Mental Navigation: Global Measures of Complex Netwroks

Guillermo Cecchi

IBM Research, T.J. Watson Center

Overview

General motivationThe lexicon networkBrain imaging networks

Global Measures of Biological Networks

Characterization of global states

Functional mechanisms

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.

Good

Bad

Knife

Fork

Mother

Father

Lion Stripes

Lion Feline Tiger Stripes

Lion Feline Tiger Stripes

Predator Prey Zebra

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).

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

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)

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.

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

Distribution of Links

Small-world: Low Clustering, Short Diameter

c = cn/(nn*(nn-1)) d = <Dmin>all pairs

Regular to Small-World

Watts & Strogatz, 1998

Clustering and Average Minimal Distance

See also Ferrer i Cancho & Sole, 2001

Impact of Polysemous Links

Dissolution of Tree Structure with Polysemy

Blind Navigation

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”.

Traffic

head

pointline

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

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:

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)

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

Preliminary Conclusions

The network analysis exposes a coherent functional organization

It provides novel functional hypotheses for further experimentation

General Conclusions

The global/network approach unveils emergent states of biological networks

Provides tools for functional dissection

Guides the search for mechanisms

Credits

Mariano Sigman, Rockefeller – INEBA, ParisVania Apkarian, Northwestern UniversityDante Chialvo, UCLAVictor Martinez, Univ. Baleares, Spain