Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.

Procesos de subjetivación y devenir corporal

El cuerpo, centro de atención de innumerables estudios y reflexiones que han buscado dar cuenta de la naturaleza del ser humano, es también la prueba más fehaciente de nuestra existencia. Sin embargo, la forma de caracterizarlo depende de los modos de subjetivación que estén atravesando un momento histórico determinado, lo cual redunda en una idea de cuerpo asociada a la manera en que individuos y colectividades construyen su existencia y sus formas de relacionarse. Esto puede ser mejor entendido bajo el concepto de corporalidad, en el sentido de diferenciar lo anteriormente descrito con la definición estereotipada y esencialista impuesta desde las ciencias positivistas, la cual enmarca al cuerpo en términos cosificados y funcionalistas. A continuación se presenta un breve recorrido histórico sobre la forma en que ciertos procesos de subjetivación han caracterizado la idea de cuerpo, y cómo esta ha marcado relaciones de poder de dominación e imposición. De esta manera pueden ser mejor entendidas, a través de un ejemplo puntual, diversas formas que tenemos de corporalizarnos desde perspectivas que superan a los poderes hegemónicos, posibilitando modos de existencia potentes, vitales

Procesos de subjetivación y devenir corporal

El cuerpo, centro de atención de innumerables estudios y reflexiones que han buscado dar cuenta de la naturaleza del ser humano, es también la prueba más fehaciente de nuestra existencia. Sin embargo, la forma de caracterizarlo depende de los modos de subjetivación que estén atravesando un momento histórico determinado, lo cual redunda en una idea de cuerpo asociada a la manera en que individuos y colectividades construyen su existencia y sus formas de relacionarse. Esto puede ser mejor entendido bajo el concepto de corporalidad, en el sentido de diferenciar lo anteriormente descrito con la definición estereotipada y esencialista impuesta desde las ciencias positivistas, la cual enmarca al cuerpo en términos cosificados y funcionalistas. A continuación se presenta un breve recorrido histórico sobre la forma en que ciertos procesos de subjetivación han caracterizado la idea de cuerpo, y cómo esta ha marcado relaciones de poder de dominación e imposición. De esta manera pueden ser mejor entendidas, a través de un ejemplo puntual, diversas formas que tenemos de corporalizarnos desde perspectivas que superan a los poderes hegemónicos, posibilitando modos de existencia potentes, vitales

Geometry of Dirac Operators

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M \hat{\mathcal{A}}(TM)\wedge \text{ch}(\mathcal{V}) \] where $\mathcal{V} =\text{Hom}_{\mathbb{C}l(TM)}(\slashed{\mathsf{S}},S)$. We prove the above statement with the means of the heat kernel of the heat semigroup $e^{-tD^2}$. The first outstanding result is the McKean-Singer theorem that describes the index in terms of the supertrace of the heat kernel. The trace of heat kernel is obtained from local geometric information. Moreover, if we use the asymptotic expansion of the kernel we will see that in the computation of the index only one term matters. The Berezin formula tells us that the supertrace is nothing but the coefficient of the Clifford top part, and at the end, Getzler calculus enables us to find the integral of these top parts in terms of characteristic classes.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Símbolos axiales en la poesía de José Ángel Valente

La poesía de José Ángel Valente posee una inusual densidad simbólica favorecida por la doble aspiración de abarcar tanto el extremo más grávido y material de la creación del autor, como aquel otro más etéreo y espiritual. Como componentes esenciales de esta búsqueda, podemos observar diversas imágenes (árbol, mandorla, hombre, cruz, etc.) que actuarán a modo de ejes simbólicos de su obra, ejes en torno a los cuales gira su universo poético. El estudio de los diferentes símbolos axiales, así como de otra serie de imágenes entendidas como proyecciones de aquéllos (laberinto, sierpe o nube), constituye el propósito del presente trabajo, tarea en la que relacionaremos cuanto vayamos descifrando con el sentido último de la poesía de José Ángel Valente.

Using virtual topology operations to generate analysis topology

Virtual topology operations have been utilized to generate an analysis topology definition suitable for downstream mesh generation. Detailed descriptions are provided for virtual topology merge and split operations for all topological entities. Current virtual topology technology is extended to allow the virtual partitioning of volume cells and the topological queries required to carry out each operation are provided. Virtual representations are robustly linked to the underlying geometric definition through an analysis topology. The analysis topology and all associated virtual and topological dependencies are automatically updated after each virtual operation, providing the link to the underlying CAD geometry. Therefore, a valid description of the analysis topology, including relative orientations, is maintained. This enables downstream operations, such as the merging or partitioning of virtual entities, and interrogations, such as determining if a specific meshing strategy can be applied to the virtual volume cells, to be performed on the analysis topology description. As the virtual representation is a non-manifold description of the sub-divided domain the interfaces between cells are recorded automatically. This enables the advantages of non-manifold modelling to be exploited within the manifold modelling environment of a major commercial CAD system, without any adaptation of the underlying CAD model. A hierarchical virtual structure is maintained where virtual entities are merged or partitioned. This has a major benefit over existing solutions as the virtual dependencies are stored in an open and accessible manner, providing the analyst with the freedom to create, modify and edit the analysis topology in any preferred sequence, whilst the original CAD geometry is not disturbed. Robust definitions of the topological and virtual dependencies enable the same virtual topology definitions to be accessed, interrogated and manipulated within multiple different CAD packages and linked to the underlying geometry.

New Organizational Leadership: Nonstate Actors in Global Economic Governance

States and international organizations have found irresistible cause in a globalizing world to coopt nonstate actors (NGOs, private standard setters and so forth) to manage the manifold problems arising under their stretched mandates and resources. The pooling of capacities in the pursuit of common goals seems perfectly sensible. Yet although the strategy of cooptation has become a policy of choice, policy makers often lack full knowledge of its implications. As Philip Selznick first showed, cooptation can have unintended consequences, shifting leadership from one organization to another. We place this fertile insight in a better specified analytical framework. That is, one capable of explaining when and how leadership shifts occur and where the status quo leaders will remain at the helm. Using original interview data and structured focused comparisons to test the framework, we reveal dramatic variation in leadership changes following the cooptation of outside actors in global financial and environmental governance.

Modeling of Turbulent Natural Gas and Biogas Flames of the Delft Jet-in-Hot-Coflow Burner: Effects of Coflow Temperature, Fuel Temperature and Fuel Composition on the Flame Lift-Off Height

The structure of a turbulent non-premixed flame of a biogas fuel in a hot and diluted coflow mimicking moderate and intense low dilution (MILD) combustion is studied numerically. Biogas fuel is obtained by dilution of Dutch natural gas (DNG) with CO2. The results of biogas combustion are compared with those of DNG combustion in the Delft Jet-in-Hot-Coflow (DJHC) burner. New experimental measurements of lift-off height and of velocity and temperature statistics have been made to provide a database for evaluating the capability of numerical methods in predicting the flame structure. Compared to the lift-off height of the DNG flame, addition of 30 % carbon dioxide to the fuel increases the lift-off height by less than 15 %. Numerical simulations are conducted by solving the RANS equations using Reynolds stress model (RSM) as turbulence model in combination with EDC (Eddy Dissipation Concept) and transported probability density function (PDF) as turbulence-chemistry interaction models. The DRM19 reduced mechanism is used as chemical kinetics with the EDC model. A tabulated chemistry model based on the Flamelet Generated Manifold (FGM) is adopted in the PDF method. The table describes a non-adiabatic three stream mixing problem between fuel, coflow and ambient air based on igniting counterflow diffusion flamelets. The results show that the EDC/DRM19 and PDF/FGM models predict the experimentally observed decreasing trend of lift-off height with increase of the coflow temperature. Although more detailed chemistry is used with EDC, the temperature fluctuations at the coflow inlet (approximately 100K) cannot be included resulting in a significant overprediction of the flame temperature. Only the PDF modeling results with temperature fluctuations predict the correct mean temperature profiles of the biogas case and compare well with the experimental temperature distributions.

Global efficiency of innovative rotational mold directly heated by thermal fluid

The article is focused on analysis of global efficiency of new mold for rotational molding of plastic parts, being directly heated by thermal fluid. The overall efficiency is based on several items such as reduction of cycle time, better uniformity of heating-cooling and low energy consumption. The new tool takes advantage of additive fabrication and electroforming for making the optimal manifold and cavity shell of the mold. Experimental test of a prototype mold was carried out on an experimental rotational molding machine, developed for this purpose, measuring wall temperature, and internal air temperature, with and without plastic material inside. Results were compared with conventional mold heated into an oven and to theoretical simulations done by Computational Fluid Dynamic software (CFD). The analysis represents considerable improvement of cycle time related to conventional methods (heated by oven) and better thermal uniformity to conventional procedures by direct heating of oil with external channels. In addition to thermal analysis an energetic efficiency study was done. POLYM. ENG. SCI., 52:1998-2005, 2012. © 2012 Society of Plastics Engineers Copyright © 2012 Society of Plastics Engineers.

Continuous statistical modelling for rapid detection of adulteration of extra virgin olive oil using mid infrared and Raman spectroscopic data

The main objective of this work was to develop a novel dimensionality reduction technique as a part of an integrated pattern recognition solution capable of identifying adulterants such as hazelnut oil in extra virgin olive oil at low percentages based on spectroscopic chemical fingerprints. A novel Continuous Locality Preserving Projections (CLPP) technique is proposed which allows the modelling of the continuous nature of the produced in-house admixtures as data series instead of discrete points. The maintenance of the continuous structure of the data manifold enables the better visualisation of this examined classification problem and facilitates the more accurate utilisation of the manifold for detecting the adulterants. The performance of the proposed technique is validated with two different spectroscopic techniques (Raman and Fourier transform infrared, FT-IR). In all cases studied, CLPP accompanied by k-Nearest Neighbors (kNN) algorithm was found to outperform any other state-of-the-art pattern recognition techniques.

Procesos de subjetivación y devenir corporal

El cuerpo, centro de atención de innumerables estudios y reflexiones que han buscado dar cuenta de la naturaleza del ser humano, es también la prueba más fehaciente de nuestra existencia. Sin embargo, la forma de caracterizarlo depende de los modos de subjetivación que estén atravesando un momento histórico determinado, lo cual redunda en una idea de cuerpo asociada a la manera en que individuos y colectividades construyen su existencia y sus formas de relacionarse. Esto puede ser mejor entendido bajo el concepto de corporalidad, en el sentido de diferenciar lo anteriormente descrito con la definición estereotipada y esencialista impuesta desde las ciencias positivistas, la cual enmarca al cuerpo en términos cosificados y funcionalistas. A continuación se presenta un breve recorrido histórico sobre la forma en que ciertos procesos de subjetivación han caracterizado la idea de cuerpo, y cómo esta ha marcado relaciones de poder de dominación e imposición. De esta manera pueden ser mejor entendidas, a través de un ejemplo puntual, diversas formas que tenemos de corporalizarnos desde perspectivas que superan a los poderes hegemónicos, posibilitando modos de existencia potentes, vitales

What is the Role of Attachment in Contemporary Psychotherapy? A Grounded Theory Exploration of the Perspective of Experienced Psychologists

Since Bowlby devised his theory of attachment, originally for clinical purposes, refinements and extensions have developed its clinical utility. The research question asked how experienced contemporary clinicians now perceive the role of attachment in the formulation and treatment of distress by reference to their clinical work. Using grounded theory methodology, underpinned by a relativist, moderate social constructionist epistemology, initial sampling consisted of 16 in-depth interviews with experienced clinicians. The tentative theoretical categories that emerged were then developed in theoretical sampling in further interviews with 5 of the initial interviewees. The final theoretical categories to emerge concerned the prevalence of caregiver-related problems, the provision of safety together with the prioritisation of the relationship with self as attachment-related treatment strategies, and attachment theory’s provision of understanding in problem formulation. Whilst this suggests that attachment-related ideas are integrated in contemporary practice, it also suggests that the clinical utility now offered by attachment theory, as established in the literature, has not found broad appeal amongst clinicians despite the commonness of attachment-related presenting problems. The implications of this are manifold. To begin with, attachment theorists have largely failed to bring the potential now offered by attachment-related therapeutic interventions to the market. This situation makes it incumbent on the next generation of attachment researchers to more clearly articulate techniques with which clinicians, of whatever theoretical orientation, can better leverage attachment-related knowledge in their clinical work. In this enterprise, perhaps the knowledge and experience of expert clinicians could be harvested, as this research has done. Moreover, researchers must expand the evidence base that such interventions actually work. Beyond the implications for clinical utility and efficacy, the findings strengthen counselling psychology’s influence on society’s perception and treatment of attachment-related problems.

The Herglotz variational problem on spheres and its optimal control approach

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.