Neste trabalho são reunidos diferentes modelos e técnicas para representar situações experimentais ou observacionais de análise de sobrevivência. Para modelar respostas bivariadas e covariáveis foi proposto o modelo de regressão Kumaraswamy-Weibull bivariado. A presen»ca de indivíduos curados foi considerada sob duas diferentes abordagens, originando o modelo de regressão com fração de cura para dados bivariados por meio de cópulas e o modelo de regressão log-linear bivariado com fração de cura. Os parâmetros dos modelos foram esti- mados pelo método de máxima verossimilhança sujeito a restriçãoo nos parâmetros por meio da função barreira adaptada. Adaptou-se uma análise de sensibilidade de forma a considerar as metodologias de Influência Global, Influência Local e Influência Local Total para verificar vários aspectos que envolvem a formulação e ajuste dos modelos propostos. Utilizou-se um conjunto de dados de insuficiência renal e retinopatia diabética são utilizados para exemplificar a aplicação dos modelos propostos. / This work brought together di®erent models and techniques to represent expe- rimental or observational situations in survival analysis. To model bivariate responses and covariates was proposed Kumaraswamy Weibull bivariate regression model. The presence of cured individuals was considered under two di®erent approaches originating the regression model with a cured fraction for bivariate data through copulas and the log-linear bivariate regression model with cured fraction. The parameters of the models were estimated by ma- ximum likelihood method subject to the restriction on the parameters through the adapted barrier function. A sensitivity analysis was adapted considering the methodologies of Global In°uence, Local In°uence and Total Local In°uence to check various aspects of the formulation and adjustment of the models proposed. Data set of renal failure and diabetic retinopathy are used to exemplify the application of the proposed models.

L’étude de la diffusion des ondes électromagnétiques par une surface rugueuse aléatoire est de première importance dans de nombreuses disciplines et conduit à diverses applications notamment pour le traitement des surfaces par télédétection. En connaissant les modes de rétrodiffusion, on peut détecter la présence de la rugosité aléatoire indésirable de la surface de réflection telle que le réflecteur d'antenne et par conséquent trouver un moyen de corriger ou compenser les erreurs de phase. Cette thèse porte sur l’obtention de l'humidité du sol de surface à partir de mesures radar. La description de la surface rugueuse de façon aléatoire est présentée, suivie par les interactions d'ondes électromagnétiques avec les média. En particulier, un modèle d'équation intégrale avancé (AIEM) est introduit. La validité du modèle AIEM, qui est adopté comme modèle de travail, se fait par une large comparaison avec des simulations numériques et des données expérimentales. On analyse également les caractéristiques des configurations radar bistatique et on étudie la sensibilité de la diffusion bistatique à l'humidité du sol et à la rugosité de surface et, dans le même temps, le cadre de la détermination de l'humidité du sol à partir de mesures radar utilisant un réseau de neurones à base de filtres de Kalman récurrents est présenté. La formation du réseau et l'inversion des données sont décrits. / Electromagnetic waves scattering from a randomly rough surface is of palpable importance in many fields of disciplines and bears itself in various applications spanned from surface treatment to remote sensing of terrain and sea. By knowing the backscattering patterns, one may detect the presence of the undesired random roughness of the reflection surface such as antenna reflector and accordingly devise a means to correct or compensate the phase errors. Therefore, it has been both theoretically and practically necessary to study the electromagnetic wave scattering from the random surfaces. This dissertation focuses on the retrieval of surface soil moisture from radar measurements. The description of the randomly rough surface is presented, followed by the electromagnetic wave interactions with the media. In particular, an advanced integral equation model (AIEM) is introduced. The validity of the AIEM model, which is adopted as a working model, is made by extensive comparison with numerical simulations and experimental data. Also analyzes the characteristics of the bistatic radar configurations and dissects the sensitivity of bistatic scattering to soil moisture and surface roughness of soil surfaces. Meanwhile presents a framework of soil moisture retrieval from radar measurements using a recurrent Kalman filter-based neural network. The network training and data inversion are described in detail.

Submitted by Maria Cristina (library@lncc.br) on 2018-06-21T13:24:04Z No. of bitstreams: 1 tese Marcel Duarte.pdf: 2095388 bytes, checksum: 09fc1bc9c7c471b83088df9744b4614a (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2018-06-21T13:24:26Z (GMT) No. of bitstreams: 1 tese Marcel Duarte.pdf: 2095388 bytes, checksum: 09fc1bc9c7c471b83088df9744b4614a (MD5) / Made available in DSpace on 2018-06-21T13:24:44Z (GMT). No. of bitstreams: 1 tese Marcel Duarte.pdf: 2095388 bytes, checksum: 09fc1bc9c7c471b83088df9744b4614a (MD5) Previous issue date: 2018-04-20 / Agência Nacional de Pesquisa / The topological derivative is a scalar field that measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation, such as the insertion of holes, inclusions, source-terms or even cracks. In this work, the concept of topological derivative is applied in the context of damage and fracture mechanics. In particular, the nucleation and propagation damaging process and the crack growth control in cracked elastic bodies are studied. In the first topic, the topological derivative is applied together with the Griffith-Francfort-Marigo damage model to propose a simple numerical scheme in order to determine the damage nucleation/propagation in brittle materials. The proposed numerical scheme is able to capture the whole nucleation and propagation damaging process, including important features like kinking and bifurcations. These properties are confirmed through several numerical experiments and by comparison with available laboratory experiments. Taking into account the promising obtained results, a simple adaptation of the Griffith-Francfort-Marigo damage model to the context of hydraulic fracture is proposed. The new model can be seen as a simplified version with respect to the real hydraulic fracture. In this sense, this second study aims to develop a simple numerical scheme which can be applied in more realistic situations later. However, important features associated with hydraulic fracture process are captured with the simplified model. In the sequence, in order to study the hydraulic fracture process in more realistic scenarios, the whole developed methodology is applied together with the Biot hydro-mechanical model. Finally, the topological derivative associated with the Griffith-Francfort-Marigo damage model extended to the context of hydraulic fracture in the three spatial dimensional case is obtained. In the second topic, the concept of topological derivative is applied to the crack growth control problem. In particular, a methodology aiming to extend the remaining useful life of cracked elastic bodies is proposed. The central idea consists in minimize a shape functional based on the famous Rice’s integral with respect to the nucleation of hard and/or soft inclusions far from the crack tip. According to the Griffith energy criterion, this simple procedure allows for increasing the remaining useful life of the cracked body. Finally, in order to show the applicability of the proposed methodology, some numerical experiments are presented. / A derivada topológica é um campo escalar que mede, em cada ponto do domínio de análise, a sensibilidade de um dado funcional de forma em relação a uma perturbação singular infinitesimal no domínio, tal como a inserção de furos, inclusões, termos fonte ou trincas. Neste trabalho, o conceito de derivada topológica é aplicado no contexto da mecânica do dano e da fratura. Em particular, são objetos de estudos a modelagem dos processos de nucleação e evolução de dano e o controle do crescimento de fraturas em corpos elásticos danificados. No primeiro tópico, a derivada topológica é inicialmente utilizada em conjunto com o modelo de dano de Griffith-Francfort-Marigo onde um esquema numérico simples e flexível para determinar a nucleação e a evolução de dano em materiais frágeis é proposto. O esquema numérico desenvolvido é capaz de capturar todo o processo de nucleação e propagação de danos, incluindo características importantes como desvios e bifurcações. Estas propriedades são confirmadas através da realização de vários experimentos numéricos e em comparação com resultados de laboratório disponíveis na literatura. Tendo em conta os bons resultados obtidos, uma extensão do modelo de Griffith-Francfort-Marigo para o contexto de fraturamento hidráulico é então proposta. O novo modelo trata-se de uma versão bastante simplificada em relação ao fraturamento hidráulico real. Neste sentido, o objetivo deste segundo estudo é o desenvolvimento de uma metodologia simples e flexível que possa ser aplicada depois em situações mais realísticas. No entanto, experimentos numéricos realizados mostram que, mesmo com a introdução de simplificações drásticas, fenômenos de grande importância associados ao processo de fraturamento hidráulico são capturados. Na sequencia, o ferramental desenvolvido é então utilizado em conjunto com o modelo hidromecânico de Biot a fim de estudar cenários mais realísticos. Finalmente, seguindo o caminho natural desta pesquisa, é então calculada a derivada topológica associada ao modelo de Griffith-Francfort-Marigo estendido para o contexto de fraturamento hidráulico em três dimensões espaciais. No segundo tópico, o conceito de derivada topológica é utilizado para analisar o controle do crescimento de fraturas. Em particular, é proposta uma metodologia que visa ampliar a vida útil remanescente de corpos elásticos parcialmente danificados. A ideia central consiste em minimizar um funcional de forma baseado na famosa integral de Rice com respeito a nucleação de inclusões rígidas e/ou complacentes longe da ponta da fratura. De acordo com o critério de Griffith, este simples procedimento permite um aumento da vida útil remanescente dos corpos danificados. A fim de ilustrar a aplicabilidade da metodologia proposta alguns experimentos numéricos são apresentados.

Le traitement des données manquantes est un sujet en pleine expansion en épidémiologie. La méthode la plus souvent utilisée restreint les analyses aux sujets ayant des données complètes pour les variables d’intérêt, ce qui peut réduire lapuissance et la précision et induire des biais dans les estimations. L’objectif de ce travail a été d’investiguer et d’appliquer une méthode d’imputation multiple à des données transversales d’enquêtes épidémiologiques et de systèmes de surveillance de maladies infectieuses. Nous avons présenté l’application d’une méthode d’imputation multiple à des études de schémas différents : une analyse de risque de transmission du VIH par transfusion, une étude cas-témoins sur les facteurs de risque de l’infection à Campylobacter et une étude capture-recapture estimant le nombre de nouveaux diagnostics VIH chez les enfants. A partir d’une base de données de surveillance de l’hépatite C chronique (VHC), nous avons réalisé une imputation des données manquantes afind’identifier les facteurs de risque de complications hépatiques graves chez des usagers de drogue. A partir des mêmes données, nous avons proposé des critères d’application d’une analyse de sensibilité aux hypothèses sous-jacentes àl’imputation multiple. Enfin, nous avons décrit l’élaboration d’un processus d’imputation pérenne appliqué aux données du système de surveillance du VIH et son évolution au cours du temps, ainsi que les procédures d’évaluation et devalidation.Les applications pratiques présentées nous ont permis d’élaborer une stratégie de traitement des données manquantes, incluant l’examen approfondi de la base de données incomplète, la construction du modèle d’imputation multiple, ainsi queles étapes de validation des modèles et de vérification des hypothèses. / The management of missing values is a common and widespread problem in epidemiology. The most common technique used restricts the data analysis to subjects with complete information on variables of interest, which can reducesubstantially statistical power and precision and may also result in biased estimates.This thesis investigates the application of multiple imputation methods to manage missing values in epidemiological studies and surveillance systems for infectious diseases. Study designs to which multiple imputation was applied were diverse: a risk analysis of HIV transmission through blood transfusion, a case-control study on risk factors for ampylobacter infection, and a capture-recapture study to estimate the number of new HIV diagnoses among children. We then performed multiple imputation analysis on data of a surveillance system for chronic hepatitis C (HCV) to assess risk factors of severe liver disease among HCV infected patients who reported drug use. Within this study on HCV, we proposedguidelines to apply a sensitivity analysis in order to test the multiple imputation underlying hypotheses. Finally, we describe how we elaborated and applied an ongoing multiple imputation process of the French national HIV surveillance database, evaluated and attempted to validate multiple imputation procedures.Based on these practical applications, we worked out a strategy to handle missing data in surveillance data base, including the thorough examination of the incomplete database, the building of the imputation model, and the procedure to validate imputation models and examine underlying multiple imputation hypotheses.

Dans ce travail, une nouvelle approche de conduite des observations radar de la forêt est proposée. Elle combine des méthodes statistiques pour l’analyse de sensibilité et les plans d’expériences numériques séquentiels et un code de calcul simulant la rétrodiffusion d’une forêt en vue de l’élaboration d’un modèle approché (métamodèle) à moindre coût numérique. L’introduction de ces outils mathématiques a pour objectif d’aider à la planification et à l’exécution des simulations radar et à l’organisation et l’analyse de leurs résultats. D’une part, les techniques de l’analyse de sensibilité sont appliquées afin de classer par ordre d’importance les paramètres d’entrée du modèle et d’identifier les paramètres de la forêt les plus significatifs ainsi que leurs effets sur le signal radar. D’autre part, la construction d’un métamodèle adaptable accélère le code de calcul, en préservant la physique du phénomène. Le cadre opérationnel de ce modèle approché sert finalement à introduire le principe du radar cognitif dans notre stratégie. Dans ce cas, une analyse rapide du signal reçu est nécessaire pour concevoir, en temps réel, le nouveau signal à émettre. De cette façon, les observations du radar simulées incluent en temps réel l’effet de l’environnement illuminé grâce aux simulations plus rapides et ciblées. / In this work, a new approach to conduct the radar observations of forests is proposed. It combines statistical methods for sensitivity analysis and adaptive design of simulation experiments and a numerical code simulating the the forest backscattering for the use of a approximate model (metamodel) with less computational cost. The introduction of these mathematical tools has as an objective to assist the design and the execution of radar simulations and at the organization and the analysis of their results. On the one hand, the sensitivity analysis techniques were applied in order to classify the input parameters by means of their importance and to identify the most significant forest parameters as well as their effects on the radar signal. On the other hand, the construction of an adaptive metamodel accelerates the simulation model, while keeping the physics of the phenomenom. The operational frame of this approximate model serves finally in the introduction of the cognitive radar principle in our strategy. In that case, a fast analysis of the received signal is necessary to design, in real time, the new signal to be emitted. That way, the simulated radar observations take into account in real time the effect of the illuminated environment, thanks to the more focused and fast simulations.

Le développement et l'utilisation de modèles intégrés transport-urbanisme sont devenus une norme pour représenter les interactions entre l'usage des sols et le transport de biens et d'individus sur un territoire. Ces modèles sont souvent utilisés comme outils d'aide à la décision pour des politiques de planification urbaine.Les modèles transport-urbanisme, et plus généralement les modèles mathématiques, sont pour la majorité conçus à partir de codes numériques complexes. Ces codes impliquent très souvent des paramètres dont l'incertitude est peu connue et peut potentiellement avoir un impact important sur les variables de sortie du modèle.Les méthodes d'analyse de sensibilité globales sont des outils performants permettant d'étudier l'influence des paramètres d'un modèle sur ses sorties. En particulier, les méthodes basées sur le calcul des indices de sensibilité de Sobol' fournissent la possibilité de quantifier l'influence de chaque paramètre mais également d'identifier l'existence d'interactions entre ces paramètres.Dans cette thèse, nous privilégions la méthode dite à base de plans d'expériences répliqués encore appelée méthode répliquée. Cette méthode a l'avantage de ne requérir qu'un nombre relativement faible d'évaluations du modèle pour calculer les indices de Sobol' d'ordre un et deux.Cette thèse se focalise sur des extensions de la méthode répliquée pour faire face à des contraintes issues de notre application sur le modèle transport-urbanisme Tranus, comme la présence de corrélation entre paramètres et la prise en compte de sorties multivariées.Nos travaux proposent également une approche récursive pour l'estimation séquentielle des indices de Sobol'. L'approche récursive repose à la fois sur la construction itérative d'hypercubes latins et de tableaux orthogonaux stratifiés et sur la définition d'un nouveau critère d'arrêt. Cette approche offre une meilleure précision sur l'estimation des indices tout en permettant de recycler des premiers jeux d'évaluations du modèle. Nous proposons aussi de combiner une telle approche avec un échantillonnage quasi-Monte Carlo.Nous présentons également une application de nos contributions pour le calage du modèle de transport-urbanisme Tranus. / Land Use and Transportation Integrated (LUTI) models have become a norm for representing the interactions between land use and the transportation of goods and people in a territory. These models are mainly used to evaluate alternative planning scenarios, simulating their impact on land cover and travel demand.LUTI models and other mathematical models used in various fields are most of the time based on complex computer codes. These codes often involve poorly-known inputs whose uncertainty can have significant effects on the model outputs.Global sensitivity analysis methods are useful tools to study the influence of the model inputs on its outputs. Among the large number of available approaches, the variance based method introduced by Sobol' allows to calculate sensitivity indices called Sobol' indices. These indices quantify the influence of each model input on the outputs and can detect existing interactions between inputs.In this framework, we favor a particular method based on replicated designs of experiments called replication method. This method appears to be the most suitable for our application and is advantageous as it requires a relatively small number of model evaluations to estimate first-order or second-order Sobol' indices.This thesis focuses on extensions of the replication method to face constraints arising in our application on the LUTI model Tranus, such as the presence of dependency among the model inputs, as far as multivariate outputs.Aside from that, we propose a recursive approach to sequentially estimate Sobol' indices. The recursive approach is based on the iterative construction of stratified designs, latin hypercubes and orthogonal arrays, and on the definition of a new stopping criterion. With this approach, more accurate Sobol' estimates are obtained while recycling previous sets of model evaluations. We also propose to combine such an approach with quasi-Monte Carlo sampling.An application of our contributions on the LUTI model Tranus is presented.

Alternative renewable energy sources such as solar, wind, and bio energy have brought uncertainties into the power flow of electric power systems. Purely deterministic tools and models are suitable to guarantee the safe operation of these systems. A necessity arises to develop and use methods that deal with uncertainties in the analysis. Several methodologies have been proposed to assess the transient stability of power systems considering uncertainties. However, most of these techniques are based on the execution of successive simulations, requiring a high computational effort. Hence, they are limited to off-line applications in small systems. In view of the foregoing, this work proposes the development of two methodologies to assess – in real time – the transient stability of power systems with parametric and operational uncertainties. The first one is an extension of PEBS, which is a direct method for stability assessment. This method, called robust PEBS, employs an interval energy function of the power system to determine a robust estimate critical clearing time. The second one is the use of optimization methods to find a robust estimate critical clearing time. Notably, we employ the Simulated Annealing and Differential Evolution algorithms. Besides developing methods to estimate the critical clearing time, this work also contributes to the analysis of power systems with uncertainties by introducing a technique to reduce the analysis effort. To be specific, a methodology is proposed to identify the most influential parameters for the transient analysis assessment based on a sensitivity analysis of the generator angles with respect to the system parameters. / A utilização crescente de fontes alternativas intermitentes de energia como eólica e solar tem trazido incertezas em relação ao nível de geração e ao fluxo de potência em Sistemas Elétricos de Potência (SEP). Assim, a utilização de modelagem e ferramentas puramente determinísticas na análise de estabilidade não são mais suficientes para garantir a operação segura destes sistemas. Torna-se necessário, então, o desenvolvimento e utilização de métodos que incluam essas incertezas nas análises. Diversas metodologias foram propostas para avaliar a estabilidade transitória de Sistemas Elétricos de Potência considerando incertezas. Porém, grande parte destas técnicas é baseada em execuções de inúmeras simulações e, portanto, exige grande esforços computacionais e são limitadas a aplicações off-line e em sistemas elétricos de pequeno porte. Face ao exposto, propõe-se o desenvolvimento de uma metodologia rápida para a avaliação de estabilidade transitória de SEPs em tempo real considerando incertezas paramétricas. Esta metodologia deverá ser capaz de fornecer rapidamente um resultado robusto sobre a estabilidade. Para tal pretende-se estender a aplicação do método direto PEBS para a análise de estabilidade de sistemas elétricos com incertezas. Além disso, neste trabalho, aplicam-se métodos de otimização para se encontrar o tempo crítico de abertura sem o uso de uma simulação de Monte Carlo e determinam-se os parâmetros que mais influenciam para o estudo de estabilidade transitória utilizando uma análise de sensibilidade dos ângulos dos geradores em relação aos parâmetros do sistema elétrico de potência.

Ce travail porte sur la quantification d'incertitude dans la modélisation des émissions de polluants atmosphériques dues au trafic routier d'une aire urbaine. Une chaîne de modélisations des émissions de polluants atmosphériques est construite, en couplant un modèle d’affectation dynamique du trafic (ADT) avec un modèle de facteurs d’émission. Cette chaîne est appliquée à l’agglomération de Clermont-Ferrand (France) à la résolution de la rue. Un métamodèle de l’ADT est construit pour réduire le temps d’évaluation du modèle. Une analyse de sensibilité globale est ensuite effectuée sur cette chaîne, afin d’identifier les entrées les plus influentes sur les sorties. Enfin, pour la quantification d’incertitude, deux ensembles sont construits avec l’approche de Monte Carlo, l’un pour l’ADT et l’autre pour les émissions. L’ensemble d’ADT est évalué et amélioré grâce à la comparaison avec les débits du trafic observés, afin de mieux échantillonner les incertitudes / This work focuses on the uncertainty quantification in the modeling of road traffic emissions in a metropolitan area. The first step is to estimate the time-dependent traffic flow at street-resolution for a full agglomeration area, using a dynamic traffic assignment (DTA) model. Then, a metamodel is built for the DTA model set up for the agglomeration, in order to reduce the computational cost of the DTA simulation. Then the road traffic emissions of atmospheric pollutants are estimated at street resolution, based on a modeling chain that couples the DTA metamodel with an emission factor model. This modeling chain is then used to conduct a global sensitivity analysis to identify the most influential inputs in computed traffic flows, speeds and emissions. At last, the uncertainty quantification is carried out based on ensemble simulations using Monte Carlo approach. The ensemble is evaluated with observations in order to check and optimize its reliability

Neste trabalho é proposta a determinação do ponto de Máximo Carregamento (PMC) em sistemas elétricos de potência por meio do método da Função Lagrangiana Barreira Modificada (FLBM), uma variante do método de Pontos Interiores (PI). Também por meio do método da FLBM, busca-se determinar qual é a barra, para cada sistema, que apresenta a maior sensibilidade em relação ao fator de carregamento, ou seja, qual seria a primeira barra que deveria sofrer corte de carga a fim de aumentar a margem de carregamento do sistema e, assim, evitar o colapso de tensão. Para comprovação dos resultados obtidos por meio do método da FLBM utiliza-se a técnica de Análise de Sensibilidade (AS). A formulação do problema tem como restrições de igualdade as equações de balanço de potência do sistema elétrico e como restrições de desigualdade os limites de tensões nas barras, assim como os limites de geração de potência reativa nas barras com controle da referida potência. Estudos de casos foram realizados em um sistema de 3 barras e nos sistemas IEEE 14, 57, 118 e 300 barras; tais estudos demonstraram a robustez e a eficiência dos algoritmos propostos. / This work proposes the determination of the Maximum Loading Point (MLP) in electric power system via Lagrangian Modified Barrier Function (LMBF) method, a variant of Interior Point (IP). The LMBF method is also used to determine which bus, for each system, has the highest sensitivity of load factor, i.e., which bus would be the first to have load shedding in order to increase the loading margin system and thus prevent voltage collapse. To validate this approach, the Sensitivity Analysis (SA) technique was used for the confirmation of the results obtained by the LMBF method. The formulation of the problem considered the equations of power balance of the electrical system equality constraints, and the buses voltage magnitude limits, as well as the limits of reactive power control at the buses of that power inequality constraints. Case studies were conducted in a system of 3 buses and IEEE systems 14, 57, 118 and 300 buses, demonstrating the robustness and efficiency of the proposed algorithms.

Macrophages are the largest cells in the immune system and they regulate inflammatory signalling and inform cell fate decisions. Many signals, including those mediated by Tumor Necrosis Factor alpha (TNFα) converge on a few key intracellular signalling pathways, including the Nuclear Factor kappa B (NFκB) network. The NFκB signalling pathway plays a vital role in the regulation of many different cellular responses, including the production of TNFα itself, which is required to sustain and propagate immune responses to, for example, infection or tissue damage. In this thesis we report on studies-both experimental and theoretical-of the NFκB signalling pathway in macrophages. Our collaborators stimulated these cells with various doses of Lipopolysaccharide (LPS), a molecule that forms the major component of the outer membrane of Gram-negative bacteria: in these experiments it serves as a proxy for bacterial infection. The macrophages, studied in vitro, respond as they are believed to do in tissues, by secreting certain signalling molecules called cytokines: the level of secretion proved to depend on the strength of the LPS stimulus. Further, heterogeneity of macrophage signalling was observed in response to a range of LPS doses. Within individual macrophages LPS stimulation results in oscillatory behaviour of NFκB localisation-NFκB shuttles in and out of the nucleus-with an amplitude (peak nuclear concentration) that also depends on the LPS dose. Heterogeneity was also observed in cells that were stimulated with the same dose intensity. This raises an important question about how immune cells coordinate inflammatory activity in the presence of this variability. In this thesis we aim to achieve an understanding of the system through the qualitative analysis of mathematical models of it. This work explores both the parametric sensitivity and bifurcation analyses for two mathematical models of NFκB in macrophages. Parametric sensitivity analysis is used to investigate the role of parameters on the model's output, especially on certain features of the signal-peak amplitudes, inter-peak intervals and areas beneath curves-that are commonly measured in single-cell experiments. Local bifurcation analysis is conducted in order to show all the possible behaviours produced when varying parameters.