This paper shows that continuous-time stochastic games of fixed duration need not possess equilibria in Markov strategies. The example requires payoffs and transitions to depend on time in a continuous but irregular (almost nowhere almost differentiable) way. This example offers a correction to the erroneous construction presented previously in Levy (Dyn Games Appl 3(2):279–312, 2013. https://doi.org/10.1007/s13235-012-0067-2 ).
Male Fischer-344 rats were given a single intrastriatal injection of kainic acid (KA; 1 microgram/rat), which caused recurrent motor seizures lasting 3–6 hr. During the convulsive period, native Met5- enkephalin-like (ME-LI) and dynorphin A (1–8)-like (DYN-LI) immunoreactivities in hippocampus decreased by 31 and 63%, respectively. By 24 hr after dosing, the hippocampal opioid peptides had returned to control levels, and by 48 hr ME-LI had increased 270% and DYN-LI 150%. Immunocytochemical analysis revealed that ME-LI and Leu5-enkephalin-like (LE-LI) immunostaining in the mossy fibers of dentate granule cells and the perforant-temporoammonic pathway had decreased visibly by 6 hr and had increased markedly by 48 hr following KA. A visible decrease in DYN-LI in mossy fiber axons within 6 hr was followed by a substantial increase by 48 hr. To determine whether the increases in hippocampal ME-LI reflected changes in ME biosynthesis, levels of mRNA coding for preproenkephalin (mRNAenk) and cryptic ME-LI cleaved by enzyme digestion from preproenkephalin were measured. Following the convulsive period (6 hr), mRNAenk was 400% of control, and by 24 hr, cryptic ME-LI was 300% of control. Increases in native and cryptic ME-LI and in mRNAenk were also noted in entorhinal cortex, but not in hypothalamus or uninjected striatum. Our data suggest that KA-induced seizures cause an increase in ME release, followed by a compensatory increase in ME biosynthesis in the hippocampus and entorhinal cortex.
Transcription factor Foxo‐1 can be inactivated via Akt‐mediated phosphorylation. Since shear stress activates Akt, we determined whether Foxo‐1 and the Foxo‐1‐dependent, angiogenesis‐related Ang‐2/Tie2‐system are influenced by shear stress in endothelial cells. Expression of Foxo‐1 and its target genes p27Kip1 and Ang‐2 was decreased under shear stress (6 dyn/cm2, 24 h), nuclear exclusion of Foxo‐1 by phosphorylation increased. eNOS and Tie2 were upregulated. No effects on Ang‐1 expression were detected. In conclusion, Foxo‐1 and Ang‐2/Tie2 are part of the molecular response to shear stress, which may regulate angiogenesis.