Abstract A collection $$S=\{S_i, \ldots , S_n\}$$ S = { i , … n } of disjoint closed convex sets in $$\mathbb {R}^d$$ R</mml:m...

We obtain lower bounds in the algebraic computation tree model for deciding the separability of two disjoint point sets. In particular, we show Ω(n log n) time lower bounds for separability by means of strips, wedges, wedges with apices on a given line, fixed-slopes double wedges, and triangles, which match the complexity of the existing algorithms, and therefore prove their optimality.

Recently in Reference [ quant-ph/0202121] a computational criterion of separability induced by greatest cross norm is proposed by Rudolph. There, Rudolph conjectured that the new criterion is not weaker than positive partial transpose criterion for separability. We show that there exist counterexample to this claim, that is, proposed criterion is weaker than the positive partial transpose crite...

Two new feature selection methods are introduced, the first based on separability criterion, the second on consistency index that includes interactions between the selected subsets of features. Comparison of accuracy was made against information-theory based selection methods on several datasets training neurofuzzy and nearest neighbor methods on various subsets of selected features. Methods ba...

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product H = H ⊗ · · ·⊗H is separable or entangled. We show that the tensor convolution ( φ . . . φ ) : G → H defined for mappings φ : G → H μ on an almost arbitrary locally compact abelian group G, give rise to formulation of an equivalent problem to the separability one.