Truly Subquadratic Exact Distance Oracles with Constant Query Time for Planar Graphs

We present a truly subquadratic size distance oracle for reporting, in constant time, the exact shortest-path distance between any pair of vertices of an undirected, unweighted planar graph G. For any ? > 0, our distance oracle requires O(n^{5/3+?}) space and is capable of answering shortest-path distance queries exactly for any pair of vertices of G in worst-case time O(log (1/?)). Previously no truly sub-quadratic size distance oracles with constant query time for answering exact shortest paths distance queries existed

Hypoxia-induced transcription of dopamine D3 and D4 receptors in human neuroblastoma and astrocytoma cells

<p>Abstract</p> <p>Background</p> <p>Dopaminergic pathways that influence mood and behaviour are severely affected in cerebral hypoxia. In contrast, hypoxia promotes the differentiation of dopaminergic neurons. In order to clarify the hypoxic sensitivity of key dopaminergic genes, we aimed to study their transcriptional regulation in the context of neuroblastoma and astrocytoma cell lines exposed to 1% hypoxia.</p> <p>Results</p> <p>Quantitative RT-PCR assays revealed that the transcription of both type D3 and D4 postsynaptic dopamine receptors (DRD3 and DRD4) was induced several fold upon 2-day hypoxia in a cell-specific manner, while the vascular endothelial growth factor gene was activated after 3-hr incubation in hypoxia. On the other hand, mRNA levels of type 2 dopamine receptor, dopamine transporter, monoamino oxidase and catechol-O-methyltransferase were unaltered, while those of the dopamine receptor regulating factor (DRRF) were decreased by hypoxia. Notably, 2-day hypoxia did not result in elevation of protein levels of DRD3 and DRD4.</p> <p>Conclusion</p> <p>In light of the relatively delayed transcriptional activation of the DRD3 and DRD4 genes, we propose that slow-reacting hypoxia sensitive transcription factors might be involved in the transactivation of DRD3 and DRD4 promoters in hypoxia.</p