The multi-stripe travelling salesman problem

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with q ≥ 1, the objective function sums the costs for travelling from one city to each of the next q cities along the tour. The resulting q-stripe TSP generalizes the TSP and forms a special case of the quadratic assignment problem. We analyze the computational complexity of the q-stripe TSP for various classes of specially structured distance matrices. We derive NP-hardness results as well as polyomially solvable cases. One of our main results generalizes a well-known theorem of Kalmanson from the classical TSP to the q-stripe TSP

Involvement of pertussis toxin-sensitive G-proteins in the hormonal inhibition of dihydropyridine-sensitive Ca2+ currents in an insulin-secreting cell line (RINm5F)

Adrenaline inhibits insulin secretion via pertussis toxin-sensitive mechanisms. Since voltage-dependent Ca2+ currents play a key role in insulin secretion, we examined whether adrenaline modulates voltage-dependent Ca2+ currents of the rat insulinoma cell line, RINm5F. In the whole-cell configuration of the patch-clamp technique, dihydropyridine- but not omega-conotoxin-sensitive Ca2+ currents were identified. Adrenaline via alpha 2-adrenoceptors inhibited the Ca2+ currents by about 50%. Somatostatin which also inhibits insulin secretion was less efficient (inhibition by 20%). The hormonal inhibition of Ca2+ currents was not affected by intracellularly applied cAMP but blocked by the intracellularly applied GDP analog guanosine 5'-O-(2-thiodiphosphate) and by pretreatment of cells with pertussis toxin. In contrast to adrenaline and somatostatin, galanin, another inhibitor of insulin secretion, reduced Ca2+ currents by about 40% in a pertussis toxin-insensitive manner. Immunoblot experiments performed with antibodies generated against synthetic peptides revealed that membranes of RINm5F cells possess four pertussis toxin-sensitive G-proteins including Gi1, Gi2, Go2, and another Go subtype, most likely representing Go1. In membranes of control but not of pertussis toxin-treated cells, adrenaline via alpha 2-adrenoceptors stimulated incorporation of the photo-reactive GTP analog [alpha-32P]GTP azidoanilide into pertussis toxin substrates comigrating with the alpha-subunits of Gi2, Go2, and the not further identified Go subtype. The present findings indicate that activated alpha 2-adrenoceptors of RINm5F cells interact with multiple G-proteins, i.e. two forms of Go and with Gi2. These G-proteins are likely to be involved in the adrenaline-induced inhibition of dihydropyridine-sensitive Ca2+ currents and in other signal transduction pathways contributing to the adrenaline-induced inhibition of insulin secretion