Validity of heavy traffic steady-state approximations in generalized Jackson Networks

We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavy-traffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a reflected Brownian motion (RBM) in the orthant, as the traffic intensity approaches unity. However, barring simple instances, it is still not known whether the stationary distribution of RBM provides a valid approximation for the steady-state of the original network. In this paper we resolve this open problem by proving that the re-scaled stationary distribution of the GJN converges to the stationary distribution of the RBM, thus validating a so-called ``interchange-of-limits'' for this class of networks. Our method of proof involves a combination of Lyapunov function techniques, strong approximations and tail probability bounds that yield tightness of the sequence of stationary distributions of the GJN.Comment: Published at http://dx.doi.org/10.1214/105051605000000638 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Encounter time of two loci governed by polymer de-condensation and local chromatin interaction

The time for a DNA sequence to find its homologous depends on a long random search process inside the cell nucleus. Using polymer models, we model and compute here the mean first encounter time (MFET) between two sites located on two different polymer chains and confined by potential wells. We find that reducing the potential (tethering) forces results in a local polymer decondensation near the loci and numerical simulations of the polymer model show that these changes are associated with a reduction of the MFET by several orders of magnitude. We derive here new asymptotic formula for the MFET, confirmed by Brownian simulations. We conclude that the acceleration of the search process after local chromatin decondensation can be used to analyze the local search step during homology search.Comment: 3 figure

Data mining of protein families using common peptides

Predicting the function of a protein from its sequence is typically addressed using sequence-similarity. Here we propose a motif-based approach, using supervised motif extraction from protein sequences belonging to one functional family. The resulting deterministic motifs form Common Peptides (CPs) that characterize this family, allow for data mining of its proteins and facilitate further partition of the family into cluster

A close examination of cosmic microwave background mirror-parity after Planck

Previous claims of significant evidence for mirror-parity in the large-scale cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe (WMAP) experiment have been recently echoed in the first study of isotropy and statistics of CMB data from Planck. We revisit these claims with a careful analysis of the latest data available. We construct statistical estimators in both harmonic and pixel space, test them on simulated data with and without mirror-parity symmetry, apply different Galactic masks, and study the dependence of the results on arbitrary choices of free parameters. We confirm that the data exhibit evidence for odd mirror-parity at a significance which reaches as high as ~ 99 per cent C.L., under some circumstances. However, given the inherent biases in the pixel-based statistic and the dependence of both pixel and harmonic space statistics on the particular form of Galactic masking and other a-posteriori choices, we conclude that these results are not in significant tension with the predictions of the concordance cosmological model.Comment: 9 pages, 5 figures, minor changes, as published in MNRA