7,682 research outputs found
Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes
We apply two non-parametric methods to test further the hypothesis that
log-periodicity characterizes the detrended price trajectory of large financial
indices prior to financial crashes or strong corrections. The analysis using
the so-called (H,q)-derivative is applied to seven time series ending with the
October 1987 crash, the October 1997 correction and the April 2000 crash of the
Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq
indices. The Hilbert transform is applied to two detrended price time series in
terms of the ln(t_c-t) variable, where t_c is the time of the crash. Taking all
results together, we find strong evidence for a universal fundamental
log-frequency corresponding to the scaling ratio . These values are in very good agreement with those obtained in
past works with different parametric techniques.Comment: Latex document 13 pages + 58 eps figure
The Cuntz splice does not preserve -isomorphism of Leavitt path algebras over
We show that the Leavitt path algebras and
are not isomorphic as -algebras. There are two key
ingredients in the proof. One is a partial algebraic translation of Matsumoto
and Matui's result on diagonal preserving isomorphisms of Cuntz--Krieger
algebras. The other is a complete description of the projections in
for a finite graph. This description is based on a
generalization, due to Chris Smith, of the description of the unitaries in
given by Brownlowe and the second named author. The
techniques generalize to a slightly larger class of rings than just
.Comment: 17 pages. Since version 2 we extended the arguments from Z to more
general ring
Global magnetohydrodynamical models of turbulence in protoplanetary disks I. A cylindrical potential on a Cartesian grid and transport of solids
We present global 3D MHD simulations of disks of gas and solids, aiming at
developing models that can be used to study various scenarios of planet
formation and planet-disk interaction in turbulent accretion disks. A second
goal is to show that Cartesian codes are comparable to cylindrical and
spherical ones in handling the magnetohydrodynamics of the disk simulations, as
the disk-in-a-box models presented here develop and sustain MHD turbulence. We
investigate the dependence of the magnetorotational instability on disk scale
height, finding evidence that the turbulence generated by the magnetorotational
instability grows with thermal pressure. The turbulent stresses depend on the
thermal pressure obeying a power law of 0.24+/-0.03, compatible with the value
of 0.25 found in shearing box calculations. The ratio of stresses decreased
with increasing temperature. We also study the dynamics of boulders in the
hydromagnetic turbulence. The vertical turbulent diffusion of the embedded
boulders is comparable to the turbulent viscosity of the flow. Significant
overdensities arise in the solid component as boulders concentrate in high
pressure regions.Comment: Changes after peer review proces
Finite-Time Singularity Signature of Hyperinflation
We present a novel analysis extending the recent work of Mizuno et al. [2002]
on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary
(1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua
(1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a
generalization of Cagan's model of inflation based on the mechanism of
``inflationary expectation'' or positive feedbacks between realized growth rate
and people's expected growth rate, we find that hyperinflations can be
characterized by a power law singularity culminating at a critical time .
Mizuno et al.'s double-exponential function can be seen as a discrete time-step
approximation of our more general nonlinear ODE formulation of the price
dynamics which exhibits a finite-time singular behavior. This extension of
Cagan's model, which makes natural the appearance of a critical time , has
the advantage of providing a well-defined end of the clearly unsustainable
hyperinflation regime. We find an excellent and reliable agreement between
theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and
Nicaragua, the super-exponential growth seems to be already contaminated
significantly by the existence of a cross-over to a stationary regime.Comment: Latex 21 pages including 2 tables and 7 eps figure
Artifactual log-periodicity in finite size data: Relevance for earthquake aftershocks
The recently proposed discrete scale invariance and its associated
log-periodicity are an elaboration of the concept of scale invariance in which
the system is scale invariant only under powers of specific values of the
magnification factor. We report on the discovery of a novel mechanism for such
log-periodicity relying solely on the manipulation of data. This ``synthetic''
scenario for log-periodicity relies on two steps: (1) the fact that
approximately logarithmic sampling in time corresponds to uniform sampling in
the logarithm of time; and (2) a low-pass-filtering step, as occurs in
constructing cumulative functions, in maximum likelihood estimations, and in
de-trending, reddens the noise and, in a finite sample, creates a maximum in
the spectrum leading to a most probable frequency in the logarithm of time. We
explore in detail this mechanism and present extensive numerical simulations.
We use this insight to analyze the 27 best aftershock sequences studied by
Kisslinger and Jones [1991] to search for traces of genuine log-periodic
corrections to Omori's law, which states that the earthquake rate decays
approximately as the inverse of the time since the last main shock. The
observed log-periodicity is shown to almost entirely result from the
``synthetic scenario'' owing to the data analysis. From a statistical point of
view, resolving the issue of the possible existence of log-periodicity in
aftershocks will be very difficult as Omori's law describes a point process
with a uniform sampling in the logarithm of the time. By construction, strong
log-periodic fluctuations are thus created by this logarithmic sampling.Comment: LaTeX, JGR preprint with AGU++ v16.b and AGUTeX 5.0, use packages
graphicx, psfrag and latexsym, 41 eps figures, 26 pages. In press J. Geophys.
Re
Reinforced carbon-carbon oxidation behavior in convective and radiative environments
Reinforced carbon-carbon, which is used as thermal protection on the space shuttle orbiter wing leading edges and nose cap, was tested in both radiant and plasma arcjet heating test facilities. The test series was conducted at varying temperatures and pressures. Samples tested in the plasma arcjet facility had consistently higher mass loss than those samples tested in the radiant facility. A method using the mass loss data is suggested for predicting mission mass loss for specific locations on the Orbiter
Dendritic flux patterns in MgB2 films
Magneto-opitcal studies of a c-oriented epitaxial MgB2 film with critical
current density 10^7 A/cm^2 demonstrate a breakdown of the critical state at
temperatures below 10 K [cond-mat/0104113]. Instead of conventional uniform and
gradual flux penetration in an applied magnetic field, we observe an abrupt
invasion of complex dendritic structures. When the applied field subsequently
decreases, similar dendritic structures of the return flux penetrate the film.
The static and dynamic properties of the dendrites are discussed.Comment: Accepted to Supercond. Sci. Techno
Dynamic filtering of static dipoles in magnetoencephalography
We consider the problem of estimating neural activity from measurements
of the magnetic fields recorded by magnetoencephalography. We exploit
the temporal structure of the problem and model the neural current as a
collection of evolving current dipoles, which appear and disappear, but whose
locations are constant throughout their lifetime. This fully reflects the physiological
interpretation of the model.
In order to conduct inference under this proposed model, it was necessary
to develop an algorithm based around state-of-the-art sequential Monte
Carlo methods employing carefully designed importance distributions. Previous
work employed a bootstrap filter and an artificial dynamic structure
where dipoles performed a random walk in space, yielding nonphysical artefacts
in the reconstructions; such artefacts are not observed when using the
proposed model. The algorithm is validated with simulated data, in which
it provided an average localisation error which is approximately half that of
the bootstrap filter. An application to complex real data derived from a somatosensory
experiment is presented. Assessment of model fit via marginal
likelihood showed a clear preference for the proposed model and the associated
reconstructions show better localisation
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