On universal central extensions of Hom-Leibniz algebras

In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, universal α-central extension and α-perfect Hom-Leibniz algebra due to the fact that the composition of two central extensions of Hom-Leibniz algebras is not central. We also provide the recognition criteria for these kind of universal central extensions. We prove that an α-perfect Hom-Lie algebra admits a universal α-central extension in the categories of Hom-Lie and Hom-Leibniz algebras and we obtain the relationships between both of them. In case α = Id we recover the corresponding results on universal central extensions of Leibniz algebras.

Anotação, numa perspectiva de Direito Penal Constitucional, de Criminologia e de Política Criminal, de alguns dos aspectos do Acórdão do Tribunal Constitucional (português) n.º 353/2012, de 5 de Julho de 2012 - o problema da legítima defesa de bens jurídicos individuais e bens jurídicos colectivos, bens jurídicos supra-individuais e/ou bens jurídicos comunitários no meio do Estado de Direito e do Estado Social

o Acórdão do Tribunal Constitucional português n.º 353/2012, de 5 de Julho de 2012, ao declarar a respectiva inconstitucionalidade com força obrigatória geral, colocou em evidência a existência de bens jurídicos individuais e bens jurídicos colectivos, bens jurídicos supra-individuais, bens jurídicos comunitários. Bens jurídicos estes que devem e têm que ser tutelados e protegidos. A legítima defesa pode existir quer em relação à agressão actual e ilícita de bens jurídicos individuais, quer em relação à agressão actual e ilícita de bens jurídicos colectivos, bens jurídicos supra-individuais e/ou bens jurídicos comunitários? Parte muito substancial e importante da Doutrina indica que sim. Mas, então, como reagir, no contexto da hipotética legítima defesa, face à eventual agressão actual e ilícita dos bens jurídicos tutelados, agora com valor reforçado, pelo próprio Tribunal Constitucional? E qual o papel do direito constitucional de resistência? Este artigo pretende fornecer um muito breve contributo para a solução das correspondentes questões. A questão dos Direitos Fundamentais, o Desenvolvimento e a modernidade. § the Sentence of the (Portuguese) Constitutional Court n. 353/2012 of July 5, 2012, declaring its generally binding unconstitutionality, has highlighted the existence of individual legal goods and collective legal goods, supra-individual legal goods, community legal goods. These legal goods, that should and must be defended and protected. Legitimate defense can be either relative to the current and illicit aggression to individual legal goods, whether in relation to the current and illicit aggression to collective legal goods, supra-individual legal goods or community legal goods? Very substantial and important part of the Doctrine would appear so. But then how to respond, in the context of hypothetical self-defense, in the face of possible current and illicit aggression of the protected legal goods, now with enhanced value, by the Constitutional Court? And what is the role of the constitutional right of resistance? This article is intended to provide a very brief contribution to the solution of the corresponding questions. The question of Fundamental Rights, Development and modernity.

Validation of percutaneous puncture trajectory during renal access using 4D ultrasound reconstruction

Background: An accurate percutaneous puncture is essential for disintegration and removal of renal stones. Although this procedure has proven to be safe, some organs surrounding the renal target might be accidentally perforated. This work describes a new intraoperative framework where tracked surgical tools are superimposed within 4D ultrasound imaging for security assessment of the percutaneous puncture trajectory (PPT). Methods: A PPT is first generated from the skin puncture site towards an anatomical target, using the information retrieved by electromagnetic motion tracking sensors coupled to surgical tools. Then, 2D ultrasound images acquired with a tracked probe are used to reconstruct a 4D ultrasound around the PPT under GPU processing. Volume hole-filling was performed in different processing time intervals by a tri-linear interpolation method. At spaced time intervals, the volume of the anatomical structures was segmented to ascertain if any vital structure is in between PPT and might compromise the surgical success. To enhance the volume visualization of the reconstructed structures, different render transfer functions were used. Results: Real-time US volume reconstruction and rendering with more than 25 frames/s was only possible when rendering only three orthogonal slice views. When using the whole reconstructed volume one achieved 8-15 frames/s. 3 frames/s were reached when one introduce the segmentation and detection if some structure intersected the PPT. Conclusions: The proposed framework creates a virtual and intuitive platform that can be used to identify and validate a PPT to safely and accurately perform the puncture in percutaneous nephrolithotomy.