740 research outputs found
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
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