On ergodic least-squares estimators of the generalized diffusion coefficient for fractional Brownian motion

We analyse a class of estimators of the generalized diffusion coefficient for fractional Brownian motion Bt of known Hurst index H, based on weighted functionals of the single time square displacement. We show that for a certain choice of the weight function these functionals possess an ergodic property and thus provide the true, ensemble-averaged, generalized diffusion coefficient to any necessary precision from a single trajectory data, but at expense of a progressively higher experimental resolution. Convergence is fastest around H ? 0.30, a value in the subdiffusive regime.

Grapheme-color synesthetes show peculiarities in their emotional brain: cortical and subcortical evidence from VBM analysis of 3D-T1 and DTI data

Grapheme-color synesthesia is a neurological phenomenon in which viewing achromatic letters/numbers leads to automatic and involuntary color experiences. In this study, voxel-based morphometry analyses were performed on T1 images and fractional anisotropy measures to examine the whole brain in associator grapheme-color synesthetes. These analyses provide new evidence of variations in emotional areas (both at the cortical and subcortical levels), findings that help understand the emotional component as a relevant aspect of the synesthetic experience. Additionally, this study replicates previous findings in the left intraparietal sulcus and, for the first time, reports the existence of anatomical differences in subcortical gray nuclei of developmental grapheme-color synesthetes, providing a link between acquired and developmental synesthesia. This empirical evidence, which goes beyond modality-specific areas, could lead to a better understanding of grapheme-color synesthesia as well as of other modalities of the phenomenon.

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Services for Satellite Data Processing

Data processing services for Meteosat geostationary satellite are presented. Implemented services correspond to the different levels of remote-sensing data processing, including noise reduction at preprocessing level, cloud mask extraction at low-level and fractal dimension estimation at high-level. Cloud mask obtained as a result of Markovian segmentation of infrared data. To overcome high computation complexity of Markovian segmentation parallel algorithm is developed. Fractal dimension of Meteosat data estimated using fractional Brownian motion models.

Inverse Problem for Fractional Diffusion Equation

MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30

Analysing Conjoint Analysis Data by a Random Coefficient Regression Model

2000 Mathematics Subject Classification: 62J12, 62K15, 91B42, 62H99.

Sediment core-top GDGT data from the Arctic, the North Pacific and the Southern Ocean

TEX86 (TetraEther indeX of tetraethers consisting of 86 carbon atoms) is a sea surface temperature (SST) proxy based on the distribution of archaeal isoprenoid glycerol dialkyl glycerol tetraethers (GDGTs). In this study, we appraise the applicability of TEX86 and TEX86L in subpolar and polar regions using surface sediments. We present TEX86 and TEX86L data from 160 surface sediment samples collected in the Arctic, the Southern Ocean and the North Pacific. Most of the SST estimates derived from both TEX86 and TEX86L are anomalously high in the Arctic, especially in the vicinity of Siberian river mouths and the sea ice margin, plausibly due to additional archaeal contributions linked to terrigenous input. We found unusual GDGT distributions at five sites in the North Pacific. High GDGT-0/crenarchaeol and GDGT-2/crenarchaeol ratios at these sites suggest a substantial contribution of methanogenic and/or methanotrophic archaea to the sedimentary GDGT pool here. Apart from these anomalous findings, TEX86 and TEX86L values in the surface sediments from the Southern Ocean and the North Pacific do usually vary with overlaying SSTs. In these regions, the sedimentary TEX86-SST relationship is similar to the global calibration, and the derived temperature estimates agree well with overlaying annual mean SSTs at the sites. However, there is a systematic offset between the regional TEX86L-SST relationships and the global calibration. At these sites, temperature estimates based on the global TEX86L calibration are closer to summer SSTs than annual mean SSTs. This finding suggests that in these subpolar settings a regional TEX86L calibration may be a more suitable equation for temperature reconstruction than the global calibration.

Sediment and pore water data of five cores from the continental slope off Uruguay

Assessing frequency and extent of mass movement at continental margins is crucial to evaluate risks for offshore constructions and coastal areas. A multidisciplinary approach including geophysical, sedimentological, geotechnical, and geochemical methods was applied to investigate multistage mass transport deposits (MTDs) off Uruguay, on top of which no surficial hemipelagic drape was detected based on echosounder data. Nonsteady state pore water conditions are evidenced by a distinct gradient change in the sulfate (SO4**2-) profile at 2.8 m depth. A sharp sedimentological contact at 2.43 m coincides with an abrupt downward increase in shear strength from approx. 10 to >20 kPa. This boundary is interpreted as a paleosurface (and top of an older MTD) that has recently been covered by a sediment package during a younger landslide event. This youngest MTD supposedly originated from an upslope position and carried its initial pore water signature downward. The kink in the SO4**2- profile approx. 35 cm below the sedimentological and geotechnical contact indicates that bioirrigation affected the paleosurface before deposition of the youngest MTD. Based on modeling of the diffusive re-equilibration of SO4**2- the age of the most recent MTD is estimated to be <30 years. The mass movement was possibly related to an earthquake in 1988 (approx. 70 km southwest of the core location). Probabilistic slope stability back analysis of general landslide structures in the study area reveals that slope failure initiation requires additional ground accelerations. Therefore, we consider the earthquake as a reasonable trigger if additional weakening processes (e.g., erosion by previous retrogressive failure events or excess pore pressures) preconditioned the slope for failure. Our study reveals the necessity of multidisciplinary approaches to accurately recognize and date recent slope failures in complex settings such as the investigated area.

Table 1 Core site, fractional abundance of individual isoprenoid GDGTs and TEX86 values

TEXL86 and TEXH86 are organic palaeothermometers based on the lipids of Group 1 Crenarchaeota, recently proposed as a modified version of the original TEX86 index, but with significantly improved geographical coverage. Since few data from the global core top calibration are from the Pacific, this study was carried out to assess whether the global core top calibration is regionally biased or not. The result of principal components analysis of the fractional abundance of GDGTs, an analysis of variance (ANOVA) and the comparison of the residuals of TEXH 86 derived sea surface temperature (SST) estimates of the Pacific subset with that of the global data set suggest that the Pacific subset has a similar TEXH 86-SST relationship with the global data set. However, the regression line through the Pacific data and an ANOVA on the residuals of TEXL 86 derived SST estimates suggest otherwise. The contradictory findings are likely to stem from the large scatter in the Pacific TEXL 86 values in the mid temperature range. While regionality does not seem to exert a strong bias on TEXL 86 and TEXH 86 calibration, it appears that there is a strong need to resolve the large scatter in the global data set, especially in the mid and high latitudes, in order to improve the calibration for a better SST estimation.