On MTL's First Decade

Three experiments used multiple methods—open-ended assessments, multiple-choice questionnaires, and interviews—to investigate the hypothesis that the development of students' understanding of the concept of real variable in algebra may be influenced in fundamental ways by their initial concept of number, which seems to be organized around the notion of natural number. In the first two experiments 91 secondary school students (ranging in age from 12.5 to 14.5 years) were asked to indicate numbers that could or could not be used to substitute literal symbols in algebraic expressions. The results showed that there was a strong tendency on the part of the students to interpret literal symbols to stand for natural numbers and a related tendency to consider the phenomenal sign of the algebraic expressions as their “real” sign. Similar findings were obtained in a third, individual interview study, conducted with tenth grade students. The results were interpreted to support the interpretation that there is a systematic natural number bias on students' substitutions of literal symbols in algebra.     

Trace Analysis Using Position-Sensitive Detection in Magnetic Sector Mass Spectrometry

Abstract

A position-sensitive ion detection system for trace analysis with magnetic sector mass spectrometers is described in detail, with particular application to high temperature mass spectrometry. The detection system consists of two stacked microchannel plates (Chevron assembly) backed by a resistive anode encoder and associated electronics. The range of masses simultaneously detectable is m to 1.2m. For electron impact ionization of silver at an electron energy of 10.5 eV, the sensitivity is 1.6 × 10^?7 Pa, and the mass resolution is 260 at mass 80 (valley 10% of the peak height definition). Additional applications for the detection system are discussed.     

A Chemiluminescent Probe for HNO Quantification and Real‐Time Monitoring in Living Cells

Azanone (HNO) is a reactive nitrogen species with pronounced biological activity and high therapeutic potential for cardiovascular dysfunction. A critical barrier to understanding the biology of HNO and furthering clinical development is the quantification and real‐time monitoring of its delivery in living systems. Herein, we describe the design and synthesis of the first chemiluminescent probe for HNO, HNOCL‐1 , which can detect HNO generated from concentrations of Angeli's salt as low as 138 nm with high selectivity based on the reaction with a phosphine group to form a self‐cleavable azaylide intermediate. We have capitalized on this high sensitivity to develop a generalizable kinetics‐based approach, which provides real‐time quantitative measurements of HNO concentration at the picomolar level. HNOCL‐1 can monitor dynamics of HNO delivery in living cells and tissues, demonstrating the versatility of this method for tracking HNO in living systems.     

Understanding Complex Electrochemical Impedance Spectroscopy in Corrosion Systems Using in‐situ Synchrotron Radiation Grazing Incidence X‐ray Diffraction

The difficulty in interpreting electrochemical impedance spectroscopy (EIS) data has limited the potential of the method despite its utility as an electrochemical method for studies of electrode reactions and interfacial structures. Taking the test case of the carbon dioxide corrosion of carbon steel, in‐situ synchrotron radiation grazing incidence X‐ray diffraction (SR‐GIXRD) has been demonstrated to be a powerful technique for validating and understanding the interfacial structures associated with complex EIS data. Carbon dioxide corrosion was found to occur in several steps, which may only be surmised by EIS, but the use of SR‐GIXRD in conjunction with EIS has enabled the establishment of a link between EIS time constants and structural changes associated with the evolution of corrosion products with time. By comparison to previous studies by the authors and others in this field, this communication provides the first direct experimental evidence linking SR‐GIXRD surface compositional data to otherwise indistinctive EIS time constants.     

Empirical versus modelling approaches to the estimation of measurement uncertainty caused by primary sampling

Measurement uncertainty is a vital issue within analytical science. There are strong arguments that primary sampling should be considered the first and perhaps the most influential step in the measurement process. Increasingly, analytical laboratories are required to report measurement results to clients together with estimates of the uncertainty. Furthermore, these estimates can be used when pursuing regulation enforcement to decide whether a measured analyte concentration is above a threshold value. With its recognised importance in analytical measurement, the question arises of 'what is the most appropriate method to estimate the measurement uncertainty?'. Two broad methods for uncertainty estimation are identified, the modelling method and the empirical method. In modelling, the estimation of uncertainty involves the identification, quantification and summation (as variances) of each potential source of uncertainty. This approach has been applied to purely analytical systems, but becomes increasingly problematic in identifying all of such sources when it is applied to primary sampling. Applications of this methodology to sampling often utilise long-established theoretical models of sampling and adopt the assumption that a 'correct' sampling protocol will ensure a representative sample. The empirical approach to uncertainty estimation involves replicated measurements from either inter-organisational trials and/or internal method validation and quality control. A more simple method involves duplicating sampling and analysis, by one organisation, for a small proportion of the total number of samples. This has proven to be a suitable alternative to these often expensive and time-consuming trials, in routine surveillance and one-off surveys, especially where heterogeneity is the main source of uncertainty. A case study of aflatoxins in pistachio nuts is used to broadly demonstrate the strengths and weakness of the two methods of uncertainty estimation. The estimate of sampling uncertainty made using the modelling approach (136%, at 68% confidence) is six times larger than that found using the empirical approach (22.5%). The difficulty in establishing reliable estimates for the input variable for the modelling approach is thought to be the main cause of the discrepancy. The empirical approach to uncertainty estimation, with the automatic inclusion of sampling within the uncertainty statement, is recognised as generally the most practical procedure, providing the more reliable estimates. The modelling approach is also shown to have a useful role, especially in choosing strategies to change the sampling uncertainty, when required.     

Single-laboratory validation of the biosense direct competitive enzyme-linked immunosorbent assay (ELISA) for determination of domoic acid toxins in shellfish

Method validation was conducted for an enzyme-linked immunosorbent assay (ELISA) for the determination of domoic acid (DA) toxins, known to give amnesic shellfish poisoning (ASP) symptoms, in shellfish. The calibration curve range of the assay is approximately 10-260 pg/mL, with a dynamic working range for DA toxins in shellfish from 0.01 to at least 250 mg/kg. The ASP ELISA showed no significant cross-reactivity to structural analogs, and proved to be robust to deliberate alterations of the optimal running conditions. The shellfish matrix effects observed with mussels, oysters, and scallops were eliminated by diluting shellfish extracts 1:200 prior to analysis, leading to a limit of detection at 0.003 mg/kg. Thirteen blank shellfish homogenates were spiked with certified mussel material containing DA to levels in the range of 0.1-25 mg DA/kg, and analyzed in quadruplicate on 3 different days. The relative standard deviation (RSD) under intra-assay repeatability conditions ranged from 6.5 to 13.1%, and under interassay repeatability conditions the RSD ranged from 5.7 to 13.4%, with a mean value of 9.3%. The recoveries ranged from 85.5 to 106.6%, with a mean recovery of 102.2%. A method comparison was conducted with liquid chromatography with ultraviolet detection, using naturally contaminated scallop samples (n = 27) with DA levels at 0-244 mg/kg. The overall correlation coefficient was 0.960 and the slope of the regression was 1.218, indicating a good agreement between the methods.     

Mixture cure models in credit scoring: If and when borrowers default

Mixture cure models were originally proposed in medical statistics to model long-term survival of cancer patients in terms of two distinct subpopulations - those that are cured of the event of interest and will never relapse, along with those that are uncured and are susceptible to the event. In the present paper, we introduce mixture cure models to the area of credit scoring, where, similarly to the medical setting, a large proportion of the dataset may not experience the event of interest during the loan term, i.e. default. We estimate a mixture cure model predicting (time to) default on a UK personal loan portfolio, and compare its performance to the Cox proportional hazards method and standard logistic regression. Results for credit scoring at an account level and prediction of the number of defaults at a portfolio level are presented; model performance is evaluated through cross validation on discrimination and calibration measures. Discrimination performance for all three approaches was found to be high and competitive. Calibration performance for the survival approaches was found to be superior to logistic regression for intermediate time intervals and useful for fixed 12 month time horizon estimates, reinforcing the flexibility of survival analysis as both a risk ranking tool and for providing robust estimates of probability of default over time. Furthermore, the mixture cure model’s ability to distinguish between two subpopulations can offer additional insights by estimating the parameters that determine susceptibility to default in addition to parameters that influence time to default of a borrower.