Two elements in an oriented matroid are inseparable if they have either the same sign in every signed circuit containing them both or opposite signs in every signed circuit containing them both. Two elements of a matroid are adjacent if there is no M(K4)-minor using them both, and in which they correspond to a matching of K4. We prove that two elements e, { of an oriented matroid are inseparabl...

Optimal taxation under income uncertainty has been extensively developed in expected utility theory, but it is still open for inseparable utility function between income and effort. As an alternative of decision-making under uncertainty, prospect theory (Kahneman and Tversky (1979), Tversky and Kahneman (1992)) has been obtained empirical support, for example, Kahneman and Tversky (1979), and C...

We introduce the separable sets of variables for trees and tree au-tomata. If a set Y of input variables is inseparable for a tree and an automaton then there a non empty family of distributive sets of Y. It is shown that if a tree t has " many " inseparable sets with respect to a tree automaton A then there is an effective way to reduce the complexity of A when running on t.

We develop an intuitive geometric interpretation of the standard support vector machine (SVM) for classification of both linearly separable and inseparable data and provide a rigorous derivation of the concepts behind the geometry. For the separable case finding the maximum margin between the two sets is equivalent to finding the closest points in the smallest convex sets that contain each clas...

Localizability of entanglement in fully inseparable states is a key ingredient of assisted quantum information protocols as well as measurement-based models of quantum computing. We investigate the existence of fully inseparable states with nonlocalizable entanglement, that is, with entanglement which cannot be localized between any pair of subsystems by any measurement on the remaining part of...