Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Prosthetic rehabilitation and treatment outcome of partially edentulous patients with severe tooth wear: 3-years results

The purpose of this study was to report on the management and treatment outcomes of partially edentulous elderly patients with severe tooth wear.

Brain responses to auditory and visual stimulus offset: Shared representations of temporal edges

Edges are crucial for the formation of coherent objects from sequential sensory inputs within a single modality. Moreover, temporally coincident boundaries of perceptual objects across different sensory modalities facilitate crossmodal integration. Here, we used functional magnetic resonance imaging in order to examine the neural basis of temporal edge detection across modalities. Onsets of sensory inputs are not only related to the detection of an edge but also to the processing of novel sensory inputs. Thus, we used transitions from input to rest (offsets) as convenient stimuli for studying the neural underpinnings of visual and acoustic edge detection per se. We found, besides modality-specific patterns, shared visual and auditory offset-related activity in the superior temporal sulcus and insula of the right hemisphere. Our data suggest that right hemispheric regions known to be involved in multisensory processing are crucial for detection of edges in the temporal domain across both visual and auditory modalities. This operation is likely to facilitate cross-modal object feature binding based on temporal coincidence. Hum Brain Mapp, 2008. (c) 2008 Wiley-Liss, Inc.

Propositional and situational representations of text

Two informationally equivalent texts were constructed which described a fictitious town, emphasizing its spatial layout. In one version (Survey text), spatial information was in geographic terms, while in the other version (Route text), the equivalent information was provided in the form of directions for driving through the town. Subjects recalled these texts and verified old as well as inference statements. In Experiment I, subjects were able to recall the texts quite well, while showing little ability to use the information they had acquired to make inferences about spatial relations in the town which had not been directly stated in the text. With simpler texts, subjects in Experiment II were able to make infereces, especially when the form of the question corresponded to the version of the text they had read. It was concluded that free recall depended on the construction of a propositional textbase during comprehension, while inferences required a situation model, either in the form of a mental map or a procedural representation of the town. It could be shown that the form of the situation model depended on both the representation invited by the text and subject biases.