Extreme operators on Choquet simplexes

On Extreme Averaging Operators

Choquet integrals as projection operators for quantified tomographic reconstruction

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Counting Simplexes in R

A finite set of vectors S ⊆ R is called a simplex iff S is linearly dependent but all its proper subsets are independent. This concept arises in particular from stoichiometry. We are interested in this paper in the number of simplexes contained in some H ⊆ R , which we denote by simp(H). This investigation is particularly interesting for H spanning R and containing no collinear vectors. Our mai...

Commutativity, Comonotonicity, and Choquet Integration of Self-adjoint Operators∗

In this work we propose a definition of comonotonicity for elements ofB (H)sa, i.e., bounded self-adjoint operators defined over a complex Hilbert space H. We show that this notion of comonotonicity coincides with a form of commutativity. Intuitively, comonotonicity is to commutativity as monotonicity is to bounded variation. We also define a notion of Choquet expectation for elements of B (H)s...

Counting Simplexes in R3

A nite set of vectors S R n is called a simplex ii S is linearly dependent but all its proper subsets are independent. This concept arises in particular from stoichiometry. We are interested in this paper in the number of simplexes contained in