Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.

Chemistry and grain-size distribution of terrigenous sediments deposited at Site GeoB9501

The Sahara Desert is the largest source of mineral dust in the world. Emissions of African dust increased sharply in the early 1970s, a change that has been attributed mainly to drought in the Sahara/Sahel region caused by changes in the global distribution of sea surface temperature. The human contribution to land degradation and dust mobilization in this region remains poorly understood, owing to the paucity of data that would allow the identification of long-term trends in desertification. Direct measurements of airborne African dust concentrations only became available in the mid-1960s from a station on Barbados and subsequently from satellite imagery since the late 1970s: they do not cover the onset of commercial agriculture in the Sahel region ~170 years ago. Here we construct a 3,200-year record of dust deposition off northwest Africa by investigating the chemistry and grain-size distribution of terrigenous sediments deposited at a marine site located directly under the West African dust plume. With the help of our dust record and a proxy record for West African precipitation we find that, on the century scale, dust deposition is related to precipitation in tropical West Africa until the seventeenth century. At the beginning of the nineteenth century, a sharp increase in dust deposition parallels the advent of commercial agriculture in the Sahel region. Our findings suggest that human-induced dust emissions from the Sahel region have contributed to the atmospheric dust load for about 200 years.

Seawater carbonate chemistry and Emiliania huxleyi mass and size, 2011

About one-third of the carbon dioxide (CO2) released into the atmosphere as a result of human activity has been absorbed by the oceans, where it partitions into the constituent ions of carbonic acid. This leads to ocean acidification, one of the major threats to marine ecosystems and particularly to calcifying organisms such as corals, foraminifera and coccolithophores. Coccolithophores are abundant phytoplankton that are responsible for a large part of modern oceanic carbonate production. Culture experiments investigating the physiological response of coccolithophore calcification to increased CO2 have yielded contradictory results between and even within species. Here we quantified the calcite mass of dominant coccolithophores in the present ocean and over the past forty thousand years, and found a marked pattern of decreasing calcification with increasing partial pressure of CO2 and concomitant decreasing concentrations of CO3. Our analyses revealed that differentially calcified species and morphotypes are distributed in the ocean according to carbonate chemistry. A substantial impact on the marine carbon cycle might be expected upon extrapolation of this correlation to predicted ocean acidification in the future. However, our discovery of a heavily calcified Emiliania huxleyi morphotype in modern waters with low pH highlights the complexity of assemblage-level responses to environmental forcing factors.

Seawater carbonate chemistry and clownfish Amphiprion percula size and otholith development during experiments, 2011

Calcification in many invertebrate species is predicted to decline due to ocean acidification. The potential effects of elevated CO2 and reduced carbonate saturation state on other species, such as fish, are less well understood. Fish otoliths (earbones) are composed of aragonite, and thus, might be susceptible to either the reduced availability of carbonate ions in seawater at low pH, or to changes in extracellular concentrations of bicarbonate and carbonate ions caused by acid-base regulation in fish exposed to high pCO2. We reared larvae of the clownfish Amphiprion percula from hatching to settlement at three pHNBS and pCO2 levels (control: ~pH 8.15 and 404 µatm CO2; intermediate: pH 7.8 and 1050 µatm CO2; extreme: pH 7.6 and 1721 µatm CO2) to test the possible effects of ocean acidification on otolith development. There was no effect of the intermediate treatment (pH 7.8 and 1050 µatm CO2) on otolith size, shape, symmetry between left and right otoliths, or otolith elemental chemistry, compared with controls. However, in the more extreme treatment (pH 7.6 and 1721 µatm CO2) otolith area and maximum length were larger than controls, although no other traits were significantly affected. Our results support the hypothesis that pH regulation in the otolith endolymph can lead to increased precipitation of CaCO3 in otoliths of larval fish exposed to elevated CO2, as proposed by an earlier study, however, our results also show that sensitivity varies considerably among species. Importantly, our results suggest that otolith development in clownfishes is robust to even the more pessimistic changes in ocean chemistry predicted to occur by 2100.

Enviromagnetic, major element, and grain-size analyses of surface sediment samples along the continental margin between East Brazil and Patagonia

Continental margin sediments of SE South America originate from various terrestrial sources, each conveying specific magnetic and element signatures. Here, we aim to identify the sources and transport characteristics of shelf and slope sediments deposited between East Brazil and Patagonia (20°-48°S) using enviromagnetic, major element, and grain-size data. A set of five source-indicative parameters (i.e., chi-fd%, ARM/IRM, S0.3T, SIRM/Fe and Fe/K) of 25 surface samples (16-1805 m water depth) was analyzed by fuzzy c-means clustering and non-linear mapping to depict and unmix sediment-province characteristics. This multivariate approach yields three regionally coherent sediment provinces with petrologically and climatically distinct source regions. The southernmost province is entirely restricted to the slope off the Argentinean Pampas and has been identified as relict Andean-sourced sands with coarse unaltered magnetite. The direct transport to the slope was enabled by Rio Colorado and Rio Negro meltwaters during glacial and deglacial phases of low sea level. The adjacent shelf province consists of coastal loessoidal sands (highest hematite and goethite proportions) delivered from the Argentinean Pampas by wave erosion and westerly winds. The northernmost province includes the Plata mudbelt and Rio Grande Cone. It contains tropically weathered clayey silts from the La Plata Drainage Basin with pronounced proportions of fine magnetite, which were distributed up to ~24° S by the Brazilian Coastal Current and admixed to coarser relict sediments of Pampean loessoidal origin. Grain-size analyses of all samples showed that sediment fractionation during transport and deposition had little impact on magnetic and element source characteristics. This study corroborates the high potential of the chosen approach to access sediment origin in regions with contrasting sediment sources, complex transport dynamics, and large grain-size variability.

Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Retrievals of a size parameter for phytoplankton and spectral light absorption by colored detrital matter from water-leaving radiances at SeaWiFS channels in a continental shelf region off Brazil

Many efforts are currently oriented toward extracting more information from ocean color than the chlorophyll a concentration. Among biological parameters potentially accessible from space, estimates of phytoplankton cell size and light absorption by colored detrital matter (CDM) would lead to an indirect assessment of major components of the organic carbon pool in the ocean, which would benefit oceanic carbon budget models. We present here 2 procedures to retrieve simultaneously from ocean color measurements in a limited number of bands, magnitudes, and spectral shapes for both light absorption by CDM and phytoplankton, along with a size parameter for phytoplankton. The performance of the 2 procedures was evaluated using different data sets that correspond to increasing uncertainties: ( 1) measured absorption coefficients of phytoplankton, particulate detritus, and colored dissolved organic matter ( CDOM) and measured chlorophyll a concentrations and ( 2) SeaWiFS upwelling radiance measurements and chlorophyll a concentrations estimated from global algorithms. In situ data were acquired during 3 cruises, differing by their relative proportions in CDM and phytoplankton, over a continental shelf off Brazil. No local information was introduced in either procedure, to make them more generally applicable. Over the study area, the absorption coefficient of CDM at 443 nm was retrieved from SeaWiFS radiances with a relative root mean square error (RMSE) of 33%, and phytoplankton light absorption coefficients in SeaWiFS bands ( from 412 to 510 nm) were retrieved with RMSEs between 28% and 33%. These results are comparable to or better than those obtained by 3 published models. In addition, a size parameter of phytoplankton and the spectral slope of CDM absorption were retrieved with RMSEs of 17% and 22%, respectively. If these methods are applied at a regional scale, the performances could be substantially improved by locally tuning some empirical relationships.