Wax coverage on developing Arabidopsis leaf epidermis cells is constant and thus synchronized with cell expansion. Wax composition shifts from fatty acid to alkane dominance, mediated by CER6 expression. Epidermal cells bear a wax-sealed cuticle to hinder transpirational water loss. The amount and composition of the cuticular wax mixture may change as organs develop, to optimize the cuticle for specific functions during growth. Here, morphometrics, wax chemical profiling, and gene expression measurements were integrated to study developing Arabidopsis thaliana leaves and, thus, further our understanding of cuticular wax ontogeny. Before 5 days of age, cells at the leaf tip ceased dividing and began to expand, while cells at the leaf base switched from cycling to expansion at day 13, generating a cell age gradient along the leaf. We used this spatial age distribution together with leaves of different ages to determine that, as leaves developed, their wax compositions shifted from C/C to C/C and from fatty acid to alkane constituents. These compositional changes paralleled an increase in the expression of the elongase enzyme CER6 but not of alkane pathway enzymes, suggesting that CER6 transcriptional regulation is responsible for both chemical shifts. Leaves bore constant numbers of trichomes between 5 and 21 days of age and, thus, trichome density was higher on young leaves. During this time span, leaves of the trichome-less gl1 mutant had constant wax coverage, while wild-type leaf coverage was initially high and then decreased, suggesting that high trichome density leads to greater apparent coverage on young leaves. Conversely, wax coverage on pavement cells remained constant over time, indicating that wax accumulation is synchronized with cell expansion throughout leaf development.
Chalmers recently published a critique of the use of ordinal [Formula: see text] proposed in Zumbo et al. as a measure of test reliability in certain research settings. In this response, we take up the task of refuting Chalmers’ critique. We identify three broad misconceptions that characterize Chalmers’ criticisms: (1) confusing assumptions with consequences of mathematical models, and confusing both with definitions, (2) confusion about the definitions and relevance of Stevens’ scales of measurement, and (3) a failure to recognize that a measurement for a true quantity is a choice, not an absolute. On dissection of these misconceptions, we argue that Chalmers’ critique of ordinal [Formula: see text] is unfounded.
Random-variable-valued measurements (RVVMs) are proposed as a new framework for treating measurement processes that generate non-deterministic sample data. They operate by assigning a probability measure to each observed sample instantiation of a global measurement process for some particular random quantity of interest, thus allowing for the explicit quantification of response process error. Common methodologies to date treat only measurement processes that generate fixed values for each sample unit, thus generating full (though possibly inaccurate) information on the random quantity of interest. However, many applied research situations in the non-experimental sciences naturally contain response process error, e.g. when psychologists assess patient agreement with various diagnostic survey items or when conservation biologists perform formal assessments to classify species-at-risk. Ignoring the sample-unit-level uncertainty of response process error in such measurement processes can greatly compromise the quality of resulting inferences. In this paper, a general theory of RVVMs is proposed to handle response process error, and several applications are considered.
Given a Cantor-type subset Ω of a smooth curve in R d+1 , we construct examples of sets that contain unit line segments with directions from Ω and exhibit analytical features similar to those of classical Kakeya sets of arbitrarily small (d + 1)dimensional Lebesgue measure. The construction is based on probabilistic methods relying on the tree structure of Ω, and extends to higher dimensions an analogous planar result of Bateman and Katz [4]. In particular, the existence of such sets implies that the directional maximal operator associated with the direction set Ω is unbounded on L p (R d+1 ) for all 1 ≤ p < ∞.
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