hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents di±cult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

Selection bias and the cross-validation of regression models for prediction

Strategies are compared for the development of a linear regression model with stochastic (multivariate normal) regressor variables and the subsequent assessment of its predictive ability. Bias and mean squared error of four estimators of predictive performance are evaluated in simulated samples of 32 population correlation matrices. Models including all of the available predictors are compared with those obtained using selected subsets. The subset selection procedures investigated include two stopping rules, C$\sb{\rm p}$ and S$\sb{\rm p}$, each combined with an 'all possible subsets' or 'forward selection' of variables. The estimators of performance utilized include parametric (MSEP$\sb{\rm m}$) and non-parametric (PRESS) assessments in the entire sample, and two data splitting estimates restricted to a random or balanced (Snee's DUPLEX) 'validation' half sample. The simulations were performed as a designed experiment, with population correlation matrices representing a broad range of data structures.^ The techniques examined for subset selection do not generally result in improved predictions relative to the full model. Approaches using 'forward selection' result in slightly smaller prediction errors and less biased estimators of predictive accuracy than 'all possible subsets' approaches but no differences are detected between the performances of C$\sb{\rm p}$ and S$\sb{\rm p}$. In every case, prediction errors of models obtained by subset selection in either of the half splits exceed those obtained using all predictors and the entire sample.^ Only the random split estimator is conditionally (on $\\beta$) unbiased, however MSEP$\sb{\rm m}$ is unbiased on average and PRESS is nearly so in unselected (fixed form) models. When subset selection techniques are used, MSEP$\sb{\rm m}$ and PRESS always underestimate prediction errors, by as much as 27 percent (on average) in small samples. Despite their bias, the mean squared errors (MSE) of these estimators are at least 30 percent less than that of the unbiased random split estimator. The DUPLEX split estimator suffers from large MSE as well as bias, and seems of little value within the context of stochastic regressor variables.^ To maximize predictive accuracy while retaining a reliable estimate of that accuracy, it is recommended that the entire sample be used for model development, and a leave-one-out statistic (e.g. PRESS) be used for assessment. ^

Identification of genetic variants that influence atherosclerosis in young persons

Atherosclerosis is widely accepted as a complex genetic phenotype and is the usual cause of cardiovascular disease, the world’s leading killer. Genetic factors have been proven to be important risk contributors for atherosclerosis and much work has been done to identify promising candidates that might play a role in the development of atherosclerosis. It is well known that many independent replications are needed to unequivocally establish a valid genotype-phenotype association across different populations before the findings are extended to clinical settings and to the expensive follow-up studies designed to identify causal genetic variants. Aiming to replicate the association with atherosclerosis in the Pathobiological Determinants of Atherosclerosis in Youth (PDAY) study, we assessed the relationship of 32 atherosclerosis candidate SNPs to atherosclerosis in the PDAY cohort, consisting of AA and EA young people aged 15-34 years who died of non-medical causes. Two association studies, a whole sample study and a 1:1 matched case control study were performed by use of multiple linear regression and logistic regression analyses, respectively. For the whole sample association study, 32 SNPs among 2,650 individuals (1,369 AA and 1,281 EA) were tested for the association with six early atherosclerosis phenotypes: abdominal aorta fatty streaks, abdominal aorta raised lesions, right coronary artery fatty streaks, right coronary artery raised lesions, thoracic aorta fatty streaks, and thoracic aorta raised lesions. For the matched case-control association study, 337 case-control paired samples were included; cases were chosen with the highest total raised lesion scores from the studied population, while controls were randomly selected from individuals that had no raised lesions and matched to cases by age, gender and race. Sixteen SNPs in 13 genes were found to be significantly associated with atherosclerosis in at least one of the PDAY association studies. Among these 16 findings: eight SNPs (rs9579646, rs6053733, rs3849150, rs10499903, rs2148079, rs5073691, rs10116277, and rs17228212) successfully replicated previous results, six SNPs (rs17222814, rs10811661, rs7028570, rs7291467, rs16996148 and rs10401969) were reported as new findings exclusive to our study, the last two of the 16 SNPs, rs501120 and rs6922269, showed either intriguing or conflicting result. SNP rs17222814 in ALOX5AP and SNP rs3849150 in LRRC18 were consistently associated with atherosclerosis in both prior and the two PDAY association studies. SNP rs3849150 was also identified to be highly correlated with a non-synonymous coding SNP, rs17772611, which may damage the protein (polyphen score = 0.996), suggesting that SNP rs17772611 may be the causal functional variant.^ In conclusion, our study added more support for the association of these candidate genes with atherosclerosis. SNPs rs3849150 and rs17772611 of LRRC18, as well as SNP rs17222814 of ALOX5AP, were the most significant findings from our study, and may be ranked among the best for further study.^

Plasmid -encoded virulence determinants of Borrelia burgdorferi

Borrelia burgdorferi, a spirochete and the causative agent of Lyme disease, infects both mammals and ticks. Its genome, sequenced in 1997, consists of one linear chromosome and over 20 linear and circular plasmids. Continuous passage of organisms in culture causes them to lose certain plasmids and also results in loss of infectivity in mammals. In this work, 19 B. burgdorferi clonal isolates were examined for infectivity in mice and for plasmid content utilizing polymerase chain reaction (PCR). Two plasmids, a 28 kilobase (kb) linear plasmid (Ip28-1) and a 25 kb linear plasmid (Ip25) were found to be required for full infectivity. Previous studies had demonstrated that Ip28-1 contains the vls locus, which is involved in antigenic variation and immune evasion. Gene BBE22 on Ip25 is predicted to encode the nicotinamidase PncA, an enzyme that converts nicotinamide to nicotinic acid as part of a pathway for NAD synthesis. To examine the potential role of BBE22 in infectivity, a shuttle vector containing BBE22 (pBBE22) was constructed and used to transform B. burgdorferi clone 5A13, which contains all plasmids except lp25. Transformation with pBBE22 restored infectivity of clone 5A13 in mice, whereas 5A13 transformed with the shuttle vector alone was not infectious. To determine whether BBE22 acts as a nicotinamidase in vivo, a Salmonella typhimurium pncA− nadB− transposon mutant was transformed with pBBE22 or with pQE30:BBE22, which contained BBE22 in an E. coli expression vector. Both constructs complemented the Salmonella mutant, permitting growth in minimal media plus nicotinamide. Salmonella cells over-expressing BBE22 also exhibited nicotinamidase activity, as determined by ammonia production in the presence of nicotinamide. Site-directed mutagenesis of BBE22 at the predicted active site (resulting in a Cys120Ala substitution) abrogated the ability to restore infectivity to B. burgdorferi 5A13 and to complement the pncA mutation in S. typhimurium. These studies indicate that BBE22 is a nicotinamidase required for NAD synthesis and survival of B. burgdorferi in mammals. This is also the first demonstration of ‘molecular Koch's postulates’ in B. burgdorferi, i.e. that a specific gene is essential for infectivity of the Lyme disease spirochete. ^

Physical properties of sediment cores from the Labrador Sea

Sediment core logs from six sediment cores in the Labrador Sea show millennial-scale climate variability during the last glacial by recording all Heinrich events and several major Dansgaard-Oeschger cycles. The same millennial-scale climate change is documented for surface-water d18O records of Neogloboquadrina pachyderma (left coiled); hence the surface-water d18O record can be derived from sediment core logging by means of multiple linear regression, providing a paleoclimate proxy record at very high temporal resolution (70 yrs). For the Labrador Sea, sediment core logs contain important information about deep-water current velocities and also reflect the variable input of IRD from different sources as inferred from grain-size analysis, benthic d18O, the relation of density and p-wave velocity, and magnetic susceptibility. For the last glacial, faster deep-water currents which correspond to highs in sediment physical properties, occurred during iceberg discharge and lasted for a several centuries to a few millennia. Those enhanced currents might have contributed to increased production of intermediate waters during times of reduced production of North Atlantic Deep Water. Hudson Strait might have acted as a major supplier of detrital carbonate only during lowered sea level (greater ice extent). During coldest atmospheric temperatures over Greenland, deep-water currents increased during iceberg discharge in the Labrador Sea, then surface water freshened shortly after, while the abrupt atmospheric temperature rise happened after a larger time lag of >=1 kyr. The correlation implies a strong link and common forcing for atmosphere, sea surface, and deep water during the last glacial at millennial time scales but decoupling at orbital time scales.

Morphology and size of Neogloboquadrina pachyderma in the North Atlantic

The variability in size and shape of shells of the polar planktonic foraminifer Neogloboquadrina pachyderma have been quantified in 33 recent surface sediment samples throughout the northern Atlantic Ocean and correlated with the properties of the ambient surface waters. The aim of the study was to determine whether any of the morphological features could be used to reconstruct sea surface properties in the polar realm of the North Atlantic, where most paleotemperature proxies appear to fail. The analyses revealed that shell morphology is only weakly controlled by habitat properties, whereas shell size showed a strong correlation with sea surface temperature. The regression of mean shell size on sea surface temperature revealed the presence of two trends among the sinistrally coiled shells: a continuous increase in shell size with decreasing SST in sediments deposited under polar water masses and a continuous increase in shell size with increasing SST in samples from transitional waters. The second trend mirrors the trend observed for dextrally coiled shells, which are frequent in the same samples and signal the presence of N. incompta. The identical mean shell size trends among the sinistral and dextral specimens in the temperate samples confirms the results of earlier genetic studies which indicated the existence of a small but distinct proportion of opposite coiling in N. incompta, to which the sinistral shells in the temperate samples could be attributed. The linear correlation between mean shell size and sea surface temperature in the polar domain (summer SST < 9 °C) has been used to develop an empirical formula for the reconstruction of past sea surface temperatures from shell sizes in fossil samples. The standard error of the residuals of the linear regression is 2.36 °C (1 sigma), which implies a much larger error than for most paleothermometers, but enough precision to allow resolution between results by individual paleothermometers in the polar domain. The resulting regression model has been applied on two sediment cores spanning the interval from the Last Glacial Maximum (LGM) to the present day. The results from core PS1906-1 are consistent with ice-free conditions during the LGM in the Norwegian Sea. The SST estimates for the LGM inferred from N. pachyderma shell size are similar or slightly higher than those for the latest Holocene. The results do not indicate anomalously high SST during the glacial and the LGM reconstructions thus appear more consistent with the results from foraminiferal transfer functions and geochemical proxies. Both sediment cores show the highest reconstructed SST during the early Holocene insolation optimum.

Strontium isotopic composition and chronology of sediments from DSDP Site 90-588

We report 261 strontium isotopic analyses of well-preserved planktonic foraminifers from three Deep Sea Drilling Project Sites (519, 588, and 607). These samples cover the period from 24 Ma to present with an average of approximately one sample per 100 ka. The combination of high sample density and uniformity of analytical procedures has produced a well-defined record of changes in the 87Sr/86Sr of seawater during the Neogene. The record can be viewed as a series of essentially linear segments with slopes ranging from as high as 0.00006/m.y. to as low as 0/m.y. The times associated with major inflections in the curve do not appear to correspond to simple geologic phenomena such as eustatic cycles, but are probably controlled by a combination of tectonic and climatic factors that influenced the abundance and isotopic composition of terrestrial strontium input to the oceans. The strontium isotopic data are consistent with a progressive increase in the chemical weathering rates of the continents during the Neogene, probably related to repeated glaciations, increased exposure of continents by lowered sea level, and increased continental relief resulting from high rates of tectonic uplift.

Paleomagnetic and radiocarbon-based chronologies of sediment cores MD99-2269 and MD99-2322

We report the intercalibration of paleomagnetic secular variation (PSV) and radiocarbon dates of two expanded postglacial sediment cores from geographically proximal, but oceanographically and sedimentologically contrasting settings. The objective is to improve relative correlation and chronology over what can be achieved with either method alone. Core MD99-2269 was taken from the Húnaflóaáll Trough on the north Iceland shelf. Core MD99-2322 was collected from the Kangerlussuaq Trough on the east Greenland margin. Both cores are well dated, with 27 and 20 accelerator mass spectrometry 14C dates for cores 2269 and 2322, respectively. Paleomagnetic measurements made on u channel samples document a strong, stable, single-component magnetization. The temporal similarities of paleomagnetic inclination and declination records are shown using each core's independent calibrated radiocarbon age model. Comparison of the PSV records reveals that the relative correlation between the two cores could be further improved. Starting in the depth domain, tie points initially based on calibrated 14C dates are either adjusted or added to maximize PSV correlations. Radiocarbon dates from both cores are then combined on a common depth scale resulting from the PSV correlation. Support for the correlation comes from the consistent interweaving of dates, correct alignment of the Saksunarvatn tephra, and the improved correlation of paleoceanographic proxy data (percent carbonate). These results demonstrate that PSV correlation used in conjunction with 14C dates can improve relative correlation and also regional chronologies by allowing dates from various stratigraphic sequences to be combined into a single, higher dating density, age-to-depth model.

Lead and strontium isotope composition, mass accumulation rates and rare earth elements of selected samples from DSDP Sites 92-597 to 92-601

Most of the Pb isotope data for the Leg 92 metalliferous sediments (carbonate-free fraction) form approximately linear arrays in the conventional isotopic plots, extending from the middle of the field for mid-ocean ridge basalts (MORB) toward the field for Mn nodules. These arrays are directed closely to the average values of Mn nodules, the composition of which reflects the Pb isotope composition of seawater (Reynolds and Dasch, 1971). Since the Leg 92 samples are almost devoid of continentally derived detritus, it can be inferred that the more radiogenic end-member is seawater. The less radiogenic end-member lies in the very middle of the MORB field, and hence can be considered to reflect the Pb isotope composition of typical ocean-ridge basalt. The array of data lying between these two end-members is most readily interpreted in terms of simple linear mixing of Pb from the two different end-member sources. According to this model, eight samples from Sites 599 to 601 contain 50 to 100% basaltic Pb. Five of these samples have compositions that are identical within the uncertainty of the analyses. We use the average of these five values to define our unradiogenic end-member in the linear mixing model. The ratios used for this average are 206Pb/204Pb = 18.425 ± 0.010; 207Pb/204Pb = 15.495 ± 0.018; 208Pb/204Pb = 37.879 ± 0.068. These values should approximate the average Pb isotope composition of discharging hydrothermal solutions, and therefore also that of the basaltic crust, over the period of time represented by these samples ( 4 m.y., from 4 to 8 Ma). Sr isotope ratios show a significant range of values, from 0.7082 to 0.7091. The lower ratios are well outside the value of 0.70910 ± 6 for modern-day seawater (Burke et al., 1982). However, most values correspond very closely to the curve of 87Sr/86Sr versus age for seawater, with older samples having progressively lower 87Sr/86Sr ratios. The simplest explanation for this progressive reduction is that recrystallization of the abundant biogenic carbonate in the sediments released older seawater Sr which was incorporated into ferromanganiferous phases during diagenesis. Leg 92 metalliferous sediments have total rare earth element (REE) contents that range on a carbonate-free basis from 131 to 301 ppm, with a clustering between 167 and 222 ppm. The patterns have strong negative Ce anomalies. Samples from Sites 599 to 601 display a slight but distinct enrichment in the heavy REE relative to the light REE, whereas those from Sites 597 to 598 show almost no heavy REE enrichment. The former patterns (those for Sites 599 to 601) are interpreted as indicating moderate diagenetic alteration of metalliferous sediments originating at the EPR axis; the latter reflect more complete diagenetic modification.

Chemical and isotope compositions of main phases of metalliferous sediments from holes of DSDP Leg 92

The carbonate-free metalliferous fraction of thirty-nine sediment samples from four DSDP Leg 92 sites has been analyzed for 12 elements, and a subset of 16 samples analyzed for Pb isotopic composition. The main geochemical features of this component are as follows: i) very high concentrations of Fe and Mn, typically 25-39% and 5-14%, respectively; ii) Al and Ca contents generally less than 2% and 5%, respectively; iii) high Cu (1000-2000 ppm), and Zn and Ni (500-1000 ppm) values; and iv) Co and Pb concentrations of 100-250 ppm. In terms of element partitioning within the metalliferous fraction, amorphous to poorly crystallized oxide-oxyhydroxides removed by the second leach carry virtually all of the Mn, and about 90% of the Ca, Sr and Ni. The well-crystallized goethite-rich material removed by the third leach carries the majority of Fe, Cu, and Pb. These relations hold for sediments as young as ~1-2 Ma, indicating early partitioning of hydrothermal Fe and Mn into separate phases. Calculated mass accumulation rates (MAR) for Fe, Mn, Cu, Pb, Zn and Ni in the bulk sediment show the same overall trends at three of the sites, with greatest MAR values near the basement, and a general decrease in MAR values towards the tops of the holes (for sediments deposited above the lysocline). These relations strongly support the concept of a declining hydrothermal contribution of these elements away from a ridge axis. Nevertheless, MAR values for these metals up to ~200 km from the ridge axis are orders of magnitude higher than on abyssal seafloor plains where there is no hydrothermal influence. Mn/Fe ratios throughout the sediment column at two sites indicate that the composition of the hydrothermal precipitates changed during transport through seawater, becoming significantly depleted in Mn beyond ~200-300 km from the axis, but maintaining roughly the same proportion of Fe. Most of the Pb isotope data for the Leg 92 metalliferous sediments form approximately linear arrays in the conventional isotopic plots, extending from the middle of the field for mid-ocean ridge basalts toward the field for Mn nodules. The array of data lying between these two end-members is most readily interpreted in terms of simple linear mixing of Pb derived from basaltic and seawater end-member sources. The least radiogenic sediments reflect the average Pb isotope composition of discharging hydrothermal solutions and ocean-ridge basalt at the EPR over the ~4-8 Ma B.P. interval. Pb in sediments deposited up to 250 km from the axis can be almost entirely of basaltic-hydrothermal origin. Lateral transport of some basaltic Pb by ocean currents appears to extend to distances of at least 1000 km west of the East Pacific Rise.

The influence of temperature and seawater carbonate saturation state on 13C-18O bond ordering in bivalve mollusks

The shells of marine mollusks are widely used archives of past climate and ocean chemistry. Whilst the measurement of mollusk delta 18O to develop records of past climate change is a commonly used approach, it has proven challenging to develop reliable independent paleothermometers that can be used to deconvolve the contributions of temperature and fluid composition on molluscan oxygen isotope compositions. Here we investigate the temperature dependence of 13C-18O bond abundance, denoted by the measured parameter Delta 47, in shell carbonates of bivalve mollusks and assess its potential to be a useful paleothermometer. We report measurements on cultured specimens spanning a range in water temperatures of 5 to 25 °C, and field collected specimens spanning a range of -1 to 29 °C. In addition we investigate the potential influence of carbonate saturation state on bivalve stable isotope compositions by making measurements on both calcitic and aragonitic specimens that have been cultured in seawater that is either supersaturated or undersaturated with respect to aragonite. We find a robust relationship between Delta 47 and growth temperature. We also find that the slope of a linear regression through all the Delta 47 data for bivalves plotted against seawater temperature is significantly shallower than previously published inorganic and biogenic carbonate calibration studies produced in our laboratory and go on to discuss the possible sources of this difference. We find that changing seawater saturation state does not have significant effect on the Delta 47 of bivalve shell carbonate in two taxa that we examined, and we do not observe significant differences between Delta 47-temperature relationships between calcitic and aragonitic taxa.

Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

Artificial Neural Nets with Interaction of Afferents

The aim is to obtain computationally more powerful, neuro physiologically founded, artificial neurons and neural nets. Artificial Neural Nets (ANN) of the Perceptron type evolved from the original proposal by McCulloch an Pitts classical paper [1]. Essentially, they keep the computing structure of a linear machine followed by a non linear operation. The McCulloch-Pitts formal neuron (which was never considered by the author’s to be models of real neurons) consists of the simplest case of a linear computation of the inputs followed by a threshold. Networks of one layer cannot compute anylogical function of the inputs, but only those which are linearly separable. Thus, the simple exclusive OR (contrast detector) function of two inputs requires two layers of formal neurons