Political Discourse Analysis, Sport and Scottish Independence: Provisional Reflections upon Fairclough and Fairclough's (2012) Analytical Framework.

This paper aims to reflect upon the potential analytical utility of the political discourse analysis framework proposed by Isabela Fairclough and Norman Fairclough (2012). This framework represents the most recent substantive development upon Norman Fairclough's past work situated within the wider school of Critical Discourse Analysis, building upon his influential position this methodological tradition. Central to this development is the additional emphasis placed upon the necessity to conceptualise all political discourse as 'argumentative' in nature, given that political actors are ultimately proposing or refuting particular courses of concrete future action. This paper will therefore apply Fairclough and Fairclough's model to provisional data derived from an ongoing doctoral thesis which considers the nature of political discourse relating to sport, the Glasgow 2014 Commonwealth Games and Scottish independence, with an ultimate aim of critically considering the benefits and limitations of applying this analytical framework as a methodological tool within this ongoing study.

A generic model for integration of Quality, Environment and Safety Management Systems

Purpose – The purpose of this paper is to propose a generic model of Integrated Management System of Quality, Environment and Safety (IMS-QES) that can be adapted and progressively to assimilate various Management Systems, of which highlights: ISO 9001 for Quality; ISO 14001 for Environment; OHSAS 18001 for Occupational Health and Safety. Design/methodology/approach – The model was designed in the real environment of a Portuguese Organization and 160 employees were surveyed. The rate response was equal to 86 percent. The conceived model was implemented in a first phase for the integration of Quality, Environment and Safety Management Systems. Findings – Among the main findings of the survey the paper highlights: the elimination of conflicts between individual systems with resources optimization; creation of added value to the business by eliminating several types of wastes; the integrated management of sustainability components in a global market; the improvement of partnerships with suppliers of goods and services; reducing the number of internal and external audits. Originality/value – This case study is one of the first Portuguese empirical researches about IMS-QES and the paper believes that it can be useful in the creation of a Portuguese guideline for integration, namely the Quality Management Systems; Environmental Management Systems and Occupational Health and Safety Management Systems among others.

A lightweight indoor localization model based on motley-keenan and COST

This paper presents a novel approach to WLAN propagation models for use in indoor localization. The major goal of this work is to eliminate the need for in situ data collection to generate the Fingerprinting map, instead, it is generated by using analytical propagation models such as: COST Multi-Wall, COST 231 average wall and Motley- Keenan. As Location Estimation Algorithms kNN (K-Nearest Neighbour) and WkNN (Weighted K-Nearest Neighbour) were used to determine the accuracy of the proposed technique. This work is based on analytical and measurement tools to determine which path loss propagation models are better for location estimation applications, based on Receive Signal Strength Indicator (RSSI).This study presents different proposals for choosing the most appropriate values for the models parameters, like obstacles attenuation and coefficients. Some adjustments to these models, particularly to Motley-Keenan, considering the thickness of walls, are proposed. The best found solution is based on the adjusted Motley-Keenan and COST models that allows to obtain the propagation loss estimation for several environments.Results obtained from two testing scenarios showed the reliability of the adjustments, providing smaller errors in the measured values values in comparison with the predicted values.

Soil sampling design and sampling techniques for soil properties monitoring – common difficulties related to forest soils

Mathematical models and statistical analysis are key instruments in soil science scientific research as they can describe and/or predict the current state of a soil system. These tools allow us to explore the behavior of soil related processes and properties as well as to generate new hypotheses for future experimentation. A good model and analysis of soil properties variations, that permit us to extract suitable conclusions and estimating spatially correlated variables at unsampled locations, is clearly dependent on the amount and quality of data and of the robustness techniques and estimators. On the other hand, the quality of data is obviously dependent from a competent data collection procedure and from a capable laboratory analytical work. Following the standard soil sampling protocols available, soil samples should be collected according to key points such as a convenient spatial scale, landscape homogeneity (or non-homogeneity), land color, soil texture, land slope, land solar exposition. Obtaining good quality data from forest soils is predictably expensive as it is labor intensive and demands many manpower and equipment both in field work and in laboratory analysis. Also, the sampling collection scheme that should be used on a data collection procedure in forest field is not simple to design as the sampling strategies chosen are strongly dependent on soil taxonomy. In fact, a sampling grid will not be able to be followed if rocks at the predicted collecting depth are found, or no soil at all is found, or large trees bar the soil collection. Considering this, a proficient design of a soil data sampling campaign in forest field is not always a simple process and sometimes represents a truly huge challenge. In this work, we present some difficulties that have occurred during two experiments on forest soil that were conducted in order to study the spatial variation of some soil physical-chemical properties. Two different sampling protocols were considered for monitoring two types of forest soils located in NW Portugal: umbric regosol and lithosol. Two different equipments for sampling collection were also used: a manual auger and a shovel. Both scenarios were analyzed and the results achieved have allowed us to consider that monitoring forest soil in order to do some mathematical and statistical investigations needs a sampling procedure to data collection compatible to established protocols but a pre-defined grid assumption often fail when the variability of the soil property is not uniform in space. In this case, sampling grid should be conveniently adapted from one part of the landscape to another and this fact should be taken into consideration of a mathematical procedure.

Cost Allocation Model for Distribution Networks Considering High Penetration of Distributed Energy Resources

The high penetration of distributed energy resources (DER) in distribution networks and the competitiveenvironment of electricity markets impose the use of new approaches in several domains. The networkcost allocation, traditionally used in transmission networks, should be adapted and used in the distribu-tion networks considering the specifications of the connected resources. The main goal is to develop afairer methodology trying to distribute the distribution network use costs to all players which are usingthe network in each period. In this paper, a model considering different type of costs (fixed, losses, andcongestion costs) is proposed comprising the use of a large set of DER, namely distributed generation(DG), demand response (DR) of direct load control type, energy storage systems (ESS), and electric vehi-cles with capability of discharging energy to the network, which is known as vehicle-to-grid (V2G). Theproposed model includes three distinct phases of operation. The first phase of the model consists in aneconomic dispatch based on an AC optimal power flow (AC-OPF); in the second phase Kirschen’s andBialek’s tracing algorithms are used and compared to evaluate the impact of each resource in the net-work. Finally, the MW-mile method is used in the third phase of the proposed model. A distributionnetwork of 33 buses with large penetration of DER is used to illustrate the application of the proposedmodel.

E-Health individual adoption - empirical model based on UTAUT 2.

The future of health care delivery is becoming more citizen-centred, as today’s user is more active, better informed and more demanding. The European Commission is promoting online health services and, therefore, member states will need to boost deployment and use of online services. This makes e-health adoption an important field to be studied and understood. This study applied the extended unified theory of acceptance and usage technology (UTAUT2) to explain patients’ individual adoption of e-health. An online questionnaire was administrated Portugal using mostly the same instrument used in UTAUT2 adapted to e-health context. We collected 386 valid answers. Performance expectancy, effort expectancy, social influence, and habit had the most significant explanatory power over behavioural intention and habit and behavioural intention over technology use. The model explained 52% of the variance in behavioural intention and 32% of the variance in technology use. Our research helps to understand the desired technology characteristics of ehealth. By testing an information technology acceptance model, we are able to determine what is more valued by patients when it comes to deciding whether to adopt e-health systems or not.

Tradução e validação para Portugal do Patient Activation Measure 13 : em pessoas com Diabetes Mellitus tipo 2

RESUMO - Introdução: A Diabetes Mellitus Tipo 2 (DM2) tem uma elevada prevalência em todo o mundo, com impacto significativo a nível de Saúde Pública, na vida dos doentes e nos custos que lhe são associados. O Patiente Activation Measure 13 (PAM13) é um questionário que possibilita a avaliação das crenças, conhecimentos, motivação e capacidades de uma pessoa em relação à sua saúde; pelo que a sua utilização na DM2 é pertinente. Objetivos: Traduzir o PAM 13, versão curta, para Português de Portugal; Estabelecer as propriedades psicométricas da versão Portuguesa do PAM 13 (PAM13-P); Validar a PAM 13-P num grupo de pessoas com DM2. Material e métodos: O processo de tradução e adaptação cultural do questionário foi composto pelas fases: 1-Tradução, 2-Reconciliação e síntese, 3-Back translation, 4-Rever e sintetizar a Back translation, 5-Harmonização, 6-Revisão do comité de peritos, 7-Cognitive debriefing e 8-Avaliação final. Para validar o PAM13-P realizou-se um estudo observacional transversal analítico com uma amostra de conveniência, de pessoas com DM2, seguidas na Associação Protectora dos Diabéticos de Portugal. O questionário foi de autopreenchimento e foi consultado o processo clínico para obtenção da HbA1c. O tratamento estatístico foi realizado através do SPSS 21® e Winsteps v3.8.1®. Resultados e discussão: O processo de tradução e adaptação cultural foi realizado de acordo com as guidelines. Foram realizados 3 painéis de e-Delphi, com 21 participantes de áreas distintas, tendo-se obtido bons níveis de concordância. As principais modificações realizadas ao questionário foram a simplificação da linguagem e dos itens, obtendo-se as equivalências necessárias. O PAM13-P foi aplicado a 201 pessoas, sendo que a taxa de resposta foi de 83%. Na amostra analisada 57.3% eram homens. Obtiveram-se as médias de idade 67.1 anos e de duração de diabetes 17.3 anos. A média do score do PAM foi 58.5±10.1(41.8-90.5) pontos e 49,7% da amostra estava no nível 3 de ativação. Relativamente aos itens verificou-se que os itens mais difíceis foram o 13(56.1) e o 8(55.4) e o com menor dificuldade foi 4(38.5). As categorias de resposta tiveram um bom ajuste ao Modelo de Rasch. O ajustamento dos itens foi infit entre 0.779-1.177 e outfit entre 0.794-1.315. A fiabilidade dos indivíduos variou entre 0.77(real) e 0.83(modelo) e dos itens foi de 0.97 (real e modelo). O Alfa de Cronbach foi bom (α=0.82). Estas estatísticas foram semelhantes aos da validação do PAM13. Existiu uma relação entre o score do PAM e os itens de validação em 51%. Das variáveis analisadas, existia um relação do nível de ativação com a idade e com a HbA1c. Conclusões: O PAM13-P foi traduzido e adaptado culturalmente para Português e foi validado em pessoas com DM2, sendo as propriedades psicométricas boas.

Quantifying diffusion in biofilms : from model hydrogels to living biofilms

Les biofilms sont des communautés de microorganismes incorporés dans une matrice exo-polymérique complexe. Ils sont reconnus pour jouer un rôle important comme barrière de diffusion dans les systèmes environnementaux et la santé humaine, donnant lieu à une résistance accrue aux antibiotiques et aux désinfectants. Comme le transfert de masse dans un biofilm est principalement dû à la diffusion moléculaire, il est primordial de comprendre les principaux paramètres influençant les flux de diffusion. Dans ce travail, nous avons étudié un biofilm de Pseudomonas fluorescens et deux hydrogels modèles (agarose et alginate) pour lesquels l’autodiffusion (mouvement Brownien) et les coefficients de diffusion mutuels ont été quantifiés. La spectroscopie par corrélation de fluorescence a été utilisée pour mesurer les coefficients d'autodiffusion dans une volume confocal de ca. 1 m3 dans les gels ou les biofilms, tandis que les mesures de diffusion mutuelle ont été faites par cellule de diffusion. En outre, la voltamétrie sur microélectrode a été utilisée pour évaluer le potentiel de Donnan des gels afin de déterminer son impact sur la diffusion. Pour l'hydrogel d'agarose, les observations combinées d'une diminution du coefficient d’autodiffusion et de l’augmentation de la diffusion mutuelle pour une force ionique décroissante ont été attribuées au potentiel de Donnan du gel. Des mesures de l'effet Donnan (différence de -30 mV entre des forces ioniques de 10-4 et 10-1 M) et l'accumulation correspondante d’ions dans l'hydrogel (augmentation d’un facteur de 13 par rapport à la solution) ont indiqué que les interactions électrostatiques peuvent fortement influencer le flux de diffusion de cations, même dans un hydrogel faiblement chargé tel que l'agarose. Curieusement, pour un gel plus chargé comme l'alginate de calcium, la variation de la force ionique et du pH n'a donné lieu qu'à de légères variations de la diffusion de sondes chargées dans l'hydrogel. Ces résultats suggèrent qu’en influençant la diffusion du soluté, l'effet direct des cations sur la structure du gel (compression et/ou gonflement induits) était beaucoup plus efficace que l'effet Donnan. De même, pour un biofilm bactérien, les coefficients d'autodiffusion étaient pratiquement constants sur toute une gamme de force ionique (10-4-10-1 M), aussi bien pour des petits solutés chargés négativement ou positivement (le rapport du coefficient d’autodiffusion dans biofilm sur celui dans la solution, Db/Dw ≈ 85 %) que pour des nanoparticules (Db/Dw≈ 50 %), suggérant que l'effet d'obstruction des biofilms l’emporte sur l'effet de charge. Les résultats de cette étude ont montré que parmi les divers facteurs majeurs qui affectent la diffusion dans un biofilm environnemental oligotrophe (exclusion stérique, interactions électrostatiques et hydrophobes), les effets d'obstruction semblent être les plus importants lorsque l'on tente de comprendre la diffusion du soluté. Alors que les effets de charge ne semblaient pas être importants pour l'autodiffusion de substrats chargés dans l'hydrogel d'alginate ou dans le biofilm bactérien, ils ont joué un rôle clé dans la compréhension de la diffusion à travers l’agarose. L’ensemble de ces résultats devraient être très utiles pour l'évaluation de la biodisponibilité des contaminants traces et des nanoparticules dans l'environnement.

Pharmacométrie de la ropivacaïne suivant l’anesthésie locorégionale chez les patients orthopédiques : caractérisation de l’intensité et de la durée du bloc sensitif

Introduction & Objectifs : Pour assurer l’analgésie postopératoire, l’anesthésiste dispose, en plus des différentes classes de médicaments administrés par voie orale ou intraveineuse, de diverses techniques pour bloquer l’influx nerveux douloureux en administrant les anesthésiques locaux (AL) de manière centrale ou périphérique. La ropivacaïne (ROP), un AL à longue durée d’action, est un médicament de première intention partout dans le monde, en raison de sa grande efficacité et de son faible risque de toxicité. Contrairement à certains pays, la ROP n'est toujours pas indiquée au Canada pour la rachianesthésie (bloc central) en raison d'un manque de données probantes. Jusqu'à présent, les efforts de recherche ont essentiellement porté sur la sécurité ainsi que sur la durée d’action du médicament lorsqu’administré par voie spinale. De plus, les doses optimales de ROP pour l’anesthésie régionale périphérique ne sont pas encore précisément connues. La posologie devrait être adaptée au site d’administration ainsi qu’à l’intensité et la durée du stimulus produit par la chirurgie. Ultimement, cela permettrait aux cliniciens d’identifier le régime optimal en fonction des facteurs démographiques qui pourraient affecter la pharmacocinétique (PK) et la pharmacodynamie (PD) de l’AL (objectif global de ces travaux). Validation de la Méthode Analytique Manuscrit 1 : Une méthode analytique spécifique et sensible permettant de déterminer les concentrations plasmatiques de ROP a d’abord été optimisée et validée. Validation du Biomarqueur Manuscrit 2 : Nous avons ensuite mis au point et évalué la fiabilité d’une méthode quantitative basée sur la mesure du seuil de perception sensorielle (CPT) chez le volontaire sain. Ce test nécessite l’application d’un courant électrique transcutané qui augmente graduellement et qui, selon la fréquence choisie, est capable de stimuler spécifiquement les fibres nerveuses impliquées dans le cheminement de l’influx nerveux douloureux. Les résultats obtenus chez les volontaires sains indiquent que la mesure CPT est fiable, reproductible et permet de suivre l’évolution temporelle du bloc sensitif. Études cliniques Manuscrit 3 : Nous avons ensuite caractérisé, pendant plus de 72 h, l’absorption systémique de la ROP lorsqu’administrée pour un bloc du nerf fémoral chez 19 patients subissant une chirurgie du genou. Le modèle PK populationnel utilisé pour analyser nos résultats comporte une absorption biphasique durant laquelle une fraction de la dose administrée pénètre rapidement (temps d’absorption moyen : 27 min, IC % 19 – 38 min) dans le flux sanguin systémique pendant que l’autre partie, en provenance du site de dépôt, est redistribuée beaucoup plus lentement (demi-vie (T1/2) : 2.6 h, IC % 1.6 – 4.3 h) vers la circulation systémique. Une relation statistiquement significative entre l’âge de nos patients et la redistribution de l’AL suggère que la perméabilité tissulaire est augmentée avec l’âge. Manuscrit 4 : Une analyse PK-PD du comportement sensitif du bloc fémoral (CPT) a été effectuée. Le modèle développé a estimé à 20.2 ± 10.1 mg la quantité de ROP nécessaire au site d’action pour produire 90 % de l’effet maximal (AE90). À 2 X la AE90, le modèle prédit un début d’action de 23.4 ± 12.5 min et une durée de 22.9 ± 5.3 h. Il s’agit de la première étude ayant caractérisé le comportement sensitif d’un bloc nerveux périphérique. Manuscrit 5 : La troisième et dernière étude clinique a été conduite chez les patients qui devaient subir une chirurgie du genou sous rachianesthésie. Tout comme pour le bloc du nerf fémoral, le modèle PK le plus approprié pour nos données suggère que l’absorption systémique de la ROP à partir du liquide céphalo-rachidien est biphasique; c.à.d. une phase initiale (T1/2 : 49 min, IC %: 24 – 77 min) suivie (délai: 18 ± 2 min) d'une phase légèrement plus lente (T1/2 : 66 min, IC %: 36 – 97 min). L’effet maximal a été observé beaucoup plus rapidement, soit aux environs de 12.6 ± 4.9 min, avant de revenir aux valeurs de base 210 ± 55 min suivant l’administration de l’agent. Ces données ont permis d’estimer une AE50 de 7.3 ± 2.3 mg pour l'administration spinale. Conclusion : En somme, ces modèles peuvent être utilisés pour prédire l’évolution temporelle du bloc sensitif de l’anesthésie rachidienne et périphérique (fémorale), et par conséquent, optimiser l’utilisation clinique de la ROP en fonction des besoins des cliniciens, notamment en ce qui a trait à l’âge du patient.

Emma Hamilton, a Model of Agency in Late Eighteenth-Century Europe

Emma Hamilton (1765-1815) eut un impact considérable à un moment charnière de l’histoire et de l’art européens. Faisant preuve d’une énorme résilience, elle trouva un moyen efficace d’affirmer son agentivité et fut une source d’inspiration puissante pour des générations de femmes et d’artistes dans leur propre quête d’expression et de réalisation de soi. Cette thèse démontre qu’Emma tira sa puissance particulière de sa capacité à négocier des identités différentes et parfois même contradictoires – objet et sujet ; modèle et portraiturée ; artiste, muse et œuvre d’art ; épouse, maîtresse et prostituée ; roturière et aristocrate ; mondaine et ambassadrice : et interprète d’une myriade de caractères historiques, bibliques, littéraires et mythologiques, tant masculins que féminins. Épouse de l’ambassadeur anglais à Naples, favorite de la reine de Naples et amante de l’amiral Horatio Nelson, elle fut un agent sur la scène politique pendant l’époque révolutionnaire et napoléonienne. Dans son ascension sociale vertigineuse qui la mena de la plus abjecte misère aux plus hauts échelons de l’aristocratie anglaise, elle sut s’adapter, s’ajuster et se réinventer. Elle reçut et divertit d’innombrables écrivains, artistes, scientifiques, nobles, diplomates et membres de la royauté. Elle participa au développement et à la dissémination du néoclassicisme au moment même de son efflorescence. Elle créa ses Attitudes, une performance répondant au goût de son époque pour le classicisme, qui fut admirée et imitée à travers l’Europe et qui inspira des générations d’interprètes féminines. Elle apprit à danser la tarentelle et l’introduisit dans les salons aristocratiques. Elle influença un réseau de femmes s’étendant de Paris à Saint-Pétersbourg et incluant Élisabeth Vigée-Le Brun, Germaine de Staël et Juliette Récamier. Modèle hors pair, elle inspira plusieurs artistes pour la production d’œuvres qu’ils reconnurent comme parmi leurs meilleures. Elle fut représentée par les plus grands artistes de son temps, dont Angelica Kauffman, Benjamin West, Élisabeth Vigée-Le Brun, George Romney, James Gillray, Joseph Nollekens, Joshua Reynolds, Thomas Lawrence et Thomas Rowlandson. Elle bouscula, de façon répétée, les limites et mœurs sociales. Néanmoins, Emma ne tentait pas de présenter une identité cohérente, unifiée, polie. Au contraire, elle était un kaléidoscope de multiples « sois » qu’elle gardait actifs et en dialogue les uns avec les autres, réarrangeant continuellement ses facettes afin de pouvoir simultanément s’exprimer pleinement et présenter aux autres ce qu’ils voulaient voir.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Preconditioner updates applied to CFD model problems

In the present paper we concentrate on solving sequences of nonsymmetric linear systems with block structure arising from compressible flow problems. We attempt to improve the solution process by sharing part of the computational effort throughout the sequence. This is achieved by application of a cheap updating technique for preconditioners which we adapted in order to be used for our applications. Tested on three benchmark compressible flow problems, the strategy speeds up the entire computation with an acceleration being particularly pronounced in phases of instationary behavior.

Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

A Multi-scale Model for Copper Dishing in Chemical-Mechanical Polishing

The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.

A Multi-scale Model for Copper Dishing in Chemical-Mechanical Polishing

The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.