Mental Navigation: Global Measures of Complex Netwroks Guillermo Cecchi IBM Research, T.J. Watson Center

Overview  General motivation  The lexicon network  Brain 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

LionStripes

LionFelineTigerStripes

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 Friend Pal Comrade Board Meanings are hierarchical (Quillian)

Semantic Relationships  Antonymy: opposite meanings good is antonym of evil.  Hypernymy – Hyponymy: generic or universal, specific or particular tree is hypernym of oak.  Meronymy – Holonymy: part of branch is meronym of tree.  Polysemy: meanings share a common word board 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?  Scaling  Evidence for self-organization  Navigation:  Small-world-ness  Navigation

Distribution of Links

Small-world: Low Clustering, Short Diameter c = cn/(nn*(nn-1)) d = 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 = C N e P ij = number of paths between i and j of length N P j k 1 N [e 1 e 1 T + ( k 2 / k 1 ) N e 2 e 2 T + …] Where k 1 is the first eigenvalue and e 1 the first eigenvector e{e i } provide a limiting behavior of a blind, non-detailed balanced navigation of the graph, or “traffic”.

Traffic head point line

Conclusions  Evidence for self-organization and small- world-ness  Polysemy organizes and shortens the network Ubiquity across languages May 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 analysis  How to characterize such a structure? 1 if Corr[v i (t)v j (t)] t m P 0 0 otherwise C ij = P 0 | { C ij } connected  Define a connectivity matrix as:

Traffic in the Brain: Chronic Pain regular graph Pain 1.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 Dendogram Group I pf1, pf2, pf4, pf5, pf6, s1 (foot), pparietal3, pparietal4 Group II thal1, thal2, thal3, venst2, psins, ancing1, ancing2 Group III amygd1, amygd2, amygd3, nacc1, nacc2, pf3, venst1, venteg1, venteg2 Group IV s2_1, s2_1, anins, pscing, PM, cereb1, cereb2, cereb3, s1-hand, motor, pparietal1, pparietal3 III 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, Paris  Vania Apkarian, Northwestern University  Dante Chialvo, UCLA  Victor Martinez, Univ. Baleares, Spain