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Virus spreading problems in wireless rechargeable sensor networks (WSNs) are becoming a hot topic, and the problem has been studied and discussed in recent years. Many epidemic spreading models have been introduced for revealing how a virus spreads and how a virus is suppressed. However, most of them assumed the sensors are not rechargeable sensors. In addition, most of existing works do not consider virus mutation problems. This paper proposes a novel epidemic model, including susceptible, infected, variant, low-energy and dead states, which considers the rechargeable sensors and the virus mutation factor. The stability of the proposed model is first analyzed by adopting the characteristic equation and constructing Lyapunov functions methods. Then, an optimal control problem is formulated to control the virus spread and decrease the cost of the networks by applying Pontryagin’s maximum principle. Finally, all of the theoretical results are confirmed by numerical simulation.

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

With the development of wireless rechargeable sensor networks (WRSNs), many scholars began to attach attention to network security under the spread of viruses. This paper mainly studies a novel low-energy-status-based model SISL (Susceptible, Infected, Susceptible, Low-Energy). The conversion process from low-energy nodes to susceptible nodes is called charging. It is noted that the time delay of the charging process in WRSNs should be considered. However, the charging process and its time delay have not been investigated in traditional epidemic models in WRSNs. Thus, the model SISL is proposed. The basic reproduction number, the disease-free equilibrium point, and the endemic equilibrium point are discussed here. Meanwhile, local stability and global stability of the disease-free equilibrium point and the endemic equilibrium point are analyzed. The addition of the time-delay term needs to be analyzed to determine whether it affects the stability. The intervention treatment strategy under the optimal control is obtained through the establishment of the Hamiltonian function and the application of the Pontryagin principle. Finally, the theoretical results are verified by simulations.

The traditional SIRS virus propagation model is used to analyze the malware propagation behavior of wireless rechargeable sensor networks (WRSNs) by adding a new concept: the low-energy status nodes. The SIRS-L model has been developed in this article. Furthermore, the influence of time delay during the charging behavior of the low-energy status nodes needs to be considered. Hopf bifurcation is studied by discussing the time delay that is chosen as the bifurcation parameter. Finally, the properties of the Hopf bifurcation are explored by applying the normal form theory and the center manifold theorem.

TMAC is a toolbox written in C++11 that implements algorithms based on a set of modern methods for large-scale optimization. It covers a variety of optimization problems, which can be both smooth and nonsmooth, convex and nonconvex, as well as constrained and unconstrained. The algorithms implemented in TMAC, such as the coordinate up- date method and operator splitting method, are scalable as they decompose a problem into simple subproblems. These algorithms can run in a multi-threaded fashion, either synchronously or asynchronously, to take advantages of all the cores available. TMAC architecture mimics how a scientist writes down an optimization algorithm. Therefore, it is easy for one to obtain a new algorithm by making simple modifications such as adding a new operator and adding a new splitting, while maintaining the multicore parallelism and other features. The package is available at https://github.com/uclaopt/TMAC.

This thesis focuses on coordinate update methods (CU), which are useful for solving problems involving large or high-dimensional datasets. Coordinate update methods decompose a problem into simple subproblems, where each updates one, or a small block of, variables while fixing others. These methods can deal with linear and nonlinear mappings, smooth and nonsmooth functions, as well as convex and nonconvex problems. In addition, they are easy to parallelize.The great performance of coordinate update methods depends on solving sim- ple subproblems. To derive simple subproblems for several new classes of appli- cations, this thesis systematically studies coordinate friendly (CF) operators that perform low-cost coordinate updates. Based on the discovered coordinate friendly operators, as well as operator splitting techniques, I obtained new coordinate up- date algorithms for a variety of problems in machine learning, image processing, as well as sub-areas of optimization. Several problems are treated with coordinate update for the first time in history.CU can be further scaled up to solve larger problems through asynchronous parallel (async-parallel) techniques. Asynchrony is crucial to parallel computing since it reduces synchronization wait, relaxes communication bottleneck, and thus speeds up computing significantly. I proposed ARock, an algorithmic framework in which multiple agents (machines, processors, or cores) update coordinates in an asynchronous parallel fashion. At each step of ARock, an agent updates a randomly selected coordinate based on possibly out-of-date information. Conver- gence results are established for solving fixed-point problems. Numerical tests on regression and equations show that ARock significantly outperforms its syn- chronous counterpart.The other novel contribution of this thesis is the introduction of an abstract framework for implementing asynchronous parallel algorithms on shared memory platforms. The programming model adopts the thread library from C++ at its lowest level. At the highest level, the goal is to enable fast prototyping of async- parallel algorithms. I developed a multilevel approach to reduce the gap between expert to low-level programming and novice-level programming. A spectrum of applications have been implemented under this framework.

In recent studies on sparse modeling, $l_q$ ($0, Comment: 35 pages, 11 figures

In recent studies on sparse modeling, $l_q$ ($0, Comment: 13 pages, 2 figures