The Complexity of Kings

A king in a directed graph is a node from which each node in the graph can be reached via paths of length at most two. There is a broad literature on tournaments (completely oriented digraphs), and it has been known for more than half a century that all tournaments have at least one king [Lan53]. Recently, kings have proven useful in theoretical computer science, in particular in the study of the complexity of the semifeasible sets [HNP98,HT05] and in the study of the complexity of reachability problems [Tan01,NT02]. In this paper, we study the complexity of recognizing kings. For each succinctly specified family of tournaments, the king problem is known to belong to $\Pi_2^p$ [HOZZ]. We prove that this bound is optimal: We construct a succinctly specified tournament family whose king problem is $\Pi_2^p$-complete. It follows easily from our proof approach that the problem of testing kingship in succinctly specified graphs (which need not be tournaments) is $\Pi_2^p$-complete. We also obtain $\Pi_2^p$-completeness results for k-kings in succinctly specified j-partite tournaments, $k,j \geq 2$, and we generalize our main construction to show that $\Pi_2^p$-completeness holds for testing k-kingship in succinctly specified families of tournaments for all $k \geq 2$

Some Characteristics of Islamic Journalism Based on Al Quran

Prophet Muhammad SAW as a role model has been made and gives examples of how the application of journalism itself. Prophet does his message through writing, that is, when he sends a letter to the kings or heads of tribes in Madinah in order to invite to the road of Islam. A journalist should be able to convince mad'u let that propaganda purposes can take place without any problem. Journalistic as a method in a very strategic propaganda.Beside it can be enjoyed by many people, the product of journalism also can be more lasting or durable, because it can be stored or read anytime. Journalism propagation of Islam is actually not a new method of propaganda, because the Prophet has implemented a method of propaganda by sending a letter of propaganda to the kings who do not know and embrace Islam

Changes In Submersed Macrophytes In Relation To Tidal Storm Surges

We analyzed long-term submersed macrophyte presence-absence data collected from 15 stations in Kings Bay/Crystal River, Florida in relation to three major storm events. The percent occurrence of most species declined immediately after storm events but the recovery pattern after the storm differed among species. Hydrilla (Hydrilla verticillata (L.F.) Royle)and Eurasian watermilfoil (Myriophyllum spicatum L.) exhibited differing recolonization behaviors. Eurasian watermilfoil recolonized quickly after storms but declined in abundance as hydrilla began to increase in abundance. Natural catastrophic events restructure submersed macrophyte communities by eliminating the dominate species, and allowing revegetation and restructuring of communities. Tidal surges may also act to maintain species diversity in the system. In addition, catastrophic events remove dense nuisance plant growth for several years, altering the public's perception of the nuisance plant problem of Kings Bay/Crystal River

Domination in Isosceles Triangular Chessboard

In this article, we are interested in the domination problem in isosceles triangular chessboard. In our study we take in account one type of piece of rooks, bishops and kings, and two different types of pieces together, kings with rooks, kings with bishops and rooks with bishops. The chessboard in this work is isosceles triangular with square cells. Also in most cases we determine the possible number of different methods of domination (total solution). Keywords: domination, Isosceles triangle chessboard, Kings, Bishops and Rooks

Reflections on the n+k Dragon Kings Problem

A dragon king is a shogi piece that moves any number of squares vertically or horizontally or one square diagonally but does not move through or jump over other pieces. We construct infinite families of solutions to the n + k dragon kings problem of placing k pawns and n + k mutually nonattacking dragon kings on an n+n board, including solutions symmetric with respect to quarter-turn or half-turn rotations, solutions symmetric with respect to one or two diagonal reflections, and solutions not symmetric with respect to any nontrivial rotation or reflection. We show that an n + k dragon kings solution exists whenever n \u3e k + 5 and that, given some extra conditions, symmetric solutions exist for n \u3e 2k + 5

Nurturing Breakthroughs: Lessons from Complexity Theory

A general theory of innovation and progress in human society is outlined, based on the combat between two opposite forces (conservatism/inertia and speculative herding "bubble" behavior). We contend that human affairs are characterized by ubiquitous ``bubbles'', which involve huge risks which would not otherwise be taken using standard cost/benefit analysis. Bubbles result from self-reinforcing positive feedbacks. This leads to explore uncharted territories and niches whose rare successes lead to extraordinary discoveries and provide the base for the observed accelerating development of technology and of the economy. But the returns are very heterogeneous, very risky and may not occur. In other words, bubbles, which are characteristic definitions of human activity, allow huge risks to get huge returns over large scales. We outline some underlying mathematical structure and a few results involving positive feedbacks, emergence, heavy-tailed power laws, outliers/kings/black swans, the problem of predictability and the illusion of control, as well as some policy implications.Comment: 14 pages, Invited talk at the workshop Trans-disciplinary Research Agenda for Societal Dynamics (http://www.uni-lj.si/trasd in Ljubljana), organized by J. Rogers Hollingsworth, Karl H. Mueller, Ivan Svetlik, 24 - 25 May 2007, Ljubljana, Sloveni

MOHIST APPROACH TO THE RULE-FOLLOWING PROBLEM

The Mohist conceives the dao-following issue as how we can put dao in words and speeches into practice. The dao-following issue is the Mohist counterpart of Wittgenstein\u27s rule-following problem. This paper aims to shed light on the rule-following issue in terms of the Mohist answer to the dao-following problem. The early Mohist takes fa(法, standard)and the later Mohist takes lei(類, analogy)as the key to the dao-following issue. I argue that the way of fa is not viable. Fa comes in various forms, but all of them are regarded as being cut off from everyday life and therefore subject to various interpretations and, hence, incapable of action-guiding. On the other hand, the Mohist lei represents a kind of life world action drama. A lei situates various elements of action in the context of an everyday life scene. I argue that lei is more qualified than fa in answering to the dao-following issue. I also show that lei substantializes what McDowell calls the course between a Scylla and a Charybdis hinted in terms of Wittgenstein\u27s idea of custom, practice, and institution in regard to the rule-following problem

The Ironic Death of Josiah in 2 Chronicles

A discussion of the various accounts of the death of Josiah in the biblical books of Kings and Chronicles. The category of irony is used to describe the version in 2 Chronicles 35