We prove a direct image theorem stating that the direct image of a Galois formula by a morphism of difference schemes is equivalent to a Galois formula modulo the theory ACFA of existentially closed difference fields. As a consequence, we obtain an effective quantifier elimination procedure and a precise algebraic-geometric description of definable sets over existentially closed difference fiel...

We study the properties of the language of Stratified Sets (first-order logic with ∈ and a stratification condition) as used in TST, TZT, and (with stratifiability instead of stratification) in Quine’s NF. We find that the syntax forms a nominal algebra for substitution and that stratification and stratifiability imply confluence and strong normalisation under rewrites corresponding naturally t...

We examine how economic stratification affects inequality and growth over time. We study economies where heterogeneous agents interact through local public goods or externalities (school funding, neighborhood effects) and economy-wide linkages (complementary skills, knowledge spillovers). We compare growth and welfare when families are stratified into homogeneous local communities and when they...

Spontaneous stratification in granular mixtures—i.e., the formation of alternating layers of small-rounded and large-faceted grains when one pours a random mixture of the two types of grains into a quasi-twodimensional vertical Hele-Shaw cell—has been recently reported by H. A. Makse et al. @Nature 386, 379 ~1997!#. Here we study experimentally the dynamical processes leading to spontaneous str...

In this paper, we investigate a sheaf-theoretic interpretation of stratification learning. Motivated by the work of Alexandroff (1937) and McCord (1978), we aim to redirect efforts in the computational topology of triangulated compact polyhedra to the much more computable realm of sheaves on partially ordered sets. Our main result is the construction of stratification learning algorithms framed...

Let G be a finite group and k a fixed algebraically closed field of characteristic p>0 . If p is odd, let H(; be the subring of H*(G,k) consisting of elements of even degree; following [20-22] we take H~=H*(G,k) if p=2, though one could just as well use the subring of elements of even degree for all p. H a is a finitely generated commutative k-algebra [13], and we let Va denote its associated a...

To design a modern control system is a complex problem which requires high qualitative software. This software must be based on robust algorithms and numerical stable methods which both can provide quantitative as well as qualitative information. In this Licentiate Thesis, the focus is on the qualitative information. The aim is to grasp the underlying advanced mathematical theory and provide al...

For any flat family of pure-dimensional coherent sheaves on a family of projective schemes, the Harder-Narasimhan type (in the sense of Gieseker semistability) of its restriction to each fiber is known to vary semicontinuously on the parameter scheme of the family. This defines a stratification of the parameter scheme by locally closed subsets, known as the Harder-Narasimhan stratification. In ...

Although currently software development often separates the design phase from the implementation, the trend towards model-driven approaches is undeniable. As models are the primary development artifact in model-driven development, one has to deal with the problems surrounding huge and therefore unmanageable models. To tackle these issues, systems are often divided into components that are model...