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The analysis of the transportation usage rate provides opportunities for evaluating the efficacy of the transportation service offered by proposing an indicator that integrates actual demand and capacity. This study aims to develop a methodology for analyzing the occupancy rate from large-scale datasets to identify gaps between supply and demand in public transportation. Leveraging the spatio-temporal granularity of data from Automatic People Counting (APC) and relying on the Generalized Linear Mixed Effects Model and the Generalized Mixed-Effect Random Forest, in this study we propose a methodology for analyzing factors determining undercrowding. The results of the model are examined at both the segment and ride levels. Initially, the analysis focuses on identifying segments more likely associated with undercrowding, understanding factors influencing the probability of undercrowding, and exploring their relationships. Subsequently, the analysis extends to the temporal distribution of undercrowding, encompassing its impact on the entire journey. The proposed methodology is applied to analyze APC data, provided by the company responsible for public transport management in Milan, on a radial route of the surface transportation network., Comment: Pre-print version

Abdominal Aortic Aneurysm consists of a permanent dilation in the abodminal portion of the aorta and, along with its associated pathologies like calcifications and intraluminal thrombi, is one of the most important pathologies of the circulatory system. The shape of the aorta is among the primary drivers for these health issues, with particular reference to all the characteristics which affects the hemodynamics. Starting from the computed tomography angiography of a patient, we propose to summarize such information using tools derived from Topological Data Analysis, obtaining persistence diagrams which describe the irregularities of the lumen of the aorta. We showcase the effectiveness of such shape-related descriptors with a series of supervised and unsupervised case studies.

This paper aims to explore the factors stimulating different tourism behaviours, with specific reference to same-day visits and overnight stays. To this aim, we employ mobile network data referred to the area of Lombardy. The paper highlights that larger availability of tourism accommodations, cultural and natural endowments are relevant factors explaining overnight stays. Conversely, temporary entertainment and transportation facilities increase municipalities attractiveness for same-day visits. The results also highlight a trade-off in the capability of municipalities of being attractive in connection to both the tourism behaviours, with higher overnight stays in areas with more limited same-day visits. Mobile data offer a spatial and temporal granularity allowing to detect relevant patterns and support the design of tourism precision policies.

Accurately estimating Origin-Destination (OD) matrices is a topic of increasing interest for efficient transportation network management and sustainable urban planning. Traditionally, travel surveys have supported this process; however, their availability and comprehensiveness can be limited. Moreover, the recent COVID-19 pandemic has triggered unprecedented shifts in mobility patterns, underscoring the urgency of accurate and dynamic mobility data supporting policies and decisions with data-driven evidence. In this study, we tackle these challenges by introducing an innovative pipeline for estimating dynamic OD matrices. The real motivating problem behind this is based on the Trenord railway transportation network in Lombardy, Italy. We apply a novel approach that integrates ticket and subscription sales data with passenger counts obtained from Automated Passenger Counting (APC) systems, making use of the Iterative Proportional Fitting (IPF) algorithm. Our work effectively addresses the complexities posed by incomplete and diverse data sources, showcasing the adaptability of our pipeline across various transportation contexts. Ultimately, this research bridges the gap between available data sources and the escalating need for precise OD matrices. The proposed pipeline fosters a comprehensive grasp of transportation network dynamics, providing a valuable tool for transportation operators, policymakers, and researchers. Indeed, to highlight the potentiality of dynamic OD matrices, we showcase some methods to perform anomaly detection of mobility trends in the network through such matrices and interpret them in light of events that happened in the last months of 2022., Comment: Codes available. Synthetic Data available. Application to train network data. 27 pages, 6 Tables, 16 Figures

In this paper we face the problem of representation of functional data with the tools of algebraic topology. We represent functions by means of merge trees, which, like the more commonly used persistence diagrams, are invariant under homeomorphic reparametrizations of the functions they represent, thus allowing for a statistical analysis which is indifferent to functional misalignment. We consider a recently defined metric for merge trees and we prove some theoretical results related to its specific implementation when merge trees represent functions, establishing also a class of consistent estimators with convergence rates. To showcase the good properties of our topological approach to functional data analysis, we test it on the Aneurisk65 dataset replicating, from our different perspective, the supervised classification analysis which contributed to make this dataset a benchmark for methods dealing with misaligned functional data. In the Appendix we provide an extensive comparison between merge trees and persistence diagrams, highlighting similarities and differences, which can guide the analyst in choosing between the two representations.

The assessment of the vulnerability of a community endangered by seismic hazard is of paramount importance for planning a precision policy aimed at the prevention and reduction of its seismic risk. We aim at measuring the vulnerability of the Italian municipalities exposed to seismic hazard, by analyzing the open data offered by the Mappa dei Rischi dei Comuni Italiani provided by ISTAT, the Italian National Institute of Statistics. Encompassing the Index of Social and Material Vulnerability already computed by ISTAT, we also consider as referents of the latent social and material vulnerability of a community, its demographic dynamics and the age of the building stock where the community resides. Fusing the analyses of different indicators, within the context of seismic risk we offer a tentative ranking of the Italian municipalities in terms of their social and material vulnerability, together with differential profiles of their dominant fragilities which constitute the basis for planning precision policies aimed at seismic risk prevention and reduction., Comment: 23 page, 20 figures; abstract corrected

Data taking value on a Riemannian manifold and observed over a complex spatial domain are becoming more frequent in applications, e.g. in environmental sciences and in geoscience. The analysis of these data needs to rely on local models to account for the non stationarity of the generating random process, the non linearity of the manifold and the complex topology of the domain. In this paper, we propose to use a random domain decomposition approach to estimate an ensemble of local models and then to aggregate the predictions of the local models through Fr\'{e}chet averaging. The algorithm is introduced in complete generality and is valid for data belonging to any smooth Riemannian manifold but it is then described in details for the case of the manifold of positive definite matrices, the hypersphere and the Cholesky manifold. The predictive performance of the method are explored via simulation studies for covariance matrices and correlation matrices, where the Cholesky manifold geometry is used. Finally, the method is illustrated on an environmental dataset observed over the Chesapeake Bay (USA).

In this paper, we generalize the metric-based permutation test for the equality of covariance operators proposed by Pigoli et al. (2014) to the case of multiple samples of functional data. To this end, the non-parametric combination methodology of Pesarin and Salmaso (2010) is used to combine all the pairwise comparisons between samples into a global test. Different combining functions and permutation strategies are reviewed and analyzed in detail. The resulting test allows to make inference on the equality of the covariance operators of multiple groups and, if there is evidence to reject the null hypothesis, to identify the pairs of groups having different covariances. It is shown that, for some combining functions, step-down adjusting procedures are available to control for the multiple testing problem in this setting. The empirical power of this new test is then explored via simulations and compared with those of existing alternative approaches in different scenarios. Finally, the proposed methodology is applied to data from wheel running activity experiments, that used selective breeding to study the evolution of locomotor behavior in mice.

We study a functional equation whose unknown maps a Euclidean space into the space of probability distributions on [0,1]. We prove existence and uniqueness of its solution under suitable regularity and boundary conditions, we show that it depends continuously on the boundary datum, and we characterize solutions that are diffuse on [0,1]. A canonical solution is obtained by means of a Randomly Reinforced Urn with different reinforcement distributions having equal means. The general solution to the functional equation defines a new parametric collection of distributions on [0,1] generalizing the Beta family., Comment: 31 pages, pre-galleys version of accepted paper