondy, Ananthanrayanan, Dougherty, Wandell, and Modha, HBM, 2009
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Binzegger, Douglas, Martin, J. Neurosci., 2004
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