0000000000403009
AUTHOR
Oliver Matz
The Monadic Quantifier Alternation Hierarchy over Grids and Graphs
AbstractThe monadic second-order quantifier alternation hierarchy over the class of finite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely finite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the difference between the levels k+1 and k of the monadic hierarchy is witnessed by a set of grids where this function is (k+1)-fold exponential. We then transfer the hierarchy result to the class of directed (or undirected) graphs, using an encoding technique called strong reduction. It is notable that one can obtain sets of graphs which occur arbitrar…
Autoantibodies in complex regional pain syndrome bind to a differentiation-dependent neuronal surface autoantigen.
Complex regional pain syndrome, which is characterised by pain and trophic disturbances, develops frequently after peripheral limb trauma. There is an increasing evidence of an involvement of the immune system in CRPS, and recently we showed that CRPS patients have autoantibodies against nervous system structures. Therefore we tested the sera of CRPS patients, neuropathy patients and healthy volunteers for surface-binding autoantibodies to primary cultures of autonomic neurons and differentiated neuroblastoma cell lines using flow cytometry. Thirteen of 30 CRPS patients, but none of 30 healthy controls and only one of the 20 neuropathy sera had specific surface binding to autonomic neurons …