MSI Weekly Bulletin - Week starting Monday 1 December, 2008

see program details at: http://wwwmaths.anu.edu.au/events/aong08/program.html

In the classic book Flatland, a romance of many dimensions, Edwin Abbott imagines a two-dimensional world inhabited by two-dimensional creatures and the difficulty they have with even conceiving of the third dimension. The lack of a third dimension might appear to reduce possibilities but Professor Vaughan Jones will explain how a new system of algebra based on two dimensional configurations is in fact very rich and where it might be useful. It has even been proposed as the basis for building a quantum computer. This ANU Public Lecture, intended for those without much mathematics background, will be enhanced by numerous anecdotes and images.

see program details at: http://wwwmaths.anu.edu.au/events/aong08/program.html

In this talk I will present $L^{p}$ estimates for approximate eigenfunctions of a differential operator restricted to a hypersurface of a compact manifold. This proof, similar to Koch, Tataru and Zworski's proof of eigenfunction estimates over the whole manifold, exploits locality to transform the problem into one concerning evolution equations. Strichartz estimates are then used, with one spatial variable taking the place of time, to achieve the required estimates.

see program details at: http://wwwmaths.anu.edu.au/events/aong08/program.html

In applications of natural language processing (automated language translation is one) it is commonly important to distinguish different senses for the same word. The task of doing this for a potentially large vocabulary is a considerable modeling and computational challenge. Probabilistic modeling methods will be described that accept reduced accuracy in exchange for computational speed. Two alternative methods were implemented as part of the project. Both use the Latent Dirichlet Allocation clustering Algorithm and code of Blei et al for a major part of the task. These approaches use "knowledge" from a topic signature database (commonly, Martinez/Agirre) to provide information on the neighboring words that are likely for each sense. This is used in combination with a word sense inventory (commonly, Wordnet). These methods are commonly described as knowledge-based (they use one or more existing databases), but unsupervised. They are unsupervised in the sense that the algorithm is not trained on a document corpus that closely matches the types of documents that are likely to appear in the target application area. Accuracy is disappointing. Recent work, using Wikipedia to supply both the word sense inventory and the topic signature information, is a promising recent development that will be discussed briefly. Both methods use LDA, but in different ways. LDA uses knowledge about which words tend to appear together in the same documents to identify clumps, called "topics", that are defined by a probability distribution over the set of words in the documents. The output from LDA can then be used to generate a likely noun-context for the target word. The first method uses a Bayesian approach. Marginalizing out over the topics, we consider the distribution of words over the document containing the target word. The assigned noun-context is then the set of most likely words. The second considers each word as vector in the topic space, then uses a dot product definition of distance between any two words to compare the LDA generated noun-context to the typical noun-context for each sense and decide the best fit. Both algorithms then compare this LDA generated noun-context to the typical noun-context for each sense and decide the best fit.

see program details at: http://wwwmaths.anu.edu.au/events/aong08/program.html

see program details at: http://wwwmaths.anu.edu.au/events/aong08/program.html