On the use of reproducing kernel Hilbert spaces in functional classification

The H\'ajek-Feldman dichotomy establishes that two Gaussian measures are either mutually absolutely continuous with respect to each other (and hence there is a Radon-Nikodym density for each measure with respect to the other one) or mutually singular. Unlike the case of finite dimensional Gaussian measures, there are non-trivial examples of both situations when dealing with Gaussian stochastic processes. This paper provides: (a) Explicit expressions for the optimal (Bayes) rule and the minimal classification error probability in several relevant problems of supervised binary classification of mutually absolutely continuous Gaussian processes. The approach relies on some classical results in the theory of Reproducing Kernel Hilbert Spaces (RKHS). (b) An interpretation, in terms of mutual singularity, for the "near perfect classification" phenomenon described by Delaigle and Hall (2012). We show that the asymptotically optimal rule proposed by these authors can be identified with the sequence of optimal rules for an approximating sequence of classification problems in the absolutely continuous case. (c) A new model-based method for variable selection in binary classification problems, which arises in a very natural way from the explicit knowledge of the RN-derivatives and the underlying RKHS structure. Different classifiers might be used from the selected variables. In particular, the classical, linear finite-dimensional Fisher rule turns out to be consistent under some standard conditions on the underlying functional model

Revisiting the problem of a crack impinging on an interface: A modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model

Artículo Open Access en el sitio web del editor. Pago por publicar en abierto.The problem of a crack impinging on an interface has been thoroughly investigated in the last three decades due to its important role in the mechanics and physics of solids. In the current investigation, this problem is revisited in view of the recent progresses on the phase field approach of brittle fracture. In this concern, a novel formulation combining the phase field approach for modeling brittle fracture in the bulk and a cohesive zone model for pre-existing adhesive interfaces is herein proposed to investigate the competition between crack penetration and deflection at an interface. The model, implemented within the finite element method framework using a monolithic fully implicit solution strategy, is applied to provide a further insight into the understanding of the role of model parameters on the above competition. In particular, in this study, the role of the fracture toughness ratio between the interface and the adjoining bulks and of the characteristic fracture-length scales of the dissipative models is analyzed. In the case of a brittle interface, the asymptotic predictions based on linear elastic fracture mechanics criteria for crack penetration, single deflection or double deflection are fully captured by the present method. Moreover, by increasing the size of the process zone along the interface, or by varying the internal length scale of the phase field model, new complex phenomena are emerging, such as simultaneous crack penetration and deflection and the transition from single crack penetration to deflection and penetration with subsequent branching into the bulk. The obtained computational trends are in very good agreement with previous experimental observations and the theoretical considerations on the competition and interplay between both fracture mechanics models open new research perspectives for the simulation and understanding of complex fracture patterns.Unión Europea FP/2007-2013/ERC 306622Ministerio de Economía y Competitividad DPI2012-37187, MAT2015-71036-P y MAT2015-71309-PJunta de Andalucía P11-TEP-7093 y P12-TEP- 105

Fotografía, voluntad e incertidumbre

En este artículo se traza un parangón entre la obra fotográfica (fija y en movimiento) de Leni Riefensthal y el pensamiento del físico cuántico Werner Heisenberg. Ambos autores son coetáneos, y guardan en común el servicio prestado al régimen nacionalsocialista de la Alemania nazi. Una, con la producción de una obra gráfica idealizadora del pueblo ario y de sus líderes; el otro, poniendo a disposición de su país su experiencia y conocimientos científicos a la hora de desarrollar la bomba atómica alemana. Sin embargo, en esta ocasión se atiende mayormente al substrato intelectual y estético subyacente en sus obras, antes que a sus biografías. Y es la fotografía el elemento que nos sirve para analizar esta coincidencia de miras y de actitudes estéticas y filosóficas. Mientras que en el caso de la fotógrafo y cineasta es el tono grandilocuente y altivo de su obra lo que resalta, en consonancia con la aguda observación de Walter Benjamin de la estetizoción que hace el fascismo de la política; en el caso del insigne físico, lo que destaca son sus conclusiones de carácter neoplatónico a raíz de la formulación de sus famosas relaciones de incertidumbre , que se deben sorprendentemente a una serie de reflexiones hechas en torno a las fotografías del trazo de las partículas atómicas tal como se manifiestan en la cámara de niebla. Ciencia y arte se dan la mano en la trastienda del pensamiento, a través de un instrumento tan moderno como es el fotográfico. Expresión y conocimiento, las dos potencialidades más destacables de la cámara, encuentran un punto en común en el pensamiento y estética sublimadores de la realidad de estos dos autores alemanes. La esencia del pueblo alemán, retratada por medio de atletas apolíneos, de voces altivas y decorados grandilocuentes de mármol y granito, como rememoración de aquel arte clásico grecolatino, regido por cánones geométricos, y aquí entendido de cartón piedra, tiende la mano al principio de indeterminación, verdadera espada de Damocles suspendida sobre la cabeza de la física moderna, e interpretado por el físico alemán como un baluarte de las relaciones formales, puras y geométricas, que definen la esencia del mundo y de las cosas. La fotografía, de ser un instrumento de observación positivista al servicio de la ciencia del siglo XIX, pasó a ser cuestionada, junto a sus productos, por un nuevo idealismo que demostraba su fuerza arrolladora y salvaje tanto en la ciencia y el arte como en la política del siglo XX.This article establishes a relationship between the photographic work (films and photography) of Leni Riefensthal and the philosophical ideas of the quantum physicist Werner Heisenberg.. These authors are contemporaries and hove in common their service to the National Socialist party in Germany. The first, through the production of an idealizing graphical work of an Aryan people and its leaders; the second, by helping the German atomic bomb project with his scientific experience and knowledge. On this occasion however we look into their intellectual and aesthetic principies rather than at their personal biographies. Photography is the element which helps us analyse a conc urrence in their artistic and philosophical outlook and attitudes. While in the case of the photographer and filmmaker Leni Riefensthal it is pomposity and arrogance which best defines her work, in accordance with Walter Benjamin 's observation of political aesthetication by fascism: in the case of the notorious physicist, his neoplatonic conc/usions as a result of his famous uncertainty relations stand out. The latter is surprisingly related to sorne observations he made after taking into consideration a number of c/oud chamber photographs of atomic portie/es. Science and art encounter each other behind thought through the modern instrument of photography. Expression and knowledge, the two m ost outstanding potentialities of the camera, find a common ground in the subliminal thinking and aesthetics of these two German authors. The essence of the German people, portrayed in film by Leni Riefensthal as Apol/onian athletes, haughty voices and grandiloquent statues of marble and granite in remembrance of c/assical Greco-latin art, ruled by geometric cannons, but understood here as cardboard work, stretches its hand to the uncertainty principie, as a truly Damoc/es sword suspended over the head of modern physics, and interpreted by Heisenberg as a bastion of those formal relationships, pure and geometric, which define the world and the essence of things. Photography and its products, after being a positivist observational instrument at the service of XIX century science, were questioned by this new idealism which showed its savage force in XX century art, science and politics.Publicad

lmage, imagination and matter

Este artículo pretende ahondar en el sentido y valor que adoptan las imágenes tecnológicas y mentales en los procesos de creación artística y documental, y de adquisición de conocimiento. El objetivo es buscar interrelaciones entre las actividades creativas y científicas fundamentadas en la utilización común de imágenes mentales e imágenes tecnológicas. La separación drástica entre ciencias y humanidades ha imposibilitado una visión de conjunto de los procesos cognitivos. La imagen, en su doble acepción: mental y técnica, nos brinda la oportunidad de realizar estudios transversales que unifiquen áreas hasta ahora entendidas tan dispares como la epistemología, la estética y la ética.This article focuses on the sense and value of technical and mental images in the process of artistic and documentary creativity as wefl as of knowledge acquisition. The main goal is to look for interrelations between creative and scientific works based on the use of mental and technological images. The extreme separation between sciences and humanities impede us a global vision of cognitive operations. lmage and its double value, as mental and technical, offers us the opportunity of developing transdisciplinary studies which put together oreas such as epistemology, aesthetics and ethics.Publicad

Imagen de la pobreza, pobreza de la imagen

La pobreza es fruto de un desequilibrio social caracterizado por el sometimiento de grandes capas de la población a condiciones infrahumanas en términos de salud, educación, alimentación, vivienda y desarrollo afectivo, y cuyas raíces se encuentran en las relaciones productivas y de dominio vigentes en cada una de las etapas de la historia. La imagen de la pobreza construida a lo largo de los siglos en las artes plásticas, la fotografía y el cine desempeña un papel de intervención ideológica al servicio de las diferentes clases y grupos sociales. El enfrentamiento dialéctico que se produce en lo social y económico entre estos grupos se refleja asimismo en la representación que se lleva a cabo de la pobreza: desde la idealización, ocultamiento y desvirtuación de la misma, a la postura crítica y comprometida que intenta devolver esa realidad a la sociedad. Analizar la pobreza a partir de la imagen que se ha construido de ella a través del tiempo, en este caso desde la revolución industrial a nuestros días, establece un cruce de caminos de sumo interés para la sociología, la antropología, la historia y la teoría de la imagen

Fracture of solar-grade anisotropic polycrystalline Silicon: A combined phase field–cohesive zone model approach

Artículo Open Access en el sitio web del editor. Pago por publicar en abierto.This work presents a novel computational framework to simulate fracture events in brittle anisotropic polycrystalline materials at the microscopical level, with application to solar-grade polycrystalline Silicon. Quasi-static failure is modeled by combining the phase field approach of brittle fracture (for transgranular fracture) with the cohesive zone model for the grain boundaries (for intergranular fracture) through the generalization of the recent FE-based technique published in [M. Paggi, J. Reinoso, Comput. Methods Appl. Mech. Engrg., 31 (2017) 145–172] to deal with anisotropic polycrystalline microstructures. The proposed model, which accounts for any anisotropic constitutive tensor for the grains depending on their preferential orientation, as well as an orientation-dependent fracture toughness, allows to simulate intergranular and transgranular crack growths in an efficient manner, with or without initial defects. One of the advantages of the current variational method is the fact that complex crack patterns in such materials are triggered without any user-intervention, being possible to account for the competition between both dissipative phenomena. In addition, further aspects with regard to the model parameters identification are discussed in reference to solar cells images obtained from transmitted light source. A series of representative numerical simulations is carried out to highlight the interplay between the different types of fracture occurring in solar-grade polycrystalline Silicon, and to assess the role of anisotropy on the crack path and on the apparent tensile strength of the material.Unión Europea FP/2007–2013/ERC 306622Ministerio de Economía y Competitividad MAT2015–71036-P y MAT2015–71309-PJunta de Andalucía P11-TEP-7093 y P12-TEP- 105