3,167 research outputs found
Exact Analysis of TTL Cache Networks: The Case of Caching Policies driven by Stopping Times
TTL caching models have recently regained significant research interest,
largely due to their ability to fit popular caching policies such as LRU. This
paper advances the state-of-the-art analysis of TTL-based cache networks by
developing two exact methods with orthogonal generality and computational
complexity. The first method generalizes existing results for line networks
under renewal requests to the broad class of caching policies whereby evictions
are driven by stopping times. The obtained results are further generalized,
using the second method, to feedforward networks with Markov arrival processes
(MAP) requests. MAPs are particularly suitable for non-line networks because
they are closed not only under superposition and splitting, as known, but also
under input-output caching operations as proven herein for phase-type TTL
distributions. The crucial benefit of the two closure properties is that they
jointly enable the first exact analysis of feedforward networks of TTL caches
in great generality
Regenerative properties of the linear hawkes process with unbounded memory
We prove regenerative properties for the linear Hawkes process under minimal
assumptions on the transfer function, which may have unbounded support. These
results are applicable to sliding window statistical estimators. We exploit
independence in the Poisson cluster point process decomposition, and the
regeneration times are not stopping times for the Hawkes process. The
regeneration time is interpreted as the renewal time at zero of a M/G/infinity
queue, which yields a formula for its Laplace transform. When the transfer
function admits some exponential moments, we stochastically dominate the
cluster length by exponential random variables with parameters expressed in
terms of these moments. This yields explicit bounds on the Laplace transform of
the regeneration time in terms of simple integrals or special functions
yielding an explicit negative upper-bound on its abscissa of convergence. These
regenerative results allow, e.g., to systematically derive long-time asymptotic
results in view of statistical applications. This is illustrated on a
concentration inequality previously obtained with coauthors
A unified approach to the performance analysis of caching systems
We propose a unified methodology to analyse the performance of caches (both
isolated and interconnected), by extending and generalizing a decoupling
technique originally known as Che's approximation, which provides very accurate
results at low computational cost. We consider several caching policies, taking
into account the effects of temporal locality. In the case of interconnected
caches, our approach allows us to do better than the Poisson approximation
commonly adopted in prior work. Our results, validated against simulations and
trace-driven experiments, provide interesting insights into the performance of
caching systems.Comment: in ACM TOMPECS 20016. Preliminary version published at IEEE Infocom
201
Infinite volume limits of polymer chains with periodic charges
The aim of this paper is twofold:
- To give an elementary and self-contained proof of an explicit formula for
the free energy for a general class of polymer chains interacting with an
environment through periodic potentials. This generalizes a result in
[Bolthausen and Giacomin, AAP 2005] in which the formula is derived by using
the Donsker-Varadhan Large Deviations theory for Markov chains. We exploit
instead tools from renewal theory.
- To identify the infinite volume limits of the system. In particular, in the
different regimes we encounter transient, null recurrent and positive recurrent
processes (which correspond to delocalized, critical and localized behaviors of
the trajectories). This is done by exploiting the sharp estimates on the
partition function of the system obtained by the renewal theory approach.
The precise characterization of the infinite volume limits of the system
exposes a non-uniqueness problem. We will however explain in detail how this
(at first) surprising phenomenon is instead due to the presence of a
first-order phase transition.Comment: 27 pages, 2 figure
Cleaning sky survey databases using Hough Transform and Renewal String approaches
Large astronomical databases obtained from sky surveys such as the
SuperCOSMOS Sky Survey (SSS) invariably suffer from spurious records coming
from artefactual effects of the telescope, satellites and junk objects in orbit
around earth and physical defects on the photographic plate or CCD. Though
relatively small in number these spurious records present a significant problem
in many situations where they can become a large proportion of the records
potentially of interest to a given astronomer. Accurate and robust techniques
are needed for locating and flagging such spurious objects, and we are
undertaking a programme investigating the use of machine learning techniques in
this context. In this paper we focus on the four most common causes of unwanted
records in the SSS: satellite or aeroplane tracks, scratches, fibres and other
linear phenomena introduced to the plate, circular halos around bright stars
due to internal reflections within the telescope and diffraction spikes near to
bright stars. Appropriate techniques are developed for the detection of each of
these. The methods are applied to the SSS data to develop a dataset of spurious
object detections, along with confidence measures, which can allow these
unwanted data to be removed from consideration. These methods are general and
can be adapted to other astronomical survey data.Comment: Accepted for MNRAS. 17 pages, latex2e, uses mn2e.bst, mn2e.cls,
md706.bbl, shortbold.sty (all included). All figures included here as low
resolution jpegs. A version of this paper including the figures can be
downloaded from http://www.anc.ed.ac.uk/~amos/publications.html and more
details on this project can be found at
http://www.anc.ed.ac.uk/~amos/sattrackres.htm
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