Дисертації з теми "Modelli deterministici"

Lo scopo di questo lavoro di tesi è quello di analizzare i modelli deterministici di dinamica delle popolazioni, dal primo e più semplice modello Malthusiano per la descrizione del comportamento dinamico di un insieme di individui considerati pressoché identici, fino ad arrivare allo studio dei sistemi del tipo preda-predatore trattati grazie al famoso modello di Lotka-Volterra. Tale modello è stato studiato nella sua versione base, in cui esso descrive la dinamica di interazione tra due specie compresenti nello stesso ambiente, sia da un punto di vista puramente matematico sia tramite simulazioni numeriche. Successivamente il modello è stato complicato per descrivere in modo migliore sistemi reali in cui non sono disponibili risorse infinite per lo sviluppo degli individui grazie all’utilizzo di un termine derivato dal modello di crescita logistica. Successivamente si è passati allo studio di un’ultima complicazione del modello, trattando i sistemi a più specie, esponendo il costrutto matematico definente tali sistemi, da un punto di vista puramente teorico per il caso ad N specie, mentre invece è stato approfondito il caso particolare del tipo preda-preda-predatore studiandone le proprietà dinamiche è commentando le soluzioni ricavate nuovamente tramite simulazione. Infine, i modelli precedentemente esposti sono stati utilizzati per operare un confronto con alcuni dati provenienti da due ricerche appartenenti a due ambiti scientifici diversi.

Railway sleepers have important roles in the complex railway system. Due to different loading condition, poor maintenance of sleeper or bad quality of ballast, a random load distribution along the sleeper-ballast interface may occur. A sleeper design, and also the track system design, which do not consider the random load distribution, could influence the performance of the sleeper and even damage the whole railway system. Thus, a numerical static and dynamic analysis for a pre-stressed concrete mono-block railway sleeper is carried out using finite element method. The structural behaviour of a single sleeper subjected to a random sleeper-ballast interaction is studied in three steps. First, four typical scenarios of support condition for sleeper are discussed in numerical analysis. Second, large enough numerical results under different random support conditions are conducted. Finally, Neural Network methodology is used to study the performance of sleeper under a stochastic support condition. Results of vertical displacement of rail seat, tensile stress at midpoint and underneath rail seat are presented. Moreover, the worst support condition is also identified.

Questa tesi introduce le basi del geomagnetismo partendo da un approccio ai modelli fluidi e alle equazioni MHS, accennando alle numerose difficoltà che portano in materia di simulazioni e calcoli. In seguito si introducono i modelli a disco con uno studio approfondito della dinamica che, pur partendo da equazioni molto più semplici e approssimate della trattazione fluida, trova riscontro con i punti fondamentali del geomagnetismo e con i comportamenti dei modelli fluidi.

Livestock is amongst Australia’s most enduring and prolific industries; however whole-body modelling approaches are limited in livestock research. Mathematical techniques are employed, extending an existing lamb growth model to adulthood. It tracks wool, protein, fat, metabolites and DNA pools, simulating whole-body metabolism. Implementation into a dynamic optimisation package allows for the optimisation of model parameters to improve model behaviour. The focus is on feed, nutrient absorption, energy expenditure, wool growth and defining appropriate initial conditions.

The horserace betting market is a subset of the financial market space, and wagering typically inherits a defined return – to – risk trade-off. For horserace betting input into institutional portfolio to be plausible, the payoff – to – risk trade-off from betting must be acceptable for the fund when compared with the return – risk trade-off from the existing mainstream assets included in portfolio investment. A new paradigm for horserace betting modelling and investing is acclaimed in this thesis, as premiss for betting input into institutional portfolio. An exchange traded betting fund is developed in the thesis that is able to generate pre-race (and within-race) investment arbitrage that offers an acceptable, defined return – risk trade-off for the risk averse investor. The extensive former horserace betting market stochastic modelling theory that forecasts racer expected outcomes and payoff, is today succeeded by this research that develops a deterministic horserace betting model (and algorithm) that generates defined payoff for the fund. This deterministic betting model challenges the existing semi-strong efficient market hypothesis toward horserace betting that no betting strategy consistently outperforms the financial market’s benchmark return. Subsequently, the primary research (alternative) hypothesis tested is H_a: profitable exchange traded horserace betting fund with deterministic payoff exists for acceptable institutional portfolio investment.
Thesis (Masters)
Master of Philosophy (MPhil)
Griffith School of Environment
Science, Environment, Engineering and Technology
Full Text

Orientador: Liliane Maria Ferrareso Lona
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica
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Resumo: Neste trabalho, foram estudados diferentes processos de polimerização: (1) homopolimerização do estireno e copolimerização do estireno com metacrilato de metila em emulsão via radical livre convencional e (2) homopolimerização do estireno em massa via radical livre no processo controlado/vivo mediado por nitróxido. A modelagem dos processos foi realizada por meio de duas abordagens diferentes: inicialmente, modelos determinísticos foram desenvolvidos para cada caso e, utilizando resultados gerados por esses modelos, redes neurais foram treinadas para a modelagem inversa dos processos. Na modelagem determinística, foram desenvolvidos programas computacionais para as polimerizações em emulsão e simulações foram realizadas para diferentes condições operacionais. Para a polimerização controlada em massa, foi utilizado um programa computacional da literatura ao qual foram introduzidas modificações. Em todos os casos, foram levantados extensos bancos de dados de parâmetros cinéticos para todos os componentes envolvidos. Para o trabalho com as redes neurais, foi utilizado um programa computacional previamente desenvolvido ao qual foram introduzidas modificações. Redes neurais foram utilizadas para modelagem inversa dos processos, sendo treinadas para a predição de condições operacionais capazes de levar à produção de polímeros com propriedades específicas. As duas metodologias utilizadas para a modelagem matemática foram capazes de extrair importantes e diferentes informações dos processos de polimerização estudados, mostrandose portanto ferramentas bastante interessantes e eficientes para aplicação na área de engenharia de polimerização
Abstract: In this work different polymerization processes were studied: (1) styrene homopolymerization and styrene/methyl methacrylate copolymerization in emulsion in the conventional freeradical process, and (2) styrene homopolymerization in bulk in the nitroxidemediated controlled/living freeradical process. Modelling was developed using two different approaches: initially deterministic models were developed in each case, and using results from these models neural networks were trained to the inverse modelling of the processes. In the deterministic modelling, computational programas were developed to the emulsion polymerizations, and simulations were performed for different operating conditions. A modified computational program from the literature was used in the controlled polymerization in bulk. In all cases, large databases of kinetic parameters to all the compounds present were searched. A modified computational program previously developed was used in the work with neural networks. Neural networks were used to the inverse modelling of the processes, and were trained to predict operating conditions that could lead to production of polymers with specific properties. The two methodologies used in the mathematical modelling were able to extract important and different information from the polymerization processes studied, showing its potential to an efficient aplication in the polymerization area
Doutorado
Desenvolvimento de Processos Químicos
Doutor em Engenharia Química

This dissertation presents the calibration-free image sensor modelling process applicable for localisation, such that these are robust to changes in environment and in sensor properties. The modelling process consists of two distinct parts, which are deterministic and stochastic techniques, and is achieved using mechanistic deconvolution, where the sensor???s mechanical and electrical properties are utilised. In the deterministic technique, the sensor???s effective focal length is first estimated by known lens properties, and is used to approximate the lens system by a thick lens and its properties. The aperture stop position offset???which is one of the thick lens properties???then derives a new factor, namely calibration-free distortion effects factor, to characterise distortion effects inherent in the sensor. Using this factor and the given pan and tilt angles of an arbitrary plane of view, the corrected image data is generated. The corrected data complies with the image sensor constraints modified by the pan and tilt angles. In the stochastic technique, the stochastic focal length and distortion effects factor are first approximated, using tolerances of the mechanical and electrical properties. These are then utilised to develop the observation likelihood necessary in recursive Bayesian estimation. The proposed modelling process reduces dependency on image data, and, as a result, do not require experimental setup or calibration. An experimental setup was constructed to conduct extensive analysis on accuracy of the proposed modelling process and its robustness to changes in sensor properties and in pan and tilt angles without recalibration. This was compared with a conventional modelling process using three sensors with different specifications and achieved similar accuracy with one-seventh the number of iterations. The developed model has also shown itself to be robust and, in comparison to the conventional modelling process, reduced the errors by a factor of five. Using area coverage method and one-step lookahead as control strategies, the stochastic sensor model was applied into a recursive Bayesian estimation application and was also compared with a conventional approach. The proposed model provided better target estimation state, and also achieved higher efficiency and reliability when compared with the conventional approach.

Orientador : Rodney Carlos Bassanezi
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Não informado.
Abstract: Not informed.
Mestrado
Mestre em Matemática Aplicada

Orientador: Rubens Maciel Filho
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica
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Resumo: O processo de copolimerização do metacrilato de metila/acetato de vinila ocorre pelo mecanismo cinético de radicais livres. Este sistema de copolimerização é interessante pois o metacrilato de metila é muito mais reativo que o acetato de vinila, como indicado por suas respectivas taxas de reatividades, 26 e 0,3. O produto é caracterizado pela fração molar de metacrilato de metila no copolímero, pelo peso molecular e pela viscosidade intrínseca. O mecanismo reacional e parâmetros cinéticos foram obtidos da literatura (Congalidis, J.P., 1989) e discutidos no capítulo 3. O processo foi modelado em malha aberta por Mattedi (2003) em um software em Fortran. Tal software foi usado em simulações e estudo do processo. O comportamento dinâmico do sistema foi avaliado. O pacote Statistica versão 7.0 foi utilizado para a execução da técnica de planejamento fatorial, sendo que a ¿planta¿ do processo foi o próprio software de simulação. Esta etapa foi fundamental para a construção de modelos empíricos e da avaliação das variáveis fundamentais para cada saída do processo. A partir das avaliações do planejamento fatorial, escolheram-se as condições para simulação do modelo, inserindo-se variações-degrau nas variáveis de entrada do reator que influenciavam preponderantemente nas variáveis de saída do processo. A fim de se obter modelos práticos para operações no processo, foram elaborados modelos inteligentes, baseados em conceitos de lógica fuzzy
Abstract: The process of solution copolymerization of methyl methacrylate and vinyl acetate occurs through free radicals mechanism. This system of copolymerization is interesting therefore the methyl methacrylate is much more reactive that the vinyl acetate, as indicated for its respective rate of reactivity 26 and 0,3. A idea of the product quality is obtained by the methyl methacrylate molar fraction in the copolymer, molecular weight and intrinsic viscosity. The reaction mechanism and parameters kinetic had been gotten of literature (Congalidis, J.P., 1989) and showed in chapter 3. The process was modeling in open system by Mattedi (2003) in a software in FORTRAN. This software was used in simulation and study of the process. The dynamic behavior of the system was evaluated. The Statistica software version 7.0 was used for the execution of the technique of factorial planning, being that the "plant" of the process was the proper software of simulation. This stage was basic for the construction of empirical models and the evaluation of the basic variable for each control variable of the process. From the evaluations of the factorial planning, one chose the conditions for simulation of the model, inserting itself variation-step in manipulated variable of the reactor that influenced preponderantly in the control variable of the process. In order to get practical models for operations in the process, intelligent models were construct, based in concepts of fuzzy logic
Mestrado
Desenvolvimento de Processos Químicos
Mestre em Engenharia Química

Orientador: Rodney Carlos Bassanezi
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Ciencia da Computação
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Resumo: o tema central da dissertação está baseado na análise dos principais modelos matemáticos determinísticos aplicados para Fitopatologia. Concentramo-nos principalmente em modelos que envolvem a resistência de determinados tipos de patógenos relativos a fungicidas normalmente utilizados. Como uma ciência, a Fitopatologia tenta aumentar nosso conhecimento das causas e do desenvolvimento das doenças de plantas, e também desenvolver controles para todas as doenças. Uma epidemia é o progresso da doença no tempo e no espaço. Epidemiologia é a ciência de populações de patógenos em populações de plantas hospedeiras, e as doenças resultantes sob a influência do meio ambiente e interferências humanas. Matemática e modelos ajudam a desemaranhar relações dos dados medidos no campo a fim de entender a estrutura e operação do sistema dinâmico natural.
Abstract: Not informed.
Mestrado
Mestre em Matemática Aplicada

We analyse various chemical reaction schemes both deterministically and stochastically. The reactions are considered to demonstrate the rich, mathematical behaviour apparent in the systems, rather than to represent realistic chemical reactions. The deterministic analysis is carried out to provide insights into the behaviour of the systems that we can then consider stochastically.

Plasmids RK2 are broad host range plasmids and they carry genes for antibioticresistance. Their central control operon, encoding two global regulators KorA and KorB, is anatural example of a negatively self-regulated operon. The aim of the work described herewas to use mathematical models to better understand the function and adaptation of KorA and orB regulation, in the context of available experimental data. The deterministic models combined with statistical inference allowed for analyses of he regulation mechanism and hypothesis generation about the system dynamics. Furthermore, the extended model was applied to data from different plasmid hosts, in order to indentify processes that might cause a difference in KorB abundance between the hosts. The stochastic multi-scale models were constructed and used in order to understand evolutionary reasons for such a negative and cooperative autoregulation. The system was tested for optimizations in mRNA production, response time, fluctuation and robustness. Moreover, the effect of cooperative regulation on the response time of the switch between vegetative and conjugative transfer, was also tested. In conclusion, the studies have deepened our understanding of the model plasmid RK2, of negative and cooperative regulation more generally, and generated hypotheses suitable for experimental validations.

A enorme complexidade dos sistemas ecológicos tem sido uma grande barreira para a compreensão e o gerenciamento da problemática ambiental. Neste sentido a modelagem matemática é uma valiosa ferramenta, devido a sua capacidade de organizar as informações disponíveis sobre estes sistemas e de fazer previsões a seu respeito para diferentes condições. Desta forma a análise de sistemas naturais vem sendo abordada de diferentes maneiras, sendo que nas últimas décadas a teoria de ecossistemas expandiu-se e ramos específicos, que permitem seguir e predizer a evolução de ecossistemas, foram formulados. Um destes enfoques, conhecido como análise do fluxo de insumo-produto, pode ser utilizado para explicar o funcionamento e estrutura dos subsistemas de um ecossistema através da descrição dos fluxos de matéria ou energia. A análise do fluxo de insumo-produto pode ser representada através de dois modelos: o modelo determinístico ou o modelo estocástico, tendo sua origem em estudos de caso com o objetivo de analisar a econômica norte-americana, sendo uma extensão prática da teoria clássica de interdependência geral. Este trabalho faz uma abordagem sintética da evolução desta análise, avaliando dados teóricos e principalmente dados referentes à Lagoa Itapeva. A análise de input-output (determinística e estocástica) com o propósito de obter informações no que diz respeito aos fluxos (matéria e energia), é bastante simples; sendo que os modelos determinísticos se prestam melhor para traçar um panorama global e para obter projeções para as variáveis já os modelos estocásticos são mais complexos, mas provêem uma descrição mais acurada. Na Lagoa Itapeva os processos determinísticos demonstraram um baixo índice de ciclagem do carbono entre os três compartimentos em estudo e o fluxo preferencial na normalização corresponde ao compartimento dos produtores primários, isto decorre de não existir loop nos compartimentos em estudo e também não existir fluxos em dois sentidos. Em relação à avaliação estocástica foram observadas uma baixa relação no sentido espacial superfície-meio-fundo da lagoa, e uma boa distribuição espacial norte-centro-sul. Quanto à distribuição temporal, foi constatada uma baixa concordância entre os dados analisados e os dados reais quanto das análises realizadas em intervalos de tempo pequeno (horas) e uma boa concordância nas medidas feitas quando o intervalo foi significativo (meses). Também em relação à Lagoa Itapeva, foi verificado nas análises estocásticas, utilizando-se operadores espaciais, que como a dinâmica biológica nem sempre é linear, os organismos não podem acompanhar imediatamente e perfeitamente as mudanças do ambiente, resultando em tempos de residência de matéria significativamente baixo. Além da análise dos fluxos ligados a este ecossistema lagunar, foram desenvolvidas técnicas de correção e adaptação de dados referentes à amostragem ocorrida na Lagoa durante um ano de campanha. Assim, propõe-se uma nova perspectiva no uso desta metodologia de forma simples e de fácil manipulação matemática.

Thesis (M.ScEng.)--Stellenbosch University, 2001.
ENGLISH ABSTRACT: Historically, urban waterresources have too often been managed without recognition that the flow in a river integrates many landscape and biological features. This has often resulted in the elimination of natural processes and their replacement by man-made streamlined structures with the effects of increased urbanisation being primarily addressed from an engineering and economics point of view to the detriment of environmental and social issues. Catchment Management, as legislated in the Water Act, No. 36 of 1998, is a management approach to address the negative consequences of an urban stormwater design philosophy restricted to flood restriction. It is a systems approach that integrates engineering and scientific skills, socio-economic concerns, and environmental constraints within a new multidisciplinary decision-making process that recognises the different components of the hydrological and aquatic cycles are linked, and each component is affected by changes in every other component. In order to make effective management decisions, catchment managers require tools to provide reliable information about the performance of alternative arrangements of stormwater management facilities and to quantify the effects of possible management decisions on the water environment. A deterministic hydrological model is such a tool, which provides the link between the conceptual understanding of the physical catchment characteristics and the empirical quantification of the hydrological, water quality and ecological response. In order to provide effective computer based decision support, the hydrological model must be part of an integrated software application in which a collection of data manipulation, analysis, modelling and interpretation tools, including GIS, can be efficiently used together to manage a large potion of the overall decision process. This decision support system must have a simple and intuitive user interface able to produce easily interpreted output. It must have powerful graphical presentation capabilities promoting effective communication and be designed to solve ill-structured problems by flexibly combining statistical analysis, models and data. The Great Lotus River canal, situated on the Cape Flats, Cape Town, has been designed and controlled through extensive canalisation and the construction of detention pond facilities to avoid the flooding of urban areas of the catchment. This approach has resulted in these channels becoming stormwater drains, transporting waste and nutrients in dissolved and particulate forms, and reducing their assimilatory capacity for water quality improvement. In order to investigate the use of hydrological modelling in decision support for Catchment Management, the semi-distributed, physically based model, SWMM, was applied to the Great Lotus River canal. SWMM consists of a number of independent modules allowing the hydrological and hydraulic simulations of urban catchments and their conveyance networks on an event or continuous basis. In order to ease the application of the Fortran based SWMM model, the GUl, PCSWMM98, was developed by Computational Hydraulics Inc (CH!). This provides decision support for SWMM through large array of tools for file management, data file creation, output visualisation and interpretation, model calibration and error analysis and storm dynamic analysis thus easing any simulations with SWMM. In addition, PCSWMM was developed with a GIS functionality for graphically creating, editing and/or querying SWMM model entities and attributes, displaying these SWMM layers with background layers and dynamic model results, and exporting data to SWMM input files thus providing an interface between a GIS and SWMM. In terms of Catchment Management, the above DSS can be used effectively to assist decisionmaking. This is to address tensions between the fundamental catchment management considerations of physical development, social considerations and maintaining ecological sustainability. It is at the stages of Assessment and Planning that the model can play the most significant role in providing decision support to the Catchment Management process. Assessment in the Catchment Management process refers to the collection, storage, modelling and interpretation of catchment information. It is in this quantification, interpretation and assessment of catchment information that a hydrological model contributes to an increase in knowledge in the Catchment Management process. In identifying and quantifying, at a sufficient temporal and spatial scale, the dominant cause and effect relationships in the urban physical environment, a hydrological model is able to highlight the main contributing factors to an issue. This is used in the Planning stage of the Catchment Management process and when combining these contributing factors with assessments of the socio-economic and administrative environments, enables the prioritisation of the principal issues requiring attention in a Catchment Management Strategy. It is possible to link the multiple decision-making requirements of Catchment Management with the abilities of a hydrological model to provide information on these requirements in a conceptual framework. This framework consists of the fundamental catchment considerations of Physical Development, Environmental Management and Social Development and resolves these considerations into the various management issues associated with each consideration ~s well as its management solution. The management solutions are linked to the model through formulating the solution in terms of the model parameters and perturbing the affected parameters in ways to simulate the management solution. This results in model output and graphical interpretation of the effects of the suggested management solution. A comparison between the simulated effects of each management solution allows the Catchment Management body to identify optimal management solutions for the various management Issues. The present model of the Great Lotus River catchment is sufficient to simulate the overland and subsurface flows from individual parts of the catchment and to route these flows and associated pollutant loadings to the catchment outlet. At its present level of complexity, the finely discretised model subcatchment and conveyance network provides decision support for Catchment Management through the simulation, at a pre-feasibility stage, of various Catchment Management issues and their proposed solutions. Given more detailed canal and drainage network dimensions and water quality data, it is possible for the model to incorporate hydraulic calculation routines to assess the implications of alternative river rehabilitation techniques and waste management strategies. This would allow greater capability in assessing the role of the various BMPs in ameliorating stormwater impacts and pollutant loading. In addition, a detailed level survey of the stormwater pipe and canal network could result in hydrological modelling being utilised to identify critical areas where stormwater upgrading would be necessary. In order to facilitate future complex, finely discretised catchment hydrological models, it is imperative that complete and detailed drainage patterns and stormwater network characteristics are available. In addition, to minimise model generation costs and time of model setup, this spatially representative data must be captured in a GIS for rapid inclusion into the model. Furthermore, complete spatially representative precipitation datasets are necessary to ensure that model error is reduced. These two issues of available spatial data and comprehensive precipitation records are crucial for the generated models to function as effective decision support systems for Catchment Management.
AFRIKAANSE OPSOMMING: Histories is stedelike waterbronne te dikwels bestuur sonder inagneming dat die vloei van die rivier baie landskap- en biologiese kenmerke insluit. Dit het dikwels daartoe gelei dat natuurlike prosesse uitgeskakel is en vervang is deur mensgemaakte, stroombelynde strukture waarvan die effek van toenemende verstedeliking hoofsaaklik aangespreek word vanuit 'n ingenieurs- en ekonomiese oogpunt tot nadeel van omgewings- en sosiale kwessies. Opvangsgebiedsbestuur, soos bepaal deur die Waterwet, Wet 36 van 1998, is 'n bestuursbenadering om die negatiewe gevolge van 'n stedelike stormwaterontwerpfilosofie wat beperk is tot vloedbeperking aan te spreek. Dit is 'n stelselbenadering wat ingenieurs- en wetenskaplike vaardighede, sosio-ekonomiese probleme en omgewingsbeperkings integreer in 'n nuwe multidissiplinêre besluitnemingsproses wat erkenning daaraan gee dat die verskillende komponente van die hidrologiese en watersiklusse verbind is, en elke komponent beïnvloed word deur veranderings in elke ander komponent. Om doeltreffende bestuursbesluite te neem, benodig opvangsgebiedsbestuur die hulpmiddels om betroubare inligting oor die prestasie van alternatiewe moontlikhede VIr stormwaterbestuurfasiliteite en om die effek van moontlike bestuursbesluite op die wateromgewing te kwantifiseer. 'n Deterministiese hidrologiese model is so 'n hulpmiddel wat die skakel daarstel tussen die konseptueie begrip van die fisiese opvangsgebiedskenmerke en die empiriese kwantifisering van die water-, waterkwaliteit- en ekologiese reaksie. Om doeltreffende rekenaarbesluitnemingsteun te verskaf, moet die hidrologiese model deel wees van 'n geïntegreerde sagteware-aanwending waarin 'n versameling datamanipulasie-, analise-, modellerings- en interpreteringshulpmiddels, insluitend GIS, doeltreffend saam gebruik kan word om 'n groot deel van die algehele besluitnemingsproses te bestuur. Hierdie besluitnemingsteunstelsel moet 'n eenvoudige en intuïtiewe gebruikersvlak hê wat in staat is om maklik interpreteerbare uitsette te lewer. Dit moet goeie grafiese voorleggingsvermoëns hê wat doeltreffende kommunikasie vergemaklik en ontwerp wees om swak gestruktureerde probleme deur die buigsame samevoeging van statistiese analise, modelle en data op te los. Die Groot Lotusrivierkanaal op die Kaapse Vlakte, Kaapstad is ontwerp en word beheer deur uitgebreide kanalisasie en die konstruksie van detensiedamfasiliteite om die oorstroming van stedelike opvangsgebiede te vermy. Hierdie benadering het daartoe gelei dat hierdie kanale stormwaterafvoerpype geword het wat afval en nutriënte in opgelosde en partikelvorm vervoer en hulle assimilasievermoë vir die verbetering van waterkwaliteit verminder. Om die gebruik van hidrologiese modelle in besluitnemingsteun vir Opvangsgebiedsbestuur te ondersoek, is die semi-verspreide, fisiesgebaseerde model, SWMM, op die Groot Lotusrivierkanaal toegepas. SWMM bestaan uit 'n aantalonafhanklike modules wat die hidrologiese en hidroulika simulasies van stedelike opvangsgebiede en hulle vervoemetwerke per geleentheid of deurlopend monitor. Om die aanwending van die Fortran gebaseerde SWMM model te vergemaklik is die GUl, PCSWMM98 deur Computational Hydraulics Inc (CHD ontwikkel. Dit verskaf besluitnemingsteun vir SWMM deur 'n groot aantal hulpmiddels vir lêerbestuur, die skep van datalêers, uitsetvisualisering en interpretasie, modelkalibrasie, foutanalise en stormdinamikaanalise om enige simulasies met SWMM te vergemaklik. Daarby is PCSWMM ontwikkel met 'n GIS funksionaliteit vir die grafiese daarstelling, redigering en/of navraagfunksie van SWMM model entiteite en kenmerke, wat hierdie SWMM vlakke met agtergrondvlakke en dinamiese modelresultate vertoon en data in SWMM inset1êers plaas en op daardie manier 'n koppelvlak tussen 'n GIS en SWMM verskaf. Volgens Opvangsgebiedsbestuur kan bogenoemde DSS doeltreffend gebruik word in besluitneming. Dit IS om die spanning tussen fundamentele opvangsgebiedsbestuursoorwegings van fisiese ontwikkeling, sosiale oorwegings en ekologiese volhoubaarheid aan te spreek. Dis in die stadiums van Waardebepaling en Beplanning wat die model die belangrikste rol kan vervul in die verskaffing van besluitnemingsteun vir die Opvangsgebiedsbestuursproses. Waardebepaling in die Opvangsgebiedbestuursproses verwys na die versameling, berging, modellering en interpretasie van opvangsgebiedsinligting. Deur hierdie kwantifisering, interpretasie en waardebepaling van opvangsgebiedsinligting dra 'n hidrologiese model by tot 'n verhoging in kennis in die Opvangsgebiedsbestuur. Deur die identifisering en kwantifisering, op 'n ruim genoeg tydelike en ruimtelike skaal, van die dominante oorsaak en gevolg verhoudings in die stedelike fisiese omgewing, kan die hidrologiese model die hoof bydraende faktore uitlig. Dit word gebruik in die Beplanningsfase van die Opvangsgebiedproses en wanneer hierdie bydraende faktore by die waardebepaling van die sosio-ekonomiese en administratiewe omgewings saamgevoeg word, maak dit moontlik om die belangrike kwessies wat aandag behoort te kry in 'n Opvangsgebiedsbestuurstrategie in volgorde van voorrang te plaas. Dit is moontlik om die verskeidenheid besluitnemingsvereistes van Opvangsgebiedsbestuur met die vermoëns van 'n hidrologiese model te koppel om inligting oor hierdie vereistes in 'n konseptuele raamwerk te verskaf. Die raamwerk bestaan uit die fundamentele opvangsgebiedsoorwegings van Fisiese Ontwikkeling, Omgewingsbestuur en Sosiale Ontwikkeling en los hierdie oorwegings op in die verskillende bestuursaangeleenthede wat met elke oorweging en die bestuuroplossing geassosieer word. Die bestuursoplossings word aan die model gekoppel deur die formulering van die oplossing volgens die modelparameters en versteuring van die relevante parameters op sekere manier om die bestuursoplossing te simuleer. Dit lei tot modeluitset en grafiese interpretasie van die effek van die voorgestelde bestuursoplossing. 'n Vergelyking tussen die gesimuleerde effek van elke bestuursoplossing laat die Opvangsgebiedsbestuursliggaam toe om die optimale bestuursoplossings vir die verskeie bestuursaangeleenthede te identifiseer. Die huidige model van die Groot Lotusrivieropvang is genoegsaam om die bo- en ondergrondse vloei vanaf individuele dele van die opvangsgebied te simuleer en om die watervloei en geassosieerde besoedelstofladings na die opvangsgebiedsuitlaatplek te lei. Op sy huidige vlak van kompleksiteit verskaf die fyn gediskretiseerde model subopvangsgebied en vervoernetwerk besluitnemingsteun aan Opvangsgebiedsbestuur deur die simulasie, teen 'n voor-lewensvatbaarheidstudie, van verskeie opvangsgebiedsbestuurkwessies en die voorgestelde oplossings. Indien meer gedetailleerde kanaal- en dreineringsnetwerkdimensies- en waterkwaliteitdata ingevoer word, is dit moontlik vir die model om hidroulikaberekeningsroetines te inkorporeer om die implikasies van alternatiewe rivierrehabilitasietegnieke en afvalbestuurstrategieë te beoordeel. Dit sou die vermoë verbeter om die waarde van die verskeie BMPs te bepaal om die impak van stormwater en besoedelstoflading te versag. Daarby kan 'n gedetailleerde vlakopname van die stormwaterpyp en -kanaalnetwerk daartoe lei dat hidrologiese modelle gebruik kan word om kritieke areas te identifiseer waar stormwateropgradering nodig is. Om toekomstige komplekse, gediskretiseerde opvangsgebiedshidrologiese modelle te verbeter, is dit noodsaaklik dat volledige en gedetailleerde dreineringspatrone en stormwaternetwerkkenmerke beskikbaar is. Om die model-ontwikkelingskoste en tyd bestee aan die opstel van 'n model te minimiseer, moet hierdie ruimtelik verteenwoordigende data ingelees word in 'n GIS vir vinnige insluiting in die model. Daarbenewens is volledige, ruimtelik verteenwoordigende presipitasie datastelle nodig om te verseker dat modelfoute verminder word. Hierdie twee kwessies van beskikbare ruimtelike data en omvattende presipitasierekords is van die uiterste belang sodat die gegenereerde modelle as doeltreffende besluitnemingsteun vir Opvangsgebiedsbestuur kan funksioneer.

This investigation concerns the transition pathway of the condensation phase transition. Under certain conditions condensation is initiated by nucleation events, which are driven by fluctuations or instabilities in the vapour phase. This involves the spontaneous formation of groups of particles, which we refer to as clusters. The clusters have a highly unstable nature and exist momentarily, before breaking up. This makes them difficult to study experimentally and model mathematically, in comparison to larger more stable systems. The aim of this study is to explore the stability of these tiny molecular clusters that exist momentarily within their environment, in terms of the time taken for the cluster to lose particles (decay). To do this we employ a microscopic cluster model of n-nonane molecules in which the cluster is treated in isolation from the vapour particles that would normally surround it. The interactions between cluster particles are modelled using empirical potentials. The cluster's dynamics is modelled using deterministic molecular dynamics simulations. The simulations generate a time evolved trajectory of all the positions, velocities and forces of all the atoms in the cluster. The process of cluster decay in n-nonane clusters is modelled using a Langevin interpretation of the decay mechanism. This treatment views cluster decay as a process of single particle escape from a confining potential of mean force, driven by a particle's interactions with the surrounding cluster particles. The motion of a cluster particle is modelled using a Langevin equation, which is parameterised using the MD generated data in order to extract the decay related parameters. The decay parameters are used to evaluate an Arrhenius type equation for the kinetic decay rate. This is used to calculate the mean timescale of cluster decay for n-nonane clusters, which we refer to as the mean cluster lifetime. We compare the dynamically generated lifetimes calculated from the model to those predicted by experimental measurements, as well as classically derived lifetimes. We discover the dynamical model predicts lifetimes that compare well to experimental predictions. The cluster decay model allows us to predict cluster decay timescales without decay events actually occurring. This makes it an essential tool for systems with long decay timescales, for which decay events can not be feasibly observed through MD simulations alone. Finally, the last chapter presents recent work that has been conducted on ice cluster embryos. The ice embryos emerge during the freezing transition of supercooled water into ice I. Unlike the previous method of treating clusters in isolation from their surroundings, this study involves the treatment of ice clusters in coexistence with their environment. We utilise a molecular dynamics trajectory of supercooled water freezing into ice, which is used to identify and extract ice cluster embryos. It is evident from the MD simulations that at the initial stages of freezing the clusters are very amorphous and disordered. We investigate cluster properties such as the size distribution and molecular connectivity, and explore whether we are able to quantify the potential of mean force in order to estimate the mean lifetime of disordered ice cluster embryos.

In this thesis a novel stochastic and deterministic mathematical model of Human papillomavirus (HPV) gene regulatory network was developed. The novelty of this project is both on methodological and biological /clinical site. The former is in line with the current challenge in recent years to have a holistic view of the basics regulatory mechanisms interconnected to form a complex machinery, where complex patterns can arise, only form the interconnection of basics modules. In fact, HPV offers a case of study of great interest in molecular systems biology. It involves a number of relevant regulatory mechanisms (e.g. transcription, translation, promoter modulation, polyadenylation regulation, splicing,…) connected together to form a complex network, albeit its genome is relatively simple, thus suitable for an accurate deterministic and even stochastic modeling. HPVs cause a series of diseases of the cutaneous and mucosal epithelium, ranging from minor lesions to precancerous cervical lesions and cervical cancer, which is considered one of the most common cancer in the women worldwide. Therefore, on the biological/clinical aspect the development of a mathematical model of HPV gene expression, is of great interest in order to dispose of an in silico simulator useful to achieve a better comprehension of the complex gene regulatory network, and capable to predict different scenarios from the first stages of viral infection up to a cervical cancer condition. As far as we know, there is no model of HPV gene regulation available in literature. A new synthesis of the HPV molecular biology with especial regard to gather/infer from literature the parameters useful for designing a dynamical model, and to shed light in what is still lacking in the biological literature, was preformed. The biological knowledge was translated into a stochastic model in terms of biochemical reactions. In particular, we modeled the HPV early and late promoters that account for the transcripts and proteins evolution during the entire viral life cycle. Even the post-transcriptional and post-translational modifications were modeled in order to properly capture the complex viral regulation known from literature. As far as we know, it is the first time a stochastic model accounts for the complex post-transcriptional control, modeling the splicing and polyadenylation sites regulation, and connect this latter to the transcriptional control layer, mediated by the promoters activities, in order to explore complex patterns that can arise only from the interconnection of different control layers. The Master Equation (ME) of the system was considered in order to predict and investigate its stochastic behavior. Because of the complex system structure it wasn't possible to solve the whole ME analytically, hence numerical exact simulations were performed by means of the Gillespie's algorithm. A quasi-equilibrium approximation of the ME was developed in order to get a deterministic approximation of the model. The model structure together with the fixed parameters we have gathered/inferred from literature was able to fit a dataset consistent of the early promoter activity and to qualitatively reproduce the main dynamical behavior of two of the most important regulatory transcripts during viral late phase. Different in silico experiments were designed to opportunely explore both the capability of the stochastic model to follows the deterministic predictions, when in fast fluctuations regimen, and to discover complex stochastic patterns, that can arise through the interconnection of the transcriptional and post-transcriptional control layers. In general, both the stochastic and deterministic formulation of the model showed the capability to reproduce the HPV gene expression dynamics, during the entire viral life cycle, in good agreement with the current biological knowledge.
In questa tesi è stato sviluppato un nuovo modello deterministico e stocastico della rete di regolazione genica dello Human papillomavirus (HPV). Gli aspetti di novità del modello ricadono sia sull'aspetto metodologico che clinico/biologico. Per quanto riguarda il primo aspetto il progetto è in linea con l'attuale sfida, presente in questi ultimi anni, di ottenere una visione olistica dei meccanismi regolatori di base interconnessi a formare un sistema complesso, all'interno del quale dinamiche complesse possono scaturire solo tramite un'interconnessione di moduli base. In linea con questo, l'HPV si pone come un caso di studio di grande interesse nella systems biology molecolare. Esso comprende una serie di importanti meccanismi regolatori (ad esempio trascrizione, traduzione, modulazione dei promotori, regolazione della poliadenilazione, splicing,...) connessi tra di loro al fine di formare una complessa rete, sebbene il genoma virale sia relativamete semplice e quindi adatto per sviluppare accuratamente una modellistica deterministica e persino stocastica. L'HPV può causare una serie di malattie della cute e della mucosa epiteliale, che spaziano da lesioni minori fino a lesioni pre-cancerogene e cancro al collo dell'utero, considerato uno dei principali tipi di cancro che affligge la popolazione femminile. Conseguentemente, da un punto di vista clinico/biologico lo sviluppo di un modello matematico dell'espressione genica dell'HPV, è di grande interesse al fine di disporre di un simulatore in silico utile per raggiungere una migliore comprensione della complessa rete di regolazione genica e capace di predire scenari differenti a partire dalle prime fasi dell'infezione virale fino all'evoluzione del cancro. Da quello che sappiamo finora, non esiste alcun modello reperibile in letterature della regolazione genica dell'HPV. E' stata effettuata una nuova sintesi della biologia molecolare dell'HPV con particolare riguardo al raccogliere/inferire da letteratura i parametri utili al fine di progettare un modello dinamico, e al fine di evidenziare le conoscenze biologiche mancanti in letteratura. La conoscenza biologica è stata tradotta in un modello stocastico in termini di un sistema di reazioni biochimiche. In particolare, sono stati modellati il primo ed il secondo promotore per tener conto della evoluzione dei trascritti e delle proteine durante l'intero ciclo virale. Sono state modellate anche le regolazioni post-trascrizionali e post-traduzionali al fine di catturare appropriatamente la complessa regolazione virale, nota in letteratura. Da quello che sappiamo finora, è la prima volta che un modello stocastico tiene conto del complesso controllo post-trascrizionale, modellando i siti di regolazione dello splicing e della poliadenilazione, e connettendo questi ultimi al modulo di controllo trascrizionale mediato dall'attività dei promotori, al fine di esplorare dinamiche complesse che possono scaturire solo dal modellare l'interconnessione dei singoli stadi di controllo. E' stata considerata la Master Equation (ME) del sistema al fine di predire a investigare il suo comportamento stocastico. A causa della complessa struttura del sistema non è stato possibile risolvere analiticamente la ME, perciò sono state effettuate simulazioni numeriche esatte facendo uso dell'algoritmo di Gillespie. Un'approssimazione al quasi-equilibrio della ME è stata sviluppata al fine di ottenere un modello deterministico. Il modello sviluppato, fissando i parametri trovati/inferiti da letteratura, è stato in grado di fittare un dataset inerente l'attività dell'early promoter e riprodurre qualitativamente il principale comportamento dinamico di due dei piu' importanti trascritti sviluppati durante la fase terminale del ciclo virale. Differenti esperimenti in silico sono stati progettati per esplorare opportunamente sia la capacità del modello stocastico di inseguire le predizioni del modello deterministico, in regime di fluttuazioni veloci, che per scoprire dinamiche complesse che possono originarsi dall'interconnessione dei moduli di regolazione trascrizionale e post-trascrizionale. In generale, sia la formulazione deterministica che stocastica del modello hanno mostrato la capacità di riprodurre, in buon accordo con l'attuale conoscenza biologica, la dinamica dell'espressione genica durante l'intero ciclo virale.

Orientador: Rodney Carlos Bassanezi
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica
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Resumo: Não informado.
Abstract: Not informed.
Doutorado
Doutor em Matemática Aplicada

Darbe nagrinėjamas gegučių ir paukščių-šeimininkų sąveikos deterministinis modelis, priimant dėmesin paukščių amžių, ir atsižvelgiant į diskrečią jauniklių aibę bei jų globą. Visi individai yra skirstomi į tris grupes: priešreprodukcinio (dar negali turėti jauniklių), reprodukcinio (gali susilaukti palikuonių) ir poreprodukcinio amžiaus. Modelis yra sudarytas iš integro-dalinių diferencialinių lygčių, atsižvelgiant į integralinio tipo sąlygas. Šių lygčių skaičius priklauso nuo maksimalaus biologiškai įmanomo šeimininko kiaušinių lizde skaičiaus. Yra tiriami separabilieji uždavinio sprendiniai bei įrodoma egzistavimo teorema.
A Common Cuckoo and a host species dynamics deterministic model taking into account a discrete set of offsprings and their care, is considered. Individuals have three age intervals: pre-reproductive, reproductive (when they can produce offsprings) and post-reproductive. The model is described by integro-partial differential equations subject to conditions of integral type, where the number of equations depends on a maximal biologically possible number of eggs produced by the host birds. Separable solutions of this model are studied and the existence theorem is proved.

In geotechnical engineering, the uncertainties such as the variability and uncertainty inherent in the geotechnical properties have caught more and more attentions from researchers and engineers. They have found that a single “Factor of Safety” calculated by traditional deterministic analyses methods can not represent the slope stability exactly. Recently in order to provide a more rational mathematical framework to incorporate different types of uncertainties in the slope stability estimation, reliability analyses and non-deterministic methods, which include probabilistic and non probabilistic (imprecise methods) methods, have been applied widely. In short, the slope non-deterministic analysis is to combine the probabilistic analysis or non probabilistic analysis with the deterministic slope stability analysis. It cannot be regarded as a completely new slope stability analysis method, but just an extension of the slope deterministic analysis. The slope failure probability calculated by slope non-deterministic analysis is a kind of complement of safety factor. Therefore, the accuracy of non deterministic analysis is not only depended on a suitable probabilistic or non probabilistic analysis method selected, but also on a more rigorous deterministic analysis method or geological model adopted. In this thesis, reliability concepts have been reviewed first, and some typical non-deterministic methods, including Monte Carlo Simulation (MCS), First Order Reliability Method (FORM), Point Estimate Method (PEM) and Random Set Theory (RSM), have been described and successfully applied to the slope stability analysis based on a numerical simulation method-Strength Reduction Method (SRM). All of the processes have been performed in a commercial finite difference code FLAC and a distinct element code UDEC. First of all, as the fundamental of slope reliability analysis, the deterministic numerical simulation method has been improved. This method has a higher accuracy than the conventional limit equilibrium methods, because of the reason that the constitutive relationship of soil is considered, and fewer assumptions on boundary conditions of slope model are necessary. However, the construction of slope numerical models, particularly for the large and complicated models has always been very difficult and it has become an obstacle for application of numerical simulation method. In this study, the excellent spatial analysis function of Geographic Information System (GIS) technique has been introduced to help numerical modeling of the slope. In the process of modeling, the topographic map of slope has been gridded using GIS software, and then the GIS data was transformed into FLAC smoothly through the program built-in language FISH. At last, the feasibility and high efficiency of this technique has been illustrated through a case study-Xuecheng slope, and both 2D and 3D models have been investigated. Subsequently, three most widely used probabilistic analyses methods, Monte Carlo Simulation, First Order Reliability Method and Point Estimate Method applied with Strength Reduction Method have been studied. Monte Carlo Simulation which needs to repeat thousands of deterministic analysis is the most accurate probabilistic method. However it is too time consuming for practical applications, especially when it is combined with numerical simulation method. For reducing the computation effort, a simplified Monte Carlo Simulation-Strength Reduction Method (MCS-SRM) has been developed in this study. This method has estimated the probable failure of slope and calculated the mean value of safety factor by means of soil parameters first, and then calculated the variance of safety factor and reliability of slope according to the assumed probability density function of safety factor. Case studies have confirmed that this method can reduce about 4/5 of time compared with traditional MCS-SRM, and maintain almost the same accuracy. First Order Reliability Method is an approximate method which is based on the Taylor\'s series expansion of performance function. The closed form solution of the partial derivatives of the performance function is necessary to calculate the mean and standard deviation of safety factor. However, there is no explicit performance function in numerical simulation method, so the derivative expressions have been replaced with equivalent difference quotients to solve the differential quotients approximately in this study. Point Estimate Method is also an approximate method involved even fewer calculations than FORM. In the present study, it has been integrated with Strength Reduction Method directly. Another important observation referred to the correlation between the soil parameters cohesion and friction angle. Some authors have found a negative correlation between cohesion and friction angle of soil on the basis of experimental data. However, few slope probabilistic studies are found to consider this negative correlation between soil parameters in literatures. In this thesis, the influence of this correlation on slope probability of failure has been investigated based on numerical simulation method. It was found that a negative correlation considered in the cohesion and friction angle of soil can reduce the variability of safety factor and failure probability of slope, thus increasing the reliability of results. Besides inter-correlation of soil parameters, these are always auto-correlated in space, which is described as spatial variability. For the reason that knowledge on this character is rather limited in literature, it is ignored in geotechnical engineering by most researchers and engineers. In this thesis, the random field method has been introduced in slope numerical simulation to simulate the spatial variability structure, and a numerical procedure for a probabilistic slope stability analysis based on Monte Carlo simulation was presented. The soil properties such as cohesion and friction angle were discretized to continuous random fields based on local averaging method. In the case study, both stationary and non-stationary random fields have been investigated, and the influence of spatial variability and averaging domain on the convergence of numerical simulation and probability of failure was studied. In rock medium, the structure faces have very important influence on the slope stability, and the rock material can be modeled as the combination of rigid or deformable blocks with joints in distinct element method. Therefore, much more input parameters like strength of joints are required to input the rock slope model, which increase the uncertainty of the results of numerical model. Furthermore, because of the limitations of the current laboratory and in-site testes, there is always lack of exact values of geotechnical parameters from rock material, even the probability distribution of these variables. Most of time, engineers can only estimate the interval of these variables from the limit testes or the expertise’s experience. In this study, to assess the reliability of the rock slope, a Random Set Distinct Element Method (RS-DEM) has been developed through coupling of Random Set Theory and Distinct Element Method, and applied in a rock slope in Sichuan province China.

Orientador: Rubens Maciel Filho
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica
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Resumo: Este trabalho apresenta um estudo sobre a modelagem matemática de um reator de lama catalítico trifásico, em regime estacionário, a partir de duas abordagens, a saber considerando sua descrição por meio de equações fenominológicas (modelos matemáticos deterministicos) e ultilizando-se de técinicas de redes neurais para sua representação. É apresentado uma revisão dos trabalhos mais relevantes da literatura sobre a modelagem de processos químicos. Em seguida, faz-se a formulação de um modelo matemático determinístico para a representação de um reator tubular em modo contínuo de operação e em regime estacionário, no qual ocorre uma reação trifásica. Um estudo da aplicabilidade de técnicas de redes neurais à analise destes sistemas, considerando-se duas abordagens é também proporcionada. A partir de simulações computacionais (utilizando programas implementados na linguagem FORTRAN), e tomando-se uma reação de hidrogenação como estudo de caso, são mostrados e analisados, de forma comparativa, os principais resultados obtidos, destacando-se a influência dos principais parâmetros e fenômenos no desempenho do reator trifásico, e evidenciando a aplicabilidade das técnicas de redes neurais na sua modelagem
Abstract: In this work, a study on the mathematical modeling of a three-phase catalytic surry reactor is developed, using two approach. In the first, the reactor is described by their phenomenological equations expressing the mass and energy balances for the system. In the second, artificial neural network techniques is considered in representing the three-phase reactor behavior. Initially, a revision of existing literature on three-phase reactor mathematical modeling and on artificial neural networks application in the chemical process analysis is presented. After, the deterministic mathematical model formulation for a three-phase catalytic slurry reactor, with a tubular configuration and operating in steady-state is developed. In the mathematical model the mass and energy balance equation for the catalytic particle are considered. The mathematical model developed is simulated and the main results are presented and discussed, highlighting the effect of the principal parameter of the process in its performace, and using data obtained by the mathematical model simulation, the applicability of artificial neural networks techniques is shown
Doutorado
Desenvolvimento de Processos Químicos
Doutor em Engenharia Química

Orientadores: Rubens Maciel Filho, Eduardo Coselli Vasco de Toledo
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica
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Mestrado

Orientador: Rubens Maciel Filho
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica
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Resumo: Três modelos computacionais diferentes foram desenvolvidos, comparados e analisados em função dos dados experimentais obtidos. Ambos os modelos correlacionam transferência de massa e hidrodinâmica para um reator "air-lift" de "loop" externo. Um dos modelos é apresentado como Modelo de Equações EmpÍricas (MEE), que é uma combinação de equações algébricas e diferenciais ordinárias, prognosticadas por diversos especialistas em sistemas multifásicos e em reatores "air-lifts". O segundo é o Modelo Determinístico Dinâmico (MDD), fundamentado nas Equações de Fick e Navier-Stokes e estendido para sistemas bifásicos. O terceiro e o último é o Modelo Híbrido Neural (MHN) que usa redes neurais em associação com as equações deterrninísticas desenvolvidas. O primeiro depende de uma metodologia de otimização integrada com as equações, o segundo de condições iniciais bem definidas, enquanto que o terceiro de uma rede neural bem treinada e de muitos dados de entrada. Os algoritmos desenvolvidos possibilitaram entender o comportamento associado da hidrodinâmica e da transferência de massa para o "ri ser" de um reator "air-lift" no sistema bifásico ar-água. As respostas dos três modelos concordaram com resultados empíricos obtidos de uma planta piloto
Abstract: Three different algorithm models were compared, the numerical output analyzed and a correlation established with the experimental data. Both models correlate' mass transfer and hydrodynamic for an External Loop Air-lift Reactor. One of them is presented as the Empirical Equations Models (EEM), which is the combination of algebraic and Ordinary Differential Equations (ODEs). Such equations were predicted for air-water multiphase systems by Air-lift reactors specialists. The second one is the Deterministic Dynamic Model (DDM). It was based on the Fick's laws and the Navier-Stokes equations extended for the biphasic systems. The last one is the Hybrid Neuronal Model (HNM), which combines neuronal network with the deterministic equations developed. The first one depends on an optirnization methodology combined with the algebraic equations, the second one must have initial condition very well defined, while the last one needs a network very well trained and a several entry data. The developed algorithm allowed to improve the knowledge of the hydrodynamic and mass transfer behaviors. Both models outputs agreed with the empirical data obtained from a pilot planto
Mestrado
Desenvolvimento de Processos Químicos
Mestre em Engenharia Química

Abstract. The interest in studying the channel characteristics is exponentially increasing with the growth of the communication systems. Various channel modelling approaches have been discussed in the past decades. The ray-tracing based channel models are distinguished from the other channel models as they consider the environmental information and thus are expected to reflect the real propagation phenomena that exist in that specific environment. The goal of this thesis is to study the propagation channel characteristics of the three different channel models. The two deterministic channel models are the simplified map-based ray tracing channel model implemented in the METIS project and the full ray tracing-based channel model implemented by the Beijing Jiaotong University. The third channel model is the hybrid model based on METIS map-based channel. It uses the deterministic part of the METIS map-based channel model. Full ray-tracing based models require detailed description of the propagation environment or map and they target on site-specific channel modelling. Such site-specific models are not typically required in performance testing of devices, where the target is to ensure device performance in a typical propagation environment and possibly to cover some extreme cases. The simplifying map-based approach contradicts with the full ray tracing method in the way that the information of the map is reduced by approximating the building shapes and introducing artificial tiles to make scattering in the walls and ground reflections. Map-based channel modelling provides additional realism in channel models compared to traditional stochastic models applied in performance testing. The urban street canyon scenario was chosen to be modelled. The comparison was carried out at 3.5 GHz by means of performance metrics such as total path loss, LOS and NLOS propagation conditions at UE positions, K-factor, RMS delay spread, statistics of angles, angle spreads, and cross polarization ratios. The results have showed similarities in the LOS UE positions and dissimilarities in the NLOS UE positions. The reasons are identified and explained in the discussion section. It is decided to investigate the radio channel characteristics of the METIS map-based channel model and hybrid channel model for the future study purpose.

Modelling wastewater temperature variations in a network of 3048 sewer pipes was achieved in this project. Recovering heat from sewers presents attractive options for producing clean energy. However, heat recovery from sewerage may result in wastewater temperature drops which may reduce the influent temperature at the wastewater treatment plant (WWTP). This drop in the WWTP influent temperature may result in the degradation of the biological treatment stage. Therefore, it is vital to predict the impact of recovering heat from sewers on the wastewater temperature. Sewer temperatures along with hydraulic data were measured for up to a year in four different Belgian sites. The measured data was utilised to calibrate a deterministic sewer pipe model that estimates the wastewater temperature variation along the sewer pipe profiles. The latter model was calibrated using data from two sites and then validated using independent data from the other two sites. The sewer pipe model was then further developed to model wastewater temperature variations in a large (3048 pipe) network. The large network model was tested by implementing three different heat recovery scenarios. It was observed that 9 MW may be recovered from the 3048 pipe network, serving a catchment with a population equivalent of 79500 inhabitants, without impacting negatively on the biological processes.

Virtual simulations of the behaviour of mechanical systems are of widespread use in academia and industry. Mechanical structures are often analysed using the finite element method, where deterministic models with one particular set of physical parameters are employed. However, the underlying assumption that the input data is precisely known is in general not valid, because there are uncertainties about the parameters, often until the last stage of the design cycle and even when the product is in service. Furthermore, every manufacturing process naturally introduces some product variability, which is inevitable. These effects can be compensated for by the application of safety factors. However, with the increasing requirements towards product performance, the effects of non-deterministic properties are of growing concern and advanced methods are needed that properly take them into account. In this context, it is often more important to predict the variation in the response than attempt to further improve the accuracy of a deterministic model. A number of viable methods to take non-deterministic properties into account already exist, but their computational efficiency and applicability have to be increased. In this thesis, a framework for the non-deterministic analysis of built-up structures using component mode synthesis (CMS) is presented. It is shown how several coordinate systems in CMS can be used advantageously for the quantification and propagation of non-deterministic data. A specific approach, based on considering the variation in component natural frequencies only, is introduced and its efficiency and accuracy investigated. The application of perturbational relations for uncertainty propagation in CMS is discussed. The framework of CMS is also used to combine qualitatively different uncertain data and the inclusion of experimental data is addressed. Overall, CMS methods can be used to reduce the numerical costs, improve the applicability of the approaches and also gain some physical insight for a structural dynamic problem with non-deterministic properties. Furthermore, several contributions are made to simulation methods that are usually applied in connection with the CMS approach. Different concepts for non-deterministic modal superposition are presented, which can be used to estimate the variation in frequency response functions from uncertain modal data. The application of the Line-Sampling simulation method, as an advanced Monte Carlo approach, to structural dynamic problems is shown. Finally, the modelling of spatial variations in components using random fields and the implementation in existing finite element models are addressed. Numerical examples are presented throughout.

The inventory routing problem (IRP) integrates two components of supply chain management, namely, inventory management and vehicle routing. These two issues have been traditionally dealt with problems in the area of logistics separately. However, these issues may reduce the total costs in which the integration can lead a greater impact on overall system performance. The IRP is a well-known NP-hard problem in the optimisation research publication. A vehicle direct delivery from the supplier with and without transhipments (Inventory Routing Problem with Transhipment, IRPT) between customers in conjunction with multi-customer routes in order to increase the flexibility of the system. The vehicle is located at a single depot, it has a limited capacity for serving a number of customers. The thesis is focused on the two main aspects: (1) Development of the optimisation models for the deterministic and stochastic demand IRP and IRPT under ML/OU replenishment polices. On the deterministic demand, the supplier deliveries products to customers whose demands are known before the vehicle arrives at the customers’ locations. Nevertheless, the stochastic demand, the supplier serves customers whose actual demands are known only when the vehicle arrives at the customers’ location. (2) Development of integrated heuristic, biased probability and simulation to solve these problems. The proposed approaches are used for solving the optimisation models of these problem in order to minimise the total costs (transportation costs, transhipment costs, penalty costs and inventory holding costs). This thesis proposed five approaches: the CWS heuristic, the Randomised CWS heuristic, the Randomised CWS and IG with local search, the Sim-Randomised CWS, and the Sim-Randomised CWS and IG with local search. Specifically, the proposed approaches are tested for solving the deterministic demand IRP and IRPT, namely, the IRP-based CWS, the IRP-based Randomised CWS, the IRP-based Randomised CWS and IG with local search. For the transhipment case are called the IRPT-based CWS, the IRPT-based Randomised CWS, and the IRP-based Randomised CWS and IG with local search. On the stochastic demand, these proposed approaches are named the SIRP-based Sim-Randomised CWS, the SIRPT-based Sim-Randomised CWS, the SIRP-based Sim-Randomised CWS and IG with local search, and the SIRPT-based Sim-Randomised CWS and IG with local search. The aim of using the sim-heuristic is to deal with stochastic demand IRP and IRPT, the stochastic behaviour is the realistic scenarios in which demand is used to be addressed using simulation. Firstly, the Sim-Randomised CWS approach, an initial solution is generated by Randomised CWS heuristic, thereafter an MCS is combined to provide further improvement in the final solution of the SIRP and the SIRPT. Secondly, the integration of Randomised CWS with MCS and IG with local search is solved on these problems. Using an IG algorithm with local search improved the solution in which it generated by Randomised CWS. The developed heuristic algorithms are experimented in several benchmark instances. Local search has been proven to be an effective technique for obtaining good solutions. In the experiments, this thesis considers the average over the five instances for each combination and the algorithms are compared. Thus, the IG algorithm and local search outperformed the solution of Sim-Randomised CWS heuristics and the best solutions in the literature. This proposed algorithm also shows a shorter computer time than that in the literature. To the best of the author’ knowledge, this is the first study that CWS, Randomised CWS heuristic, Sim-Randomised CWS and IG with local search algorithms are used to solve the deterministic and stochastic demand IRP and IRPT under ML/OU replenishment policies, resulting of knowledge contribution in supply chain and logistics domain.

Orientador: Rubens Maciel Filho
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica
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Doutorado
Doutor em Engenharia Química

Relevance of research. Due to the rapid deployment of the non-dispatchable (intermittent) generation sources in the smart grid, such as integration of the photovoltaic power plants and wind turbines in the distribution systems; this caused a problem of the uncertainty increase of simulation results for decision-making for power supply systems, these uncertainties of power systems are getting more and more notice. At the same time, the classical power systems models cannot give accurate simulation results. Wherein; it became necessary to define new models to represent the specific parameters of power system. wherein; this research reveals to the benefits of using probabilistic mathematical approaches to define and calculate the specific economic parameters, as well as the technical parameters for power supply system with the integration renewable energy generators, which are characterising by randomness and uncertainty due to the high penetration to the renewables. Monte Carlo Method, and Point Estimation Method are used to handle the uncertainties of renewable energy resources. The standard functions to represent the stochastic parameters of the model are analyzed with the use of three-point estimation technique for the distribution functions of their probable values. A synthetic skewed probability density function was analytically constructed basing on the standard normal distribution, which is suitable for analytic representation of the predicted and/or statistical random sampling of the uncertain model parameters of energy system with renewables, and analytical expressions were obtained to compute the moments of proposed synthetic probability function. Relationship of work with scientific programs, plans, themes. is to demonstrate the possibility of describing the input parameters of the simulation Deterministic and Stochastic Modeling by probability Density Functions by the use of three-point approximation techniques and to obtain analytical expressions for the characteristics of such distributions, suitable for non-iterative (as opposed to Monte Carlo Method) probabilistic method applications, namely the Point Estimation Method. Purpose and tasks of the research. Increasing the simulation accuracy results for estimation economic and technical parameters characterising photovoltaic power plant based on based on the life cycle model; as well as development of different algorithms based on deterministic and stochastic modeling of power system with non-dispatchable sources and minimize the computation time. Object of research. Processes of determining the estimated technical and economic parameters characterising a photovoltaic power plant located in Ukraine basing on stochastic modeling. Subject of research. Use of the Monte Carlo Method and Point Estimation Method to estimate the various economic and technical information characteristic of alternative power plants in order to obtain accurate simulation results. Practical value of the results. Practical techniques of the three-point approximation are used to construct the probability density function of the model uncertain (stochastic) parameter, which dominantly influences the modeling result: an event occurrence probability, the result attainability, whatsoever. This technique is an effective tool for the practical evaluating of an uncertain value of a technological or economic factor of material and/or economic object, and widely used for overall Levelized Energy Cost (LCOE – LEC) which is directly or indirectly engaged into analytic representation of the power systel model. Usually, the model of a kind is designed to solve technical and/or economic problem by means of Deterministic and Stochastic Modeling. Scientific novelty of the obtained results is the development of algorithms and mathematical solutions using a probabilistic approach basing Point Estimation Method instead of Monte Carlo Melthod to obtain more accurate estimation simulation results, as well as to obtain computational results in less time for useful decision-making in alternative power plant projects.

One of the main objectives of combining radiation treatment and chemotherapy is to obtain a therapeutic gain by an improved tumour control with less or no enhancement of normal tissue toxicity. The optimal schedule for the combined treatment of cisplatin-radiation is still under investigation. Neither the optimal time interval, nor the most adequate sequence of administration of cisplatin and radiation are known. The results of the trials are also inconclusive. Some trials showed a supra-additive effect from the administration of cisplatin before radiotherapy, others, on contrary, from the injection of drug after radiotherapy. The present work encompasses the major challenges brought by the combined modality treatment: cisplatin-radiotherapy. The major goal of this work was to investigate the optimal treatment sequencing between cisplatin and radiotherapy and also the optimal schedule for head and neck carcinomas. Therefore, a computer-based tumour model with literature-given biological parameters has been developed which has allowed the simulation of treatment with radiation and chemotherapy. Radiotherapy has been simulated on the virtual tumour and the effects of radiotherapy on tumour regression and regrowth have been analyzed. Also, the mechanisms of cisplatin's action on tumour have been implemented, and the phenomena of drug resistance and tumour repopulation during chemotherapy studied. Finally, the combined modality treatment has been simulated, and the effect of drug-radiation interaction on tumour behaviour evaluated. The current investigation has shown that cisplatin administered immediately before radiation gives similar tumour control to the post-radiation sequencing of the drug. Furthermore, the killing effect of the combined modality treatment on tumour increases with the increase in cell recruitment. The individual cell kill produced by cisplatin and radiation leads to an additive-only tumour response when the treatments are given concurrently, and for a synergistic effect cisplatin must potentiate the effect of radiation. The final conclusion, by which cisplatin administered on a daily basis leads to a better tumour control than cisplatin administered weekly, is in accordance with the latest trial results on head and neck cancers. Therefore, treatment regimens that correlate better with the pharmacokinetics and the radiobiological properties of the therapeutic agents result in better outcomes.
Thesis (Ph.D.)--School of Chemistry and Physics, 2004.

Phytoplankton are single celled organisms capable of phytosynthesis, and are present in all the major oceans and lakes in the world. Phytoplankton contribute to 50% of the total primary production on Earth, and are the dominating primary producer in most aquatic ecosystems. This thesis is based on the 1D deterministic model by Jäger et. al. (2010) which models phytoplankton dynamics in freshwater lakes, where phytoplankton growth is limited by the availability of light and phosphorus. The original model is here extended to two dimensions to include a horizontal dimension as well as a vertical dimension, in order to simulate phytoplankton dynamics under varying lake bottom topographies. The model was solved numerically using a grid transform and a finite volume method in MATLAB. Using the same parameter settings as the 1D case studied by Jäger et. al. (2010), an initial study of plankton dynamics was done by varying the horizontal and vertical diffusion coefficients independently.

Questões ambientais estão no centro das discussões nas últimas décadas. A poluição atmosférica, causada pela expansão pós-revolução industrial fez surgir a necessidade de aprender a descrever, usando modelos matemáticos, esse fenômeno. Com esse conhecimento pode-se propor soluções que mitiguem a poluição e os danos colaterais causados ao ambiente. A dispersão de poluentes modelada por soluções analíticas, a partir das equações de advecção-difusão oferecem um conhecimento sobre cada componente que constrói a equação, característica inexistente em outras abordagens, como a numérica. Entretanto ela era incapaz de descrever propriedades que se referem à turbulência, as estruturas coerentes, causadas por componentes não-lineares suprimidas por construção das equações governantes do modelo. Este trabalho estudou uma forma de recuperar características associadas à turbulência através de uma componente fundamental em estruturas coerentes, a fase. Essa é incluída no modelo que passa a descrever manifestações da turbulência em processos de dispersão através de flutuações de pequena escala na concentração da solução do modelo sesquilinear, que é determinístico-estocástico. No decorrer do trabalho há um estudo através de variações de parâmetros para compreender os efeitos da fase no modelo. Ele também foi aplicado ao experimento de Copenhagen e a dois cenários reais com a intenção de compreender o modelo frente à variáveis micrometeorológicas assim como aprimorá-lo para simular a dispersão de poluentes oriundos de fontes de forma realística.
Environmental issues have been at the center of discussions in the last few decades. Atmospheric pollution, caused by post-industrial revolution, has increased the necessity to describe, using mathematical models, this phenomenon. With this knowledge is possible to propose solutions mitigating the pollution and collateral damages caused in the environment. The pollutant dispersion modeled by analytical solutions, from advection-diffusion equations, offers a knowledge about each component that constructs the equation, a characteristic that does not exist in other approaches, such as numerical. However it was unable to describe properties that refer to turbulence, coherent structures, caused by nonlinear components suppressed by constructing the model governing equations. This work studied a way to recover characteristics associated with turbulence through a fundamental component in coherent structures, the phase. This is included in the model which describes manifestations of turbulence in the dispersion process through the presence of small-scale concentration fluctuations in the sesquilinear model, which is deterministicstochastic. In the course of this work there is a study through variations of parameters to understand the phase effects in the model. It was also applied to Copenhagen experiment and to two real scenarios with the intention of understanding the model regarding micrometeorological variables as well as improving it to simulate the pollutant dispersion from sources in a realistic way.

Orientador: Liliane Maria Ferrareso Lona
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica
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Resumo: O presente trabalho tem como objetivo modelar um reator de polimerização operando em regime batelada, usando como caso estudo a polimerização em massa e solução do metilmetacrilato (MMA). Serão utilizadas redes neurais artificiais, para o desenvolvimento de um modelo híbrido, visando eliminar a necessidade da utilização de correlações empíricas que ajustam a constante da taxa de terminação (kt), devido a ocorrência do efeito gel. Processos poliméricos se caracterizam por sua complexidade devido ao elevado número de reações paralelas à reação de formação do polímero e pelos fenômenos difusivos que causam ou ocorrem durante a polimerização. As maiores fontes de problemas encontrados em processos de polimerização são a liberação de calor das reações altamente exotérmicas e o grande aumento da viscosidade do meio reacional ao longo da reação de polimerização. Esta alta geração de calor aliada, à baixa difusividade térmica da mistura reacional, geralmente leva a um descontrole térmico, e consequentemente a dificuldades no controle do processo, e no comportamento das características físicas finais do polímero. Redes neurais são métodos matemáticos baseados na estrutura neurológica do cérebro. Trata-se de uma técnica de inteligência artificial, cuja característica é o "aprendizado" de uma lógica existente em um determinado conjunto de dados a fim de predizer valores diferentes daqueles utilizados para o treinamento da rede. O modelo híbrido busca superar as desvantagens presentes nos modelos determinístico e puramente neural. A modelagem híbrida visa a fusão de todo o conhecimento disponível do processo, com a metodologia das redes. Foram treinadas duas redes a fim de diminuir a faixa de variação da saída da rede utilizando como neurônio de saída, ktCp2 (concentração de polímero morto) e log(ktCp2), visando diminuir erro no escalonamento das variáveis, tornando desta forma, a resposta da rede mais precisa. A rede que utilizou como neurônio de saída log(ktCp2), em relação à outra rede testada. A predição desta rede, não se mostrou precisa o suficiente para representar de forma adequada o perfil de conversão, quando aplicada ao modelo híbrido. Devido à alta não linearidade do característica dos processos poliméricos, e graças a grandes problemas difusionais, devido ao efeito gel, o modelo híbrido produziu altas conversões em baixíssimos tempos de reação
Abstract: In the present work, the objective is modeling of a batch reactor, using methylmethacrylate as a case study. Neural networks will be used, in a hybrid mOdel, in order to by pass the use of empirical correlations to correct the constant or termination rate kt to the gel effect. Polymeric processes are known for its high complexity due to the large number of parallel reactions and diffusional phenomena. Most of the problem sources are the heat release, due to the exothermical reactions and the high viscosity during the polymerization. These two factors usually leads to a thermal runaway, which affects the final properties or the polymeric material. Neural networks are a mathematical method based on the neurologic structure of the brain, and in its leaning capacity. It is an artificial intelligence technique, which is characterized for learn from a certain pattern data. The hybrid model seeks to overcome the difficulties of the deterministic mode!. Two neural networks were trained in order to compare the efficiency of the linearization of the output, using a logarithm. The network that used the linearized output exhibited better results in comparison to the other. Although its prediction, wasn't accurate enough to represent the conversion profile. Due to the high non-linearity of the polymeric processes and the diffusional effects that causes the gel effect. The hybrid model exibed high conversions in a very short time
Mestrado
Desenvolvimento de Processos Químicos
Mestre em Engenharia Química

In this thesis, the effect of pitch based optimisation was explored for a 80 turbine wind farm. Using a modified Jensen wake model and the Particle Swarm Optimisation (PSO) model, a pitch optimisation strategy was created for the dominant turbulence and atmospheric condition for the wind farm. As the wake model was based on the FLORIS model developed by P.M.O Gebraad et. al., the wake and power model was compared with the FLORIS model and a -0.090% difference was found. To determine the dynamic predictive capability of the wake model, measurement values across a 10 minute period for a 19 wind turbine array were used and the wake model under predicted the power production by 17.55%. Despite its poor dynamic predictive capability, the wake model was shown to accurately match the AEP production of the wind farm when compared to a CFD simulation done in FarmFlow and only gave a 3.10% over-prediction. When the optimisation model was applied with 150 iterations and particles, the AEP production of the wind farm increased by 0.1052%, proving that the pitch optimisation method works for the examined wind farm. When the iterations and particles used for the optimisation was increased to 250, the power improvement between optimised results improved by 0.1144% at a 222.5% increase in computational time, suggesting that the solution has yet to fully converge. While the solutions did not fully converge, they converged sufficiently and an increase in iterations gave diminishing results. From the results, the pitch optimisation model was found to give a significant increase in power production, especially in wake intensive wind directions. However, the dynamic predictive capabilities will have be improved upon before the control strategy can be applied to an operational wind farm.

Contexto: As infecções causadas pelo Staphylococcus aureus resistente a meticilina tem conseqüências graves aos pacientes e aos serviços de saúde. As medidas gerais de controle de infecção são fundamentais para conter a disseminação desta bactéria, mas não são sempre suficientes, e estratégias mais agressivas são empregadas muitas vezes para obter-se uma diminuição das taxas. Os estudos publicados para a avaliação da efetividade das medidas tem recebido criticas pela sua qualidade, e ainda não ha consenso sobre o assunto. Objetivos: Quantificar a prevalência de pacientes colonizados pelo Staphylococcus aureus resistentes a meticilina admitidos em um hospital terciário universitário, avaliar aspectos associados a transmissão da bactéria e estimar, através de modelo matemático, o efeito de medidas de isolamento de pacientes com Staphylococcus aureus resistentes meticilina na aquisic5o de colonização. Métodos: Um estudo de coorte prospectivo, com pacientes clínicos admitidos no hospital selecionados aleatoriamente na sua admissão. Os pacientes foram entrevistados na admissão e a cada semana e houve coleta de swab nasal para identificação de colonização pelo MRSA na admissão e a cada semana de internação. Os fatores de risco associados com a presença de colonização na admissão e sua aquisição durante a hospitalização foram investigados. Construiu-se um modelo determinístico de aquisição de MRSA considerando-se o impacto da prevalência de colonização basal pelo MRSA, a adesão a higienização das mãos e o use de isolamento na carga de trabalhos de enfermeiros e nas taxas de infecção pelo MRSA. Resultados: Foram selecionados 301 pacientes adultos e 189 pediátricos. A prevalência de MRSA na admissão foi de 5,3% (IC 95%: 3,1% a 8,5%) na população adulta, e 1,6% (1C95%: 0,3% a 4,6%) entre as crianças. A analise multivariável identificou os seguintes fatores de risco associados com a colonização em adultos na admissão: idade acima de 60 anos (RP = 2,9, IC 95%: 1,1 a 7,6), e internação no ano anterior (RP = 5,4, IC 95%: 1,3 a 23,4). A analise da incidência foi realizada em 285 pacientes que não eram portadores de MRSA na admissão, e que tiveram uma segunda amostra coletada. Entre estes, 9,5% (1C95%: 8,1 a 11,1) adquiriram colonização ou infecção durante a hospitalização. A taxa de colonização foi de 5,5/1.000 pacientes-dia entre os adultos (1C95%: 3,36 a 8,49), e de 1,6/1.000 pacientes-dia entre as crianças (1C95%: 0,33 a 4,61). 0 risco de aquisição aumentou conforme aumentou o tempo de internação, e este aumento foi estatisticamente significativo. No modelo proposto, se isolamento de pacientes aumenta o volume de trabalho dos trabalhadores da saúde, reduzindo a adesão aos protocolos básicos de prevenção de infecção, a execução das medidas de isolamento podem provocar o aumento da prevalência de MRSA. Entretanto, a aplicação de medidas de isolamento pode ter resultados diferentes dependendo da prevalência inicial MRSA e da carga de trabalho dos trabalhadores. A redução da carga de trabalho é mais custo-efetivo quando implementada para impedir a transição de um estado de baixa endemicidade para de alta. Conclusões: A identificação de portadores nasais de MRSA poderia ajudar a diminuir a pressão de colonização dentro do hospital e reduzir o alto índice de aquisição nesses pacientes. Entretanto, as medidas de controle devem ser cuidadosamente avaliadas num cenário com altas taxas de infecção, pois o grande numero de pacientes em isolamento pode comprometer a adesão a higienização de mãos ao aumentar a carga de trabalho dos enfermeiros, tendo efeito contrario ao desejado na prevenção de infecções.
Background: Infections caused by methicillin-resistant Staphylococcus aureus have serious consequences for patients and healthcare services. Basic infection control measures are essential to contain the spread of the bacteria, but are not always sufficient, and more aggressive strategies are often employed to obtain a reduction of rates. Studies published to assess the effectiveness of the measures have received criticism for its quality, and there is no consensus if the search and destroy policy is necessary Objectives: To quantify the prevalence of patients colonized by methicillin-resistant Staphylococcus aureus admitted in a tertiary university hospital, evaluate factors associated with transmission of the bacteria and to estimate, through a deterministic mathematical model, the effect of isolation measures of patients with the bacteria in the acquisition of colonization. Methods: A prospective cohort with clinical patients randomly selected in their entry to a hospital. Patients were interviewed on admission and weekly, with collection of nasal swab for identification of MRSA colonization at admission and every week of hospitalization. Risk factors associated with the presence of colonization on admission, and associated to its acquisition during hospitalization were investigated. A deterministic model for acquisition of MRSA was built, considering the impact of the baseline prevalence of MRSA colonization, adherence to hand hygiene and use of isolation measures in the workload healthcare workers and on the rates of MRSA infection. Results: We randomly selected 301 adult and 189 pediatric patients. The prevalence of MRSA at admission was 5.3% (95% CI, 3.1% to 8.5%) in adults and 1.6% (95% CI, 0.3% to 4.6%) among children. Multivariate analysis identified the following risk factors associated with colonization of adults at admission: age over 60 years (PR = 2.9 95% CI 1.1 10 7.6) and hospitalization in the previous year (PR = 5.4, 95% CI 1.3 to 23.4). The analysis of incidence was performed in 285 patients who were not carriers of MRSA on admission, and who had a second sample collected. Of these, 9.5% (95% CI 8.1 to 11.1) acquired colonization or infection during hospitalization. The colonization rate was 5.5 / 1,000 patient-days among adults (1C95%, from 3.36 to 8.49) and 1.6 / 1,000 patient-days among children (95% Cl, 0.33 to 4.61). The risk of acquisition increases as the length of stay increases, and this increase is statistically significant. In the proposed model, if isolation of patients increases the workload of health workers, and reduces adherence to the basic protocols for infection prevention, the implementation isolation can increase the prevalence of MRSA. However, the application of isolation can have different results depending on the initial prevalence of MRSA and the effect on healthcare workers workload. The reduction in workload is more cost-effective when implemented to prevent the transition from a state of low to hitzh. endemicity. Conclusions: The identification of nasal carriers of MRSA could help reduce the colonization pressure within the hospital and reduce the high rate of acquisition in these patients, but the measures of control should be carefully evaluated in a setting with high rates of infection, because the great number of patients in isolation can compromise adherence to hand hygiene of increasing the workload of the nurses, and result in the opposite effect in preventing infections.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Nesta dissertação, propõe-se uma metodologia para a analise da resposta dinâmica de pontes rodoviárias devido à travessia de comboios de diversos tipos de veículos sobre o tabuleiro irregular dessas obras de arte. Para tal, desenvolve-se uma análise paramétrica extensa com o objetivo de avaliarem-se os efeitos dinâmicos provenientes das irregularidades superficiais existentes no tabuleiro sobre o comportamento das pontes rodoviárias. A metodologia de análise é desenvolvida no domínio do tempo de acordo com um modelo estatístico. O modelo matemático é concebido de forma a simular o conjunto dos veículos e do tabuleiro, denominado neste trabalho comumente de sistema veículo-ponte (ou sistema veículo-estrutura). Considera-se a participação da massa e da rigidez dos veículos na definição das freqüências do conjunto e, conseqüentemente, a força de interação entre os veículos e a ponte é afetada pela flexibilidade desta. Simula-se o tabuleiro das obras de arte por uma viga modelada com base em elementos finitos de barra unidimensionais, com massas concentradas em seus nós e flexibilidade distribuída. Aos nós estão associados os movimentos de rotação no plano e de translação vertical. Desprezam-se a inércia de rotação e a deformação por cisalhamento. São considerados 04 (quatro) modelos distintos para representar os veículos do comboio na análise paramétrica, sendo estes: veículos com um eixo e uma massa, viaturas com um eixo e duas massas, veículos com dois eixos e três massas e carros com três eixos e quatro massas. Todos os veículos são simulados por sistemas de massas, molas e amortecedores e são descritos por graus de liberdade à translação e rotação no plano. As irregularidades da pista são definidas por um modelo matemático não- determinístico, com base na densidade espectral do perfil do pavimento, obtida experimentalmente. Os perfis irregulares do pavimento são considerados associados a processos fracamente estacionários e ergódicos. O carregamento sobre a superestrutura das pontes é constituído por uma sucessão infinita de veículos, igualmente espaçados e deslocando-se com velocidade constante sobre o tabuleiro. Devido à própria natureza das irregularidades superficiais e do comboio de veículos, atenção especial é concentrada na fase permanente da resposta do sistema veículo-ponte. São estudadas as respostas dos modelos estruturais, com base em tabuleiros isostáticos de concreto armado, com e sem balanços, em seção do tipo caixão, em termos de deslocamentos e esforços nas seções onde ocorrem os efeitos máximos. As conclusões deste trabalho versam sobre a adequação do modelo matemático empregado, observando- se a influência do tipo de modelo de veículo utilizado (com um ou mais eixos) sobre aresposta dinâmica das pontes rodoviárias analisadas e, bem como, à magnitude dos efeitos dinâmicos provenientes das irregularidades superficiais e suas conseqüências sobre as atitudes correntes de projeto.
In this investigation an analysis methodology is developed to evaluate the vehicle- structure response. A parametric study is carried to evaluate the dynamical effects, displacements and stresses, on highway bridge decks, due to vehicles crossing on rough pavement surfaces defined by a probabilistic model. The analysis methodology was considered following a statistical model, in the time domain. The mathematical model assumes a finite element representation of a beam like deck and the vehicle simulation uses concentrated parameters of mass, stiffness and damping. Four different models are developed in order to represent the vehicles. The vehicles are modeled as one axle, with one or two masses, and two and three axles, with three and four masses, respectively. All vehicles are simulated as mass-spring-damper systems and the degrees of freedom of these cars are defined as in plane vertical translations and rotations. The deck surface roughness is defined by a well known power spectrum probability density of road pavement profiles. The irregular pavement surface was defined like a weakly stationary and ergodic random process. The moving load is formed by an infinite succession of vehicles moving with constant velocity and equally spaced. Only steady-state response is considered. Response data are produced on concrete box girder elements assembled as simple beams, including cantilever spans. Conclusions are concerned with the fitness of the developed analysis methodology and the magnitude of the response amplification due to the surface irregularities.

This research developed comprehensive model updating systems for real structures including a hybrid approach which enhanced existing deterministic model updating techniques by providing measures to incorporate uncertainties in a computationally efficient way compared to probabilistic model updating approaches. Further, utilizing the developed hybrid approach a methodology was developed to assess the deterioration of reinforced concrete buildings under serviceability loading conditions. The developed methodologies in the research were successfully validated utilizing two real benchmark structures at Queensland University of Technology equipped with continuous monitoring systems.

Este trabalho está divido em duas partes. Na primeira apresentamos as funções logaritmo e exponencial generalizadas. A partir delas uma grande variedade de outras funções generalizadas pode ser obtida, permitindo uma formulação única dos comportamentos oscilatório, exponencial e lei de potência, característicos dos principais fenômenos físicos. Também mostramos que é possível generalizar a função densidade de probabilidade (pdf) exponencial estendida (stretched exponential) e, a partir dela, uma vasta gama de outras pdfs, que caracterizam os sistemas complexos em Física. As funções logaritmo e exponencial generalizadas também são úteis na generalização de vários modelos contínuos de crescimento em uma formulação única: o modelo de crescimento generalizado de Tsoullaris e Wallace. O mesmo pode ser feito para modelos discretos de crescimento, obtendo, como modelo mais geral, o -Ricker generalizado. Encerrando a primeira parte, mostramos que a pdf gaussiana generalizada (um caso particular da exponencial estendida generalizada) é a solução da equação de difusão não-linear, que caracteriza a caminhada determinista do turista. Na segunda parte deste trabalho é apresentada a caminhada do turista e suas duas versões originais: a determinista (CDT) e a estocástica (CET). A primeira delas é uma caminhada parcialmente autorrepulsiva, caracterizada por uma memória , em um meio desordenado multidimensional formado por N pontos. Em um ambiente unidimensional, ela apresenta uma transição entre uma exploração local e outra global, em um valor bem definido de memória 1 = log2N. Em sua versão estocástica (da qual a CDT é um caso particular), a dinâmica de movimentação é regida pela memória e pela temperatura T, responsável, em última instância, pelas probabilidades de deslocamento. Da mesma forma que a CDT, a CET também apresenta uma transição entre os regimes de exploração, caracterizada por uma memória e uma temperatura críticas e pela idade Np da caminhada (efeito de envelhecimento). Dada a dificuldade em tratar analiticamente a CET, introduzimos a caminhada estocástica modificada do turista (CEMT). Nesta versão, o parâmetro T passa a representar o alcance máximo de um passo da caminhada. Esta modificação permitiu tratar analiticamente a caminhada, sendo possível obter uma expressão analítica geral para a transição, em função dos parâmetros , T e Np. Estes resultados foram validados por experimentos numéricos.
The present work is splitted into two parts. In the first one we present the generalized logarithm and exponential functions. From them, a wide variety of other generalized functions can be obtained, that allow a unique formulation of oscillatory, exponential an power-law behaviors, that characterize physical phenomena. We also show that it is possible to generalize the stretched exponential probability density function (pdf) and, from there, a wide range of other pdfs that characterize complex systems in Physics. The generalized logarithm and exponential functions are also useful to generalize several continuous growth models into a single formulation: the generalized Tsoullaris and Wallace growth model. The same can be done for discrete growth models, getting, as more general model, the generalized -Ricker growth model. Concluding the first part, we show that the generalized Gaussian pdf (a special case of the generalized stretched exponential) is a solution of the nonlinear diffusion equation, which is a characteristic of deterministic tourist walk. In the second part we present the tourist walk and its two original versions: the deterministic one (DTW) and stochastic one (STW). The first one is a partially self-avoiding walk over a disordered multidimensional medium formed by N points and characterized by a memory . In a one-dimensional environment, it presents a transition from a local exploration to a global one at a well-defined memory value 1 = log2N. In its stochastic version (from which DTW is a particular case), the movement dynamics is ruled by the memory and a temperature T which is responsible by the displacement probabilities. Similar to DTW, STW also has a transition between exploration schemes, characterized by a critical memory and temperature and the walking age (Np) (aging effect). Due the difficulty on analytical treatment of the CET, we introduced the modified stochastic tourist walk (MSTW). In this version, the parameter T plays the role of a maximum distance of one walking step. This modification allowed us to treat analytically the walk, being possible to obtain a general analytical expression for the transition, as function to the parameters , T and Np. These results were validated by numerical experiments.

Захист відбудеться «02» жовтня 2020 р. о 12 00 годині на засіданні спеціалізованої вченої ради Д58.052.01 в Тернопільському національному технічному університеті імені Івана Пулюя, 46001, м. Тернопіль, вул. Руська, 56, ауд. 79.
Дисертація присвячена вирішенню проблеми розвитку математичного моделювання та обчислювальних методів у напрямку створення та дослідження нових компартментних математичних моделей кіберфізичних систем медико- біологічних процесів. Розроблено компартментні математичні моделі кіберфізичних систем медико-біологічних процесів з використанням решітчастих диференціальних та різницевих рівнянь із запізненням на прямокутній та гексагональній решітках. Запропоновано методи обчислювальної математики для дослідження перманентності, екстинкції та стійкості компартментних математичних моделей кіберфізичних систем медико-біологічних процесів. Розроблено нові методи моделювання кіберфізичних біосенсорних систем з використанням гібридного програмування та інтерпретацією результатів моделювання у вигляді зображення фазових площин, решітчастих портретів та електричних сигналів. Запропоновано методи дослідження експоненційної стійкості рекурентних нейромережевих моделей для кіберфізичних систем медико-біологічних процесів. Розроблено алгоритм оптимального керування в моделі кіберфізичної системи лабораторної діагностики на основі полімеразно-ланцюгової реакції. Програмно реалізовані методи дослідження стійкості кіберфізичних систем медико-біологічних процесів.
Диссертация посвящена решению проблемы развития математического моделирования и вычислительных методов в направлении создания и исследования новых компартментных математических моделей киберфизических систем медико- биологических процессов. Разработаны компартментные математические модели киберфизических систем медико-биологических процессов с использованием решётчастых дифференциальных и разностных уравнений с запаздыванием на прямоугольной и гексагональной решётках. Предложенные методы вычислительной математики для исследования перманентности, экстинкции и устойчивости компартментных математических моделей киберфизических систем медико- биологических процессов. Разработаны новые методы моделирования киберфизических биосенсорных систем с использованием гибридного программирования и интерпретацией результатов моделирования в виде изображения фазовых плоскостей, решётчастых портретов и электрических сигналов. Предложенные методы исследования экспоненциальной устойчивости рекуррентных нейросетевых моделей для киберфизических систем медико- биологических процессов. Разработан алгоритм оптимального управления в модели киберфизической системы лабораторной диагностики на основе полимеразно- цепной реакции. Программно реализованы методы исследования устойчивости киберфизических систем медико-биологических процессов.
The dissertation is devoted to the solution of the problem of development of mathematical modelling and computational methods in the direction of creation and investigation of new compartmental mathematical models of cyber-physical systems of medical and biological processes. A methodology for designing cyber-physical biosensor systems used for automated monitoring of biomedical processes has been developed. On the basis of the suggested methodology, compartmental mathematical models of cyber- physical systems of medical and biological processes have been developed using lattice differential and difference equations with delay on rectangular and hexagonal lattices. The developed compartmental mathematical models take into account all the properties that are characteristic of lattice cyber-physical systems of medical and biological processes. Taking into account the lattice structure, the research has been carried out by the use of appropriate interactions between pixels of rectangular and hexagonal lattices, spatial operators and coordinations of biopixels. Methods of computational mathematics have been developed for solving problems of studying the permanence, extinction and stability of compartmental mathematical models of cyber-physical systems of medical and biological processes by using lattice differential and difference equations with delay on rectangular and hexagonal lattices. The basic numbers of reproduction have been suggested as a tool for studying the stability of compartmental lattice-type mathematical models. The conditions of stability, stability state without antibodies, stability state without antigens and antibodies, identical and non-identical endemic stability state have been investigated. Тhe study of local and global asymptotic stability has presented qualitative and quantitative results of numerical simulation of cyber-physical systems of medical and biological processes. The numerical simulation results show that the time delay has the greatest influence on the stability of the developed mathematical models of cyber-physical biosensor systems on rectangular and hexagonal lattices using lattice differential and difference equations with delay. New methods of organizing and optimizing the processes of simulation of cyber-physical biosensor systems using hybrid programming and interpretation of simulation results in the form of phase planes, lattice portraits have been developed. A mathematical model of dynamic logic for the systems under study has been developed by using the basic terms of the hybrid programming language. The results of numerical simulation of the developed cyber-physical biosensor system have been presented in the form of electrical signals from transducers characterizing the number of fluorescent pixels. Methods of computational mathematics have been worked out to solve the problems of exponential stability research of recurrent neural network models for cyber-physical systems of medical and biological processes. The algorithm of optimal control in the model of cyber-physical system of laboratory diagnostics based on polymerase-chain reaction has been developed. Using the obtained results, it is possible to control the temperature to minimize the required time of implementation of the annealing stage with the possibility of using a minimum amount of primer. The practical significance of the results of the dissertation research consists in the fact that, on the basis of the developed compartmental mathematical models of cyber- physical systems of medical and biological processes, the study of stability on rectangular and hexagonal lattices with the use of lattice differential and difference equations, it has been established that the constant delay is the most important parameter that affects the stability of the systems under study. A software complex has been developed to study the stability of cyber-physical systems of medical-biological processes, consisting of a block of identification and input of the parameters of the studied models, a software module for investigation of continuous dynamics, the block of modelling of the lattice images of antigens and antibodies, the block of obtaining the lattice images of connections of antigens with antibodies, the module of the study of discrete dynamics on the stability of the cyber-physical biosensor system and the visualization unit. The developed software complex and the obtained practical results are suitable for use in the design of modern cyber-physical systems of medical and biological processes with ensuring their stability during storage and use.
Перелік основних умовних позначень, символів і скорочень 42 Вступ 46 Розділ 1. Аналітичний огляд кіберфізичних систем медико- біологічних процесів та їх математичних моделей 57 1.1. Огляд практичних задач, пов’язаних із застосуванням кіберфізичних систем медико-біологічних процесів 58 1.1.1. Портативні кіберфізичні системи медико-біологічних процесів 59 1.1.2. Кіберфізичні біосенсорні системи для комплексного моніторингу біохімічних показників 60 1.1.3. Кіберфізичні біосенсорні системи для моніторингу прийому лікарських препаратів 62 1.1.4. Кіберфізичні системи медико-біологічних процесів для моніторингу рівня глюкози 63 1.1.5. Селективні елементи кіберфізичних систем медико- біологічних досліджень 68 1.2. Задача проектування та технічні характеристики кіберфізичних систем медико-біологічних процесів 74 1.3. Математичні моделі біосенсорів у кіберфізичних системах медико-біологічних процесів 81 1.3.1. Статичні математичні моделі біосенсорів у кіберфізичних системах медико-біологічних процесів 81 1.3.1.1. Модель оптичного біосенсора на основі поверхневого плазмонного резонансу 81 1.3.1.2. Багатошарова модель оптичного біосенсора 83 1.3.2. Динамічні математичні моделі біосенсорів на основі звичайних диференціальних рівнянь 86 1.3.2.1. Модель біосенсора першого порядку 86 1.3.2.2. Динамічна модель біосенсора другого порядку 89 1.3.3. Динамічні моделі біосенсорів у вигляді диференціальних рівнянь в частинних похідних 91 1.3.3.1. Модель біосенсора на основі рівнянь реакції-дифузії 91 1.3.3.2. Моделі біосенсорів, які використовують кінетику Міхаеліса-Ментена 92 1.3.3.3. Математична модель електрохімічного біосенсора 95 1.3.3.4. Модель біосенсора для визначення рівня глюкози 98 1.3.3.5. Модель для оптимізації розроблення біосенсорних кіберфізичних систем 100 1.3.3.6. Модель біосенсора в циліндричних координатах 101 1.4. Математична модель решітчастої динамічної системи в медико- біологічних дослідженнях 102 1.5. Математична модель Г.І. Марчука та використання її в кіберфізичних системах медико-біологічних процесів 106 1.6. Властивості, які повинні мати компартментні математичні моделі кіберфізичних систем медико-біологічних процесів 108 1.7. Висновки до першого розділу 114 Розділ 2. Розробка компартментних математичних моделей кіберфізичних біосенсорних систем 116 2.1. Математичне моделювання медико-біологічних процесів 117 2.2. Математична модель біосенсора на прямокутній решітці з використаням решітчастих диференціальних рівнянь із запізненням 120 2.3. Математична модель біосенсора на прямокутній решітці з використанням різницевих рівнянь із запізненням 125 2.4. Математична модель біосенсора на гексагональній решітці з використаням решітчастих диференціальних рівнянь із запізненням 129 2.5. Математична модель біосенсора на гексагональній решітці з використанням різницевих рівнянь із запізненням 132 2.6. Математична модель компартментних медико-біологічних процесів на основі клітинних автоматів 136 2.7. Модель кіберфізичної системи з атаками стану та вимірювань на основі стохастичних різницевих рівнянь 137 2.8. Ідентифікація параметрів у решітчастих диференціальних рівняннях із запізненням 140 2.9. Математична модель бутирилхолінестеразного біосенсора для визначення α-чаконіну 146 2.10. Висновки до другого розділу 149 Розділ 3. Дослідження неперервної та дискретної динаміки компартментних математичних моделей решітчастого типу 151 3.1. Ендемічні стани рівноваги компартментних математичних моделей решітчастого типу в кіберфізичних біосенсорних системах 152 3.1.1. Ендемічні стани рівноваги математичних моделей біосенсора на прямокутній решітці з використанням диференціальних та різницевих рівнянь 152 3.1.2. Ендемічні стани рівноваги математичних моделей біосенсора на гексагональній решітці з використанням диференціальних та різницевих рівнянь 153 3.2. Базові числа репродукції як інструмент дослідження стійкості компартментних математичних моделей решітчастого типу 155 3.3. Умови локальної асимптотичної стійкості компартментних математичних моделей біосенсорів решітчастого типу 159 3.3.1. Умови локальної асимптотичної стійкості математичної моделі біосенсора на основі диференціальних рівнянь на прямокутній решітці 159 3.3.2. Умови перманентності математичної моделі біосенсора на основі різницевих рівнянь на прямокутній решітці 164 3.3.3. Умови локальної асимптотичної стійкості математичної моделі біосенсора на основі диференціальних рівнянь на гексагональній решітці 173 3.3.4. Умови перманентності математичної моделі біосенсора на основі різницевих рівнянь на гексагональній решітці 174 3.4. Умови глобальної асимптотичної стійкості компартментних математичних моделей решітчастого типу 175 3.4.1. Умови глобальної асимптотичної стійкості математичної моделі біосенсора на основі диференціальних рівнянь на прямокутній решітці 175 3.4.2. Умови глобальної притягувальності математичної моделі біосенсора на основі різницевих рівнянь на прямокутній решітці 182 3.5. Виникнення біфуркації та детермінованого хаосу в компартментних математичних моделях решітчастого типу 187 3.5.1. Виникнення біфуркації та детермінованого хаосу в математичній моделі біосенсора з використанням решітчастих диференціальних рівнянь із запізненням на прямокутній решітці 187 3.5.2. Виникнення біфуркації та детермінованого хаосу в математичній моделі біосенсора з використанням решітчастих диференціальних рівнянь із запізненням на гексагональній решітці 192 3.5.3. Виникнення біфуркації та детермінованого хаосу в математичній моделі біосенсора на основі різницевих рівнянь на прямокутній решітці 193 3.5.4. Виникнення біфуркації та детермінованого хаосу в математичній моделі біосенсора на основі різницевих рівнянь на гексагональній решітці 198 3.6. Дослідження на основі чисельних характеристик нелінійної динаміки 199 3.6.1. Результати чисельного моделювання математичної моделі біосенсора з використанням диференціальних рівнянь на прямокутній решітці 199 3.6.2. Результати чисельного моделювання математичної моделі біосенсора з використанням диференціальних рівнянь на гексагональній решітці 203 3.6.3. Результати чисельного моделювання математичної моделі біосенсора з використанням різницевих рівнянь на прямокутній решітці 206 3.6.4. Результати чисельного моделювання математичної моделі біосенсора з використанням різницевих рівнянь на гексагональній решітці 207 3.7. Дослідження стійкості математичної моделі бутирилхолінестеразного біосенсора для визначення α-чаконіну 211 3.8. Висновки до третього розділу 214 Розділ 4. Розроблення та дослідження математичних моделей динамічної логіки кіберфізичних біосенсорних систем 216 4.1. Концептуальна модель архітектури кіберфізичних систем медико- біологічних процесів 216 4.2. Проектування динамічних процесів в кіберфізичних біосенсорних системах 219 4.3. Принцип вимірювання медико-біологічних показників кіберфізичними біосенсорними системами 222 4.4. Моделювання неперервної динаміки кіберфізичних біосенсорних систем 224 4.5. Основні терміни мови гібридного програмування 225 4.6. Моделі динамічної логіки кіберфізичних біосенсорних систем 228 4.6.1. Динамічне логічне моделювання кіберфізичної біосенсорної системи на прямокутній решітці з використаням решітчастих диференціальних рівнянь із запізненням 228 4.6.2. Динамічне логічне моделювання КФБСС на гексагональній решітці з використаням решітчастих диференціальних рівнянь із запізненням 230 4.7. Експериментальні дослідження математичних моделей динамічної логіки в кіберфізичних системах 232 4.7.1. Дослідження динамічної логіки кіберфізичної біосенсорної системи на прямокутній решітці з використаням решітчастих диференціальних рівнянь із запізненням 232 4.7.2. Дослідження динамічної логіки кіберфізичної біосенсорної системи на гексагональній решітці з використанням решітчастих диференціальних рівнянь із запізненням 238 4.7.3. Дослідження динамічної логіки кіберфізичної біосенсорної системи на прямокутній решітці з використанням різницевих рівнянь із запізненням 243 4.7.4. Дослідження динамічної логіки кіберфізичної біосенсорної системи на гексагональній решітці з використанням різницевих рівнянь із запізненням 248 4.8. Порівняльний аналіз результатів чисельного моделювання математичних моделей кіберфізичних біосенсорних систем на прямокутній та гексагональній решітках з використанням решітчастих диференціальних рівнянь 253 4.9. Порівняльний аналіз результатів чисельного моделювання математичних моделей кіберфізичних біосенсорних систем на прямокутній та гексагональній решітках з використанням решітчастих різницевих рівнянь 254 4.10. Висновки до четвертого розділу 256 Розділ 5. Розроблення методів дослідження нейромережевих моделей кіберфізичних біосенсорних систем медико-біологічних процесів 258 5.1. Нейромережеві моделі кіберфізичних систем медико-біологічних процесів та методи їх дослідження 258 5.2. Модель кіберфізичної біосенсорної системи на основі рекурентної нейромережі 260 5.3. Розроблення методу експоненціального оцінювання рекурентної нейромережі 261 5.3.1. Метод Кертеша та етапи побудови оцінки експоненціального згасання 261 5.3.2. Оцінка для похідної функціонала Ляпунова 262 5.3.3. Різницева нерівність для функціонала Ляпунова 265 5.4. Непрямий метод дослідження стійкості моделі нейронної мережі з дискретно розподіленим запізненням 269 5.4.1. Методи дослідження стійкості нейромережевих моделей 269 5.4.2. Модель нейронної мережі з дискретно розподіленим запізненням 271 5.4.3. Непрямий метод дослідження стійкості рекурентної нейронної мережі з дискретно розподіленим запізненням 273 5.5. Дослідження моделі нейронної мережі з дискретним та неперервним запізненням 282 5.6. Експериментальне дослідження якісної поведінки моделі рекурентної нейромережі 289 5.6.1. Чисельне дослідження динамічної поведінки двонейронної мережі з чотирма дискретними запізненнями 289 5.6.2. Чисельне дослідження динамічної поведінки нейронної мережі з трьома нейронами 291 5.6.3. Чисельне дослідження динамічної поведінки рекурентної двонейронної мережі зі змішаним запізненням 292 5.7. Висновки до п’ятого розділу 296 Розділ 6. Розроблення і дослідження компартментних математичних моделей медико-біологічних процесів лабораторної діагностики 298 6.1. Полімеразно-ланцюгова реакція, як універсальний метод лабораторної діагностики 298 6.2. Розроблення компартментної моделі стадій полімеразно- ланцюгової реакції 304 6.3. Дослідження стійкості полімеразно-ланцюгової реакції 305 6.4. Розроблення алгоритму оптимального керування полімеразно- ланцюговою реакцією 306 6.5. Задача оптимального керування стадією відпалу в ПЛР 307 6.6. Задача оптимального керування стадією елонгації в ПЛР 312 6.7. Чисельне моделювання кіберфізичної системи лабораторної діагностики на прикладі полімерезно-ланцюгової рекції для стадії відпалу 316 6.8. Висновки до шостого розділу 323 Розділ 7. Розроблення програмного забезпечення для реалізації методів математичного моделювання компартментних медико- біологічних процесів 325 7.1. Програмний комплекс для дослідження стійкості КФБСС 326 7.1.1. Розробка програмного комплексу для дослідження стійкості КФБСС 326 7.1.2. Програмний модуль для дослідження фазових площин в КФБСС на прямокутній решітці з використанням диференціальних рівнянь із запізненням 328 7.1.3. Програмний модуль для дослідження фазових площин в КФБСС на гексагональній решітці з використанням диференціальних рівнянь із запізненням 331 7.2. Програмний модуль дослідження інтенсивності імунної відповіді 333 7.2.1. Комп’ютерне моделювання контактів антигенів із антитілами в кіберфізичних біосенсорних системах на прямокутній решітці з використанням диференціальних рівнянь із запізненням 333 7.2.2. Комп’ютерне моделювання контактів антигенів із антитілами в кіберфізичних біосенсорних системах на гексагональній решітці з використанням диференціальних рівнянь із запізненням 334 7.3. Програмна реалізація вихідних сигналів кіберфізичної системи 336 7.3.1. Програмний комплекс аналізу дискретизованого сигналу з перетворювача КФБСС на прямокутній решітці з використанням диференціальних рівнянь із запізненням 336 7.3.2. Результати чисельного аналізу електричного сигналу з перетворювача кіберфізичної біосенсорної системи 337 7.4. Розроблення та використання програмного забезпечення кіберфізичних систем аналізу біосигналів 338 7.4.1. Програмний комплекс для аналізу біосигналів в поліграфах 338 7.4.2. Використання відкритих ресурсів біосигналів PhysioNet для розробки кіберфізичних систем кардіодіагностики 339 7.5. Телемедичні технології у кіберфізичних системах 343 7.6. Використання методу індукції дерев рішень в кіберфізичних системах для потреб судово-медичної експертної практики 344 7.7. Використання комп’ютерних програм при проектуванні та дослідженні кіберфізичних медико-біологічних систем 346 7.8. Ідентифікація параметрів математичної моделі бутирилхолінестеразного біосенсора для визначення α-чаконіну 350 7.9. Дослідження стійкості кіберфізичних біосенсорних систем під впливом електромагнітного випромінювання 354 7.10. Висновки до сьомого розділу 355 Висновки 357 Список використаних джерел 360 Додатки 427 Додаток А. Класифікація та використання кіберфізичних біосенсорних систем 428 A.1. Електрохімічні кіберфізичні біосенсорні системи 428 A.2. Оптичні кіберфізичні біосенсорні системи 429 A.3. Кіберфізичні біосенсорні системи на основі оксиду кремнію 429 A.4. Кіберфізичні біосенсорні системи на основі наноматеріалів 430 A.5. Генетично кодовані кіберфізичні біосенсорні системи 431 A.6. Клітинні кіберфізичні біосенсорні системи 432 A.7. Порівняльний аналіз кіберфізичних біосенсорних систем 433 Додаток Б. Базові числа репродукції математичної моделі біосенсора на прямокутній та гексагональній решітках 437 Б.1. Базові числа репродукції математичної моделі біосенсора на прямокутній решітці з використанням різницевих рівнянь 437 Б.2. Базові числа репродукції математичних моделей біосенсора на гексагональній решітці з використанням диференціальних та різницевих рівнянь 440 Додаток В. Доведення умов локальної асимптотичної стійкості математичної моделі біосенсора на основі диференціальних рівнянь на гексагональній решітці 443 Додаток Д. Доведення квазіперманентності математичної моделі біосенсора на основі різницевих рівнянь на гексагональній решітці 448 Додаток Е. Умови глобальної асимптотичної стійкості математичної моделі біосенсора на основі диференціальних рівнянь на гексагональній решітці 453 Додаток Ж. Умови глобальної притягувальності математичної моделі біосенсора на основі різницевих рівнянь на гексагональній решітці 461 Додаток И. Фазові діаграми популяцій антигенів щодо антитіл в біопікселях кіберфізичної біосенсорної системи на прямокутній решітці 467 Додаток К. Дослідження кіберфізичної системи з атаками стану та вимірювань на основі стохастичних різницевих рівнянь 473 Додаток Л. Семантика гібридних програм та приклад їх застосування 480 Л.1. Семантика гібридних програм 480 Л.2. Приклад застосування гібридної програми 482 Додаток М. Динамічне логічне моделювання КФБСС на прямокутній та гексагональній решітках 484 М.1. Динамічне логічне моделювання КФБСС на прямокутній решітці з використанням різницевих рівнянь із запізненням 484 М.2. Динамічне логічне моделювання КФБСС на гексагональній решітці з використаням решітчастих різницевих рівнянь із запізненням 486 Додаток Н. Результати чисельного моделювання дискретної динаміки кіберфізичної біосенсорної системи на прямокутній решітці з використаням решітчастих диференціальних рівнянь із запізненням 489 Додаток П. Результати чисельного моделювання дискретної динаміки кіберфізичної біосенсорної системи на гексагональній решітці з використанням решітчастих диференціальних рівнянь із запізненням 499 Додаток Р. Результати чисельного моделювання дискретної динаміки кіберфізичної біосенсорної системи на прямокутній решітці з використаням решітчастих різницевих рівнянь із запізненням 506 Додаток С. Результати чисельного моделювання дискретної динаміки кіберфізичної біосенсорної системи на гексагональній решітці з використанням решітчастих різницевих рівнянь із запізненням 514 Додаток Т. Етапи створення медичних нейромережевих експертних кіберфізичних систем 522 Додаток У. Ієрархічна модель якісного аналізу решітчастих компартментних математичних моделей кіберфізичних медико- біологічних систем 523 Додаток Ф. Використання пакету R для розроблення та дослідження кіберфізичних систем медико-біологічних процесів 526 Ф.1. Пакет R як середовище програмування для статистичного аналізу даних 526 Ф.2. Короткий опис функцій пакета R deSolve 528 Ф.3. Приклад моделювання в пакеті R моделі типу Лотки– Вольтерри 529 Додаток Х. Фрагмент програми для дослідження фазових діаграм кіберфізичної біосенсорної системи на прямокутній решітці з використанням диференціальних рівнянь із запізненням 533 Додаток Ц. Фрагмент програми для дослідження біфуркаційних діаграм в кіберфізичній біосенсорній системі на прямокутній решітці з використанням диференціальних рівнянь із запізненням 543 Додаток Ш. Фрагмент програми для дослідження фазових діаграм кіберфізичної біосенсорної системи на гексагональній решітці з використанням диференціальних рівнянь із запізненням 545 Додаток Щ. Фрагмент програми для дослідження біфуркаційних діаграм в кіберфізичній біосенсорній системі на гексагональній решітці з використанням диференціальних рівнянь із запізненням 554 Додаток Ю. Фрагмент програми для дослідження електричного сигналу з перетворювача кіберфізичної біосенсорної системи на прямокутній решітці з використанням диференціальних рівнянь із 556 запізненням Додаток Я. Фрагмент програми для дослідження електричного сигналу з перетворювача кіберфізичної біосенсорної системи на гексагональній решітці з використанням диференціальних рівнянь із запізненням 557 Додаток АА. Список публікацій здобувача за темою дисертації 559 Додаток АБ. Свідоцтва про реєстрацію авторського права на комп’ютерні програми, патент 582 Додаток АВ. Акти впроваджень 597

Le changement climatique dû à l'augmentation des émissions de gaz à effet de serre est considéré comme l'un des principaux défis pour les êtres humains dans 21ème siècle. Il conduira à des changements dans les précipitations, l'humidité atmosphérique, augmentation de l'évaporation et probablement augmenter la fréquence des événements extrêmes. Les conséquences de ces phénomènes auront une influence sur de nombreux aspects de la société humaine. Donc, il y a une nécessité d'avoir une estimation robuste et précise de la variation des facteurs naturels dus au changement climatique, au moins dans les événements de cycle et d'inondation hydrologiques pour fournir une base solide pour atténuer les impacts du changement climatique et s'adapter à ces défis. Le but de cette étude est de présenter une méthodologie pour évaluer les impacts de différents scénarios de changement climatique sur une zone inondable du bassin de la rivière côtière dans la région centrale du Viet Nam - bassin versant de Vu Gia Thu Bon. Les simulations hydrologiques sont basées sur un modèle hydrologique déterministe validé qui intègre la géologie, les sols, la topographie, les systèmes fluviaux et les variables climatiques. Le climat de la journée présente, sur la période de 1991-2010 a été raisonnablement simulée par le modèle hydrologique. Climat futur (2091-2100) information a été obtenue à partir d'une réduction d'échelle dynamique des modèles climatiques mondiaux. L'étude analyse également les changements dans la dynamique des inondations de la région de l'étude, le changement hydrologique et les incertitudes du changement climatique simulation
Climate change due to the increase of greenhouse gas emissions is considered to be one of the major challenges to mankind in the 21st century. It will lead to changes in precipitation, atmospheric moisture, increase in evaporation and probably a higher frequency of extreme events. The consequences of these phenomena will have an influence on many aspects of human society. Particularly at river deltas, coastal regions and developing countries, the impacts of climate change to socio-economic development become more serious. So there is a need for a robust and accurate estimation of the variation of natural factors due to climate change, at least in the hydrological cycle and flooding events to provide a strong basis for mitigating the impacts of climate change and to adapt to these challenges. The aim of this study is to present a methodology to assess the impacts of different climate change scenarios on a flood prone area of a coastal river basin in the central region of Viet Nam – Vu Gia Thu Bon catchment. The hydrological simulations are based on a validated deterministic hydrological model which integrates geology, soil, topography, river systems and climate variables. The present day climate, over the period of 1991-2010 was reasonably simulated by the hydrological model. Future climate (2091-2100) information was obtained from a dynamical downscaling of the global climate models. The study also analyzes the changes in the flood dynamics of the study region, the hydrological shift and the uncertainties of climate change simulation

La parcelle de culture, unite caracteristique du paysage et echelle operationnelle pour l'agriculteur, constitue la surface elementaire de gestion de l'eau et de l'environnement. Aussi ce memoire s'attache a caracteriser a cette echelle variabilite des rendements des cultures et des bilans hydriques en confrontant approche experimentale et modelisation. Une meme methodologie a ete appliquee sur deux sites mediterraneens: en tunisie pour trois cultures pluviales et en france pour deux essais de sorghos irrigues par aspersion. La variabilite spatiale des rendements, de l'humidite du premier metre de sol et de l'irrigation est etudiee par la geostatistique. Puis les bilans hydriques locaux in situ sont etablis sur des stations tensioneutroniques representatives. La modelisation stationnelle est realisee en utilisant un modele deterministe simplifie du bilan hydrique de type capacitif, pilote et, dans le cas de montpellier, une fonction de rendement. En complement, une etude de sensibilite du modele a montre l'importance de l'estimation de la reserve mobilisable et de la variable reserve initiale. La variabilite simultanee, a l'echelle parcellaire, du sol (reserve mobilisable rm et reserve initiale ri) et de l'irrigation i a ete prise en compte grace a une version stochastique du modele, en utilisant la methode des bandes tournantes. Il a ainsi ete mis en evidence que: la variabilite du sol a une influence preponderante sur l'etr et le rendement ; la variance maximale de l'etr est observee en debut de stress ; les variogrammes des sorties du modele ont des structures emboitees fortement dependantes de la correlation entre ri et rm. L'approche developpee ici est la seule qui apprehende l'effet de la variabilite simultanee du sol et de l'irrigation sur le bilan hydrique et le rendement

Le analisi contenute nel presente elaborato di tesi costituiscono uno strumento conoscitivo di base, indispensabile per tutte quelle zone in cui i movimenti franosi o altre dinamiche inducono pericolosità geologica interferendo con l’ambiente e le strutture antropiche, consentendo una buona conoscenza, anche di territori con estensione piuttosto ampia, a costi molto ridotti.Tutte le procedure e software utilizzati nel presente lavoro sono disponibili open-source e fruibili gratuitamente online. Il rilevamento geomorfologico è stato condotto in tre aree di studio, caratterizzate da contesti geologico-strutturali diversi tra loro. Tale rilevamento, coadiuvato da un'analisi multitemporale condotta mediante fotointerpretazione, si è rivelato molto utile per individuare i limiti dei movimenti franosi, il loro grado di attività e la loro evoluzione nel tempo. Le analisi statistiche hanno consentito di individuare la variabilità dei parametri predisponenti nelle diverse aree di studio e di indicare quali classi, tra i parametri, sono caratterizzate dal maggior numero di frane e, dunque, più prone al franamento. Gli studi di suscettibilità effettuati per le diverse aree di studio con la metodologia di statistica bivariata mostrano un’elevata percentuale di aree in frana ricadenti all’interno delle aree predette a più elevata suscettibilità e possono essere applicati sia a piccola sia a grande scala, per diverse tipologie di frane. Infine, i risultati ottenuti tramite il modello prevalentemente deterministico basato sul modulo r.slope.stability (http://www.slopestability.org/) sono piuttosto attendibili e rappresentativi della situazione reale, come dimostrato dai risultati della validazione tramite la stima di AROC. L’opportunità di utilizzare software GIS, non solo per la manipolazione dei dati ma anche per il loro aggiornamento e per l’esecuzione automatica delle procedure bivariate (ad es. attraverso il codice in linguaggio Python creato durante questo lavoro di tesi), incrementa notevolmente la possibilità di estendere queste analisi a nuove e diverse aree di studio, con costi pressoché nulli.

From factories to power grids, industrial systems are increasingly being digitally controlled and networked. While networking these systems together improves their efficiency and convenience, it also opens them up to attack by malicious actors. When these attacks occur, forensic investigators need to quickly be able to determine what was compromised and which corrective actions should be taken. In this thesis, a method is proposed for investigating attacks on industrial control systems by simulating the logged inputs of the system over time using a model constructed from the control programs that make up the system. When evaluated, this led to the detection of attacks which perturbed the normal operation of the system by comparing the simulated output to the actual output. It also allowed for dependency tracing between the inputs and outputs of the system, so that attacks could be traced from their unwanted effects to their source and vice-versa. This method can thus greatly aid investigators in recovering the complete attack story using only logs of inputs and outputs to an industrial control system.

Tese de doutoramento (co-tutela), Biology (Population Biology), Vrije Uiversity Amesterdam, Universidade de Lisboa, 2012
Throughout human history, infectious diseases have caused debilitation and pre- mature death to large portions of the human population, leading to serious social- economic concerns. Many factors have contributed to the persistence and increa- se in the occurrence of infectious disease (such as demographic factors, political, social and economic changes, environmental change, public health care and infra- structure, microbial adaptation, etc.). According to the World Health Organiza- tion (WHO), are the second leading cause of death globally after cardiovascular diseases (WHO, 2010). In recent years, mathematical modeling became an im- portant tool for the understanding of infectious disease epidemiology and has led to great advances in conceiving disease control strategies, including vaccination programs. One of the most important infectious diseases is dengue, a major international public health concern with more than 55% of world population at risk of acquiring the infection. Dengue is a viral mosquito-borne infection, a leading cause of illness and death in the tropics and subtropics. Dengue fever is caused by four antigenically distinct viruses, designated dengue types 1, 2, 3 and 4. Infection by one serotype confers life-long immunity to only that serotype, and temporary cross-immunity to other related serotypes. The temporary cross-immunity period lasts from three to nine months and it is related to antibody levels created during the immune response to a previous dengue infection. It is stated that such high antibody levels would be enough to protect the individual against an immediately new dengue infection caused by a different but related serotype. Two variants of the disease exist: dengue fever (DF), a non-fatal form of illness, and dengue hemorrhagic fever (DHF), which may evolve toward a severe form known as dengue shock syndrome (DSS). Epidemiological studies support the association of DHF with secondary dengue infection. There is good evidence that sequential infection increases the risk of developing DHF due to a process described as antibody-dependent enhancement (ADE), where the pre-existing antibodies to previous dengue infection cannot neutralize but rather enhance the new infection. Treatment of uncomplicated dengue cases is only supportive, and severe den- gue cases requires careful attention to fluid management and proactive treatment of hemorrhagic symptoms. A vaccine against dengue is not yet available, since it would have to simulate a protective immune response to all four serotypes, although several candidates of tetravalent vaccines are at various stages of de- velopment. So far, prevention of exposure and vector control remain the only alternatives to prevent dengue transmission. In recent years, mathematical modeling became an interesting tool for the un- derstanding of infectious diseases epidemiology and dynamics. A series of deter- ministic compartment models such as Susceptible-Infected (SI) and Susceptible- Infected-Recovered (SIR) for example, have been proposed based on the flow patterns between compartments of hosts. The SIR epidemic model divides the population into three classes concerning the disease stages: susceptible (S), In- fected (I) and Recovered (R). This model framework can represent infectious diseases where waning immunity can happen. Assuming that the transmission of the disease is contagious from person to person, the susceptibles become infected and infectious, are cured and become recovered. After a waning immunity period, the recovered individual can become susceptible again to reinfection. Multi-strain dynamics, such as dengue epidemiology, are generally modeled with extended SIR-type models. Dengue fever dynamic is well known to be particularly complex with large fluctuations of disease incidences. To capture differences in primary and secondary dengue infections, a two-strain SIR-type model for the host population has to be considered. Dengue models including multi-strain interactions via ADE, but without temporary cross-immunity, have shown already deterministic chaos when strong infectivity on secondary infection was assumed. The addition of the temporary cross-immunity period in such models brings a new chaotic attractor in wider and unexpected parameter region. In this thesis we present different extensions of the classical single-strain SIR model motivated by modeling dengue fever epidemiology with its peculiar ADE phenomenology. We focus on a minimalistic model, where the notion of at least two different strains is needed to describe differences between primary and se- condary dengue infections. The models divide the host population into suscepti- ble, infected and recovered individuals with subscripts for the respective strains. The individuals can be (1) susceptibles without a previous dengue infection; (2) infected and recovered for the first time; (3) susceptible with an experienced pre- vious dengue infection and (4) infected for the second time with a different strain, more likely to be hospitalized due to the ADE effect leading to severe disease. Our analysis shows a rich dynamic structure, including deterministic chaos in wi- der and more biologically realistic parameter regions, just by adding temporary cross-immunity to previously existing dengue models. In Chapter 1 we present the properties of the basic SIR epidemic model applied to infectious diseases. A summary of the analysis of the dynamics identifying the thresholds and equilibrium points in order to introduce notation and terminology are presented. These results were then generalized to a more advanced models motivated by dengue fever epidemiology. In Chapter 2 the basic two-strain SIR- type model motivated by modeling dengue fever epidemiology is presented. In this chapter we focused on the multi-strain aspect and its effects on the host population. The effects of the vector dynamics or seasonality is taken in account only by the effective parameters of the SIR-type model, but these mechanisms are not modeled explicitly. In Chapter 3 a detailed bifurcation analysis for the basic multi-strain dengue model is presented where the ADE parameter A and the temporary cross-immunity parameter R are studied. In Chapter 4 the seasonally forced system with temporary cross-immunity and possible secondary infection is analyzed. This study was motivated by dengue hemorrhagic fever monitoring data. The role of seasonality and import of infected individuals are now considered as biologically relevant effects to determine the dynamical behavior of the system. A comparative study between three different scenarios (non-seasonal, low seasonal and high seasonal with a low import of infected individuals) is presented. The extended models show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. At the moment only such minimalistic models have a chance to be qualitati- vely understood well and eventually tested against existing data. The simplicity of the model (low number of parameters and state variables) offer a promising perspective on parameter values inference from the DHF case notifications. Such a technical parameter estimation is notoriously difficult for chaotic time series due to the long term unpredictability versus short term predictability. Recent- ly, this short term predictability has been used for temporally local approaches in statistical inference on the cost of difficulty in obtaining a final definite best answer to the parameter estimation problem. Being able to predict future outbreaks of dengue in the absence of human interventions is a major goal if one wants to understand the effects of control measures. Even after a dengue virus vaccine has become accessible or available, this holds true for the implementation of a vaccination program. For example, to perform a vaccine trial in a year where the disease epidemic generate a low number of cases, would make the statistical tests of vaccine efficacy much more difficult compared with the information provided by a vaccine trial performed in a epidemic year with much higher numbers of cases. Thus predictability of the next season’s height of the dengue peak, on the basis of deterministic balance of infected and susceptible, would be of major practical use. Although the fact that disease propagation is an inherently stochastic phe- nomenon, dengue models are mainly expressed mathematically as a set of de- terministic differential equations, which are easier to analyze. The mean field approximation, an approximation of stochastic processes leading to deterministic dynamics, is a good approximation to be used in order to understand better the behavior of the stochastic systems in certain parameter regions, where the dyna- mics of the mean quantities are approximated by neglecting correlations. Howe- ver, it is only stochastic, as opposed to deterministic, models that can capture the fluctuations observed in some of the available time series data. In Chapter 5 the stochastic version of the minimalistic multi-strain model is presented. In this chapter we investigate the interplay between stochasticity, seasonality and impor- ted cases of the disease. The introduction of stochasticity reveal a scenario where noise and complex deterministic skeleton strongly interact. For large enough population size, the stochastic system could be well described by the determinis- tic skeleton, where the essential dynamics are captured, gaining insight into the relevant parameter values purely on topological information of the dynamics. The two-strain dengue model is a 9 dimensional system and therefore, future statistical inference can still attempt to estimate all initial conditions as well as the few model parameters. Concerning data availability, long term epidemiologi- cal data consist on monthly incidences of hospitalized DHF cases. For such a data scenario, models that are able to generate both primary and secondary infection cases (with a different strain, without the need of considering differences on the dynamics of different co-circulating dengue serotypes), have shown a good quali- tative agreement between empirical data and model output (see Chapter 4 and Chapter 5). These results were obtained just by combining the ADE effect, ge- nerating difference in transmissibility on primary and secondary infections, with the temporary cross-immunity aspect. Differently from the minimalistic dengue model, the four-strain model is mathematically represented by a system of 26 ODE’ s. It becomes a very high dimensional system and obviously very difficult to be used for parameter inference due to the high number of initial conditions. In Chapter 6 we present the multi-strain dengue model for the four existing se- rotypes. For four different strains, 1, 2, 3 and 4, we now label the SIR classes for the hosts that have seen each one of the possible strains. Again, without epidemi- ological asymmetry between strains, once the serotype data are recent and very short to give any realistic information concerning difference in biological parame- ters (such as infection and recovery rates) for a given strain. In this chapter we present the bifurcation diagram comparison for both two-strain and four-strain model. In the relevant parameter region of  < 1, when dengue patients in a secondary infection evolving to severe disease due to the ADE phenomenon con- tribute less to the force of infection, the bifurcation points appear to happen at similar parameter regions, well below the region of interest   1. We conclude that the two-strain model in its simplicity is a good model to be analyzed giving the expected complex behavior to explain the fluctuations observed in empirical data. Statistical inference to estimate the basic parameters of transmission, infectivity, disease severity (ADE parameter) and temporary cross-immunity period using empirical data of incidence of severe disease is needed to identify eventual deviations from the simplest symmetric case investigated here. Further work on the parameter estimation using the minimalistic dengue model is in progress. The vector dynamics might also play a role in understanding the final picture when comparing the model output with the available empirical data. Following the investigations described in this thesis, a number of research directions could be addressed, involving the minimalistic dengue model. Future work would be to investigate extensions of the multi-strain model to address the following questi- ons and issues: (1) How much (more or less than first infection) does secondary infection contribute to the force of infection? (2) Does there exist a difference between the forces of infection for the different strains and to what extent can the bifurcation structure explain the viral diversity contribution? (3) Formulate hy- potheses using the mechanism of temporary cross-immunity suitable to recurrent infections protection. (4) Model the vaccine trials based on short term predic- tability of chaotic systems to be applied when tetravalent vaccines will become available. And (5) propose targets for intervention and control design according to the expected impact of the disease. My special interest would be to get the model fully parametrized on data referring to incidence of severe disease and pre- valence of infection. With such a model framework we would be able to give an insight into the predictability of upcoming dengue outbreaks. This epidemiolo- gical tool would help to understand the effects of control measures and therefore to guide the policies of prevention and control of the dengue virus transmission
Ao longo da história, as doenças infecciosas veem causado o enfraquecimento e morte prematura de grandes parte da população humana, gerando sérias preocupações sociais e económicas. Muitos são os fatores quem têm contribuído para a persistência e o aumento na ocorrência de doenças infecciosas, tais como factores demográficos, mudanças políticas, sociais e económicas, mudanças ambientais, adaptação microbiana, etc. Segundo a Organizão Mundial de Saúde (OMS), as doenças infecciosas são a segunda principal causa de morte no mundo, depois das doenças cardiovasculares (WHO, 2010). Dentre as doenças transmissíveis mais preocupantes, o dengue ´e, de acordo com a OMS, um problema de saúde pública internacional, com mais de 55% da população mundial vivendo em áreas com risco de transmissão da infecção. O dengue, uma infecção ao viral transmitida por mosquitos, é uma das principais causas de doença e morte nos trópicos e subtrópicos. A infecção pelo vírus do dengue pode ser causada por qualquer uma das quatro cepas existentes, designadas por serotipos DEN − 1, DEN − 2, DEN − 3 e DEN − 4. Estes serotipos são distintos, porém, antigenicamente relacionados. A infecção gerada por um determinado serotipo confere imunidade total e permanente (ao longo da vida) para apenas aquele serotipo, e também imunidade cruzada temporária para os outros serotipos. A imunidade cruzada temporária tem uma duração estimada que varia de três a nove meses, e está relacionada com os n´níveis de anticorpos gerados durante a resposta imune a uma primeira infecção pelo vírus do dengue. Afirma-se que o alto nível destes anticorpos seria suficiente para a proteção contra outras infecções causadas por patogenos antigenicamente relacionados. O dengue pode se manifestar em duas formas clínicas: dengue clássico (DC), uma forma não-fatal da doença, e dengue hemorrágica (DH), que pode evoluir para uma forma muito grave conhecida como síndrome do choque do dengue (DSS). Estudos epidemiológicos associam os casos graves da doença (DH) com a segunda infecção do dengue. Existem boas evidências relacionando as infecções sequenciais pelos vírus do dengue e o aumento para os riscos do desenvolvimento do dengue hemorrágico. Esta associação se deve a um processo imunológico chamado de antibody-dependent enhancemet (ADE). O antibody-dependent enhan- cement ocorre quando os anticorpos pré-existentes, provenientes de uma primeira infecção do dengue, não neutralizam mas sim realçam a nova infecção pelo vírus do dengue. Não existe uma medicação específica para a infecção do dengue. O tratamento dos casos de dengue clássico é apenas de suporte e para os casos de dengue hemorrágico a hospitalização é frequentemente necessária para obtenção de um tratamento adequado. A vacina contra o dengue ainda não está disponível, uma vez que terá que simular proteccão para todos os quatro serotipos existentes. Atu- almente, algumas vacinas candidatas encontram-se em diversos estágios de desenvolvimento. Até o presente momento, a prevenção na exposição e o controle dos vetores são as únicas alternativas para a prevenção da transmissão do dengue. A modelação matemática tornou-se uma ferramenta importante para a compreensão da epidemiologia e da dinâmica das doenças infecciosas. Uma série de modelos deterministicos, tais como o modelo Susceptível-Infectado (SI) e o modelo Susceptível-Infectado-Recuperado (SIR), por exemplo, têm sido propostos com base nos padrões de fluxo para cada um dos compartimentos representando os estágios da doença. O modelo epidemiológico SIR divide a população de indivíduos em três classes: Susceptíveis (S), Infectados (I) e Recuperados (R). Este tipo de modelo pode ser utilizado para representar, por exemplo, as doenças infecciosas que não conferem imunidade permanente, possibilitando a reinfecçã. Assumindo que a transmissão da doença se faz de pessoa para pessoa, os indivíduos susceptíveis tornam-se infectados e infecciosos (capazes de transmitir a doença), se curam e se tornam recuperados (com imunidade temporária ao patógeno causador da doença). Depois de um determinado período tempo, acontece a perda desta imunidade e o indivíduo tornar-se novamente susceptível, podendo se reinfectar. A dinâmica multi-estirpe é geralmente modelada utilizando extensões dos modelos do tipo SIR. Para capturar as diferenças entre a primeira e a segunda infecção é preciso considerar pelo menos dois serotipos diferentes na composição do modelo do tipo SIR. A dinâmica da epidemiologia do dengue é particularmente complexa, com grandes flutuações (variações em quantidade ao longo do tempo) na incidência da doença. Modelos matemáticos recentes para a transmissão do vírus do den- gue se concentram no efeito ADE e na imunidade cruzada temporária. Estes modelos apresentam resultados de flutuações críticas com distribuição em lei de potência para os casos da doença, caos determinístico e dessincronização caótica, devido a sua estrutura multi-estirpe. O comportamento caótico é obtido quando assumindo infectividade muito alta para a segunda infecção do dengue, isto é, assumindo que os indivíduos na segunda infecção pelo vírus do dengue transmitem a doença com uma taxa muita mais elevada do que os indivíduos na primeira infecção. Considerações da imunidade cruzada temporária associada ao efeito ADE gera uma nova janela caótica inesperada e biologicamente mais realistas, onde a infectividade dos indivíduos na segunda infecção do dengue é reduzida devido a severidade da doença e a provável hospitalização causada pelo processo imunológico do ADE. Nesta tese apresentamos a análise e os resultados obtidos em diferentes extensões do modelo clássico SIR. Estes modelos foram motivado pela epidemiologia do dengue e a sua peculiar característica imunológica causada pelo antibody- dependent enhancement. O nosso estudo se concentra em um modelo minimalístico, em que pelo menos dois serotipos diferentes são necessários para descrever as diferenças entre as infecções primária e secundária causadas pelas diferentes cepas do vírus do dengue. Os modelos dividem a população humana em susceptíveis, infectados e recuperados, e utiliza índices para diferenciar cada um dos serotipos. Os indivíduos podem ser: (1) susceptíveis sem nenhuma infecção prévia pelo vírus do dengue, (2) infectados e recuperados pela primeira vez, (3) susceptíveis com um histórico de infecção prévia e (4) infectados pela segunda vez (por uma cepa diferente da primeira infecção) e, provavelmente hospitalizados devido ao processo de ADE. O modelo minimalístico apresenta uma dinâmica estrutural rica ao incorporar aos modelos já existentes para a transmissão do dengue, o período de imunidade cruzada temporária associada ao processo de antibody-dependent enhancement capaz de gerar diferenças nas taxas de transmissão para as infecçoes primárias e secundárias da doença. No Capítulo 1 apresentamos as propriedades do modelo básico SIR aplicado ao estudo das doenças transmissíveis. A análise da dinâmica apresentada, identificando os limites e os pontos de equilíbrio, com o objectivo de introduzir a notação e a terminologia utilizada. Estes resultados são posteriormente generalizados para os modelos motivados pela epidemiologia do dengue. No Capítulo 2, o modelo básico do tipo SIR para dois serotipos diferentes é apresentado e analisado. Este capítulo enfatiza o aspecto multi-estirpe e seus efeitos sobre a população humana. Os efeitos da dinâmica dos vetores e ou da sazonalidade não são modelados explicitamente, sendo levados em conta apenas pelos parâmetros efetivos do modelo. No Capítulo 3 apresentamos uma análise detalhada dos pontos de bifurcações encontrados para os parâmetros de ADE () e de imunidade cruzada temporária (). No Capítulo 4, o modelo sazonal do dengue é apresentado. Com base nos dados disponíveis de monitoramento do dengue, o papel da força sazonal e os casos importados da doença foram considerados como efeitos biologicamente relevantes para a determinação do comportamento dinâmico do sistema. O comparativo entre três cenários distintos (não-sazonal, sazonal e sazonal com casos importados da doença) é apresentado neste capítulo. A adição da sazonalidade e de possíveis casos importados da doença institui complexidade à dinâmica e apresenta boa concordância qualitativa entre os dados empíricos dos casos graves da doença (DH) e o output do modelo. Até o momento, apenas esses modelos minimalísticos têm a possibilidade de ser qualitativamente bem compreendido e, eventualmente testados contra os dados existentes. A simplicidade do modelo (poucos parâmetros e poucas variáveis de estado) oferece uma perspectiva promissora na inferência dos valores dos parâmetros, utilizando os dados referentes ao número de casos de dengue hemorrágico. A estimação de parâmetros em séries temporais caóticas é notoriamente difícil devido á imprevisibilidade a longo prazo versus previsibilidade a curto prazo. Recentemente, esta previsibilidade a curto prazo tem sido usada em inferência estatísticapara para abordagens temporalmente localizadas encontrandi dificuldades na obtenção de uma resposta final definitiva para a melhor estimativa dos parâmetros A capacidade de prever os futuros surtos do dengue na ausência de intervenção humana tem como objetivo compreender o efeitos das medidas de controle da doença, incluindo a implementação de programas de vacinação, quando esta estiver disponível e acessível. Os ensaio com esta vacina deverão ser realizados em um ano em que o número de casos da doença for suficientemente altos (e não em um ano em que o número de casos da doença fossem naturalmente baixos) afim de facilitar os testes estatísticos para a eficácia da vacina. Desta maneira, a previsão do número de casos da doença com base no balanço determinístico do número de indivíduos infectados e indivíduos susceptíveis seria de grande utilidade prática. A propagação de doenças é um fenómeno inerentemente estocástico, mas os modelos para a propagação do dengue são em sua maioria expressos matematicamente por um conjunto equações diferenciais determinísticas, que são mais fáceis de analisar. A aproximação do campo médio, uma aproximação utilizada em processos estocásticos para a obtenção de dinâmicas determinísticas, é uma boa aproximação para ser utilizada a fim de compreender melhor o comportamento dos sistemas estocásticos em determinadas regiões de parâmetro. No entanto, apenas os modelos estocásticos, ao contrário dos modelos determinísticos, podem captar as flutuações observadas em algumas das séries temporais de dados empíricos. No Capítulo 5, a versão estocástica do modelo multi-estirpe minimalístico é apresentado. Neste capítulo investigamos a interacção entre estocasticidade, sazonalidade e casos importados da doença. A introdução de estocasticidade é capaz de explicar as flutuações observadas em algumas séries temporais de dados para os casos graves do dengue, revelando um cenário onde o ruído e o esqueleto determinístico se interagem fortemente. Para uma população suficientemente grande, o modelo estocástico é bem descrito pelo esqueleto determinístico, capturando a dinâmica essencial da doença. O modelo estocástico gera, a partir das informações topológicas da dinâmica, a percepção sobre os valores relevantes dos parâmetros do modelo. O modelo minimalístico do dengue é um sistema com 9 dimensões e, tem boas chances de poder se utilizado em uma futura inferência estatística, para estimar todas as condições iniciais e os poucos parâmetros do modelo. Os dados empíricos disponíveis para os casos de dengue hemorrágico consistem na incidência mensal de casos hospitalizados e, para este tipo de dados, o modelo capaz de gerar infecções primária e secundária causadas por diferentes serotipos do dengue (sem a necessidade de se considerar diferenças nas dinâmicas para cada um dos diferentes serotipos existentes), apresenta uma boa concordância qualitativa entre os dados empíricos e o output do modelo (ver Capítulo 4 e Capítulo 5). Diferentemente do modelo minimalístico multi-estirpe para a transmissão do dengue, o modelo incluindo os quatro serotipos é matematicamente representado por um sistema com 26 equações diferenciais. Este sistema apresenta uma dimensão elevada (25 dimensões) e dificilmente poderá ser utilizado em inferência estatística, devido ao elevado número de variáveis e condições iniciais. No Captulo 6, o modelo para a transmissão do dengue incluindo todos os serótipos existentes é apresentado. Com os quatro serótipos, DEN −1, DEN −2, DEN − 3 e DEN − 4, as classes SIR são identificadas por índices para cada um dos serotipos. A assimetria epidemiológica entre as cepas continua a não ser considerada. Os dados serológicos existentes para cada um dos serotipos em separado são recentes e escassos, não sendo capazes de fornecer informações fidedignas às possíveis diferenças existentes entre os parâmetros biológicos (tais como as taxas de infecção e taxas de recuperação) para cada uma das quatro cepas do vírus do dengue. Neste capítulo apresentamos a comparação entre os diagramas de bifurcação para os dois modelos multi-estirpe, assumindo respectivamente 2 e 4 serotipos diferentes na transmissão da doença. Para a região de interesse biológico (onde os indivíduos infectados pela segunda vez transmitem menos do que os indivíduos infectados pela primeira vez, devido a severidade da doença) os pontos de bifurcação acontecem em regiões similares para o parâmetro do efeito ADE. A lei da parcimónia favorece o mais simples dos dois modelos concorrentes e desta forma, concluímos que o modelo minimalístico para a transmissão do dengue (dois serotipos), na sua simplicidade, é um bom modelo para ser analisado. O modelo minimalístico do dengue é capaz de produzir a complexidade esperada para explicar as flutuações observadas nos dados empíricos da doença e apresenta, dentro da possibilidade, baixa dimensionalidade. A Inferência estatística utilizando os dados empíricos para estimar os parâmetros básicos de transmissão, infectividade, a gravidade da doença (parmetro ADE) e período de imunidade cruzada temporária, é de extrema importância e definitivamente necessária para identificar os eventuais desvios do caso mais simples de simetria, que foram investigados aqui. O estudo da estimação dos parâmetros utilizando o modelo minimalístico do dengue está em andamento. A dinâmica vetorial também pode desempenhar um papel importante na compreensão da epidemiologia do dengue. As investigações descritas nesta tese sugerem uma série de possíveis direcções para a continuidade desta pesquisa e, em termos de trabalho futuro, a investigação de extensões do modelo minimalístico poderá abordar as seguintes questões e problemas: (1) Qual é a real contribuição das infecções primárias e secundárias para a fora de infecção? Indivíduos na segunda infecção transmitem mais ou menos do que a indivíduos na primeira infecção? (2) Existem diferenças significativas entre as taxas de infecção para cada um dos serotipos existentes? Até que ponto a estrutura de bifurcação pode explicar a real contribuição da diversidade viral? (3) Formular hipóteses usando o mecanismo adequado de imunidade cruzada temporária e a proteção gerada em infecções recorrentes. (4) Modelar ensaios de vacinas, com base na previsibilidade a curto prazo em sistemas caóticos, para futura implementação de programas de imunização, quando a(s) vacina(s) tetravalente estiver disponível e acessível. E finalmente (5) propor alvos para a intervenção e para o planeamento de medidas controle, baseando-se no impacto esperado da doença. O Meu interesse especial se concentra na possível parametrização do modelo a partir dos dados referentes à incidência da doença grave e na prevalência de infecção. Esta ferramenta epidemiológica ajudaria a compreender os efeitos das medidas de controle e, poderia ser utilizada para orientar as políticas de prevenção e controle da transmissão do vírus do dengue, gerando uma percepção sobre a previsão dos surtos futuros do dengue.
Fundação para a Ciência e a Tecnologia (FCT, SFRH/BD/43236/2008, projeto PTDC/MAT/115168/2009); EU project DENFREE under Framework Program 7