From n+1-level atom chains to n-dimensional noises

In quantum physics, the state space of a countable chain of (n+1)-level atoms becomes, in the continuous field limit, a Fock space with multiplicity n. In a more functional analytic language, the continuous tensor product space over R of copies of the space C^{n+1} is the symmetric Fock space Gamma_s(L^2(R;C^n)). In this article we focus on the probabilistic interpretations of these facts. We show that they correspond to the approximation of the n-dimensional normal martingales by means of obtuse random walks, that is, extremal random walks in R^n whose jumps take exactly n+1 different values. We show that these probabilistic approximations are carried by the convergence of the basic matrix basis a^i_j(p) of \otimes_N \CC^{n+1} to the usual creation, annihilation and gauge processes on the Fock space.Comment: 22 page

Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

PRESY: A Context Based Query Reformulation Tool for Information Retrieval on the Web

Problem Statement: The huge number of information on the web as well as the growth of new inexperienced users creates new challenges for information retrieval. It has become increasingly difficult for these users to find relevant documents that satisfy their individual needs. Certainly the current search engines (such as Google, Bing and Yahoo) offer an efficient way to browse the web content. However, the result quality is highly based on uses queries which need to be more precise to find relevant documents. This task still complicated for the majority of inept users who cannot express their needs with significant words in the query. For that reason, we believe that a reformulation of the initial user's query can be a good alternative to improve the information selectivity. This study proposes a novel approach and presents a prototype system called PRESY (Profile-based REformulation SYstem) for information retrieval on the web. Approach: It uses an incremental approach to categorize users by constructing a contextual base. The latter is composed of two types of context (static and dynamic) obtained using the users' profiles. The architecture proposed was implemented using .Net environment to perform queries reformulating tests. Results: The experiments gives at the end of this article show that the precision of the returned content is effectively improved. The tests were performed with the most popular searching engine (i.e. Google, Bind and Yahoo) selected in particular for their high selectivity. Among the given results, we found that query reformulation improve the first three results by 10.7% and 11.7% of the next seven returned elements. So as we can see the reformulation of users' initial queries improves the pertinence of returned content.Comment: 8 page