I am reading Judea Pearl's "Causality" (second edition 2009) and in section 1.1.5 Conditional Independence and Graphoids, he states:


  The following is a (partial) list of properties satisfied by the 
  conditional independence relation (X_||_Y | Z). 
  
  
  Symmetry: (X_||_ Y | Z) ==> (Y_||_X | Z).
  Decomposition: (X_||_ YW | Z)  ==> (X_||_Y | Z).
  Weak union: (X_||_ YW | Z)  ==> (X_||_Y | ZW). 
  Contraction: (X_||_ Y | Z) &amp; (X_||_ W | ZY) ==> (X_||_ YW | Z).
  Intersection: (X_||_  W | ZY) &amp; (X_||_  Y | ZW) (X_||_  YW | Z). 
  
  
  (Intersection is valid in strictly positive probability distributions.)
  
  (formula (1.28) given earlier in the publicatiob: [(X_||_ Y | Z) iff P(X | Y,Z ) = P(X | Z)  )


But what is an  "strictly positive distribution" in general terms, and what distinguishes a "strictly positive distribution" form a distribution that is not strictly positive?


Question: abelian higgs vortices
Answer: The study of vortices in Abelian Higgs models in the context of relativistic QFT goes back to the paper by Nielsen and Olesen, Nucl.Phys.B61:45-61,1973. They in turn were directly inspired by the study of vortices carrying quantized magnetic flux in type II superconductors which goes back to Abrikosov (see his Nobel lecture here: http://nobelprize.org/nobel_prizes/physics/laureates/2003/abrikosov-lecture.html). In that context the Abelian gauge field is identified with the electromagnetic field and the Higgs field with the Cooper pair of electrons. I have not gone back to the original papers by Abrikosov (which are probably in Russian) but I would guess that the term vortex is based on an analogy to fluid mechanics with the vorticity of the fluid  vortex (curl of the velocity field) being analogous to the magnetic field of the Abelian Higgs vortex (curl of the vector potential).