A stochastic analysis of resource sharing with logarithmic weights

The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to $\log(1+x)$, the logarithm of its current load. A detailed fluid scaling analysis of such a network with two nodes is presented. It is shown that the interaction of several time scales plays an important role in the evolution of such a system, in particular its coordinates may live on very different time and space scales. As a consequence, the associated stochastic processes turn out to have unusual scaling behaviors. A heavy traffic limit theorem for the invariant distribution is also proved. Finally, we present a generalization to the resource sharing algorithm for which the $\log$ function is replaced by an increasing function. Possible generalizations of these results with $J>2$ nodes or with the function $\log$ replaced by another slowly increasing function are discussed.Comment: Published at http://dx.doi.org/10.1214/14-AAP1057 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonclassical rotational inertia for a supersolid under rotation

As proposed by Leggett [4], the supersolidity of a crystal is characterized by the Non Classical Rotational Inertia (NCRI) property. Using a model of quantum crystal introduced by Josserand, Pomeau and Rica [5], we prove that NCRI occurs. This is done by analyzing the ground state of the aforementioned model, which is related to a sphere packing problem, and then deriving a theoretical formula for the inertia momentum. We infer a lower estimate for the NCRI fraction, which is a landmark of supersolidity

Supersolid under rotation and sphere packing problem

We use the model proposed by Josserand, Pomeau, Rica to prove properties on the ground state of a supersolid crystal and relate it to a sphere packing problem. This allows us to find, in the limit of small rotation, an approximate theoretical value for the reduction of the moment of inertia of a supersolid set in rotation, with respect to its classical value

A Role for Methyl-CpG Binding Domain Protein 2 in the Modulation of the Estrogen Response of pS2/TFF1 Gene

Background: In human Estrogen Receptor alpha (ER alpha)-positive breast cancers, 59 end dense methylation of the estrogen-regulated pS2/TFF1 gene correlates with its transcriptional inhibition. However, in some ER alpha-rich biopsies, pS2 expression is observed despite the methylation of its TATA-box region. Herein, we investigated the methylation-dependent mechanism of pS2 regulation. Methodology/Principal Findings: We observed interplay between Methyl-CpG Binding Domain protein 2 (MBD2) transcriptional repressor and ER alpha transactivator: (i) the pS2 gene is poised for transcription upon demethylation limited to the enhancer region containing the estrogen responsive element (ERE); (ii) MBD2-binding sites overlapped with the methylation status of the pS2 59 end; (iii) MBD2 depletion elevated pS2 expression and ectopic expression of ER alpha partially overcame the inhibitory effect of MBD2 when the ERE is unmethylated. Furthermore, serial chromatin immunoprecipitation assays indicated that MBD2 and ER alpha could simultaneously occupy the same pS2 DNA molecule; (iv) concomitant ectopic ER alpha expression and MBD2 depletion resulted in synergistic transcriptional stimulation, while the pS2 promoter remains methylated. Conclusions/Significance: MBD2 and ER alpha drive opposite effects on pS2 expression, which are associated with specific steady state levels of histone H3 acetylation and methylation marks. Thus, epigenetic silencing of pS2 could be dependent on balance of the relative intracellular concentrations of ER alpha and MBD2

A Role for Methyl-CpG Binding Domain Protein 2 in the Modulation of the Estrogen Response of pS2/TFF1 Gene

In human Estrogen Receptor alpha (ERalpha)-positive breast cancers, 5' end dense methylation of the estrogen-regulated pS2/TFF1 gene correlates with its transcriptional inhibition. However, in some ERalpha-rich biopsies, pS2 expression is observed despite the methylation of its TATA-box region. Herein, we investigated the methylation-dependent mechanism of pS2 regulation.We observed interplay between Methyl-CpG Binding Domain protein 2 (MBD2) transcriptional repressor and ERalpha transactivator: (i) the pS2 gene is poised for transcription upon demethylation limited to the enhancer region containing the estrogen responsive element (ERE); (ii) MBD2-binding sites overlapped with the methylation status of the pS2 5' end; (iii) MBD2 depletion elevated pS2 expression and ectopic expression of ERalpha partially overcame the inhibitory effect of MBD2 when the ERE is unmethylated. Furthermore, serial chromatin immunoprecipitation assays indicated that MBD2 and ERalpha could simultaneously occupy the same pS2 DNA molecule; (iv) concomitant ectopic ERalpha expression and MBD2 depletion resulted in synergistic transcriptional stimulation, while the pS2 promoter remains methylated.MBD2 and ERalpha drive opposite effects on pS2 expression, which are associated with specific steady state levels of histone H3 acetylation and methylation marks. Thus, epigenetic silencing of pS2 could be dependent on balance of the relative intracellular concentrations of ERalpha and MBD2

On the shape of vortices for a rotating Bose Einstein condensate

For a Bose-Einstein condensate placed in a rotating trap, we study the simplified energy of a vortex line derived in Aftalion-Riviere Phys. Rev. A 64, 043611 (2001) in order to determine the shape of the vortex line according to the rotational velocity and the elongation of the condensate. The energy reflects the competition between the length of the vortex which needs to be minimized taking into account the anisotropy of the trap and the rotation term which pushes the vortex along the z axis. We prove that if the condensate has the shape of a pancake, the vortex stays straight along the z axis while in the case of a cigar, the vortex is bent

Mandible Behavior in Obstructive Sleep Apnea Patients Under CPAP Treatment

Aim: To investigate whether obstructive sleep apnea (OSA) patients present different behaviors of mandible movements before and under CPAP therapy. Materials and Methodology: In this retrospective study, patients were selected according to inclusion criteria: both the diagnostic polysomnography recording showing an OSA with an apnea-hypopnea index (AHI) greater than 25 (n/h) and the related CPAP therapy control recordings were available, presence of mandible movement and mask pressure signals in the recordings, and tolerance to the applied positive pressure. Statistical analysis on four parameters, namely the apneahypopnea index (AHI), the arousal index (ArI), the average of the mandible lowering during sleep (aLOW), and the average amplitude of the oscillations of the mandible movement signal (aAMPL), was performed on two sets of recordings: OSA and CPAP therapy. Results: Thirty-four patients satisfied the inclusion criteria, thus both OSA and CPAP groups included thirty-four recordings each. Significant difference (p < 0.001) was found in the OSA group compared with the CPAP group when considering either the four parameters or only the two ones related to mandible movements. Conclusions: When an efficient CPAP pressure is applied, the mouth is less open and presents fewer broad sharp closure movements, and oscillating mandible movements are absent or very small.Peer reviewe

Specific association between the methyl-CpG-binding domain protein 2 and the hypermethylated region of the human telomerase reverse transcriptase promoter in cancer cells

Human telomerase reverse transcriptase (hTERT) is expressed in most cancer cells. Paradoxically, its promoter is embedded in a hypermethylated CpG island. A short region escapes to this alteration, allowing a basal level of transcription. However, the methylation of adjacent regions may play a role in the maintenance of low hTERT expression. It is now well established that methyl-CpG binding domain proteins mediate the transcriptional silencing of hypermethylated genes. The potential involvement of these proteins in the control of hTERT expression was firstly investigated in HeLa cells. Chromatin immunoprecipitation assays showed that only methyl-CpG-binding domain protein 2 (MBD2) associated the hypermethylated hTERT promoter. In MBD2 knockdown HeLa cells, constitutively depleted in MBD2, neither methyl CpG binding protein 2 (MeCP2) nor MBD1 acted as substitutes for MBD2. MBD2 depletion by transient or constitutive RNA interference led to an upregulation of hTERT transcription that can be downregulated by expressing mouse Mbd2 protein. Our results indicate that MBD2 is specifically and directly involved in the transcriptional repression of hTERT in HeLa cells. This specific transcriptional repression was also observed in breast, liver and neuroblastoma cancer cell lines. Thus, MBD2 seems to be a general repressor of hTERT in hTERT-methylated telomerase-positive cell

Loss of α-Synuclein Does Not Affect Mitochondrial Bioenergetics in Rodent Neurons.

Increased α-synuclein (αsyn) and mitochondrial dysfunction play central roles in the pathogenesis of Parkinson's disease (PD), and lowering αsyn is under intensive investigation as a therapeutic strategy for PD. Increased αsyn levels disrupt mitochondria and impair respiration, while reduced αsyn protects against mitochondrial toxins, suggesting that interactions between αsyn and mitochondria influences the pathologic and physiologic functions of αsyn. However, we do not know if αsyn affects normal mitochondrial function or if lowering αsyn levels impacts bioenergetic function, especially at the nerve terminal where αsyn is enriched. To determine if αsyn is required for normal mitochondrial function in neurons, we comprehensively evaluated how lowering αsyn affects mitochondrial function. We found that αsyn knockout (KO) does not affect the respiration of cultured hippocampal neurons or cortical and dopaminergic synaptosomes, and that neither loss of αsyn nor all three (α, β and γ) syn isoforms decreased mitochondria-derived ATP levels at the synapse. Similarly, neither αsyn KO nor knockdown altered the capacity of synaptic mitochondria to meet the energy requirements of synaptic vesicle cycling or influenced the localization of mitochondria to dopamine (DA) synapses in vivo. Finally, αsyn KO did not affect overall energy metabolism in mice assessed with a Comprehensive Lab Animal Monitoring System. These studies suggest either that αsyn has little or no significant physiological effect on mitochondrial bioenergetic function, or that any such functions are fully compensated for when lost. These results implicate that αsyn levels can be reduced in neurons without impairing (or improving) mitochondrial bioenergetics or distribution