We introduce a non-increasing tree growth process $((T_n,{\sigma}_n),\, n\ge 1)$, where Tn is a rooted labelled tree on n vertices and σn is a permutation of the vertex labels. The construction of (Tn, σn) from (Tn−1, σn−1) involves rewiring a random (possibly empty) subset of edges in Tn−1 towards the newly added vertex; as a consequence Tn−1 ⊄ Tn with positive probability. The key feature of the process is that the shape of Tn has the same law as that of a random recursive tree, while the degree distribution of any given vertex is not monotone in the process.

We present two applications. First, while couplings between Kingman’s coalescent and random recursive trees were known for any fixed n, this new process provides a non-standard coupling of all finite Kingman’s coalescents. Second, we use the new process and the Chen–Stein method to extend the well-understood properties of degree distribution of random recursive trees to extremal-range cases. Namely, we obtain convergence rates on the number of vertices with degree at least $c\ln n$, c ∈ (1, 2), in trees with n vertices. Further avenues of research are discussed.

Isolation is a concept originally conceived in the context of clique enumeration in static networks, mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest of the graph. Motivated by recent work on enumerating cliques in temporal networks, we transform the isolation concept to the temporal setting. We discover that the addition of the time dimension leads to six distinct natural isolation concepts. Our main contribution is the development of parameterized enumeration algorithms for five of these six isolation types for clique enumeration, employing the parameter “degree of isolation.” In a nutshell, this means that the more isolated these cliques are, the faster we can find them. On the empirical side, we implemented and tested these algorithms on (temporal) social network data, obtaining encouraging results.

X-ray tomography has applications in various industrial fields such as sawmill industry, oil and gas industry, as well as chemical, biomedical, and geotechnical engineering. In this article, we study Bayesian methods for the X-ray tomography reconstruction. In Bayesian methods, the inverse problem of tomographic reconstruction is solved with the help of a statistical prior distribution which encodes the possible internal structures by assigning probabilities for smoothness and edge distribution of the object. We compare Gaussian random field priors, that favor smoothness, to non-Gaussian total variation (TV), Besov, and Cauchy priors which promote sharp edges and high- and low-contrast areas in the object. We also present computational schemes for solving the resulting high-dimensional Bayesian inverse problem with 100,000–1,000,000 unknowns. We study the applicability of a no-U-turn variant of Hamiltonian Monte Carlo (HMC) methods and of a more classical adaptive Metropolis-within-Gibbs (MwG) algorithm to enable full uncertainty quantification of the reconstructions. We use maximum a posteriori (MAP) estimates with limited-memory BFGS (Broyden–Fletcher–Goldfarb–Shanno) optimization algorithm. As the first industrial application, we consider sawmill industry X-ray log tomography. The logs have knots, rotten parts, and even possibly metallic pieces, making them good examples for non-Gaussian priors. Secondly, we study drill-core rock sample tomography, an example from oil and gas industry. In that case, we compare the priors without uncertainty quantification. We show that Cauchy priors produce smaller number of artefacts than other choices, especially with sparse high-noise measurements, and choosing HMC enables systematic uncertainty quantification, provided that the posterior is not pathologically multimodal or heavy-tailed.

The burden of multidrug-resistant tuberculosis (MDR-TB) related to mortality in resource-poor countries remains high. This study aimed to estimate the incidence and predictors of death among MDR-TB patients in central Ethiopia. A retrospective follow-up study was conducted at three hospitals in the Amhara region on 451 patients receiving treatment for MDR-TB from September 2010 to January 2017. Data were collected from patient registration books, charts and computer databases. Data were fitted to a parametric frailty model and survival was expressed as an adjusted hazard ratio (AHR) with a 95% confidence interval (CI). The median follow-up time of participants was 20 months (interquartile range: 12, 22) and 46 (10.20%) of patients died during this period. The incidence rate of mortality was 7.42 (95% CI 5.56–9.91)/100 person-years. Older age (AHR = 1.04, 95% CI 1.01–1.08), inability to self-care (AHR = 13.71, 95% CI 5.46–34.40), co-morbidity (AHR = 5.74, 95% CI 2.19–15.08), low body mass index (AHR = 4.13, 95% CI 1.02–16.64), acute lung complications (AHR = 4.22, 95% CI 1.66–10.70) and lung consolidation at baseline (AHR = 5.27, 95% CI 1.06–26.18) were independent predictors of mortality. Most of the identified predictor factors of death in this study were considered to be avoidable if the TB programme had provided nutritional support for malnourished patients and ensured a close follow-up of the elderly, and patients with co-morbidities.

Bisphenol-A (BPA) is associated with adverse health outcomes and is found in many canned foods. It is not understood if some BPA contamination can be washed away by rinsing. The objective of this single-blinded crossover experiment was to determine whether BPA exposure, as measured by urinary concentrations, could be decreased by rinsing canned beans prior to consumption. Three types of hummus were prepared from dried beans, rinsed, and unrinsed canned beans. Fourteen healthy participants ate two samples of each hummus over six experimental days and collected spot urine specimens for BPA measurement. The geometric mean BPA levels for dried beans BPA (GM = 0.97 ng/ml, 95%CI = 0.74,1.26) was significantly lower than rinsed (GM = 1.89 ng/ml, 1.37,2.59) and unrinsed (GM = 2.46 ng/ml, 1.44,4.19). Difference-in-difference estimates showed an increase in GM BPA from pre- to post-hummus between unrinsed and rinsed canned beans of 1.39 ng/ml, p-value = 0.0400. Rinsing canned beans was an effective method to reduce BPA exposure.