Linear Information Coupling Problems

Many network information theory problems face the similar difficulty of single letterization. We argue that this is due to the lack of a geometric structure on the space of probability distribution. In this paper, we develop such a structure by assuming that the distributions of interest are close to each other. Under this assumption, the K-L divergence is reduced to the squared Euclidean metric in an Euclidean space. Moreover, we construct the notion of coordinate and inner product, which will facilitate solving communication problems. We will also present the application of this approach to the point-to-point channel and the general broadcast channel, which demonstrates how our technique simplifies information theory problems.Comment: To appear, IEEE International Symposium on Information Theory, July, 201

The Linear Information Coupling Problems

Many network information theory problems face the similar difficulty of single-letterization. We argue that this is due to the lack of a geometric structure on the space of probability distribution. In this paper, we develop such a structure by assuming that the distributions of interest are close to each other. Under this assumption, the K-L divergence is reduced to the squared Euclidean metric in an Euclidean space. In addition, we construct the notion of coordinate and inner product, which will facilitate solving communication problems. We will present the application of this approach to the point-to-point channel, general broadcast channel, and the multiple access channel (MAC) with the common source. It can be shown that with this approach, information theory problems, such as the single-letterization, can be reduced to some linear algebra problems. Moreover, we show that for the general broadcast channel, transmitting the common message to receivers can be formulated as the trade-off between linear systems. We also provide an example to visualize this trade-off in a geometric way. Finally, for the MAC with the common source, we observe a coherent combining gain due to the cooperation between transmitters, and this gain can be quantified by applying our technique.Comment: 27 pages, submitted to IEEE Transactions on Information Theor

Location of Poles for the Hastings-McLeod Solution to the Second Painlev\'{e} Equation

We show that the well-known Hastings-McLeod solution to the second Painlev\'{e} equation is pole-free in the region $\arg x \in [-\frac{\pi}{3},\frac{\pi}{3}]\cup [\frac{2\pi}{3},\frac{ 4 \pi}{3}]$, which proves an important special case of a general conjecture concerning pole distributions of Painlev\'{e} transcedents proposed by Novokshenov. Our strategy is to construct explicit quasi-solutions approximating the Hastings-McLeod solution in different regions of the complex plane, and estimate the errors rigorously. The main idea is very similar to the one used to prove Dubrovin's conjecture for the first Painlev\'{e} equation, but there are various technical improvements.Comment: 31 pages, 2 figures. Minor revision, to appear in Constructive Approximatio

What is Religious Misconduct: A Typological Analysis of the Crimes Motivated by Polytheistic Religion, Using the Chinese Folk Religion as an Example

In terms of political function, religion is usually defined by criminologists/sociologists as an institution of social control. While religion can assist state managers to maintain the status quo and to safeguard social order, religion, under certain circumstances, can become an antisocial force as well. In this paper, the criminogenic side of religions will be examined. By using the Chinese folk religion as an example, this paper will demonstrate that polytheistic religions can become unstable social organizations. Four topics will be addressed in this paper. First, the research paradigms that can help crime researchers examine the subject of religious misconduct will be summarized. Then the features shared by polytheistic religions will be proposed. The third part will look at the primary traits of Chinese folk religion. Finally, by using the Chinese folk religion as an instance, the diverse contexts under which polytheistic religions can breed deviant/criminal behaviors will be analyzed

Neuro-evolution search methodologies for collective self-driving vehicles

Recently there has been an increasing amount of research into autonomous vehicles for real-world driving. Much progress has been made in the past decade with many automotive manufacturers demonstrating real-world prototypes. Current predictions indicate that roads designed exclusively for autonomous vehicles will be constructed and thus this thesis explores the use of methods to automatically produce controllers for autonomous vehicles that must navigate with each other on these roads. Neuro-Evolution, a method that combines evolutionary algorithms with neural networks, has shown to be effective in reinforcement-learning, multi-agent tasks such as maze navigation, biped locomotion, autonomous racing vehicles and fin-less rocket control. Hence, a neuro-evolution method is selected and investigated for the controller evolution of collective autonomous vehicles in homogeneous teams. The impact of objective and non-objective search (and a combination of both, a hybrid method) for controller evolution is comparatively evaluated for robustness on a range of driving tasks and collection sizes. Results indicate that the objective search was able to generalise the best on unseen task environments compared to all other methods and the hybrid approach was able to yield desired task performance on evolution far earlier than both approaches but was unable to generalise as effectively over new environments

Environmental justice and public participation :a case study of nuclear waste managment and policy in Taiwan

PhD Thesisusing an environmental justice approach. This research comprises three parts: first, the nature of radioactive waste; second, the theory of environmental justice; and third, the case study of nuclear waste siting policy in Taiwan. In the first part, background information is provided to understand what nuclear waste is; how it has been managed in different countries; and the difficulties and uncertainties of nuclear waste management. In the second part of this research, the idea of environmental justice is employed as a theoretical framework to interpret nuclear waste policy and the policy process in Taiwan. Environmental justice is derived from the environmental justice movement in the late 1970s and early 1980s. Environmental justice issues are two-fold: distributive justice refers to the distribution of environmental risks among different communities, and procedural justice refers to the access of citizens to decision-making processes that affect their environment. Finally, the case study of nuclear waste management and politics in Taiwan serves as the third part of this project. Through the lens of principles of environmental justice, the historical development of nuclear waste in Taiwan is examined. The process and progress of protracted attempts to site a new nuclear waste repository in Taiwan is investigated in considerable detail by conducting interviews with government officials, NGOs, and members of local communities. Particular attention was paid to the decision-making process and to the involvement of minority and low income iii communities in that process. The overall purpose of this project is to determine how far the ideas and principles of environmental justice have informed the nuclear waste management policies of Taiwan. By examining how consistent nuclear waste management in Taiwan complies with the idea of environmental justice, this project contributes to the growing literature on an urgent policy issue, and helps members of local communities, government officials and politicians to develop a greater awareness of the problems and issues of nuclear waste