Towards a generalisation of formal concept analysis for data mining purposes

In this paper we justify the need for a generalisation of Formal Concept Analysis for the purpose of data mining and begin the synthesis of such theory. For that purpose, we first review semirings and semimodules over semirings as the appropriate objects to use in abstracting the Boolean algebra and the notion of extents and intents, respectively. We later bring to bear powerful theorems developed in the field of linear algebra over idempotent semimodules to try to build a Fundamental Theorem for K-Formal Concept Analysis, where K is a type of idempotent semiring. Finally, we try to put Formal Concept Analysis in new perspective by considering it as a concrete instance of the theory developed

Second Rang et Desequilibre

Equilibre Economique

A closed-form solution for the optimal release times for the F2 vertical bar deteriorating jobs vertical bar Sigma w(j)C(j) problem

We consider job scheduling on a flow-line production system, which covers a wide range of real-world manufacturing situations from plastic molding, steel milling to machine maintenance, and the service industry, where the duration of a task performed on a job is an arbitrary monotone non-decreasing function of the time the job has spent in the system. Our model is set in a deterministic environment with the initial conditions (i.e., job release times rj) as decision variables (determined by the parameters γ1,γ2,…,γn, which control the time elapsed since the first machine becomes available). The main feature of the problem to minimize the sum of weighted completion times–as compared to, say, the problem to minimize the makespan considered earlier (Wagneur and Sriskandarajah (1993) [23])–is that its solution depends on the rate of growth of the processing time functions. We confine our study to the two-machine case for the sake of simplicity. We derive a closed-form formula for the optimal job release times for a finite set of jobs. This result also applies to the problem to minimize the flow time as a special case.Department of Logistics and Maritime Studie

Active Measurement for Multiple Link Failures Diagnosis in IP Networks

Simultaneous link failures are common in IP networks [1]. In this paper, we develop a technique for locating multiple failures in Service Provider or Enterprise IP networks using active measurement. We propose a two-phased approach that minimizes both the additional traffic due to probe messages and the measurement infrastructure costs. In the first phase, using elements from max-plus algebra theory, we show that the optimal set of probes can be determined in polynomial time, and we provide an algorithm to find this optimal set of probes. In the second phase, given the optimal set of probes, we compute the location of a minimal set of measurement points (beacons) that can generate these probes. We show that the beacon placement problem is NP-hard and propose a constant factor approximation algorithm for this problem. We then apply our algorithms to existing ISP networks using topologies inferred by the Rocketfuel tool [2]. We study in particular the difference between the number of probes and beacons that are required for multiple and single failure(s) diagnosi

A Note on Tropical Triangles in the Plane

We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically independent and they tropically span a classical hexagon whose sides have slopes ∞, 0, 1. Using this classical hexagon, we determine a parameter space for transversal tropical triangles. The coordinates of the vertices of a transversal tropical triangle determine a tropically regular matrix. Triangulations of the tropical plane are obtained