Counting is a spatial process: evidence from eye movements

Spatial-numerical associations (small numbers-left/lower space and large numbers-right/upper space) are regularly found in simple number categorization tasks. These associations were taken as evidence for a spatially oriented mental number line. However, the role of spatial-numerical associations during more complex number processing, such as counting or mental arithmetic is less clear. Here, we investigated whether counting is associated with a movement along the mental number line. Participants counted aloud upward or downward in steps of 3 for 45 s while looking at a blank screen. Gaze position during upward counting shifted rightward and upward, while the pattern for downward counting was less clear. Our results, therefore, confirm the hypothesis of a movement along the mental number line for addition. We conclude that space is not only used to represent number magnitudes but also to actively operate on numbers in more complex tasks such as counting, and that the eyes reflect this spatial mental operation.

Methods for preparing and counting biochemical varves

Four different preparation and counting methods for biochemical varves were compared in order to assess counting errors and to standardize these techniques. The properties of two embedding methods, namely the shock-freeze, freeze-dry and the water-acetone-epoxy-exchange method, are discussed. Varve counts were carried out on fresh sediment and on sediment thin-sections, on the latter by manual and by automated counting using image-analysis software. Counting on fresh sediment and using image-analysis generally underestimated the number of varves, especially in sections with inconspicuous varves. A comparison between multiple varve counts carried out by a single analyst and different analysts showed no significant differences in the mean varve counts.

Measurement of isotopic uranium in water for compliance monitoring by liquid scintillation counting with alpha/beta discrimination

A simple and inexpensive method is described for analysis of uranium (U) activity and mass in water by liquid scintillation counting using $\alpha$/$\beta$ discrimination. This method appears to offer a solution to the need for an inexpensive protocol for monitoring U activity and mass simultaneously and an alternative to the potential inaccuracy involved when depending on the mass-to-activity conversion factor or activity screen.^ U is extracted virtually quantitatively into 20 ml extractive scintillator from a 1-$\ell$ aliquot of water acidified to less than pH 2. After phase separation, the sample is counted for a 20-minute screening count with a minimum detection level of 0.27 pCi $\ell\sp{-1}$. $\alpha$-particle emissions from the extracted U are counted with close to 100% efficiency with a Beckman LS6000 LL liquid scintillation counter equipped with pulse-shape discrimination electronics. Samples with activities higher than 10 pCi $\ell\sp-1$ are recounted for 500-1000 minutes for isotopic analysis. Isotopic analysis uses events that are automatically stored in spectral files and transferred to a computer during assay. The data can be transferred to a commercially available spreadsheet and retrieved for examination or data manipulation. Values for three readily observable spectral features can be rapidly identified by data examination and substituted into a simple formula to obtain $\sp{234}$U/$\sp{238}$U ratio for most samples. U mass is calculated by substituting the isotopic ratio value into a simple equation.^ The utility of this method for the proposed compliance monitoring of U in public drinking water supplies was field tested with a survey of drinking water from Texas supplies that had previously been known to contain elevated levels of gross $\alpha$ activity. U concentrations in 32 samples from 27 drinking water supplies ranged from 0.26 to 65.5 pCi $\ell\sp{-1}$, with seven samples exceeding the proposed Maximum Contaminant Level of 20 $\mu$g $\ell\sp{-1}$. Four exceeded the proposed activity screening level of 30 pCi $\ell\sp{-1}$. Isotopic ratios ranged from 0.87 to 41.8, while one sample contained $\sp{234}$U activity of 34.6 pCi $\ell\sp{-1}$ in the complete absence of its parent, $\sp{238}$U. U mass in the samples with elevated activity ranged from 0.0 to 103 $\mu$g $\ell\sp{-1}$. A limited test of screening surface and groundwaters for contamination by U from waste sites and natural processes was also successful. ^

Automated Tools for Layer Recognition (BMPix) and Counting (PEAK)

We present tools for rapid and quantitative detection of sediment lamination. The BMPix tool extracts color and gray-scale curves from images at pixel resolution. The PEAK tool uses the gray-scale curve and performs, for the first time, fully automated counting of laminae based on three methods. The maximum count algorithm counts every bright peak of a couplet of two laminae (annual resolution) in a smoothed curve. The zero-crossing algorithm counts every positive and negative halfway-passage of the curve through a wide moving average, separating the record into bright and dark intervals (seasonal resolution). The same is true for the frequency truncation method, which uses Fourier transformation to decompose the curve into its frequency components before counting positive and negative passages. We applied the new methods successfully to tree rings, to well-dated and already manually counted marine varves from Saanich Inlet, and to marine laminae from the Antarctic continental margin. In combination with AMS14C dating, we found convincing evidence that laminations in Weddell Sea sites represent varves, deposited continuously over several millennia during the last glacial maximum. The new tools offer several advantages over previous methods. The counting procedures are based on a moving average generated from gray-scale curves instead of manual counting. Hence, results are highly objective and rely on reproducible mathematical criteria. Also, the PEAK tool measures the thickness of each year or season. Since all information required is displayed graphically, interactive optimization of the counting algorithms can be achieved quickly and conveniently.