Mental Navigation: Global Measures of Complex Netwroks

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

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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. - PowerPoint PPT Presentation

Transcript of Mental Navigation: Global Measures of Complex Netwroks

  • Mental Navigation: Global Measures of Complex NetwroksGuillermo Cecchi

    IBM Research, T.J. Watson Center

  • OverviewGeneral motivationThe lexicon networkBrain imaging networks

  • Global Measures of Biological Networks

    Characterization of global states

    Functional mechanisms

  • Motivation: Approaches to Quantify MeaningReductionist: meaning is molecular, piece-wise, and verificationist. Each linguistic item corresponds to an object in the world. There arestatements, 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, ambiguityis part of the message. Ref.: Quine, Kuhn.

  • Good

  • Bad

  • Knife

  • Fork

  • Mother

  • Father

  • LionStripes

  • LionFelineTigerStripes

  • LionFelineTigerStripesPredator Prey Zebra

  • Diffusion in the Semantic NetworkPsychophysical 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 dog2 of 6 senses of dogSense 1dog, 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: packSense 5pawl, detent, click, dog PART OF: ratchet, rachet, ratch

  • Organization of the Semantic NetworkDoes a Canary Sing?

    Does a Canary Fly?

    Does a Canary Breathe?

    Meanings are not in one to one correspondence with wordsCommitteePiece of woodFriendPalComradeBoardMeanings are hierarchical (Quillian)

  • Semantic RelationshipsAntonymy: opposite meaningsgood is antonym of evil.Hypernymy Hyponymy: generic or universal, specific or particulartree 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-organizationNavigation: Small-world-nessNavigation

  • Distribution of Links

  • Small-world: Low Clustering, Short Diameterc = cn/(nn*(nn-1))d = all pairs

  • Regular to Small-WorldWatts & Strogatz, 1998

  • Clustering and Average Minimal DistanceSee also Ferrer i Cancho & Sole, 2001

  • Impact of Polysemous Links

  • Dissolution of Tree Structure with Polysemy

  • Blind Navigation

  • Measuring Network NavigationC connectivity matrix, P exponentiation:P = CN e Pij = number of paths between i and j of length NP j k1N [e1 e1T + (k2/k1)N e2e2T + ] Where k1 is the first eigenvalue and e1 the first eigenvector{ei} provide a limiting behavior of a blind, non-detailedbalanced navigation of the graph, or traffic.

  • Trafficheadpointline

  • ConclusionsEvidence for self-organization and small-world-nessPolysemy organizes and shortens the networkUbiquity across languagesMay reflect preeminence of metaphoric thinkingThe global perspective reveals possible mechanisms

  • Brain Activity as a NetworkBrain activity revealed by imaging:Need for non-stimulus driven analysisHow to characterize such a structure?

  • Traffic in the Brain: Chronic Painregular graphPainThalamus (1/3)S1 (hand)Cerebellum (1/3)Posterior Parietal (1/4)Prefrontal (1/6)Prefrontal (2/6)S1 (foot)

    Pain SurrogatePrefrontal (2/6)

    Visual SurrogatePrefrontal (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

  • Preliminary ConclusionsThe network analysis exposes a coherent functional organization

    It provides novel functional hypotheses for further experimentation

  • General ConclusionsThe global/network approach unveils emergent states of biological networks

    Provides tools for functional dissection

    Guides the search for mechanisms

  • CreditsMariano Sigman, Rockefeller INEBA, ParisVania Apkarian, Northwestern UniversityDante Chialvo, UCLAVictor Martinez, Univ. Baleares, Spain

    We want Here talk about the need to quantify meaning, as an outstanding problem in logic, philosophy and computer science, not to mention brain science. Ultimately, we are still under the spell of Aristotle.The reductionist approach has been very influential in logic, philosophy and epistemology, whereas the holistic approach typically has lacked a formal bearing. In any case, it is clear that the holistic approach has the upper hand, and it is now a matter of finding the right analytic framework. Perhaps, this is not independent of the advent of distributed computation and the increase knowledge of brain function. We will argue that this latter aspect is fundamental.Talk about different measures of traffic in a graph, and the implications for models of neural instances of semantic networks. Imaging studies have shown that the activation of semantically related meanings is contiguous in language areas, and there is conscious and pre-conscious spread of activation when meanings are presented, including somato-sensorial and motor areas. The evidence is even more clear in the case of psychophysical priming effects.Wordnet is a systematic attempt to characterize semantic relationships between meanings, which we will argue is what defines meaning.We are looking for a graph-theoretical measure that can relate to our intuition of meaning. Foremost among them are the measures related to the navigation of the graph, the reason for which will become apparent further in the talk.Distribution of number of links per node, showing an indication that wordnet is scale-free as many networks arising from self-organized processes.Small-worldness: it has been shown that many natural networks are sw, I.e. having a relatively low clustering they posses a short diameter, what makes convenient the navigation while sparing the cost of high connectivity.Here we can see how the polysemous links impact the structure of wordnet, creating short-cuts that significantly reduce the diameter of the graph. Polymous links keep the clustering high, nevertheless. The comparison with semi-random graphs is relevant because it shows that polysemous links are essentially random and leading to the reduction of the diameter of the network.Another exemplification of the same effect. The main effect is that the addition of polysemous links is equivalent to the addition of random links, the effect of which is to render the network a small-world. The clustering, however, remains high as opposed to a typical small-world network.The effect of polysemy on the hierarchical structure of the rest of the semantic relationships. The tree structure is essentially dissolved by polysemy.Example tree of wordnet. In red are displayed polysemy links, clearly showing the creation of shortcuts between the other, more hierarchical or structured semantic relationships.Traffic shows the existence of clusters determined by highly polysemous meanings, which dominate the circulation in the graph. Interestingly, there is no correlation with the average minimal distance and the connectivity, suggesting that traffic is a valid alternate measure.Some possible ramifications of these ideas. One interesting possibility is to measure semantics in a quantitative way, perhaps by quantifying the change in the navigation pattern when a meaning is added/deleted or presented.