In this paper, we aim to overcome three major shortcomings of the FDH (Free Disposal Hull) directional distance function through developing two new, named Linear and Fractional CDFDH, complete FDH measures of efficiency. To accomplish this, we integrate the concepts of similarity and FDH directional distance function. We prove that the proposed measures are translation invariant and unit invari...

An extended eigenvalue for an operator A is a scalar λ for which the operator equation AX = λXA has a nonzero solution. Several scenarios are investigated where the existence of non-unimodular extended eigenvalues leads to invariant or hyperinvariant subspaces. For a bounded operator A on a complex Hilbert space H, the set EE(A) of extended eigenvalues for A is defined to be the set of those co...

We provide the first effectively computable, modulo a mild conjecture, complete invariant for simultaneous conjugacy in Garside groups. This invariant generalizes the notion of super summit set of a conjugacy class, and provides a solution of the simultaneous conjugacy problem in Garside groups, of complexity a small degree polynomial in the sizes of the invariant and the input parameters. Comp...

We investigate the existence of a common hypercyclic vector for family $(T_\lambda)_{\lambda\in \Lambda}$ hypercyclic operators acting on same Banach space $X$. give positive and negative results involving dimension $\Lambda$ regularity each map $\lambda\in \Lambda\mapsto T_\lambda^n x$, $x\in X$, $n\in\mathbb N$.

We study the problem of recursively recovering a time sequence of sparse vectors, St, from measurements Mt := St + Lt that are corrupted by structured noise Lt which is dense and can have large magnitude. The structure that we require is that Lt should lie in a low dimensional subspace that is either fixed or changes “slowly enough”; and the eigenvalues of its covariance matrix are “clustered”....

We study the problem of recursively recovering a time sequence of sparse vectors, St, from measurements Mt := St + Lt that are corrupted by structured noise Lt which is dense and can have large magnitude. The structure that we require is that Lt should lie in a low dimensional subspace that is either fixed or changes “slowly enough”; and the eigenvalues of its covariance matrix are “clustered”....

A symmetry of a game is a permutation of the player set and their strategy sets that leaves the payoff functions invariant. In this paper we introduce and discuss two relatively mild symmetry properties for set-valued solution concepts (that are equivalent when the solution concepts are singlevalued) and show using examples that stable sets satisfy neither version. These examples also show that...

We use shift-invariant Non-negative Matrix Factorization (NMF) for decomposing continuous-valued time series into a number of characteristic primitives, i.e. the basis vectors, and their activations, which results in a modelindependent and fully data driven parts-based representation. We interpret the basis vectors as short parts of motion that are shared between all trajectories in the data se...