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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 Modha IBM Research – Almaden Raghavendra Singh   IBM Research – India
Consensus dendrogram of a network of species Clauset, Moore, Newman, Nature, 2008 Topological modules in  E. coli  metabolism Ravasz, Somera, Mongru, Oltvai, Barabasi Science, 2002 Cartographic representation of the metabolic network of  E. Coli Guimera, Amaral, Nature 2005 Map of protein–protein interactions Jeong, Mason, Barabasi, Oltvai, Nature 2001 Networks are Everywhere
The human brain is the most complex mass of  protoplasm on earth-perhaps even in our galaxy.   Marian C. Diamond, Arnold B. Scheibel
Gray and White Matter
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
Nicolaus Steno, 1669 “ white matter is nature’s finest masterpiece”
CoCoMac 413 literature reports 7007 brain sites 8003 mapping details 2508 tracer injections 39748 connection details   Rolf Kotter, Klass Stephen, 2000
Divergent Nomenclature and Abundant Conflicts FV91-V1 AP84-TE PG91b-IT BP82-46 SP89a-46 FV91-V4 FV91-TF RV99-TF RV99-CA1 BR98-CA1 FV91-TH BR98-TH = כ כ PFCd 9 = PCi  IPL PF#1  7b = = CCa  24 24d 24c CMAr 24c כ כ = = = = =
 
Occipital Lobe: 23 Brain Regions
Temporal Lobe: 88 Brain Regions
Insula & Cingulate Cortex: 12 & 18 Brain Regions
Parietal Lobe: 41 Brain Regions
Frontal Lobe: 81 Brain Regions
Thalamus: 75 Brain Regions
Basal Ganglia: 41 Brain Regions
383 Brain Regions
1 connection
6,602 Connections
Bundling Algorithm by Holten, 2006
 
 
 
Notable Collations 1,500 95 Scannell et al., 99 1,139 65 Scannell et al., 95 Cat 2,402 95 Kaiser, Hilgetag, 06 700 70 Young, 93 305 32 Felleman, Van Essen, 91 Monkey Connections Brain Regions Study Species
Notable Collations 1,500 95 Scannell et al., 99 6,602 383 This Collection Monkey 1,139 65 Scannell et al., 95 Cat 2,402 95 Kaiser, Hilgetag, 06 700 70 Young, 93 305 32 Felleman, Van Essen, 91 Monkey Connections Brain Regions Study Species
Kaiser, Hilgetag, 2006
Felleman, Van Essen, 1991
Ungerleider, Mishkin, 1982
 
Arcuate Fasciculus Schmahmann & Pandya, 2006
Cingulum Bundle Schmahmann & Pandya, 2006
Extreme Capsule Schmahmann & Pandya, 2006
Fronto-occipital Fasciculus Schmahmann & Pandya, 2006
Inferior Longitudinal Fasciculus Schmahmann & Pandya, 2006
Middle Longitudinal Fasciculus Schmahmann & Pandya, 2006
Superior Longitudinal Fasciculus Schmahmann & Pandya, 2006
Uncinate Fasciculus Schmahmann & Pandya, 2006
Connectivity between Cortex and Thalamus
Connectivity between Cortex and Amygdala
Connectivity between Cortex and Striatum/Claustrum
Connectivity between Amygdala and Diencephalon
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
Brain is small-world SCC: 351 brain regions, 6,491 projections; Sparse: 4.5% 0.0528 0.33 Average Clustering Coefficient 5.34% 42% Reciprocity 2.30 2.62 Characteristic Path Length 3.93 6 Diameter Random (100 trials) Brain
“ Organized Complexity” – Weaver, 1948 27.45 24.64 20.71 19.16 20.45 15.85 14.25 14.16 Out-Degree  (avg) 14.27 21.94 30.16 17.67 20.67 11.09 15.83 8.5 In-Degree  (avg) 12 18 81 88 41 23 41 75 #Areas 14 13 101 78 41 0 44 15 Insula 10 39 202 63 48 0 22 37 CgG#2 32 151 695 238 178 12 145 197 FL#2 28 70 388 684 99 60 172 92 TL#2 21 55 251 83 178 38 47 103 Pl#6 0 6 46 77 53 77 16 61 OC#2 24 14 95 140 8 8 186 37 BG 26 25 600 105 160 37 10 10 DiE Insula CgG#2 FL#2 TL#2 Pl#6 OC#2 BG DiE
 
 
Degree Distribution Consistent with Exponential
302 Neuron Network in  C. Elegans  is Exponential Watts and Strogatz; Amaral et al, 2000
Metrics for Topologically Centrality 11 12l 23c 24 12o PIT 36r 46 MD 32 PageRank PS 13 PIT TF 32 MD 13a LIP 46 24 Betweeness Intermediary PM#3 23 32 13 TH TE TF 9 24 46 Hubs 12 45,23 PGm LIP TH 9 TE TF 24 46 Out-Closeness V2 PGm TE,LIP TH 13a 13 9 TF 24 46 Out-Degree Distributor 9 MD F7 14 24 12l 11 46 12o 32 Authorities LIP,F7 8B 23c 8A MD 12l 24 32,11 12o 46 In-Closeness LIP 8A 14 F7 24 11 12l 12o 46 32 In-Degree Integrator 10 9 8 7 6 5 4 3 2 1 Rank Characteristic
Prefrontal Cortex is Topologically Central Yellow = PfC 11 12l 23c 24 12o PIT 36r 46 MD 32 PageRank PS 13 PIT TF 32 MD 13a LIP 46 24 Betweeness Intermediary PM#3 23 32 13 TH TE TF 9 24 46 Hubs 12 45,23 PGm LIP TH 9 TE TF 24 46 Out-Closeness V2 PGm TE,LIP TH 13a 13 9 TF 24 46 Out-Degree Distributor 9 MD F7 14 24 12l 11 46 12o 32 Authorities LIP,F7 8B 23c 8A MD 12l 24 32,11 12o 46 In-Closeness LIP 8A 14 F7 24 11 12l 12o 46 32 In-Degree Integrator 10 9 8 7 6 5 4 3 2 1 Rank Characteristic
 
 
Brain is small-world, Core is “tiny”-world! Core contains only 32% of vertices  yet 88% of all edges originate or terminate in the core 0.39 0.33 Average Clustering Coefficient 1.95 2.62 Characteristic Path Lengh 4 6 Diameter Core Brain
Core contains correlated-anti-correlated networks and may be a key to higher cognition & consciousness Fox, Snyder, Vincent, Corbetta, Van Essen, and Raichle, 2005
 
Rachel Jones,  Nature Rev. Neurosci.,   2002
Sherbondy, Ananthanrayanan, Dougherty, Wandell, and Modha, HBM, 2009
Binzegger, Douglas, Martin, J. Neurosci., 2004
 
 

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THE MANDALA OF THE MIND