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 $f = 1.02 \pm 0.05$ corresponding to the scaling ratio $\lambda = 2.67 \pm 0.12$. 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 Z\mathbb{Z}

We show that the Leavitt path algebras $L_{2,\mathbb{Z}}$ and $L_{2-,\mathbb{Z}}$ 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 $L_{\mathbb{Z}}(E)$ for $E$ a finite graph. This description is based on a generalization, due to Chris Smith, of the description of the unitaries in $L_{2,\mathbb{Z}}$ given by Brownlowe and the second named author. The techniques generalize to a slightly larger class of rings than just $\mathbb{Z}$.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 $t_c$. 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 $t_c$, 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