Pre-marital and pre-unional financial agreements and their circulation in the context of the new EU regulations 2016/1103 and 2016/1104

Regulations (EU) 2016/1103 and 2016/1104 provide spouses and partners with the possibility to conclude agreements for the organization of their property regime but do not detail their content and structure. Moreover, while the possibility to conclude those agreements even prior to the marriage or the conclusion of a registered partnership is a valuable innovation in comparison with other European Regulations in family matters, some choices made by the European legislator on applicable law will likely be source of inconveniences. Furthermore, as for their recognition and enforcement in the participating Member States ? which will be based on the same rules enacted for decisions, authentic instruments, and court settlements ? attention should be paid to their admissibility in some of them, like Italy, where the jurisprudence of the Supreme Court is steadily opposed to their acceptance

Regularity theory and high order numerical methods for the (1D)-fractional Laplacian

This paper presents regularity results and associated high-order numerical methods for one-dimensional Fractional-Laplacian boundary-value problems. On the basis of a factorization of solutions as a product of a certain edge-singular weight $w$ times a ``regular´´ unknown, a characterization of the regularity of solutions is obtained in terms of the smoothness of the corresponding right-hand sides. In particular, for right-hand sides which are analytic in a Bernstein Ellipse, analyticity in the same Bernstein Ellipse is obtained for the ``regular´´ unknown. Moreover, a sharp Sobolev regularity result is presented which completely characterizes the co-domain of the Fractional-Laplacian operator in terms of certain weighted Sobolev spaces introduced in (Babu{s}ka and Guo, SIAM J. Numer. Anal. 2002). The present theoretical treatment relies on a full eigendecomposition for a certain weighted integral operator in terms of the Gegenbauer polynomial basis. The proposed Gegenbauer-based Nystr"om numerical method for the Fractional-Laplacian Dirichlet problem, further, is significantly more accurate and efficient than other algorithms considered previously. The sharp error estimates presented in this paper indicate that the proposed algorithm is spectrally accurate, with convergence rates that only depend on the smoothness of the right-hand side. In particular, convergence is exponentially fast (resp. faster than any power of the mesh-size) for analytic (resp. infinitely smooth) right-hand sides. The properties of the algorithm are illustrated with a variety of numerical results.Fil: Acosta, Gabriel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Borthagaray, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Bruno, Oscar Ricardo. California Institute Of Technology; Estados UnidosFil: Maas, Martín Daniel. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin

Some properties of the growth and of the algebraic entropy of group endomorphisms

We study the growth of group endomorphisms, a generalization of the classical notion of growth of finitely generated groups, which is strictly related to algebraic entropy. We prove that the inner automorphisms of a group have the same growth type and the same algebraic entropy as the identity automorphism. Moreover, we show that endomorphisms of locally finite groups cannot have intermediate growth. We also find an example showing that the Addition Theorem for algebraic entropy does not hold for endomorphisms of arbitrary groups

State-dependent changes of connectivity patterns and functional brain network topology in Autism Spectrum Disorder

Anatomical and functional brain studies have converged to the hypothesis that Autism Spectrum Disorders (ASD) are associated with atypical connectivity. Using a modified resting-state paradigm to drive subjects' attention, we provide evidence of a very marked interaction between ASD brain functional connectivity and cognitive state. We show that functional connectivity changes in opposite ways in ASD and typicals as attention shifts from external world towards one's body generated information. Furthermore, ASD subject alter more markedly than typicals their connectivity across cognitive states. Using differences in brain connectivity across conditions, we classified ASD subjects at a performance around 80% while classification based on the connectivity patterns in any given cognitive state were close to chance. Connectivity between the Anterior Insula and dorsal-anterior Cingulate Cortex showed the highest classification accuracy and its strength increased with ASD severity. These results pave the path for diagnosis of mental pathologies based on functional brain networks obtained from a library of mental states