Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Regression models with MoPs Bayesian networks

We present a model of Bayesian network for continuous variables, where densities and conditional densities are estimated with B-spline MoPs. We use a novel approach to directly obtain conditional densities estimation using B-spline properties. In particular we implement naive Bayes and wrapper variables selection. Finally we apply our techniques to the problem of predicting neurons morphological variables from electrophysiological ones.

Truncation error estimation in the Discontinuous Galerkin Spectral Element Method

En esta tesis, el método de estimación de error de truncación conocido como restimation ha sido extendido de esquemas de bajo orden a esquemas de alto orden. La mayoría de los trabajos en la bibliografía utilizan soluciones convergidas en mallas de distinto refinamiento para realizar la estimación. En este trabajo se utiliza una solución en una única malla con distintos órdenes polinómicos. Además, no se requiere que esta solución esté completamente convergida, resultando en el método conocido como quasi-a priori T-estimation. La aproximación quasi-a priori estima el error mientras el residuo del método iterativo no es despreciable. En este trabajo se demuestra que algunas de las hipótesis fundamentales sobre el comportamiento del error, establecidas para métodos de bajo orden, dejan de ser válidas en esquemas de alto orden, haciendo necesaria una revisión completa del comportamiento del error antes de redefinir el algoritmo. Para facilitar esta tarea, en una primera etapa se considera el método conocido como Chebyshev Collocation, limitando la aplicación a geometrías simples. La extensión al método Discontinuouos Galerkin Spectral Element Method presenta dificultades adicionales para la definición precisa y la estimación del error, debidos a la formulación débil, la discretización multidominio y la formulación discontinua. En primer lugar, el análisis se enfoca en leyes de conservación escalares para examinar la precisión de la estimación del error de truncación. Después, la validez del análisis se demuestra para las ecuaciones incompresibles y compresibles de Euler y Navier Stokes. El método de aproximación quasi-a priori r-estimation permite desacoplar las contribuciones superficiales y volumétricas del error de truncación, proveyendo información sobre la anisotropía de las soluciones así como su ratio de convergencia con el orden polinómico. Se demuestra que esta aproximación quasi-a priori produce estimaciones del error de truncación con precisión espectral. ABSTRACT In this thesis, the τ-estimation method to estimate the truncation error is extended from low order to spectral methods. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimation, only one grid with different polynomial orders is used in this work. Furthermore, a non timeconverged solution is used resulting in the quasi-a priori τ-estimation method. The quasi-a priori approach estimates the error when the residual of the time-iterative method is not negligible. It is shown in this work that some of the fundamental assumptions about error tendency, well established for low order methods, are no longer valid in high order schemes, making necessary a complete revision of the error behavior before redefining the algorithm. To facilitate this task, the Chebyshev Collocation Method is considered as a first step, limiting their application to simple geometries. The extension to the Discontinuous Galerkin Spectral Element Method introduces additional features to the accurate definition and estimation of the error due to the weak formulation, multidomain discretization and the discontinuous formulation. First, the analysis focuses on scalar conservation laws to examine the accuracy of the estimation of the truncation error. Then, the validity of the analysis is shown for the incompressible and compressible Euler and Navier Stokes equations. The developed quasi-a priori τ-estimation method permits one to decouple the interfacial and the interior contributions of the truncation error in the Discontinuous Galerkin Spectral Element Method, and provides information about the anisotropy of the solution, as well as its rate of convergence in polynomial order. It is demonstrated here that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error.

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Enhancing regression models for complex systems using evolutionary techniques for feature engineering

This work proposes an automatic methodology for modeling complex systems. Our methodology is based on the combination of Grammatical Evolution and classical regression to obtain an optimal set of features that take part of a linear and convex model. This technique provides both Feature Engineering and Symbolic Regression in order to infer accurate models with no effort or designer's expertise requirements. As advanced Cloud services are becoming mainstream, the contribution of data centers in the overall power consumption of modern cities is growing dramatically. These facilities consume from 10 to 100 times more power per square foot than typical office buildings. Modeling the power consumption for these infrastructures is crucial to anticipate the effects of aggressive optimization policies, but accurate and fast power modeling is a complex challenge for high-end servers not yet satisfied by analytical approaches. For this case study, our methodology minimizes error in power prediction. This work has been tested using real Cloud applications resulting on an average error in power estimation of 3.98%. Our work improves the possibilities of deriving Cloud energy efficient policies in Cloud data centers being applicable to other computing environments with similar characteristics.

System failure prediction through rare-events elastic-net logistic regression

Predicting failures in a distributed system based on previous events through logistic regression is a standard approach in literature. This technique is not reliable, though, in two situations: in the prediction of rare events, which do not appear in enough proportion for the algorithm to capture, and in environments where there are too many variables, as logistic regression tends to overfit on this situations; while manually selecting a subset of variables to create the model is error- prone. On this paper, we solve an industrial research case that presented this situation with a combination of elastic net logistic regression, a method that allows us to automatically select useful variables, a process of cross-validation on top of it and the application of a rare events prediction technique to reduce computation time. This process provides two layers of cross- validation that automatically obtain the optimal model complexity and the optimal mode l parameters values, while ensuring even rare events will be correctly predicted with a low amount of training instances. We tested this method against real industrial data, obtaining a total of 60 out of 80 possible models with a 90% average model accuracy.

Polynomial regression using a perceptron with axo-axonic connections

Social behavior is mainly based on swarm colonies, in which each individual shares its knowledge about the environment with other individuals to get optimal solutions. Such co-operative model differs from competitive models in the way that individuals die and are born by combining information of alive ones. This paper presents the particle swarm optimization with differential evolution algorithm in order to train a neural network instead the classic back propagation algorithm. The performance of a neural network for particular problems is critically dependant on the choice of the processing elements, the net architecture and the learning algorithm. This work is focused in the development of methods for the evolutionary design of artificial neural networks. This paper focuses in optimizing the topology and structure of connectivity for these networks

Age regression from soft aligned face images using low computational resources

The initial step in most facial age estimation systems consists of accurately aligning a model to the output of a face detector (e.g. an Active Appearance Model). This fitting process is very expensive in terms of computational resources and prone to get stuck in local minima. This makes it impractical for analysing faces in resource limited computing devices. In this paper we build a face age regressor that is able to work directly on faces cropped using a state-of-the-art face detector. Our procedure uses K nearest neighbours (K-NN) regression with a metric based on a properly tuned Fisher Linear Discriminant Analysis (LDA) projection matrix. On FG-NET we achieve a state-of-the-art Mean Absolute Error (MAE) of 5.72 years with manually aligned faces. Using face images cropped by a face detector we get a MAE of 6.87 years in the same database. Moreover, most of the algorithms presented in the literature have been evaluated on single database experiments and therefore, they report optimistically biased results. In our cross-database experiments we get a MAE of roughly 12 years, which would be the expected performance in a real world application.

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

In this paper three p-adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous Galerkin methods. The truncation error is approximated by means of a ? -estimation procedure and enables the identification of mesh regions that require adaptation. Three adaptation strategies are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. All strategies require fine solutions, which are obtained by enriching the polynomial order, but while the former needs time converged solutions, the last two rely on non-converged solutions, which lead to faster computations. In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier?Stokes equations. It is shown that the two quasi- a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively.

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

In this work a p-adaptation (modification of the polynomial order) strategy based on the minimization of the truncation error is developed for high order discontinuous Galerkin methods. The truncation error is approximated by means of a truncation error estimation procedure and enables the identification of mesh regions that require adaptation. Three truncation error estimation approaches are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. Fine solutions, which are obtained by enriching the polynomial order, are required to solve the numerical problem with adequate accuracy. For the three truncation error estimation methods the former needs time converged solutions, while the last two rely on non-converged solutions, which lead to faster computations. Based on these truncation error estimation methods, algorithms for mesh adaptation were designed and tested. Firstly, an isotropic adaptation approach is presented, which leads to equally distributed polynomial orders in different coordinate directions. This first implementation is improved by incorporating a method to extrapolate the truncation error. This results in a significant reduction of computational cost. Secondly, the employed high order method permits the spatial decoupling of the estimated errors and enables anisotropic p-adaptation. The incorporation of anisotropic features leads to meshes with different polynomial orders in the different coordinate directions such that flow-features related to the geometry are resolved in a better manner. These adaptations result in a significant reduction of degrees of freedom and computational cost, while the amount of improvement depends on the test-case. Finally, this anisotropic approach is extended by using error extrapolation which leads to an even higher reduction in computational cost. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. The main result is that the two quasi-a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of a factor of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively. RESUMEN En este trabajo se ha desarrollado una estrategia de adaptación-p (modificación del orden polinómico) para métodos Galerkin discontinuo de alto orden basada en la minimización del error de truncación. El error de truncación se estima utilizando el método tau-estimation. El estimador permite la identificación de zonas de la malla que requieren adaptación. Se distinguen tres técnicas de estimación: a posteriori, quasi a priori y quasi a priori con correción. Todas las estrategias requieren una solución obtenida en una malla fina, la cual es obtenida aumentando de manera uniforme el orden polinómico. Sin embargo, mientras que el primero requiere que esta solución esté convergida temporalmente, el resto utiliza soluciones no convergidas, lo que se traduce en un menor coste computacional. En este trabajo se han diseñado y probado algoritmos de adaptación de malla basados en métodos tau-estimation. En primer lugar, se presenta un algoritmo de adaptacin isótropo, que conduce a discretizaciones con el mismo orden polinómico en todas las direcciones espaciales. Esta primera implementación se mejora incluyendo un método para extrapolar el error de truncación. Esto resulta en una reducción significativa del coste computacional. En segundo lugar, el método de alto orden permite el desacoplamiento espacial de los errores estimados, permitiendo la adaptación anisotropica. Las mallas obtenidas mediante esta técnica tienen distintos órdenes polinómicos en cada una de las direcciones espaciales. La malla final tiene una distribución óptima de órdenes polinómicos, los cuales guardan relación con las características del flujo que, a su vez, depenen de la geometría. Estas técnicas de adaptación reducen de manera significativa los grados de libertad y el coste computacional. Por último, esta aproximación anisotropica se extiende usando extrapolación del error de truncación, lo que conlleva un coste computational aún menor. Las estrategias se verifican y se comparan en téminors de precisión y coste computacional utilizando las ecuaciones de Euler y Navier Stokes. Los dos métodos quasi a priori consiguen una reducción significativa del coste computacional en comparación con aumento uniforme del orden polinómico. En concreto, para una capa límite viscosa, obtenemos una mejora en tiempo de computación de 6.6 y 7.6 respectivamente, para las aproximaciones quasi-a priori y quasi-a priori con corrección.

Conditional switching of vascular endothelial growth factor (VEGF) expression in tumors: Induction of endothelial cell shedding and regression of hemangioblastoma-like vessels by VEGF withdrawal

We have recently shown that VEGF functions as a survival factor for newly formed vessels during developmental neovascularization, but is not required for maintenance of mature vessels. Reasoning that expanding tumors contain a significant fraction of newly formed and remodeling vessels, we examined whether abrupt withdrawal of VEGF will result in regression of preformed tumor vessels. Using a tetracycline-regulated VEGF expression system in xenografted C6 glioma cells, we showed that shutting off VEGF production leads to detachment of endothelial cells from the walls of preformed vessels and their subsequent death by apoptosis. Vascular collapse then leads to hemorrhages and extensive tumor necrosis. These results suggest that enforced withdrawal of vascular survival factors can be applied to target preformed tumor vasculature in established tumors. The system was also used to examine phenotypes resulting from over-expression of VEGF. When expression of the transfected VEGF cDNA was continuously “on,” tumors became hyper-vascularized with abnormally large vessels, presumably arising from excessive fusions. Tumors were significantly less necrotic, suggesting that necrosis in these tumors is the result of insufficient angiogenesis.

Evidence for protein X binding to a discontinuous epitope on the cellular prion protein during scrapie prion propagation

Studies on the transmission of human (Hu) prions to transgenic (Tg) mice suggested that another molecule provisionally designated protein X participates in the formation of nascent scrapie isoform of prion protein (PrPSc). We report the identification of the site at which protein X binds to the cellular isoform of PrP (PrPC) using scrapie-infected mouse (Mo) neuroblastoma cells transfected with chimeric Hu/MoPrP genes even though protein X has not yet been isolated. Substitution of a Hu residue at position 214 or 218 prevented PrPSc formation. The side chains of these residues protrude from the same surface of the C-terminal α-helix and form a discontinuous epitope with residues 167 and 171 in an adjacent loop. Substitution of a basic residue at positions 167, 171, or 218 also prevented PrPSc formation: at a mechanistic level, these mutant PrPs appear to act as “dominant negatives” by binding protein X and rendering it unavailable for prion propagation. Our findings seem to explain the protective effects of basic polymorphic residues in PrP of humans and sheep and suggest therapeutic and prophylactic approaches to prion diseases.

Interleukin 12 and B7-1 costimulatory molecule expressed by an adenovirus vector act synergistically to facilitate tumor regression

Stimulation of antitumor immune mechanisms is the primary goal of cancer immunotherapy, and accumulating evidence suggests that effective alteration of the host–tumor relationship involves immunomodulating cytokines and also the presence of costimulatory molecules. To examine the antitumor effect of direct in vivo gene transfer of murine interleukin 12 (IL-12) and B7-1 into tumors, we developed an adenovirus (Ad) vector, AdIL12–B7-1, that encodes the two IL-12 subunits in early region 1 (E1) and the B7-1 gene in E3 under control of the murine cytomegalovirus promoter. This vector expressed high levels of IL-12 and B7-1 in infected murine and human cell lines and in primary murine tumor cells. In mice bearing tumors derived from a transgenic mouse mammary adenocarcinoma, a single intratumoral injection with a low dose (2.5 × 107 pfu/mouse) of AdIL12–B7-1 mediated complete regression in 70% of treated animals. By contrast, administration of a similar dose of recombinant virus encoding IL-12 or B7-1 alone resulted in only a delay in tumor growth. Interestingly, coinjection of two different viruses expressing either IL-12 or B7-1 induced complete tumor regression in only 30% of animals treated at this dose. Significantly, cured animals remained tumor free after rechallenge with fresh tumor cells, suggesting that protective immunity had been induced by treatment with AdIL12–B7-1. These results support the use of Ad vectors as a highly efficient delivery system for synergistically acting molecules and show that the combination of IL-12 and B7-1 within a single Ad vector might be a promising approach for in vivo cancer therapy.

The heme oxygenase gene (pbsA) in the red alga Rhodella violacea is discontinuous and transcriptionally activated during iron limitation

Heme oxygenase (HO) catalyzes the opening of the heme ring with the release of iron in both plants and animals. In cyanobacteria, red algae, and cryptophyceae, HO is a key enzyme in the synthesis of the chromophoric part of the photosynthetic antennae. In an attempt to study the regulation of this key metabolic step, we cloned and sequenced the pbsA gene encoding this enzyme from the red alga Rhodella violacea. The gene is located on the chloroplast genome, split into three distant exons, and is presumably expressed by a trans-splicing mechanism. The deduced polypeptide sequence is homologous to other reported HOs from organisms containing phycobilisomes (Porphyra purpurea and Synechocystis sp. strain PCC 6803) and, to a lesser extent, to vertebrate enzymes. The expression is transcriptionally activated under iron deprivation, a stress condition frequently encountered by algae, suggesting a second role for HO as an iron-mobilizing agent in photosynthetic organisms.

Interferon-β gene therapy inhibits tumor formation and causes regression of established tumors in immune-deficient mice

Despite the potential of type 1 interferons (IFNs) for the treatment of cancer, clinical experience with IFN protein therapy of solid tumors has been disappointing. IFN-β has potent antiproliferative activity against most human tumor cells in vitro in addition to its known immunomodulatory activities. The antiproliferative effect, however, relies on IFN-β concentrations that cannot be achieved by parenteral protein administration because of rapid protein clearance and systemic toxicities. We demonstrate here that ex vivo IFN-β gene transduction by a replication-defective adenovirus in as few as 1% of implanted cells blocked tumor formation. Direct in vivo IFN-β gene delivery into established tumors generated high local concentrations of IFN-β, inhibited tumor growth, and in many cases caused complete tumor regression. Because the mice were immune-deficient, it is likely that the anti-tumor effect was primarily through direct inhibition of tumor cell proliferation and survival. Based on these studies, we argue that local IFN-β gene therapy with replication-defective adenoviral vectors might be an effective treatment for some solid tumors.