Practical Use of Formal Concept Analysis in Service-Oriented Computing

International audiencePervasive applications are encountered in a number of settings, including smart houses, intelligent buildings or connected plants. Service-Oriented Computing is today the technology of choice for implementing and exposing resources in such environments. The selection of appropriate services at the right moment in order to compose meaningful applications is however a real issue. In this paper, we propose a FCA-based solution to this problem.We have integrated FCA algorithms in our pervasive gateways and adapted them in order to allow efficient runtime selection of heterogeneous and dynamic services. This work has been applied to realistic use cases in the scope of a European project

Beyond Hypergraph Dualization

International audienceThis problem concerns hypergraph dualization and generalization to poset dualization. A hypergraph H = (V, E) consists of a finite collection E of sets over a finite set V , i.e. E ⊆ P(V) (the powerset of V). The elements of E are called hyperedges, or simply edges. A hypergraph is said simple if none of its edges is contained within another. A transversal (or hitting set) of H is a set T ⊆ V that intersects every edge of E. A transversal is minimal if it does not contain any other transversal as a subset. The set of all minimal transversal of H is denoted by T r(H). The hypergraph (V, T r(H)) is called the transversal hypergraph of H. Given a simple hypergraph H, the hypergraph dualization problem (Trans-Enum for short) concerns the enumeration without repetitions of T r(H). The Trans-Enum problem can also be formulated as a dualization problem in posets. Let (P, ≤) be a poset (i.e. ≤ is a reflexive, antisymmetric, and transitive relation on the set P). For A ⊆ P , ↓ A (resp. ↑ A) is the downward (resp. upward) closure of A under the relation ≤ (i.e. ↓ A is an ideal and ↑ A a filter of (P, ≤)). Two antichains (B + , B −) of P are said to be dual if ↓ B + ∪ ↑ B − = P and ↓ B + ∩ ↑ B − = ∅. Given an implicit description of a poset P and an antichain B + (resp. B −) of P , the poset dualization problem (Dual-Enum for short) enumerates the set B − (resp. B +), denoted by Dual(B +) = B − (resp. Dual(B −) = B +). Notice that the function dual is self-dual or idempotent, i.e. Dual(Dual(B)) = B

A Partial-Closure Canonicity Test to Increase the Efficiency of CbO-Type Algorithms

Computing formal concepts is a fundamental part of Formal Concept Analysis and the design of increasingly efficient algorithms to carry out this task is a continuing strand of FCA research. Most approaches suffer from the repeated computation of the same formal concepts and, initially, algorithms concentrated on efficient searches through already computed results to detect these repeats, until the so-called canonicity test was introduced. The canonicity test meant that it was sufficient to examine the attributes of a computed concept to determine its newness: searching through previously computed concepts was no longer necessary. The employment of this test in Close-by-One type algorithms has proved to be highly effective. The typical CbO approach is to compute a concept and then test its canonicity. This paper describes a more efficient approach, whereby a concept need only be partially computed in order to carry out the test. Only if it passes the test does the computation of the concept need to be completed. This paper presents this ‘partial-closure’ canonicity test in the In-Close algorithm and compares it to a traditional CbO algorithm to demonstrate the increase in efficiency

Providing Alternative Declarative Descriptions for Entity Sets Using Parallel Concept Lattices

We propose an approach for modifying a declarative description of a set of entities (e.g., a SPARQL query) for the purpose of finding alternative declarative descriptions for the entities. Such a shift in representation can help to get new insights into the data, to discover related attributes, or to find a more concise description of the entities of interest. Allowing the alternative descriptions furthermore to be close approximations of the original entity set leads to more flexibility in finding such insights. Our approach is based on the construction of parallel formal concept lattices over different sets of attributes for the same entities. Between the formal concepts in the parallel lattices, we define mappings which constitute approximations of the extent of the concepts. In this paper, we formalise the idea of two types of mappings between parallel concept lattices, provide an implementation of these mappings and evaluate their ability to find alternative descriptions in a scenario of several real-world RDF data sets. In this scenario we use descriptions for entities based on RDF classes and seek for alternative representations based on properties associated with the entities

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A parameterizable enumeration algorithm for sequence mining

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A parameterizable enumeration algorithm for sequence mining

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Wideband chaos generation using a delayed oscillator and a two-dimensional nonlinearity induced by a quadrature phase-shift-keying electro-optic modulator

International audienceWe present a new optoelectronic architecture intended for chaotic optical intensity generation. The principle relies on an electro-optic nonlinear delay dynamics, where the nonlinearity originates from an integrated four-wave optical interferometer, involving two independent electro-optic modulation inputs. Consequently, the setup involves both two-dimensional nonlinearity and dual-delay feedback dynamics, which results in enhanced chaos complexity of particular interest in chaos encryption schemes. The generated chaos observed with large feedback gains has a bandwidth ranging from 30 kHz to 13 GHz and is confirmed by numerical simulations of the proposed dynamical model and bifurcation diagram calculation

Maximal Antichain Lattice Algorithms for Distributed Computations

Abstract. The lattice of maximal antichains of a distributed computation is generally much smaller than its lattice of consistent global states. We show that a useful class of predicates can be detected on the lattice of maximal antichains instead of the lattice of consistent cuts obtaining significant (exponential for many cases) savings. We then propose new online and offline algorithms to construct and enumerate the lattice of maximal antichains. Previously known algorithm by Nourine and Raynoud [NR99,NR02] to construct the lattice takes O(n 2 m) time where n is the number of events in the computation, and m is the size of the lattice of maximal antichains. The algorithm by Jourdan, Rampon and Jard [JRJ94] takes O((n + w 2)wm) time where w is the width of the computation. All these algorithms assume as input the lattice of maximal antichains prior to the arrival of a new event. We present a new online incremental algorithm, OLMA, that computes the newly added elements to the lattice without requiring the prior lattice. Since the lattice may be exponential in the size of the computation, we get a significant reduction in the space complexity. The OLMA algorithm takes O(mw 2 log wL) time and O(wLw log n) space where wL is the width of the lattice of maximal antichains. The lower space complexity makes our algorithm applicable for online global predicate detection in a distributed system. For the purposes of analyzing offline traces, we also propose new enumeration algorithms to traverse the lattice.

Dynamics of a Nonlinear electro-optical delay oscillator and its application for multi-Gbit/s chaos-communication

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