Most of the strategies that have been proposed to determine the number of components that account for the most variation in a principal components analysis of a correlation matrix rely on the analysis of the eigenvalues and on numerical solutions. The Cattell’s scree test is a graphical strategy with a nonnumerical solution to determine the number of components to retain. Like Kaiser’s rule, this test is one of the most frequently used strategies for determining the number of components to retain. However, the graphical nature of the scree test does not definitively establish the number of components to retain. To circumvent this issue, some numerical solutions are proposed, one in the spirit of Cattell’s work and dealing with the scree part of the eigenvalues plot, and one focusing on the elbow part of this plot. A simulation study compares the efficiency of these solutions to those of other previously proposed methods. Extensions to factor analysis are possible and may be particularly useful with many low-dimensional components.

Science education studies have revealed that students often have misconceptions about how nature works, but what happens to misconceptions after a conceptual change remains poorly understood. Are misconceptions rejected and replaced by scientific conceptions, or are they still present in students' minds, coexisting with newly acquired scientific conceptions? In this study, we use functional magnetic resonance imaging (fMRI) to compare brain activation between novices and experts in science when they evaluate the correctness of simple electric circuits. Results show that experts, more than novices, activate brain areas involved in inhibition when they evaluate electric circuits in which a bulb lights up, even though there is only one wire connecting it to the battery. These findings suggest that experts may still have a misconception encoded in the neural networks of their brains that must be inhibited in order to answer scientifically.

A near-infrared camera in use at the Canada-France-Hawaii Telescope (CFHT) and at the 1.6-m telescope of the Observatoire du Mont-Mégantic is described. The camera is based on a Hawaii-1 1024×1024 HgCdTe array detector. Its main feature is to acquire three simultaneous images at three wavelengths across the methane absorption bandhead at 1.6 µm, enabling, in theory, an accurate subtraction of the stellar point spread function (PSF) and the detection of faint close methanated companions. The instrument has no coronagraph and features fast data acquisition, yielding high observing efficiency on bright stars.The performance of the instrument is described, and it is illustrated by laboratory tests and CFHT observations of the nearby stars GL526, υ And and χ And.TRIDENT can detect (6σ) a methanated companion with ∆H = 9.5 at 0.5 ′′ separation from the star in one hour of observing time. Non-common path aberrations and amplitude modulation differences between the three optical paths are likely to be the limiting factors preventing further PSF attenuation. Instrument rotation and reference star subtraction improve the detection limit by a factor of 2 and 4 respectively. A PSF noise attenuation model is presented to estimate the non-common path wavefront difference effect on PSF subtraction performance.

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