An understanding of the mechanical properties of viral capsids (protein assemblies forming shell containers) has become necessary as their perceived use as nano-materials for targeted drug delivery. In this thesis, a heterogeneous, spatially detailed model of the viral capsid is considered. This model takes into account the increased degrees of freedom between the capsomers (capsid sub-structures) and the interactions between them to better reflect their deformation properties. A spatially realistic finite element multi-domain decomposition of viral capsid shells is also generated from atomistic PDB (Protein Data Bank) information, and non-linear continuum elastic simulations are performed. These results are compared to homogeneous shell simulation re- sults to bring out the importance of non-homogenous material properties in determining the deformation of the capsid. Finally, multiscale methods in structural analysis are reviewed to study their potential application to the study of nanoindentation of viral capsids. / text

X-ray crystallography is a technique for determining the structure (positions of atoms in space) of molecules. It is a well developed technique, and is applied routinely to both small inorganic and large organic molecules. However, the determination of the structures of large biological molecules by x-ray crystallography can still be an experimentally and computationally expensive task. The data in an x-ray experiment are the amplitudes of the Fourier transform of the electron density in the crystalline specimen. The structure determination problem in x-ray crystallography is therefore identical to a phase retrieval problem in image reconstruction, for which iterative transform algorithms are a common solution method. This thesis is concerned with iterative projection algorithms, a generalized and more powerful version of iterative transform algorithms, and their application to macromolecular x-ray crystallography. A detailed study is made of iterative projection algorithms, including their properties, convergence, and implementations. Two applications to macromolecular crystallography are then investigated. The first concerns reconstruction of binary image and the application of iterative projection algorithms to determining molecular envelopes from x-ray solvent contrast variation data. An effective method for determining molecular envelopes is developed. The second concerns the use of symmetry constraints and the application of iterative projection algorithms to ab initio determination of macromolecular structures from crystal diffraction data. The algorithm is tested on an icosahedral virus and a protein tetramer. The results indicate that ab initio phasing is feasible for structures containing 4-fold or 5-fold non-crystallographic symmetry using these algorithms if an estimate of the molecular envelope is available.

Our symposium will bring together experts from the German and international 'Inverse Problems Community' and young scientists. The focus will be on ill-posedness phenomena, regularization theory and practice, and on the analytical, numerical, and stochastic treatment of applied inverse problems in natural sciences, engineering, and finance.

Spanning tree congestion was defined by Ostrovskii (2004) as a measure of how well a network can perform if only minimal connection can be maintained. We compute the parameter for several families of graphs. In particular, by partitioning a hypercube into pieces with almost optimal edge-boundaries, we give tight estimates of the parameter thereby disproving a conjecture of Hruska (2008). For a typical random graph, the parameter exhibits a zigzag behaviour reflecting the feature that it is not monotone in the number of edges. This motivates the study of the most congested graphs where we show that any graph is close to a graph with small congestion. Next, we enumerate independent sets. Using the independent set polynomial, we compute the extrema of averages in trees and graphs. Furthermore, we consider inverse problems among trees and resolve a conjecture of Wagner (2009). A result in a more general setting is also proved which answers a question of Alon, Haber and Krivelevich (2011). After briefly considering polynomial invariants of general graphs, we specialize into trees. Three levels of tree distinguishing power are exhibited. We show that polynomials which do not distinguish rooted trees define typically exponentially large equivalence classes. On the other hand, we prove that the rooted Ising polynomial distinguishes rooted trees and that the Negami polynomial determines the subtree polynomial, strengthening results of Bollobás and Riordan (2000) and Martin, Morin and Wagner (2008). The top level consists of the chromatic symmetric function and it is proved to be a complete invariant for caterpillars.

The sparse coding is approximation/representation of signals with the minimum number of coefficients using an overcomplete set of elementary functions. This kind of approximations/ representations has found numerous applications in source separation, denoising, coding and compressed sensing. The adaptation of the sparse approximation framework to the coding problem of signals is investigated in this thesis. Open problems are the selection of appropriate models and their orders, coefficient quantization and sparse approximation method. Some of these questions are addressed in this thesis and novel methods developed. Because almost all recent communication and storage systems are digital, an easy method to compute quantized sparse approximations is introduced in the first part. The model selection problem is investigated next. The linear model can be adapted to better fit a given signal class. It can also be designed based on some a priori information about the model. Two novel dictionary selection methods are separately presented in the second part of the thesis. The proposed model adaption algorithm, called Dictionary Learning with the Majorization Method (DLMM), is much more general than current methods. This generality allowes it to be used with different constraints on the model. Particularly, two important cases have been considered in this thesis for the first time, Parsimonious Dictionary Learning (PDL) and Compressible Dictionary Learning (CDL). When the generative model order is not given, PDL not only adapts the dictionary to the given class of signals, but also reduces the model order redundancies. When a fast dictionary is needed, the CDL framework helps us to find a dictionary which is adapted to the given signal class without increasing the computation cost so much. Sometimes a priori information about the linear generative model is given in format of a parametric function. Parametric Dictionary Design (PDD) generates a suitable dictionary for sparse coding using the parametric function. Basically PDD finds a parametric dictionary with a minimal dictionary coherence, which has been shown to be suitable for sparse approximation and exact sparse recovery. Theoretical analyzes are accompanied by experiments to validate the analyzes. This research was primarily used for audio applications, as audio can be shown to have sparse structures. Therefore, most of the experiments are done using audio signals.

Two inverse problems are investigated in this dissertation, taking into account both the spatial and temporal aspects. The first problem addresses the under determined image reconstruction problem for dynamic SPECT. The quality of the reconstructed image is often limited due to having fewer observations than the number of voxels. The proposed algorithms make use of the generalized α-divergence function to improve the estimation performance. The first algorithm is based on an alternating minimization framework to minimize a regularized α-divergence objective function. We demonstrate that selecting an adaptive α policy depending on the time evolution of the voxels gives better performance than a fixed α assignment. The second algorithm is based on Newton's method. A regularized approach has been taken to avoid stability issues. Newton's method is generally computationally demanding due to the complexity associated with inverting the Hessian matrix. A fast Newton-based method is proposed using majorization-minimization techniques that diagonalize the Hessian matrix. In dynamically evolving systems, the prediction matrix plays an important role in the estimation process. An estimation technique is proposed to estimate the prediction matrix using the α-divergence function. The simulation results show that our algorithms provide better performance than the techniques based on the Kullback-Leibler distance. The second problem is the recovery of data transmitted over free-space optical communication channels using orbital angular momentum (OAM). In the presence of atmospheric turbulence, crosstalk occurs among OAM optical modes resulting in an error floor at a relatively high bit error rate. The modulation format considered for the underlying problem is Q-ary pulse position modulation (PPM). We propose and evaluate three joint detection strategies to overcome the OAM crosstalk problem: i) maximum likelihood sequence estimation (MLSE). ii) Q-PPM factor graph detection. iii) branch-and-bound detection. We compare the complexity and the bit-error-rate performance of these strategies in realistic scenarios.

In contrast with traditional extended depth-of-field approaches, we propose a depth-based deconvolution technique that realizes the depth-variant nature of the point spread function of an ordinary fixed-focus camera. The developed technique brings a single blurred image to focus at different depth planes which can be stitched together based on a depth map to output a full-focus image. Strategies to suppress the deconvolution's ringing artifacts are implemented on three levels: block tiling to eliminate boundary artifacts, reference maps to reduce ringing initiated by sharp edges, and depth-based masking to mitigate artifacts raised by neighboring depth-transition surfaces. The performance is validated numerically for planar and multidepth objects. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)

This work employs statistical and Bayesian techniques to analyze mathematical forward models with several sources of uncertainty. The forward models usually arise from phenomenological and physical phenomena and are expressed through regression-based models or partial differential equations (PDEs) associated with uncertain parameters and input data. One of the critical challenges in real-world applications is to quantify uncertainties of the unknown parameters using observations. To this purpose, methods based on the likelihood function, and Bayesian techniques constitute the two main statistical inferential approaches considered here. Two problems are studied in this thesis. The first problem is the prediction of fatigue life of metallic specimens. The second part is related to inverse problems in linear PDEs. Both problems require the inference of unknown parameters given certain measurements. We first estimate the parameters by means of the maximum likelihood approach. Next, we seek a more comprehensive Bayesian inference using analytical asymptotic approximations or computational techniques. In the fatigue life prediction, there are several plausible probabilistic stress-lifetime (S-N) models. These models are calibrated given uniaxial fatigue experiments. To generate accurate fatigue life predictions, competing S-N models are ranked according to several classical information-based measures. A different set of predictive information criteria is then used to compare the candidate Bayesian models. Moreover, we propose a spatial stochastic model to generalize S-N models to fatigue crack initiation in general geometries. The model is based on a spatial Poisson process with an intensity function that combines the S-N curves with an averaged effective stress that is computed from the solution of the linear elasticity equations.

Pour répondre au besoin de miniaturisation des spectromètres de terrain travaillant dans l’infrarouge, l’ONERA a développé un nouveau concept baptisé MICROSPOC. Ce dispositif est un détecteur infrarouge auquel a été intégré un interféromètre à deux ondes, constituant un spectromètre statique par transformée de Fourier. Ce plan focal infrarouge modifié, qui fusionne la fonction interférométrique et la fonction de détection, associé à une optique de tête simplifiée, permet d’envisager la réalisation d’instruments très compacts. L’objectif de cette thèse est de concevoir un spectromètre infrarouge miniature basé sur le dispositif MICROSPOC. Dans un premier temps, un travail théorique a été mené, dans l’objectif de dimensionner un système optique très compact. Notre choix s’étant orienté vers un système optique de collection (le détecteur voit une source étendue à distance finie), l’étude de l’acceptance angulaire de MICROSPOC dans ces conditions d’éclairement est indispensable afin de prévoir le contraste et la forme des franges d’interférence. Les résultats montreront la grande acceptance angulaire de MICROSPOC.Dans un second temps, un démonstrateur basé sur un composant MICROSPOC et sur le système optique simplifié a été réalisé. Ce démonstrateur a été caractérisé en laboratoire puis utilisé sur le terrain lors d’une campagne de mesures. Ces différentes exploitations ont montré la robustesse de l’instrument malgré l’obtention d’interférogrammes présentant divers défauts.Dans un troisième temps, une chaîne de traitement a été développée afin d’estimer un spectre à partir d’un interférogramme obtenu à l’aide du démonstrateur. Du fait des caractéristiques intrinsèques de MICROSPOC, la transformée de Fourier n’est pas la meilleure solution pour estimer un spectre. Nous l’avons montré en nous intéressant aux effets des disparités de longueur d’onde de coupure du détecteur sur l’estimation d’un spectre. Nous nous sommes alors tournés vers une approche consistant à utiliser la caractérisation spectrale de l’instrument pour inverser la mesure. Cette approche donne des résultats satisfaisants.Enfin, le but principal de cette thèse a été élargi par la conception et la réalisation de différents démonstrateurs combinant une fonction d’imagerie à une fonction de spectrométrie. Les premières pistes pour la conception d’un spectromètre qui tient dans la main ont été données. / In order to satisfy the need for handheld infrared spectrometers, the ONERA developed a new concept called MICROSPOC. This device is an infrared focal plane array with a built-in two-wave wedge-like interferometer and forms a static Fourier-transform spectrometer. This modified focal plane array, which merges the detection function and the interferometric function, in association with a simplified optical system, allows to consider the realisation of a much compact instrument. The goal of this thesis is to design and to realize a miniaturized infrared spectrometer based on the MICROSPOC concept.Firstly, a theoritical work has been led in order to design a compact optical system. Since we have chosen a collection optical system (the focal plane array sees an extended source placed at a finite distance), the study of MICROSPOC angular acceptance in these lightening conditions is needed in order to predict the contrast and the shape of interference fringes. The huge angular acceptance of MICROSPOC will be established with the results of this study.Secondly, a demonstrator based on MICROSPOC device and on the simplified optical system has been realized. This demonstrator has been caracterized in the laboratory and used in real conditions of a measurement campaign. These different exploitations have shown the robustness of the instrument despite some defaults on acquired interferograms.Then, a processing chain has been developed in order to estimate a spectrum from an interferogram acquired with our demonstrator. Considering the MICROSPOC’s own characteristics, the Fourier-transform is not the best way to estimate a spectrum. We have come to this conclusion by studying the effects of cut-off wavelenghts disparities of the detector on the spectrum estimation. At this point we have considered an approach that consists of using the spectral characterization of the instrument in order to inverse the measure. This approach gives satisfying results.Finaly, the main goal has been widened with the design and the realisation of other instruments that combine a spectrometric function and a imaging function. The first elements for the design of a handheld spectrometer have been given.

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