730,771 research outputs found
Point-occurrence self-similarity in crackling-noise systems and in other complex systems
It has been recently found that a number of systems displaying crackling
noise also show a remarkable behavior regarding the temporal occurrence of
successive events versus their size: a scaling law for the probability
distributions of waiting times as a function of a minimum size is fulfilled,
signaling the existence on those systems of self-similarity in time-size. This
property is also present in some non-crackling systems. Here, the uncommon
character of the scaling law is illustrated with simple marked renewal
processes, built by definition with no correlations. Whereas processes with a
finite mean waiting time do not fulfill a scaling law in general and tend
towards a Poisson process in the limit of very high sizes, processes without a
finite mean tend to another class of distributions, characterized by double
power-law waiting-time densities. This is somehow reminiscent of the
generalized central limit theorem. A model with short-range correlations is not
able to escape from the attraction of those limit distributions. A discussion
on open problems in the modeling of these properties is provided.Comment: Submitted to J. Stat. Mech. for the proceedings of UPON 2008 (Lyon),
topic: crackling nois
Catalog Dynamics: Impact of Content Publishing and Perishing on the Performance of a LRU Cache
The Internet heavily relies on Content Distribution Networks and transparent
caches to cope with the ever-increasing traffic demand of users. Content,
however, is essentially versatile: once published at a given time, its
popularity vanishes over time. All requests for a given document are then
concentrated between the publishing time and an effective perishing time.
In this paper, we propose a new model for the arrival of content requests,
which takes into account the dynamical nature of the content catalog. Based on
two large traffic traces collected on the Orange network, we use the
semi-experimental method and determine invariants of the content request
process. This allows us to define a simple mathematical model for content
requests; by extending the so-called "Che approximation", we then compute the
performance of a LRU cache fed with such a request process, expressed by its
hit ratio. We numerically validate the good accuracy of our model by comparison
to trace-based simulation.Comment: 13 Pages, 9 figures. Full version of the article submitted to the ITC
2014 conference. Small corrections in the appendix from the previous versio
Mathematical Models of Gene Expression
In this paper we analyze the equilibrium properties of a large class of
stochastic processes describing the fundamental biological process within
bacterial cells, {\em the production process of proteins}. Stochastic models
classically used in this context to describe the time evolution of the numbers
of mRNAs and proteins are presented and discussed. An extension of these
models, which includes elongation phases of mRNAs and proteins, is introduced.
A convergence result to equilibrium for the process associated to the number of
proteins and mRNAs is proved and a representation of this equilibrium as a
functional of a Poisson process in an extended state space is obtained.
Explicit expressions for the first two moments of the number of mRNAs and
proteins at equilibrium are derived, generalizing some classical formulas.
Approximations used in the biological literature for the equilibrium
distribution of the number of proteins are discussed and investigated in the
light of these results. Several convergence results for the distribution of the
number of proteins at equilibrium are in particular obtained under different
scaling assumptions
Stochastic Multipath Model for the In-Room Radio Channel based on Room Electromagnetics
We propose a stochastic multipath model for the received signal for the case
where the transmitter and receiver, both with directive antennas, are situated
in the same rectangular room. This scenario is known to produce channel impulse
responses with a gradual specular-to-diffused transition in delay. Mirror
source theory predicts the arrival rate to be quadratic in delay, inversely
proportional to room volume and proportional to the product of the antenna beam
coverage fractions. We approximate the mirror source positions by a homogeneous
spatial Poisson point process and their gain as complex random variables with
the same second moment. The multipath delays in the resulting model form an
inhomogeneous Poisson point process which enables derivation of the
characteristic functional, power/kurtosis delay spectra, and the distribution
of order statistics of the arrival delays in closed form. We find that the
proposed model matches the mirror source model well in terms of power delay
spectrum, kurtosis delay spectrum, order statistics, and prediction of mean
delay and rms delay spread. The constant rate model, assumed in e.g. the
Saleh-Valenzuela model, is unable to reproduce the same effects.Comment: 14 pages, Manuscript Submitted to IEEE Transaction on Antennas and
Propagatio
Segmentation algorithm for non-stationary compound Poisson processes
We introduce an algorithm for the segmentation of a class of regime switching
processes. The segmentation algorithm is a non parametric statistical method
able to identify the regimes (patches) of the time series. The process is
composed of consecutive patches of variable length, each patch being described
by a stationary compound Poisson process, i.e. a Poisson process where each
count is associated to a fluctuating signal. The parameters of the process are
different in each patch and therefore the time series is non stationary. Our
method is a generalization of the algorithm introduced by Bernaola-Galvan, et
al., Phys. Rev. Lett., 87, 168105 (2001). We show that the new algorithm
outperforms the original one for regime switching compound Poisson processes.
As an application we use the algorithm to segment the time series of the
inventory of market members of the London Stock Exchange and we observe that
our method finds almost three times more patches than the original one.Comment: 11 pages, 11 figure
Detecting the harmonics of oscillations with time-variable frequencies
A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology
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