Insertion pre-Lie products and translation of rough paths based on multi-indices

We use the diagram-free approach to regularity structures introduced by Otto et. al. to build rough paths based on multi-indices. We identify the analogue of the insertion pre-Lie algebra of trees and use it to build the corresponding group of translations of rough paths. We make this identification precise by showing that the natural dictionary between trees and multi-indices is a pre-Lie morphism under insertion, which in turn yields a Hopf algebra morphism to the rooted tree Hopf algebra equipped with the extraction-contraction coproduct.Comment: 37 page

On a tree-free approach to regularity structures for quasi-linear stochastic partial differential equations

We consider the approach to regularity structures introduced by Otto, Sauer, Smith and Weber to obtain a priori bounds for quasi-linear SPDEs. This approach replaces the index set of trees, used in the original constructions of Hairer et. al., by multi-indices describing products of derivatives of the corresponding nonlinearity. The two tasks of this thesis are: - Construction and estimates of the model. We first provide the construction of a model in the regular, deterministic setting, where negative renormalization can be avoided. We later extend these ideas to the singular case, incorporating BPHZ-renormalization under spectral gap assumptions as a convenient input for an automated proof of the stochastic estimates of the singular model in the full subcritical regime. - Characterization of the algebraic structures generated by the multi-index setting. We consider natural actions on functionals of the nonlinearity and build a (pre-)Lie algebra from them. We use this as the starting point of an algebraic path towards the structure group, which as in the regularity structures literature is based on a Hopf algebra. This approach further allows us to explore the relation between multi-indices and trees, which we express through pre-Lie and Hopf algebra morphisms, in certain semi-linear equations. All the results are based on a series of joint works with Otto, Tempelmayr and Tsatsoulis

A top-down approach to algebraic renormalization in regularity structures based on multi-indices

We provide an algebraic framework to describe renormalization in regularity structures based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is ``top-down", in the sense that we postulate the form of the counterterm and use the renormalized equation to build a canonical smooth model for it. The core of the construction is a generalization of the Hopf algebra of derivations in [LOT23], which is extended beyond the structure group to describe the model equation via an exponential map: This allows to implement a renormalization procedure which resembles the preparation map approach in our context.Comment: 65 page

Desarrollo de nuevos acabados sostenibles y energías renovables en módulos preindustrializados

Estudio de nuevas soluciones de acabados ecoeficientes y sostenibles en módulos pre-industrializados y prefabricados. Implantación de dichas soluciones para realizaciones en las que se prevea una minimización de la problemática de la puesta en obra con una importante reducción de plazo en su instalación

The structure group for quasi-linear equations via universal enveloping algebras

We consider the approach of replacing trees by (fewer) multi-indices as an index set of the abstract model space $\mathsf{T}$ to tackle quasi-linear singular SPDEs. We show that this approach is consistent with the postulates of regularity structures when it comes to the structure group $\mathsf{G}$. In particular, $\mathsf{G}\subset{\rm Aut}(\mathsf{T})$ arises from a Hopf algebra $\mathsf{T}^+$ and a comodule $\Delta\colon\mathsf{T}\rightarrow \mathsf{T}^+\otimes\mathsf{T}$. This approach allows to interpret $\mathsf{G}^*\subset{\rm Aut}(\mathsf{T}^*)$ as a Lie group arising from a Lie algebra $\mathsf{L} \subset{\rm End}(\mathsf{T}^*)$ consisting of derivations; these derivations in turn are the infinitesimal generators arising from actions on the space of pairs (nonlinearities, functions of space-time). The Hopf algebra $\mathsf{T}^+$ arises from a coordinate representation of the universal enveloping algebra ${\rm U}(\mathsf{L})$ of the Lie algebra $\mathsf{L}$. The coordinates arise from an underlying pre-Lie algebra structure of $\mathsf{L}$. Strong finiteness properties, which are enforced by gradedness and the restrictive definition of $\mathsf{T}$, allow to define these structures in our infinite-dimensional setting.Comment: 50 page

Diseño de un filtro de condensadores conmutados Fleisher-Laker mediante técnicas P2D

En muchas aplicaciones de la electrónica contemporánea se requiere la implementación de filtros analógicos o conversores analógico-digitales. Cuando las frecuencias de las señales objetivo de estos circuitos son del orden de los kHz o inferiores, el ruido de baja frecuencia, especialmente el de tipo flicker, se hace dominante. Recientemente se ha propuesto la estructura pseudo-pseudo diferencial para paliar los efectos de este ruido en los circuitos de condensadores conmutados. Sin embargo, aún no se ha publicado ninguna estructura que permita aplicar esta técnica en un filtro completo. En este trabajo se estudia la posibilidad de aplicar la técnica pseudo-pseudo diferencial en una sección bicuadrática Fleisher-Laker, ofreciendo una posible forma de solventar las dificultades que acarrea y exponiendo las limitaciones que entraña. Además, se realiza una implementación de un filtro de estas características en una tecnología de 180 nm y se presentan los resultados obtenidos.Universidad de Sevilla. Grado en Ingeniería de las Tecnologías de Telecomunicació

Relación entre la actividad endoscópica e histológica, el desarrollo microvascular y la expresión de los factores angiogénicos y linfangiogénicos en la mucosa cólica de pacientes con enfermedad inflamatoria intestinal

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Medicina, Departamento de Medicina. Fecha de lectura: 27-06-2016Objetivo: Investigar la relación entre la angiogénesis y la linfangiogénesis en biopsias de mucosa intestinal y la actividad endoscópica e histológica de pacientes con enfermedad inflamatoria intestinal (EII). Métodos: Se incluyeron prospectivamente pacientes con y sin EII que acudieron a realizarse una colonoscopia por práctica clínica. El grado de actividad endoscópica se determinó mediante el subíndice endoscópico de Mayo para la colitis ulcerosa (CU) y el SES-CD para enfermedad de Crohn (EC). La expresión de los factores en mucosa cólica se determinó por inmunohistoquímica. Los resultados de la expresión de VEGF-A, -C, -D, -R1, -R2, -R3 y PlGF se clasificaron como sigue: (++) si se tiñeron más del 50% de las células del tejido, (+) por debajo del 50% y (-) tinción negativa. Ang-1, Ang-2 y Tie-2, y la densidad microvascular CD34 y D2.40, se evaluaron mediante el recuento directo en cinco campos de visión a un aumento de 40x. Resultados: Se incluyeron 58 pacientes con EII (36 CU y 22 EC) y 19 controles, y se evaluó un total de 101 biopsias. Se observó una mayor expresión de Ang-1 y -2 en las biopsias procedentes de segmentos intestinales con inflamación endoscópica grave comparada con las procedentes de tramos sin actividad endoscópica (p<0,01). La expresión de VEGF-D (p<0,05), PlGF (p<0,05) y VEGFR-3 (p<0,01), y la media de recuento de Ang-1 (p<0,05) y Ang-2 (p<0,01), fueron diferentes en función de la actividad histológica. La intensidad de la expresión aumentó en paralelo con la gravedad de las lesiones histológicas, excepto la de VEGF-D, que disminuyó. La expresión y el recuento medio de Ang-1, Ang-2, VEGFR-2 (p<0,01) y VEGF-C, -R1 y Tie-2 fueron mayores en las muestras de pacientes con CU que en las de EC (p<0,05). En los pacientes con EC, el recuento medio de Ang-1, y la expresión de VEGF-C, -D, -R2, -R3 y PlGF fue mayor (p<0,05), y del resto de los factores menor, que en los controles. La expresión de Ang-2 (p<0,05) y la de todos los factores estudiados fue mayor en las muestras de EC activa que en las inactivas. La expresión de todos los factores fue mayor en los pacientes con CU que en los controles (p<0,05). El recuento medio y la expresión de Ang-1, Ang-2 y VEGF-D fue menor (p<0,05) en las muestras con CU activa. El mayor área bajo la curva ROC para el diagnóstico de actividad endoscópica en CU fue de 0,72 para la Ang-1 (punto de corte 42,2: sensibilidad 53% y especificidad 67%). Conclusiones: La expresión de VEGF-A, -D, -R3, PlGF y Ang-1 y -2 en las biopsias de mucosa se correlaciona con la actividad histológica de la EII. La expresión de Ang-1 en muestras de mucosa constituye un marcador de desarrollo angiogénico en la EII. Los factores angiogénicos se expresan de manera diferente en la mucosa de los pacientes con EC y CU. Estos resultados sugieren un papel de estos factores en la actividad de la EIIAim: To evaluate the relationship between angiogenesis and lymphangiogenesis in colonic mucosa biopsies with the endoscopic and histological activity in patients with inflammatory bowel disease (IBD). Methods: Patients with and without IBD that underwent a colonoscopy because of medical criteria were prospectively included. Endoscopic activity was assessed by endoscopic Mayo subscore for ulcerative colitis (UC) and SES-CD for Crohn’s disease (CD). Protein expression in colonic mucosa was determined by immunohistochemistry. VEGF-A, -C, -D, -R1, -R2, -R3 and PlGF expression results were graded as follows: (++) over 50% of the tissue cells were stained, (+) below 50%, and (-) completely negative. Ang-1, Ang-2 and Tie-2, and micro vessel density CD34 and D2.40, were assessed as the average density of five hot spots at a magnification of x40. Results: 58 patients with IBD (36 UC and 22 CD) and 19 controls were included, and a total of 101 biopsies were evaluated. Higher expression of Ang-1 and Ang-2 was found when the endoscopic activity was severe compared to inactive disease (p<0.01). Expression of VEGF-D (p<0.05), PlGF (p<0.05) and VEGFR-3 (p<0.01), and mean count of Ang-1 (p<0.05) and Ang-2 (p<0.01) were also significantly different depending on the histological activity. These expressions were increased in parallel with the severity of histological lesions excepting for VEGF-D, which was decreased with the severity of the activity. Expression and mean count of Ang-1, Ang-2, VEGFR-2 (p<0.01), and VEGF-C, -R1 and Tie-2 were higher in samples from patients with UC compared to CD (p<0.05). In patients with CD, Ang-1 mean count, and expression of VEGF-C, -D, -R2, PlGF, and VEGFR-3, were higher (p<0.05), and the rest of factors were lower, than in controls. Expression of Ang-2 (p<0.05) and of all the studied factors were higher in active samples than in non-active CD; on the opposite, VEGF-D and -R3 were lower. In UC, expression of all factors were higher in patients with UC than in controls (p<0.05). Mean count and expression of Ang-1, Ang-2 were higher, and VEGF-D was lower (p<0.05) in samples with active, compared to inactive UC. The best area under the ROC curve for the diagnosis of endoscopic activity in UC was 0.72 for Ang-1 (cut-off at 42.2: 53% sensitivity and 67% specificity). Conclusions: The expression of VEGF-A, -D, -R3, PlGF, and Ang-1 and -2 in mucosal biopsies correlates with the histological activity of IBD. Ang-1 expression in mucosal samples is a marker of angiogenic development in IBD. Angiogenic factors are differentially expressed in mucosa from patients with CD and UC. These findings might support a role of angiogenic factors in IBD activit

La salud: monopolización o empoderamiento

Tesis de maestríaSe pretende analizar la temática jurídica y económica de la salud en Colombia, desde la Ley 100 de 1993 y, la Ley 209 de 2013, según ésta última, para brindar un mejor servicio y calidad en el Sistema de Salud. El análisis busca definir si lo que se pretende es darle participación a la comunidad, o, crear un monopolio estatal.MaestríaMagister en Ciencia Polític

Activated Carbon Fibre Monoliths for Hydrogen Storage

Porous adsorbents are currently investigated for hydrogen storage application. From a practical point of view, in addition to high porosity developments, high material densities are required, in order to confine as much material as possible in a tank device. In this study, we use different measured sample densities (tap, packing, compacted and monolith) for analyzing the hydrogen adsorption behavior of activated carbon fibres (ACFs) and activated carbon nanofibres (ACNFs) which were prepared by KOH and CO2 activations, respectively. Hydrogen adsorption isotherms are measured for all of the adsorbents at room temperature and under high pressures (up to 20 MPa). The obtained results confirm that (i) gravimetric H2 adsorption is directly related to the porosity of the adsorbent, (ii) volumetric H2 adsorption depends on the adsorbent porosity and importantly also on the material density, (iii) the density of the adsorbent can be improved by packing the original adsorbents under mechanical pressure or synthesizing monoliths from them, (iv) both ways (packing under pressure or preparing monoliths) considerably improve the storage capacity of the starting adsorbents, and (v) the preparation of monoliths, in addition to avoid engineering constrains of packing under mechanical pressure, has the advantage of providing high mechanical resistance and easy handling of the adsorbent