Ranking of agents competing with each other in complex systems may lead to paradoxes according to the pre-chosen different measures. A discussion is presented on such rank-rank, similar or not, correlations based on the case of European countries ranked by UEFA and FIFA from different soccer competitions. The first question to be answered is whether an empirical and simple law is obtained for s...

An efficient algorithm for the direct solution of a linear system associated with the discretization of boundary integral equations with oscillatory kernels (in two dimensions) is described without having to compute the complete matrix of the linear system. This algorithm is based on the unitary-weight representation, for which a new construction based on adaptive cross approximation is propose...

The pivoted QLP decomposition is computed through two consecutive QR decompositions. It an approximation to the computationally prohibitive singular value (SVD). This work concerned with a partial of matrices exploitation random sampling. method presented tailored for low-rank and called Random...

Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to rank problem, nuclear norm, an effective technique solve problem with strong performance guarantees. However, nonconvex relaxations have less estimation bias than norm can more accurately reduce effect noise on measurements. W...

We consider the problem of the presence of short cycles in the graphs of nonzero elements of matrices which have sublinear rank and nonzero entries on the main diagonal, and analyze the connection of these properties to the rigidity of matrices. In particular, we exhibit a family of matrices which shows that sublinear rank does not imply the existence of triangles. This family can also be used ...

In this paper I propose B-Rank, an efficient ranking algorithm for recommender systems. B-Rank is based on a random walk model on hypergraphs. Depending on the setup, B-Rank outperforms other state of the art algorithms in terms of precision, recall ∼ (19%− 50%) and inter list diversity ∼ (20%− 60%). B-Rank captures well the difference between popular and niche objects. The proposed algorithm p...

A group of finite Morley rank is a group whose definable subsets have a notion of dimension satisfying several basic axioms [BN94, p. 57]. Such groups arise naturally in model theory; initially as א1-categorical groups, i.e. as groups determined up to isomorphism by their first order theory, and here the simple groups correspond exactly. More recently groups of finite Morley rank have appeared ...