Pseudofinite fields, procyclic fields and model-completion

Pseudodefinite Fields, Procyclic Fields and Model-Completion

On algebraic closure in pseudofinite fields

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F . We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F . For almost all completions of the theory, we show that algebraic closure agrees with definable closure, as soon as A contains the relative algebraic closure of the prime field.

Procyclic Galois Extensions of Algebraic Number Fields

6 1 Iwasawa’s theory of Zp-extensions 9 1.

Biharmonic fields and mesh completion

We discuss bi-harmonic fields which approximate signed distancefields. We conclude that the bi-harmonic field approximation can be apowerful tool for mesh completion in general and complex cases. Wepresent an adaptive, multigrid algorithm to extrapolate signeddistance fields. By defining a volume mask in a closed region boundingthe area that must be repaired, the algorithm computes a signeddist...

Probabilistic Anatomical Connectivity Using Completion Fields

Diffusion magnetic resonance imaging has led to active research in the analysis of anatomical connectivity in the brain. Many approaches have been proposed to model the diffusion signal and to obtain estimates of fibre tracts. Despite these advances, the question of defining probabilistic connectivity indices which utilize the relevant information in the diffusion MRI signal to indicate connect...