Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

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Table Of Integrals Series And Products

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

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The knowledge complexity of interactive proof-systems

Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

Fixed Point Theory

Internet of Things security

This paper investigates a critical access control issue in the Internet of Things (IoT). In particular, we propose a smart contract-based framework, which consists of multiple access control contracts (ACCs), one judge contract (JC), and one register contract (RC), to achieve distributed and trustworthy access control for IoT systems. Each ACC provides one access control method for a subject-object pair, and implements both static access right validation based on predefined policies and dynamic access right validation by checking the behavior of the subject. The JC implements a misbehavior-judging method to facilitate the dynamic validation of the ACCs by receiving misbehavior reports from the ACCs, judging the misbehavior and returning the corresponding penalty. The RC registers the information of the access control and misbehavior-judging methods as well as their smart contracts, and also provides functions (e.g., register, update, and delete) to manage these methods. To demonstrate the application of the framework, we provide a case study in an IoT system with one desktop computer, one laptop and two Raspberry Pi single-board computers, where the ACCs, JC, and RC are implemented based on the Ethereum smart contract platform to achieve the access control.

Smart Contract-Based Access Control for the Internet of Things

Adaptive traffic signal control, which adjusts traffic signal timing according to real-time traffic, has been shown to be an effective method to reduce traffic congestion. Available works on adaptive traffic signal control make responsive traffic signal control decisions based on human-crafted features (e.g. vehicle queue length). However, human-crafted features are abstractions of raw traffic data (e.g., position and speed of vehicles), which ignore some useful traffic information and lead to suboptimal traffic signal controls. In this paper, we propose a deep reinforcement learning algorithm that automatically extracts all useful features (machine-crafted features) from raw real-time traffic data and learns the optimal policy for adaptive traffic signal control. To improve algorithm stability, we adopt experience replay and target network mechanisms. Simulation results show that our algorithm reduces vehicle delay by up to 47% and 86% when compared to another two popular traffic signal control algorithms, longest queue first algorithm and fixed time control algorithm, respectively.

Adaptive Traffic Signal Control: Deep Reinforcement Learning Algorithm with Experience Replay and Target Network

Wireless communication is one of the key technologies that actualize the Internet of Things (IoT) concept into the real world. Understanding the security performance of wireless communications lays the foundation for the security management of IoT. Eavesdropper collusion represents a significant threat to wireless communication security, while physical-layer security serves as a promising approach to providing a strong form of security guarantee. This paper studies the important secrecy outage performance of wireless communications under eavesdropper collusion, where the physical layer security is adopted to counteract such attack. Based on the classical Probability Theory, we first conduct analysis on the secrecy outage of the simple noncolluding case in which eavesdroppers do not collude and operate independently. For the secrecy outage analysis of the more hazardous M-colluding scenario, where any $M$ eavesdroppers can combine their observations to decode the message, the techniques of Laplace transform, keyhole contour integral, and Cauchy Integral Theorem are jointly adopted to work around the highly cumbersome multifold convolution problem involved in such analysis, such that the related signal-to-interference ratio modeling for all colluding eavesdroppers can be conducted and thus the corresponding secrecy outage probability can be analytically determined. Finally, simulation and numerical results are provided to illustrate our theoretical achievements. An interesting observation suggests that the SOP increases first superlinearly and then sublinearly with $M$ .

On Secure Wireless Communications for IoT Under Eavesdropper Collusion

The Internet of Things has been widely deployed in various areas of daily life through heterogeneous communications protocols. Each unstandardized protocol focuses on a specific IoT communication pattern. Inspired by the Internet architecture over which divergent devices can easily be accessed and a considerable number of applications can be run, we propose a generic architecture for IoT. This architecture supports two DIY areas: network DIY for data aggregation and application DIY for service cooperation. To connect these two DIYs, a centralized controller has been designed to provide standardized interfaces for data acquisition, organization, and storage, and to support elastic and supportive computing. With these properties, divergent devices can coexist in a uniform microworld, and rich services can be developed and provided on demand to interoperate with physical devices. This article discusses the background, design principles, and advantages of the proposed architecture, as well as open problems and our initial solution, which substantiates a novel IoT architecture and new research ground.

MicroThings: A Generic IoT Architecture for Flexible Data Aggregation and Scalable Service Cooperation

This paper investigates the fundamental issues of mode selection and spectrum partition in cellular networks with in-band device-to-device (D2D) communication from the physical-layer security (PLS) perspective. We consider a mode selection scheme allowing each D2D pair to probabilistically switch between the underlay and overlay modes, and also a spectrum partition scheme where the system spectrum is orthogonally partitioned between cellular and overlay D2D communications. We first develop a general theoretical framework to model the secrecy outage and secrecy capacity performance of cellular users as well as the outage and capacity performance of D2D pairs. Optimization problems are also solved to identify the optimal mode selection and spectrum partition for secrecy capacity maximization and secrecy outage probability minimization. A case study is then provided to demonstrate the application of our theoretical framework for performance modeling and optimization, and also to illustrate the impacts of mode selection and spectrum partition on the PLS performances of in-band D2D communications.

Yulong Shen

Papers

Smart Contract-Based Access Control for the Internet of Things

Adaptive Traffic Signal Control: Deep Reinforcement Learning Algorithm with Experience Replay and Target Network

On Secure Wireless Communications for IoT Under Eavesdropper Collusion

MicroThings: A Generic IoT Architecture for Flexible Data Aggregation and Scalable Service Cooperation

Mode Selection and Spectrum Partition for D2D Inband Communications: A Physical Layer Security Perspective