Constructing liberal and conservative supertrees and exact solutions for reduced consensus problems

This thesis studies two different approaches to extracting information from collections of phylogenetic trees: supertrees and reduced consensus. Supertree methods combine the phylogenetic information from multiple partially-overlapping trees into a larger phylogenetic tree called a supertree. Several supertree construction methods have been proposed to date, but most of these are not designed with any specific properties in mind. Recently, Cotton and Wilkinson proposed extensions of the majority-rule consensus tree method to the supertree setting that inherit many of the appealing properties of the former. We study a variant of one of Cotton and Wilkinson\u27s methods, called majority-rule (+) supertrees. After proving that a key underlying problem for constructing majority-rule (+) supertrees is NP-hard, we develop a polynomial-size exact integer linear programming formulation of the problem. We then present a data reduction heuristic that identifies smaller subproblems that can be solved independently. While this technique is not guaranteed to produce optimal solutions, it can achieve substantial problem-size reduction. Finally, we report on a computational study of our approach on various real data sets, including the 121-taxon, 7-tree Seabirds data set of Kennedy and Page. The results indicate that our exact method is computationally feasible for moderately large inputs. For larger inputs, our data reduction heuristic makes it feasible to tackle problems that are well beyond the range of the basic integer programming approach. Comparisons between the results obtained by our heuristic and exact solutions indicate that the heuristic produces good answers. Our results also suggest that the majority-rule (+) approach, in both its basic form and with data reduction, yields biologically meaningful phylogenies. Generalizations of the strict and loose consensus methods to the supertree setting, recently introduced by McMorris and Wilkinson, are studied. The supertrees these methods produce are conservative in the sense that they only preserve information (in the form of splits) that is supported by at least one the input trees and that is not contradicted by any of the input trees. Alternative, equivalent, formulations of these supertrees are developed. These are used to prove the NP-completeness of the underlying optimization problems and to give exact integer linear programming solutions. For larger data sets, a divide and conquer approach is adopted, based on the structural properties of these supertrees. Experiments show that it is feasible to solve problems with several hundred taxa and several hundred trees in a reasonable amount of time. A rogue taxon in a collection of phylogenetic trees is one whose position varies drastically from tree to tree. The presence of such taxa can greatly reduce the resolution of the consensus tree (e.g., the majority-rule or strict consensus) for a collection. The reduced consensus approach aims to identify rogue taxa and to produce more informative consensus trees. Given a collection of phylogenetic trees over the same leaf set, the goal is to find a set of taxa whose removal maximizes the number of internal edges in the consensus tree of the collection. This problem is proven to be NP-hard for strict and majority-rule consensus. We describe exact integer linear programming formulations for computing reduced strict, majority and loose consensus trees. In experimental tests, our exact solutions show significant improvement over heuristic methods on several problem instances

Calligraphy Tablets in the Forbidden City

The calligraphy tablets hung over each main gate and building in Beijing’s Forbidden City, although often neglected by visitors, actually are special embodiments of traditional Chinese concepts either well known or maybe unexpected by their readers. Besides explaining architectural functions, the tablets also can be read as means of decorating the architecture, conveying political ideals, advocating academic achievements, expressing good wishes and depicting charming sceneries

A study of the applicability of policy making theories in post-Mao China (1978-1995)

PhD ThesisTo examine the applicability of a range of policy making theories and models, which created by Western scholars, to the practice of post-Mao China is significant in view of what follows. First, to explore to what extent they are applicable to interpret China's practice is beneficial for both absorbing the useful elements from them and discovering and understanding the general features of China's policy making process. Second, particularly, in the post-Mao period, some remarkable changes in China's policy-making pattern have ended a period of stagnation which had lasted for nearly two centuries, and started a course of rejuvenation characterised by rapid economic growth and social prosperity. Thus, these changes and development are well worthy of study with the assistance of above-mentioned theories and models. Aiming at exploring the applicability of these theories and models and how and to what extent these changes occurred and influenced China's policy making processes in all major aspects including policy makers, motivation, policy-making methods, political environment and institutions, this thesis studied the development course (1978-1995) of China's Special Economic Zones (SEZ), which was an important programme of China's reform and opening-up strategy. In doing so, the thesis adopted a method that probes the major features, changes and development of the policy making process in post-Mao China, through examining the applicability of some selected policy making theories and models in China's practice. These selected theories and models consist of those concerning how policy is made, and those relating to how policy should be made. The above examination achieved two goals, which include (a) demonstrating the extent to which each of these theories and models can be used to observe and analyse Chinese policy making practice respectively and their reasons as well, and (b) obtaining the main findings of the thesis about China's policy making process in the post-Mao period as below. (1) Although Marxism was still the fundamental guiding thought of China's policy making, a great flexibility had been adopted, which enabled a series of new policies to be made in last two decades. (2) The twin approaches of incrementalism and pragmatism were the foundation of China's policy-making mechanism, which powerfully promoted its successful operation. (3) The rise of a pluralist tendency significantly influenced China's policy process, which included the increasing involvement of the non-CPC (Communist Party of China) or non-government political and social forces. (4) Political elites continued to dominate China's policy-making process, and this central role was much more prominent than it was in other modern countries. (5) Existing institutions were decisive in shaping China's policy-making mode, by determining the power structure and the power relations within which the policy-making actions taken place