A first step is taken towards articulating a constructive empiricist philosophy of mathematics, thus extending van Fraassen's account to this domain. In order to do so, I adapt Field's nominalisation programme, making it compatible with an empiricist stance. Two changes are introduced: (a) Instead of taking conservativeness as the norm of mathematics, the empiricist countenances the weaker noti...

By associating a ‘motivic integral’ to every complex projective variety X with at worst canonical, Gorenstein singularities, Kontsevich [Kon95] proved that, when there exists a crepant resolution of singularities φ : Y → X, the Hodge numbers of Y do not depend upon the choice of the resolution. In this article we provide an elementary introduction to the theory of motivic integration, leading t...

We give an elementary construction of the compact real form of the Lie algebra g2. This construction exhibits the group 23·L3(2) as a group of automorphisms. We also show that there is a unique 14-dimensional real Lie algebra invariant under the action of this group.

We study a model of dynamic two-stage R&D competition where the competing firms are uncertain about the difficulty of the first stage. Staying in the competition is costly and a firm can also choose whether and when to quit. When a firm solves the first stage, it can choose whether and when to disclose the solution. We find that there exists a unique symmetric equilibrium, in which each firm wi...

We show that, given two probability measures in the plane, there exists a 4-fan that simultaneously equipartitions them. In other words, there is a point and four half-lines emanating from it such that each of the four sectors have measure 1 4 in both measures.

A graph G = (V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) ∈ E for each x 6= y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. A graph is representable if and only if it is k-representable for some k [1]. In this note, we introduce the applicability of represe...

The paper shows that movement or equivalent computational structure-changing operations of any kind at the level of logical form can be dispensed with entirely in capturing quantifier scope ambiguity. It offers a new semantics whereby the effects of quantifier scope alternation can be obtained by an entirely monotonic derivation, without typechanging rules. The paper follows Fodor (1982), Fodor...

We study cooperation structures with the following property: Given any two feasible coalitions with non-empty intersection, its union is a feasible coalition again. These combinatorial structures have a direct relationship with conference structures la Myerson. Characterizations of the Myer-son value in this context are provided by means of the introduction of the concept of basis for union sta...

BACKGROUND Quantitative PCR (qPCR) is a workhorse laboratory technique for measuring the concentration of a target DNA sequence with high accuracy over a wide dynamic range. The gold standard method for estimating DNA concentrations via qPCR is quantification cycle () standard curve quantification, which requires the time- and labor-intensive construction of a standard curve. In theory, the sha...