Effect of Systematic Uncertainty Estimation on the Muon g - 2 Anomaly

The statistical significance that characterizes a discrepancy between a measurement and theoretical prediction is usually calculated assuming that the statistical and systematic uncertainties are known. Many types of systematic uncertainties are, however, estimated on the basis of approximate procedures and thus the values of the assigned errors are themselves uncertain. Here the impact of the uncertainty on the assigned uncertainty is investigated in the context of the muon g - 2 anomaly. The significance of the observed discrepancy between the Standard Model prediction of the muon’s anomalous magnetic moment and measured values are shown to decrease substantially if the relative uncertainty in the uncertainty assigned to the Standard Model prediction exceeds around 30%. The reduction in sensitivity increases for higher significance, so that establishing a 5σ effect will require not only small uncertainties but the uncertainties themselves must be estimated accurately to correspond to one standard deviation.

pyisotopomer: A Python package for obtaining nitrous oxide isotopocules from isotope ratio mass spectrometry

Obtaining nitrous oxide isotopocule measurements with isotope ratio mass spectrometry (IRMS) requires measuring the m/z ratios of the nitrous oxide (N2O) molecule as well as those of the NO+ fragment ion. This measurement depends on correcting for a phenomenon referred to as “scrambling” in the ion source, whereby the NO+ fragment ion contains the outer N atom from the N2O molecule. While descriptions of the scrambling correction exist in the literature, there has yet to be published a unified software package and method for performing this correction. We developed a user-friendly Python package (pyisotopomer), with a MATLAB alternative, to determine two coefficients that describe scrambling in the ion source of a given IRMS, and then to use this calibration to obtain N2O isotopocule measurements. We assess the sensitivity of pyisotopomer to its input parameters and discuss the relevant assumptions. We show that the scrambling behavior of an IRMS can vary with time, necessitating regular calibrations. We show that to obtain a relative uncertainty in site preference of <1‰, the relative uncertainty in each scrambling coefficient should be <0.2%. Finally, we present an intercalibration between two IRMS laboratories, using pyisotopomer to calculate scrambling and obtain N2O isotopocule data. Given these considerations, we discuss how to use this software package to obtain high-quality N2O isotopocule data from IRMS systems, including the use of appropriate reference materials and frequency of calibration.

Application of Air-Coupled Ultrasonic Nondestructive Testing in the Measurement of Elastic Modulus of Materials

It is difficult to measure elastic modulus simply and accurately in the testing of mechanical properties of materials. Combined with static tensile method, this paper presents a method for measuring elastic modulus of materials based on air-coupled ultrasonic nondestructive testing. Firstly, the 1–3 piezoelectric composite material and the matching material of low acoustic impedance are self-made, and 400 kHz air-coupled ultrasonic transducer is fabricated. Then, the performance of the transducer is tested, and the insertion loss and bandwidth of −6 dB are −33.5 dB and 23.4%, respectively. Compared with the traditional instrument for measuring elastic modulus, the measurement of elastic modulus of carbon steel rod material is realized in this paper, and the measured results are in agreement with the accepted value. In addition, from the angle of relative uncertainty, how to reduce the measurement error by improving the device is analyzed. It can be shown that the method has high linearity, high symmetry, and good stability and repeatability. This paper provides a new way for the selection and design of measuring instrument components.

Trait Somatic Anxiety is Associated With Reduced Directed Exploration and Underestimation of Uncertainty

Exploration is at the core of many real-life decisions, helping people gain information about the environment and make better choices in the long run. Although anxiety has been related to decreased physical exploration and avoidance behavior, past findings on the interaction between anxiety and exploration during decision-making under uncertainty were inconclusive. The current study provides a holistic picture of the anxiety-exploration relationship by focusing on latent factors of trait anxiety and different exploration strategies when facing volatility-induced uncertainty. Across two well-powered online studies (N = 984), we demonstrated that people used a hybrid of directed, random, and undirected exploration strategies, which were respectively sensitive to relative uncertainty, total uncertainty, and value difference. The somatic factor of trait anxiety, the propensity to experience physical symptoms of anxiety, was inversely correlated with directed exploration and undirected exploration, manifesting as being less likely to choose the uncertain option and reducing choice stochasticity regardless of uncertainty. Trait somatic anxiety was also related to underestimation of relative uncertainty, which could potentially account for its negative impact on directed exploration. Together, these results reveal the selective role of trait somatic anxiety in modulating both uncertainty-driven and value-driven exploration strategies. More crucially, the differential effects of trait anxiety components underscore the importance of adopting a dimensional approach in future studies.

Simultaneous bicolor interrogation in thulium optical clock providing very low systematic frequency shifts

Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty, demonstrating incredible control over external perturbations of the clock transition frequency. At the same time, there is an increasing demand for atomic (ionic) transitions and new interrogation and readout protocols providing minimal sensitivity to external fields and possessing practical operational wavelengths. One of the goals is to simplify the clock operation while maintaining the relative uncertainty at a low 10−18 level achieved at the shortest averaging time. This is especially important for transportable and envisioned space-based optical clocks. Here, we demonstrate implementation of a synthetic frequency approach for a thulium optical clock with simultaneous optical interrogation of two clock transitions. Our experiment shows suppression of the quadratic Zeeman shift by at least three orders of magnitude. The effect of the tensor lattice Stark shift in thulium can also be reduced to below 10−18 in fractional frequency units. This makes the thulium optical clock almost free from hard-to-control systematic shifts. The “simultaneous” protocol demonstrates very low sensitivity to the cross-talks between individual clock transitions during interrogation and readout.

Uncertainties in eddy covariance air–sea CO₂ flux measurements and implications for gas transfer velocity parameterisations

Air–sea carbon dioxide (CO2) flux is often indirectly estimated by the bulk method using the air–sea difference in CO2 fugacity (ΔfCO2) and a parameterisation of the gas transfer velocity (K). Direct flux measurements by eddy covariance (EC) provide an independent reference for bulk flux estimates and are often used to study processes that drive K. However, inherent uncertainties in EC air–sea CO2 flux measurements from ships have not been well quantified and may confound analyses of K. This paper evaluates the uncertainties in EC CO2 fluxes from four cruises. Fluxes were measured with two state-of-the-art closed-path CO2 analysers on two ships. The mean bias in the EC CO2 flux is low, but the random error is relatively large over short timescales. The uncertainty (1 standard deviation) in hourly averaged EC air–sea CO2 fluxes (cruise mean) ranges from 1.4 to 3.2 mmolm-2d-1. This corresponds to a relative uncertainty of ∼ 20 % during two Arctic cruises that observed large CO2 flux magnitude. The relative uncertainty was greater (∼ 50 %) when the CO2 flux magnitude was small during two Atlantic cruises. Random uncertainty in the EC CO2 flux is mostly caused by sampling error. Instrument noise is relatively unimportant. Random uncertainty in EC CO2 fluxes can be reduced by averaging for longer. However, averaging for too long will result in the inclusion of more natural variability. Auto-covariance analysis of CO2 fluxes suggests that the optimal timescale for averaging EC CO2 flux measurements ranges from 1 to 3 h, which increases the mean signal-to-noise ratio of the four cruises to higher than 3. Applying an appropriate averaging timescale and suitable ΔfCO2 threshold (20 µatm) to EC flux data enables an optimal analysis of K.