A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences

One of the main implications of the effcient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stock prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example

A near-IR line of Mn I as a diagnostic tool of the average magnetic energy in the solar photosphere

We report on spectropolarimetric observations of a near-IR line of Mn I located at 15262.702 A whose intensity and polarization profiles are very sensitive to the presence of hyperfine structure. A theoretical investigation of the magnetic sensitivity of this line to the magnetic field uncovers several interesting properties. The most important one is that the presence of strong Paschen-Back perturbations due to the hyperfine structure produces an intensity line profile whose shape changes according to the absolute value of the magnetic field strength. A line ratio technique is developed from the intrinsic variations of the line profile. This line ratio technique is applied to spectropolarimetric observations of the quiet solar photosphere in order to explore the probability distribution function of the magnetic field strength. Particular attention is given to the quietest area of the observed field of view, which was encircled by an enhanced network region. A detailed theoretical investigation shows that the inferred distribution yields information on the average magnetic field strength and the spatial scale at which the magnetic field is organized. A first estimation gives ~250 G for the mean field strength and a tentative value of ~0.45" for the spatial scale at which the observed magnetic field is horizontally organized.Comment: 42 pages, 17 figures, accepted for publication in the Astrophysical Journal. Figures 1 and 9 are in JPG forma

Teleconnection in the martian atmosphere during the 2001 planet-encircling dust storm

Introduction: In July 2001 (Martian year 25), Mars was enshrouded by a thick veil of dust which lasted for several months and obscured the observation of its surface to spacecraft cameras and ground-based telescopes. The emergence and rapid evolution (within a few days) of multiple, isolated, regional dust storms which eventually attained planetary scale extent were observed by NASA’s Mars Global Surveyor (MGS) spacecraft using high resolution camera images and the thermal profiles and dust opacity measurements pro-vided by the Thermal Emission Spectrometer (TES) [1, 2]. We have applied a technique used in Terrestrial meteorology (sequential data assimilation, [3]) to ob-tain a complete, four-dimensional evolution of all the atmospheric variables during the period of this planet-encircling dust storm, even those which were not di-rectly observed by the MGS satellite, such as surface pressure and winds. We assimilated TES nadir-pointing thermal profiles and total dust opacities in a global circulation model of the Martian atmosphere, developed jointly by the University of Oxford and the Open University in the United Kingdom, with the col-laboration of the Laboratoire de Météorologie Dyna-mique in Paris (UK-MGCM) [4, 5, 6]

Fractal Descriptors in the Fourier Domain Applied to Color Texture Analysis

The present work proposes the development of a novel method to provide descriptors for colored texture images. The method consists in two steps. In the first, we apply a linear transform in the color space of the image aiming at highlighting spatial structuring relations among the color of pixels. In a second moment, we apply a multiscale approach to the calculus of fractal dimension based on Fourier transform. From this multiscale operation, we extract the descriptors used to discriminate the texture represented in digital images. The accuracy of the method is verified in the classification of two color texture datasets, by comparing the performance of the proposed technique to other classical and state-of-the-art methods for color texture analysis. The results showed an advantage of almost 3% of the proposed technique over the second best approach.Comment: Chaos, Volume 21, Issue 4, 201

Fluorescent Ly-alpha emission from the high-redshift intergalactic medium

We combine a high-resolution hydro-simulation of the LambdaCDM cosmology with two radiative transfer schemes (for continuum and line radiation) to predict the properties, spectra and spatial distribution of fluorescent Ly-alpha emission at z~3. We focus on line radiation produced by recombinations in the dense intergalactic medium ionized by UV photons. In particular, we consider both a uniform background and the case where gas clouds are illuminated by a nearby quasar. We find that the emission from optically thick regions is substantially less than predicted from the widely used static, plane-parallel model. The effects induced by a realistic velocity field and by the complex geometric structure of the emitting regions are discussed in detail. We make predictions for the expected brightness and size distributions of the fluorescent sources.Our results account for recent null detections and can be used to plan new observational campaigns both in the field (to measure the intensity of the diffuse UV background) and in the proximity of bright quasars (to understand the origin of high colum-density absorbers).Comment: 15 pages, 12 figures, accepted for publication in Ap

Abrupt wind regime changes in the North Atlantic Ocean during the past 30,000-60,000 years

The inputs of higher plants in Blake Outer Ridge (subtropical western North Atlantic) during marine isotope stage 3 (MIS3) have been recorded at high resolution by quantification of C23–C33 odd carbon numbered n-alkanes and C20–C30 even carbon numbered n-alkan-1-ols in sediment sections of Ocean Drilling Program Site 1060. The changes of these proxies at this open marine site are mainly related to eolian inputs. Their concentrations and fluxes exhibit major abrupt variations that are correlated with Dansgaard/Oeschger (D/O) patterns in Greenland ice cores. The ratios between interstadials and stadials range between 2 and 9 times. The intense flux increases in the D/O stadials are linked to strong enhancements of the westerly wind regime at these subtropical latitudes during stadials. The observed variation was paralleled by changes in wind-blown dust and the polar circulation index in Greenland ice, which is in agreement with previously hypothesized atmospheric teleconnections between northern and middle-low latitudes of the Northern Hemisphere. The close correspondence between sedimentary and ice core proxies is evidence that crossings of the glacial climate thresholds involved major reorganizations of the troposphere. The observed large rise in higher plant biomarkers indicates that climate stabilization in the D/O stadial conditions led to main increases in wind intensity

Remarks on Bootstrap Percolation in Metric Networks

We examine bootstrap percolation in d-dimensional, directed metric graphs in the context of recent measurements of firing dynamics in 2D neuronal cultures. There are two regimes, depending on the graph size N. Large metric graphs are ignited by the occurrence of critical nuclei, which initially occupy an infinitesimal fraction, f_* -> 0, of the graph and then explode throughout a finite fraction. Smaller metric graphs are effectively random in the sense that their ignition requires the initial ignition of a finite, unlocalized fraction of the graph, f_* >0. The crossover between the two regimes is at a size N_* which scales exponentially with the connectivity range \lambda like_* \sim \exp\lambda^d. The neuronal cultures are finite metric graphs of size N \simeq 10^5-10^6, which, for the parameters of the experiment, is effectively random since N<< N_*. This explains the seeming contradiction in the observed finite f_* in these cultures. Finally, we discuss the dynamics of the firing front

Single Hole Green's Functions in Insulating Copper Oxides at Nonzero Temperature

We consider the single hole dynamics in a modified $t-J$ model at finite temperature. The modified model includes a next nearest ($t'$) and next-next nearest ($t''$) hopping. The model has been considered before in the zero temperature limit to explain angle resolved photo-emission measurements. We extend this consideration to the case of finite temperature where long-range anti-ferromagnetic order is destroyed, using the self-consistent Born approximation. The Dyson equation which relates the single hole Green's functions for a fixed pseudo-spin and for fixed spin is derived. The Green's function with fixed pseudo-spin is infrared stable but the Green's function with fixed spin is close to an infrared divergency. We demonstrate how to renormalize this Green's function in order to assure numerical convergence. At non-zero temperature the quasi-particle peaks are found to shift down in energy and to be broadened.Comment: 7 pages, RevTex, 5 Postscript figure