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Bayesian Inference Frameworks for Fluorescence Microscopy Data AnalysisJanuary 2019 (has links)
abstract: In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on synthetic data. These three frameworks are self-contained, and can be used concurrently so that the fluorescence profile and emitter locations are both considered unknown and, under some conditions, learned simultaneously. The framework I present is flexible and may be adapted to accommodate the inference of other parameters, such as emission photophysical kinetics and the trajectories of moving molecules. My TIRF-specific implementation may find use in the study of structures on cell membranes, or in studying local sample properties that affect fluorescent molecule photon emission rates. / Dissertation/Thesis / Masters Thesis Applied Mathematics 2019
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Modelos de campos de tensões para a análise de regiões de descontinuidadeMota, Bruno Oliveira Teixeira da Mota January 2011 (has links)
Tese de mestrado integrado. Engenharia Civil. Faculdade de Engenharia. Universidade do Porto. 2011
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Imprévus et pièges des cordes vibrantes chez D'Alembert (1755-1783).<br />Doutes et certitudes sur les équations aux dérivées partielles, les séries et les fonctionsJouve, Guillaume 10 July 2007 (has links) (PDF)
Cette thèse se situe dans le cadre de l'entreprise de longue haleine d'édition critique et commentée des Oeuvres complètes de D'Alembert. Ce savant est indiscutablement le pionnier des équations aux dérivées partielles et de leur application aux sciences physiques. Toutefois, seule une partie de ses écrits sur le sujet a vraiment été examinée jusqu'ici par les historiens des sciences. Une étude approfondie de ses mémoires tardifs permet de modifier de nombreuses perspectives, notamment sur les points suivants: intégration et résolution des équations avec ou sans ce que nous appellerions des "conditions aux limites", problèmes de définition et de régularité des fonctions, convergence et divergence des séries, développement des fonctions en séries entières ou trigonométriques. Nous montrons ici la pertinence et le fécondité des résultats de D'Alembert, mais aussi de ses doutes et des pistes qu'il propose pour les éclairer.
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Regularization of Parameter Problems for Dynamic Beam ModelsRydström, Sara January 2010 (has links)
The field of inverse problems is an area in applied mathematics that is of great importance in several scientific and industrial applications. Since an inverse problem is typically founded on non-linear and ill-posed models it is a very difficult problem to solve. To find a regularized solution it is crucial to have a priori information about the solution. Therefore, general theories are not sufficient considering new applications. In this thesis we consider the inverse problem to determine the beam bending stiffness from measurements of the transverse dynamic displacement. Of special interest is to localize parts with reduced bending stiffness. Driven by requirements in the wood-industry it is not enough considering time-efficient algorithms, the models must also be adapted to manage extremely short calculation times. For the developing of efficient methods inverse problems based on the fourth order Euler-Bernoulli beam equation and the second order string equation are studied. Important results are the transformation of a nonlinear regularization problem to a linear one and a convex procedure for finding parts with reduced bending stiffness.
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Nonlinear Analysis of Beams Using Least-Squares Finite Element Models Based on the Euler-Bernoulli and Timoshenko Beam TheoriesRaut, Ameeta A. 2009 December 1900 (has links)
The conventional finite element models (FEM) of problems in structural
mechanics are based on the principles of virtual work and the total potential
energy. In these models, the secondary variables, such as the bending moment
and shear force, are post-computed and do not yield good accuracy. In addition,
in the case of the Timoshenko beam theory, the element with lower-order equal
interpolation of the variables suffers from shear locking. In both Euler-Bernoulli
and Timoshenko beam theories, the elements based on weak form Galerkin
formulation also suffer from membrane locking when applied to geometrically
nonlinear problems. In order to alleviate these types of locking, often reduced
integration techniques are employed. However, this technique has other
disadvantages, such as hour-glass modes or spurious rigid body modes. Hence,
it is desirable to develop alternative finite element models that overcome the
locking problems. Least-squares finite element models are considered to be
better alternatives to the weak form Galerkin finite element models and,
therefore, are in this study for investigation. The basic idea behind the least-squares finite element model is to compute the residuals due to the
approximation of the variables of each equation being modeled, construct
integral statement of the sum of the squares of the residuals (called least-squares
functional), and minimize the integral with respect to the unknown parameters
(i.e., nodal values) of the approximations. The least-squares formulation helps to
retain the generalized displacements and forces (or stress resultants) as
independent variables, and also allows the use of equal order interpolation
functions for all variables.
In this thesis comparison is made between the solution accuracy of finite
element models of the Euler-Bernoulli and Timoshenko beam theories based on
two different least-square models with the conventional weak form Galerkin
finite element models. The developed models were applied to beam problems
with different boundary conditions. The solutions obtained by the least-squares
finite element models found to be very accurate for generalized displacements
and forces when compared with the exact solutions, and they are more accurate
in predicting the forces when compared to the conventional finite element
models.
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Analytical Study on Adhesively Bonded Joints Using Peeling Test and Symmetric Composite Models Based on Bernoulli-Euler and Timoshenko Beam Theories for Elastic and Viscoelastic MaterialsSu, Ying-Yu 2010 December 1900 (has links)
Adhesively bonded joints have been investigated for several decades. In most analytical studies, the Bernoulli-Euler beam theory is employed to describe the behaviour of adherends. In the current work, three analytical models are developed for adhesively bonded joints using the Timoshenko beam theory for elastic material and a Bernoulli-Euler beam model for viscoelastic materials.
One model is for the peeling test of an adhesively bonded joint, which is described using a Timoshenko beam on an elastic foundation. The adherend is considered as a Timoshenko beam, while the adhesive is taken to be a linearly elastic foundation. Three cases are considered: (1) only the normal stress is acting (mode I); (2) only the transverse shear stress is present (mode II); and (3) the normal and shear stresses co-exist (mode III) in the adhesive. The governing equations are derived in terms of the displacement and rotational angle of the adherend in each case. Analytical solutions are obtained for the displacements, rotational angle, and stresses. Numerical results are presented to show the trends of the displacements and rotational angle changing with geometrical and loading conditions.
In the second model, the peeling test of an adhesively bonded joint is represented using a viscoelastic Bernoulli-Euler beam on an elastic foundation. The adherend is considered as a viscoelastic Bernoulli-Euler beam, while the adhesive is taken to be a linearly elastic foundation. Two cases under different stress history are considered: (1) only the normal stress is acting (mode I); and (2) only the transverse shear stress is present (mode II). The governing equations are derived in terms of the displacements. Analytical solutions are obtained for the displacements. The numerical results show that the deflection increases as time and temperature increase.
The third model is developed using a symmetric composite adhesively bonded joint. The constitutive and kinematic relations of the adherends are derived based on the Timoshenko beam theory, and the governing equations are obtained for the normal and shear stresses in the adhesive layer. The numerical results are presented to reveal the normal and shear stresses in the adhesive.
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Regularization of Parameter Problems for Dynamic Beam ModelsRydström, Sara January 2010 (has links)
<p>The field of inverse problems is an area in applied mathematics that is of great importance in several scientific and industrial applications. Since an inverse problem is typically founded on non-linear and ill-posed models it is a very difficult problem to solve. To find a regularized solution it is crucial to have <em>a priori</em> information about the solution. Therefore, general theories are not sufficient considering new applications.</p><p>In this thesis we consider the inverse problem to determine the beam bending stiffness from measurements of the transverse dynamic displacement. Of special interest is to localize parts with reduced bending stiffness. Driven by requirements in the wood-industry it is not enough considering time-efficient algorithms, the models must also be adapted to manage extremely short calculation times.</p><p>For the developing of efficient methods inverse problems based on the fourth order Euler-Bernoulli beam equation and the second order string equation are studied. Important results are the transformation of a nonlinear regularization problem to a linear one and a convex procedure for finding parts with reduced bending stiffness.</p>
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Méthode de Dandelin-Graeffe et méthode de BakerDiouf, Ismaïla Mignotte, Maurice. January 2007 (has links) (PDF)
Thèse de doctorat : Mathématiques : Strasbourg 1 : 2007. / Titre provenant de l'écran-titre. Bibliogr. p. 99-100.
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APPROXIMATE ANALYSIS OF RE-ENTRANT LINES WITH BERNOULLI RELIABILITY MODELSWang, Chong 01 January 2007 (has links)
Re-entrant lines are widely used in many manufacturing systems, such as semiconductor, electronics, etc. However, the performance analysis of re-entrant lines is largely unexplored due to its complexity. In this thesis, we present iterative procedures to approximate the production rate of re-entrant lines with Bernoulli reliability of machines. The convergence of the algorithms, uniqueness of the solution, and structural properties, have been proved analytically. The accuracy of the procedures is investigated numerically. It is shown that the approaches developed can either provide a lower bound or a closed estimate of the system production rate. Finally, a case study of automotive ignition component line with re-entrant washing operations is introduced to illustrate the applicability of the method. The results of this study suggest a possible route for modeling and analysis of re-entrant systems.
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MODELING AND ANALYSIS OF SPLIT AND MERGE PRODUCTION SYSTEMSLiu, Yang 01 January 2008 (has links)
Many production systems have split and merge operations to increase production capac- ity and variety, improve product quality, and implement product control and scheduling policies. This thesis presents analytical methods to model and analyze split and merge production systems with Bernoulli and exponential reliability machines under circulate, priority and percentage policies. The recursive procedures for performance analysis are de- rived, and the convergence of the procedures and uniqueness of the solutions, along with the structural properties, are proved analytically, and the accuracy of the estimation is justi¯ed numerically with high precision. In addition, comparisons among the e®ects of di®erent policies in system performance are carried out.
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