Asymptotic Normality of Degree Counts in a Preferential Attachment Model

Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are asymptotically normal even though node or count based network data is nothing like classical data from independently replicated experiments. We therefore study asymptotic normality of degree counts for a sequence of growing simple undirected preferential attachment graphs. The methods of proof rely on identifying martingales and then exploiting the martingale central limit theorems

Modeling Adaptation with Klaim

In recent years, it has been argued that systems and applications, in order to deal with their increasing complexity, should be able to adapt their behavior according to new requirements or environment conditions. In this paper, we present an investigation aiming at studying how coordination languages and formal methods can contribute to a better understanding, implementation and use of the mechanisms and techniques for adaptation currently proposed in the literature. Our study relies on the formal coordination language Klaim as a common framework for modeling some well-known adaptation techniques: the IBM MAPE-K loop, the Accord component-based framework for architectural adaptation, and the aspect- and context-oriented programming paradigms. We illustrate our approach through a simple example concerning a data repository equipped with an automated cache mechanism

On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond

An improved understanding of the divergence-free constraint for the incompressible Navier--Stokes equations leads to the observation that a semi-norm and corresponding equivalence classes of forces are fundamental for their nonlinear dynamics. The recent concept of {\em pressure-robustness} allows to distinguish between space discretisations that discretise these equivalence classes appropriately or not. This contribution compares the accuracy of pressure-robust and non-pressure-robust space discretisations for transient high Reynolds number flows, starting from the observation that in generalised Beltrami flows the nonlinear convection term is balanced by a strong pressure gradient. Then, pressure-robust methods are shown to outperform comparable non-pressure-robust space discretisations. Indeed, pressure-robust methods of formal order $k$ are comparably accurate than non-pressure-robust methods of formal order $2k$ on coarse meshes. Investigating the material derivative of incompressible Euler flows, it is conjectured that strong pressure gradients are typical for non-trivial high Reynolds number flows. Connections to vortex-dominated flows are established. Thus, pressure-robustness appears to be a prerequisite for accurate incompressible flow solvers at high Reynolds numbers. The arguments are supported by numerical analysis and numerical experiments.Comment: 43 pages, 18 figures, 2 table

On the irrelevant disorder regime of pinning models

Recent results have lead to substantial progress in understanding the role of disorder in the (de)localization transition of polymer pinning models. Notably, there is an understanding of the crucial issue of disorder relevance and irrelevance that is now rigorous. In this work, we exploit interpolation and replica coupling methods to obtain sharper results on the irrelevant disorder regime of pinning models. In particular, in this regime, we compute the first order term in the expansion of the free energy close to criticality and this term coincides with the first order of the formal expansion obtained by field theory methods. We also show that the quenched and quenched averaged correlation length exponents coincide, while, in general, they are expected to be different. Interpolation and replica coupling methods in this class of models naturally lead to studying the behavior of the intersection of certain renewal sequences and one of the main tools in this work is precisely renewal theory and the study of these intersection renewals.Comment: Published in at http://dx.doi.org/10.1214/09-AOP454 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning Science In A Secondary School In Papua New Guinea

This study investigated teaching and learning, and the classroom learning environment in which the electricity topic was taught by the regular class teacher within the prescribed Grade 9 syllabus in a Secondary School in Papua New Guinea. The study was motivated by the perceived problems students had with understanding science concepts and the lack of classroom-based studies that provide a better understanding of teaching and learning science and the influence of the classroom learning environment on students' learning. An interpretive with embedded case study was conducted in a Grade 9 class over a period of 12 weeks in which data was gathered using mixed and multiple methods. Findings of the study revealed the presence and influence of aspects of the indigenous traditional teaching and learning approach impacting on the formal modern Western oriented teaching and learning approach in this particular classroom. The study recommended that in order to maximise students' learning and understanding of science concepts in the classroom observed, cultural sensitivity should be incorporated in the pedagogy

User costs and informal payments for care in the largest maternity hospital in Kathmandu, Nepal

Background: Maternity care costs in Nepal include formal and informal payment. Formal include for example the cost for blood or drugs; Informal payments can be voluntary such as gratitude payments, or bribes which patients are ‘expected’ to pay to get decent care or any care at all. One problem is that these payments are missing from formal accounts and they are not taken into account in health-policy decision-making. The aim of the present study was to estimate out-of-pocket expenses (formal/informal) for delivery care in the largest government maternity hospital in Kathmandu, Nepal and establish factors that affect informal costs. Methods: We used mixed-methods approach. We used questionnaire-based interviews with 234 women who had delivered in this hospital followed by semi-structured in-depth interviews with sub-sample of ten couples. SPSS software was used for analysis and cross tabulations and chi square tests, binary logistic regression were performed. Results: Women occurred various costs during a hospital confinement. The qualitative data suggested that some, but not all had started to save prior to the delivery. There is a significant association between making informal payments and whether or not the birth was planned to be in hospital or whether it was an emergency, p=0.025, ANC visits, p=0.008, woman’s occupation,p=0.025 and husband’s employment, p=0.022. Logistic regression suggested four factors associated with making informal payments, indicating a possible socio-economic link with ability to make informal payments. Conclusions: Although informal payments around birth itself were not substantial, such payments are very common. Better understanding of informal payments is important as the illegal status of unofficial health care payments means that it is difficult to establish the prevalence of this phenomenon. Moreover it forms a part of the private health expenditure rarely included in the national health statistics, they create perverse incentives, potentially reduce motivation for reform and will provide information about economic barriers to care