We establish a number of results concerning the limiting behaviour of the longest edges in the genealogical tree generated by a continuous-time Galton–Watson process. Separately, we consider the large-time behaviour of the longest pendant edges, the longest (strictly) interior edges, and the longest of all the edges. These results extend the special case of long pendant edges of birth–death processes established in Bocharov et al. (2023).

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.

There is a growing trend for studies run by academic and nonprofit organizations to have regulatory submission requirements. As a result, there is greater reliance on REDCap, an electronic data capture (EDC) widely used by researchers in these organizations. This paper discusses the development and implementation of the Rapid Validation Process (RVP) developed by the REDCap Consortium, aimed at enhancing regulatory compliance and operational efficiency in response to the dynamic demands of modern clinical research. The RVP introduces a structured validation approach that categorizes REDCap functionalities, develops targeted validation tests, and applies structured and standardized testing syntax. This approach ensures that REDCap can meet regulatory standards while maintaining flexibility to adapt to new challenges. Results from the application of the RVP on recent successive REDCap software version releases illustrate significant improvements in testing efficiency and process optimization, demonstrating the project’s success in setting new benchmarks for EDC system validation. The project’s community-driven responsibility model fosters collaboration and knowledge sharing and enhances the overall resilience and adaptability of REDCap. As REDCap continues to evolve based on feedback from clinical trialists, the RVP ensures that REDCap remains a reliable and compliant tool, ready to meet regulatory and future operational challenges.

Epidemiological and clinical trial evidence indicates that n-6 polyunsaturated fatty acid (PUFA) intake is cardioprotective. Nevertheless, claims that n-6 PUFA intake promotes inflammation and oxidative stress prevail. This narrative review aims to provide health professionals with an up-to-date evidence overview to provide the requisite background to address patient/client concerns about oils containing predominantly unsaturated fatty acids (UFA), including MUFA and PUFA. Edible plant oils, commonly termed vegetable oils, are derived from vegetables, nuts, seeds, fruits and cereal grains. Substantial variation exists in the fatty acid composition of these oils; however, all are high in UFA, while being relatively low in saturated fatty acids (SFA), except for tropical oils. Epidemiological evidence indicates that higher PUFA intake is associated with lower risk of incident CVD and type 2 diabetes mellitus (T2DM). Additionally, replacement of SFA with PUFA is associated with reduced risk of CVD and T2DM. Clinical trials show higher intake of UFA from plant sources improves major CVD risk factors, including reducing levels of atherogenic lipids and lipoproteins. Importantly, clinical trials show that increased n-6 PUFA (linoleic acid) intake does not increase markers of inflammation or oxidative stress. Evidence-based guidelines from authoritative health and scientific organisations recommend intake of non-tropical vegetable oils, which contain MUFA and n-6 PUFA, as part of healthful dietary patterns. Specifically, vegetable oils rich in UFA should be consumed instead of rich sources of SFA, including butter, tallow, lard, palm and coconut oils.

One-g samples of a montmorillonite, a metabentonite, an illite, two kaolinites, and three halloysites were treated with 50 ml of hydrochloric acid (6·45 N, 1: 1), acetic acid (4·5 N, 1: 3), sodium hydroxide (2·8N), sodium chloride solution (pH 6·10; Na = 35‰; Cl = 21·5‰), and natural sea water (pH 7·85; Na = 35·5‰; Cl = 21·5‰) for a 10-day period in stoppered plastic vials. The supernatant solutions were removed from the clay minerals and analyzed for SiO2, Al2O3, CaO, MgO, Na2O, and K2O. All the solutions removed some SiO2, Al2O3, and Fe2O3 from the samples, but the quantities were small. Sodium hydroxide attacked the kaolin group minerals more strongly than it did montmorillonite, metabentonite, or illite. Halloysite was more strongly attacked by hydrochloric acid than was any of the other experimental minerals. Hydrochloric acid removed iron oxide coatings from soil clay minerals, but acetic acid did not remove them completely. The samples most strongly attacked by HCl and NaOH were examined by X-ray diffraction. Acid treatment did not destroy the structure of the clays, but the halloysite structure was partially destroyed. Sodium hydroxide attacked the halloysite structure, as shown by chemical analysis and X-ray diffraction. These experiments show that treatment in dilute acids has no harmful effect in the preparation of clays for X-ray diffraction. Acetic acid is preferred to hydrochloric acid for this purpose. Hydrochloric acid cleans clay minerals by removing free iron oxide from the surface; acetic acid is less effective.

In our paper testing the Cutler–Hawkins hypothesis that suffixes are easier to process than prefixes (Harris & Samuel 2025), we report little experimental support for the hypothesis. Several sources treat clitics as being similar to affixes (e.g. Himmelmann 2014, Asao 2015), and some argue that there is a parallel preference for enclitics over proclitics (Cysouw 2005, Dryer 2017). On this basis, we test an extension of the Cutler–Hawkins hypothesis to clitics because if true, that too could explain the suffixing preference (as well as the putative enclitic preference). Cutler et al. (1985) also state a hypothesis about the processing of infixes. Udi provides an excellent language for testing both hypotheses, since each person clitic in this language can occur before the verb, after the verb, between morphemes of the verb or inside the verbal root, under certain circumstances (Harris 2002). Although European Portuguese does not place clitics inside roots, it utilizes the other three placements. We have conducted three experiments on each language. The results demonstrate that an explanation for either the suffixing preference or the putative enclitic preference is unlikely to be grounded in the processing factors suggested by Cutler & Hawkins.

The hypothesis that affixes following a stem are easier to process than ones preceding has not been tested in a straightforward manner in any language, as far as we know. Cutler, Hawkins & Gilligan (1985) and Hawkins & Cutler (1988) adduce some evidence that supports this hypothesis indirectly, but they do not conduct experiments to test it directly. They use this hypothesis to explain in part the suffixing preference. Some others, such as Asao (2015), continue to assume the correctness of the hypothesis. We do not aim to explain the suffixing preference at all but to test the hypothesis that affixes preceding the stem (informally, prefixes) disrupt the comprehension of a word more than affixes that follow (informally, suffixes) do. In this paper we test this hypothesis (henceforth the ‘Cutler--Hawkins hypothesis’) on Georgian, because it has a wide variety of prefixes and suffixes, and in a single experiment on English. In Georgian we test a prefix and a suffix that mark the person of the subject in a verb, a circumfix and a suffix that mark derivation in nouns, and a prefix and a suffix that form intransitive verbs (usually called ‘passives’ in Georgian). Across the set of experiments, we find little support for the Cutler--Hawkins hypothesis.

The Upper Cretaceous Gammon Shale has served as both source bed and reservoir rock for accumulations of natural gas. Gas-producing and nonproducing zones in the Gammon Shale are differentiated on the basis of geophysical log interpretation. To determine the physical basis of the log responses, mineralogical, cation-exchange, textural, and chemical analyses were conducted on core samples from both producing and nonproducing portions of a well in the Gammon Shale from southwestern North Dakota. Statistical treatment (2 sample t-test and discriminant function analysis) of the laboratory data indicate that the producing and nonproducing zones differ significantly in mixed-layer clay content (7 vs. 12%), weight proportion of the clay-size (0.5-1.0 μm) fraction (5.3 vs. 6.3%) ratio of Ca2+ to Na+ extracted during ion exchange (1.4 vs. 1.0), and abundance of dolomite (10 vs. 8%). The geophysical logs apparently record subtle differences in composition and texture which probably reflect variations in the original detrital constituents of the Gammon sediments. Successfully combining log interpretation and clay petrology aids in understanding the physical basis of log response in clay-rich rocks and enhances the effectiveness of logs as predictive geologic tools.

The name volkonskoite was first used in 1830 to describe a bright blue-green, chromiumbearing clay material from the Okhansk region, west of the Ural Mountains, U.S.S.R. Since that time, the name has been applied to numerous members of the smectite group of clay minerals, although the reported chromium content has ranged from 1% to about 30% Cr2O3. The name has also been applied to some chromian chlorites. Because volkonskoite has been used for materials that differ not only in their chromium content but also in their basic structure, the species status of the mineral has been unclear.

To resolve this uncertainty, two specimens of volkonskoite from (1) Mount Efimiatsk, the type locality in the Soviet Union (USNM 16308) and (2) the Okhansk region in the Perm Basin, U.S.S.R. (USNM R4820), were examined by several mineralogical techniques. Neotype sample 16308 has the following structural formula:

$({\text{Ca}}_{0.11}{\text{Mg}}_{0.11}{\text{Fe}}^{2+}{\hspace{0.17em}}_{0.03}{\text{K}}_{0.02})({\text{Cr}}_{1.18}{\text{Mg}}_{0.78}{\text{Fe}}^{3+}{\hspace{0.17em}}_{0.29}\text{Ca}{}_{0.02})({\text{Si}}_{3.50}{\text{Al}}_{0.51}){\text{O}}_{10}{(\text{OH})}_2\cdot 3.64{\text{H}}_2\text{O}.$

Sample R4820 has the following structural formula:

$({\text{Ca}}_{0.25}{\text{Mg}}_{0.05}{\text{Fe}}^{2+}{\hspace{0.17em}}_{0.01}{\text{K}}_{0.03}{\text{Mn}}_{0.01})({\text{Cr}}_{1.07}{\text{Mg}}_{0.75}{\text{Fe}}^{3+}{\hspace{0.17em}}_{0.35}({\text{Si}}_{3.59}{\text{Al}}_{0.43}){\text{O}}_{10}{(\text{OH})}_2\cdot 4.22{\text{H}}_2\text{O}.$

Mössbauer spectroscopy indicates that 91% and 98% of the iron is present as Fe3+ in samples 16308 and R4820, respectively. X-ray powder diffraction patterns of both samples have broad lines corresponding to minerals of the smectite group.

On the basis of these data, volkonskoite appears to be a dioctahedral member of the smectite group that contains chromium as the dominant cation in the octahedral layer. Smectites containing less than this amount of octahedral chromium should not be called volkonskoite, but should be named by chemical element adjectives, e.g., chromian montmorillonite, chromian nontronite.

This paper describes the implementation of curricula for Liberia's first-ever psychiatry training programme in 2019 and the actions of the only two Liberian psychiatrists in the country at the time in developing and executing a first-year postgraduate psychiatry training programme (i.e. residency) with support from international collaborators. It explores cultural differences in training models among collaborators and strategies to synergise them best. It highlights the assessment of trainees’ (residents’) basic knowledge on entry into the programme and how it guided immediate and short-term priority teaching objectives, including integrated training in neuroscience and neurology. The paper describes the strengths and challenges of this approach as well as opportunities for continued growth.

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.

Community involvement in research is key to translating science into practice, and new approaches to engaging community members in research design and implementation are needed. The Community Scientist Program, established at the MD Anderson Cancer Center in Houston in 2018 and expanded to two other Texas institutions in 2021, provides researchers with rapid feedback from community members on study feasibility and design, cultural appropriateness, participant recruitment, and research implementation. This paper aims to describe the Community Scientist Program and assess Community Scientists' and researchers' satisfaction with the program. We present the analysis of the data collected from 116 Community Scientists and 64 researchers who attended 100 feedback sessions, across three regions of Texas including Northeast Texas, Houston, and Rio Grande Valley between June 2018 and December 2022. Community Scientists stated that the feedback sessions increased their knowledge and changed their perception of research. All researchers (100%) were satisfied with the feedback and reported that it influenced their current and future research methods. Our evaluation demonstrates that the key features of the Community Scientist Program such as follow-up evaluations, effective bi-directional communication, and fair compensation transform how research is conducted and contribute to reducing health disparities.