The fossil record of bioerosion on rudists is commonly restricted to brief mentions that mainly use general terms and do not constitute detailed ichnological studies. This contribution comprises a detailed study of the bioerosion structures present on the shells of different species of rudists from the Upper Cretaceous (Maastrichtian) of Cuba. In addition, paleobiological, paleoecological and taphonomic implications of these boring are inferred. Among the studied material, seventeen rudist shells exhibits bioerosion structures. Based on their morphological features the borings have been ascribed to Gastrochaenolites isp. and Entobia isp. Gastrochaenid bivalves and clionaid sponges, respectively, have been proposed as their more likely producers. The modes of occurrence, density, and position of such bioerosion structures rule out a syn-vivo relationship between rudists and boring bivalves and sponges, demonstrating that colonization mainly was postmortem. Furthermore, the combination of these data together with previous paleoecological interpretations and the fact that the most parts of the rudist shells are filled by sediment, provides enough evidence to propose a subsequent process of reworking and reburial of these shells in shallow marine settings.

A wide range of approaches for batch processes monitoring can be found in the literature. This kind of process generates a very peculiar data structure, in which successive measurements of many process variables in each batch run are available. Traditional approaches do not take into account the time series nature of the data. The main reason is that the time series inference theory is not based on replications of time series, as it is in batch process data. It is based on the variability in a time domain. This fact demands some adaptations of this theory in order to accommodate the model coefficient estimates, considering jointly the batch to batch samples variability (batch domain) and the serial correlation in each batch (time domain). In order to address this issue, this paper proposes a new approach grounded in a group of control charts based on the classical ARMA model for monitoring and diagnostic of batch processes dynamics. The model coefficients are estimated (through the ordinary least square method) for each historical time series sample batch and modified Hotelling and t-Student distributions are derived and used to accommodate those estimates. A group of control charts based on that distributions are proposed for monitoring the new batches. Additionally, those groups of charts help to fault diagnosis, identifying the source of disturbances. Through simulated and real data we show that this approach seems to work well for both purposes.

The feeding behavior of growing-finishing pigs was analyzed to study prandial correlations and the probability of starting a new feeding event. The data were collected in real-time based on 157,632 visits by a group of 70 growing-finishing pigs (from 30.4 to 115.5 kg body weight, BW) to automatic feeders. The data were collected over 84 days, during which period the pigs were kept in conventional (by phase and by group) or precision (with daily and individual adjustments) feeding programs. A criterion to delimit each meal was then defined based on the probability of an animal starting a new feeding event within the next minute since the last visit. Prandial correlations were established between meal size and interval before meal (pre-prandial) or interval after meal (post-prandial) using Pearson correlation analysis. Post-prandial correlations (which can be interpreted as hunger-regulating mechanisms) were slightly stronger than pre-prandial correlations (which can be interpreted as satiety regulation mechanisms). Both correlations decreased as the animals’ age increased but were little influenced by the feeding programs. The information generated in this study allows a better understanding of pigs’ feeding behavior regulation mechanisms and could be used in the future to improve precision feeding programs.

Clustering methods are valuable tools for the identifcation of patterns in high dimensional data with applications in many scientifc felds. However, quantifying uncertainty in clustering is a challenging problem, particularly when dealing with High Dimension Low Sample Size (HDLSS) data. We develop a U-statistics based clustering approach that assesses statistical signifcance in clustering and is specifcally tailored to HDLSS scenarios. These non-parametric methods rely on very few assumptions about the data, and thus can be applied to a wide range of dataset for which the Euclidean distance captures relevant features. Our main result is the development of a hierarchical signifcance clustering method. In order to do so, we first introduce an extension of a relevant U-statistic and develop its asymptotic theory. Additionally, as a preliminary step, we propose a binary non-nested signifcance clustering method and show its optimality in terms of expected values. Our approach is tested through multiple simulations and found to have more statistical power than competing alternatives in all scenarios considered. They are further showcased in three applications ranging from genetics to image recognition problems.