Towards Collaborative Conceptual Exploration

In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a consortium, based on closure systems of attribute sets and the well-known attribute exploration algorithm from formal concept analysis. To this end, we introduce (weak) local experts for subdomains of a given knowledge domain. These entities are able to refute and potentially accept a given (implicational) query for some closure system that is a restriction of the whole domain. On this we build up a consortial expert and show first insights about the ability of such an expert to answer queries. Furthermore, we depict techniques on how to cope with falsely accepted implications and on combining counterexamples. Using notions from combinatorial design theory we further expand those insights as far as providing first results on the decidability problem if a given consortium is able to explore some target domain. Applications in conceptual knowledge acquisition as well as in collaborative interactive ontology learning are at hand.Comment: 15 pages, 2 figure

Distributed Formal Concept Analysis Algorithms Based on an Iterative MapReduce Framework

While many existing formal concept analysis algorithms are efficient, they are typically unsuitable for distributed implementation. Taking the MapReduce (MR) framework as our inspiration we introduce a distributed approach for performing formal concept mining. Our method has its novelty in that we use a light-weight MapReduce runtime called Twister which is better suited to iterative algorithms than recent distributed approaches. First, we describe the theoretical foundations underpinning our distributed formal concept analysis approach. Second, we provide a representative exemplar of how a classic centralized algorithm can be implemented in a distributed fashion using our methodology: we modify Ganter's classic algorithm by introducing a family of MR* algorithms, namely MRGanter and MRGanter+ where the prefix denotes the algorithm's lineage. To evaluate the factors that impact distributed algorithm performance, we compare our MR* algorithms with the state-of-the-art. Experiments conducted on real datasets demonstrate that MRGanter+ is efficient, scalable and an appealing algorithm for distributed problems.Comment: 17 pages, ICFCA 201, Formal Concept Analysis 201

Clones in Graphs

Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this approach is ineffective in data mining since real world data does not exhibit enough structural regularity. Here we step in with a novel approach based on mappings that preserve the maximal cliques. For this we exploit the well known correspondence between bipartite graphs and the data structure formal context $(G,M,I)$ from Formal Concept Analysis. From there we utilize the notion of clone items. The investigation of these is still an open problem to which we add new insights with this work. Furthermore, we produce a substantial experimental investigation of real world data. We conclude with demonstrating the generalization of clone items to permutations.Comment: 11 pages, 2 figures, 1 tabl

A Requirement-centric Approach to Web Service Modeling, Discovery, and Selection

Service-Oriented Computing (SOC) has gained considerable popularity for implementing Service-Based Applications (SBAs) in a flexible\ud and effective manner. The basic idea of SOC is to understand users'\ud requirements for SBAs first, and then discover and select relevant\ud services (i.e., that fit closely functional requirements) and offer\ud a high Quality of Service (QoS). Understanding users’ requirements\ud is already achieved by existing requirement engineering approaches\ud (e.g., TROPOS, KAOS, and MAP) which model SBAs in a requirement-driven\ud manner. However, discovering and selecting relevant and high QoS\ud services are still challenging tasks that require time and effort\ud due to the increasing number of available Web services. In this paper,\ud we propose a requirement-centric approach which allows: (i) modeling\ud users’ requirements for SBAs with the MAP formalism and specifying\ud required services using an Intentional Service Model (ISM); (ii)\ud discovering services by querying the Web service search engine Service-Finder\ud and using keywords extracted from the specifications provided by\ud the ISM; and(iii) selecting automatically relevant and high QoS services\ud by applying Formal Concept Analysis (FCA). We validate our approach\ud by performing experiments on an e-books application. The experimental\ud results show that our approach allows the selection of relevant and\ud high QoS services with a high accuracy (the average precision is\ud 89.41%) and efficiency (the average recall is 95.43%)

Using formal concept analysis to detect and monitor organised crime

This paper describes some possible uses of Formal Concept Analysis in the detection and monitoring of Organised Crime. After describing FCA and its mathematical basis, the paper suggests, with some simple examples, ways in which FCA and some of its related disciplines can be applied to this problem domain. In particular, the paper proposes FCA-based approaches for finding multiple instances of an activity associated with Organised Crime, finding dependencies between Organised Crime attributes, and finding new indicators of Organised Crime from the analysis of existing data. The paper concludes by suggesting that these approaches will culminate in the creation and implementation of an Organised Crime ‘threat score card’, as part of an overall environmental scanning system that is being developed by the new European ePOOLICE projec

The Jacobi orientation and the two-variable elliptic genus

We explain the relationship between the sigma orientation and Witten genus on the one hand and the two-variable elliptic genus on the other. We show that if E is an elliptic spectrum, then the Theorem of the Cube implies the existence of canonical SU-orientation of the associated spectrum of Jacobi forms. In the case of the elliptic spectrum associated to the Tate curve, this gives the two-variable elliptic genus. We also show that the two-variable genus arises as an instance of the circle-equivariant sigma orientation.Comment: Revised to better exhibit complex orientation of MSU^(CP^\infty_{-infty}

On the high-density expansion for Euclidean Random Matrices

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows to group the diagrams in a small number of topological classes, providing a simple way to determine the infrared (small momenta) behavior of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.Comment: 29 page

On the homomorphism order of labeled posets

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined.Comment: 14 page

Influence éventuelle de la Chlortetracycline, mélangée à la nourriture du poulet comme adjuvant d’alimentation, sur la teneur en cholestérol des principaux organes et sur l’apparition d’athérosclérose

Dubost P., Ganter P., Julou L., Pascal S., Bressou C. Influence de la chlorté-tracycline, mélangée à la nourriture du poulet comme adjuvant d’alimentation sur la teneur en cholestérol des principaux organes et sur l’apparition d’athérosclérose. In: Bulletin de l'Académie Vétérinaire de France tome 113 n°7, 1960. pp. 399-410