On linear combinations of L-orthogonal polynomials associated with distributions belonging to symmetric classes

This paper deals with the classes S-3(omega, beta, b) of strong distribution functions defined on the interval [beta(2)/b, b], 0 < beta < b <= infinity, where 2 omega epsilon Z. The classification is such that the distribution function psi epsilon S-3(omega, beta, b) has a (reciprocal) symmetry, depending on omega, about the point beta. We consider properties of the L-orthogonal polynomials associated with psi epsilon S-3(omega, beta, b). Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some omega epsilon S-3(1/2, beta, b). (c) 2004 Elsevier B.V. All rights reserved.

Nonforward parton distributions of the pion within an effective single instanton approximation

We develop a relativistic quark model for pion structure, which incorporates the nontrivial structure of the vacuum of quantum chromodynamics as modelled by instantons. Pions are bound states of quarks and the strong quark-pion vertex is determined from an instanton induced effective Lagrangian. The interaction of the constituents of the pion with the external electromagnetic field is introduced in gauge invariant form. The parameters of the model, i.e., effective instanton radius and constituent quark mass, are obtained from the vacuum expectation values of the lowest dimensional quark and gluon operators and the low-energy observables of the pion. We apply the formalism to the calculation of the pion form factor by means of the isovector nonforward parton distributions and find agreement with the experimental data. © 2000 Elsevier Science B.V.

Off-Diagonal Quark Distributions in Pions in the Effective Single-Instanton Approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables. © 2000 MAIK Nauka/Interperiodica.

Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described.

An evaluation of the distributions of polychlorinated biphenyls and organic matter in coastal sediments

The objective of this thesis is to improve the understanding of what processes and mechanism affects the distribution of polychlorinated biphenyls (PCBs) and organic carbon in coastal sediments. Because of the strong association of hydrophobic organic contaminants (HOCs) such as PCBs with organic matter in the aquatic environment, these two entities are naturally linked. The coastal environment is the most complex and dynamic part of the ocean when it comes to both cycling of organic matter and HOCs. This environment is characterised by the largest fluxes and most diverse sources of both entities. A wide array of methods was used to study these processes throughout this thesis. In the field sites in the Stockholm archipelago of the Baltic proper, bottom sediments and settling particulate matter were retrieved using sediment coring devices and sediment traps from morphometrically and seismically well-characterized locations. In the laboratory, the samples have been analysed for PCBs, stable carbon isotope ratios, carbon-nitrogen atom ratios as well as standard sediment properties. From the fieldwork in the Stockholm Archipelago and the following laboratory work it was concluded that the inner Stockholm archipelago has a low (≈ 4%) trapping efficiency for freshwater-derived organic carbon. The corollary is a large potential for long-range waterborne transport of OC and OC-associated nutrients and hydrophobic organic pollutants from urban Stockholm to more pristine offshore Baltic Sea ecosystems. Theoretical work has been carried out using Geographical Information Systems (GIS) and statistical methods on a database of 4214 individual sediment samples, each with reported individual PCB congener concentrations. From this work it was concluded that the continental shelf sediments are key global inventories and ultimate sinks of PCBs. Depending on congener, 10-80% of the cumulative historical emissions to the environment are accounted for in continental shelf sediments. Further it was concluded that the many infamous and highly contaminated surface sediments of urban harbours and estuaries of contaminated rivers cannot be of importance as a secondary source to sustain the concentrations observed in remote sediments. Of the global shelf PCB inventory < 1% are in sediments near population centres while ≥ 90% is in remote areas (> 10 km from any dwellings). The remote sub-basin of the North Atlantic Ocean contains approximately half of the global shelf sediment inventory for most of the PCBs studied.

Kinematic description of the rupture from strong motion data: strategies for a robust inversion

We present a non linear technique to invert strong motion records with the aim of obtaining the final slip and rupture velocity distributions on the fault plane. In this thesis, the ground motion simulation is obtained evaluating the representation integral in the frequency. The Green’s tractions are computed using the discrete wave-number integration technique that provides the full wave-field in a 1D layered propagation medium. The representation integral is computed through a finite elements technique, based on a Delaunay’s triangulation on the fault plane. The rupture velocity is defined on a coarser regular grid and rupture times are computed by integration of the eikonal equation. For the inversion, the slip distribution is parameterized by 2D overlapping Gaussian functions, which can easily relate the spectrum of the possible solutions with the minimum resolvable wavelength, related to source-station distribution and data processing. The inverse problem is solved by a two-step procedure aimed at separating the computation of the rupture velocity from the evaluation of the slip distribution, the latter being a linear problem, when the rupture velocity is fixed. The non-linear step is solved by optimization of an L2 misfit function between synthetic and real seismograms, and solution is searched by the use of the Neighbourhood Algorithm. The conjugate gradient method is used to solve the linear step instead. The developed methodology has been applied to the M7.2, Iwate Nairiku Miyagi, Japan, earthquake. The estimated magnitude seismic moment is 2.6326 dyne∙cm that corresponds to a moment magnitude MW 6.9 while the mean the rupture velocity is 2.0 km/s. A large slip patch extends from the hypocenter to the southern shallow part of the fault plane. A second relatively large slip patch is found in the northern shallow part. Finally, we gave a quantitative estimation of errors associates with the parameters.

Anomalous Velocity Distributions in Active Brownian Suspensions

Large-scale simulations and analytical theory have been combined to obtain the nonequilibrium velocity distribution, f(v), of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalized to include friction. They reveal strongly anomalous but largely universal distributions, which are independent of volume fraction and collision processes, which suggests a one-particle model should capture all the essential features. We have formulated this one-particle model and solved it analytically in the limit of strong damping, where we find that f (v) decays as 1/v for multiple decades, eventually crossing over to a Gaussian decay for the largest velocities. Many particle simulations and numerical solution of the one-particle model agree for all values of the damping.

Statistical characterization and development of summary measures of non-normal distributions of nuclear morphometry data from prostate cancer cells for use as prognostic indicators

Nuclear morphometry (NM) uses image analysis to measure features of the cell nucleus which are classified as: bulk properties, shape or form, and DNA distribution. Studies have used these measurements as diagnostic and prognostic indicators of disease with inconclusive results. The distributional properties of these variables have not been systematically investigated although much of the medical data exhibit nonnormal distributions. Measurements are done on several hundred cells per patient so summary measurements reflecting the underlying distribution are needed.^ Distributional characteristics of 34 NM variables from prostate cancer cells were investigated using graphical and analytical techniques. Cells per sample ranged from 52 to 458. A small sample of patients with benign prostatic hyperplasia (BPH), representing non-cancer cells, was used for general comparison with the cancer cells.^ Data transformations such as log, square root and 1/x did not yield normality as measured by the Shapiro-Wilks test for normality. A modulus transformation, used for distributions having abnormal kurtosis values, also did not produce normality.^ Kernel density histograms of the 34 variables exhibited non-normality and 18 variables also exhibited bimodality. A bimodality coefficient was calculated and 3 variables: DNA concentration, shape and elongation, showed the strongest evidence of bimodality and were studied further.^ Two analytical approaches were used to obtain a summary measure for each variable for each patient: cluster analysis to determine significant clusters and a mixture model analysis using a two component model having a Gaussian distribution with equal variances. The mixture component parameters were used to bootstrap the log likelihood ratio to determine the significant number of components, 1 or 2. These summary measures were used as predictors of disease severity in several proportional odds logistic regression models. The disease severity scale had 5 levels and was constructed of 3 components: extracapsulary penetration (ECP), lymph node involvement (LN+) and seminal vesicle involvement (SV+) which represent surrogate measures of prognosis. The summary measures were not strong predictors of disease severity. There was some indication from the mixture model results that there were changes in mean levels and proportions of the components in the lower severity levels. ^

Measurement of the electroweak production of dijets in association with a Z-boson and distributions sensitive to vector boson fusion in proton-proton collisions at √s = 8 TeV using the ATLAS detector

Measurements of fiducial cross sections for the electroweak production of two jets in association with a Z-boson are presented. The measurements are performed using 20.3 fb−1 of proton-proton collision data collected at a centre-of-mass energy of p s = 8TeV by the ATLAS experiment at the Large Hadron Collider. The electroweak component is extracted by a fit to the dijet invariant mass distribution in a fiducial region chosen to enhance the electroweak contribution over the dominant background in which the jets are produced via the strong interaction. The electroweak cross sections measured in two fiducial regions are in good agreement with the Standard Model expectations and the background-only hypothesis is rejected with significance above the 5ơ level. The electroweak process includes the vector boson fusion production of a Z-boson and the data are used to place limits on anomalous triple gauge boson couplings. In addition, measurements of cross sections and differential distributions for inclusive Z-boson-plus-dijet production are performed in five fiducial regions, each with different sensitivity to the electroweak contribution. The results are corrected for detector effects and compared to predictions from the Sherpa and Powheg event generators.

Environmental correlates of species rank − abundance distributions in global drylands

Theoretical models predict lognormal species abundance distributions (SADs) in stable and productive environments, with log-series SADs in less stable, dispersal driven communities. We studied patterns of relative species abundances of perennial vascular plants in global dryland communities to: (i) assess the influence of climatic and soil characteristics on the observed SADs, (ii) infer how environmental variability influences relative abundances, and (iii) evaluate how colonisation dynamics and environmental filters shape abundance distributions. We fitted lognormal and log-series SADs to 91 sites containing at least 15 species of perennial vascular plants. The dependence of species relative abundances on soil and climate variables was assessed using general linear models. Irrespective of habitat type and latitude, the majority of the SADs (70.3%) were best described by a lognormal distribution. Lognormal SADs were associated with low annual precipitation, higher aridity, high soil carbon content, and higher variability of climate variables and soil nitrate. Our results do not corroborate models predicting the prevalence of log-series SADs in dryland communities. As lognormal SADs were particularly associated with sites with drier conditions and a higher environmental variability, we reject models linking lognormality to environmental stability and high productivity conditions. Instead our results point to the prevalence of lognormal SADs in heterogeneous environments, allowing for more evenly distributed plant communities, or in stressful ecosystems, which are generally shaped by strong habitat filters and limited colonisation. This suggests that drylands may be resilient to environmental changes because the many species with intermediate relative abundances could take over ecosystem functioning if the environment becomes suboptimal for dominant species.

Cold-Water Coral Distributions in the Drake Passage Area from Towed Camera Observations - Initial Interpretations

Seamounts are unique deep-sea features that create habitats thought to have high levels of endemic fauna, productive fisheries and benthic communities vulnerable to anthropogenic impacts. Many seamounts are isolated features, occurring in the high seas, where access is limited and thus biological data scarce. There are numerous seamounts within the Drake Passage (Southern Ocean), yet high winds, frequent storms and strong currents make seafloor sampling particularly difficult. As a result, few attempts to collect biological data have been made, leading to a paucity of information on benthic habitats or fauna in this area, particularly those on primarily hard-bottom seamounts and ridges. During a research cruise in 2008 six locations were examined (two on the Antarctic margin, one on the Shackleton Fracture Zone, and three on seamounts within the Drake Passage), using a towed camera with onboard instruments to measure conductivity, temperature, depth and turbidity. Dominant fauna and bottom type were categorized from 200 randomized photos from each location. Cold-water corals were present in high numbers in habitats both on the Antarctic margin and on the current swept seamounts of the Drake Passage, though the diversity of orders varied. Though the Scleractinia (hard corals) were abundant on the sedimented margin, they were poorly represented in the primarily hard-bottom areas of the central Drake Passage. The two seamount sites and the Shackleton Fracture Zone showed high numbers of stylasterid (lace) and alcyonacean (soft) corals, as well as large numbers of sponges. Though data are preliminary, the geological and environmental variability (particularly in temperature) between sample sites may be influencing cold-water coral biogeography in this region. Each area observed also showed little similarity in faunal diversity with other sites examined for this study within all phyla counted. This manuscript highlights how little is understood of these isolated features, particularly in Polar regions.

Seasonal Distributions of Satellite-Measured Phytoplankton Pigment Concentration Along the Chilean Coast

Five years (1979-1983) of Coastal Zone Color Scanner satellite ocean color data are used to examine seasonal patterns of phytoplankton pigment concentration along the Chilean coast from 20 degrees S to 45 degrees S. Four kilometer resolution, 2-4 day composites document the presence of filaments of elevated pigment concentration extending offshore throughout the study area, with maximum offshore extension at higher latitudes. In three years, 1979, 1981, and 1983, sufficient data exist in monthly composites to allow recreation of portions of the seasonal cycle. Data in 1979 are the most complete. Near-shore concentrations and cross-shelf extension of pigment concentrations in 1979 are maximum in austral winter throughout the study area and minimum in summer. Available data from 1981 and 1983 are consistent with this temporal pattern but with concentrations approximately double those of 1979. Seasonal, spatial patterns within 10 km of shore and 50 km offshore indicate a latitudinal discontinuity both in absolute concentration and in the magnitude of the seasonal cycle at approximately 33 degrees S in both 1979 and in the climatological time series. The discontinuity is strongest ill fall-winter and weakest in summer. South of this latitude, concentrations are relatively high (2-3 mg m(-3) in 1979), a strong seasonal cycle is present, and patterns 50 km offshore are correlated with those within 10 km of shore. North of 33 degrees S, concentrations are < 1.5 mg m(-3) (in 1979), and the seasonal cycle within 10 km of shore is present but much weaker and less obviously correlated with that 50 km offshore. The seasonal cycle of pigment concentrations is 180 degrees out of phase with monthly averaged upwelling favorable winds. Noncoincident Pathfinder sea surface temperature data show that over most latitudes, coastal low surface temperatures lag wind forcing by 1-2 months, but these too are out of phase with the pigment seasonal cycle. These data point to control of pigment patterns along the Chilean coast by the interaction of upwelling with circulation patterns unconnected to local wind forcing.

Stable carbon isotopes, Methane Index, and distributions of different GDGTs

Gas hydrates represent one of the largest pools of readily exchangeable carbon on Earth's surface. Releases of the greenhouse gas methane from hydrates are proposed to be responsible for climate change at numerous events in geological history. Many of these inferred events, however, were based on carbonate carbon isotopes which are susceptible to diagenetic alterations. Here we propose a molecular fossil proxy, i.e., the "Methane Index (MI)", to detect and document the destabilization and dissociation of marine gas hydrates. MI consists of the relative distribution of glycerol dibiphytanyl glycerol tetraethers (GDGTs), the core membrane lipids of archaea. The rational behind MI is that in hydrate-impacted environments, the pool of archaeal tetraether lipids is dominated by GDGT-1, -2 and -3 due to the large contribution of signals from the methanotrophic archaeal community. Our study in the Gulf of Mexico cold-seep sediments demonstrates a correlation between MI and the compound-specific carbon isotope of GDGTs, which is strong evidence supporting the MI-methane consumption relationship. Preliminary applications of MI in a number of hydrate-impacted and/or methane-rich environments show diagnostic MI values, corroborating the idea that MI may serve as a robust indicator for hydrate dissociation that is useful for studies of global carbon cycling and paleoclimate change.

Grain-size distributions and bulk chemistry of sediment core MD00-2361

The terrigenous fraction of sediments from a deep-sea sediment core recovered from the northwestern Western Australian continental slope offshore North West Cape, SE Indian Ocean, reveals a history of Western Australian climate throughout the last 550 ka. End-member modelling of a data set of grain-size distributions (n = 438) of the terrigenous sediment fraction allows to interpret the record in terms of aeolian and fluvial sediment deposition, both related to palaeo-environmental conditions in the North West Cape area. The data set can be best described by two aeolian end members and one fluvial one. Changes in the ratio of the two aeolian end members over the fluvial one are interpreted as aridity variations in northwestern Western Australia. These grain-size data are compared with bulk geochemical data obtained by XRF scans of the core. Log-ratios of the elements Zr/Fe and Ti/Ca, which indicate a terrigenous origin, corroborate the grain-size data. We postulate that the mid- to late Quaternary near North West Cape climate was relatively arid during the glacial and relatively humid during the interglacial stages, owing to meridional shifts in the atmospheric circulation system. Opposite to published palaeo-environmental records from the same latitude (20°S) offshore Chile and offshore Namibia, the Australian aridity record does not show the typical southern hemisphere climate variability of humid glacials and dry interglacials, which we interpret to be the result of the relatively large land mass of the Australian continent, which emphasises a strong monsoonal climatic system.