Os conceitos presentes na Física Moderna e Contemporânea (FMC), como aqueles relacionados à estrutura da matéria, rompem com ideias do cotidiano e envolvem fenômenos e entidades que são parte de uma realidade tecnicamente construída e não podem ser percebidos de forma direta pelos sentidos humanos. Seu ensino requer meios representativos, e as simulações computacionais atendem a esta necessidade. Nesta pesquisa, tendo como marco teórico ideias relacionadas ao estudo dos modelos mentais e conceituais, ideias provenientes da epistemologia da ciência de Bachelard, e considerando algumas ideias presentes na teoria das situações didáticas de Brousseau, buscamos identificar obstáculos de aprendizagem que atuam no ensino de conceitos do tópico Estrutura da Matéria em que são utilizadas simulações computacionais. Tendo como pano de fundo um processo iterativo de desenho, implementação e redesenho de um curso sobre a estrutura da matéria e aceleradores de partículas, analisamos a emersão de possíveis obstáculos epistemológicos, e verificamos como obstáculos didático-pedagógicos facilitavam esta emersão. Como resultados, identificamos obstáculos epistemológicos e didático-pedagógicos de diferentes naturezas, entre os quais, alguns relacionados à percepção ingênua de fenômenos do cotidiano, alguns relacionados ao uso de metáforas e imagens, e outros relacionados a um raciocínio limitado e incongruente. Acreditamos que as análises e conclusões desta pesquisa contribuem para uma reflexão sobre o ensino de tópicos de Física Moderna e Contemporânea, e sobre o uso de simulações computacionais como ferramentas pedagógicas. / The concepts of Modern and Contemporary Physics (MCP), such as those related to the structure of matter, break with the everyday ideas and involve phenomena and entities that are part of a reality technically built that cannot be directly perceived by human senses. Its teaching requires representative media, and the computer simulations meet this need. In this research, having as theoretical framework ideas related to the study of mental and conceptual models, ideas from the epistemology of science of Bachelard, and considering some of the ideas present in the theory of didactic situations of Brousseau, we seek to identify learning obstacles who work in teaching concepts of the topic Structure of Matter in which computer simulations are used. Against the backdrop of an iterative process of design, implementing and redesign of a course on the structure of matter and particle accelerators, we analyze the possible emergence of epistemological obstacles, and check how didactic-pedagogical obstacles facilitated this emersion. As a result, we identified epistemological obstacles and didactic-pedagogical obstacles of different nature, including some related to the naive perception of everyday phenomena, some related to the use of metaphors and images, and other related to a limited reasoning and incongruous. We believe that the analysis and conclusions of this research contribute to a reflection on the teaching of Modern and Contemporary Physics topics, and on the use of computer simulations as educational tools.

The aim of this study is to make an inquiry on the nature and the development of dualities in Bergson&rsquo / s philosophy. Since the nature of each duality differs from the others and the dualistic pattern inherent in Bergsonian philosophy is subject to change, we base our study on a chronological structure in order to comprehend better how this pattern changes. We claim that such an inquiry will yield relevant outcomes with regard to ontological and epistemological evolution of Bergson&rsquo / s thought. To state more precisely, we are of the idea that the modification in the dualistic pattern in Bergson&rsquo / s ontology is reflected in a parallel manner in his epistemology. The fundamental question that shows us the way to follow in our study is whether the elements of the dualities (whether they be ontological or epistemological) are reconciled by Bergson or they are left as absolutely distinct elements. At the end of the inquiry regarding that question, which we believe can be taken as an inspiring point in developing new approaches especially to epistemological problems, our conviction is that Bergson points out to a meeting point.

Os conceitos presentes na Física Moderna e Contemporânea (FMC), como aqueles relacionados à estrutura da matéria, rompem com ideias do cotidiano e envolvem fenômenos e entidades que são parte de uma realidade tecnicamente construída e não podem ser percebidos de forma direta pelos sentidos humanos. Seu ensino requer meios representativos, e as simulações computacionais atendem a esta necessidade. Nesta pesquisa, tendo como marco teórico ideias relacionadas ao estudo dos modelos mentais e conceituais, ideias provenientes da epistemologia da ciência de Bachelard, e considerando algumas ideias presentes na teoria das situações didáticas de Brousseau, buscamos identificar obstáculos de aprendizagem que atuam no ensino de conceitos do tópico Estrutura da Matéria em que são utilizadas simulações computacionais. Tendo como pano de fundo um processo iterativo de desenho, implementação e redesenho de um curso sobre a estrutura da matéria e aceleradores de partículas, analisamos a emersão de possíveis obstáculos epistemológicos, e verificamos como obstáculos didático-pedagógicos facilitavam esta emersão. Como resultados, identificamos obstáculos epistemológicos e didático-pedagógicos de diferentes naturezas, entre os quais, alguns relacionados à percepção ingênua de fenômenos do cotidiano, alguns relacionados ao uso de metáforas e imagens, e outros relacionados a um raciocínio limitado e incongruente. Acreditamos que as análises e conclusões desta pesquisa contribuem para uma reflexão sobre o ensino de tópicos de Física Moderna e Contemporânea, e sobre o uso de simulações computacionais como ferramentas pedagógicas. / The concepts of Modern and Contemporary Physics (MCP), such as those related to the structure of matter, break with the everyday ideas and involve phenomena and entities that are part of a reality technically built that cannot be directly perceived by human senses. Its teaching requires representative media, and the computer simulations meet this need. In this research, having as theoretical framework ideas related to the study of mental and conceptual models, ideas from the epistemology of science of Bachelard, and considering some of the ideas present in the theory of didactic situations of Brousseau, we seek to identify learning obstacles who work in teaching concepts of the topic Structure of Matter in which computer simulations are used. Against the backdrop of an iterative process of design, implementing and redesign of a course on the structure of matter and particle accelerators, we analyze the possible emergence of epistemological obstacles, and check how didactic-pedagogical obstacles facilitated this emersion. As a result, we identified epistemological obstacles and didactic-pedagogical obstacles of different nature, including some related to the naive perception of everyday phenomena, some related to the use of metaphors and images, and other related to a limited reasoning and incongruous. We believe that the analysis and conclusions of this research contribute to a reflection on the teaching of Modern and Contemporary Physics topics, and on the use of computer simulations as educational tools.

We study the convergence of a nonlinear approximation method introduced in the engineering literature for the numerical solution of a high-dimensional Fokker--Planck equation featuring in Navier--Stokes--Fokker--Planck systems that arise in kinetic models of dilute polymers. To do so, we build on the analysis carried out recently by Le~Bris, Leli\`evre and Maday (Const. Approx. 30: 621--651, 2009) in the case of Poisson's equation on a rectangular domain in $\mathbb{R}^2$, subject to a homogeneous Dirichlet boundary condition, where they exploited the connection of the approximation method with the greedy algorithms from nonlinear approximation theory explored, for example, by DeVore and Temlyakov (Adv. Comput. Math. 5:173--187, 1996). We extend the convergence analysis of the pure greedy and orthogonal greedy algorithms considered by Le~Bris, Leli\`evre and Maday to the technically more complicated situation of the elliptic Fokker--Planck equation, where the role of the Laplace operator is played out by a high-dimensional Ornstein--Uhlenbeck operator with unbounded drift, of the kind that appears in Fokker--Planck equations that arise in bead-spring chain type kinetic polymer models with finitely extensible nonlinear elastic potentials, posed on a high-dimensional Cartesian product configuration space $\mathsf{D} = D_1 \times \dotsm \times D_N$ contained in $\mathbb{R}^{N d}$, where each set $D_i$, $i=1, \dotsc, N$, is a bounded open ball in $\mathbb{R}^d$, $d = 2, 3$. We exploit detailed information on the spectral properties and elliptic regularity of the Ornstein--Uhlenbeck operator to give conditions on the true solution of the Fokker--Planck equation which guarantee certain rates of convergence of the greedy algorithms. We extend the analysis to discretized versions of the greedy algorithms.

Krivelevich and Patkós conjectured in 2009 that χ(G(n, p)) ∼ χ=(G(n, p)) ∼ χ∗=(G(n, p)) for C/n < p < 1 − ε, where ε > 0. We prove this conjecture for n−1+ε1 < p < 1 − ε2 where ε1, ε2 > 0. We investigate several measures that have been proposed to indicate centrality of nodes in networks, and find examples of networks where they fail to distinguish any of the vertices nodes from one another. We develop a new method to investigate core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes. Finally, we present an experiment and an analysis of empirical networks, functional human brain networks. We found that reconfiguration patterns of dynamic communities can be used to classify nodes into a stiff core, a flexible periphery, and a bulk. The separation between this stiff core and flexible periphery changes as a person learns a simple motor skill and, importantly, it is a good predictor of how successful the person is at learning the skill. This temporally defined core-periphery organisation corresponds well with the core- periphery detected by the method that we proposed earlier the static networks created by averaging over the subjects dynamic functional brain networks.

In this work, we are interested in Growth of Galton-Watson trees under two different models: (1) Galton-Watson (GW) forests with lifetimes and/or immigrants, and (2) Galton-Watson forests with mutation, which we call Galton-Watson-Clone-Mutant forests, or GWCMforests. Under each model, we study certain consistent families (Fλ)λ≥0 of GW/GWCM forests and associated decompositions that include backbone decomposition as studied by many authors. Specifically, consistency here refers to the property that for each μ ≤ λ, the forest Fμ has the same distribution as the subforest of Fλ spanned by the blue leaves in a Bernoulli leaf colouring, where each leaf of Fλ is coloured in blue independently with probability μ/λ. In the first model, the case of exponentially distributed lifetimes and no immigration was studied by Duquesne and Winkel and related to the genealogy of Markovian continuous-state branching processes (CSBP). We characterise here such families in the framework of arbitrary lifetime distributions and immigration according to a renewal process, and show convergence to Sagitov’s (non-Markovian) generalisation of continuous-state branching renewal processes, and related processes with immigration. In the second model, we characterise such families in terms of certain bivariate CSBP with branching mechanisms studied previously by Watanabe and show associated convergence results. This is related to, but more general than Bertoin’s study of GWCM trees, and also ties in with work by Abraham and Delmas, who study directly some of the limiting processes.

Confocal single-molecule fluorescence is a powerful tool for monitoring conformational dynamics, and has provided new insight into the enzymatic activities of complex biological molecules such as DNA and RNA polymerases. Though useful, such studies are typically qualitative in nature, and performed almost exclusively in highly purified, in vitro settings. In this work, I focus on improving the methodology of confocal single-molecule fluorescence in two broad ways: (i) by enabling the quantitative identification of molecular dynamics in proteins and nucleic acids in vitro, and (ii) developing the tools needed to perform these analyses in vivo. Toward the first goal, and together with several colleagues, I have developed three novel methods for the quantitative identification of dynamics in biomolecules: (i) Burst Variance Analysis (BVA), which unambiguously identifies dynamics in single-molecule FRET experiments; (ii) Dynamic Probability Density Analysis (PDA), which hypothesis-tests specific kinetic models against smFRET data and extracts rate information; and (iii) a novel molecular counting method useful for studying single-molecule thermodynamics. We validated these methods against Monte Carlo simulations and experimental DNA controls, and demonstrated their practical application in vitro by analyzing the “fingers-closing” conformational change in E.coli DNA Polymerase I; these studies identified unexpected conformational flexibility which may be important to the fidelity of DNA synthesis. To enable similar studies in the context of a living cell, we generated a nuclease-resistant DNA analogue of the Green Fluorescent Protein, or “Green Fluorescent DNA,” and developed an electroporation method to efficiently transfer it into the cytoplasm of E.coli. We demonstrate in vivo confocal detection of smFRET from this construct, which is both bright and photostable in the cellular milieu. In combination with PDA, BVA and our novel molecular counting method, this Green Fluorescent DNA should enable the characterization of DNA and protein-DNA dynamics in living cells, at the single-molecule level. I conclude by discussing the ways in which these methods may be useful in investigating the dynamics of processes such as transcription, translation and recombination, both in vitro and in vivo.

Membrane protein mechanotransduction is the altered function of an integral membrane protein in response to mechanical force. Such mechanosensors are found in all kingdoms of life, and increasing numbers of membrane proteins have been found to exhibit mechanosensitivity. How they mechanotransduce is an active research area and the topic of this thesis. The methodology employed is classical molecular dynamics (MD) simulations. MD systems are complex, and two programs were developed to reduce this apparent complexity in terms of both visual abstraction and statistical analysis. Bendix detects and visualises helices as cylinders that follow the helix axis, and quantifies helix distortion. The functionality of Bendix is demonstrated on the symporter Mhp1, where a state is identified that had hitherto only been proposed. InterQuant tracks, categorises and orders proximity between parts of an MD system. Results from multiple systems are statistically interrogated for reproducibility and significant differences at the resolution of protein chains, residues or atoms. Using these tools, the interaction between membrane and the Escherichia coli mechanosensitive channel of small conductance, MscS, is investigated. Results are presented for crystal structures captured in different states, one of which features electron density proposed to be lipid. MD results supports this hypothesis, and identify differential lipid interaction between closed and open states. It is concluded that propensity for lipid to leave for membrane bulk drives MscS state stability. In a subsequent study, MscS is opened by membrane surface tension for the first time in an MD setup. The gating mechanism of MscS is explored in terms of both membrane and protein deformation in response to membrane stretch. Using novel tension methodology and the longest MD simulations of MscS performed to date, a molecular basis for the Dashpot gating mechanism is proposed. Lipid emerges as an active structural element with the capacity to augment protein structure in the protein structure-function paradigm.

This biomedical engineering thesis explores the opportunities and challenges of 2D+t contrast echocardiography for left ventricle functional analysis, both clinically and within a computer vision atlas-based deformable template model framework. A database was created for the experiments in this thesis, with 21 studies of contrast Dobutamine Stress Echo, in all 4 principal planes. The database includes clinical variables, human expert hand-traced myocardial contours and visual scoring. First the problem is studied from a clinical perspective. Quantification of endocardial global and local function using standard measures shows expected values and agreement with human expert visual scoring, but the results are less reliable for myocardial thickening. Next, the problem of segmenting the endocardium with a computer is posed in a standard landmark and atlas-based deformable template model framework. The underlying assumption is that these models can emulate human experts in terms of integrating previous knowledge about the anatomy and physiology with three sources of information from the image: texture, geometry and kinetics. Probabilistic atlases of contrast echocardiography are computed, while noting from histograms at selected anatomical locations that modelling texture with just mean intensity values may be too naive. Intensity analysis together with the clinical results above suggest that lack of external boundary definition may preclude this imaging technique for appropriate measuring of myocardial thickening, while endocardial boundary definition is appropriate for evaluation of wall motion. Geometry is presented in a Principal Component Analysis (PCA) context, highlighting issues about Gaussianity, the correlation and covariance matrices with respect to physiology, and analysing different measures of dimensionality. A popular extension of deformable models ---Active Appearance Models (AAMs)--- is then studied in depth. Contrary to common wisdom, it is contended that using a PCA texture space instead of a fixed atlas is detrimental to segmentation, and that PCA models are not convenient for texture modelling. To integrate kinetics, a novel spatio-temporal model of cardiac contours is proposed. The new explicit model does not require frame interpolation, and it is compared to previous implicit models in terms of approximation error when the shape vector changes from frame to frame or remains constant throughout the cardiac cycle. Finally, the 2D+t atlas-based deformable model segmentation problem is formulated and solved with a gradient descent approach. Experiments using the similarity transformation suggest that segmentation of the whole cardiac volume outperforms segmentation of individual frames. A relatively new approach ---the inverse compositional algorithm--- is shown to decrease running times of the classic Lucas-Kanade algorithm by a factor of 20 to 25, to values that are within real-time processing reach.