Bounding Standard Gaussian Tail Probabilities

We review various inequalities for Mills' ratio (1 - Φ)= Ø, where Ø and Φ denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds.

The inverse problem for Schwinger pair production

The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism) depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

Spatial distribution of orofacial cleft birth defects and uranium-radium concentrations in tap water in Atascosa, Bee, Brooks, Calhoun, Duval, Goliad, Hidalgo, Jim Hogg, Jim Wells, Karnes, Kleberg, Live Oak, McMullen, Nueces, San Patricio, Refugio, Starr, Victoria, Webb, and Zavala Counties, Texas

Background Past and recent evidence shows that radionuclides in drinking water may be a public health concern. Developmental thresholds for birth defects with respect to chronic low level domestic radiation exposures, such as through drinking water, have not been definitely recognized, and there is a strong need to address this deficiency in information. In this study we examined the geographic distribution of orofacial cleft birth defects in and around uranium mining district Counties in South Texas (Atascosa, Bee, Brooks, Calhoun, Duval, Goliad, Hidalgo, Jim Hogg, Jim Wells, Karnes, Kleberg, Live Oak, McMullen, Nueces, San Patricio, Refugio, Starr, Victoria, Webb, and Zavala), from 1999 to 2007. The probable association of cleft birth defect rates by ZIP codes classified according to uranium and radium concentrations in drinking water supplies was evaluated. Similar associations between orofacial cleft birth defects and radium/radon in drinking water were reported earlier by Cech and co-investigators in another of the Gulf Coast region (Harris County, Texas).50, 55 Since substantial uranium mining activity existed and still exists in South Texas, contamination of drinking water sources with radiation and its relation to birth defects is a ground for concern. ^ Methods Residential addresses of orofacial cleft birth defect cases, as well as live births within the twenty Counties during 1999-2007 were geocoded and mapped. Prevalence rates were calculated by ZIP codes and were mapped accordingly. Locations of drinking water supplies were also geocoded and mapped. ZIP codes were stratified as having high combined uranium (≥30μg/L) vs. low combined uranium (<30μg/L). Likewise, ZIP codes having the uranium isotope, Ra-226 in drinking water, were also stratified as having elevated radium (≥3 pCi/L) vs. low radium (<3 pCi/L). A linear regression was performed using STATA® generalized linear model (GLM) program to evaluate the probable association between cleft birth defect rates by ZIP codes and concentration of uranium and radium via domestic water supply. These rates were further adjusted for potentially confounding variables such as maternal age, education, occupation, and ethnicity. ^ Results This study showed higher rates of cleft births in ZIP codes classified as having high combined uranium versus ZIP codes having low combined uranium. The model was further improved by adding radium stratified as explained above. Adjustment for maternal age and ethnicity did not substantially affect the statistical significance of uranium or radium concentrations in household water supplies. ^ Conclusion Although this study lacks individual exposure levels, the findings suggest a significant association between elevated uranium and radium concentrations in tap water and high orofacial birth defect rates by ZIP codes. Future case-control studies that can measure individual exposure levels and adjust for contending risk factors could result in a better understanding of the exposure-disease association.^

Distribution of planktonic foraminifera in Pleistocene sediments of the New Jersey margin, NW Atlantic Ocean

Abundance records of planktonic foraminifera (>150 µm) from the upper 520 m of ODP Site 1073 (Hole 1073A, Leg 174A, 639 m water depth) have been integrated with SPECMAP-derived isotope stratigraphy, percentage of calcium carbonate, and coarse sediment fraction data in order to investigate the Pleistocene climatic history of the New Jersey margin. Six planktonic taxonomic groups dominate the foraminiferal assemblage at Site 1073: Neogloboquadrina pachyderma (d) (mean 33.8%), Turborotalita quinqueloba (18.5%), N. pachyderma (s) (18.4%), Globigerina bulloides group (11.4%), Globorotalia inflata group (9.4%), and Globigerinita glutinata (4.1%). Based on the distributions of these six foraminiferal groups, the Pleistocene section can be divided into three paleoclimatic intervals: Interval I (intermediate) corresponds to the Quaternary sediments from sequence boundary pp1 to the seafloor (79.5-0 mbsf; Emiliania huxleyi acme [85 ka] at 72 mbsf); Interval II (warm) occurs between sequence boundaries pp3 and pp1 (325-79.5 mbsf; last occurrence of Pseudoemiliania lacunosa [460 ka] at 330 mbsf); and Interval III (coldest) occurs between sequence boundaries pp4 and pp3 (520-325 mbsf; Calcareous nannofossils and dinocysts in proximity to pp4 indicate that the sedimentary record for 0.9-1.7 Ma is either missing altogether or highly condensed within the basal few meters of the section). Neogloboquadrina pachyderma (d) displays eight peaks of abundance which correlate, for the most part, with depleted delta18O values, increases in calcium carbonate percentages, low coarse fraction percentages, increased planktonic fragmentation (greater dissolution), and low N. pachyderma (s) abundances. These intervals are interpreted as representing warmer/interglacial conditions. Neogloboquadrina pachyderma (s) displays seven peaks of abundance which correlate, for the most part, with delta18O increases, decreases in calcium carbonate percentages, increases in coarse fraction percentages, and low N. pachyderma (d) abundances. These intervals are interpreted as representing cooler/glacial conditions. In Interval III, a faunal response to relative changes in sea-surface temperature is reflected by abundance peaks in Neogloboquadrina pachyderma (d), followed by Turborotalita quinqueloba and then N. pachyderma (s) (proceeding from warmest to coolest, respectively). This tripartite response is consistent with the oxygen isotope record and, although not as clear, also occurs in Intervals I and II. Six peaks/peak intervals of Globigerina bulloides abundance are closely matched by peaks in Globigerinita glutinata and occur within oxygen isotope stage (OIS) 2 (latter part) 3, 4, 5, 8, 9, 13(?), 14(?), and 15(?). We speculate that these intervals reflect increased upwelling and nutrient levels during both glacials and interglacials. Eight peak intervals of Globorotalia inflata show a general inverse correlation with G. bulloides and may reflect lowered nutrient and warmer surface waters.

Distribution of Pliocene diatom faunas in the Northwest Pacific

High-resolution quantitative diatom data are tabulated for the early part of the late Pliocene ( 3.25 to 2.08 Ma ) at DSDP Site 580 in the northwestern Pacific. Sample spacing averages 11 k.y. between 3.1 and 2.8 Ma, but increases to 14 to 19 k.y. prior to 3.1 Ma and after 2.8 Ma. Q-mode factor analysis of the middle Pliocene assemblage reveals four factors which explain 92.4% of the total variance of the 47 samples studied between 3.25 and 2.55 Ma. Three of the factors are closely related to modern subarctic, transitional, and subtropical elements, while the fourth factor, which is dominated by Coscinodiscus marginatus and the extinct Pliocene species Neodenticula kamtschatica, appears to correspond to a middle Pliocene precursor of the subarctic water mass. Knowledge of the modern and generalized Pliocene paleoclimatic relationships of various diatom taxa is used to generate a paleoclimate curve ("Twt") based on the ratio of warm-water (subtropical) to cold-water diatoms with warm-water transitional taxa (Thalassionema nitzschioides, Thalassiosira oestrupii, and Coscinodiscus radiatus) factored into the equation at an intermediate (0.5) value. The "Twt" ratios at more southerly DSDP Sites 579 and 578 are consistently higher (warmer) than those at Site 580 throughout the Pliocene, suggesting the validity of the ratio as a paleoclimatic index. Diatom paleoclimatic data reveal a middle Pliocene (3.1 to 3.0 Ma) warm interval at Site 580 during which paleotemperatures may have exceeded maximum Holocene values by 3 °- 5.5 °C at least three times. This middle Pliocene warm interval is also recognized by planktic foraminifers in the North Atlantic, and it appears to correspond with generalized depleted oxygen isotope values suggesting polar warming. The diatom "Twt" curve for Site 580 compares fairly well with radiolarian and silicoflagellate paleoclimatic curves for Site 580, planktic foraminiferal sea-surface temperature estimates for the North Atlantic, and benthic oxygen isotope curves for late Pliocene, although higher resolution studies on paired samples are required to test the correspondence of these various paleoclimatic indices.

Novel fast random search clustering approach for mixing matrix identification in MIMO linear blind inverse problems with sparse inputs

In this paper we propose a novel fast random search clustering (RSC) algorithm for mixing matrix identification in multiple input multiple output (MIMO) linear blind inverse problems with sparse inputs. The proposed approach is based on the clustering of the observations around the directions given by the columns of the mixing matrix that occurs typically for sparse inputs. Exploiting this fact, the RSC algorithm proceeds by parameterizing the mixing matrix using hyperspherical coordinates, randomly selecting candidate basis vectors (i.e. clustering directions) from the observations, and accepting or rejecting them according to a binary hypothesis test based on the Neyman–Pearson criterion. The RSC algorithm is not tailored to any specific distribution for the sources, can deal with an arbitrary number of inputs and outputs (thus solving the difficult under-determined problem), and is applicable to both instantaneous and convolutive mixtures. Extensive simulations for synthetic and real data with different number of inputs and outputs, data size, sparsity factors of the inputs and signal to noise ratios confirm the good performance of the proposed approach under moderate/high signal to noise ratios. RESUMEN. Método de separación ciega de fuentes para señales dispersas basado en la identificación de la matriz de mezcla mediante técnicas de "clustering" aleatorio.

Generalized flows, intrinsic stochasticity, and turbulent transport

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows, which are families of probability distributions on the space of solutions to the associated ordinary differential equations which no longer satisfy the uniqueness theorem for ordinary differential equations. Two most natural regularizations of this problem, namely the regularization via adding small molecular diffusion and the regularization via smoothing out the velocity field, are considered. White-in-time random velocity fields are used as an example to examine the variety of phenomena that take place when the velocity field is not spatially regular. Three different regimes, characterized by their degrees of compressibility, are isolated in the parameter space. In the regime of intermediate compressibility, the two different regularizations give rise to two different scaling behaviors for the structure functions of the passive scalar. Physically, this means that the scaling depends on Prandtl number. In the other two regimes, the two different regularizations give rise to the same generalized flows even though the sense of convergence can be very different. The “one force, one solution” principle is established for the scalar field in the weakly compressible regime, and for the difference of the scalar in the strongly compressible regime, which is the regime of inverse cascade. Existence and uniqueness of an invariant measure are also proved in these regimes when the transport equation is suitably forced. Finally incomplete self similarity in the sense of Barenblatt and Chorin is established.

The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

Response of Catch-Per-Unit-Effort to Spatial and Environmental Factors: an Exploratory Data Analysis Using Generalized Additive Models

Understanding spatial distributions and how environmental conditions influence catch-per-unit-effort (CPUE) is important for increased fishing efficiency and sustainable fisheries management. This study investigated the relationship between CPUE, spatial factors, temperature, and depth using generalized additive models. Combinations of factors, and not one single factor, were frequently included in the best model. Parameters which best described CPUE varied by geographic region. The amount of variance, or deviance, explained by the best models ranged from a low of 29% (halibut, Charlotte region) to a high of 94% (sablefish, Charlotte region). Depth, latitude, and longitude influenced most species in several regions. On the broad geographic scale, depth was associated with CPUE for every species, except dogfish. Latitude and longitude influenced most species, except halibut (Areas 4 A/D), sablefish, and cod. Temperature was important for describing distributions of halibut in Alaska, arrowtooth flounder in British Columbia, dogfish, Alaska skate, and Aleutian skate. The species-habitat relationships revealed in this study can be used to create improved fishing and management strategies.

Use of an Inverse Method for Time Series to Estimate the Dynamics of and Management Strategies for the Box Jellyfish Carybdea marsupialis

Frequently, population ecology of marine organisms uses a descriptive approach in which their sizes and densities are plotted over time. This approach has limited usefulness for design strategies in management or modelling different scenarios. Population projection matrix models are among the most widely used tools in ecology. Unfortunately, for the majority of pelagic marine organisms, it is difficult to mark individuals and follow them over time to determine their vital rates and built a population projection matrix model. Nevertheless, it is possible to get time-series data to calculate size structure and densities of each size, in order to determine the matrix parameters. This approach is known as a “demographic inverse problem” and it is based on quadratic programming methods, but it has rarely been used on aquatic organisms. We used unpublished field data of a population of cubomedusae Carybdea marsupialis to construct a population projection matrix model and compare two different management strategies to lower population to values before year 2008 when there was no significant interaction with bathers. Those strategies were by direct removal of medusae and by reducing prey. Our results showed that removal of jellyfish from all size classes was more effective than removing only juveniles or adults. When reducing prey, the highest efficiency to lower the C. marsupialis population occurred when prey depletion affected prey of all medusae sizes. Our model fit well with the field data and may serve to design an efficient management strategy or build hypothetical scenarios such as removal of individuals or reducing prey. TThis This sdfsdshis method is applicable to other marine or terrestrial species, for which density and population structure over time are available.

New Orleans, Louisiana, Water Distribution System, 1902 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Map of the city of New Orleans : showing proposed water distribution system, [by] Sewerage and Water Board New Orleans, LA.; Geo. G. Earl, genl. sup't. It was published by the Sewerage and Water Board New Orleans in 1902. Scale [ca. 1:50,900]. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Louisiana State Plane Coordinate System, South NAD83 (in Feet) (Fipszone 1702). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, or other information associated with the principal map. This map shows water distribution features such as existing and proposed water mains (with sizes), suction pipes, and water purification station sites. Also shows other features such as roads, canals, levees, drainage, cemeteries, Parish boundaries, and more. Shaded to show built-up and unbuilt areas for construction. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Validation of the Swiss methane emission inventory by atmospheric observations and inverse modelling

Atmospheric inverse modelling has the potential to provide observation-based estimates of greenhouse gas emissions at the country scale, thereby allowing for an independent validation of national emission inventories. Here, we present a regional-scale inverse modelling study to quantify the emissions of methane (CH₄) from Switzerland, making use of the newly established CarboCount-CH measurement network and a high-resolution Lagrangian transport model. In our reference inversion, prior emissions were taken from the "bottom-up" Swiss Greenhouse Gas Inventory (SGHGI) as published by the Swiss Federal Office for the Environment in 2014 for the year 2012. Overall we estimate national CH₄ emissions to be 196 ± 18 Gg yr⁻¹ for the year 2013 (1σ uncertainty). This result is in close agreement with the recently revised SGHGI estimate of 206 ± 33 Gg yr⁻¹ as reported in 2015 for the year 2012. Results from sensitivity inversions using alternative prior emissions, uncertainty covariance settings, large-scale background mole fractions, two different inverse algorithms (Bayesian and extended Kalman filter), and two different transport models confirm the robustness and independent character of our estimate. According to the latest SGHGI estimate the main CH₄ source categories in Switzerland are agriculture (78 %), waste handling (15 %) and natural gas distribution and combustion (6 %). The spatial distribution and seasonal variability of our posterior emissions suggest an overestimation of agricultural CH₄ emissions by 10 to 20 % in the most recent SGHGI, which is likely due to an overestimation of emissions from manure handling. Urban areas do not appear as emission hotspots in our posterior results, suggesting that leakages from natural gas distribution are only a minor source of CH₄ in Switzerland. This is consistent with rather low emissions of 8.4 Gg yr⁻¹ reported by the SGHGI but inconsistent with the much higher value of 32 Gg yr⁻¹ implied by the EDGARv4.2 inventory for this sector. Increased CH₄ emissions (up to 30 % compared to the prior) were deduced for the north-eastern parts of Switzerland. This feature was common to most sensitivity inversions, which is a strong indicator that it is a real feature and not an artefact of the transport model and the inversion system. However, it was not possible to assign an unambiguous source process to the region. The observations of the CarboCount-CH network provided invaluable and independent information for the validation of the national bottom-up inventory. Similar systems need to be sustained to provide independent monitoring of future climate agreements.

Spatial distribution of key zooplankton species using continuous plankton recorder (CPR) data from the North Atlantic (2000-2009)

The continuous plankton recorder (CPR) survey is an upper layer plankton monitoring program that has regularly collected samples, at monthly intervals, in the North Atlantic and adjacent seas since 1946. Water from approximately 6 m depth enters the CPR through a small aperture at the front of the sampler and travels down a tunnel where it passes through a silk filtering mesh of 270 µm before exiting at the back of the CPR. The plankton filtered on the silk is analyzed in sections corresponding to 10 nautical miles (approx. 3 m**3 of seawater filtered) and the plankton microscopically identified (Richardson et al., 2006 and reference therein). In the present study we used the CPR data to investigate the current basin scale distribution of C. finmarchicus (C5-C6), C. helgolandicus (C5-C6), C. hyperboreus (C5-C6), Pseudocalanus spp. (C6), Oithona spp. (C1-C6), total Euphausiida, total Thecosomata and the presence/absence of Cnidaria and the Phytoplankton Colour Index (PCI). The PCI, which is a visual assessment of the greenness of the silk, is used as an indicator of the distribution of total phytoplankton biomass across the Atlantic basin (Batten et al., 2003). Monthly data collected between 2000 and 2009 were gridded using the inverse-distance interpolation method, in which the interpolated values were the nodes of a 2 degree by 2 degree grid. The resulting twelve monthly matrices were then averaged within the year and in the case of the zooplankton the data were log-transformed (i.e. log10 (x+1).

Ensemble prediction distribution maps of macroalgae for current conditions and four climate change scenarios and high resultion bathymetry for Potter Cove, WAP, Antarctica

Species distribution models (SDM) predict species occurrence based on statistical relationships with environmental conditions. The R-package biomod2 which includes 10 different SDM techniques and 10 different evaluation methods was used in this study. Macroalgae are the main biomass producers in Potter Cove, King George Island (Isla 25 de Mayo), Antarctica, and they are sensitive to climate change factors such as suspended particulate matter (SPM). Macroalgae presence and absence data were used to test SDMs suitability and, simultaneously, to assess the environmental response of macroalgae as well as to model four scenarios of distribution shifts by varying SPM conditions due to climate change. According to the averaged evaluation scores of Relative Operating Characteristics (ROC) and True scale statistics (TSS) by models, those methods based on a multitude of decision trees such as Random Forest and Classification Tree Analysis, reached the highest predictive power followed by generalized boosted models (GBM) and maximum-entropy approaches (Maxent). The final ensemble model used 135 of 200 calculated models (TSS > 0.7) and identified hard substrate and SPM as the most influencing parameters followed by distance to glacier, total organic carbon (TOC), bathymetry and slope. The climate change scenarios show an invasive reaction of the macroalgae in case of less SPM and a retreat of the macroalgae in case of higher assumed SPM values.