arXiv subjects
Publications and source records attributed to Lu Liu.
We prove that $\mathsf{RCA}_0+\mathsf{RT}_2^2\not\rightarrow \mathsf{WKL}_0$ by showing that for any set $C$ not of PA-degree and any set $A$, there exists an infinite subset $G$ of $A$ or $\bar{A}$, such that $G\oplus C$ is also not of PA-degree.
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional integration/differentiation, and the simulation of fractional order systems. Time to time, being asked about which tool is suitable for a specific application, the authors decide to carry out this survey to present recapitulative information of the available tools in the literature, in hope of benefiting researchers with different academic backgrounds. With this motivation, the present article collects the scattered tools into a dashboard view, briefly introduces their usage and algorithms, evaluates the accuracy, compares the performance, and provides informative comments for selection.
Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We investigate entanglement detection using sets of MUMs and derived separability criteria for $d$-dimensional multipartite systems, and arbitrary high-dimensional bipartitie and multipartite systems. These criteria provide experimental implementation in detecting entanglement of unknown quantum states.
Multi-radio multi-channel (MR-MC) networks contribute significant enhancement in the network throughput by exploiting multiple radio interfaces and non-overlapping channels. While throughput optimization is one of the main targets in allocating resource in MR-MC networks, recently, the network energy efficiency is becoming a more and more important concern. Although turning on more radios and exploiting more channels for communication is always beneficial to network capacity, they may not be necessarily desirable from an energy efficiency perspective. The relationship between these two often conflicting objectives has not been well-studied in many existing works. In this paper, we investigate the problem of optimizing energy efficiency under full capacity operation in MR-MC networks and analyze the optimal choices of numbers of radios and channels. We provide detailed problem formulation and solution procedures. In particular, for homogeneous commodity networks, we derive a theoretical upper bound of the optimal energy efficiency and analyze the conditions under which such optimality can be achieved. Numerical results demonstrate that the achieved optimal energy efficiency is close to the theoretical upper bound.
The Enhanced Distributed Channel Access (EDCA) specification in the IEEE 802.11e standard supports heterogeneous backoff parameters and arbitration inter-frame space (AIFS), which makes a selfish node easy to manipulate these parameters and misbehave. In this case, the network-wide fairness cannot be achieved any longer. Many existing misbehavior detectors, primarily designed for legacy IEEE 802.11 networks, become inapplicable in such a heterogeneous network configuration. In this paper, we propose a novel real-time hybrid-share (HS) misbehavior detector for IEEE 802.11e based wireless local area networks (WLANs). The detector keeps updating its state based on every successful transmission and makes detection decisions by comparing its state with a threshold. We develop mathematical analysis of the detector performance in terms of both false positive rate and average detection rate. Numerical results show that the proposed detector can effectively detect both contention window based and AIFS based misbehavior with only a short detection window.
MapReduce has emerged as a popular method to process big data. In the past few years, however, not just big data, but fast data has also exploded in volume and availability. Examples of such data include sensor data streams, the Twitter Firehose, and Facebook updates. Numerous applications must process fast data. Can we provide a MapReduce-style framework so that developers can quickly write such applications and execute them over a cluster of machines, to achieve low latency and high scalability? In this paper we report on our investigation of this question, as carried out at Kosmix and WalmartLabs. We describe MapUpdate, a framework like MapReduce, but specifically developed for fast data. We describe Muppet, our implementation of MapUpdate. Throughout the description we highlight the key challenges, argue why MapReduce is not well suited to address them, and briefly describe our current solutions. Finally, we describe our experience and lessons learned with Muppet, which has been used extensively at Kosmix and WalmartLabs to power a broad range of applications in social media and e-commerce.
This paper presents Privilege Calculus (PC) as a new approach of knowledge representation for Separation of Duty (SD) in the view of process and intents to improve the reconfigurability and traceability of SD. PC presumes that the structure of SD should be reduced to the structure of privilege and then the regulation of system should be analyzed with the help of forms of privilege.