On the Imitation Strategy for Games on Graphs

In evolutionary game theory, repeated two-player games are used to study strategy evolution in a population under natural selection. As the evolution greatly depends on the interaction structure, there has been growing interests in studying the games on graphs. In this setting, players occupy the vertices of a graph and play the game only with their immediate neighbours. Various evolutionary dynamics have been studied in this setting for different games. Due to the complexity of the analysis, however, most of the work in this area is experimental. This paper aims to contribute to a more complete understanding, by providing rigorous analysis. We study the imitation dynamics on two classes of graph: cycles and complete graphs. We focus on three well known social dilemmas, namely the Prisoner's Dilemma, the Stag Hunt and the Snowdrift Game. We also consider, for completeness, the so-called Harmony Game. Our analysis shows that, on the cycle, all four games converge fast, either to total cooperation or total defection. On the complete graph, all but the Snowdrift game converge fast, either to cooperation or defection. The Snowdrift game reaches a metastable state fast, where cooperators and defectors coexist. It will converge to cooperation or defection only after spending time in this state which is exponential in the size, n, of the graph. In exceptional cases, it will remain in this state indefinitely. Our theoretical results are supported by experimental investigations.Comment: 32 page

A triangle process on graphs with given degree sequence

The triangle switch Markov chain is designed to generate random graphs with given degree sequence, but having more triangles than would appear under the uniform distribution. Transition probabilities of the chain depends on a parameter, called the activity, which is used to assign higher stationary probability to graphs with more triangles. In previous work we proved ergodicity of the triangle switch chain for regular graphs. Here we prove ergodicity for all sequences with minimum degree at least 3, and show rapid mixing of the chain when the activity and the maximum degree are not too large. As far as we are aware, this is the first rigorous analysis of a Markov chain algorithm for generating graphs from a a known non-uniform distribution.Comment: 35 page

The complexity of approximating conservative counting CSPs

We study the complexity of approximately solving the weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, there is a classification known for the case in which the domain of functions in F is Boolean. In this paper, we give a classification for the more general problem where functions in F have an arbitrary finite domain. We define the notions of weak log-modularity and weak log-supermodularity. We show that if F is weakly log-modular, then #CSP(F)is in FP. Otherwise, it is at least as difficult to approximate as #BIS, the problem of counting independent sets in bipartite graphs. #BIS is complete with respect to approximation-preserving reductions for a logically-defined complexity class #RHPi1, and is believed to be intractable. We further sub-divide the #BIS-hard case. If F is weakly log-supermodular, then we show that #CSP(F) is as easy as a (Boolean) log-supermodular weighted #CSP. Otherwise, we show that it is NP-hard to approximate. Finally, we give a full trichotomy for the arity-2 case, where #CSP(F) is in FP, or is #BIS-equivalent, or is equivalent in difficulty to #SAT, the problem of approximately counting the satisfying assignments of a Boolean formula in conjunctive normal form. We also discuss the algorithmic aspects of our classification.Comment: Minor revisio

Analysis of KrF excimer laser beam modification resulting from ablation under closed thick film flowing filtered water

The application of closed thick film liquid to immerse the ablation etching mechanism of an excimer laser poses interesting possibilities concerning debris control, modification of machined feature topography and modification of ablation rate. Further more, these parameters have been shown to be dependant on flow velocity; hence offering further user control of machining characteristics. However the impact of this technique requires investigation. This contribution offers comparison of the calculated ablation pressure and the effect on feature surface characteristics given for laser ablation of bisphenol A polycarbonate using KrF excimer laser radiation in ambient air against laser ablation of the same substrate under closed thick film flowing filtered water immersion. Also, the impact of such immersion equipment on the optical performance of the micromachining centre used is quantified and reviewed. The pressure is calculated to have risen some 53% when using the liquid immersed ablation technique. This increase in pressure is proposed to have promoted the frequency of surface Plasmons and asperities with a surface area less than 16 µm2. The focal length of the optical system was accurately predicted to be increased by 2.958 mm when using the equipment composed of a 5 mm thick ultraviolet grade fused silica window covering a 1.5 mm thick film of filtered water flowing at 1.85 m/s. This equipment was predicted to have increased the optical depth of focus via reduction in the angle of convergence of the two defining image rays, yet the perceived focus, measured by mean feature wall angle as a discrete indication, was found to be 25% smaller when using the closed thick film flowing filtered water immersion technique than when laser ablating in ambient air. A compressed plume interaction is proposed as a contributing factor in this change

Longitudinal patterns of emerging literacy in beginning deaf and hearing readers

The emerging reading and spelling abilities of 24 deaf and 23 hearing beginning readers were followed over 2 years. The deaf children varied in their language backgrounds and preferred mode of communication. All children were given a range of literacy, cognitive and language-based tasks every 12 months. Deaf and hearing children made similar progress in literacy in the beginning stages of reading development and then their trajectories began to diverge. The longitudinal correlates of beginning reading in the deaf children were earlier vocabulary, letter-sound knowledge, and speechreading. Earlier phonological awareness was not a longitudinal correlate of reading ability once earlier reading levels were controlled. Only letter name knowledge was longitudinally related to spelling ability. Speechreading was also a strong longitudinal correlate of reading and spelling in the hearing children. The findings suggested that deaf and hearing children utilize slightly different reading strategies over the first 2 years of schooling

Perception and knowledge of the Sirex woodwasp and other forest pests in South Africa

1. Sirex noctilio is one of the most serious invasive pests of pine. In South Africa, there has been a national effort to control S. noctilio, including an awareness campaign to increase awareness of the pest amongst the local forestry community. 2. We considered the impacts that the arrival of the pest and the awareness campaign has had on perceptions and knowledge of S. noctilio, as well as other forestry pests, amongst members of the forestry community. 3. For the data collection, a survey questionnaire was developed and used in telephone interviews. 4. Results of the study showed that the Sirex awareness campaign had increased knowledge of forestry pests in general. However, basic knowledge regarding the identification and symptoms of specific pests, such as S. noctilio, was poor. This will negatively influence monitoring efficacy. 5. Traditional paper-based media and personal contact contributed most to enhanced awareness. Electronic media were less effective and improvement would require a more focused effort. It was of concern that private farmers and contractors, as well as non-European first language speakers, were less well informed about forestry pests. 6. Clearly, a fragmented landscape in terms of ownership and language, presents challenges for effective communication of forestry pest threats.Forestry South Africa (FSA), the Department of Water Affairs and Forestry, the University of Pretoria and the THRIP initiative of the Department of Trade and Industry (DTI), South Africa.http://onlinelibrary.wiley.comab201

A Comparison of Deaf and Hearing Childrenʼs Reading Comprehension Profiles

Purpose: Although deaf children typically exhibit severe delays in reading achievement, there is a paucity of research looking at their text-level comprehension skills. We present a comparison of deaf and normally hearing readers' profiles on a commonly used reading comprehension assessment: the Neale Analysis of Reading Ability II. Methods: Comprehension questions were coded into 3 types: literal questions; local cohesion questions; and global coherence questions. Deaf children were matched to 3 groups of hearing children: chronological age-matched controls; reading-age-matched controls; and a group of poor comprehenders. Results: Deaf children had significantly weaker reading comprehension skills than both chronological age- and reading-age-matched controls, but their skills were commensurate with poor comprehenders. All groups found it easier to make inferences to establish local cohesion than those required to establish global coherence. Discussion/Conclusions: These results suggest that deaf children's reading comprehension profiles are remarkably similar to those of poor comprehenders. These findings are discussed in light of the potential differences in underlying causes of reading difficulties in these 2 groups