Internal Precision Research Articles

Adaptación de una escala de satisfacción laboral general desde la teoría de la psicología del trabajo

Economic and technological changes, aligned to the pandemic scenario and world restrictions have expanded informal and precarious forms of work. The Psychology of Work Theory is a theoretical perspective of career and work, including formal and informal workers. In order to fill a gap of instruments for assessing job satisfaction characteristics in this context, the General Job Satisfaction Scale was adapted by the survey study with two waves of data collection. In the first sample of 709 workers, was explored the internal structure and precision aspects based on exploratory factorial procedures. The second sample of 600 participants, the one-dimensional structure was reassessed by confirmatory factor procedures, in addition to checking the instrument's invariance in terms of subjective social class (AB and CDE), gender (man and women) and work’s nature (formal and informal). Results pointed to a measure with good psychometric properties and an invariant metric for all categorical variables investigated.

Vibration control of MR whole-spacecraft under medium–high frequency and small amplitude considering actuator time-delay

The satellite bears complex vibration loads transmitted from the satellite-rocket interface during launch, where medium–high frequency and small amplitude vibration is highly likely to harm the satellite’s internal precision instruments. Under such special conditions, the time-delay factor of the MR damper as the actuator cannot be ignored in the vibration control of the magnetorheological (MR) whole-spacecraft. To compensate actuator time-delay, and consider the system’s nonlinear characteristics under medium–high frequency and small amplitude conditions, a gray prediction time-delay compensation method is proposed based on the human-simulated intelligent controller (HSIC). After verifying through simulation and experiment that actuator time-delay affects the vibration response of the MR whole-spacecraft, the HSIC based on gray prediction is designed. Then, the control effect of HSIC with or without time-delay is simulated numerically. The results reveal that after considering the time-delay factor, the resonance peak increases by 17%, and the transmissibility of the concerned particularly frequency band (40 Hz) increases by 62%, which implies a significant deterioration in the control effect. Following, to make up for the response deterioration caused by the time-delay, the HSIC based on gray prediction is used for numerical simulation. The results confirm that reasonable time-delay compensation can effectively improve the system dynamics. This study provides a reference for the practical application of the whole-spacecraft controller.

The CARMENES search for exoplanets around M dwarfs

The large amounts of astrophysical data being provided by existing and future instrumentation require efficient and fast analysis tools. Transfer learning is a new technique promising higher accuracy in the derived data products, with information from one domain being transferred to improve the accuracy of a neural network model in another domain. In this work, we demonstrate the feasibility of applying the deep transfer learning (DTL) approach to high-resolution spectra in the framework of photospheric stellar parameter determination. To this end, we used 14 stars of the CARMENES survey sample with interferometric angular diameters to calculate the effective temperature, as well as six M dwarfs that are common proper motion companions to FGK-type primaries with known metallicity. After training a deep learning (DL) neural network model on synthetic PHOENIX-ACES spectra, we used the internal feature representations together with those 14+6 stars with independent parameter measurements as a new input for the transfer process. We compare the derived stellar parameters of a small sample of M dwarfs kept out of the training phase with results from other methods in the literature. Assuming that temperatures from bolometric luminosities and interferometric radii and metallicities from FGK+M binaries are sufficiently accurate, DTL provides a higher accuracy than our previous state-of-the-art DL method (mean absolute differences improve by 20 K for temperature and 0.2 dex for metallicity from DL to DTL when compared with reference values from interferometry and FGK+M binaries). Furthermore, the machine learning (internal) precision of DTL also improves as uncertainties are five times smaller on average. These results indicate that DTL is a robust tool for obtaining M-dwarf stellar parameters comparable to those obtained from independent estimations for well-known stars.

Evaluating U-Pb accuracy and precision by comparing zircon ages from 12 standards using TIMS and LA-ICP-MS methods

U-Pb geochronological studies based on LA-ICP-MS isotopic measurements often require a profound understanding of the accuracy, precision, and preferred ages derived from this methodology. To enhance such awareness, an approximately 60,000 record U-Pb database is compiled from LA-ICP-MS zircon analyses of 12 standards (reference materials), with the standards having ages ranging from 3500 Ma to 0 Ma. Because the 12 standards are dated with the highly accurate and precise TIMS methods, a means exists for assessing the accuracy and precision of corresponding LA-ICP-MS ages. For each standard, the LA-ICP-MS ages are separated by concordance classes, and then age distributions are calculated for each concordance class using four age models: 206Pb/238U, 207Pb/206Pb, IsoplotR concordia, and non-iterative probability ages. Preferred U-Pb ages are determined by the model from which LA-ICP-MS ages consistently align with TIMS ages across the entire age continuum from 3500 Ma to present. The results favor the non-iterative probability model, which indicate that LA-ICP-MS ages have a mean accuracy of ±1.4 myr when comparing median LA-ICP-MS ages with mean TIMS ages; however, LA-ICP-MS ages have relatively poor 2σ internal precision, which is age-dependent and generally ranges from ±3 myr to ±25 myr, with mean 2σ internal precision of 15 myr. Additionally, the results suggest that U-Pb discordance has at least two primary sources: (a) inherent LA-ICP-MS imprecision due to repeated measurement errors of 206Pb/238U and 207Pb/206Pb ratios, is likely the primary cause of proximal-Wetherill discordance, whereas (b) Pb-loss is likely the primary contributor to distal-Wetherill discordance.

Tumor Area Positivity (TAP) score of programmed death-ligand 1 (PD-L1): a novel visual estimation method for combined tumor cell and immune cell scoring

BackgroundDetermination of programmed death-ligand 1 (PD-L1) protein expression level in tumor cells and tumor-associated immune cells is critical for identifying patients eligible for immunotherapy. PD-L1 manual scoring algorithms can generally be divided into two categories: cell counting and visual estimation. Cell counting can be time-consuming and is not in sync with pathology practice, which classically uses a Gestalt approach based on pattern recognition and visual estimation. In this study, we introduce the Tumor Area Positivity (TAP) score, which is a novel, straightforward method for scoring tumor cells and immune cells together using visual estimation.MethodsTo demonstrate the reproducibility of TAP scoring among pathologists, between- and within-reader precision studies were performed both within (internal) and outside of (external) our organization. We also compared the TAP score to the Combined Positive Score (CPS), which is based on cell counting, for concordance and time efficacy.ResultsThe average positive agreement, average negative agreement, and overall percent agreement between and within readers were all above 85% for both internal and combined external reader precision studies. TAP score had high concordance rate at 5% cutoff compared with CPS at cutoff 1: positive percent agreement, negative percent agreement, and overall percent agreement were all above 85%.ConclusionsOur study showed the TAP scoring method to be straightforward, significantly less time-consuming, and highly reproducible with a high concordance rate between TAP score and CPS.

A Spectroscopic Analysis of a Sample of K2 Planet-host Stars: Stellar Parameters, Metallicities and Planetary Radii

The physical properties of transiting exoplanets are connected with the physical properties of their host stars. We present a homogeneous spectroscopic analysis based on the spectra of FGK-type stars observed with the Hydra spectrograph on the WIYN telescope. We derived the effective temperatures, surface gravities, and metallicities, for 81 stars observed by K2 and 33 by Kepler 1. We constructed an Fe i and ii line list that is adequate for the analysis of R ∼ 18,000 spectra covering 6050–6350 Å and adopted the spectroscopic technique based on equivalent-width measurements. The calculations were done in LTE using Kurucz model atmospheres and the qoyllur-quipu (q 2) package. We validated our methodology via an analysis of a benchmark solar twin and solar proxies, which are used as a solar reference. We estimated the effects that including Zeeman-sensitive Fe i lines have on the derived stellar parameters for young and possibly active stars in our sample and found them not to be significant. Stellar masses and radii were derived by combining the stellar parameters with Gaia EDR3 and V magnitudes and isochrones. The measured stellar radii have a 4.2% median internal precision, leading to a median internal uncertainty of 4.4% in the derived planetary radii. With our sample of 83 confirmed planets orbiting K2 host stars, the radius gap near R planet ∼ 1.9 R ⊕ is detected, in agreement with previous findings. Relations between the planetary radius, orbital period, and metallicity are explored and these also confirm previous findings for Kepler 1 systems.

Comparison of the fluctuations of the signals measured by ICP-MS after laser ablation of powdered geological materials prepared by four methods.

Sample preparation is a crucial point for quantitative multi-elemental analses by LA-ICP-MS of powdered geological materials. Four different methods are compared in this study with respect to signal stability and intensity as follows: the preparation of glass beads (GlassB) by alkaline fusion method and three grinding and pelletizing methods relying on the use of an organic binder (VanBind, vanillic acid), an adhesive binder (MixGlue, methyl methacrylate) and a sol-gel process for glass formation (SolGel, chemical reaction of tetraethoxysilane), respectively. Sixty elements were analyzed by means of a ns-UV (213nm) laser ablation system coupled to a single collector sector field ICP-MS with a low or medium mass resolution. Signal stability was found to strongly depend on the sample homogeneity provided by the preparation method. These methods were applied to three geological standard materials (CRM). The following criteria were used to evaluate and compare the methods: (1) proportion of the measurement cycles which are above a given signal intensity threshold (defined here as signal average ± 3 times the standard deviation), (2) signal stability of the analyzed nuclides (internal precision estimated by the relative standard deviations on raw count rates), (3) signal stability of the internal standards added to the samples, (4) external precision estimated by the relative standard deviation over five preparations for each geological CRM. For the majority of the analyzed elements, signals measured for samples prepared with the four methods are reproducible. Specific contamination in one or several elements (Cr, Fe, Co, Ni, Cu, Mo, W, Au and Bi) was observed depending on the sample preparation method. In addition, compared to grinding made with PTFE material, grinding performed with tungsten carbide material was found to produce better homogeneity, especially for the sol-gel and mixing with glue protocols, although some metallic contamination (W and Co) was observed. Thanks to the suppression of grain effects by alkaline melting, the glass bead method systematically provided signal stability and percentage of "over the threshold" close to those of the NIST glasses. This may be explained by the preparation of more homogeneous samples by alkaline melting. Finally, the described methods were found to be reproducible for the majority of the analyzed elements.

16O/18O- exchange internal standard preparation enhancing reliability of bio-sample natural bioactive compounds absolute quantitation

Natural bioactive compounds (NBCs) are regarded as candidates for many medical applications widely. Due to the complicated structure and biosynthesis source, only a few NBCs were supplied with commercial isotopic labeled standards. This shortage resulted in poor quantitation reliability in bio-samples for most NBCs, considering the remarkable matrix effects. NBCs metabolism and distribution studies would be restricted consequently. Those properties played critical roles in drug discovery and development. In this study, a fast, convenient, widely adopting 16O/18O exchange reaction was optimized for stable, available, affordable NBCs 18O-labeled standards preparation. With 18O- labeled internal standard, a UPLC-MRM-based NBCs pharmacokinetics analysis strategy was formed. Pharmacokinetics of caffeic acid with Hyssopus Cuspidatus Boriss extract (SXCF) dosed mice was carried out by established strategy. Compared with traditional external standards quantitation, adapting 18O-labeled internal standards, both accuracy and precision were enhanced significantly. Thus, the platform built by this work would accelerate the pharmaceutical research with NBCs, by providing a reliable, wide-adapted, affordable, isotopic internal standard-based bio-samples NBCs absolute quantitation strategy.

Low-cost and sensitive method for Pb isotope determination using a novel β-Si3N4 emitter by thermal ionization mass spectrometry

Thermal ionization mass spectrometry (TIMS) is the workhorse for lead isotopic ratio analysis due to its excellent precision. Silica gel as ionization activator on Re filament is proved to the best emitter that can provide excellent sensitivity even small Pb sample size. However, the price of Re filament is three times that of Ta filament that leads to high experimental cost for TIMS laboratory. Here, we first present a novel silicon nitride (β-Si3N4) emitter on the Ta filament with good sensitivity for Pb isotopic ratio measurements. Hence, the cost of filament material is cut down ∼70%. The β-Si3N4 emitter can yield stable and long-life Pb+ signal, about 2–3 V 208Pb and 0.65–0.90 V 208Pb for 20 ng and 5 ng NIST SRM981 sample size that is applicable to the most geological materials for bulk analysis. A suite of silicate reference materials were analyzed to verify the reliability and accuracy of our method. For 206Pb/204Pb, 207Pb/204Pb and 208Pb/204Pb isotope ratios of geological samples, excellent internal precisions (2 SE) of ±0.005%–0.013% are achieved. Replicate digestions and analyses of the basalt standard BCR-2 and coal fly ash standard GBW08401 demonstrate that good external precision is obtainable that is 0.10–0.18% (n = 6, 2 SD) for 206Pb/204Pb, 207Pb/204Pb and 208Pb/204Pb ratios.

A uvbyCaHβ CCD Analysis of the Open Cluster Standard, M67, and Its Relation to NGC 752

Precision CCD uvbyCaHβ photometry is presented of the old cluster, M67, covering one square degree with typical internal precision at the 0.005–0.020 mag level to V ∼ 17. The photometry is calibrated using standards over a wide range in luminosity and temperature from NGC 752 and zeroed to the standard system via published photoelectric observations. Relative to NGC 752, differential offsets in reddening and metallicity are derived using astrometric members, supplemented by radial velocity information. From single-star members, offsets in the sense (M67−NGC 752) are δ E(b − y) = −0.005 ± 0.001 (sem) mag from 327 F/G dwarfs and δ[Fe/H] = 0.062 ± 0.006 (sem) dex from the combined m 1 and hk indices of 249 F dwarfs, leading to E(b − y) = 0.021 ± 0.004 (sem) and [Fe/H]M67 = +0.030 ± 0.016 (sem) assuming [Fe/H]Hyades = +0.12. With probable binaries eliminated using c 1, (b − y) indices, 83 members with (π/σ π ) > 50 generate (m − M)0 = 8.220 ± 0.005 (sem) for NGC 752 and an isochronal age of 1.45 ± 0.05 Gyr. Using the same parallax restriction for 312 stars, M67 has (m − M) = 9.77 ± 0.02 (sem), leading to an age tied solely to the luminosity of the subgiant branch of 3.70 ± 0.03 Gyr. The turnoff color spread implies ±0.1 Gyr, but the turnoff morphology defines a younger age/higher mass for the stars, consistent with recent binary analysis and broadband photometry indicating possible missing physics in the isochrones. Anomalous stars positioned blueward of the turnoff are discussed.

Investigation and optimization of methane purification method for natural gas by two-column gas chromatography: A preliminary test for doubly substituted isotopologue (13CH3D) measurements

In this study, optimization of the methane purification method by gas chromatography (GC) is described for the determination of methane clumped isotope compositions of natural gas. Methane was purified under the carrying of helium on the assembly line composed of a vacuum apparatus and two-column gas chromatography. Once methane was detected by the passive thermal conductivity detector (TCD) on the GC, it was collected through a silica trap immersed in liquid nitrogen. Optimum conditions of chromatographic column diameter (1/4 inch outside diameter), temperature (25 °C), and flow rate (50.8 ml min-1) have been determined. When N2/CH4 (by volume) is<8.7%, the purification experiment can be undertaken once, while a double purification experiment is required when natural gas samples have an N2/CH4 of 8.7-78.0%. The purification method yielded a purity of 98.4-98.8% with a recovery of 97.3-98.7% on purified methane samples verified by GC determination. N2 was the main source that contributed to the loss of the purity, however, the N-bearing isobaric interferences (14NH3+ and 14NH4+) in purified samples presented<1‰ intensity compared to the methane isotopologues (13CH4+ and 13CH3D+), thus we concluded that these interferences have no impact on clumped isotope determinations. The conventional δ13CVPDB and δDVSMOW values of purified methane samples were consistent with those of pure methane. A preliminary measurement of Δ13CH3D (working gas) of purified samples revealed differences of -0.27‰, which was within the internal precision of the measurement. The entire process of a single purification can be completed within two hours. Our proposed method could be used for the clumped isotope purification of natural gas with higher than ~50% methane.

Precise measurement of 226Ra/230Th disequilibria in deep-sea sediments by high-sensitivity ICP-MS

We describe a new method suitable for the precise and accurate determination of 226Ra in porewater and sediment samples using a single-collector sector field ICP-MS (ThermoFisher Element XR) equipped with an Apex-Q desolvation device and a high-sensitivity Jet-X interface. In combination with 230Th measurements in parallel sediment samples, this method allows precise and accurate quantification of the 226Ra/230Th disequilibria in surface sediment cores, thereby enabling the use of this isotope pair as a tracer of solute transfer across the sediment-water interface in the deep ocean. The method integrates a step of isotope dilution with 228Ra as an internal spike, a pre-concentration of Ra and Ba by MnO2 precipitation, and an efficient separation of Ra from other undesirable elements using a cation exchange resin and a Triskem Sr-spec resin. With the inclusion of one or two additional cation resin columns and the use of up to 16 bed-volumes of a lower molarity (1.7 M) HCl eluent, our procedure eliminates the complicated matrix effects persistently encountered in previous studies, and provides a highly purified solution suitable for 226Ra measurement using an Element XR ICP-MS apparatus. Consequently, we are able to determine the activity of 226Ra in ∼20–50 ml of porewater or 100 mg of sediment with an internal precision of ∼1.0% and an accuracy of ∼99.2%. The precise measurements of porewater and solid phase 226Ra in a sediment core from the North Pacific Ocean allowed the distribution coefficient (Kd) of 226Ra to be constrained tightly within a range of 4700–11,600 ml g−1. Moreover, with the aid of a one-dimensional exchange model, the combination of the 226Ra and 230Th measurements allowed us to estimate a 226Ra flux of 1140 ± 20 dpm m−2 y−1 from the sediment core.

STABLE ISOTOPES OF OXYGEN AND HYDROGEN IN WATER: ANALYTICAL METHOD EVALUATION AND THE DETERMINATION OF δ18O AND δ2 H ON A CONTROL SAMPLE

Evaluation studies contribute to the identification of parameters that can affect the accuracy and precision of analytical methods. This study describes the analysis of δ18O and δ2H in water samples by the equilibrium method at the Isotope Geology Laboratory (LGI), Center for studies in Petrology and Geochemistry (CPGq) of the Federal University of Rio Grande do Sul (UFRGS). For that, six batches of analyzes were carried out under different ambient temperature conditions. For the reproducibility tests, four aliquots of the control sample were analyzed at the Polar Climate Center (CPC). Results showed that ambient temperature did not significantly affect the accuracy of the oxygen analysis. However, the mean result at 20 °C showed greater accuracy and acceptable precision. Hydrogen analyzes at a room temperature of 18 °C showed an external standard deviation and an internal precision exceeding the recommended, while at 20 and 22 °C the results were statistically acceptable, being the first more accurate. From that, it is possible to conclude that the determination of δ18O and δ2H in water at the LGI, employing the equilibrium method at an ambient temperature of 20 °C, showed satisfactory repeatability and reproducibility.

Internal attention is the only retroactive mechanism for controlling precision in working memory.

Recent research has suggested that humans can assert control over the precision of working memory (WM) items. However, the mechanisms that enable this control are unclear. While some studies suggest that internal attention improves precision, it may not be the only factor, as previous work also demonstrated that WM storage is disentangled from attention. To test whether there is a precision control mechanism beyond internal attention, we contrasted internal attention and precision requirements within the same trial in three experiments. In every trial, participants memorized two items briefly. Before the test, a retro-cue indicated which item would be tested first, thus should be attended. Importantly, we encouraged participants to store the unattended item with higher precision by testing it using more similar lure colors at the probe display. Accuracy was analyzed on a small proportion of trials where the target-lure similarity, hence the task difficulty, was equal for attended and unattended items. Experiments 2 and 3 controlled for output interference by the first test and involuntary precision boost by the retro-cue, respectively. In all experiments, the unattended item had lower accuracy than the attended item, suggesting that individuals were not able to remember it more precisely than the attended item. Thus, we conclude that there is no precision control mechanism beyond internal attention, highlighting the close relationship between attentional and qualitative prioritization within WM. We discuss the important implications of these findings for our understanding of the fundamentals of WM and WM-driven behaviors.

Internal Attention and Precision in Working Memory are Inseparable

Internal Attention and Precision in Working Memory are Inseparable

Fit, Precision, and Trueness of 3D-Printed Zirconia Crowns Compared to Milled Counterparts.

Precise fit of a crown and accurate reproduction of the digital design are paramount for successful treatment outcomes and preservation of clinician and technician time. The study aimed to compare the internal fit, marginal adaptation, precision, and trueness of 3D-printed zirconia crowns compared to their milled counterpart. A total of 20 monolithic 3 mol% yttria stabilized-zirconia crowns (n = 10) were made using computer-assisted design (CAD) followed by additive (3D-printed) and subtractive (milled) manufacturing. Digital scanning of the master die with and without a fit checker followed by image superimposition, and analysis was performed to evaluate internal and marginal adaptation in four areas (occlusal, axial, marginal, and overall). ISO 12836:2015 standard was followed for precision and trueness evaluation. Statistical analysis was achieved using a t-test at α = 0.05. Internal fit and marginal adaptation revealed no significant difference between the two test groups (p > 0.05). The significant difference in trueness (p < 0.05) was found between the two groups in three areas (occlusal, axial, and internal). The best and worst trueness values were seen with 3D-printed crowns at occlusal (8.77 ± 0.89 µm) and Intaglio (23.90 ± 1.60 µm), respectively. The overall precision was statistically better (p < 0.05) in the 3D-printed crowns (9.59 ± 0.75 µm) than the milled (17.31 ± 3.39 µm). 3D-printed and milled zirconia crowns were comparable to each other in terms of internal fit and marginal adaptation. The trueness of the occlusal and axial surfaces of 3D-printed crowns was better, whereas the trueness of fitting surface of milled crowns was better. 3D-printed crowns provided a higher level of precision than milled crowns. Although the internal and marginal fit of both production techniques were comparable, 3D printing of zirconia produced more precise crowns.

Rapid detection of phenytoin sodium by partial-least squares and linear regression models combined with surface-enhanced Raman spectroscopy

Surface-enhanced Raman spectroscopy (SERS) for quantitative analysis is challenging owing to the unstable enhanced effect. However, it can be improved by combining it with chemometrics. In this study, we established a quantitative analysis method for phenytoin sodium (PS) based on partial least-squares (PLS) and linear regression (LR) models combined with SERS. Gold nanoparticles (AuNPs) were optimally enhanced substrates for PS. 180 PS samples in the concentration range of 0.98 − 980 μg mL−1 were used to establish a quantitative prediction model by PLS regression, and an accurate and robust prediction was achieved. Furthermore, we found that SERS peak intensity showed a good linear correlation with the concentration of PS in the concentration range of 1 – 80 μg mL −1. After using P-mercaptobenzoic acid as an internal standard, the accuracy and precision of the LR model were significantly improved compared with that of the model without an internal standard. In general, PLS chemometrics and LR model with internal standard which were combined with SERS in this paper provide new possible analytical methods for analytes to develop a rapid and sensitive quantitative analysis method.

Automatic Observation of Astronomical Coordinates Using the Shandong University of Science and Technology/National Astronomical Observatories Digital Zenith Tube

Abstract The digital zenith tube (DZT) is developed based on the astrogeodetic and photogrammetric theory. One prototype of DZT integrating techniques of global positioning system (GPS) and charge-coupled device (CCD) photogrammetry has been developed jointly by Shandong University of Science and Technology and National Astronomical Observatories of Chinese Science Academy, China. It can automatically estimate astronomical coordinates in real time by CCD star image processing and GPS data processing. The DZT’s errors are analyzed in three aspects, namely, the instrument error, observation error, and data processing error. Reliability and accuracy of DZT integrating GPS and CCD are verified by the practical field operations. Observing results on many unknown points by the repeated observations of each point show the internal precision of the astronomical latitude and longitude. Observing results on several known points and the comparison with the EGM2008-derived results verify the external accuracy of the DZT, and the differences of these points in astronomical latitude and longitude are within ±0.15″ and greater than 1″, respectively.

A Mass–Magnitude Relation for Low-mass Stars Based on Dynamical Measurements of Thousands of Binary Star Systems

Stellar mass is a fundamental parameter that is key to our understanding of stellar formation and evolution, as well as the characterization of nearby exoplanet companions. Historically, stellar masses have been derived from long-term observations of visual or spectroscopic binary star systems. While advances in high-resolution imaging have enabled observations of systems with shorter orbital periods, measurements of stellar masses remain challenging, and relatively few have been precisely measured. We present a new statistical approach to measuring masses for populations of stars. Using Gaia astrometry, we analyze the relative orbital motion of >3800 wide binary systems comprising low-mass stars to establish a mass–magnitude relation in the Gaia G RP band spanning the absolute magnitude range 14.5 > > 4.0, corresponding to a mass range of 0.08 M ⊙ ≲ M ≲ 1.0 M ⊙. This relation is directly applicable to >30 million stars in the Gaia catalog. Based on comparison to existing mass–magnitude relations calibrated for K s magnitudes from the Two Micron All Sky Survey, we estimate that the internal precision of our mass estimates is ∼10%. We use this relation to estimate masses for a volume-limited sample of ∼18,200 stars within 50 pc of the Sun and the present-day field mass function for stars with M ≲ 1.0 M ⊙, which we find peaks at 0.16 M ⊙. We investigate a volume-limited sample of wide binary systems with early-K dwarf primaries, complete for binary mass ratios q > 0.2, and measure the distribution of q at separations >100 au. We find that our distribution of q is not uniform, rather decreasing toward q = 1.0.

A reasonably gradual type theory

Gradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized gradual type theory that admits three variants, each sacrificing one of these properties. For devising a gradual proof assistant based on CIC, normalization and conservativity with respect to CIC are key, but the tension with graduality needs to be addressed. Additionally, several challenges remain: (1) The presence of two wildcard terms at any type---the error and unknown terms---enables trivial proofs of any theorem, jeopardizing the use of a gradual type theory in a proof assistant; (2) Supporting general indexed inductive families, most prominently equality, is an open problem; (3) Theoretical accounts of gradual typing and graduality so far do not support handling type mismatches detected during reduction; (4) Precision and graduality are external notions not amenable to reasoning within a gradual type theory. All these issues manifest primally in CastCIC, the cast calculus used to define GCIC. In this work, we present an extension of CastCIC called GRIP. GRIP is a reasonably gradual type theory that addresses the issues above, featuring internal precision and general exception handling. By adopting a novel interpretation of the unknown term that carefully accounts for universe levels, GRIP satisfies graduality for a large and well-defined class of terms, in addition to being normalizing and a conservative extension of CIC. Internal precision supports reasoning about graduality within GRIP itself, for instance to characterize gradual exception-handling terms, and supports gradual subset types. We develop the metatheory of GRIP using a model formalized in Coq, and provide a prototype implementation of GRIP in Agda.