Non-local control in the conduction coefficients: well posedness and convergence to the local limit

We consider a problem of optimal distribution of conductivities in a system governed by a non-local diffusion law. The problem stems from applications in optimal design and more specifically topology optimization. We propose a novel parametrization of non-local material properties. With this parametrization the non-local diffusion law in the limit of vanishing non-local interaction horizons converges to the famous and ubiquitously used generalized Laplacian with SIMP (Solid Isotropic Material with Penalization) material model. The optimal control problem for the limiting local model is typically ill-posed and does not attain its infimum without additional regularization. Surprisingly, its non-local counterpart attains its global minima in many practical situations, as we demonstrate in this work. In spite of this qualitatively different behaviour, we are able to partially characterize the relationship between the non-local and the local optimal control problems. We also complement our theoretical findings with numerical examples, which illustrate the viability of our approach to optimal design practitioners

Risk and protective factors for release in outpatients with schizophrenia

eposterWe aim to determine risk and protective factors influencing relapse incidence in outpatient with schizophrenia. A longitudinal, observational study was done with outpatients with schizophrenia (F20) or schizoaffective disorder (F25)(DMS-IV and ICD-10), without hospitalization during the previous 6 months. The patients were consecutively included into the study to received oral (O-A) or long-acting injectable (depot-A) antipsychotics. Clinical stage evolution, compliance, efficacy and safety assessments (including PANSS, CGI-SSI, hospitalization rates, and adverse events) were recorded before and after 6 and 12 months of treatment. Results: 60 outpatients (aged 34.5±8.9, male 73%), 75% schizophrenia and 25% schizoaffective disorder diagnosis, 68.3% fewer than 15 years of schizophrenia evolution, 76.7% fewer than 5 times previous hospitalizations were treated with O-A (41.7%) or depot-A (58.3%) antipsychotics for at least one year. Depot-A treated patients showed a significant higher compliance compared to O-A patients during the all following time, lower PANSS (total, positive and negative) scores and CGI-SSI score (p<0.01), and a delayed relapse incidence and re-hospitalization to more than 1 year in the 48% of patients (relapse % depot/% oral) after 6 months 22.9%/52.0%, and after 12 months 48.6%/4.0%. Conclusion: There were protective factors which delayed relapse incidence in schizophrenia: Use of sustained-release preparations, family support. There were risk factors for occurrence of relapse in schizophrenia: cocaine, heroin and alcohol consumption, absence of family support, greater severity of patients assessed through CGI-SI, male sex, age older than 25 years and long-term evolution of the disorder.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Brane Inflation from Rotation of D4 Brane

In this paper, a inflationary model from the rotation of D4-brane is constructed. We show that for a very wide rage of parameter, this model satisfies the observation and find that regarded as inflaton, the rotation of branes may be more nature than the distance between branes. Our model offers a new avenue for brane inflation.Comment: 6 pages, no figure

Los colores subliminales en la obra de José Guerrero. Metodología y análisis para el deleite

José Guerrero’ s Art Centre collection shows a considerable number of paintings by this author, which are a great part of his artistic work. In the last years, thanks to the understanding and collaboration among different public entities, the controversy regarding the permanence of the collection in the museum has ended. A wide research has been done about the paintings through the colorimetrical study of its pictorial surfaces, which shows new artistic aspects of them. Some of these are: graduated shading in apparent stains of plain colours, linear limits or shades among different parts and, specially, areas with almost negligible colour through natural visual analysis. These have been shown thanks to the scientific methodology used.The research has also contributed to learn about the creative techniques, the colours and the expressivity of his paintings, verifying their quality. Their range of colours is visual stimulus that for many observers may seem consciously imperceptible due to their capacity of differenciating the colours shown. However, they may have an influence on the reactions the observers might experience when they contemplate the paintings because of the unconscious appreciation. The subliminal apparently appreciated and the synesthesia justify this phenomenon.La colección del Centro José Guerrero de Granada cuenta con un considerable número de pinturas de este autor, que suponen una muestra importante de su producción artística. En los últimos años, gracias al entendimiento y la colaboración entre diferentes organismos públicos, se ha terminado con la polémica sobre la permanencia de esta colección en el museo. Una extensa investigación realizada sobre las obras, mediante el estudio colorimétrico de sus superficies pictóricas, ha permitido conocer novedosos aspectos artísticos de ellas, como degradados en aparentes manchas de colores planos, límites lineales o difuminados entre diferentes zonas y, especialmente, áreas de coloridos casi inapreciables mediante análisis visual al natural, aspectos que han quedado demostrados mediante metodología científica.El trabajo también ha contribuido a conocer mejor las técnicas creativas y los colores utilizados, junto a la expresividad de las obras, aspectos que han verificado su calidad. Sus gamas de colores son estímulos visuales que para muchos observadores resultan inapreciables conscientemente, debido a las capacidades de diferenciación del color que poseen, pero que pueden influir en las reacciones que experimentan ante su contemplación, a causa de la apreciación inconsciente. La percepción subliminal de los colores no visibles aparentemente y la sinestesia justifican este hecho

Galaxy correlations and the BAO in a void universe: structure formation as a test of the Copernican Principle

A suggested solution to the dark energy problem is the void model, where accelerated expansion is replaced by Hubble-scale inhomogeneity. In these models, density perturbations grow on a radially inhomogeneous background. This large scale inhomogeneity distorts the spherical Baryon Acoustic Oscillation feature into an ellipsoid which implies that the bump in the galaxy correlation function occurs at different scales in the radial and transverse correlation functions. We compute these for the first time, under the approximation that curvature gradients do not couple the scalar modes to vector and tensor modes. The radial and transverse correlation functions are very different from those of the concordance model, even when the models have the same average BAO scale. This implies that if void models are fine-tuned to satisfy average BAO data, there is enough extra information in the correlation functions to distinguish a void model from the concordance model. We expect these new features to remain when the full perturbation equations are solved, which means that the radial and transverse galaxy correlation functions can be used as a powerful test of the Copernican Principle.Comment: 12 pages, 8 figures, matches published versio

From nonlocal Eringen's model to fractional elasticity

Eringen's model is one of the most popular theories in nonlocal elasticity. It has been applied to many practical situations with the objective of removing the anomalous stress concentrations around geometric shape singularities, which appear when the local modelling is used. Despite the great popularity of Eringen's model in mechanical engineering community, even the most basic questions such as the existence and uniqueness of solutions have been rarely considered in the research literature for this model. In this work we focus on precisely these questions, proving that the model is in general ill-posed in the case of smooth kernels, the case which appears rather often in numerical studies. We also consider the case of singular, non-smooth kernels, and for the paradigmatic case of the Riesz potential we establish the well-posedness of the model in fractional Sobolev spaces. For such a kernel, in dimension one the model reduces to the well-known fractional Laplacian. Finally, we discuss possible extensions of Eringen's model to spatially heterogeneous material distributions