Multifractal Height Cross-Correlation Analysis: A New Method for Analyzing Long-Range Cross-Correlations

We introduce a new method for detection of long-range cross-correlations and multifractality - multifractal height cross-correlation analysis (MF-HXA) - based on scaling of qth order covariances. MF-HXA is a bivariate generalization of the height-height correlation analysis of Barabasi & Vicsek [Barabasi, A.L., Vicsek, T.: Multifractality of self-affine fractals, Physical Review A 44(4), 1991]. The method can be used to analyze long-range cross-correlations and multifractality between two simultaneously recorded series. We illustrate a power of the method on both simulated and real-world time series.Comment: 6 pages, 4 figure

Quantitative features of multifractal subtleties in time series

Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian distribution, both uncorrelated and correlated in time, are used. For the uncorrelated series at the border (q=5/3) between the Gaussian and the Levy basins of attraction asymptotically we find a phase-like transition between monofractal and bifractal characteristics. This indicates that these may solely be the specific nonlinear temporal correlations that organize the series into a genuine multifractal hierarchy. For analyzing various features of multifractality due to such correlations, we use the model series generated from the binomial cascade as well as empirical series. Then, within the temporal ranges of well developed power-law correlations we find a fast convergence in all multifractal measures. Besides of its practical significance this fact may reflect another manifestation of a conjectured q-generalized Central Limit Theorem

Spitzer observations of the Orion OB1 association: disk census in the low mass stars

We present new Spitzer Space Telescope observations of two fields in the Orion OB1 association. We report here IRAC/MIPS observations for 115 confirmed members and 41 photometric candidates of the ~10 Myr 25 Orionis aggregate in the OB1a subassociation, and 106 confirmed members and 65 photometric candidates of the 5 Myr region located in the OB1b subassociation. The 25 Orionis aggregate shows a disk frequency of 6% while the field in the OB1b subassociation shows a disk frequency of 13%. Combining IRAC, MIPS and 2MASS photometry we place stars bearing disks in several classes: stars with optically thick disks (class II systems), stars with an inner transitional disks (transitional disk candidates) and stars with "evolved disks"; the last exhibit smaller IRAC/MIPS excesses than class II systems. In all, we identify 1 transitional disk candidate in the 25 Orionis aggregate and 3 in the OB1b field; this represents ~10% of the disk bearing stars, indicating that the transitional disk phase can be relatively fast. We find that the frequency of disks is a function of the stellar mass, suggesting a maximum around stars with spectral type M0. Comparing the infrared excess in the IRAC bands among several stellar groups we find that inner disk emission decays with stellar age, showing a correlation with the respective disk frequencies. The disk emission at the IRAC and MIPS bands in several stellar groups indicates that disk dissipation takes place faster in the inner region of the disks. Comparison with models of irradiated accretion disks, computed with several degrees of settling, suggests that the decrease in the overall accretion rate observed in young stellar groups is not sufficient to explain the weak disk emission observed in the IRAC bands for disk bearing stars with ages 5 Myr or older.Comment: Accepted in the Astrophysical Journa

The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all the pairs considered are well described by the nonextensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the nonextensivity q-parameter values for different exchange rates and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all the exchange rates with a varying degree of symmetry of the singularity spectrum f(alpha) however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations which excludes description in terms of q-Gaussians. The multifractal characteristics for these residual returns reveal such anomalous properties like negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with the diffusion limited aggregation and with turbulence. We find that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales. Although the currency market is much more liquid than the stock markets and it has much larger transaction frequency, the building-up of correlations takes up to several hours - time that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect

A simplified protocol for detecting two systemic bait markers (Rhodamine B and iophenoxic acid) in small mammals

We developed a method of quantifying levels of fluorescence in the whiskers of wild stoats (Mustela erminea) using fluorescence microscopy and Axiovision 3.0.6.1 software. The method allows for discrimination between natural fluorescence present in or on a whisker, and the fluorescence resulting from the ingestion of the systemic marker Rhodamine B (RB), although some visual judgement is still required. We also developed a new high performance liquid chromatography (HPLC) protocol for detecting the systemic marker iophenoxic acid (IPA) in the blood of laboratory rats (Rattus norvegicus) and wild stoats. With this method, the blood of an animal that has consumed IPA can be tested for the presence of the foreign IPA compound itself. This is a more reliable test than the previous method, which measured the raised level of natural blood protein-bound iodine correlated with IPA absorption. The quantity of blood required from animal subjects is very small (10 μl), so the testing is less intrusive and the method can be extended to smaller species. The extraction technique uses methanol, rather than acids and heavy metal salts, thereby simplifying the procedure. Recovery of IPA is quantitative, giving a highly reliable reading. In experiments on captive rats the IPA method proved successful. Of 12 positively marked carcasses, two that had not been frozen for the 24 h before blood samples were taken showed relatively lower IPA levels. The same IPA detection method, as well as the whisker analysis for RB, was applied successfully to a population of wild stoats to which both Rhodamine B and IPA were made available at bait stations. The presence of both bait markers was detectable in rats for at least 21 days and in stoats for at least 27 days

Integrating ASCAT surface soil moisture and GEOV1 leaf area index into the SURFEX modelling platform: a land data assimilation application over France

The land monitoring service of the European Copernicus programme has developed a set of satellite-based biogeophysical products, including surface soil moisture (SSM) and leaf area index (LAI). This study investigates the impact of joint assimilation of remotely sensed SSM derived from Advanced Scatterometer (ASCAT) backscatter data and the Copernicus Global Land GEOV1 satellite-based LAI product into the the vegetation growth version of the Interactions between Soil Biosphere Atmosphere (ISBA-A-gs) land surface model within the the externalised surface model (SURFEX) modelling platform of Météo-France. The ASCAT data were bias corrected with respect to the model climatology by using a seasonal-based CDF (Cumulative Distribution Function) matching technique. A multivariate multi-scale land data assimilation system (LDAS) based on the extended Kalman Filter (EKF) is used for monitoring the soil moisture, terrestrial vegetation, surface carbon and energy fluxes across the domain of France at a spatial resolution of 8 km. Each model grid box is divided into a number of land covers, each having its own set of prognostic variables. The filter algorithm is designed to provide a distinct analysis for each land cover while using one observation per grid box. The updated values are aggregated by computing a weighted average. <br><br> In this study, it is demonstrated that the assimilation scheme works effectively within the ISBA-A-gs model over a four-year period (2008–2011). The EKF is able to extract useful information from the data signal at the grid scale and distribute the root-zone soil moisture and LAI increments throughout the mosaic structure of the model. The impact of the assimilation on the vegetation phenology and on the water and carbon fluxes varies from one season to another. The spring drought of 2011 is an interesting case study of the potential of the assimilation to improve drought monitoring. A comparison between simulated and in situ soil moisture gathered at the twelve SMOSMANIA (Soil Moisture Observing System–Meteorological Automatic Network Integrated Application) stations shows improved anomaly correlations for eight stations

A multi-wavelength analysis for interferometric (sub-)mm observations of protoplanetary disks: radial constraints on the dust properties and the disk structure

Theoretical models of grain growth predict dust properties to change as a function of protoplanetary disk radius, mass, age and other physical conditions. We lay down the methodology for a multi-wavelength analysis of (sub-)mm and cm continuum interferometric observations to constrain self-consistently the disk structure and the radial variation of the dust properties. The computational architecture is massively parallel and highly modular. The analysis is based on the simultaneous fit in the uv-plane of observations at several wavelengths with a model for the disk thermal emission and for the dust opacity. The observed flux density at the different wavelengths is fitted by posing constraints on the disk structure and on the radial variation of the grain size distribution. We apply the analysis to observations of three protoplanetary disks (AS 209, FT Tau, DR Tau) for which a combination of spatially resolved observations in the range ~0.88mm to ~10mm is available (from SMA, CARMA, and VLA), finding evidence of a decreasing maximum dust grain size (a_max) with radius. We derive large a_max values up to 1 cm in the inner disk between 15 and 30 AU and smaller grains with a_max~1 mm in the outer disk (R > 80AU). In this paper we develop a multi-wavelength analysis that will allow this missing quantity to be constrained for statistically relevant samples of disks and to investigate possible correlations with disk or stellar parameters.Comment: 19 pages, 15 figures, accepted for publication in A&