707 research outputs found
Effects of Diversity and Procrastination in Priority Queuing Theory: the Different Power Law Regimes
Empirical analysis show that, after the update of a browser, the publication
of the vulnerability of a software, or the discovery of a cyber worm, the
fraction of computers still using the older version, or being not yet patched,
or exhibiting worm activity decays as power laws with over time scales of years. We present a simple model for this
persistence phenomenon framed within the standard priority queuing theory, of a
target task which has the lowest priority compared with all other tasks that
flow on the computer of an individual. We identify a "time deficit" control
parameter and a bifurcation to a regime where there is a non-zero
probability for the target task to never be completed. The distribution of
waiting time till the completion of the target task has the power
law tail , resulting from a first-passage solution of an
equivalent Wiener process. Taking into account a diversity of time deficit
parameters in a population of individuals, the power law tail is changed into
with , including the well-known case .
We also study the effect of "procrastination", defined as the situation in
which the target task may be postponed or delayed even after the individual has
solved all other pending tasks. This new regime provides an explanation for
even slower apparent decay and longer persistence.Comment: 32 pages, 10 figure
The log-periodic-AR(1)-GARCH(1,1) model for financial crashes
This paper intends to meet recent claims for the attainment of more rigorous
statistical methodology within the econophysics literature. To this end, we
consider an econometric approach to investigate the outcomes of the
log-periodic model of price movements, which has been largely used to forecast
financial crashes. In order to accomplish reliable statistical inference for
unknown parameters, we incorporate an autoregressive dynamic and a conditional
heteroskedasticity structure in the error term of the original model, yielding
the log-periodic-AR(1)-GARCH(1,1) model. Both the original and the extended
models are fitted to financial indices of U. S. market, namely S&P500 and
NASDAQ. Our analysis reveal two main points: (i) the
log-periodic-AR(1)-GARCH(1,1) model has residuals with better statistical
properties and (ii) the estimation of the parameter concerning the time of the
financial crash has been improved.Comment: 17 pages, 4 figures, 12 tables, to appear in Europen Physical Journal
Multiplicative processes and power laws
[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of
stochastic processes with multiplicative noise, which have been studied in
several different contexts over the past decades. We focus on the regime, found
for a generic set of control parameters, in which stochastic processes with
multiplicative noise produce intermittency of a special kind, characterized by
a power law probability density distribution. We briefly explain the physical
mechanism leading to a power law pdf and provide a list of references for these
results dating back from a quarter of century. We explain how the formulation
in terms of the characteristic function developed by Takayasu et al. can be
extended to exponents , which explains the ``reason of the lucky
coincidence''. The multidimensional generalization of (\ref{eq1}) and the
available results are briefly summarized. The discovery of stretched
exponential tails in the presence of the cut-off introduced in \cite{Taka} is
explained theoretically. We end by briefly listing applications.Comment: Extended version (7 pages). Phys. Rev. E (to appear April 1998
Rank-Ordering Statistics of Extreme Events: Application to the Distribution of Large Earthquakes
Rank-ordering statistics provides a perspective on the rare, largest elements
of a population, whereas the statistics of cumulative distributions are
dominated by the more numerous small events. The exponent of a power law
distribution can be determined with good accuracy by rank-ordering statistics
from the observation of only a few tens of the largest events. Using analytical
results and synthetic tests, we quantify the systematic and the random errors.
We also study the case of a distribution defined by two branches, each having
a power law distribution, one defined for the largest events and the other for
smaller events, with application to the World-Wide (Harvard) and Southern
California earthquake catalogs. In the case of the Harvard moment catalog, we
make more precise earlier claims of the existence of a transition of the
earthquake magnitude distribution between small and large earthquakes; the
-values are for large shallow earthquakes and for smaller shallow earthquakes. However, the cross-over
magnitude between the two distributions is ill-defined. The data available at
present do not provide a strong constraint on the cross-over which has a
probability of being between magnitudes and for shallow
earthquakes; this interval may be too conservatively estimated. Thus, any
influence of a universal geometry of rupture on the distribution of earthquakes
world-wide is ill-defined at best. We caution that there is no direct evidence
to confirm the hypothesis that the large-moment branch is indeed a power law.
In fact, a gamma distribution fits the entire suite of earthquake moments from
the smallest to the largest satisfactorily. There is no evidence that the
earthquakes of the Southern California catalog have a distribution with tw
Response Functions to Critical Shocks in Social Sciences: An Empirical and Numerical Study
We show that, provided one focuses on properly selected episodes, one can
apply to the social sciences the same observational strategy that has proved
successful in natural sciences such as astrophysics or geodynamics. For
instance, in order to probe the cohesion of a policy, one can, in different
countries, study the reactions to some huge and sudden exogenous shocks, which
we call Dirac shocks. This approach naturally leads to the notion of structural
(as opposed or complementary to temporal) forecast. Although structural
predictions are by far the most common way to test theories in the natural
sciences, they have been much less used in the social sciences. The Dirac shock
approach opens the way to testing structural predictions in the social
sciences. The examples reported here suggest that critical events are able to
reveal pre-existing ``cracks'' because they probe the social cohesion which is
an indicator and predictor of future evolution of the system, and in some cases
foreshadows a bifurcation. We complement our empirical work with numerical
simulations of the response function (``damage spreading'') to Dirac shocks in
the Sznajd model of consensus build-up. We quantify the slow relaxation of the
difference between perturbed and unperturbed systems, the conditions under
which the consensus is modified by the shock and the large variability from one
realization to another
On the Occurrence of Finite-Time-Singularities in Epidemic Models of Rupture, Earthquakes and Starquakes
We present a new kind of critical stochastic finite-time-singularity, relying
on the interplay between long-memory and extreme fluctuations. We illustrate it
on the well-established epidemic-type aftershock (ETAS) model for aftershocks,
based solely on the most solidly documented stylized facts of seismicity
(clustering in space and in time and power law Gutenberg-Richter distribution
of earthquake energies). This theory accounts for the main observations (power
law acceleration and discrete scale invariant structure) of critical rupture of
heterogeneous materials, of the largest sequence of starquakes ever attributed
to a neutron star as well as of earthquake sequences.Comment: Revtex document of 4 pages including 1 eps figur
Tri-critical behavior in rupture induced by disorder
We discover a qualitatively new behavior for systems where the load transfer
has limiting stress amplification as in real fiber composites. We find that the
disorder is a relevant field leading to tri--criticality, separating a
first-order regime where rupture occurs without significant precursors from a
second-order regime where the macroscopic elastic coefficient exhibit power law
behavior. Our results are based on analytical analysis of fiber bundle models
and numerical simulations of a two-dimensional tensorial spring-block system in
which stick-slip motion and fracture compete.Comment: Revtex, 10 pages, 4 figures available upon reques
Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis
The basic purpose of the paper is to draw the attention of researchers to new
possibilities of differentiation of similar signals having different nature.
One of examples of such kind of signals is presented by seismograms containing
recordings of earthquakes (EQ's) and technogenic explosions (TE's). We propose
here a discrete stochastic model for possible solution of a problem of strong
EQ's forecasting and differentiation of TE's from the weak EQ's. Theoretical
analysis is performed by two independent methods: with the use of statistical
theory of discrete non-Markov stochastic processes (Phys. Rev. E62,6178 (2000))
and the local Hurst exponent. Time recordings of seismic signals of the first
four dynamic orthogonal collective variables, six various plane of phase
portrait of four dimensional phase space of orthogonal variables and the local
Hurst exponent have been calculated for the dynamic analysis of the earth
states. The approaches, permitting to obtain an algorithm of strong EQ's
forecasting and to differentiate TE's from weak EQ's, have been developed.Comment: REVTEX +12 ps and jpg figures. Accepted for publication in Phys. Rev.
E, December 200
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