Network science has provided useful answers to research questions in many fields, from biology to social science, from ecology to urban science. The first analyses of networked systems focused on binary networks, where only the topology of the connections were considered. Soon network scientists started considering weighted networks, to represent interactions with different strength, cost, or distance in space and time. Also, connections are not fixed but change over time. This is why in more recent years, a lot of attention has been devoted to temporal or time-varying networks. We now entered the era of multi-layer networks, or multiplex networks, relational systems whose units are connected by different relationships, with links of distinct types embedded in different layers. Multiplexity has been observed in many contexts, from social network analysis to economics, medicine and ecology. The new challenge consists in applying the new tools of multiplex theory to unveil the richness associated to this novel level of complexity. How do agents organise their interactions across layers? How does this affect the dynamics of the system? In the first part of the thesis, we provide a mathematical framework to deal with multiplex networks. We suggest metrics to unveil multiplexity from basic node, layer and edge properties to more complicated structure at the micro- and meso-scale, such as motifs, communities and cores. Measures are validated through the analysis of real-world systems such as social and collaboration networks, transportation systems and the human brain. In the second part of the thesis we focus on dynamical processes taking place on top of multiplex networks, namely biased random walks, opinion dynamics, cultural dynamics and evolutionary game theory. All these examples show how multiplexity is crucial to determine the emergence of unexpected and instrinsically multiplex collective behavior, opening novel perspectives for the field of non-linear dynamics on networks.

Piecewise-smooth stochastic systems have attracted a lot of interest in the last decades in engineering science and mathematics. Many investigations have focused only on one-dimensional problems. This thesis deals with simple two-dimensional piecewise-smooth stochastic systems in the absence of detailed balance. We investigate the simplest example of such a system, which is a pure dry friction model subjected to coloured Gaussian noise. The nite correlation time of the noise establishes an additional dimension in the phase space and gives rise to a non-vanishing probability current. Our investigation focuses on stick-slip transitions, which can be related to a critical value of the noise correlation time. Analytical insight is provided by applying the uni ed coloured noise approximation. Afterwards, we extend our previous model by adding viscous friction and a constant force. Then we perform a similar analysis as for the pure dry friction case. With parameter values close to the deterministic stick-slip transition, we observe a non-monotonic behaviour of the probability of sticking by increasing the correlation time of the noise. As the eigenvalue spectrum is not accessible for the systems with coloured noise, we consider the eigenvalue problem of a dry friction model with displacement, velocity and Gaussian white noise. By imposing periodic boundary conditions on the displacement and using a Fourier ansatz, we can derive an eigenvalue equation, which has a similar form in comparison to the known one-dimensional problem for the velocity only. The eigenvalue analysis is done for the case without a constant force and with a constant force separately. Finally, we conclude our ndings and provide an outlook on related open problems.

This study investigated female students’ practices and experiences of using mobile technology for learning in Saudi higher education during the period of 2014-2017, and built a theoretical framework for mobile learning in this context. The rapid expansion of higher education in Saudi Arabia, coupled with the rapid increase in student numbers, is raising the need to find more effective ways to teach, reach and communicate with such a large student body. Mobile technology has been widely used in the context of Saudi higher education by both students and university teachers, but little is known about female students’ experiences of using mobile technology to support their learning. A better understanding of the context of mobile use in higher education in Saudi Arabia might help in exploiting the affordances of mobile technology for learning purposes and uses. As a contribution to innovations in Saudi higher education, this study explored mobile learning experiences of Saudi female students at one of the universities in Saudi Arabia, King Saud University. The study implemented a case study methodology and used a qualitative-led mixed methods design. A large-scale online survey of 7,865 female students provided information about the ownership and practices of mobile technology among higher education students; the extent of Internet access via mobile technology, as well as times, locations, and purposes of the use. The study also investigated the opportunities provided by mobile technology that enhance and foster learning experiences for higher education students through an in-depth investigation of 52 participants through personal diaries, group interviews and in-depth, semistructured interviews. The contribution to knowledge lays in the development of a theoretical framework for mobile learning to describe contemporary practices and experiences in Saudi higher education. Themes of mobile learners’ ubiquitous use, mobile learners’ movement, and mobile learners’ strategies for achieving learning goals emerged through the analysis. One major conclusion of the research is that, as a country with a gender segregated education system and very strong cultural demands on women, mobile learning enables Saudi females to negotiate their way through the different constraints, restrictions and boundaries that prevent or hinder them in their learning process, while maintaining their own cultural values, principles and traditions. The research concluded that the mobile learning framework, in the context of Saudi females in higher education, is about active learners showing their agency through appropriating tools and resources, crossing boundaries of contexts, and personalizing their learning with and through the use of their mobile technology as a cultural resource and boundary-crossing tool to accomplish learning tasks, purposes and goals.

Thesis (M.S.)--Rutgers University, 2009. / "Graduate Program in Mathematical Sciences." Includes bibliographical references (p. 40).

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematical Sciences." Includes bibliographical references (p. 74).

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