Traces and Extensions of Bounded Divergence-Measure Fields on Rough Open Sets

We prove that an open set $\Omega \subset \mathbb{R}^n$ can be approximated by smooth sets of uniformly bounded perimeter from the interior if and only if the open set $\Omega$ satisfies \begin{align*} &\qquad \qquad\qquad\qquad\qquad\qquad\qquad \mathscr{H}^{n-1}(\partial \Omega \setminus \Omega^0)<\infty, \qquad &&\quad\qquad\qquad \qquad\qquad (*) \end{align*} where $\Omega^0$ is the measure-theoretic exterior of $\Omega$. Furthermore, we show that condition (*) implies that the open set $\Omega$ is an extension domain for bounded divergence-measure fields, which improves the previous results that require a strong condition that $\mathscr{H}^{n-1}(\partial \Omega)<\infty$. As an application, we establish a Gauss-Green formula up to the boundary on any open set $\Omega$ satisfying condition (*) for bounded divergence-measure fields, for which the corresponding normal trace is shown to be a bounded function concentrated on $\partial \Omega \setminus \Omega^0$. This new formula does not require the set of integration to be compactly contained in the domain where the vector field is defined. In addition, we also analyze the solvability of the divergence equation on a rough domain with prescribed trace on the boundary, as well as the extension domains for bounded $BV$ functions.Comment: 29 page

COMPARATIVE GENOMICS AND MOLECULAR EVOLUTION: NEW GENOMIC RESOURCES FOR THE HYMENOPTERA AND EVOLUTIONARY STUDIES ON THE GENES OF THE \u3ci\u3eNasonia vitripennis\u3c/i\u3e HOX COMPLEX.

Research on insects, the most successful group from all metazoans on earth, has important societal, as well as scientific benefits. Insects occupy a wide range of roles, which have an effect on human life either because the former pose serious threats to public health and commercial crops as well as in some cases represent the only way to propagate food resources. Despite their tremendous importance, insect genomics remained an uneven territory dominated by studies in the Drosophila group and the mosquitoes. This dissertation attempts to: 1) report on advances in the development and characterization of genomic tools for species of the order Hymenoptera in the hopes of helping to close this gap; and 2) to shed light on the organization, origin and evolution of genes of the Hox cluster in species of the order Hymenoptera through molecular evolution analyses that were possible thanks to the availability of the aforementioned genomic resources

MobilitApp: Analysing mobility data of citizens in the metropolitan area of Barcelona

MobilitApp is a platform designed to provide smart mobility services in urban areas. It is designed to help citizens and transport authorities alike. Citizens will be able to access the MobilitApp mobile application and decide their optimal transportation strategy by visualising their usual routes, their carbon footprint, receiving tips, analytics and general mobility information, such as traffic and incident alerts. Transport authorities and service providers will be able to access information about the mobility pattern of citizens to o er their best services, improve costs and planning. The MobilitApp client runs on Android devices and records synchronously, while running in the background, periodic location updates from its users. The information obtained is processed and analysed to understand the mobility patterns of our users in the city of Barcelona, Spain

Homogeneously bright, flexible and foldable lighting devices with functionalised graphene electrodes

Alternating current electroluminescent technology allows the fabrication of large area, flat and flexible lights. Presently the maximum size of a continuous panel is limited by the high resistivity of available transparent electrode materials causing a visible gradient of brightness. Here, we demonstrate that the use of the best known transparent conductor FeCl$_{3}$-intercalated few-layer graphene boosts the brightness of electroluminescent devices by 49$\%$ compared to pristine graphene. Intensity gradients observed for high aspect ratio devices are undetectable when using these highly conductive electrodes. Flat lights on polymer substrates are found to be resilient to repeated and flexural strains.Comment: Published on ACS Materials and Interface

Solute carrier nutrient transporters in rheumatoid arthritis fibroblast-like synoviocytes

Metabolomic studies show that rheumatoid arthritis (RA) is associated with metabolic disruption. Metabolic changes in fibroblast-like synoviocytes (FLS) likely contribute to FLS abnormal response and strongly contribute to joint destruction. These changes often involve increased expression of nutrient transporters to meet a high demand for energy or biomolecules. The solute carrier (SLC) transporter families are nutrient transporters and serve as 'metabolic gates' for cells by mediating the transport of several different nutrients such as glucose, amino acids, vitamins, neurotransmitters, and inorganic/metal ions. In RA FLS SLC-mediated transmembrane transport was one pathway associated with different epigenetic landscape between RA and osteoarthritis (OA) FLS. These highlight that transporters from the SLC family offer unique targets for further research and offer the promise of future therapeutic targets for RA