Multiple Scales in Small-World Networks

Small-world architectures may be implicated in a range of phenomena from networks of neurons in the cerebral cortex to social networks and propogation of viruses. Small-world networks are interpolations of regular and random networks that retain the advantages of both regular and random networks by being highly clustered like regular networks and having small average path length between nodes, like random networks. While most of the recent attention on small-world networks has focussed on the effect of introducing disorder/randomness into a regular network, we show that that the fundamental mechanism behind the small-world phenomenon is not disorder/ randomness, but the presence of connections of many different length scales. Consequently, in order to explain the small-world phenomenon, we introduce the concept of multiple scale networks and then state the multiple length scale hypothesis. We show that small-world behavior in randomly rewired networks is a consequence of features common to all multiple scale networks. To support the multiple length scale hypothesis, novel network architectures are introduced that need not be a result of random rewiring of a regular network. In each case it is shown that whenever the network exhibits small-world behavior, it also has connections of diverse length scales. We also show that the distribution of the length scales of the new connections is significantly more important than whether the new connections are long range, medium range or short range

Mapping spatial relations

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2004.Includes bibliographical references (p. 155-160).One of the fundamental issues in cognitive science is the problem of grounding concepts in the perceptual world. In this thesis, I present a computational theory for how spatial relations are grounded in the perceptual world. Three constraints are critical to this theory: abstractness, groundedness and flexibility all of which need to be satisfied in order to explain the structure of spatial concepts. I then show how a formal framework, based on the mathematical notions of category theory can be used to model the grounding problem. The key computational ideas are that of minimal mapping and derivations. A minimal mapping of two categories, A and B, is the "smallest' category, C, that contains A and B. A derivation is a sequence of categories that follow a minimal mapping rule. Derivations and minimal mappings are used to model three domains - the semantics of prepositions, the structure of a toy "Jigsaw World" and the semantics of generic terms and quantifiers. In each case, I show how the computational theory gives rise to insights that are not available upon a purely empirical analysis. In particular, the derivational account shows the importance of stable, non-accidental features and of multiple scales in spatial cognition.by Rajesh Kasturirangan.Ph.D

Space and time in language as a pattern in general fictivity

Systematic parallelism between spatial and temporal expressions in a language is conceived here as a pattern in general fictivity arising from an underlying cognitive manifold. Under this situation, we try to articulate some of the questions pertinent to the spatial and temporal cognition from the viewpoint of patterns in general fictivity

Intervening with Interjections: A Comprehensive Approach to Study Ambiguity in Natural Conversations

Ambiguity during communication, in which a linguistic or gestural sign has multiple meanings, is often considered to be a deterrent to successful communicative interactions. The resolution of ambiguity, therefore, has been a concern in linguistics and in communication studies. This paper critiques certain prevalent experimental paradigms, which have been the most popular approaches to investigate ambiguity resolution, and proposes an alternative methodology to understand and address this phenomenon

Sensory cues employed for the acquisition of familiarity-dependent recognition of a shoal of conspecifics by climbing perch (Anabas testudineus Bloch)

In this study we showed that a freshwater fish, the climbing perch (Anabas testudineus) is incapable of using chemical communication but employs visual cues to acquire familiarity and distinguish a familiar group of conspecifics from an unfamiliar one. Moreover, the isolation of olfactory signals from visual cues did not affect the recognition and preference for a familiar shoal in this species