The study of many population growth models is complicated by only partial observation of the underlying stochastic process driving the model. For example, in an epidemic outbreak we might know when individuals show symptoms to a disease and are removed, but not when individuals are infected. Motivated by the above example and the long-established approximation of epidemic processes by branching processes, we explore the number of individuals alive in a time-inhomogeneous branching process with a general phase-type lifetime distribution given only (partial) information on the times of deaths of individuals. Deaths are detected independently with a detection probability that can vary with time and type. We show that the number of individuals alive immediately after the kth detected death can be expressed as the mixture of random variables each of which consists of the sum of k independent zero-modified geometric distributions. Furthermore, in the case of an Erlang lifetime distribution, we derive an easy-to-compute mixture of negative binomial distributions as an approximation of the number of individuals alive immediately after the kth detected death.

This paper presents the results from an investigation of the true probability distributions of the range of rank totals. A procedure for generating an approximation to the true distributions is also given. A comparison of the results of this approximation with an extensive criterion of generated true and sample distributions, and with other approximations is indicated. Accurate estimates of the critical ranges necessary to reach significance at three commonly used alpha levels, where the number of judges and items is less than or equal to sixteen, are presented in tabular form.

Traditional approaches for evaluating the impact of scientific research – mainly scholarship (i.e., publications, presentations) and grant funding – fail to capture the full extent of contributions that come from larger scientific initiatives. The Translational Science Benefits Model (TSBM) was developed to support more comprehensive evaluations of scientific endeavors, especially research designed to translate scientific discoveries into innovations in clinical or public health practice and policy-level changes. Here, we present the domains of the TSBM, including how it was expanded by researchers within the Implementation Science Centers in Cancer Control (ISC3) program supported by the National Cancer Institute. Next, we describe five studies supported by the Penn ISC3, each focused on testing implementation strategies informed by behavioral economics to reduce key practice gaps in the context of cancer care and identify how each study yields broader impacts consistent with TSBM domains. These indicators include Capacity Building, Methods Development (within the Implementation Field) and Rapid Cycle Approaches, implementing Software Technologies, and improving Health Care Delivery and Health Care Accessibility. The examples highlighted here can help guide other similar scientific initiatives to conceive and measure broader scientific impact to fully articulate the translation and effects of their work at the population level.

Clays and clay minerals dissolve over a broad pH range, such as during sediment diagenesis and in a variety of applications, including nuclear waste storage, landfills, and geopolymer binders in the construction industry. The solubility depends on process parameters (pH, temperature, pressure, etc.) and material properties (phase content, clay mineral composition, particle size, etc.). Pretreatments such as calcination or severe grinding change the material properties and could enhance solubility, which is called activation. The aim of the current study was to determine the solubility of three different clay minerals after calcination (metakaolinite, metamontmorillonite, and metaillite) in high molar alkaline solutions (NaOH) up to 10.79 mol/L and pH = 14.73. Furthermore, the solubility of an Al(OH)3 powder in alkaline solution (NaOH) was analyzed, as it can be used to adjust the Si:Al ratio of geopolymer precursors. The residues of the clay minerals after the alkaline treatment were investigated to disclose potential alterations in their phase contents. Based on the results of the thermal and alkaline activation, conclusions about the suitability as geopolymer precursors were made. All clay minerals showed an increase in solubility proportional to the concentration of the alkaline solution. The solubility decreased in the order metakaolinite > metamontmorillonite > metaillite. Thereby, dissolution was incomplete for all three clay minerals (<90%) after 7 days and congruent for metakaolinite and metaillite but incongruent for metamontmorillonite.

Kaolins and clays are important raw materials for production of supplementary cementitious materials and geopolymer precursors through thermal activation by calcination beyond dehydroxylation (DHX). Both types of clay contain different polytypes and disordered structures of kaolinite but little is known about the impact of the layer stacking of dioctahedral 1:1 layer silicates on optimum thermal activation conditions and following reactivity with alkaline solutions. The objective of the present study was to improve understanding of the impact of layer stacking in dioctahedral 1:1 layer silicates on the thermal activation by investigating the atomic structure after dehydroxylation. Heating experiments by simultaneous thermal analysis (STA) followed by characterization of the dehydroxylated materials by nuclear magnetic resonance spectroscopy (NMR) and scanning electron microscopy (SEM) together with first-principles calculations were performed. Density functional theory (DFT) was utilized for correlation of geometry-optimized structures to thermodynamic stability. The resulting volumes of unit cells were compared with data from dilatometry studies. The local structure changes were correlated with experimental results of increasing DHX temperature in the following order: disordered kaolinite, kaolinite, and dickite, whereupon dickite showed two dehydroxylation steps. Intermediate structures were found that were thermodynamically stable and partially dehydroxylated to a degree of DHX of 75% for kaolinite, 25% for disordered kaolinite, and 50% for dickite. These thermodynamically stable, partially dehydroxylated intermediates contained AlV while metakaolinite and metadickite contained only AlIV with a strongly distorted coordination shell. These results indicate strongly the necessity for characterization of the structure of dioctahedral 1:1 layer silicates in kaolins and clays as a key parameter to predict optimized calcination conditions and resulting reactivity.

Sub-micrometer clay particles are of interest in clay-polymer applications, especially when transparency is important. The scattering of light can be reduced by the adjustment of the refractive index (RI) of the clays to that of the matrix. In this study, the RI of sub-micrometer illite particles was changed by treatment with 5 M HCl for treatment times ranging between 2 and 24 h. The dissolution of Fe leads to a decrease in the RI of illite from 1.587 for the unaltered material to 1.502 after 24 h. The layer structure of the illite particles was preserved during the treatment. The RI of the sub-micrometer illite particles was determined by means of a photospectrometer measuring the light intensity passing through suspensions containing the clay particles, with varying refractive indices.

We consider an SIR (susceptible $\to$ infective $\to$ recovered) epidemic in a closed population of size n, in which infection spreads via mixing events, comprising individuals chosen uniformly at random from the population, which occur at the points of a Poisson process. This contrasts sharply with most epidemic models, in which infection is spread purely by pairwise interaction. A sequence of epidemic processes, indexed by n, and an approximating branching process are constructed on a common probability space via embedded random walks. We show that under suitable conditions the process of infectives in the epidemic process converges almost surely to the branching process. This leads to a threshold theorem for the epidemic process, where a major outbreak is defined as one that infects at least $\log n$ individuals. We show further that there exists $\delta \gt 0$, depending on the model parameters, such that the probability that a major outbreak has size at least $\delta n$ tends to one as $n \to \infty$.

During an epidemic outbreak, typically only partial information about the outbreak is known. A common scenario is that the infection times of individuals are unknown, but individuals, on displaying symptoms, are identified as infectious and removed from the population. We study the distribution of the number of infectives given only the times of removals in a Markovian susceptible–infectious–removed (SIR) epidemic. Primary interest is in the initial stages of the epidemic process, where a branching (birth–death) process approximation is applicable. We show that the number of individuals alive in a time-inhomogeneous birth–death process at time $t \geq 0$, given only death times up to and including time t, is a mixture of negative binomial distributions, with the number of mixing components depending on the total number of deaths, and the mixing weights depending upon the inter-arrival times of the deaths. We further consider the extension to the case where some deaths are unobserved. We also discuss the application of the results to control measures and statistical inference.

This paper examines conditions that do or do not lead to accurate judgments of frequency (JOF) and judgments of duration (JOD). In three experiments, duration and frequency of visually presented stimuli are varied orthogonally in a within-subjects design. Experiment 1 reveals an asymmetric judgment pattern. JOFs reflected actual presentation frequency quite accurately and were unbiased by exposure duration. Conversely, JODs were almost insensitive to actual exposure duration and were systematically biased by presentation frequency. We show, however, that a tendency towards a symmetric judgment pattern can be obtained by manipulating encoding conditions. Sustaining attention during encoding (Experiment 2) or enhancing richness of the encoded stimuli (Experiment 3) increases judgment sensitivity in JOD and yields biases in both directions (JOF biased by exposure duration, JOD biased by presentation frequency). The implications of these findings for underlying memory mechanisms are discussed.

Shade coffee is a well-studied cultivation strategy that creates habitat for tropical birds while also maintaining agricultural yield. Although there is a general consensus that shade coffee is more “bird-friendly” than a sun coffee monoculture, little work has investigated the effects of specific shade tree species on insectivorous bird diversity. This study involved avian foraging observations, mist-netting data, temperature loggers, and arthropod sampling to investigate bottom-up effects of two shade tree taxa - native Cordia sp. and introduced Grevillea robusta - on insectivorous bird communities in central Kenya. Results indicate that foliage-dwelling arthropod abundance, and the richness and overall abundance of foraging birds were all higher on Cordia than on Grevillea. Furthermore, multivariate analyses of the bird community indicate a significant difference in community composition between the canopies of the two tree species, though the communities of birds using the coffee understorey under these shade trees were similar. In addition, both shade trees buffered temperatures in coffee, and temperatures under Cordia were marginally cooler than under Grevillea. These results suggest that native Cordia trees on East African shade coffee farms may be better at mitigating habitat loss and attracting insectivorous birds that could promote ecosystem services. Identifying differences in prey abundance and preferences in bird foraging behaviour not only fills basic gaps in our understanding of the ecology of East African coffee farms, it also aids in developing region-specific information to optimize functional diversity, ecosystem services, and the conservation of birds in agricultural landscapes.