LOWESS Fit Research Articles

Comparisons of age estimates from Strontium-isotope values versus other Chronostratigraphy methods

Strontium-isotope stratigraphy enables estimates of numerical dates for marine carbonate-bearing sediments by comparing their 87Sr/86Sr ratio to a reference curve of 87Sr/86Sr variations of global seawater through geologic time. That seawater reference curve is a published statistical LOWESS fit to a very large dataset (ca. 14,000) of 87Sr/86Sr measurements of carbonate fossils from known biozones which is converted to numerical ages using published timescales. In this study, we compute the numerical dates projected by this method for suites 87Sr/86Sr ratios from seven stratigraphic sections ranging from Ordovician through Oligocene. The strontium-isotope stratigraphy from the Dawangou section in Tarim Basin of NW China that hosts the Auxiliary GSSP for the base of the Late Ordovician is a new dataset; and the others are published datasets. These 87Sr/86Sr-derived dates are compared to those estimated for the same horizons in these sections by other chronostratigraphic methods, including cyclostratigraphy calibrated to radioisotopic dates and standard biochronostratigraphy. Except for a published study of Lower Triassic strata from Chaohu section in Anhui, China and Middle Devonian strata Jebel Mech Lrdane section of Morocco, all the 87Sr/86Sr-derived dates are within the estimated uncertainties of the dates from the other chronostratigraphic methods, thereby validating the usefulness of strontium-isotope stratigraphy as one tool for obtaining the ages of marine carbonate-bearing deposits. However, the datasets from all three Paleozoic sections (two Ordovician, one Devonian) did display a noticeable offset bias toward older ages, which may be partly an artifact of inadequate adjustment of the LOWESS reference curve to current age models for the biozones. The 87Sr/86Sr-derived dates from Chaohu section of Early Triassic conodont zones were unacceptably systematically younger by ca. 1.45 Myr; thereby indicating higher-than-expected 87Sr/86Sr values, which may have been partially the result of a combination of a semi-restricted basin that was slightly diluted by 87Sr-enriched fluvial waters from the chemical weathering of adjacent landmasses and of the laser ablation (LA-ICP-MS) analytical method applied to those samples that seems to yield higher 87Sr/86Sr ratios than the solution-mode ICP-MS method for 87Sr/86Sr measurements. In summary, with rare exceptions, the method of strontium-isotope stratigraphy and the statistical 87Sr/86Sr seawater curve is an important method to obtain semi-precise numerical dates from marine carbonate sediments.

The relationship between axial length, age and intraocular pressure in children with primary congenital glaucoma

Whilst axial length (AxL) from ultrasound examination is a useful clinical parameter for monitoring progression in younger children with glaucoma, distinguishing AxL changes due to raised intraocular pressure (IOP) from age is often challenging. Existing normograms have included a limited number of children with glaucoma. The aim of this study was to evaluate the relationship between AxL with age and IOP in children with primary congenital glaucoma (PCG) and develop a model for expected AxL increase with age. All children (n = 208; 397 eyes) with PCG who attended our tertiary eye care facility from June 2014 and July 2018 and had AxL and IOP measurements were included. The relationship of AxL with age and IOP was studied by applying a LOWESS fit and then mixed effects models. In the final model, age was the most significant factor influencing the growth of AxL (coefficient age 3.14[95% CI 2.91–3.35, p < 0.001], coefficient age2 − 0.53[95% CI, − 0.59 to − 0.47, p < 0.001]), and this association was influenced by the interaction of IOP with sex (p = 0.098 for girls relative to boys), the number of antiglaucoma medications (AGM [p < 0.001 for ≥ 3 AGM]) and glaucoma surgery (p = 0.015). This model enabled us to derive predicted values for clinical use in children with PCG to predict those with progressive glaucoma.

Abstract 2177: Sensitive single cell copy number profiling using a novel microfluidic droplet based platform

Abstract Intratumoral genetic heterogeneity may relate to aggressiveness and treatment-resistance. However, the genomic abnormalities underlie this heterogeneity remain poorly characterized. To better describe the picture of tumour heterogeneity, single cell approaches to accommodate larger number of cells are highly in demand. Here, we present results of single cell DNA sequencing by using a novel microfluidic droplet system. We applied this approach to discover copy number profiles in two common and therapeutically challenging cancers, isocitrate dehydrogenase wild-type glioblastoma (GBM) and breast cancer. The GBM cells were extracted from patients operated on site and cultured for 2 months in restricted media to isolate glioma stem cells. The breast cancer cells were extracted from patient-derived xenografts (PDXs). A novel microfluidic droplet based platform (10x GenomicsTM) was used to perform sensitive copy number profiling of thousands of single cells simultaneously. Briefly, the platform integrates single cell encapsulation, cell lysis, genomic amplification, and barcoding with oligonucleotides. The barcoded genomic DNA fragments from individual cells were pooled and converted into libraries that are compatible with Illumina sequencers. Thus far, we sequenced one glioma stem cell sample and two breast cancer PDXs. Uniquely mapped reads were counted in variable-bins with GC bias corrected by lowess fit. The Circular Binary Segmentation was performed and the integer copy number was estimated by least square fitting. The single cell copy number profiles were clustered by hierarchical clustering. We achieved approximately 2% and 6% coverage of the genome per cell for the glioblastoma and the breast tumors, respectively. The uniformity of coverage was comparable to other whole genome amplification and single cell multiplex approaches, while requiring 700k-2.1mi reads/single cell with the median absolute deviation of pair-wise differences in read counts between neighboring bins between 0.17-0.21 vs 0.16)1. We identified two major clonal subpopulations in the glioblastoma sample. One subclone had chr1q amplification and the other subclone had a 9.8Mb deletion on chr4. The clonal CNVs observed were validated using single-cell RNA-seq-based CNV analysis, and the frequent CNVs using fluorescent in situ hybridization. We also identified the HER2 copy number profile within a basal like triple-negative breast cancer as 40% of 2.5N and 25% of 3N. This was previously validated by fluorescence in situ hybridization2. By applying this new microfluidic system, our work will provide more insights into genomic heterogeneity for malignant properties of cancers. 1. Navin, N. et al. Tumour evolution inferred by single-cell sequencing. Nature 472, 90-94 (2011). 2. Savage P. et al. A Targetable EGFR-Dependent Tumor-Initiating Program in Breast Cancer. Cell Rep. 21, 1140-1149 (2017). Citation Format: Rui Li, Charles Couturier, Paul Savage, Jean Monlong, Guillaume Bourque, Kevin Petrecca, Morag Park, Jiannis Ragoussis. Sensitive single cell copy number profiling using a novel microfluidic droplet based platform [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 2177.

Modeling the paleo-seawater radiogenic strontium isotope record: A case study of the Late Jurassic-Early Cretaceous

While uniformitarianism underlies many aspects of the Earth sciences, modeling geochemical cycles throughout Earth history requires critically assessing the reliability and constancy of projecting modern fluxes and their isotope ratios into deep geologic time. In this study, we develop an iterative technique for modeling the radiogenic strontium isotope composition (R87=87Sr/86Sr) of seawater (sw) during the Phanerozoic utilizing as a constraint the composite record of McArthur et al. (2012) (McArthur, J. M., Howarth, R. J., & Shields, G. A. (2012). Strontium isotope stratigraphy. In F. M. Gradstein, J. G. Ogg, M. Schmitz, & G. Ogg (Eds.), The Geologic Time Scale 2012 (pp. 127–144): Elsevier). The model yields estimates for the Sr isotope composition of the riverine, submarine groundwater discharge, and diagenetic input fluxes. We use the Late Jurassic-Early Cretaceous segment of the marine Sr isotope record as a case study to demonstrate the efficacy of the new method. To begin, 87Sr/86Sr ratios are calculated for a combined riverine and submarine groundwater discharge flux (tw=total weathering) using a prescribed time-variable ddtR87,sw determined from the LOWESS FIT 5 of McArthur et al. (2012). The calculated R87,tw values are checked against the range of R87,sw for the time interval of interest, as well as older carbonates available for weathering, to determine the reasonableness of the estimates. From these estimates, different prescribed R87,tw values are tested to identify the best match with target seawater 87Sr/86Sr ratios and the range of ddtR87,sw. For model runs focusing on long time intervals (≳10Myr), a single prescribed R87,tw value does not produce a reasonable match to the Sr isotope record. Testing the frequency of variation in R87,tw indicates that during the Early Cretaceous, R87,tw varied at least every 5Myr, if not more frequently. The minimum frequency at which R87,tw changes likely varied throughout the Phanerozoic, as it depends on the variability of ddtR87,sw and residence time of Sr. Model results also demonstrate the significance of estimating variation in the total hydrothermal (high and low temperature) input flux of Sr along with seawater Sr concentrations in the geologic past, which are key for properly estimating R87,tw.

A Generalized Additive Model For Microarray Gene Expression Data Analysis

Microarray technology allows the measurement of expression levels of a large number of genes simultaneously. There are inherent biases in microarray data generated from an experiment. Various statistical methods have been proposed for data normalization and data analysis. This paper proposes a generalized additive model for the analysis of gene expression data. This model consists of two sub-models: a non-linear model and a linear model. We propose a two-step normalization algorithm to fit the two sub-models sequentially. The first step involves a non-parametric regression using lowess fits to adjust for non-linear systematic biases. The second step uses a linear ANOVA model to estimate the remaining effects including the interaction effect of genes and treatments, the effect of interest in a study. The proposed model is a generalization of the ANOVA model for microarray data analysis. We show correspondences between the lowess fit and the ANOVA model methods. The normalization procedure does not assume the majority of genes do not change their expression levels, and neither does it assume two channel intensities from the same spot are independent. The procedure can be applied to either one channel or two channel data from the experiments with multiple treatments or multiple nuisance factors. Two toxicogenomic experiment data sets and a simulated data set are used to contrast the proposed method with the commonly known lowess fit and ANOVA methods.

Normalization Methods for Analysis of Microarray Gene-Expression Data

This paper investigates subset normalization to adjust for location biases (e.g., splotches) combined with global normalization for intensity biases (e.g., saturation). A data set from a toxicogenomic experiment using the same control and the same treated sample hybridized to six different microarrays is used to contrast the different normalization methods. Simple t-tests were used to compare two samples for dye effects and for treatment effects. The numbers of genes that reproducibly showed significant p-values for the unnormalized data and normalized data from different methods were evaluated for assessment of different normalization methods. The one-sample t-statistic of the ratio of red to green samples was used to test for dye effects using only control data. For treatment effects, in addition to the one-sample t-test of the ratio of the treated to control samples, the two-sample t-test for testing the difference between treated and control samples was also used to compare the two approaches. The method that combines a subset approach (median or lowessfit) for location adjustment with a global lowess fit for intensity adjustment appears to perform well.

Sr isotopes of the Seoguipo Formation (Korea) and their application to geologic age

The Seoguipo Formation, Cheju Island, Korea is a shallow-marine to nonmarine sedimentary formation formed by the earliest stage of volcanism and simultaneous volcanogenic sedimentation of the island. The formation contains signatures of glacioeustasy, providing an opportunity to study Neogene paleoceanographic changes in the northwestern Pacific. The proposed geologic age of the formation varies widely from Pliocene to Pleistocene in spite of an abundance of biostratigraphic and paleomagnetic data. This situation has hampered establishment of a time framework on which paleoenvironmental interpretations can be based. In this study, strontium isotopic ratios were measured from diverse macrofossils obtained from the fossiliferous lower part of the formation to constrain the carbonate ages. All macrofossils retain the original mineralogy and microstructures, negating the possibility of postdepositional diagenesis. The stable oxygen and carbon isotopic compositions of the specimens also show little sign of alteration. 87Sr/86Sr ratios of the shells display a wide range of values (0.70863–0.70919), categorized into two groups; calcitic pectenids, brachiopods, and an aragonitic bivalve showing high 87Sr/86Sr values (greater than 0.70909), and the rest of bivalves and an aragonitic gastropod showing unusually low values. The low 87Sr/86Sr ratios of the latter group are interpreted to be due to the local variation of the paleoseawater condition in which the organisms grew, probably caused by contemporaneous volcanic activities and weathering of volcaniclastic materials in a restricted environment. The average 87Sr/86Sr ratio of the heavy group yields a carbonate age of 0.86 (+0.40/−0.57)Ma by the LOWESS fit to the marine Sr-isotope curve of Howarth and McArthur (J. Geol., 105 (1997) 441). The Sr isotope age, in conjunction with radiometric and biostratigraphic ages, suggests that the deposition of the Seoguipo Formation began since the early Pleistocene, and the surface exposure of the formation belongs mostly to the middle Pleistocene (∼0.86–0.4Ma).

Strontium Isotope Stratigraphy: LOWESS Version 3: Best Fit to the Marine Sr‐Isotope Curve for 0–509 Ma and Accompanying Look‐up Table for Deriving Numerical Age

An improved and updated version of the statistical LOWESS fit to the marine 87Sr/86Sr record and a revised look-up table (V3:10/99; available from j.mcarthur@ucl.ac.uk) based upon it enables straightforward conversion of 87Sr/86Sr to numerical age, and vice versa, for use in strontium isotope stratigraphy (SIS). The table includes 95% confidence intervals on predictions of numerical age from 87Sr/86Sr. This version includes the Triassic and Paleozoic record (0509 Ma) omitted from previous versions because of the paucity of adequate data at the time of preparation. We highlight differences between the previous versions of the table and the current version and discuss some aspects of the 87Sr/86Sr record that may have geological significance. We give examples of how the table can be used and where it has proven useful.

Subjective and objective indices of sleepiness (ESS and MWT) are not equally useful in patients with sleep apnea.

To understand the relationship between subjective and objective indices of sleepiness, we studied the relationship of the Epworth Sleepiness Scale (ESS) and the Maintenance of Wakefulness Test (MWT) in 41 consecutive patients complaining of snoring and excessive day-time sleepiness. The correlation between ESS and MWT was significant but small (rho = -0.39). There was considerable discordance between the two tests. The Lowess fit line between the ESS and the MWT indicates that the ESS falls as the MWT rises to about 4 min. It then stays at a plateau until the MWT rises to about 12 min. Thereafter, it resumes its downward slope as the MWT rises further. Thus, in patients who are severely sleepy on the MWT, the ESS may not be sensitive to different levels of sleepiness. We conclude that the ESS and the MWT are not equally useful in assessing sleepiness in patients with sleep apnea.