The chromatic polynomial of a graph, is a polynomial that when evaluated at a positive integer k, is the number of proper k colorings of the graph. We can then find the orbital chromatic polynomial of a graph and a group of automorphisms of the graph, which is a polynomial whose value at a positive integer k is the number of orbits of k-colorings of a graph when acted upon by the group. By considering the roots of the orbital chromatic and chromatic polynomials, the similarities and differences of these polynomials is studied. Specifically we work toward proving a conjecture concerning the gap between the real roots of the chromatic polynomial and the real roots of the orbital chromatic polynomial.

Since the beginning of the last century, many studies have been performed in order to improve our understanding on the milling process. Recently, Mishra and Rajamani (1992) applied the Discrete Element Method (DEM) to solve the milling problem. Since then, this method gained considerable success due to its ability to predict load motion and power draw by tumbling mills as affected by operating conditions. The application of this method at an industrial stage requires a more rigorous validation in order to produce realistic output. Lifter profiles play a key role in the performance of tumbling mills since they influence the motion of mill charge. Since lifters change profiles during their useful life due to wear, the performance of tumbling mills will correspondingly vary as a function of time. There is therefore a need to predict forces and wear on mill lifters in order not only to chose or design an initial lifter profile which optimizes tumbling mills performance over the lifters’ useful life but also to evaluate lifter replacement time and type and also modifications which can be performed on lifters and/or operating mill conditions in order to extend the lifters’ useful life. Despite the importance related to this subject, few works has been done in this field. In this thesis, we firstly assess the ability of the Discrete Element Method to model the tangential and normal forces exerted by the mill charge on lifters. Data from an experimental two-dimensional mill designed in order to record the normal and tangential forces exerted on an instrumented lifter were available. The measured results obtained at different speeds and percentages of filling have been compared to the Discrete Element Method simulated results in the same conditions. A good agreement has been found between the experimental and the simulated results in terms of toe, shoulder positions and amplitude of forces. After this validation of the DEM, we secondly assess the ability of this method to predict the wear of lifters in dry milling conditions. We derived a mathematical wear equation describing the removal of materials from lifters which takes into account all types of wear occurring in dry milling environment. We introduce a new approach to implement this equation in the DEM code in order to produce realistic simulated profiles. Our new method developed has been tested against laboratory and industrial data of evolving lifter profiles due to wear. Good agreement has been found between the simulated and the measured profiles. The variation of the load behaviour as a function of lifter wear in industrial tumbling mills studied was also investigated in this thesis. The objectives were to improve the understanding of the grinding process and quantify the variation of load behaviour as a function of lifter wear. Lifter modifications were also explored in order to extend lifters useful life. An attempt was also made in this thesis to derive, from the description of the load behaviour, equations in order to predict the wear of lifters without using the Discrete Element Method. Equations derived show the difficulty to use this approach. Success in this case was achieved only in a particular case where no significant changes occur in the load behaviour as a function of lifters wear. This finding confirms the DEM as the adequate tool to model forces and wear of tumbling mill lifters. The results obtained are of great economical significance since they can improve the profitability of mineral processing plants. A step forward in the use of the DEM not only to design milling equipments but also to improve the understanding, optimise and quantify the change occurring as a function of lifters wear was achieved.

Orientador: José Paulo Fernandes Garcia / Banca: Laurence Duarte Colvara / Banca: Ivan Nunes da Silva / Resumo: O enfoque principal do trabalho foi dado ao Controle Discreto com Modos Deslizantes(CDMD) aplicado em sistemas que possuem atraso no processamento do sinal de controle e acesso somente à saída do sistema. A estratégia de controle tem por objetivo a utilização de técnicas de controle com modos deslizantes para a elaboração de uma lei de controle simples e robusta às incertezas da planta e ao atraso. O observador de estados apresentado possui características de modo deslizante, o qual realiza a estimação robusta do vetor de estados que na maioria dos casos práticos não é totalmente acessível. Os métodos de projetos propostos podem ser aplicados no controle de plantas estáveis ou instáveis com atraso no sinal de controle e acesso somente à saída da planta. Para comprovar a eficiência dos projetos apresentados neste trabalho, analisou-se o controlador atuando com acesso a todos estados e o controlador atuando juntamente com o observador robusto para a estimação dos estados. Os resultados foram obtidos através de simulações no Sistema Bola e Viga, Sistema Pêndulo Invertido Linear e Sistema Pêndulo Invertido Rotacional que são exemplos de plantas de natureza instável. / Abstract: The main focus was placed on the Discrete Sliding Mode Control (DSMC) applied to systems that have a delay in the processing of the control signal and access to the system output only. The control strategy is intended to use control techniques of sliding modes to elaborate a simple and robust control law against the uncertainties of the plant and the delay. The states observer presented has the characteristics of a sliding mode, which performs the robust estimation of the states vector that, in most practical cases, is not fully accessible. The design methods proposed may be applied to the control of stable or unstable plants with delay on the control signal and access to the plant output only. In order to attest the efficiency of the design presented in this work, the controller was analyzed at work with access to all states and jointly with the robust observer to estimate the states. The results were obtained by means of simulations in the Ball and Beam System, Linear Inverted Pendulum System, and Rotational Inverted Pendulum System, which are examples of plants of unstable nature. / Mestre

São apresentados resultados envolvendo subespaços discretos em diversos tipos de problemas em Topologia Geral. São também apresentadas construções de contraexemplos tanto em ZFC como com axiomas extras. / It is presented some results involving discrete subspaces in many kind of problems in General Topology. It is also presented some constructions of counterexamples in ZFC and assuming extra axioms.

Vehicular Ad-hoc Network (VANET) is considered to be a viable technology for inter- vehicle communications for the purpose of improving road safety and efficiency. The En- hanced Distribution Channel Access (EDCA) mechanism and multichannel operations are introduced to ensure the Quality of Service (QoS). Therefore, it is necessary to create an accurate vehicular network simulator that guarantees the vehicular communications will work as described in the protocols. A comprehensive vehicular network simulator should consider the interaction between mobility models and network protocols. In this dissertation, a novel vehicular network simulation environment, VANET Toolbox, designed using discrete-event system (DES) is presented. The APP layer DES Module of the proposed simulator integrates vehicular mo- bility operations with message generation functions. The MAC layer DES module supports single channel and multichannel EDCA operations. The PHY layer DES module supports bit-level processing. Compared with packet-based simulator such as NS-3, the proposed PHY layer is more realistic and accurate. The EDCA scheme is evaluated and compared with the traditional Carrier-Sensing Mul- tiple Access (CSMA) scheme, with the simulations proving that data with different priorities can coexist in the same channel. The multichannel operation for the EDCA scheme is also analyzed in this dissertation. The multichannel switching operation and coordination may cause packet dropping or increased latency to the communication. The simulations show that with heavy network traffic, multichannel communication performs better than single channel communication. From the perspective of safety-related messages, the multichannel operation is able to isolate the interference from the non-safety messages in order to achieve a better packet delivery rate and latency. On the other hand, the non-safety messages can achieve high throughput with reasonable latency from multichannel communication under heavy load traffic scenario.

Symbicort Turbuhaler is a medical device produced by the pharmaceutical company AstraZeneca for the treatment of asthma and symptoms of chronic obstructive pulmonary disease. The delivery reliability of the product is dependent on the performance of the whole supply chain and as part of the chain the results from the department, Quality Control (QC), are mandatory to release the produced batches to the market. The performance of QC is thus an important part of the supply chain. In order to reduce the risk of supply problems and market shortage, it is very important to investigate whether the performance of QC can be improved. The purpose of the thesis is to provide AstraZeneca with scientifically based data to identify sensitive parameters and readjust work procedures in order to improve the performance of QC. The goal of this thesis is to map out the flow of the QC Symbicort Turbuhaler operation and construct a model of it. The model is intended to be used to simulate and optimize different parameters, such as the inflow of batch samples, the utilization of the instrumentation and staff workload. QC is modelled in a simulation software. The model is used to simulate and optimize different scenarios following a discrete event simulation and an optimization technique based on evolution strategies. By reducing the number of analytical robots from 14 to 10, it is possible to maintain existing average lead time. Through a reduction, the utilization of the robots increases, simultaneously the workload decreases for some of the staff. However, it is not possible to extend the durability of the system suitability test (SST), and still achieve existing average lead time. From the investigation of different parameters, it is found that, an added laboratory engineer at the high-performance liquid chromatography (HPLC) station has the best outcome on lead time and overall equipment effectiveness. However, a reduced laboratory engineer at the Minispice robots has the worst outcome. With the resources available today the lead times cannot be maintained in the long run, if the inflow is of 35 batch samples a week or more. By adding a laboratory engineer at the HPLC station and by using a SST with durability of 48 hours, the best outcome in terms of average lead time and number of batch samples with a lead time less than 10 days is received. / Symbicort Turbuhaler är en medicinsk enhet som tillverkas av läkemedelsföretaget AstraZeneca för behandling av astma och symptomen för kronisk obstruktiv lungsjukdom. Leveranssäkerheten för produkten är beroende av hela försörjningskedjans prestanda och som en del utav kedjan är resultaten från kvalitetskontrollen (QC) obligatoriska för att släppa en batch av produkten till marknaden. QCs prestanda är därför en viktig del av försörjningskedjan. För att minska risken för leveransproblem och produktbrist på marknaden är det viktigt att undersöka huruvida prestandan hos QC kan förbättras. Syftet med arbetet är att ge AstraZeneca vetenskapligt baserat data för att identifiera känsliga parametrar och justera arbetssätt för att förbättra prestandan hos QC. Målet med detta arbete är att kartlägga flödet av QC Symbicort Turbuhaler och konstruera en modell utifrån det flödet. Modellen är avsedd för att simulera och optimera olika parametrar, såsom inflödet av batchprover, utnyttjande av instrumentering och arbetsbelastning av personal. Genom att minska antalet analytiska robotar från 14 till 10, är det möjligt att bibehålla befintlig genomsnittlig ledtid. Genom denna minskning ökar utnyttjandet av robotarna, samtidigt som arbetsbelastningen minskar för en del av bemanningen. Det är inte möjligt att förlänga hållbarheterna på robotarnas systemtest (SST) och fortfarande uppnå befintlig genomsnittlig ledtid. Vid undersökning av olika parametrar indikerar resultatet att en ytterligare laboratorieingenjör vid högpresterande vätskekromatografi-stationen (HPLC) har den bästa effekten på ledtid och produktionseffektivitet. En laboratorieingenjör som reduceras från Minispice-robotarna har däremot den värsta effekten. Med de resurser som finns tillgängliga idag kan ledtiderna inte bibehållas långsiktigt om inflödet är 35 batchprover per vecka eller mer. Genom att addera en laboratorieingenjör vid HPLC-stationen och användaen SST med en hållbarhet på 48 timmar, erhålls det bästa resultatet i termer av genomsnittlig ledtid och antal batchprover som har en individuell ledtid på mindre än 10 dagar.

Cette thèse s’inscrit au carrefour du monde de la modélisation et simulation de systèmes d’une part et du monde de l’ingénierie logicielle d’autre part. Elle vise à faire bénéficier un formalisme de spécification de systèmes à évènements discrets (DEVS) des apports de l’ingénierie dirigée par les modèles (IDM) avec l’une de ses incarnations les plus populaires : MDA (Model Driven Architecture). Le formalisme DEVS de par son adaptabilité et son extensibilité permet l’expression et la simulation de modèles dans des domaines très variés, mais l’existence de plusieurs plateformes dédiées à ce langage nuit fortement à l’interopérabilité de ces modèles. Ces difficultés, si elles ne sont pas nouvelles, représentent cependant un défi d’autant plus important que les modèles considérés sont complexes (i.e composés en général de nombreux sous modèles et interagissant fortement entre eux). L’objectif de la thèse est de proposer une réponse à la problématique de l’interopérabilité des modèles DEVS, vis-À-Vis d’autres formalismes voisins de DEVS et également vis-À-Vis des différents simulateurs existants. Le cœur de notre travail est constitué par MetaDEVS, méta-Modèle offrant une représentation des modèles DEVS indépendante des plateformes. MetaDEVS est également le nom donné à l’approche globale qui vise à fournir des passerelles génériques entre différents formalismes et DEVS («Model-To-Model»). Cette approche montre également comment, à partir de modèles DEVS spécifiés selon MetaDEVS, du code orienté-Objet, simulable, peut être automatiquement généré («Model-To-Text»).Les formalismes choisis pour faire l’objet d’une transformation vers DEVS sont BasicDEVS, un petit formalisme pédagogique créé pour l’occasion, ainsi que les automates à états finis (FSM). La plateforme de destination choisie pour la génération de code est la plateforme éducative PyDEVS, compatible avec la plateforme DEVSimPy, utilisée par les chercheurs du projet TIC de l’Università di Corsica. / This thesis takes place at the intersection between the world of modeling and simulation, and the world of software engineering. Its provides a contribution to a discrete-Event specification formalism (DEVS) using techniques of Model-Driven Engineering, with one of its most popular incarnations : MDA (Model Driven Architecture). The DEVS formalism, thanks to its adaptability and its extensibility, is able to express and simulate models in various domains. However, the existence of many dedicated platforms damages the interoperability of those models. Those difficulties, even if they are not new, are a challenge which is all the greater as the studied models are complex (i.e. usually composed of several submodels with a strong interaction).The main purpose of this thesis is to tackle the problem of the DEVS models interoperability, with respect to other formalisms close to DEVS, and also with respect to the different existing simulators. The core of our work is constituted by MetaDEVS, a metamodel that offers a platform-Independent representation of DEVS models. MetaDEVS is also the name given to the global approach which aims to provide generic bridges between different formalisms and DEVS (“Model-To-Model”). This approach also shows how, starting from DEVS models specified with MetaDEVS, object-Oriented code can be automatically generated (“Model-To-Text”).The formalisms chosen to be transformed into DEVS are BasicDEVS, a small pedagogical formalism create for our needs, and the finite state machines (FSM). The chosen target platform for the code generation is the educative framework PyDEVS, compliant with the DEVSimPy framework used by the researchers of the TIC project of the University of Corsica.

The present investigation examined observational learning during equivalence-based instruction using the PEAK Equivalence curriculum, across five children with disabilities. A multiple baseline across skills was used to evaluate observational learning across the participants, including directly observed relations, as well as derived symmetrical and transitive relations. Each skill contained 5 stimulus classes, where a subset of relations for a single class was trained for each participant. The remaining 4 class subsets were observed by each of the participants. For the derived relations, participants never observed peers contact reinforcement for correct responding nor did they themselves contact reinforcement for correct responding. After multiple sessions, results indicated increases in both observed directly trained relations, as well as emergent derived relations. Over the course of the sessions, the participants average correct answers increased from an average of 12% during baseline to100% at the end of the training phase and during a follow-up test probe. The results have implications for equivalence-based ABA instruction in schools and other settings where group-based instruction is common in application with individuals with disabilities.

The main objective of this thesis is to take one step forward to practical and realisable devices for antenna and microwave engineering, using the technique of discrete coordinate transformation (DCT), which is a practical implementation of the coordinate transformation method. During this thesis, the DCT technique was demonstrated and analysed from the theory, and was proved to provide an all-dielectric approach to design devices under certain conditions. Two schemes were proposed on how to use this technique in a practical design. The first one is to transform an existing device into a flattened profile, meanwhile maintaining its electromagnetic performance. As examples, a flat reflector and a flat lens were created from a parabolic reflector and a convex lens, respectively. The second scheme is to project the propagating paths of an electromagnetic wave, and then generate a distorted space according to the paths by engineering the electromagnetic properties of the media. In this scheme, two examples of application were presented: an undetectable antenna composed of a carpet cloak and a conducting cavity, and a broadband device which can extraordinarily enhance the transmission through a sub-wavelength aperture. Numerical simulations based on the Finite-Difference Time-Domain (FDTD) method were implemented to verify all the designs. Several specific configurations were employed in the modelling in order to simulate the DCT based devices more efficiently and precisely. Performance of these devices was validated and analysed, and the advantages and disadvantages of this technique were investigated. Realisation and fabrication methods i were also studied, and a prototype was designed, fabricated and measured. At the end, as an extension, a multiple discrete coordinate transformation method was proposed and presented. This multiple transformation was proved to effectively relax the limitation of the one-step transformation, and was used to design an all-dielectric thin absorber from a conventional pyramidal one for demonstration.

This thesis lies in the field of probabilistic and extremal combinatorics: we study discrete structures, with a focus on thresholds, when the behaviour of a structure changes from one mode into another. From a probabilistic perspective, we consider models for a random structure depending on some parameter. The questions we study are then: When (i.e. for what values of the parameter) does the probability of a given property go from being almost 0 to being almost 1? How do the models behave as this transition occurs? From an extremal perspective, we study classes of structures depending on some parameter. We are then interested in the following questions: When (for what value of the parameter) does a particular property become unavoidable? What do the extremal structures look like? The topics covered in this thesis are random geometric graphs, dependent percolation, extremal hypergraph theory and combinatorics in the hypercube.