Data set for figures in the paper titled "Compact Homodyne Extrapolation System (CHEXS)".Abstract: We present on a novel gain extrapolation antenna range, the Compact Homodyne Extrapolation System (CHEXS), that can achieve absolute antenna gain measurements with uncertainties of +/-0.1 dB or better with as few at 10 data points and is significantly more compact, up to six times shorter than conventional gain extrapolation ranges. This compact gain extrapolation range achieves these beneficial attributes by measuring the homodyne signal that occurs naturally between two directional antennas that often exhibit strong third order mutual coupling at close proximity. The design and operation of the CHEXS is presented along with gain measurements of NIST reference standard gain antennas which are shown to be equivalent to those obtained using a conventional gain extrapolation range.

We present an overview on a recently developed technique for performing antenna gain measurements with gain extrapolation that uses significantly fewer data points and at shorter distances than traditional gain extrapolation. This enhanced technique purposely incorporates third-order mutual coupling between antennas, which can be thought of as a useful homodyne signal, rather than an unwanted degradation of the antenna-to-antenna coupling signal as has been the historically accepted viewpoint. From Wacker’s fundamental extrapolation equations, we give the development of the third-order signal which underpins this technique. From the third-order signal the framing of gain extrapolation can be approached as a measure of interference fringes, as opposed to a by-rote curve fitting problem, and thus provides ways of specifying the number of required data points and measurement distances so as to reduce both significantly from the traditional gain extrapolation approach. The truncation order of the full signal expansion, as it relates to the conditioning of the problem, is presented in light of the behavior of the design matrix that defines the gain extrapolation scenario and the orders of scattering, thus leading to fewer required samples. Along with considerations of the matrix conditioning, guidelines are presented from the thirdorder signal and interference fringes for sampling criteria and sampling accuracy criteria. These aid in choices of measurement system accuracy and precision requirements based on known values of the operating frequency, wavelength, and antenna dimensions. Bounds for gain uncertainty based on these sampling criteria are also given. Results comparing NIST reference antenna measurements made with the traditional gain extrapolation and enhanced gain extrapolation technique are presented. It is shown that the enhanced technique can produce gain values in agreement and within uncertainties of the traditional technique for the reference antennas.

In this paper we describe an enhanced three-antenna gain extrapolation technique that allows one to determine antenna gain with significantly fewer data points and at closer distances than with the well-established traditional three-antenna gain extrapolation technique that has been in use for over five decades. As opposed to the traditional gain extrapolation technique, where high-order scattering is purposely ignored so as to isolate only the direct antenna-to-antenna coupling, we show that by incorporating third-order scattering the enhanced gain extrapolation technique can be obtained. The theoretical foundation using third-order scattering is developed and experimental results are presented comparing the enhanced technique and traditional technique for two sets of internationally recognized NIST reference standard gain horn antennas at X-band and Ku-band. We show that with the enhanced technique gain values for these antennas are readily obtained to within stated uncertainties of ±0.07 dB using as few as 10 data points per antenna pair, as opposed to approximately 4000 -to- 8000 data points per antenna pair that is needed with the traditional technique. Furthermore, with the described enhanced technique, antenna-to-antenna distances can be reduced by a factor of three, and up a factor of six in some cases, compared to the traditional technique, a significant reduction in the overall size requirement of facilities used to perform gain extrapolation measurements.

An R Rda-file containing the four hypothetical datasets used in the analysis (Flat, increasing, decreasing, unimodal). These are stored in a single data-frame, where the 400 rows correspond to observations. For each dataset there are three variables: an event indicator = 1 for if death was during follow-up, else = 0 (suffix "_dead"), the true time of death (suffix "_time") and the observed follow-up time, which will = 1 if the true time of death > 1 (suffix "_obs"). Hence there are twelve columns.A script is provided seperately within this project (Analysis.R) which includes the code used to analyse this dataset in order to obtain the results reported in the manuscript "How uncertain is the survival extrapolation? A study of the impact of different parametric survival models on extrapolated uncertainty about hazard functions, lifetime mean survival and cost-effectiveness."

In drug discovery, molecules are optimized towards desired properties. In this context, machine learning is used for extrapolation in drug discovery projects. The limits of extrapolation for regression models are known. However, a systematic analysis of the effectiveness of extrapolation in drug discovery has not yet been performed. In response, this study examined the capabilities of six machine learning algorithms to extrapolate from 243 datasets. The response values calculated from the molecules in the datasets were molecular weight, cLogP, and the number of sp3-atoms. Three experimental set ups were chosen for response values. Shuffled data were used for interpolation, whereas data for extrapolation were sorted from high to low values, and the reverse. Extrapolation with sorted data resulted in much larger prediction errors than extrapolation with shuffled data. Additionally, this study demonstrated that linear machine learning methods are preferable for extrapolation.

Global Mean Sea Level, Trajectory and Extrapolation

This file contains Global Mean Sea Level (GMSL) variations along, data for the quadratic fit (trajectory) to the GMSL variations, and an extrapolation of this trajectory to 2050.

The GMSL variations(column 2) are computed at the NASA Goddard Space Flight Center under the auspices of the NASA Sea Level Change program. The GMSL was generated using the Integrated Multi-Mission Ocean Altimeter Data for Climate Research (http://podaac.jpl.nasa.gov/dataset/MERGED_TP_J1_OSTM_OST_ALL_V51). It combines Sea Surface Heights from the TOPEX/Poseidon, Jason-1, OSTM/Jason-2, Jason-3, and Sentinel-6 Michael Freilich missions.

In addition, the rate and acceleration are estimated from full record of GMSL relative to the midpoint of the record and then used to generate a quadratic fit to the data. This quadratic fit is provided in column 3. The rate associated with this quadratic fit at any time in the record is also provided (column 4).

The parameters estimated from the quadratic fit are also used to generated an extrapolated time series out to 2050 (column 5). These are provided at yearly intervals. This is not a projection and is only considered an extrapolation of the current trajectory of GMSL variations. This also differs from Nerem et al. (2022) and Sweet et al. (2022) as additional signals are not removed from GMSL prior to estimating the rate and acceleration parameters. The yearly rate associated with this extrapolation is also provided (column 6)

If you use these data please cite:
Willis, J.K., Hamlington, B.D., and Fournier, S., Global Mean Sea Level Time Series, Trajectory and Extrapolation. Dataset access [YYYY-MM-DD] at 10.5281/zenodo.7702315.

GSFC. 2021. Global Mean Sea Level Trend from Integrated Multi-Mission Ocean Altimeters TOPEX/Poseidon, Jason-1, OSTM/Jason-2, and Jason-3 Version 5.1. Ver. 5.1 PO.DAAC, CA, USA. Dataset accessed [YYYY-MM-DD] at https://doi.org/10.5067/GMSLM-TJ151.

***Users of the 2024 release of this product should note that several updates were made since the previous release to improve the accuracy of the record. These include newly reprocessed data for the TOPEX/Poseidon satellite, primarily affecting the first decade of the record, as well as corrections of small errors in more recent missions like Jason-2 and Jason-3, primarily affecting data after 2010. Changes to the estimate of global mean sea level were on the order of a few mm, in both the early and late parts of the record. These changes improved agreement between the satellite altimeters and independent observations from tide gauges and other types satellites.

The net effect of the changes was to slightly reduce the total amount of rise by about 3/4 of a centimeter during the 30 year record. However, the acceleration of the rate of global rise was almost unchanged, with the rate getting faster by about 0.8 mm/year, each decade.

For more details on the changes, please see the relevant sections of the 2022 and 2023 yearly reports from the Ocean Surface Topography Science Team:

https://www.aviso.altimetry.fr/fileadmin/documents/OSTST/2022/OSTST_2022_Meeting_Report.pdf
https://www.aviso.altimetry.fr/fileadmin/documents/OSTST/2023/OSTST_2023_Meeting_Report.pdf

References:

Nerem, R. S., Frederikse, T., & Hamlington, B. D. (2022). Extrapolating Empirical Models of Satellite‐Observed Global Mean Sea Level to Estimate Future Sea Level Change. Earth's Future, 10(4), e2021EF002290.

Sweet, W. V., Hamlington, B. D., Kopp, R. E., Weaver, C. P., Barnard, P. L., Bekaert, D., ... & Zuzak, C. (2022). Global and regional sea level rise scenarios for the United States: updated mean projections and extreme water level probabilities along US coastlines. Interagency Technical Report.

Inland lake data from the LAGOS-NE database. Multi-scale covariates available for ~8,000 lakes with observed and unobserved water quality response variables. Lake data used for identifying and characterizing extrapolation in multivariate response data. Analyzed as part of PLOS One manuscript. Also available are output data with extrapolation index values and CART model fit with data.

1. Diet is a key trait of an organism’s life history that influences a broad spectrum of ecological and evolutionary processes. Kissling et al. (2014) compiled a species-specific dataset of diet preferences of mammals for 38% of a total of 5364 terrestrial mammalian species assessed for the International Union for Conservation of Nature’s Red List, to facilitate future studies. The authors imputed dietary data for the remaining 62% by using extrapolation from phylogenetic relatives. 2. We collected dietary information for 1261 mammalian species for which data were extrapolated by Kissling et al. (2014), in order to evaluate the success with which such extrapolation can predict true diets. 3. The extrapolation method devised by Kissling et al. (2014) performed well for broad dietary categories (consumers of plants and animals). However, the method performed inconsistently, and sometimes poorly, for finer dietary categories, varying in accuracy in both dietary categories and mammalian orders. 4. The results of the extrapolation performance serve as a cautionary tale. Given the large variation in extrapolation performance, we recommend a more conservative approach for inferring mammalian diets, whereby dietary extrapolation is implemented only when there is a high degree of phylogenetic conservatism for dietary traits. Phylogenetic comparative methods can be used to detect and measure phylogenetic signal in diet. If data for species are needed, then only the broadest feeding categories should be used. This would ensure a greater level of accuracy and provide a more robust dataset for further ecological and evolutionary analysis.

Data for paper "Zone extrapolations in parametric timed automata"

This data set comes with two zip files:

artifact.zip contains the current version of IMITATOR, all models and necessary scripts to reproduce all experiments on our benchmarks set. A file named README.md gives all instructions for reproducibility.

results.zip contains an HTML page with a table summarizing all results, and all raw results (.res) as well.

🇺🇸 미국 English We present an overview on a recently developedtechnique for performing antenna gain measurements with gainextrapolation that uses significantly fewer data points and atshorter distances than traditional gain extrapolation. This enhancedtechnique purposely incorporates third-order mutualcoupling between antennas, which can be thought of as a usefulhomodyne signal, rather than an unwanted degradation of theantenna-to-antenna coupling signal as has been the historicallyaccepted viewpoint. From Wacker’s fundamental extrapolationequations, we give the development of the third-order signalwhich underpins this technique. From the third-order signal theframing of gain extrapolation can be approached as a measureof interference fringes, as opposed to a by-rote curve fittingproblem, and thus provides ways of specifying the numberof required data points and measurement distances so as toreduce both significantly from the traditional gain extrapolationapproach. The truncation order of the full signal expansion,as it relates to the conditioning of the problem, is presentedin light of the behavior of the design matrix that defines thegain extrapolation scenario and the orders of scattering, thusleading to fewer required samples. Along with considerations ofthe matrix conditioning, guidelines are presented from the thirdordersignal and interference fringes for sampling criteria andsampling accuracy criteria. These aid in choices of measurementsystem accuracy and precision requirements based on knownvalues of the operating frequency, wavelength, and antennadimensions. Bounds for gain uncertainty based on these samplingcriteria are also given. Results comparing NIST reference antennameasurements made with the traditional gain extrapolationand enhanced gain extrapolation technique are presented. It isshown that the enhanced technique can produce gain values inagreement and within uncertainties of the traditional techniquefor the reference antennas.

The Plasma-Prescribed Active Region Static Extrapolation (PARSE) Dataset consists of approximately seven thousand magnetohydrostatic extrapolations of solar active regions for use in statistical or machine learning applications. The extrapolations are based on the Spaceweather HMI Active Region Patch (SHARP) library (doi 10.1007/s11207-014-0529-3), and the magnetohydrostatic extrapolation is performed by the routine detailed in Mathews et al 2022 (doi 10.1016/j.jcp.2022.111214).

Species distribution and ecological niche models (hereafter SDMs) are popular tools with broad applications in ecology, biodiversity conservation, and environmental science. Many SDM applications require projecting models in environmental conditions non-analog to those used for model training (extrapolation), giving predictions that may be statistically unsupported and biologically meaningless. We introduce a novel method, Shape, a model-agnostic approach that calculates the extrapolation degree for a given projection data point by its multivariate distance to the nearest training data point. Such distances are relativized by a factor that reflects the dispersion of the training data in environmental space. Distinct from other approaches, Shape incorporates an adjustable threshold to control the binary discrimination between acceptable and unacceptable extrapolation degrees. We compared Shape’s performance to five extrapolation metrics based on their ability to detect analog environmental conditions in environmental space and improve SDMs suitability predictions. To do so, we used 760 virtual species to define different modeling conditions determined by species niche tolerance, distribution equilibrium condition, sample size, and algorithm. All algorithms had trouble predicting species niches. However, we found a substantial improvement in model predictions when model projections were truncated independently of extrapolation metrics. Shape’s performance was dependent on extrapolation threshold used to truncate models. Because of this versatility, our approach showed similar or better performance than the previous approaches and could better deal with all modeling conditions and algorithms. Our extrapolation metric is simple to interpret, captures the complex shapes of the data in environmental space, and can use any extrapolation threshold to define whether model predictions are retained based on the extrapolation degrees. These properties make this approach more broadly applicable than existing methods for creating and applying SDMs. We hope this method and accompanying tools support modelers to explore, detect, and reduce extrapolation errors to achieve more reliable models. Methods The experiment was based on virtual species created with the same protocol as (Andrade et al., 2019). Also, are provided the codes used to run the experiment.

This is a python package to perform thermodynamic extrapolation andinterpolation of observables calculated from molecular simulations. This allowsfor more efficient use of simulation data for calculating how observables changewith simulation conditions, including temperature, density, pressure, chemicalpotential, or force field parameters.

AM1EPHNE is the Terra Near Real Time (NRT) 2-hour spacecraft Extrapolated ephemeris data file in native format. The file name format is the following: AM1EPHNE.Ayyyyddd.hhmm.vvv.yyyydddhhmmss where from left to right: E = Extrapolated; N = Native format; A = AM1 (Terra); yyyy = data year, ddd = Julian data day, hh = data hour, mm = data minute; vvv = Version ID; yyyy = production year, ddd = Julian production day, hh = production hour, mm = production minute, and ss = production second. Data set information:http://modis.gsfc.nasa.gov/sci_team/

In many practical problems, there is interest in the estimation of mixed effect projections for new data that are outside the range of the training data. Examples include predicting extreme small area means for rare populations or making treatment decisions for patients who do not fit typical risk profiles. Standard methods have long been known to struggle with such problems since the training data may not provide enough information about potential model changes for these new data values (extrapolation bias). We propose a new framework called Prediction Using Random-effect Extrapolation (PURE) which involves constructing a generalized independent variable hull (gIVH) to isolate a minority training set which is “close” to the prediction space, followed by a regrouping of the minority data according to the response variable which results in a new (but misspecified) random effect distribution. This misspecification reflects “extrapolated random effects” which prove vital to capture information that is needed for accurate model projections. Projections are then made using classified mixed model prediction (CMMP) (?) with the regrouped minority data. Comprehensive simulation studies and analysis of data from the National Longitudinal Mortality Study (NLMS) demonstrate superior predictive performance in these very challenging paradigms. An asymptotic analysis reveals why PURE results in more accurate projections. Supplementary materials for this article are available online.

Data for reproducibility of the numerical simulations of the research paper: Grassmann Extrapolation for Accelerating Geometry Optimization

Context

Create a model which can help impute/extrapolate data to fill in the missing data gaps in the store level POS data currently received.

Task:

Build an imputation and/or extrapolation model to fill the missing data gaps for select stores by analyzing the data and determine which factors/variables/features can help best predict the store sales.

Linking in vitro bioactivity and in vivo toxicity on a dose basis enables the use of high-throughput in vitro assays as an alternative to traditional animal studies. In this study, we evaluated assumptions in the use of a high-throughput, physiologically based toxicokinetic (PBTK) model to relate in vitro bioactivity and rat in vivo toxicity data. The fraction unbound in plasma (fup) and intrinsic hepatic clearance (Clint) were measured for rats (for 67 and 77 chemicals, respectively), combined with fup and Clint literature data for 97 chemicals, and incorporated in the PBTK model. Of these chemicals, 84 had corresponding in vitro ToxCast bioactivity data and in vivo toxicity data. For each possible comparison of in vitro and in vivo endpoint, the concordance between the in vivo and in vitro data was evaluated by a regression analysis. For a base set of assumptions, the PBTK results were more frequently better associated than either the results from a “random” model parameterization or direct comparison of the “untransformed” values of AC50 and dose (performed best in 51%, 28%, and 21% of cases, respectively). We also investigated several assumptions in the application of PBTK for IVIVE, including clearance and internal dose selection. One of the better assumptions sets–restrictive clearance and comparing free in vivo venous plasma concentration with free in vitro concentration–outperformed the random and untransformed results in 71% of the in vitro-in vivo endpoint comparisons. These results demonstrate that applying PBTK improves our ability to observe the association between in vitro bioactivity and in vivo toxicity data in general. This suggests that potency values from in vitro screening should be transformed using in vitro-in vivo extrapolation (IVIVE) to build potentially better machine learning and other statistical models for predicting in vivo toxicity in humans.

For nearly 25 years CDIAC has been issuing essentially annual updates to its data set on CO2 emissions from burning fossil fuels and manufacturing cement. Estimates for years since 1950 are based on energy data from the United Nations and cement data from the US Geological Survey. Occasionally we refer to national or other data sources when there are questionable or missing values in these primary data sets. Emissions estimates for years prior to 1950 have been constructed using a variety of sources. Collection, organization, and release of energy data by the United Nations Statistics Office is time and labor intensive and typically requires 2 to 2 ½ years after the end of a calendar year. Because of this time lag and because of wide interest in having an indication of CO2 emissions for the most recent years, we provide preliminary emissions estimates for two years more recent than the end of the UN energy data set. The formal CDIAC data set of CO2 emissions is now current through 2005 and this spread sheet offers estimates for the global total and for many of the major emitting countries for 2006 and 2007. Our experience with this process suggests that these preliminary numbers provide a good estimation of recent trends but there will be refinements in these numbers as full UN energy data become available for 2006 and 2007 and data for years up to 2005 are revised and updated.Estimates for 2006 and 2007 are based on energy data from the energy company BP. The BP energy data are published in June of each year and cover years up to the most recently completed calendar year. We use the BP data to extrapolate two additional years beyond the end of the UN energy data set. For emissions from cement we extrapolate the UN cement-production time series for two years and for emissions from gas flaring we assume that emissions are unchanged from the 2005 values.

Supplementary Material 2