The Complexity of Nash Equilibria in Stochastic Multiplayer Games

We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game G, does there exist a Nash equilibrium of G where Player 0 wins with probability 1? Moreover, this problem remains undecidable when restricted to pure strategies or (pure) strategies with finite memory. One way to obtain a decidable variant of the problem is to restrict the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively. Finally, we single out a special case of the general problem that, in many cases, admits an efficient solution. In particular, we prove that deciding the existence of an equilibrium in which each player either wins or loses with probability 1 can be done in polynomial time for games where the objective of each player is given by a parity condition with a bounded number of priorities

Adenosine A2A receptors in Parkinson’s disease treatment

Latest results on the action of adenosine A2A receptor antagonists indicate their potential therapeutic usefulness in the treatment of Parkinson’s disease. Basal ganglia possess high levels of adenosine A2A receptors, mainly on the external surfaces of neurons located at the indirect tracts between the striatum, globus pallidus, and substantia nigra. Experiments with animal models of Parkinson’s disease indicate that adenosine A2A receptors are strongly involved in the regulation of the central nervous system. Co-localization of adenosine A2A and dopaminergic D2 receptors in striatum creates a milieu for antagonistic interaction between adenosine and dopamine. The experimental data prove that the best improvement of mobility in patients with Parkinson’s disease could be achieved with simultaneous activation of dopaminergic D2 receptors and inhibition of adenosine A2A receptors. In animal models of Parkinson’s disease, the use of selective antagonists of adenosine A2A receptors, such as istradefylline, led to the reversibility of movement dysfunction. These compounds might improve mobility during both monotherapy and co-administration with L-DOPA and dopamine receptor agonists. The use of adenosine A2A receptor antagonists in combination therapy enables the reduction of the L-DOPA doses, as well as a reduction of side effects. In combination therapy, the adenosine A2A receptor antagonists might be used in both moderate and advanced stages of Parkinson’s disease. The long-lasting administration of adenosine A2A receptor antagonists does not decrease the patient response and does not cause side effects typical of L-DOPA therapy. It was demonstrated in various animal models that inhibition of adenosine A2A receptors not only decreases the movement disturbance, but also reveals a neuroprotective activity, which might impede or stop the progression of the disease. Recently, clinical trials were completed on the use of istradefylline (KW-6002), an inhibitor of adenosine A2A receptors, as an anti-Parkinson drug

The GRAVITY young stellar object survey: IX. Spatially resolved kinematics of hot hydrogen gas in the star-disk interaction region of T Tauri stars

Stars and planetary system

The GRAVITY young stellar object survey: VIII. Gas and dust faint inner rings in the hybrid disk of HD141569

Stars and planetary system