Assessment of antibiotic use in children by their parents in Saudi Arabia

This project assessed the factors influencing the parents' use of antibiotics in children in Saudi Arabia. It was conducted through the development and validation of the Parental Perceptions on Antibiotics (PAPA) Scales, which is the first valid and reliable instrument directed to measure these factors on a population-based level. This is also the first population-based study that measures the patterns of antibiotic use in children in Saudi Arabia, where a very high association was found between the use of antibiotics and the number of cold episodes a year, which suggests a potential of overuse of antibiotics in Saudi Arabia. Also, it was found that antibiotic use decreases significantly with parents having higher scores in knowledge and beleifs, behaviors, and eagerness to seek health-related information.

Identifying the spatial scale of land use that most strongly influences overall river ecosystem health score

Catchment and riparian degradation has resulted in declining ecosystem health of streams worldwide. With restoration a priority in many regions, there is an increasing interest in the scale at which land use influences stream ecosystem health. Our goal was to use a substantial data set collected as part of a monitoring program (the Southeast Queensland, Australia, Ecological Health Monitoring Program data set, collected at 116 sites over six years) to identify the spatial scale of land use, or the combination of spatial scales, that most strongly influences overall ecosystem health. In addition, we aimed to determine whether the most influential scale differed for different aspects of ecosystem health. We used linear-mixed models and a Bayesian model-averaging approach to generate models for the overall aggregated ecosystem health score and for each of the five component indicators (fish, macroinvertebrates, water quality, nutrients, and ecosystem processes) that make up the score. Dense forest close to the survey site, mid-dense forest in the hydrologically active nearstream areas of the catchment, urbanization in the riparian buffer, and tree cover at the reach scale were all significant in explaining ecosystem health, suggesting an overriding influence of forest cover, particularly close to the stream. Season and antecedent rainfall were also important explanatory variables, with some land-use variables showing significant seasonal interactions. There were also differential influences of land use for each of the component indicators. Our approach is useful given that restoring general ecosystem health is the focus of many stream restoration projects; it allowed us to predict the scale and catchment position of restoration that would result in the greatest improvement of ecosystem health in the regions streams and rivers. The models we generated suggested that good ecosystem health can be maintained in catchments where 80% of hydrologically active areas in close proximity to the stream have mid-dense forest cover and moderate health can be obtained with 60% cover.

STI-GMaS : an open-source environment for simulation of sexually-transmitted infections

Background Sexually-transmitted pathogens often have severe reproductive health implications if treatment is delayed or absent, especially in females. The complex processes of disease progression, namely replication and ascension of the infection through the genital tract, span both extracellular and intracellular physiological scales, and in females can vary over the distinct phases of the menstrual cycle. The complexity of these processes, coupled with the common impossibility of obtaining comprehensive and sequential clinical data from individual human patients, makes mathematical and computational modelling valuable tools in developing our understanding of the infection, with a view to identifying new interventions. While many within-host models of sexually-transmitted infections (STIs) are available in existing literature, these models are difficult to deploy in clinical/experimental settings since simulations often require complex computational approaches. Results We present STI-GMaS (Sexually-Transmitted Infections – Graphical Modelling and Simulation), an environment for simulation of STI models, with a view to stimulating the uptake of these models within the laboratory or clinic. The software currently focuses upon the representative case-study of Chlamydia trachomatis, the most common sexually-transmitted bacterial pathogen of humans. Here, we demonstrate the use of a hybrid PDE–cellular automata model for simulation of a hypothetical Chlamydia vaccination, demonstrating the effect of a vaccine-induced antibody in preventing the infection from ascending to above the cervix. This example illustrates the ease with which existing models can be adapted to describe new studies, and its careful parameterisation within STI-GMaS facilitates future tuning to experimental data as they arise. Conclusions STI-GMaS represents the first software designed explicitly for in-silico simulation of STI models by non-theoreticians, thus presenting a novel route to bridging the gap between computational and clinical/experimental disciplines. With the propensity for model reuse and extension, there is much scope within STI-GMaS to allow clinical and experimental studies to inform model inputs and drive future model development. Many of the modelling paradigms and software design principles deployed to date transfer readily to other STIs, both bacterial and viral; forthcoming releases of STI-GMaS will extend the software to incorporate a more diverse range of infections.

The 3rd Knowledge Cities World Summit Proceedings

FROM KCWS 2010 Ch airs and Summit Proceeding Ed ito rs ‘Knowledge’ is a resource, which relies on the past for a better future. In the 21st century, more than ever before, cities around the world depend on the knowledge of their citizens, their institutions and their firms and enterprises. The knowledge image, the human competence and the reputation of their public and private institutions and corporations profiles a city. It attracts investment, qualified labour and professionals, as well as students and researchers. And it creates local life spaces and professional milieus, which offer the quality of life to the citizens that are seeking to cope with the challenges of modern life in a competitive world. Integrating knowledge-based development in urban strategies and policies, beyond the provision of schools and locations for higher education, has become a new ambitious arena of city politics. Coming from theory to practice, and bringing together the manifold knowledge stakeholders in a city and preparing joint visions for the knowledge city is a new challenge for city managers, urban planners and leaders of the civic society . It requires visionary power, creativity, holistic thinking, the willingness to cooperate with all groups of the local civil society, and the capability to moderate communication processes to overcome conflicts and to develop joint action for a sustainable future. This timely Melbourne 2010 – The Third Knowledge City World Summit makes an important reminder that ‘knowledge’ is the key notion in the 21st Century development. Considering this notion, the summit aims to shed light on the multi-faceted dimensions and various scales of building the ‘knowledge city’ and on ‘knowledge-based development’ paradigms. At this summit, the theoretical and practical maturing of knowledge-based development paradigms will be advanced through the interplay between the world’s leading academic’s theories and the practical models and strategies of practitioners’ and policy makers’ drawn from around the world. As chairs of The Melbourne 2010 Summit, we have compiled this summit proceeding in order to disseminate the knowledge generated and shared in Melbourne with the wider research, governance, and practice communities. The papers in the proceedings reflect the broad range of contributions to the summit. They report on recent developments in planning and managing knowledge cities and ICT infrastructure, they assess the role of knowledge institutions in regional innovation systems and of the intellectual capital of cities and regions; they describe the evolution of knowledge-based approaches to urban development in differing cultural environments; they finally bridge the discourse on the knowledge city to other urban development paradigms such as the creative city, the ubiquitous city or the compact city. The diversity of papers presented shows how different scholars from planning cultures around the world interpret the knowledge dimension in urban and regional development. All papers of this proceeding have gone through a double-blind peer review process and been reviewed by our summit editorial review and advisory board members. We cordially thank the members of the Summit Proceeding Editorial Review and Advisory Board for their diligent work in the review of the papers. We hope the papers in this proceeding will inspire and make a significant contribution to the research, governance, and practice circles.

The 4th Knowledge Cities World Summit Proceedings

FROM KCWS 2011 CHAIRS AND SUMMIT PROCEEDING EDITORS In recent years, with the impact of global knowledge economy, a more comprehensive development approach has gained significant popularity. This new development approach, so called ‘knowledgebased development’, is different from its traditional predecessor. With a much more balanced focus on all of the four key development domains – economic, enviro-urban, institutional, and sociocultural – this contemporary approach, aims to bring economic prosperity, environmental sustainability and local institutional competence with a just socio-spatial order to our cities and regions. The ultimate goal of knowledge-based development is to produce a city purposefully designed to encourage the continuous production, circulation and commercialisation of social and scientific knowledge – this will in turn establish a ‘knowledge city’. A city following the ‘knowledge city’ concept embarks on a strategic mission to firmly encourage and nurture locally focussed innovation, science and creativity within the context of an expanding knowledge economy and society. In this regard a ‘knowledge city’ can be seen as an integrated city, which physically and institutionally combines the functions of a science and technology park with civic and residential functions and urban amenities. It also offers one of the effective paradigms for the sustainable cities of our time. This fourth edition of KCWS – The 4th Knowledge Cities World Summit 2011 – makes an important reminder that the 'knowledge city' concept is a key notion in the 21st Century development. Considering this notion, the Summit sheds light on the multi-faceted dimensions and various scales of building a ‘knowledge city’ via 'knowledge-based development' paradigm by particularly focusing on the overall Summit theme of ‘Knowledge Cities for Future Generations’. At this summit, the theoretical and practical maturing of knowledge-based development paradigms are advanced through the interplay between the world’s leading academics’ theories and the practical models and strategies of practitioners’ and policy makers’ drawn from around the world. This summit proceeding is compiled in order to disseminate the knowledge generated and shared in KCWS 2011 with the wider research, governance, and practice communities the knowledge cocreated in this summit. All papers of this proceeding have gone through a double-blind peer review process and been reviewed by our summit editorial review and advisory board members. We, organisers of the summit, cordially thank the members of the Summit Proceeding Editorial Review and Advisory Board for their diligent work in the review of the papers. We hope the papers in this proceeding will inspire and make a significant contribution to the research, governance, and practice circles.

Integration of science and monitoring of river ecosystem health to guide investments in catchment protection and rehabilitation

1. Stream ecosystem health monitoring and reporting need to be developed in the context of an adaptive process that is clearly linked to identified values and objectives, is informed by rigorous science, guides management actions and is responsive to changing perceptions and values of stakeholders. To be effective, monitoring programmes also need to be underpinned by an understanding of the probable causal factors that influence the condition or health of important environmental assets and values. This is often difficult in stream and river ecosystems where multiple stressors, acting at different spatial and temporal scales, interact to affect water quality, biodiversity and ecosystem processes. 2. In this article, we describe the development of a freshwater monitoring programme in South East Queensland, Australia, and how this has been used to report on ecosystem health at a regional scale and to guide investments in catchment protection and rehabilitation. We also discuss some of the emerging science needs to identify the appropriate scale and spatial arrangement of rehabilitation to maximise river ecosystem health outcomes and, at the same time, derive other benefits downstream. 3. An objective process was used to identify potential indicators of stream ecosystem health and then test these across a known catchment land-use disturbance gradient. From the 75 indicators initially tested, 22 from five indicator groups (water quality, ecosystem metabolism, nutrient cycling, invertebrates and fish) responded strongly to the disturbance gradient, and 16 were subsequently recommended for inclusion in the monitoring programme. The freshwater monitoring programme was implemented in 2002, funded by local and State government authorities, and currently involves the assessment of over 120 sites, twice per year. This information, together with data from a similar programme on the region's estuarine and coastal marine waters, forms the basis of an annual report card that is presented in a public ceremony to local politicians and the broader community. 4. Several key lessons from the SEQ Healthy Waterways Programme are likely to be transferable to other regional programmes aimed at improving aquatic ecosystem health, including the importance of a shared common vision, the involvement of committed individuals, a cooperative approach, the need for defensible science and effective communication. 5. Thematic implications: this study highlights the use of conceptual models and objective testing of potential indicators against a known disturbance gradient to develop a freshwater ecosystem health monitoring programme that can diagnose the probable causes of degradation from multiple stressors and identify the appropriate spatial scale for rehabilitation or protection. This approach can lead to more targeted management investments in catchment protection and rehabilitation, greater public confidence that limited funds are being well spent and better outcomes for stream and river ecosystem health.

A comparison of spatially explicit landscape representation methods and their relationship to stream condition

1. Biodiversity, water quality and ecosystem processes in streams are known to be influenced by the terrestrial landscape over a range of spatial and temporal scales. Lumped attributes (i.e. per cent land use) are often used to characterise the condition of the catchment; however, they are not spatially explicit and do not account for the disproportionate influence of land located near the stream or connected by overland flow. 2. We compared seven landscape representation metrics to determine whether accounting for the spatial proximity and hydrological effects of land use can be used to account for additional variability in indicators of stream ecosystem health. The landscape metrics included the following: a lumped metric, four inverse-distance-weighted (IDW) metrics based on distance to the stream or survey site and two modified IDW metrics that also accounted for the level of hydrologic activity (HA-IDW). Ecosystem health data were obtained from the Ecological Health Monitoring Programme in Southeast Queensland, Australia and included measures of fish, invertebrates, physicochemistry and nutrients collected during two seasons over 4 years. Linear models were fitted to the stream indicators and landscape metrics, by season, and compared using an information-theoretic approach. 3. Although no single metric was most suitable for modelling all stream indicators, lumped metrics rarely performed as well as other metric types. Metrics based on proximity to the stream (IDW and HA-IDW) were more suitable for modelling fish indicators, while the HA-IDW metric based on proximity to the survey site generally outperformed others for invertebrates, irrespective of season. There was consistent support for metrics based on proximity to the survey site (IDW or HA-IDW) for all physicochemical indicators during the dry season, while a HA-IDW metric based on proximity to the stream was suitable for five of the six physicochemical indicators in the post-wet season. Only one nutrient indicator was tested and results showed that catchment area had a significant effect on the relationship between land use metrics and algal stable isotope ratios in both seasons. 4. Spatially explicit methods of landscape representation can clearly improve the predictive ability of many empirical models currently used to study the relationship between landscape, habitat and stream condition. A comparison of different metrics may provide clues about causal pathways and mechanistic processes behind correlative relationships and could be used to target restoration efforts strategically.

Governance Systems Analysis (GSA) : a framework for reforming governance systems

Most commentators understand that contemporary social, economic and environmental challenges require quality governance from global to local scales. While public scrutiny of governance has increased in recent years, the literature on frameworks and methods for analysis in complex, poly-centric and multi-thematic governance systems remains fragmented; displaying many disciplinary or sectoral biases. This paper establishes a stronger theory-based foundation for the analysis of complex governance systems. It also develops a clear analytical framework applicable across a vast array of differing governance themes, domains and scales (GSA). The key methodological steps and evaluative criteria for the GSA framework are determined and practical guidance for its application in reform is provided.

Conceptualising, evaluating and reporting social resilience in vulnerable regional and remote communities facing climate change in tropical Queensland : marine and tropical sciences research facility transition project final report

Regional and remote communities in tropical Queensland are among Australia’s most vulnerable in the face of climate change. At the same time, these socially and economically vulnerable regions house some of Australia’s most significant biodiversity values. Past approaches to terrestrial biodiversity management have focused on tackling biophysical interventions through the use of biophysical knowledge. An equally important focus should be placed on building regional-scale community resilience if some of the worst biodiversity impacts of climate change are to be avoided or mitigated. Despite its critical need, more systemic or holistic approaches to natural resource management have been rarely trialed and tested in a structured way. Currently, most strategic interventions in improving regional community resilience are ad hoc, not theory-based and short term. Past planning approaches have not been durable, nor have they been well informed by clear indicators. Research into indicators for community resilience has been poorly integrated within adaptive planning and management cycles. This project has aimed to resolve this problem by: * Reviewing the community and social resilience and adaptive planning literature to reconceptualise an improved framework for applying community resilience concepts; * Harvesting and extending work undertaken in MTSRF Phase 1 to identifying the learnings emerging from past MTSRF research; * Distilling these findings to identify new theoretical and practical approaches to the application of community resilience in natural resource use and management; * Reconsidering the potential interplay between a region’s biophysical and social planning processes, with a focus on exploring spatial tools to communicate climate change risk and its consequent environmental, economic and social impacts, and; * Trialling new approaches to indicator development and adaptive planning to improve community resilience, using a sub-regional pilot in the Wet Tropics. In doing so, we also looked at ways to improve the use and application of relevant spatial information. Our theoretical review drew upon the community development, psychology and emergency management literature to better frame the concept of community resilience relative to aligned concepts of social resilience, vulnerability and adaptive capacity. Firstly, we consider community resilience as a concept that can be considered at a range of scales (e.g. regional, locality, communities of interest, etc.). We also consider that overall resilience at higher scales will be influenced by resilience levels at lesser scales (inclusive of the resilience of constituent institutions, families and individuals). We illustrate that, at any scale, resilience and vulnerability are not necessarily polar opposites, and that some understanding of vulnerability is important in determining resilience. We position social resilience (a concept focused on the social characteristics of communities and individuals) as an important attribute of community resilience, but one that needs to be considered alongside economic, natural resource, capacity-based and governance attributes. The findings from the review of theory and MTSRF Phase 1 projects were synthesized and refined by the wider project team. Five predominant themes were distilled from this literature, research review and an expert analysis. They include the findings that: 1. Indicators have most value within an integrated and adaptive planning context, requiring an active co-research relationship between community resilience planners, managers and researchers if real change is to be secured; 2. Indicators of community resilience form the basis for planning for social assets and the resilience of social assets is directly related the longer term resilience of natural assets. This encourages and indeed requires the explicit development and integration of social planning within a broader natural resource planning and management framework; 3. Past indicator research and application has not provided a broad picture of the key attributes of community resilience and there have been many attempts to elicit lists of “perfect” indicators that may never be useful within the time and resource limitations of real world regional planning and management. We consider that modeling resilience for proactive planning and prediction purposes requires the consideration of simple but integrated clusters of attributes; 4. Depending on time and resources available for planning and management, the combined use of well suited indicators and/or other lesser “lines of evidence” is more flexible than the pursuit of perfect indicators, and that; 5. Index-based, collaborative and participatory approaches need to be applied to the development, refinement and reporting of indicators over longer time frames. We trialed the practical application of these concepts via the establishment of a collaborative regional alliance of planners and managers involved in the development of climate change adaptation strategies across tropical Queensland (the Gulf, Wet Tropics, Cape York and Torres Strait sub-regions). A focus on the Wet Tropics as a pilot sub-region enabled other Far North Queensland sub-region’s to participate and explore the potential extension of this approach. The pilot activities included: * Further exploring ways to innovatively communicate the region’s likely climate change scenarios and possible environmental, economic and social impacts. We particularly looked at using spatial tools to overlay climate change risks to geographic communities and social vulnerabilities within those communities; * Developing a cohesive first pass of a State of the Region-style approach to reporting community resilience, inclusive of regional economic viability, community vitality, capacitybased and governance attributes. This framework integrated a literature review, expert (academic and community) and alliance-based contributions; and * Early consideration of critical strategies that need to be included in unfolding regional planning activities with Far North Queensland. The pilot assessment finds that rural, indigenous and some urban populations in the Wet Tropics are highly vulnerable and sensitive to climate change and may require substantial support to adapt and become more resilient. This assessment finds that under current conditions (i.e. if significant adaptation actions are not taken) the Wet Tropics as a whole may be seriously impacted by the most significant features of climate change and extreme climatic events. Without early and substantive action, this could result in declining social and economic wellbeing and natural resource health. Of the four attributes we consider important to understanding community resilience, the Wet Tropics region is particularly vulnerable in two areas; specifically its economic vitality and knowledge, aspirations and capacity. The third and fourth attributes, community vitality and institutional governance are relatively resilient but are vulnerable in some key respects. In regard to all four of these attributes, however, there is some emerging capacity to manage the possible shocks that may be associated with the impacts of climate change and extreme climatic events. This capacity needs to be carefully fostered and further developed to achieve broader community resilience outcomes. There is an immediate need to build individual, household, community and sectoral resilience across all four attribute groups to enable populations and communities in the Wet Tropics region to adapt in the face of climate change. Preliminary strategies of importance to improve regional community resilience have been identified. These emerging strategies also have been integrated into the emerging Regional Development Australia Roadmap, and this will ensure that effective implementation will be progressed and coordinated. They will also inform emerging strategy development to secure implementation of the FNQ 2031 Regional Plan. Of most significance in our view, this project has taken a co-research approach from the outset with explicit and direct importance and influence within the region’s formal planning and management arrangements. As such, the research: * Now forms the foundations of the first attempt at “Social Asset” planning within the Wet Tropics Regional NRM Plan review; * Is assisting Local government at regional scale to consider aspects of climate change adaptation in emerging planning scheme/community planning processes; * Has partnered the State government (via the Department of Infrastructure and Planning and Regional Managers Coordination Network Chair) in progressing the Climate Change adaptation agenda set down within the FNQ 2031 Regional Plan; * Is informing new approaches to report on community resilience within the GBRMPA Outlook reporting framework; and * Now forms the foundation for the region’s wider climate change adaptation priorities in the Regional Roadmap developed by Regional Development Australia. Through the auspices of Regional Development Australia, the outcomes of the research will now inform emerging negotiations concerning a wider package of climate change adaptation priorities with State and Federal governments. Next stage research priorities are also being developed to enable an ongoing alliance between researchers and the region’s climate change response.

How to sequence and annotate insect mitochondrial genomes for systematic and comparative genomics research

Over the past decade the mitochondrial (mt) genome has become the most widely used genomic resource available for systematic entomology. While the availability of other types of ‘–omics’ data – in particular transcriptomes – is increasing rapidly, mt genomes are still vastly cheaper to sequence and are far less demanding of high quality templates. Furthermore, almost all other ‘–omics’ approaches also sequence the mt genome, and so it can form a bridge between legacy and contemporary datasets. Mitochondrial genomes have now been sequenced for all insect orders, and in many instances representatives of each major lineage within orders (suborders, series or superfamilies depending on the group). They have also been applied to systematic questions at all taxonomic scales from resolving interordinal relationships (e.g. Cameron et al., 2009; Wan et al., 2012; Wang et al., 2012), through many intraordinal (e.g. Dowton et al., 2009; Timmermans et al., 2010; Zhao et al. 2013a) and family-level studies (e.g. Nelson et al., 2012; Zhao et al., 2013b) to population/biogeographic studies (e.g. Ma et al., 2012). Methodological issues around the use of mt genomes in insect phylogenetic analyses and the empirical results found to date have recently been reviewed by Cameron (2014), yet the technical aspects of sequencing and annotating mt genomes were not covered. Most papers which generate new mt genome report their methods in a simplified form which can be difficult to replicate without specific knowledge of the field. Published studies utilize a sufficiently wide range of approaches, usually without justification for the one chosen, that confusion about commonly used jargon such as ‘long PCR’ and ‘primer walking’ could be a serious barrier to entry. Furthermore, sequenced mt genomes have been annotated (gene locations defined) to wildly varying standards and improving data quality through consistent annotation procedures will benefit all downstream users of these datasets. The aims of this review are therefore to: 1. Describe in detail the various sequencing methods used on insect mt genomes; 2. Explore the strengths/weakness of different approaches; 3. Outline the procedures and software used for insect mt genome annotation, and; 4. Highlight quality control steps used for new annotations, and to improve the re-annotation of previously sequenced mt genomes used in systematic or comparative research.

Multi-scale bio-inspired place recognition

This paper presents a novel place recognition algorithm inspired by the recent discovery of overlapping and multi-scale spatial maps in the rodent brain. We mimic this hierarchical framework by training arrays of Support Vector Machines to recognize places at multiple spatial scales. Place match hypotheses are then cross-validated across all spatial scales, a process which combines the spatial specificity of the finest spatial map with the consensus provided by broader mapping scales. Experiments on three real-world datasets including a large robotics benchmark demonstrate that mapping over multiple scales uniformly improves place recognition performance over a single scale approach without sacrificing localization accuracy. We present analysis that illustrates how matching over multiple scales leads to better place recognition performance and discuss several promising areas for future investigation.

The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.