The paper deals with the problem of the fuzzy data clustering. In other words, objects attributes can be represented by fuzzy numbers or fuzzy intervals. A direct algorithm of possibilistic clustering is the basis of an approach to the fuzzy data clustering. The paper provides the basic ideas of the method of clustering and a plan of the direct possibilistic clustering algorithm. Definitions of...

We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which is designed for a particular spectral density function and then used to predict the values of a random process having a different spectral density. The logari...

We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error ε . When ε = 0 we retrieve the usual notions of bisimulation and simulation on PAs. We give logical characterisations of these notions by choosing suitable logics which differ from the elementary ones, L and L ¬, by the modal operator. Using flow networks, we show how to compute the r...

We address the problem of computing distances between permutations that take into account similarities between elements of the ground set dictated by a graph. The problem may be summarized as follows: Given two permutations and a positive cost function on transpositions that depends on the similarity of the elements involved, find a smallest cost sequence of transpositions that converts one per...

We give a 5-approximation algorithm to the rooted Subtree-Prune-and-Regraft (rSPR) distance between two phylogenies, which was recently shown to be NP-complete. This paper presents the first approximation result for this important tree distance. The algorithm follows a standard format for tree distances. The novel ideas are in the analysis. In the analysis, the cost of the algorithm uses a "cas...

Introduction Many existing brain network distances are based on matrix norms. The element-wise differences may fail to capture underlying topological differences. Further, matrix norms are sensitive to outliers. A few extreme edge weights may severely affect the distance. There is a need to develop network distances that recognize topology. We introduce Gromov-Hausdorff (GH) and KolmogorovSmirn...

In this work we propose an efficient solution to calculate the minimum editing distance between membrane structures of arbitrary P systems. We use a new model of tree automata based on multisets of states and symbols linked to the finite control. This new model accepts a set of trees with symmetries between their internal nodes (mirrored trees). Once we have calculated the editing distance betw...

These notes accompany a lecture at the summer school on mathematics for bioinformatics, Centre de Recherches Mathematiques, Montreal, August 2003. I develop basic Markov models for sequence evolution and show how these may be used to estimate evolutionary divergences between sequences. I then discuss extensions of the basic model to situations where the evolutionary rate varies over time and fo...

We give two efficient algorithms for computing distances between partial rankings (i.e. rankings with ties). Given two partial rankings over n elements, and with b and c equivalence classes, respectively, our first algorithm runs in O(n log n/ log log n) time, and the second in O(n log min{b, c}) time.

Behaviour distances to measure the resemblance of two states in a (nondeterministic) fuzzy transition system have been proposed recently in the literature. Such a distance, defined as a pseudo-ultrametric over the state space of the model, provides a quantitative analogue of bisimilarity. In this paper, we focus on the problem of computing these distances. We first extend the definition of the ...