Investigating relationships within and between category networks in Wikipedia

This work maps and analyses cross-citations in the areas of Biology, Mathematics, Physics and Medicine in the English version of Wikipedia, which are represented as an undirected complex network where the entries correspond to nodes and the citations among the entries are mapped as edges. We found a high value of clustering coefficient for the areas of Biology and Medicine, and a small value for Mathematics and Physics. The topological organization is also different for each network, including a modular structure for Biology and Medicine, a sparse structure for Mathematics and a dense core for Physics. The networks have degree distributions that can be approximated by a power-law with a cut-off. The assortativity of the isolated networks has also been investigated and the results indicate distinct patterns for each subject. We estimated the betweenness centrality of each node considering the full Wikipedia network, which contains the nodes of the four subjects and the edges between them. In addition, the average shortest path length between the subjects revealed a close relationship between the subjects of Biology and Physics, and also between Medicine and Physics. Our results indicate that the analysis of the full Wikipedia network cannot predict the behavior of the isolated categories since their properties can be very different from those observed in the full network. (C) 2011 Elsevier Ltd. All rights reserved.

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

Inglés : 850 palabras básicas en español = Category: basic english 850 words

[ES] Glosario de las 850 palabras más usadas en inglés

Modulating the granularity of category formation by global cortical states

The unsupervised categorization of sensory stimuli is typically attributed to feedforward processing in a hierarchy of cortical areas. This purely sensory-driven view of cortical processing, however, ignores any internal modulation, e.g., by top-down attentional signals or neuromodulator release. To isolate the role of internal signaling on category formation, we consider an unbroken continuum of stimuli without intrinsic category boundaries. We show that a competitive network, shaped by recurrent inhibition and endowed with Hebbian and homeostatic synaptic plasticity, can enforce stimulus categorization. The degree of competition is internally controlled by the neuronal gain and the strength of inhibition. Strong competition leads to the formation of many attracting network states, each being evoked by a distinct subset of stimuli and representing a category. Weak competition allows more neurons to be co-active, resulting in fewer but larger categories. We conclude that the granularity of cortical category formation, i.e., the number and size of emerging categories, is not simply determined by the richness of the stimulus environment, but rather by some global internal signal modulating the network dynamics. The model also explains the salient non-additivity of visual object representation observed in the monkey inferotemporal (IT) cortex. Furthermore, it offers an explanation of a previously observed, demand-dependent modulation of IT activity on a stimulus categorization task and of categorization-related cognitive deficits in schizophrenic patients.

Semantic, perceptual and number space: relations between category width and spatial processing.

Coarse semantic encoding and broad categorization behavior are the hallmarks of the right cerebral hemisphere's contribution to language processing. We correlated 40 healthy subjects' breadth of categorization as assessed with Pettigrew's category width scale with lateral asymmetries in perceptual and representational space. Specifically, we hypothesized broader category width to be associated with larger leftward spatial biases. For the 20 men, but not the 20 women, this hypothesis was confirmed both in a lateralized tachistoscopic task with chimeric faces and a random digit generation task; the higher a male participant's score on category width, the more pronounced were his left-visual field bias in the judgement of chimeric faces and his small-number preference in digit generation ("small" is to the left of "large" in number space). Subjects' category width was unrelated to lateral displacements in a blindfolded tactile-motor rod centering task. These findings indicate that visual-spatial functions of the right hemisphere should not be considered independent of the same hemisphere's contribution to language. Linguistic and spatial cognition may be more tightly interwoven than is currently assumed.