An hp-Local Discontinuous Galerkin method for Parabolic\ud Integro-Differential Equations

In this article, a priori error analysis is discussed for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that the L2 -norm of the gradient and the L2 -norm of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

Gravitational fields with sources, regular black holes, quasiblack holes, and analogue black holes

We discuss recent developments in gravitational fields with sources, regular black holes, quasiblack holes, and analogue black holes, related to the talks presented at the corresponding Parallel Session AT3 of the 13th Marcel Grossmann Meeting.Comment: Report of the Parallel Session AT3 at the Marcel Grossmann Meeting 13, Stockholm 2012, Proceedings of the Conference. 9 page

Optimal L2 estimates for semidiscrete Galerkin methods for\ud parabolic integro-differential equations with nonsmooth data

In this article, we discuss an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth initial data. It is based on energy arguments and on a repeated use of time integration, but without using parabolic type duality technique. Optimal L2-error estimate is derived for the semidiscrete approximation, when the initial data is in L2

An a posteriori error analysis of a mixed finite element Galerkin approximation to second order linear parabolic problems

In this article, a posteriori error estimates are derived for a mixed finite element Galerkin approximation to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstruction method, a posteriori error estimates in $L^\infty(L^2)$ and $L^2(L^2)$-norms with optimal order of convergence for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on backward Euler method, a completely discrete scheme is analyzed and a posteriori bounds are derived, which improves earlier results on a posteriori estimates for mixed parabolic problems

Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data

In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result

Quasinormal Modes Beyond Kerr

The quasinormal modes (QNMs) of a black hole spacetime are the free, decaying oscillations of the spacetime, and are well understood in the case of Kerr black holes. We discuss a method for computing the QNMs of spacetimes which are slightly deformed from Kerr. We mention two example applications: the parametric, turbulent instability of scalar fields on a background which includes a gravitational QNM, and the shifts to the QNM frequencies of Kerr when the black hole is weakly charged. This method may be of use in studies of black holes which are deformed by external fields or are solutions to alternative theories of gravity.Comment: Proceedings of the Sant Cugat Forum on Astrophysics (2014). Session on 'Gravitational Wave Astrophysics.' 7 page

Digital libraries: The challenge of integrating instagram with a taxonomy for content management

Interoperability and social implication are two current challenges in the digital library (DL) context. To resolve the problem of interoperability, our work aims to find a relationship between the main metadata schemas. In particular, we want to formalize knowledge through the creation of a metadata taxonomy built with the analysis and the integration of existing schemas associated with DLs. We developed a method to integrate and combine Instagram metadata and hashtags. The final result is a taxonomy, which provides innovative metadata with respect to the classification of resources, as images of Instagram and the user-generated content, that play a primary role in the context of modern DLs. The possibility of Instagram to localize the photos inserted by users allows us to interpret the most relevant and interesting informative content for a specific user type and in a specific location and to improve access, visibility and searching of library content

Neural correlates of cognitive control of reaching movements in the dorsal premotor cortex of rhesus monkeys

Mirabella G, Pani P, Ferraina S. Neural correlates of cognitive control of reaching movements in the dorsal premotor cortex of rhesus monkeys. J Neurophysiol 106: 1454-1466, 2011. First published June 22, 2011; doi: 10.1152/jn.00995.2010.-Canceling a pending movement is a hallmark of voluntary behavioral control because it allows us to quickly adapt to unattended changes either in the external environment or in our thoughts. The countermanding paradigm allows the study of inhibitory processes of motor acts by requiring the subject to withhold planned movements in response to an infrequent stop-signal. At present the neural processes underlying the inhibitory control of arm movements are mostly unknown. We recorded the activity of single units in the rostral and caudal portion of the dorsal premotor cortex (PMd) of monkeys trained in a countermanding reaching task. We found that among neurons with a movement-preparatory activity, about one-third exhibit a modulation before the behavioral estimate of the time it takes to cancel a planned movement. Hence these neurons exhibit a pattern of activity suggesting that PMd plays a critical role in the brain networks involved in the control of arm movement initiation and suppression.Mirabella G, Pani P, Ferraina S. Neural correlates of cognitive control of reaching movements in the dorsal premotor cortex of rhesus monkeys. J Neurophysiol 106: 1454-1466, 2011. First published June 22, 2011; doi: 10.1152/jn.00995.2010.-Canceling a pending movement is a hallmark of voluntary behavioral control because it allows us to quickly adapt to unattended changes either in the external environment or in our thoughts. The countermanding paradigm allows the study of inhibitory processes of motor acts by requiring the subject to withhold planned movements in response to an infrequent stop-signal. At present the neural processes underlying the inhibitory control of arm movements are mostly unknown. We recorded the activity of single units in the rostral and caudal portion of the dorsal premotor cortex (PMd) of monkeys trained in a countermanding reaching task. We found that among neurons with a movement-preparatory activity, about one-third exhibit a modulation before the behavioral estimate of the time it takes to cancel a planned movement. Hence these neurons exhibit a pattern of activity suggesting that PMd plays a critical role in the brain networks involved in the control of arm movement initiation and suppression