On the agreement between manual and automated methods for single-trial detection and estimation of features from event-related potentials

The agreement between humans and algorithms on whether an event-related potential (ERP) is present or not and the level of variation in the estimated values of its relevant features are largely unknown. Thus, the aim of this study was to determine the categorical and quantitative agreement between manual and automated methods for single-trial detection and estimation of ERP features. To this end, ERPs were elicited in sixteen healthy volunteers using electrical stimulation at graded intensities below and above the nociceptive withdrawal reflex threshold. Presence/absence of an ERP peak (categorical outcome) and its amplitude and latency (quantitative outcome) in each single-trial were evaluated independently by two human observers and two automated algorithms taken from existing literature. Categorical agreement was assessed using percentage positive and negative agreement and Cohen's κ, whereas quantitative agreement was evaluated using Bland-Altman analysis and the coefficient of variation. Typical values for the categorical agreement between manual and automated methods were derived, as well as reference values for the average and maximum differences that can be expected if one method is used instead of the others. Results showed that the human observers presented the highest categorical and quantitative agreement, and there were significantly large differences between detection and estimation of quantitative features among methods. In conclusion, substantial care should be taken in the selection of the detection/estimation approach, since factors like stimulation intensity and expected number of trials with/without response can play a significant role in the outcome of a study

Social foundations of the mathematics curriculum: a rationale for change

The nature of educational aims as criteria for worthwhile curriculum practice is explored and a cross-section of aims for mathematics education is discussed. An aim for mathematics education which emphasises the social aspect of the subject in its being, its conduct and its applications is identified and epistemological foundations for such a view of the nature of the subject are explored. It is argued that such an epistemological perspective of mathematics would be reflected in the social context of the mathematics classroom, arising from a methodology in which the subject would become more problematic and open to change, investigation and hypothesis. The aims of two major mathematics curriculum development projects (the Nuffield Mathematics Project and the School Mathematics Project) are examined to determine the extent to which their aims may take the 'social' nature of mathematics into account. The probable social context of mathematics classrooms using their materials is postulated in an attempt to characterise the nature of the subject as it is reflected in these materials. A view of the nature of mathematics held by practising teachers and by pupils is then established by drawing upon, and extrapolating from, evidence relating to the social context of mathematics classrooms at primary and secondary level. Conclusions follow, which suggest that fundamental change in mathematics education requires, as a first step, the adoption of a new epistemological perspective of the subject in order that the pursuit of the aim which emphasises the social nature of mathematics is achieved. It is suggested that this, in turn, ultimately could lead to the desired balance in the mathematics curriculum which hitherto has been lacking

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum