Using basis sets of scar functions

We present a method to efficiently compute the eigenfunctions of classically chaotic systems. The key point is the definition of a modified Gram-Schmidt procedure which selects the most suitable elements from a basis set of scar functions localized along the shortest periodic orbits of the system. In this way, one benefits from the semiclassical dynamical properties of such functions. The performance of the method is assessed by presenting an application to a quartic two-dimensional oscillator whose classical dynamics are highly chaotic. We have been able to compute the eigenfunctions of the system using a small basis set. An estimate of the basis size is obtained from the mean participation ratio. A thorough analysis of the results using different indicators, such as eigenstate reconstruction in the local representation, scar intensities, participation ratios, and error bounds, is also presentedThis work was supported by MINECO (Spain), under projects MTM2009-14621 and ICMAT Severo Ochoa SEV-2011-0087, and by CEAL Banco de Santander–UAM. F.R. is grateful for the support from a doctoral fellowship from UPM and the hospitality of the members of the Departamento de Física in the Laboratorio TANDAR–Comisión Nacional de la Energía Atómica, where part of this work was don

Coherent states for compact Lie groups and their large-N limits

The first two parts of this article surveys results related to the heat-kernel coherent states for a compact Lie group K. I begin by reviewing the definition of the coherent states, their resolution of the identity, and the associated Segal-Bargmann transform. I then describe related results including connections to geometric quantization and (1+1)-dimensional Yang--Mills theory, the associated coherent states on spheres, and applications to quantum gravity. The third part of this article summarizes recent work of mine with Driver and Kemp on the large-N limit of the Segal--Bargmann transform for the unitary group U(N). A key result is the identification of the leading-order large-N behavior of the Laplacian on "trace polynomials."Comment: Submitted to the proceeding of the CIRM conference, "Coherent states and their applications: A contemporary panorama.

BioDR : semantic indexing networks for biomedical document retrieval

In Biomedical research, retrieving documents that match an interesting query is a task performed quite frequently. Typically, the set of obtained results is extensive containing many non-interesting documents and consists in a flat list, i.e., not organized or indexed in any way. This work proposes BioDR, a novel approach that allows the semantic indexing of the results of a query, by identifying relevant terms in the documents. These terms emerge from a process of Named Entity Recognition that annotates occurrences of biological terms (e.g. genes or proteins) in abstracts or full-texts. The system is based on a learning process that builds an Enhanced Instance Retrieval Network (EIRN) from a set of manually classified documents, regarding their relevance to a given problem. The resulting EIRN implements the semantic indexing of documents and terms, allowing for enhanced navigation and visualization tools, as well as the assessment of relevance for new documents.Fundação para a Ciência e a Tecnologia (FCT)Maria Barbeito” contract XuntaHUELLA financed by the Consellería de Sanidade (Xunta de Galicia de Galicia

Biomedical text mining applied to document retrieval and semantic indexing

In Biomedical research, the ability to retrieve the adequate information from the ever growing literature is an extremely important asset. This work provides an enhanced and general purpose approach to the process of document retrieval that enables the filtering of PubMed query results. The system is based on semantic indexing providing, for each set of retrieved documents, a network that links documents and relevant terms obtained by the annotation of biological entities (e.g. genes or proteins). This network provides distinct user perspectives and allows navigation over documents with similar terms and is also used to assess document relevance. A network learning procedure, based on previous work from e-mail spam filtering, is proposed, receiving as input a training set of manually classified documents

Applying lazy learning algorithms to tackle concept drift in spam filtering

A great amount of machine learning techniques have been applied to problems where data is collected over an extended period of time. However, the disadvantage with many real-world applications is that the distribution underlying the data is likely to change over time. In these situations, a problem that many global eager learners face is their inability to adapt to local concept drift. Concept drift in spam is particularly difficult as the spammers actively change the nature of their messages to elude spam filters. Algorithms that track concept drift must be able to identify a change in the target concept (spam or legitimate e-mails) without direct knowledge of the underlying shift in distribution. In this paper we show how a previously successful instance-based reasoning e-mail filtering model can be improved in order to better track concept drift in spam domain. Our proposal is based on the definition of two complementary techniques able to select both terms and e-mails representative of the current situation. The enhanced system is evaluated against other well-known successful lazy learning approaches in two scenarios, all within a cost-sensitive framework. The results obtained from the experiments carried out are very promising and back up the idea that instance-based reasoning systems can offer a number of advantages tackling concept drift in dynamic problems, as in the case of the anti-spam filtering domain

SpamHunting: An instance-based reasoning system for spam labelling and filtering

n this paper we show an instance-based reasoning e-mail filtering model that outperforms classical machine learning techniques and other successful lazy learners approaches in the domain of anti-spam filtering. The architecture of the learning-based anti-spam filter is based on a tuneable en-hanced instance retrieval network able to accurately generalize e-mail representations. The reuse of similar messages is carried out by a simple unanimous voting mechanism to determine whether the tar-get case is spam or not. Previous to the final response of the system, the revision stage is only performed when the assigned class is spam whereby the system employs general knowledge in the form of meta-rules

Tracking Concept Drift at Feature Selection Stage in SpamHunting: An Anti-spam Instance-Based Reasoning System

In this paper we propose a novel feature selection method able to handle concept drift problems in spam filtering domain. The proposed technique is applied to a previous successful instance-based reasoning e-mail filtering system called SpamHunting. Our achieved information criterion is based on several ideas extracted from the well-known information measure introduced by Shannon. We show how results obtained by our previous system in combination with the improved feature selection method outperforms classical machine learning techniques and other well-known lazy learning approaches. In order to evaluate the performance of all the analysed models, we employ two different corpus and six well-known metrics in various scenarios

A Comparative Performance Study of Feature Selection Methods for the Anti-spam Filtering Domain

In this paper we analyse the strengths and weaknesses of the mainly used feature selection methods in text categorization when they are applied to the spam problem domain. Several experiments with different feature selection methods and content-based filtering techniques are carried out and discussed. Information Gain, χ 2-text, Mutual Information and Document Frequency feature selection methods have been analysed in conjunction with Naïve Bayes, boosting trees, Support Vector Machines and ECUE models in different scenarios. From the experiments carried out the underlying ideas behind feature selection methods are identified and applied for improving the feature selection process of SpamHunting, a novel anti-spam filtering software able to accurate classify suspicious e-mails

A gauge model for quantum mechanics on a stratified space

In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified K\"ahler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure furnishes a costratified Hilbert space, that is, a Hilbert space together with a system which consists of the subspaces associated with the strata of the reduced phase space and of the corresponding orthoprojectors. The costratified Hilbert space structure reflects the stratification of the reduced phase space. For the special case where the structure group is $\mathrm{SU}(2)$, we discuss the tunneling probabilities between the strata, determine the energy eigenstates and study the corresponding expectation values of the orthoprojectors onto the subspaces associated with the strata in the strong and weak coupling approximations.Comment: 38 pages, 9 figures. Changes: comments on the heat kernel and coherent states have been adde