The arithmetic of quaternions is recalled from a constructive point of view. A Hecke module is introduced, defined as a free abelian group on right ideal classes of a quaternion order, together with a natural action of Hecke operators. An equivalent construction in terms of Shimura curves is then introduced, and the quaternion construction is applied to the analysis of specific modular and Shim...

Calibration, the statistical consistency of forecast distributions and the observations, is a central requirement for probabilistic predictions. Calibration of continuous forecasts is typically assessed using the probability integral transform histogram. In this article, we propose significance tests based on scoring rules to assess calibration of continuous predictive distributions. For an ide...

Biological dosimetry (biodosimetry) is based on the investigation of radiation-induced biological effects (biomarkers), mainly dicentric chromosomes, in order to correlate them with radiation dose. To interpret the dicentric score in terms of absorbed dose, a calibration curve is needed. Each curve should be constructed with respect to basic physical parameters, such as the type of ionizing rad...

The emission spectra calibration curves for a fluorescence indicator and the F(min), F(max), and K(d) formula were shown to be related. Using the known calibrated fluorescence emitted by Sodium Green (Na-Green) and photo-multiplier-tube quantum efficiency, we calculated the detection signal over a range of sodium concentrations. The calculated calibration curves were compared for optical filter...

Program authorship attribution has implications for the privacy of programmers who wish to contribute code anonymously. While previous work has shown that complete files that are individually authored can be attributed, we show here for the first time that accounts belonging to open source contributors containing short, incomplete, and typically uncompilable fragments can also be effectively at...

The properties of iridium oxide pH sensors produced by electrochemically induced deposition on gold electrodes were examined as a function of the composition of the deposition solution, as well as the electrochemical deposition protocol. The composition of the Ir IV deposition solutions, which included oxalate or ethylene diamine tetraacetic acid complexing agent or no complexing agent, had no ...

Chewing of gum contributes to the maintenance of oral health. Many oral diseases, including caries and periodontal disease, are caused by bacteria. However, it is unknown whether chewing of gum can remove bacteria from the oral cavity. Here, we hypothesize that chewing of gum can trap bacteria and remove them from the oral cavity. To test this hypothesis, we developed two methods to quantify nu...

Noise is a major problem in analyzing tracking data of cargos moved by molecular motors. We use Bayesian statistics to incorporate what is known about the noise in parsing the trajectory of a cargo into a series of constant velocity segments. Tracks with just noise and no underlying motion are fit with constant velocity segments to produce a calibration curve of fit quality versus average segme...

Based on the piezoelectric effect of piezoelectric quartz crystal, a two-dimensional force sensor with good dynamic characteristics is designed, whose sensitive component is single-cut piezoelectric quartz wafers, and it realizes the measurement of force by measuring the charge which is generated by piezoelectric quartz crystal. This paper analyzes measurement principle of the sensor based on t...

The immunoreactivity of various LH and FSH calibration standards and recombinant preparations in the enzyme-linked immunoassay (EIA) systems for gonadotrophins developed for the Special Programme of Research in Human Reproduction of the World Health Organization (WHO) were compared. The preparations tested included three LH and two FSH pituitary standards (calibrated against LH 80/552 and 68/40...