A common way of blending between two planar curves is to linearly interpolate their signed curvature functions and to reconstruct the intermediate curve from the interpolated curvature values. But if both input curves are closed, this strategy can lead to open intermediate curves. We present a new algorithm for solving this problem, which finds the closed curve whose curvature is closest to the...

Extending results of Christie and Irving, we examine the action of reversals and transpositions on finite strings over an alphabet of size k. We show that determining reversal, transposition or signed reversal distance between two strings over a finite alphabet is NP-hard, while for ‘dense’ instances we give a polynomial-time approximation scheme. We also give a number of extremal results, as w...

The Wilcoxon signed-rank test is exploited for document organization and retrieval in this paper. A novel modeling method for documents and a distance metric between documents are proposed. Both document modeling and document comparisons are based on signed-ranks and are applied to the frequency of occurrence of the document bigrams. A metric using the Wilcoxon signed-rank test exploits these s...

QUALIFLEX (QUALItative FLEXible multiple criteria method) is a very useful outranking method to deal simultaneously with the cardinal and ordinal information in decision making process. The purpose of this paper is to develop a hesitant fuzzy QUALIFLEX with a signed distance-based comparison method for handling multi-criteria decision-making problems in which both the assessments of alternative...

We consider two generalizations of signed Sorting By Reversals (SBR), both aimed at formalizing the problem of reconstructing the evolutionary history of a set of species. In particular, we address Multiple SBR, calling for a signed permutation at minimum reversal distance from a given set of signed permutations, and Tree SBR, calling for a tree with the minimum number of edges spanning a given...

The use of neural networks in safety-critical systems requires safe and robust models, due to the existence adversarial attacks. Knowing minimal perturbation any input x, or, equivalently, knowing distance x from classification boundary, allows evaluating robustness, providing certifiable predictions. Unfortunately, state-of-the-art techniques for computing such a are computationally expensive ...