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Mental Navigation: Global Measures of Complex Netwroks
Guillermo Cecchi
IBM Research, T.J. Watson Center
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Overview
General motivationThe lexicon networkBrain imaging networks
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Global Measures of Biological Networks
Characterization of global states
Functional mechanisms
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Motivation: Approaches to Quantify Meaning
Reductionist: meaning is molecular, piece-wise, and verificationist. Each linguistic item corresponds to an object in the world. There are
statements, and they can only be true or false. Ex., the moon is blue.
Natural language is "corrupt", fraught with inconsistency and ambiguity.
Ref.: Aristotle, logical positivism.
Holistic: meaning arises as a collective phenomenon within a sentence,
with the whole language and the external world. Ex., in a blue moon.
Natural language is "embodied" and intertwined with the context, ambiguity
is part of the message. Ref.: Quine, Kuhn.
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Good
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Bad
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Knife
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Fork
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Mother
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Father
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Lion Stripes
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Lion Feline Tiger Stripes
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Lion Feline Tiger Stripes
Predator Prey Zebra
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Diffusion in the Semantic Network
Psychophysical evidence of “priming” of related meanings (Quillian, Burguess, Posner)
Imaging evidence for spread of activation to the neural representation of related meanings (Damasio, Ungerleider).
Fast and unconscious spread of activation (Dehaene).
Mental and neural navigation (Spitzer).
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Wordnet: Building Sets of Meanings Wordnet attempts to characterize the set of linguistic meanings, the words
that represent their relationships. Those include hypernimy, hyponimy, synonimy, antonimy, among others. A typical entry in wordnet reads:
%zahir> wn dog -hholn
Holonyms of noun dog
2 of 6 senses of dog
Sense 1
dog, domestic dog, Canis familiaris
MEMBER OF: Canis, genus Canis
MEMBER OF: Canidae, family Canidae
MEMBER OF: Carnivora, order Carnivora
MEMBER OF: Eutheria, subclass Eutheria
MEMBER OF: Mammalia, class Mammalia
MEMBER OF: Vertebrata, subphylum Vertebrata, Craniata, subphylum Craniata
MEMBER OF: Chordata, phylum Chordata
MEMBER OF: Animalia, kingdom Animalia, animal kingdom
MEMBER OF: pack
Sense 5
pawl, detent, click, dog
PART OF: ratchet, rachet, ratch
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Organization of the Semantic Network
•Does a Canary Sing?
•Does a Canary Fly?
•Does a Canary Breathe?
Meanings are not in one to one correspondence with words
Committee
Piece of wood
FriendPal
Comrade
Board
Meanings are hierarchical (Quillian)
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Semantic Relationships
Antonymy: opposite meaningsgood is antonym of evil.
Hypernymy – Hyponymy: generic or universal, specific or particular tree is hypernym of oak.
Meronymy – Holonymy: part ofbranch is meronym of tree.
Polysemy: meanings share a common wordboard as official body of persons, and as slab of wood.
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What to Measure
Wordnet can be embedded in a graph of ~70,000 nodes and ~200,000 edges. What are the collective properties of the graph?
ScalingEvidence for self-organization
Navigation: Small-world-nessNavigation
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Distribution of Links
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Small-world: Low Clustering, Short Diameter
c = cn/(nn*(nn-1)) d = <Dmin>all pairs
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Regular to Small-World
Watts & Strogatz, 1998
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Clustering and Average Minimal Distance
See also Ferrer i Cancho & Sole, 2001
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Impact of Polysemous Links
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Dissolution of Tree Structure with Polysemy
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Blind Navigation
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Measuring Network Navigation
C connectivity matrix, P exponentiation:
P = CN Pij = number of paths between i and j of length N
P 1N [e1 e1
T + (2/1)N e2e2T + …]
Where 1 is the first eigenvalue and e1 the first eigenvector
{ei} provide a limiting behavior of a blind, non-detailed
balanced navigation of the graph, or “traffic”.
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Traffic
head
pointline
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Conclusions
Evidence for self-organization and small-world-ness
Polysemy organizes and shortens the networkUbiquity across languagesMay reflect preeminence of metaphoric thinking
The global perspective reveals possible mechanisms
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Brain Activity as a Network
Brain activity revealed by imaging:Need for non-stimulus driven analysisHow to characterize such a structure?
1 if Corr[vi(t)vj(t)]t P0
0 otherwise
Cij =
P0 | { Cij } connected
Define a connectivity matrix as:
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Traffic in the Brain: Chronic Pain
regular graph
Pain1. Thalamus (1/3)2. S1 (hand)3. Cerebellum (1/3)4. Posterior Parietal (1/4)5. Prefrontal (1/6)6. Prefrontal (2/6)7. S1 (foot)
Pain Surrogate• Prefrontal (2/6)
Visual Surrogate• Prefrontal (3/6)
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Connections DendogramGroup Ipf1, pf2, pf4, pf5, pf6, s1 (foot), pparietal3, pparietal4
Group IIthal1, thal2, thal3, venst2, psins, ancing1, ancing2
Group IIIamygd1, amygd2, amygd3, nacc1, nacc2, pf3, venst1, venteg1, venteg2
Group IVs2_1, s2_1, anins, pscing, PM, cereb1, cereb2, cereb3, s1-hand, motor, pparietal1, pparietal3
I II
III
IV
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Preliminary Conclusions
The network analysis exposes a coherent functional organization
It provides novel functional hypotheses for further experimentation
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General Conclusions
The global/network approach unveils emergent states of biological networks
Provides tools for functional dissection
Guides the search for mechanisms
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Credits
Mariano Sigman, Rockefeller – INEBA, ParisVania Apkarian, Northwestern UniversityDante Chialvo, UCLAVictor Martinez, Univ. Baleares, Spain