Orientador: Rodney Carlos Bassanezi / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T04:06:10Z (GMT). No. of bitstreams: 1 SaleseSilva_JoseGilson_M.pdf: 1291910 bytes, checksum: b6f441a8e24badc2915c8f5301ca28ce (MD5) Previous issue date: 2009 / Resumo: Apresentamos uma abordagem resumida da epidemiologia matemática, dos modelos epidemiológicos tipo SI, SIS e SIR, bem como um embasamento sobre as equações de diferenças finitas. Utilizamos um modelo matemático determinístico em tempo discreto tipo SI, simplificado, para interpreta¸c¿ao e análise da epidemia de hanseníase do município de Imperatriz-MA, com base em dados relativos ao número de contatos registrados e casos notificados no per'iodo de 1994 a 2007. Apresentamos também uma validação do modelo e histórico da epidemia em Imperatriz. / Abstract: We present an approach summarized from epidemiology mathematics , from the models epidemiological type Oneself SI SS e SIR , as well as a basement on the subject of the equations of differences finite. Uses a model mathematical deterministic in time discreet type SI about to interpretation e analysis from epidemics from hansen'iase of the county of Imperatriz-MA , based on dice relative the number of contacts registered e cases notifying into the period of 1994 the 2007. We present also a validation of the model e historical from epidemics in the Imperatriz. / Mestrado / Biomatematica / Mestre em Matemática

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Relata-se o entendimento da dinÃmica de fluxo entre o riacho SÃo Josà e o aquÃfero Rio da Batateira, localizados na regiÃo do Cariri cearense. As vazÃes do riacho foram monitoradas atravÃs do mÃtodo do traÃador quÃmico, que obteve uma boa correlaÃÃo linear com o da calha Parshall. De acordo com o mÃtodo CN do SCS, nÃo houve escoamento superficial nos dias anteriores aos de mediÃÃo de vazÃo, indicando que o incremento nas vazÃes durante o perÃodo chuvoso corresponde a variaÃÃes nos fluxos sub-superficial e de base do riacho. A condutividade hidrÃulica mÃdia do aquÃfero, estimada em 1,69 x 10-5 m s-1, foi obtida por geoestatÃstica, utilizando a tÃcnica da krigagem. A produÃÃo especÃfica do aquÃfero (5%) e a condutÃncia do leito do riacho (16.800 m dia-1) foram obtidas na calibraÃÃo do modelo de fluxo riacho-aquÃfero, utilizando o aplicativo MODFLOW. Na calibraÃÃo em regime estacionÃrio obteve-se a recarga anual de 45 mm e em regime transiente foi possÃvel distribuir esta recarga nos meses de abril (16 mm) e maio de 2009 (29 mm). As recargas sà ocorreram nos meses de precipitaÃÃo superior a 200 mm. Como o MODFLOW simula apenas o fluxo no meio saturado, a vazÃo calculada do riacho corresponde apenas ao fluxo de base e o excedente observado ao escoamento sub-superficial nÃo calculado. A simulaÃÃo de quatro cenÃrios, considerando valores extremos de precipitaÃÃo anual registrados em pluviÃmetros da regiÃo e mudanÃas na Ãrea de recarga da bacia hidrogrÃfica, mostrou a necessidade de um planejamento urbano na Ãrea, visando o disciplinamento futuro do uso e ocupaÃÃo do solo com foco na preservaÃÃo dos recursos hÃdricos superficiais e subterrÃneos. / It relates the understanding of the flow dynamics between the SÃo Josà stream and Rio da Batateira aquifer, located in the Cariri region in CearÃ. The stream discharges were monitored by the chemical tracer method, which obtained a good linear correlation with the Parshall flume. According to the SCS-CN method, there was no runoff in the days prior to flow measurement, indicating that the increase in flow during the rainy season corresponds to changes in the pattern of subsurface flow and base-flow of the stream. The average hydraulic conductivity of the aquifer, estimated at 1.69 x10-5 m s-1, was obtained from geostatistics, using the technique of kriging. The specific production of the aquifer (5%) and the conductance of the stream bed (16,800 m dia-1) were obtained in the stream-aquifer flow model calibration flow by using the MODFLOW application. In the steady state calibration we obtained the annual recharge of 45 mm and in the transient state it was possible to distribute this recharge into the months of April (16 mm) and May 2009 (29 mm). Recharges occurred only in the months having rainfall exceeding 200 mm. As MODFLOW only simulates the flow in saturated media, the flow rate calculated for the stream corresponds only to the base flow and the excess observed corresponds to the subsurface flow not calculated. The simulation for four scenarios, considering the extreme values of annual rainfall recorded in pluviometers of the region and changes in the recharge area of the river catchment, showed the need for urban planning in the area, aiming at the future control of soil use and occupation with a focus on preservation of groundwater and surface water resources.

Neste trabalho foi elaborada uma estrutura de modelos probabilísticos simples que pudessem descrever o processo de tomada de decisão de agentes humanos que são confrontados com a tarefa de prever elementos de uma sequência aleatória gerada por uma cadeia de Markov de memória L. Essa estrutura partiu de uma abordagem bayesiana em que o agente infere uma distribuição de probabilidades a partir de uma série de observações da sequência e de suas próprias respostas, considerando que o agente tenha uma memória de tamanho K. Como resultado da abordagem bayesiana, o agente adota uma estratégia ótima que consiste na perseveração na alternativa mais provável dado o histórico das últimas tentativas; por conta disso e de observações experimentais de que humanos tendem a adotar nesse tipo de problema estratégias sub-ótimas, por exemplo a de pareamento de probabilidades (probability matching), foram desenvolvidas variações sobre esse modelo que tentassem descrever mais de perto o comportamento adotado por humanos. Nesse sentido, foram adotadas as variáveis de troca de resposta (possível ação tomada pelo agente) e de recompensa (possível resultado da ação) na formulação do modelo e foram adicionados parâmetros, inspirados em modelos de ação dopaminérgica, que permitissem um desvio da estratégia ótima resultante da abordagem bayesiana. Os modelos construídos nessa estrutura foram simulados computacionalmente para diversos valores dos parâmetros, incluindo as memórias K e L do agente e da cadeia de Markov, respectivamente. Através de análises de correlação, esses resultados foram comparados aos dados experimentais, de um grupo de pesquisa do Instituto de Ciências Biomédicas da USP, referentes a tarefas de tomada de decisão envolvendo pessoas de diversas faixas etárias (de 3 a 73 anos) e cadeias de Markov de memórias 0, 1 e 2. Nessa comparação, concluiu-se que as diferenças entre grupos etários no experimento podem ser explicadas em nossa modelagem através da variação da memória K do agente crianças de até 5 anos mostram um limite K = 1, e as de até 12 anos mostram um limite K = 2 e da variação de um parâmetro de reforço de aprendizado dependendo do grupo e da situação de decisão à qual os indivíduos eram expostos, o valor ajustado desse parâmetro variou de 10% para baixo até 30% para cima do seu valor original de acordo com a abordagem bayesiana. / In this work we developed a simple probabilistic modeling framework that could describe the process of decision making in human agents that are presented with the task of predicting elements of a random sequence generated by a Markov chain with memory L. Such framework arised from a Bayesian approach in which the agent infers a probability distribution from a series of observations on the sequence and on its own answers, and considers that the agent\'s memory has length K. As a result of the Bayesian approach, the agent adopts an optimal strategy that consists in perseveration of the most likely alternative given the history of the last few trials; because of that and of experimental evidence that humans tend, in such kinds of problems, to adopt suboptimal strategies such as probability matching, variations on that model were developed in an attempt to have a closer description of the behavior adopted by humans. In that sense, the `shift\' (possible action taken by the agent on its response) and `reward\' (possible result of the action) variables were adopted in the formulation of the model, and parameters inspired by models of dopaminergic action were added to allow deviation from the optimal strategy that resulted from the Bayesian approach. The models developed in that framework were computationally simulated for many values of the parameters, including the agent\'s and the Markov chain\'s memory lengths K and L respectively. Through correlation analysis these results were compared to experimental data, from a research group from the Biomedical Science Institute at USP, regarding decision making tasks that involved people of various ages (3 to 73 years old) and Markov chains of orders 0, 1 and 2. In this comparison it was concluded that the differences between age groups in the experiment can be explained in our modeling through variation of the agent\'s memory length K children up to 5 years old exhibited a limitation of K = 1, and those up to 12 years old were limited to K = 2 and through variation of a learning reinforcement parameter depending on the group and the decision situation to which the candidates were exposed, the fitted value for that parameter ranged from 10% below to 30% above its original value according to the Bayesian approach.

O metabolismo das células S2 (Schneider 2) de Drosophila melanogaster ainda não é totalmente conhecido. Existem poucos estudos específicos sobre o metabolismo de células S2, sejam elas selvagens ou recombinantes (rS2), como por exemplo aquelas transfectadas para a expressão da glicoproteína do vírus da raiva (GPV). Como o genoma da Drosophila melanogaster já foi mapeado, as principais enzimas que atuam nos processos metabólicos em geral já foram identificadas e estão à disposição no KEGG (Kyoto Encyclopedia of Genes and Genomes). Assim, o KEGG apresenta todas as possíveis vias metabólicas com as enzimas que podem ser codificadas. Diante deste quadro, foi proposto um modelo metabólico baseado em um conjunto de vias de assimilação de glicose e glutamina e foram encontrados os modos elementares característicos do sistema através do programa Metatool. Em seguida, foi definido o modelo matemático mediante o equacionamento desses modos elementares. Esse processo se repetiu até se encontrar um conjunto de vias metabólicas que, através da modelagem matemática, respondesse coerentemente a um conjunto de dez ensaios em diferentes condições de concentrações iniciais de glicose, glutamina e oxigênio dissolvido. Chegou-se então, a um metabolismo básico para a rS2 contendo 33 vias metabólicas englobando a glicólise, a via das pentoses, o ciclo de Krebs e a fosforilação oxidativa. Dados anteriores indicavam elevada flexibilidade metabólica dessa célula, o que foi prevista através de algumas reações propostas como reversíveis nas vias de degradação e síntese de glutamina. Essa proposta de metabolismo resultou em 37 modos elementares. Outra característica interessante da modelagem foi a utilização da produção de purinas e pirimidinas para a estimativa do crescimento celular. Depois de realizada a modelagem, as mesmas condições iniciais dos ensaios foram simuladas através de um programa de simulação do comportamento cinético das células rS2 desenvolvido em MATLAB. Esse simulador foi utilizado também para simulação com diferentes meios e condições iniciais de cultivo. Chegando-se a um ajuste geral entre valores experimentais e simulados com coeficiente de correlação de 0,88. / The metabolism of the S2 cells (Schneider 2) Drosophila melanogaster is not yet fully known. There have been few specific studies on the metabolism of S2 cells, whether recombinant or wild (rS2), such as those transfected for expressing the rabies virus glycoprotein (RVGP). As the genome of Drosophila melanogaster have been mapped, the key enzymes that act on the metabolic processes in general have been identified and are available in the KEGG (Kyoto Encyclopedia of Genes and Genomes). Thus, KEGG presents all possible pathways with the enzymes that can be encoded. Given this context, it was proposed a metabolic model based on a set metabolic glucose and glutamine assimilation pathways and were found characteristic elementary modes of the system through the Metatool program. Then the mathematical model was defined by addressing these elementary modes. This process was repeated until a set of metabolic pathways, by mathematical modelling, consistently responded to a set of ten experiments (in various conditions). We came to a basic metabolism for rS2 containing 33 pathways comprising glycolysis, pentose, Krebs cycle and oxidative phosphorylation. Previous data indicate that rS2 is a cell with high metabolic flexibility, which was confirmed by some reactions in the process proposed as reverse breakdown and synthesis of glutamine. The proposed metabolism resulted in 37 elementary modes. Another interesting model characteristic was the use of the production of purines and pyrimidines for the estimation of cell growth. After the modelling performed, the same initial runs conditions were simulated using a software of Simulation of the Kinetic behaviour of rS2 cells, developed in MATLAB. This simulator was also used for simulation of other experiments with different initial conditions and methods of cultivation. Coming to a general adjustment of experimental and simulated values with correlation coefficient of 0.88.

Abstract Examples of numerical modelling of surface water hydrodynamics and water quality are presented. Their meaning for the development of the EIA 3D model system is analyzed from the almost 70 tracer studies (mainly 1971–1974) until the 3-dimensional (3D) solutions which became dominant since 1982. Up to summer 2008, the number of 3D applications has increased to almost 230 while the number of all applications exceeds 300. The specific applications considered are from: Porttipahta reservoir in Northern Finland (I), Porttipahta and Lokka reservoirs (II), combination of reservoirs, lake, river sections, Kemi estuary and the sea (III), Kemi estuary and other coastal applications in the Gulf of Bothnia (IV), Lake Haukivesi in Eastern Finland (V), Lake Näsiselkä in South-West Central Finland (VI), and Kymi River and Kotka estuary in Southern Finland (VII). A detailed description of the 3D model system is given in the application of Näsiselkä (VI). It is completed with drastically changing water levels, drying and wetting of immersed areas, characteristics of pulsing system, and internal loading in the application of Porttipahta (I). The application of the Kymi River and Kotka estuary (VII) shows the sensitivity of tracers as transport indicators and the validity of the transport model. In Lokka and Porttipahta (II) the methods of validity tests are extended to include field tests, laboratory experiments, and comparisons with expert evaluations and analytical solutions. A strong indication of model validity is obtained in Näsiselkä (VI). When the loading after the model work was changed according to a plan included in the computation, the observed changes of water quality corresponded closely with those predicted by the model. Another severe indication of the model validity is from Porttipahta and Lokka (I, II). With the parameter values based on data from 1967–1986, a recent application indicated a close agreement with the observed data from 2000–2006. In Haukivesi (V) and Näsiselkä (VI) the agreement between the model and observed results is extended to the biological indicators of the algal biomass. The integrated application to the network of a planned and two existing reservoirs, a strongly regulated lake, river sections, Kemi estuary and the sea (III) shows the usability of the model system to all types of water bodies. As a practical result it highlights the decay of the effects of a new impoundment with time and distance, including fast dilution in the estuary and the sea.

Dense flows of grains are commonplace throughout natural and industrial environments, from snow-avalanches down the sides of mountains to flows of cereal down chutes as it is transported from one part of a factory to another. A ubiquitous feature in all of these flows is their ability to separate the different grain types when shaken, stirred, sheared or vibrated. Many flows are sheared through gravity and these flows are particularly efficient at segregating particles based on their size, with small particles percolating to the bottom of the flow and large particles collecting at the top. Within this mechanism, an asymmetry between the large and small particles has been observed, with small particles percolating downwards through many large particles at a faster rate than large particles rise upwards through many small particles. This alternative format thesis presents a revised continuum model for segregation of a bidisperse mixture that can account for this asymmetry. A general class of asymmetric segregation flux functions is introduced that gives rise to asymmetric velocities between the large and small grains. Exact solutions for segregation down an inclined chute, with homogenous and normally graded inflow conditions, show that the asymmetry can significantly enhance the distance for complete segregation. Experiments performed using a classical shear-box with refractive index matched scanning are able to quantify the asymmetry between large and small particles on both bulk and particle scales. The dynamics of a single small particle indicate that it not only falls down faster than a single large particle rises, but that it also exhibits a step-like motion compared to the smooth ascent of the large grain. This points towards an underlying asymmetry between the different sized constituents. The relationship between the segregation-time and the volume fraction of small grains is analysed, and solutions presented for the steady-state balance between segregation and diffusive remixing. These help to show the good agreement between the asymmetric model and experimental data. Segregation at the front of natural avalanches produces a recirculation zone, known as a `breaking size-segregation wave', in which large particles are initially segregated upwards, sheared towards the front of the flow, and overrun before being resegregated again. Solutions for the structure of this recirculation zone are derived using the asymmetric flux model, revealing a novel `lens-tail' structure. Critically, it is seen that a few large particles starting close to the bottom of the flow are swept a long way upstream and take a very long time to recirculate. The breaking size-segregation waves highlight the important interplay between segregation and the bulk velocity field. The properties of flowing monodisperse grains are explored through experiments on a cone that produce a beautiful radial fingering pattern. Equations developed in a conical coordinate system reproduce the measured linear relationship between fingering radius and initial flux, whilst also predicting the slowing and thinning dynamics of the flow. Overall, these results illustrate the complex nature of the granular rheology and provide perspectives for future modelling of segregation in dense granular flows.

Some non-newtonian fluids exhibit nonmonotonous dependence of the shear stress on shear rate. This nonmonoticity leads to flow instabilities which result in formation of banded flow, namely in shear banding and vorticity banding. An important role is played here by so called stress diffusion which uniquely determines size of bands in the flow. If the classical kinetic approach is employed and the spatial inhomogeneity of the flow is taken into the account, then stress diffusion can be obtained in the fluid model, however this approach has difficulties with identifying heat transfer within the continuum. In this thesis, we present alternative approach how to introduce stress diffusion to fluid models. We employ thermodynamical framework proposed by Rajagopal and Srinivasa (2000), this approach guaranties thermodynamical consistency of resulting model and also the interplay between stress diffusion and heat transfer can be easily established. Furthermore, we extend this framework such that wider range of viscoelastic models can be obtained, in particular we derive Johnson-Segalman model. Powered by TCPDF (www.tcpdf.org)

Abstract Composition Adjustment by Sealed argon bubbling – Oxygen Blowing (CAS-OB) process is a ladle treatment process that was developed for chemical heating and alloying of steel. The main stages of the process are heating, (possible) alloying and reduction of slag. The CAS-OB process aims for homogenization and control of the composition and temperature of steel. In this dissertation, a mathematical reaction model was developed for the slag reduction stage of the CAS-OB process. Slag reduction is carried out by applying vigorous bottom stirring from porous plugs at the bottom of the ladle. Due to the bottom stirring a circular steel flow is induced which disrupts top slag layer and due to shear stress at the steel-slag interface small slag droplets are detached. This induces an immense increase in the interfacial area between steel and slag which provides favourable conditions for the reduction reactions. In order to model reduction reactions, a sub-model for describing the interfacial area was needed. For this the slag droplet formation was studied using computational fluid dynamics (CFD) and based on these studies, a sub-model for droplet formation was developed. The model for the reduction stage of the CAS-OB process takes into account not only the reaction during the reduction but also the heat transfer between the phases, ladle and surroundings. The reduction stage model was validated using validation data obtained from the CAS-OB station of the SSAB Raahe steel plant in Finland. It was concluded that the model was able to predict steel and slag compositions as well as the steel temperature very well. / Tiivistelmä CAS-OB -prosessi on sulametallurgiassa käytettävä senkkakäsittelyprosessi, joka on kehitetty teräksen kemialliseen lämmittäseen ja seostukseen. CAS-OB-prosessin pääprosessivaiheet ovat lämmitysvaihe, mahdollinen seostusvaihe ja kuonan pelkistysvaihe. CAS-OB -prosessilla tavoitellaan teräksen koostumuksen homogenisointiin ja lämpötilan kontrollointiin. Tässä tutkimuksessa kehitettiin matemaattinen reaktiomalli CAS-OB -prosessin kuonan pelkistysvaiheen kuvaamiseen. Kuonan pelkistys tapahtuu senkan pohjassa olevien huuhtelutiilien avulla suoritettavan voimakkaan kaasuhuuhtelun avulla. Pohjahuuhtelu aiheuttaa kiertävän teräsvirtauksen senkassa. Teräsvirtaus irrottaa teräksen päällä olevasta kuonakerroksesta pisaroita ja kuonan ja teräksen välinen reaktiopinta-ala kasvaa voimakkaasti. Tämä tarjoaa suotuisat olosuhteet pelkistysreaktiolle senkassa. Pelkistysreaktioiden mallintamiseksi tässä työssä kehitettiin CFD-simulaatioiden avulla alimalli, jonka avulla voidaan kuvata teräksen ja kuonan välisen pinta-alan suuruutta. Pelkistysvaiheen mallissa huomioidaan reaktioiden lisäksi myös systeemissä tapahtuva lämmösiirto. Pelkistysmalli validoitiin mittausdatalla, joka hankittiin SSAB Raahen terässulaton CAS-OB -asemalla järjestetyssä validointikampanjassa. Tutkimuksessa havaittiin, että malli kykenee hyvin ennustamaan teräksen ja kuonan koostumuksen sekä teräksen lämpötilan.

Alteration in the tone of pulmonary arteries may lead to disease such as pulmonary hypertension often associated with major cardiac complications. This dysfunction is partly in the pulmonary arterial smooth muscle cells (PASMCs) where the excitation-contraction coupling is modified by ion channel behaviour to increase the contractile force. Mathematical models of systemic smooth muscle cells (SMCs) that incorporate electrophysiological and chemomechanical mechanisms to understand the underlying cellular physiology have been successfully employed. Models of pulmonary arterial smooth muscle cells (PASMCs) are only beginning to emerge. Mathematical model prototyping with available experimental data and model investigation from different parameter values is a time-consuming and complex process. This thesis is concerned with the development and validation of mathematical models of excitation-contraction coupling in three types of PASMCs of the rat species, one homogeneous type originating from the distal pulmonary arteries and two from proximal pulmonary arteries. Some key novel additions from previous vascular SMC models include the distinct modelling of Ca2+ in the subplasmalemmal cytosolic region, incorporation of subunit-specific currents from the K+ channel family and a generic G-protein receptor model able to reproduce complex Ca2+ profiles. The main pulmonary and systemic arteries statistically differ in its response to phenylephrine in a wire myograph. The ionic currents of the models were validated against experimental data largely from rat species. The models replicate the recordings of Ca2+ and the resting potential (Em) profiles arising from agonist-induced cytosolic Ca2+ ([Ca2+]i) stimulation (G-protein activation), nifedipine, ryanodine, caffeine and niflumic acid. The distal PASMC model was sensitive to an increase in [Ca2+]i from G-protein activation although were less likely to reproduce Ca2+ oscillations than proximal PASMCs. The proximal models determined the likely proximal PASMC type in literature experiments recording [Ca2+]i and Em. I have developed software that enables other users to simulate Ca2+ and Em changes in SMC studies and the ability to parse a master file describing the mathematical model into different language formats to increase productivity. These models provide a foundation for further studies to better understand PASMC function in the context of normal physiology as well as pathological conditions.

Many genes demonstrate highly dynamic pulsatile expression, with characteristic bursts of activity. Dynamic expression of the human prolactin (hPrl) gene in pituitary cells has previously been investigated identifying key temporal characteristics, influenced by the process of chromatin remodelling. Earlier work on the related pituitary human growth hormone (hGH) proximal promoter (-496/+1bp) indicated that it displayed similar dynamic behaviour. The human GH gene contains an extensive long-distance regulatory sequence, including a locus control region (-14/-32kbp) that has been shown to regulate chromatin remodelling and confer tissue-specificity of hGH expression. In this work I aimed to study dynamic regulation of the hGH gene promoter in detail. Initially I investigated the efficiency of several methods to express the luciferase gene in a 180kb hGH genomic fragment using bacterial artificial chromosome recombineering, to allow the investigation of single cell transcription dynamics. Although a functional recombinant BAC was not finalised during the course of the work, I carried out detailed time course studies using shorter hGH-reporter constructs. Using quantitative microscopy to study live single cells, I compared the dynamic characteristics of a 5kb hPrl promoter fragment with those of -840/+1bp and -3348/+1bp hGH-luciferase promoter-reporter constructs. Whilst previous hPrl analysis utilised a binary mathematical model assuming a simplified two-state (ON/OFF) process of gene transcription, I validated and applied a novel stochastic switch model (SSM), assuming instead that transcription rate can switch between any variable states at any time. Through doing so I observed an asymmetry in transcription rate switching, suggesting an all-or-nothing activation of a single UP-switch, with a greater number of rate decreasing DOWN-switches. The -3348/+1bp construct produced double the number of DOWN-switches, whilst the -840/+1bp construct produced 1.5 DOWN-switches in a 48h period. The cycling of transcriptional activity seen by the shorter construct was modified through the addition of forskolin, activating cAMP signalling. However, significant modification of the transcriptionally inactive refractory period seen with the -3348/+1bp construct (reduced from 3h to 1.9h) required histone modification through application of trichostatin A, a HDAC inhibitor. In conclusion, different promoter elements confer different transcriptional timing and dynamics. A subtler transcriptional modelling, such as used here in the SSM, reveals new insights into the phenomena of transcriptional switching, but the mechanisms involved remain to be determined.