Infinitesimal Gunk

Gunk, Topology and Measure

Atoms, Gunk, and the Limits of 'composition'

This predicate1 has played a central role in the debate on the special composition question and on related metaphysical issues concerning the mereological structure of objects. In this note we show that the characterization in (1) is nonetheless inadequate. We do so by constructing a mereological model M where everything qualifies as composed of atoms even though some elements in the domain are...

Histograms of Infinitesimal Neighbourhoods

Image analysis methods that use histograms defined over non-zero-sized local neighbourhoods have been proposed [1-4]. To better understand such methods, one can study the histograms of infinitesimal neighbourhoods. In this paper we show how the properties of such histograms can be derived through limit arguments. We show that in many cases the properties of these histograms are given by simple ...

Infinitesimal Hopf algebras

Infinitesimal bialgebras were introduced by Joni and Rota [J-R]. An infinitesimal bialgebra is at the same time an algebra and a coalgebra, in such a way that the comultiplication is a derivation. In this paper we define infinitesimal Hopf algebras, develop their basic theory and present several examples. It turns out that many properties of ordinary Hopf algebras possess an infinitesimal versi...

The infinitesimal model

Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. We first review the long history of the infinit...