Minkowski valuations provide a systematic framework for quantifying different aspects of morphology. In this paper we apply vector- and tensor-valued Minkowski valuations to neuronal cells from the cat's retina in order to describe their morphological structure in a comprehensive way. We introduce the framework of Minkowski valuations, discuss their implementation for neuronal cells and show ho...

Valuation based systems verifying an idem-potent property are studied. A partial order is deened between the valuations giving them a lattice structure. Then, two diierent strategies are introduced to represent valuations: as innmum of the most informative valuations or as supremum of the least informative ones. It is studied how to carry out computations with both representations in an eecient...

We define the notion of valuation on simplicial maps between geometric realizations of simplicial complexes in R. Valuations on simplicial maps are analogous to valuations on sets. In particular, we define the Lefschetz volumes, which are analogous to the intrinsic volumes of subsets of R. Our definition not only provides a generalization of the Lefschetz number, but also yields a Hadwigerstyle...

Using the theory of valuations, we establish a generalization of an identity of Perles-Shephard for non-convex polytopes. By considering spherical valuations, we obtain the Gram-Euler, Descartes and Euler-Poincar e theorems for non-convex polytopes.

The concept of pseudo valuations on hoop-algebras is introduced, and then the relationship between pseudo-valuations filers investigated. Some conditions for a real-valued function to be valuation are provided. Finally, we prove fact that binary operations uniformly continuous based notion valuation.

I study auctions in which there exists an asymmetry in bidders’ knowledge about their interdependent valuations. Bidders consist of two groups: the insiders, who are perfectly informed of their valuations, and the outsiders, who only observe onedimensional signals, thus being partially informed of their valuations. When only one insider and one outsider exist, both English and second-price auct...

A core element of microeconomics and game theory is that consumers have valuation functions over bundles of goods and that these valuation functions drive their purchases. In particular, the value assigned to a bundle need not be the sum of values on the individual items but rather is often a more complex function of how the items relate. The literature considers a hierarchy of valuation classe...

We consider an auction with risk neutral agents having independent private valuations for several heterogenous objects. Most of the literature on revenuemaximizing auctions has focused on the sale of one good or on the sale of several identical units (thus yielding one-dimensional informational models). Two reasons for ine¢ciency in revenue-maximizing auctions have been identi...ed 1) The (mono...

We extend the topos-theoretic treatment given in previous papers [2, 3, 4] of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth value to a proposition that the value of a quantity lies in a certain set ∆ ⊆ IR. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather ...

In this work, we design simple and e cient iterative auctions for selling multiple items in settings where bidders’ valuations belong to a special class (tree valuations) that can exhibit both value complementarity and substitutability. Our first contribution is to provide a compact linear programming formulation of the e cient allocation problem and use it to establish the existence of a Walra...