Recent content by Sebastien77

Yes, I was inaccurate, they should be distinct subsets. Yes, I meant "infinite if and only if k_i \notin v_j ", thanks for the correction. Yes, "member of exactly one" (problem 2) and "member of exactly one or not member of any" (problem 1). The elements of S are the edges of a planar graph...

Yes, sorry. I hope the following will clarify: S is a finite set of elements ki V is a subset of S, e.g. v4={k1,k3} E is a finite ensemble of V, e.g. E = { v1={k1}, v2={k1,k2}, v4={k1,k3}, v4={k2,k4,k5} } f(S, V) → ]-∞,∞], (ki,vj) → wij, with wij infinite only if ki ⊄ vj. The problem is to...

Hi all, I am looking for an efficient solution to solve the following problem. Can anybody help? Assume a set S of elements ki and a set V of possible groupings Gj. A grouping Gj is a subset of S. Associate a weight wij to each mapping ki to Gj. The weights are infinite if ki ⊄ Gj, and finite...

Hi Simon, thanks for your answer and references! I am somehow familiar with vector field theory and the Euclidian geometry and understand that the dimension of an hyperplane is the minimum number of linearly independent vectors (of its embedding N-dimensional space) that are required to...

Let’s imagine a moving point bound to a 2D plane. If we wrap this plane on a sphere within a 3D space the point would now eventually end up at the same position while moving in a seemingly fixed direction (it is actually not fixed in the 3D space). I am now wondering: Can a 3D hyperplane be...