Travelling Randomly on the Poincar\'e Half-Plane with a Pythagorean Compass

A random motion on the Poincar\'e half-plane is studied. A particle runs on the geodesic lines changing direction at Poisson-paced times. The hyperbolic distance is analyzed, also in the case where returns to the starting point are admitted. The main results concern the mean hyperbolic distance (and also the conditional mean distance) in all versions of the motion envisaged. Also an analogous motion on orthogonal circles of the sphere is examined and the evolution of the mean distance from the starting point is investigated

Fractional diffusions with time-varying coefficients

This paper is concerned with the fractionalized diffusion equations governing the law of the fractional Brownian motion $B_H(t)$. We obtain solutions of these equations which are probability laws extending that of $B_H(t)$. Our analysis is based on McBride fractional operators generalizing the hyper-Bessel operators $L$ and converting their fractional power $L^{\alpha}$ into Erd\'elyi--Kober fractional integrals. We study also probabilistic properties of the r.v.'s whose distributions satisfy space-time fractional equations involving Caputo and Riesz fractional derivatives. Some results emerging from the analysis of fractional equations with time-varying coefficients have the form of distributions of time-changed r.v.'s

Ergodicity breaking in strong and network-forming glassy system

The temperature dependence of the non-ergodicity factor of vitreous GeO$_2$, $f_{q}(T)$, as deduced from elastic and quasi-elastic neutron scattering experiments, is analyzed. The data are collected in a wide range of temperatures from the glassy phase, up to the glass transition temperature, and well above into the undercooled liquid state. Notwithstanding the investigated system is classified as prototype of strong glass, it is found that the temperature- and the $q$-behavior of $f_{q}(T)$ follow some of the predictions of Mode Coupling Theory. The experimental data support the hypothesis of the existence of an ergodic to non-ergodic transition occurring also in network forming glassy systems

Invasive Crayfish moving Northwards: management challenges and policy implications at the local scale

Freshwater ecosystems in Italy, as most European countries, have been severely impacted by the invasion of alien crayfish. The two most widespread species in Trentino (NE Italy) are Procambarus clarkii and Faxionus limosus; for both species, the high elevation and cold climate of most of the Trentino territory represent a climatic barrier to their northwards spread. Procambarus clarkii is present in one small lake at 950 m asl, and Faxionus limosus in a group of 5 lakes at 450 m asl, over an area of about 80km2. the introduction of both species is associated with fish restocking, and lead to the extinction of existing populations of the native stone crayfish Austropotamobius pallipes. The Management Plan of Austropotamobius pallipes in Trentino listed the eradication/containment of these IAS populations among the conservation priorities for the native populations. The eradication campaigns of P. clarkii started in 2018 with a release/recapture campaign aimed at assessing the abundance of the populations, and continued in 2020, 2021, 2022. As a result, the capture efficiency decreased, suggesting a population reduction trend. The containment of Faxionus limosus is more difficult, given its presence in a higher number of lakes, three of which are hydrologically connected. A first containment campaign to prevent its spread in the river network is planned for summer 2023. The financial support to these activities has been granted by the local Nature 2000 networks and by the local administrations, which have also promoted the communication with citizens and stakeholders to raise consensus and collaboratio

Customer experience challenges: bringing together digital, physical and social realms

This paper discusses important societal issues, such as individual and societal needs for privacy, security, and transparency. It sets out potential avenues for service innovation in these areas

Large deviations for a damped telegraph process

In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as the level goes to infinity). Finally we compare our results with the analogous well-known results for the standard telegraph process

On the Decreasing Failure Rate property for general counting process. Results based on conditional interarrival times

In the present paper we consider general counting processes stopped at a random time $T$, independent of the process. Provided that $T$ has the decreasing failure rate (DFR) property, we give sufficient conditions on the arrival times so that the number of events occurring before $T$ preserves the DFR property of $T$. These conditions involve the study of the conditional interarrival times. As a main application, we prove the DFR property in a context of maintenance models in reliability, by the consideration of Kijima type I virtual age models under quite general assumptions

Le script de service fondements du concept et application au marketing des services

L'objectif de cet article est de clarifier et d\u2019approfondir le concept de script de service, un concept qui s\u2019origine dans la th\ue9orie psychologique des scripts cognitifs. L'article commence par la d\ue9finition du concept et l'analyse de ses fonctions. Il pr\ue9sente ensuite l'apport des scripts cognitifs \ue0 l'\ue9tude de trois th\ue8mes de recherche en marketing des services : la relation entre personnel en contact et client, le comportement du client et sa satisfaction. Enfin, il illustre les diff\ue9rentes mesures du script cognitif, discute les limites de ce concept et ses applications future