Mental Navigation: Global Measures of Complex Netwroks

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

2. Overview • General motivation • The lexicon network • Brain imaging networks

3. Global Measures of Biological Networks • Characterization of global states • Functional mechanisms

4. 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.

5. Good

6. Bad

7. Knife

8. Fork

9. Mother

10. Father

11. Lion Stripes

12. Lion Feline Tiger Stripes

13. Lion Feline Tiger Stripes Predator Prey Zebra

15. 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).

16. 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

17. Organization of the Semantic Network Meanings are hierarchical (Quillian) • Does a Canary Sing? • Does a Canary Fly? • Does a Canary Breathe? Meanings are not in one to one correspondence with words Committee Board Piece of wood Comrade Friend Pal

18. 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.

19. 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

20. Distribution of Links

21. Small-world: Low Clustering, Short Diameter d = <Dmin>all pairs c = cn/(nn*(nn-1))

22. Regular to Small-World Watts & Strogatz, 1998

23. Clustering and Average Minimal Distance See also Ferrer i Cancho & Sole, 2001

24. Impact of Polysemous Links

25. Dissolution of Tree Structure with Polysemy

27. Blind Navigation

28. Measuring Network Navigation • C connectivity matrix, P exponentiation: • P = CNe Pij = number of paths between i and j of length N • P jk1N [e1 e1T+ (k2/k1)Ne2e2T + …] • Where k1 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”.

29. Traffic head point line

30. 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

31. Define a connectivity matrix as: • 1 if Corr[vi(t)vj(t)]tm P0 Cij = • 0 otherwise • P0 | { Cij } connected Brain Activity as a Network • Brain activity revealed by imaging: • Need for non-stimulus driven analysis • How to characterize such a structure?

33. Traffic in the Brain: Chronic Pain • Pain • Thalamus (1/3) • S1 (hand) • Cerebellum (1/3) • Posterior Parietal (1/4) • Prefrontal (1/6) • Prefrontal (2/6) • S1 (foot) • Pain Surrogate • Prefrontal (2/6) • Visual Surrogate • Prefrontal (3/6) regular graph

34. III I II IV 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

35. Preliminary Conclusions • The network analysis exposes a coherent functional organization • It provides novel functional hypotheses for further experimentation

36. General Conclusions • The global/network approach unveils emergent states of biological networks • Provides tools for functional dissection • Guides the search for mechanisms

37. Credits • Mariano Sigman, Rockefeller – INEBA, Paris • Vania Apkarian, Northwestern University • Dante Chialvo, UCLA • Victor Martinez, Univ. Baleares, Spain