Functional Hemispherectomy in Adults: All We Have to Sphere Is Sphere Itself

'The only thing we have to fear is fear itself'.

Sphere tracing and all that

1 Distance Fields Given an implicit surface ∂S with S ⊆ R the corresponding distance field (also called signed distance function) D : R → R which maps a point p from the domain of the distance field R to a real-valued distance value is obtained by distance transforming the surface using the formula D(p) = sign(p) ·min{d(p, q) : q ∈ S} (1) The metric d(p, q) used is the standard Euclidean metric...

Public sphere and intellectual discourses in Iran

A Computing all maps into a sphere

Given topological spaces X,Y , a fundamental problem of algebraic topology is understanding the structure of all continuous maps X → Y . We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y ], i.e., all homotopy classes of such maps. We solve this problem in the stable range, where for some d ≥ 2, we have dimX ≤ 2d−2 and Y is (...

The Urysohn Sphere Is Pseudofinite

We show that the Urysohn sphere is pseudofinite. As a consequence, we derive an approximate 0-1 law for finite metric spaces of diameter at most 1.