In the framework of Object Oriented Data Analysis, a permutation approach to the two-sample testing problem for network-valued data is proposed. In details, the present framework proceeds in four steps: (i) matrix representation of the networks, (ii) computation of the matrix of pairwise (inter-point) distances, (iii) computation of test statistics based on inter-point distances and (iv) embedding of the test statistics within a permutation test. The proposed testing procedures are proven to be exact for every finite sample size and consistent. Two new test statistics based on inter-point distances (i.e., IP-Student and IP-Fisher) are defined and a method to combine them to get a further inferential tool (i.e., IP-StudentFisher) is introduced. Simulated data shows that tests with our statistic exhibit a statistical power that is either the best or second-best but very close to the best on a variety of possible $ Corresponding author alternatives hypotheses and other statistics. A second simulation study that aims at better understanding which features are captured by specific combinations of matrix representations and distances is presented. Finally, a case study on mobility networks in the city of Milan is carried out. The proposed framework is fully implemented in the R package nevada (NEtwork-VAlued Data Analysis).

Networks are a natural way of representing the human brain for studying its structure and function and, as such, have been extensively used. In this framework, case–control studies for understanding autism pertain to comparing samples of healthy and autistic brain networks. In order to understand the biological mechanisms involved in the pathology, it is key to localize the differences on the brain network. Motivated by this question, we hereby propose a general non‐parametric finite‐sample exact statistical framework that allows to test for differences in connectivity within and between prespecified areas inside the brain network, with strong control of the family‐wise error rate. We demonstrate unprecedented ability to differentiate children with non‐syndromic autism from children with both autism and tuberous sclerosis complex using electroencephalography data. The implementation of the method is available in the R package nevada.

This work describes the challenges, techniques, and methodologies to develop a digital tool that aims to improve framework conditions and tools for better utilization of Alpine natural resources in health tourism. Starting from the literature analysis and an online survey, the system implemented a comprehensive knowledge base adopted for an ontology-based Decision Support System leveraging on identified Key Performance Indicators (KPIs). Relying on this knowledge, the digital tool provides a list of tailored and customized recommendations for each destination within the Alpine area. This result helps the stakeholders capitalize on the nature-based health tourism potentials of their region in relation to the existence of the natural resources and different target users’ health conditions. This strategic digital tool is developed as a web-based application for destinations’ policy-makers and managers to fill the online survey and receive customized suggestions, recommendations, and insights on how to further exploit their natural resources in order to enhance nature-based health tourism.