Representations and Positive Definite Functions on Hypergroups

Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed.

From icon to naturalised icon:a linguistic analysis of media representations of the BP Deepwater Horizon crisis

This research explores how news media reports construct representations of a business crisis through language. In an innovative approach to dealing with the vast pool of potentially relevant texts, media texts concerning the BP Deepwater Horizon oil spill are gathered from three different time points: immediately after the explosion in 2010, one year later in 2011 and again in 2012. The three sets of 'BP texts' are investigated using discourse analysis and semi-quantitative methods within a semiotic framework that gives an account of language at the semiotic levels of sign, code, mythical meaning and ideology. The research finds in the texts three discourses of representation concerning the crisis that show a movement from the ostensibly representational to the symbolic and conventional: a discourse of 'objective factuality', a discourse of 'positioning' and a discourse of 'redeployment'. This progression can be shown to have useful parallels with Peirce's sign classes of Icon, Index and Symbol, with their implied movement from a clear motivation by the Object (in this case the disaster events), to an arbitrary, socially-agreed connection. However, the naturalisation of signs, whereby ideologies are encoded in ways of speaking and writing that present them as 'taken for granted' is at its most complete when it is least discernible. The findings suggest that media coverage is likely to move on from symbolic representation to a new kind of iconicity, through a fourth discourse of 'naturalisation'. Here the representation turns back towards ostensible factuality or iconicity, to become the 'naturalised icon'. This work adds to the study of media representation a heuristic for understanding how the meaning-making of a news story progresses. It offers a detailed account of what the stages of this progression 'look like' linguistically, and suggests scope for future research into both language characteristics of phases and different news-reported phenomena.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.

Linear Classifiers Based on Binary Distributed Representations

Binary distributed representations of vector data (numerical, textual, visual) are investigated in classification tasks. A comparative analysis of results for various methods and tasks using artificial and real-world data is given.

Bridging the Gap Between Human Language and Computer-Oriented Representations

Information can be expressed in many ways according to the different capacities of humans to perceive it. Current systems deals with multimedia, multiformat and multiplatform systems but another « multi » is still pending to guarantee global access to information, that is, multilinguality. Different languages imply different replications of the systems according to the language in question. No solutions appear to represent the bridge between the human representation (natural language) and a system-oriented representation. The United Nations University defined in 1997 a language to be the support of effective multilinguism in Internet. In this paper, we describe this language and its possible applications beyond multilingual services as the possible future standard for different language independent applications.

An Approach to Collaborative Filtering by ARTMAP Neural Networks

Recommender systems are now widely used in e-commerce applications to assist customers to find relevant products from the many that are frequently available. Collaborative filtering (CF) is a key component of many of these systems, in which recommendations are made to users based on the opinions of similar users in a system. This paper presents a model-based approach to CF by using supervised ARTMAP neural networks (NN). This approach deploys formation of reference vectors, which makes a CF recommendation system able to classify user profile patterns into classes of similar profiles. Empirical results reported show that the proposed approach performs better than similar CF systems based on unsupervised ART2 NN or neighbourhood-based algorithm.