Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator

We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at $\pm \infty$. We use this result to determine the asymptotic distribution of the eigenvalues and to compute some of the eigenvalues numerically. We compare these to earlier calculations by other authors.Comment: 29 pages, corrections to section 3, added section

Convergence of eigenvalues for a highly non-self-adjoint differential operator

In this paper we study a family of operators dependent on a small parameter $\epsilon > 0$, which arise in a problem in fluid mechanics. We show that the spectra of these operators converge to N as $\epsilon \to 0$, even though, for fixed $\epsilon > 0$, the eigenvalue asymptotics are quadratic.Comment: 16 page

Education externalities in rural Ethiopia: evidence from average and stochastic frontier production functions.

Education will have externality effects in agriculture if, in the course of conducting their own private economic activities, educated farmers raise the productivity of uneducated farmers with whom they come into contact. This paper seeks to determine the potential size and source of such benefits for rural areas of Ethiopia. Average and stochastic frontier production function methodologies are employed to measure productivity and efficiency of farmers. In each case, internal and external returns to schooling are compared. We find that there are substantial and significant externality benefits of education in terms of higher average farm output and a shifting outwards of the production frontier. External benefits of schooling may be several times as high as internal benefits in this regard. However, we are unable to find any evidence of externality benefits to schooling in terms of improvements in technological efficiency in the use of a given technology. This suggests that the source of externalities to schooling is in the adoption and spread of innovations, which shift out the production frontier.

Evaluation of LTAG parsing with supertag compaction

One of the biggest concerns that has been raised over the feasibility of using large-scale LTAGs in NLP is the amount of redundancy within a grammar¿s elementary tree set. This has led to various proposals on how best to represent grammars in a way that makes them compact and easily maintained (Vijay-Shanker and Schabes, 1992; Becker, 1993; Becker, 1994; Evans, Gazdar and Weir, 1995; Candito, 1996). Unfortunately, while this work can help to make the storage of grammars more efficient, it does nothing to prevent the problem reappearing when the grammar is processed by a parser and the complete set of trees is reproduced. In this paper we are concerned with an approach that addresses this problem of computational redundancy in the trees, and evaluate its effectiveness

Learning to predict distributions of words across domains

Although the distributional hypothesis has been applied successfully in many natural language processing tasks, systems using distributional information have been limited to a single domain because the distribution of a word can vary between domains as the word’s predominant meaning changes. However, if it were possible to predict how the distribution of a word changes from one domain to another, the predictions could be used to adapt a system trained in one domain to work in another. We propose an unsupervised method to predict the distribution of a word in one domain, given its distribution in another domain. We evaluate our method on two tasks: cross-domain part-of-speech tagging and cross-domain sentiment classification. In both tasks, our method significantly outperforms competitive baselines and returns results that are statistically comparable to current state-of-the-art methods, while requiring no task-specific customisations

Cross-domain sentiment classification using a sentiment sensitive thesaurus

Automatic classification of sentiment is important for numerous applications such as opinion mining, opinion summarization, contextual advertising, and market analysis. However, sentiment is expressed differently in different domains, and annotating corpora for every possible domain of interest is costly. Applying a sentiment classifier trained using labeled data for a particular domain to classify sentiment of user reviews on a different domain often results in poor performance. We propose a method to overcome this problem in cross-domain sentiment classification. First, we create a sentiment sensitive distributional thesaurus using labeled data for the source domains and unlabeled data for both source and target domains. Sentiment sensitivity is achieved in the thesaurus by incorporating document level sentiment labels in the context vectors used as the basis for measuring the distributional similarity between words. Next, we use the created thesaurus to expand feature vectors during train and test times in a binary classifier. The proposed method significantly outperforms numerous baselines and returns results that are comparable with previously proposed cross-domain sentiment classification methods. We conduct an extensive empirical analysis of the proposed method on single and multi-source domain adaptation, unsupervised and supervised domain adaptation, and numerous similarity measures for creating the sentiment sensitive thesaurus

Online learning : towards enabling choice

Education is rapidly evolving from an opportunity that was provided mainly for an elite to one that is available to a mass markets and as such is prone to the forces generated by this environment. Where, in the established pattern, commercial interest was limited mainly to the use of skills developed during the educational process, the future model of educational provision will involve extensive commercial activity in the production, delivery and marketing of material. Already there are a number of commercial companies offering framework products enabling "off the shelf solutions" for the construction and delivery of web based courses in any subject area. The commercialisation of education is underway and it is inevitable that it will be viewed, by entrepreneurs and customers alike, as any other commercial product. It would seem reasonable that the consumer should be able to evaluate the performance of these new modes of working in a similar manner to other commercial products. This paper draws together current thinking on the problems associated with evaluating computer and communication based learning

Parsing with an extended domain of locality

One of the claimed benefits of Tree Ad- joining Grammars is that they have an extended domain of locality (EDOL). We consider how this can be exploited to limit the need for feature structure uni- fication during parsing. We compare two wide-coverage lexicalized grammars of English, LEXSYS and XTAG, finding that the two grammars exploit EDOL in different ways