Electrons are round, π are squared

Which digraphs are round?

A digraph D is round if the vertices of D can be circularly ordered as VI, V2, ... , Vn so that, for each vertex Vi, the out-neighbours of Vi appear consecutively following Vi and the in-neighbours of Vi appear consecutively preceding Vi in the ordering. We characterize round digraphs in terms of forbidden substructures. Our proof implies a polynomial algorithm to decide if a digraph is round.

What are Stem Cells?

  Stem cells are undifferentiated self regenerating multi potential cells. There are three types of stem cells categories by the ability to form after cells and correlated with the body’s development process. Totipotent: these stem cells can form an entire organism such as fertilized egg. Ploripotent: ploripotent cells are those that can form any cell in the body but cannot form an entire organ...

4 Electrons Are Cheap ; Society Is Dear

Complex Reflection Arrangements Are K ( Π , 1 )

Let V be a finite dimensional complex vector space and W ⊆ GL(V ) be a finite complex reflection group. Let V reg be the complement in V of the reflecting hyperplanes. We prove that V reg is a K(π, 1) space. This was predicted by a classical conjecture, originally stated by Brieskorn for complexified real reflection group. The complexified real case follows from a theorem of Deligne and, after ...

π/2-Angle Yao Graphs are Spanners

We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor 8 √ 2(29 + 23 √ 2).