On the upper bound in Varadhan's Lemma

In this paper, we generalize the upper bound in Varadhan's Lemma. The standard formulation of Varadhan's Lemma contains two important elements, namely an upper semicontinuous integrand and a rate function with compact sublevel sets. However, motivated by results from queueing theory, we do not assume that rate functions have compact sublevel sets. Moreover, we drop the assumption that the integrand is upper semicontinuous and replace it by a weaker condition. We prove that the upper bound in Varadhan's Lemma still holds under these weaker conditions. Additionally, we show that only measurability of the integrand is required when the rate function is continuous.Comment: 5 page

Transform-domain analysis of packet delay in network nodes with QoS-aware scheduling

In order to differentiate the perceived QoS between traffic classes in heterogeneous packet networks, equipment discriminates incoming packets based on their class, particularly in the way queued packets are scheduled for further transmission. We review a common stochastic modelling framework in which scheduling mechanisms can be evaluated, especially with regard to the resulting per-class delay distribution. For this, a discrete-time single-server queue is considered with two classes of packet arrivals, either delay-sensitive (1) or delay-tolerant (2). The steady-state analysis relies on the use of well-chosen supplementary variables and is mainly done in the transform domain. Secondly, we propose and analyse a new type of scheduling mechanism that allows precise control over the amount of delay differentiation between the classes. The idea is to introduce N reserved places in the queue, intended for future arrivals of class 1

Methylation Defect in Imprinted Genes Detected in Patients with an Albright's Hereditary Osteodystrophy Like Phenotype and Platelet Gs Hypofunction

Pseudohypoparathyroidism (PHP) indicates a group of heterogeneous disorders whose common feature is represented by impaired signaling of hormones that activate Gsalpha, encoded by the imprinted GNAS gene. PHP-Ib patients have isolated Parathormone (PTH) resistance and GNAS epigenetic defects while PHP-Ia cases present with hormone resistance and characteristic features jointly termed as Albright's Hereditary Osteodystrophy (AHO) due to maternally inherited GNAS mutations or similar epigenetic defects as found for PHP-Ib. Pseudopseudohypoparathyroidism (PPHP) patients with an AHO phenotype and no hormone resistance and progressive osseous heteroplasia (POH) cases have inactivating paternally inherited GNAS mutations.We here describe 17 subjects with an AHO-like phenotype that could be compatible with having PPHP but none of them carried Gsalpha mutations. Functional platelet studies however showed an obvious Gs hypofunction in the 13 patients that were available for testing. Methylation for the three differentially methylated GNAS regions was quantified via the Sequenom EpiTYPER. Patients showed significant hypermethylation of the XL amplicon compared to controls (36 ± 3 vs. 29 ± 3%; p<0.001); a pattern that is reversed to XL hypomethylation found in PHPIb. Interestingly, XL hypermethylation was associated with reduced XLalphaS protein levels in the patients' platelets. Methylation for NESP and ExonA/B was significantly different for some but not all patients, though most patients have site-specific CpG methylation abnormalities in these amplicons. Since some AHO features are present in other imprinting disorders, the methylation of IGF2, H19, SNURF and GRB10 was quantified. Surprisingly, significant IGF2 hypermethylation (20 ± 10 vs. 14 ± 7%; p<0.05) and SNURF hypomethylation (23 ± 6 vs. 32 6%; p<0.001) was found in patients vs. controls, while H19 and GRB10 methylation was normal.In conclusion, this is the first report of methylation defects including GNAS in patients with an AHO-like phenotype without endocrinological abnormalities. Additional studies are still needed to correlate the methylation defect with the clinical phenotype