We aim to understand the transient dynamics of a susceptible-infected (SI) epidemic process over a large network. The SI model has been largely overlooked in the literature, while it is naturally a good fit for modeling the malware propagation in view of the difficulty of its immediate countermeasure, which makes other recovery-enabled epidemic models impractical. Nonetheless, its analysis is simply nontrivial, as its important dynamics are all transient and the usual stability/steady-state analysis no longer applies. To this end, we develop a theoretical framework that allows us to obtain an accurate closed-form approximate solution to the original SI dynamics on a general graph, capturing the temporal dynamics over all time, and also to provide a new interpretation via reliability theory. As its applications, we further develop vaccination policies with or without knowledge of already-infected nodes, to mitigate the future epidemic spreading to the extent possible, and demonstrate their effectiveness through numerical simulations.

Recent years have witnessed that online social networks (OSNs) change the way people interact with each other and trigger a tremendous amount of attention in various disciplines because of their extensive applications and massive useful data. They are simply too large to be downloaded or stored locally, and the sheer size forces us to resort to ���������������sampling������������������ for estimation and inference of massive networks in a compact manner. In particular, sampling via random-walk crawling has been commonly considered as the only viable solution, which is feasible via the public yet restrictive local-neighborhood-only interfaces provided by OSNs, for estimating the properties of users (nodes), their relationships (edges), and more sophisticated relationship among multiple users (subgraph patterns). Whereas there have been many efforts in the literature to advance our understanding on sampling via random-walk crawling, there are still important challenges that have been generally overlooked and remained unsolved. The long-term goal of the proposed research is to build a strong theoretical foundation for the optimal sampling strategies and the optimal control of multiple random walks for the estimation and inference of massive networks in the cost-constrained environments in reality, going beyond the current Markov Chain Monte Carlo (MCMC) driven statistical theories and practices for graph sampling in the literature.

The practice and experience in more than a decade have demonstrated that spectrum sharing is difficult: opportunistic spectrum access by secondary systems has a major technical hurdle it is difficult to accurately sense the spectrum band status and detect a new primary signal while the secondary communication is ongoing. At the same time, it is factual that we have many existing and upcoming wireless access technologies, which have an acute demand for spectrum sharing and better utilization than today. We believe that the current difficulty to realize the full potential of radio spectrum is due to the binding of a wireless service to a specific radio spectrum. In other words, most of the prior studies focused on algorithms and protocols to improve spectrum efficiency, but paid less attentions to how these solutions will eventually benefit the users. With today's huge number of wireless devices and ever-increasing new wireless services, we need a new paradigm to separate wireless services from radio spectrum, so that the radio spectrum is abstracted and mapped to a wireless service only when it is needed, rather than a static binding for years. Therefore, we propose to study a Multi-Layer wireless networks in the sense that each access technology being a radio layer, and each wireless device being able to user multiple wireless interfaces for opportunistic access. Our objective is to build a theoretical framework that stemming from detecting and identifying radio spectrum in a geographical region, to selecting an optimal access band or channel from an individual device's perspective, and further to achieve rendezvous with common channels for pair-wise communications, and eventually building device-to-device communications via single-hop and multi-hop networking architecture.

In this project, we plan to explore fundamental issues that advance our understanding of using mobile clouds in deliverying wireless data traffic. In other words, we aim to find out whether and under what conditions mobile clouds are feasible for providing mobile application services or not and whether there exist theoretical limits or guidelines that can help or hinder the development of mobile clouds. An in-depth understanding of such questions would greatly help emerging new applications over mobile platform. Therefore, we propose to focus on four inter-correlated, equally important issues toward building blocks of a theoretical foundation for mobile cloud computing, that is, evolution of single-hop mobile cloudlet, performance of opportunistic mobile cloudlet, efficient discovery of neighboring cloudlets and spatial-temporal properties of mobile-to-cloud. In particular, we consider the data transportation over the wireless sector in which our main objective is to have a close-up of formation and evolution of mobile cloudlet over time, with possible intermediate relays, and ends up with base stations or access points.

Designing efficient and distributed algorithms has been central to almost all large networked systems. Examples include crawling-based sampling of large online social networks, statistical estimation or inference from massive scale of networked data, efficient searching algorithms in unstructured peerto-peer networks, randomized routing and duty-cycling algorithm for better performance-energy tradeoff in wireless sensor networks, and distributed scheduling algorithms leading to maximal throughput and smaller delay in multihop wireless networks, to list a few. Except for small-sized, static networks for which centralized design is not much of an issue, virtually all large networks necessarily demand distributed algorithms for inherent lack of global information and also randomized algorithms for autonomous load balancing and their resilience/robustness against possible points of failure/attacks, yet often with close-to-optimal performance.

Over the last several decades, mobility has been central to various applications, ranging from the classical problems of searching for a moving target and rescue mission in military and disaster settings, to deploying mobile ad-hoc/sensor networks for surveillance and data communication over hostile terrain and underwater. In particular, recent technological advances in communicating/sensing devices as well as abundant network protocols designed for mobile ad-hoc/sensor networks have opened up a new possibility for viable networks with satisfying performance over such unpredictable, mobile, and disadvantaged environments. While the random mobility pattern of mobile nodes in these networks has posed serious challenges and been considered as the main source of uncertainty and disruption of communication links among nodes, the mobility can also enable us to achieve reliable and predictable performance, if it is properly controlled and actively exploited. The long-term goal of this proposed research is to develop a unified methodology for efficient protocol design and control of nodes in heterogeneous MANETs under non-Poisson contacts. While the non-Poisson contacts and inherent heterogeneity among mobile nodes pose serious challenge, we take this challenge as a golden opportunity toward `high-performance' MANETs, by exploiting unknown heterogeneity and non-Poisson dynamics in an adaptive but rigorous manner. Our goal further extends to the use of mobile nodes with controllable mobility that can autonomously exploit the changing diversity in non-Poisson heterogeneous dynamics of nodes' mobility.

This proposal focuses on the theoretical foundation for wireless mobile networks, particularly on the characterization of link-level dynamics by a stochastic analysis approach. Advancements in embedded wireless devices, together with the wireless networking technologies, have driven a ``mobile social networks'' which are a dominant part of our working and non-working lives. The usage of wireless devices unavoidably induce user mobility in diverse settings over multiple space/time scales, ranging from traditional cellular phone users and Wi-Fi users in moderate-to-dense networks, to nomadic users and mobile robots/sensors in multi-hop wireless ad-hoc networks and delay/disruption-tolerant networks (DTNs) over larger space/time scales. In all these scenarios, the users' mobility is the fundamental source of uncertainty and randomness as it translates into spatial-temporal changes in the link-level dynamics, which in turn affects every corner of the performance of network algorithms and protocols running over these mobile users. A detailed research plan is proposed which addresses the unique challenges presented by mobility-induced link dynamics. This plan concerns not only fundamental understanding of {\em delay-sensitive} communication networks, it also studies contact/inter-contact dynamics in {\em delay-tolerant} networks which may play an important role in mobile social networks. In particular, the research plan focuses on three issues: (1) Modeling, analysis, and statistical characterization of mobility-induced link dynamics. Our objective is to study a set of metrics at the link-level, such as inter-contact time, residual link lifetime, path-breakage rate, and more because of their immediate effects on network design and performance. More importantly, we will provide a plethora of statistical properties over a wide range of {\em timescales} as well as {\em physical environments} via microscopic link modeling and stochastic ordering. These works, which have not been carefully investigate before, clearly distinguish our proposed work. (2) Spatial-Temporal Dynamics in mobility modeling in multiple space/time scales rather than being dependent on {\em a priori} networking environments. In particular, we take a multiscale mobility modeling approach to capture the interdependency between spatial and temporal dynamics of mobile nodes, such as diffusive behaviors. In a stochastic setting, mean square displacement (MSD) is used to study {\em micro-scale, meso-scale, macro-scale} mobility trajectory and their impact on link-level dynamics by quantifying the degree of spatio-temporal interdependencies among link-level metrics and the network operating points. Therefore, our results will provide an integrated framework of mobility modeling and operation regime. (3) The scaling limits for link-level metrics under various network operating regimes. As a new research thrust, we will develop a systematic approach to explore scaling regime subject to network architecture and configuration, such as the number of mobile nodes, size of the domain, and employed forwarding/routing algorithms. Specifically, we will identify the inherent causes of Poisson limits as a limiting random process that occurs in various mobile ad-hoc networks. Further, we will find the scaling regime that is valid for different time-scale link-level dynamics.

The current Internet is the most complicated man-made system in which an enormous degree of largeness coexists with heterogeneity. As the size of the network and the number of concurrent end-users increases, the number of possible states for all users in the network also grows at an exponential rate. The sheer dimension of a space over which those interactions take place severely limits our ability to describe and analyze such a large network. For a large network with many users, the so-called ``fluid'' modeling or ``mean-field'' approach has proven extremely successful and versatile. From a microscopic point of view, each user or flow in a network is subject to network protocols or probabilistic laws that specify how it should evolve depending on the current status of all users. When the network consists of an extremely large number of such users interacting with each other, however, it is impossible to obtain a complete, probabilistic description of the network status because there are so many probabilistic equations to solve. Instead of enumerating all possible interactions among users and the corresponding transitions to their next states, the mean-field approach, relying on probabilistic limit theories such as the law of large numbers, allows us to describe the average macroscopic behavior of network dynamics in terms of a set of relatively simple and deterministic difference/differential equations. As the fluid or mean-field approach offers intuitive and manageable solutions to describing large network dynamics, it has been the de facto technique for almost every aspect of current networking problems including congestion control, stability analysis, optimization-based techniques, as well as wireless multi-hop communications network. However, this mean-field type of approach has fundamental limitations; it is valid only when the system is scaled as required by the underlying theory. For other type of scaling the systems, the mean-field approach may break down and often wrongfully predict even the first-order system dynamics. Unfortunately, however, there hardly exists any result or even attempt to address these limitations and problems associated with the mean-field approach, and this confines our choice of network design to a very small subset of what can actually be chosen. Our goal in this project is to understand the fundamental limitations of the fluid or mean-field approach to many network problems, and as a remedy, to develop a stochastic approach to the analysis and design of large networks. By judiciously applying appropriate limit theory with key randomness inherent in the network dynamics still intact, we will provide new guidelines on large network design and achieve far better resource utilization, all of which are impossible to obtain via the traditional fluid or mean-field approach.