Abstract It is shown that every self-adjoint operator in a $$\sigma $$ σ -finite von Neumann factor of type III can be written as real linear combination 3 projections. This stark contrast to factors $$I_\infty ,\, II_1$$ I ∞ ,</mml:m...

Humans and animals engage in rich social interactions. It is often theorized that a relatively small number of basic interactions give rise to the full range behavior observed. But no computational theory explaining how combine together has been proposed before. We do so here. take model, Social MDP, which able express interactions, extend it represent linear combinations Practically for roboti...