Two systems of factor analysis—factoring correlations with units in the diagonal cells and factoring correlations with communalities in the diagonal cells—are considered in relation to the commonly used statistical procedure of separating a set of data (scores) into two or more parts. It is shown that both systems of factor analysis imply the separation of the observed data into two orthogonal parts. The matrices used to achieve the separation differ for the two systems of factor analysis.

A simple proof that the squared multiple correlation of a variable with the remaining variables in the set of variables is a lower bound to the communality of that variable is presented.

A solution is presented to the problem of determining a proper correction for spuriousness in correlation coefficients. The general case developed is the estimate of correlation between u and v, both being linear functions of the same set of variables. Special formulae relate to overlapping scales correlations, part-whole correlations, and item-total test correlations.

Considering only population values, it is shown that the complete set of factors of a correlation matrix with units in the diagonal cells may be transformed into the factors derived by factoring these correlations with communalities in the diagonal cells. When the correlations are regarded as observed values, the common factors derived as a transformation of the complete set of factors of the correlation matrix with units in the diagonal cells satisfy Lawley's requirement for a maximum likelihood solution and are a first approximation to Rao's canonical factors.

An examination of the determinantal equation associated with Rao's canonical factors suggests that Guttman's best lower bound for the number of common factors corresponds to the number of positive canonical correlations when squared multiple correlations are used as the initial estimates of communality. When these initial communality estimates are used, solving Rao's determinantal equation (at the first stage) permits expressing several matrices as functions of factors that differ only in the scale of their columns; these matrices include the correlation matrix with units in the diagonal, the correlation matrix with squared multiple correlations as communality estimates, Guttman's image covariance matrix, and Guttman's anti-image covariance matrix. Further, the factor scores associated with these factors can be shown to be either identical or simply related by a scale change. Implications for practice are discussed, and a computing scheme which would lead to an exhaustive analysis of the data with several optional outputs is outlined.

Analogs of Pearson's coefficient of racial likeness and of Mahalanobis' distance measure have been proposed as descriptive statistics for comparing two individuals. This paper shows that two different definitions of “uncorrelated” variables—one associated with an inverse transformation and the other with a principal-axis transformation—give rise to these two descriptive statistics. The effects of putting the data into certain forms, such as equalizing the variances of the variables or equalizing the means of the persons, prior to using either of the two transformations, are discussed.

A general framework for obtaining all possible factor analytic solutions, orthogonal and oblique, for a given common factor space is developed in detail. Interestingly, and seemingly paradoxically, any one of these solutions may be obtained by orthogonal transformations of selected matrices; thus an oblique solution may be determined by orthogonal transformations. Within the possible oblique solutions, two distinct categories of solutions emerge, a special case of the simpler of which apparently provides a definitive solution to the problem of independent, but correlated, clusters. Possible further specializations of the general approach to specific problems are discussed.

Hydroxy-interlayered vermiculite (HIV) is a ubiquitous phyllosilicate in the <0.05-mm fraction of sandy soils on the U.S. southeastern coastal plain. Extensive areas of soils with abundant HIV (i.e., peninsular Florida) have no detectable mica; yet the coarseness, platy habit, and nonexchangeable K associated with HIV grains suggest a mica precursor. The objectives of this study were: (1) to probe for mica zones (1.0-nm) within HIV grains, using high-resolution transmission electron microscopy (HRTEM), and (2) to determine intragrain elemental distributions via electron microprobe analysis (EMA). HIV grains from a Quartzipsamment medium-silt fraction, which contained no detectable mica by X-ray diffraction (XRD), were concentrated via high-density liquid separation. EMA transects and X-ray dot maps showed zonation or trends of K depletion near edges of some grains, with K2O contents ranging from trace levels to >40 g kg-1. Elemental oxide data indicated a dioctahedral phyllosilicate structure, with some octahedral substitution of Fe and Mg for Al. Intermittent 1.0-nm lattice-fringe images obtained by HRTEM supported the presence of mica zones within grains. There were no detectable 1.4-nm fringes, despite the dominance of a 1.4-nm XRD peak, indicating the instability of the HIV specimen under the electron beam. Results support a transformational link between mica and HIV in these soils. Rapid incursion and polymerization of Al following loss of K from mica may limit the extent of the vermiculite intermediate. The latter idea is consistent with the paucity of vermiculite in Florida soils. Traces of occluded mica may be the last remnants of the precursor grain. A sand-sized mica precursor would likely have weathered in place during the period when colloidal components such as kaolinite illuviated to deeper zones. Thus, the transformation product (HIV) would comprise a significant proportion of the <0.05-mm fraction persisting in sandy eluvial horizons.

Nonexchangeable polymers in interlayers of expansible phyllosilicates influence thermal dehydration in ways not completely understood. Thermal dehydration of hydroxy-interlayered vermiculite (HIV) from Florida soils, for example, results in irreversible d001 shifts. This study was conducted to characterize HIV dehydration as a function of time (t) and temperature (T), and to determine how reversibility of dehydration is affected by elevated T. Clay-sized HIV from 3 soils was heated incrementally and d-spacing shifts (Δd) were monitored by X-ray diffraction (XRD) at low relative humidity (RH). Samples were then mounted on a metal heating strip in the XRD focal plane and scanned repeatedly at constant T levels to monitor Δd with t. Finally, Δd in response to RH shifts from <5% to >85% was determined at 25°C and at elevated temperatures. Incremental heating revealed a Δd plateau roughly corresponding to the z dimension of hexameric octahedrally coordinated Al. The initial slope of Δd-vs-t curves increased with T. The same maximum Δd reached at 200°C was reached at 160°C, but more slowly. All samples exhibited reversible and irreversible dehydration, the former being attributable to sites in equilibrium with external vapor and the latter to sites requiring heat for desorption. Reversible sites were not perturbed by moderate heating, but were apparently eliminated by polymer dehydroxytation. The dehydration behavior of HIV could be explained by steric resistance of water vapor diffusion within a tortuous interlayer polymeric network. Alternatively, new polymer/oxygen-surface bonds exceeding the hydration energy of interlayer components could form via heat-induced re-articulation of polymer/oxygen-surface bonds at smaller basal spacings.

A low-charge Na-montmorillonite (SWy-2) was exchanged with hexadecyltrimethyl-ammonium (HDTMA) at levels equal to 20, 40, 60, 70, 80, 90, 100, 150 and 200% of the cation exchange capacity (819 mmol(+)/kg) to determine the nature of adsorption and the ionic composition of the clay interlayers. In contrast with earlier work with smaller aliphatic cations, which suggested random interstratification of interlayers occupied by either organic or metallic cations, there was no evidence of cation segregation into homogeneous interlayers. Instead, X-ray analysis indicated that the organic cations assumed two dominant configurations which were roughly equivalent in prevalence at ∼70% coverage of the CEC. Below 70% exchange the organocations existed predominantly in heterogeneous monolayers with Na+, attaining basal spacings of between 1.41 and 1.44 nm which were sensitive to changes in relative humidity. Relative humidity effects indicated that Na+ and HDTMA occupied functionally discrete domains within the interlayer as shown by the free interaction of water and a neutral organic solute, naphthalene, with Na+ and HDTMA, respectively. At greater levels of HDTMA exchange (up to 100% of the CEC), the organocations assumed a predominantly bilayer configuration. Transition to a fully-developed bilayer indicated by a 1.77 nm d-spacing at 100% coverage was gradual, suggesting some interstratification of the monolayers and bilayer configurations between 70 and 100% exchange. Sorption of naphthalene to the organoclays within this range of coverage was well correlated with clay organic carbon content, consistent with relatively unimpeded interlayer access of neutral organic molecules.

The reactivity of colloidal particles is regulated by their surface properties. These properties affect the wettability, flocculation-dispersion characteristics, ion exchange, sorption capacities and transport of inorganic colloids. Most studies have focused on hydrophilic, charged-particle surfaces, often ignoring the alterations in surface properties produced by the adsorption of natural organic matter, surfactants and other compounds. Adsorption of these substances can potentially render a surface substantially more hydrophobic. Nevertheless, comparatively little is known about changes in surface properties and reactivity of minerals upon sorption of hydrophobic organic compounds. In this study, the properties of four minerals (kaolinite, pyrophyllite, montmorillonite and Min-U-Sil®) and two inorganic materials (X-ray amorphous Al hydroxide and X-ray amorphous Si oxide) were compared before and after treatment with the common silylating agent, trimethylchlorosilane (TMCS). The samples were characterized by measurements of total carbon, cation exchange capacity (CEC), particle size, specific surface area (SSA), electrophoretic mobility, contact angle, particle aggregation, and by X-ray diffraction and diffuse reflectance infrared spectroscopy. For the layer silicates, surface coverage was limited to ∼2% trimethyl silane (TMSi). TMSi covered 7.5% of the Min-U-Sil® surface and 33% of the X-ray amorphous Si oxide. Treatment did not affect the structure of the minerals but reduced the CEC, SSA and electrophoretic mobilities. Water contact angles increased to between 18 and 114° with treatment. While the apolar characteristic of the surfaces decreased minimally with treatment, the Lewis acid/base properties were substantially reduced and interfacial free energy shifted from positive to negative values indicating a more hydrophobic surface character. For all the samples except kaolinite, these changes affected the stability of the colloids in suspension depending upon solution pH. Although the grafting of TMSi altered colloidal mineral surface properties and increased their hydrophobicity, these changes were not sufficient to predict colloid aggregation behavior.

Conservation monitoring is paramount for the gathering of information on species and populations in need of conservation actions. However, monitoring of the mountain bongo Tragelaphus eurycerus isaaci, a Critically Endangered antelope endemic to Kenya, has hitherto been limited to surveillance (i.e. focused on persistence of the species in particular areas), thus limiting the information that could be retrieved on the status and trends of these populations. Using a newly developed identification system, we implemented robust design mark–recapture using existing camera-trap records of four wild subpopulations of the bongo. We provide data on sex and age structure and the first estimates of population size in the wild. Males and calves seem to be suffering higher mortality than females, and only two of the four monitored populations include adults of both sexes and calves. The combined size of these two breeding populations is estimated to be 29–50. Our findings confirm the critical situation of the mountain bongo in the wild and highlight the need for conservation actions to reinforce the wild populations for the long-term conservation of this antelope.

Clostridium botulinum causes infant botulism by colonising the intestines and producing botulinum neurotoxin in situ. Previous reports have linked infant botulism cases to C. botulinum spores in household dust, yet the baseline incidence of C. botulinum spores in residential households is currently unknown. Vacuum cleaner dust from 963 households in 13 major Canadian cities was tested for C. botulinum using a novel real-time PCR assay directed against all known subtypes of the botulinum neurotoxin gene. None of the samples tested positive for C. botulinum. Analysis of a random subset of samples by MALDI Biotyper revealed that the most common anaerobic bacterial isolates were of the genus Clostridium and the most common species recovered overall was Clostridium perfringens. Dust that was spiked with C. botulinum spores of each toxin type successfully produced positive real-time PCR reactions. These control experiments indicate that this is a viable method for the detection of C. botulinum spores in household dust. We make several recommendations for future work that may help discover a common environmental source of C. botulinum spores that could lead to effective preventative measures for this rare but deadly childhood disease.

New technologies and disruptions related to Coronavirus disease-2019 have led to expansion of decentralized approaches to clinical trials. Remote tools and methods hold promise for increasing trial efficiency and reducing burdens and barriers by facilitating participation outside of traditional clinical settings and taking studies directly to participants. The Trial Innovation Network, established in 2016 by the National Center for Advancing Clinical and Translational Science to address critical roadblocks in clinical research and accelerate the translational research process, has consulted on over 400 research study proposals to date. Its recommendations for decentralized approaches have included eConsent, participant-informed study design, remote intervention, study task reminders, social media recruitment, and return of results for participants. Some clinical trial elements have worked well when decentralized, while others, including remote recruitment and patient monitoring, need further refinement and assessment to determine their value. Partially decentralized, or “hybrid” trials, offer a first step to optimizing remote methods. Decentralized processes demonstrate potential to improve urban-rural diversity, but their impact on inclusion of racially and ethnically marginalized populations requires further study. To optimize inclusive participation in decentralized clinical trials, efforts must be made to build trust among marginalized communities, and to ensure access to remote technology.