Fabio Rapallo

Missing binary predictors are common in reliability, quality control, and industrial decision systems, yet imputation methods are often chosen by convenience rather than evidence. We conduct a Monte Carlo study comparing mode substitution, sequential hot‐deck, missForest, MICE, and KNN with three neighbourhood sizes under MCAR, MAR, and MNAR missingness, across missingness rates from 5% to 50% and two predictor‐dependence structures. Performance is evaluated on three targets: exact recovery of missing binary cells, recovery of logistic‐regression coefficients, and downstream classification using logistic regression, naive Bayes, support vector machines, and random forests. The results reveal a clear trade‐off. KNN is strongest for exact cell recovery under MCAR and MAR, whereas missForest performs best under MNAR. MICE is the most reliable choice for downstream predictive performance across learners and missingness mechanisms. By contrast, mode imputation and sequential hot‐deck achieve the best coefficient recovery. The main implication is operational: in binary‐data environments, imputation should be chosen to match the analytical objective–reconstruction, inference, or prediction–because no single method dominates all targets simultaneously.

In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint distribution, but instead define a family of admissible distributions that share the same pairwise dependence while potentially differing in higher-order interactions. In this paper, we introduce a geometric framework to describe the entire feasible set of such joint distributions with uniform margins. We show that this admissible set forms a convex polytope, analyze its symmetry properties, and characterize its extreme rays. These extremal distributions provide fundamental insights into how higher-order dependence structures may vary while preserving the prescribed pairwise information. Unlike traditional methods for table generation, which return a single table, our framework makes it possible to explore and understand the full admissible space of dependence structures, enabling more flexible choices for modeling and simulation. We illustrate the usefulness of our theoretical results through examples and a real case study on rater agreement.

Background/Objectives: The pharyngeal microbiota plays a critical role in respiratory health by supporting immune modulation, colonization resistance, and metabolic functions. Disruptions in this microbial ecosystem are associated with respiratory diseases; however, standard diagnostics often target individual pathogens, overlooking overall microbial dynamics. This study investigates the composition and diversity of the pharyngeal microbiota in three populations: individuals with pre-COPD (with and without concurrent acute respiratory infection [ARI]) and those with stable COPD. Methods: Pharyngeal swabs were analyzed using 16S rDNA sequencing on the Illumina MiSeq platform. Taxonomic and functional profiles were generated with MicrobAT^®, while microbial diversity was evaluated using the Shannon index and PERMANOVA. Group differences in microbiota composition were assessed via Kruskal–Wallis tests and robust PCA. The sample size was estimated at 8 subjects per group to detect significant differences (α = 0.05, 80% power, SD ≈ 20). Results: Twenty-nine swabs were collected: 11 from pre-COPD subjects (PC), 9 from ARI patients receiving antibiotics, and 9 from individuals with stable severe COPD. Microbial diversity was preserved in the PC group (100%) but markedly reduced in ARI (25%) and COPD (15%). Microbiota composition differed significantly across groups (R² = 0.371, p = 0.001), particularly at the phylum level. Functional analysis revealed minimal deficits in PC (<10%) but major impairments in ARI (81%) and COPD (56%), indicating reduced microbial functional capacity. Conclusions: Broad-spectrum microbial analysis highlights the importance of assessing pharyngeal microbiota beyond traditional pathogen detection, offering potential for innovative diagnostic and therapeutic approaches.

In this work, we study the finite-population behaviour of the Reed-Frost epidemic model. Our analysis relies on the exact expression for the final epidemic size, replaced by Monte Carlo simulations in cases where the exact formula becomes numerically unstable. When the initial reproduction number is greater than a critical threshold, the distribution of the final size becomes bimodal. We therefore define the probabilities of small and large outbreaks, providing an intuitive answer to the question posed in the title through simple arguments based on the geometric distribution. Finally, an agent-based simulation confirms that the Reed-Frost model offers a good approximation in the case of the COVID-19 outbreak.

Since the 19th century, the cultivation of Ocimum basilicum L. has increasingly been established in Liguria, with the in situ reproduction of seeds. Over the years, Ligurian basil accessions were crossed with allochthonous genomes to obtain disease-resistant plants. To preserve the original genetic resource, nine old Ligurian accessions (CV1–9) were recovered. As part of the PSR 2014–2022 Mis. 10.2 of Liguria Region, this work aimed to characterize these CVs by morphological and phytochemical analyses to safeguard their biodiversity. Commercial O. basilicum Genovese Superbo grown in Liguria (SL) was added for comparison. The micro-morphological investigation showed significantly different trichome densities among the samples. CV4 showed the highest densities of both peltate and capitate trichomes, while CV9 and CV1 had the lowest peltate and capitate densities, respectively. In addition, to perform the germplasm characterization, seed morphometric data and germinability were evaluated. Volatile Organic Compounds (VOCs) analysis was carried out on CV1–9, SL, and Superbo plants grown in Piedmont (SP), to test the influence of territory on basil aromatic profiles. The results showed that the old accessions and SL were rich in linalool, eugenol, and bergamotene. Only CV1 slightly differed, with higher levels of methyl eugenol, eucalyptol, and camphor. On the contrary, SP had very high levels of methyl eugenol and camphor. These data represent valuable insights for preserving Ligurian old basil accessions and maintaining the production of Genovese Basil PDO (Protected Designation of Origin) in the future.

Since the 19th century, cultivation of Ocimum basilicum L. has increasingly been established in Liguria, with in situ reproduction of seeds. Over the years, Ligurian basil accessions were crossed with allochthonous genomes to obtain disease-resistant plants. To preserve the original genetic resource, nine old Ligurian accessions (CV1-9) were recovered. As part of the PSR 2014-2022 Mis. 10.2 of Liguria Region, this work aimed at characterizing these CVs by morphological and phytochemical analyses to safeguard their biodiversity. Commercial O. basilicum Genovese Superbo grown in Liguria (SL) was added for comparison. Micro-morphological investigation showed a significantly different trichomes density among the samples. CV4 showed the highest density of both peltate and capitate trichomes, while CV9 and CV1 had the lowest one of peltate and capitate, respectively. VOCs analysis was performed on CV1-9, SL and on a plant of Superbo grown in Piedmont (SP), to test the influence of the territory on basil aromatic profile. Indeed, the old accessions and SL were rich in linalool, eugenol, and bergamotene. Only CV1 slightly differed for higher levels of methyl eugenol, eucalyptol, and camphor. On the contrary, SP had very high levels of methyl eugenol and camphor. This data represents valuable insights for preserving Ligurian old basil accessions and maintaining Genovese Basil PDO production in the future.