917 research outputs found
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 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 âthreat score cardâ, 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 Ă©ventuelle de la Chlortetracycline, mĂ©langĂ©e Ă la nourriture du poulet comme adjuvant dâalimentation, sur la teneur en cholestĂ©rol des principaux organes et sur lâapparition dâathĂ©rosclĂ©rose
Dubost P., Ganter P., Julou L., Pascal S., Bressou C. Influence de la chlortĂ©-tracycline, mĂ©langĂ©e Ă la nourriture du poulet comme adjuvant dâalimentation sur la teneur en cholestĂ©rol des principaux organes et sur lâapparition dâathĂ©rosclĂ©rose. In: Bulletin de l'AcadĂ©mie VĂ©tĂ©rinaire de France tome 113 n°7, 1960. pp. 399-410
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