On shape dependence of holographic entanglement entropy in AdS4/CFT3

We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS4, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS4, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence

Progress of elemental anomalies of hippocampal formation in the pilocarpine model of temporal lobe epilepsy, X-ray fluorescence microscopy study

In the present paper, X-ray fluorescence microscopy was applied to follow the processes occurring in rat hippocampal formation during the post-seizure period. In the study, one of the status epilepticus animal models of epilepsy was used, namely the model of temporal lobe epilepsy with pilocarpine-induced seizures. In order to analyze the dynamics of seizure-induced elemental changes, the samples taken from seizure-experiencing animals 3 h and 1, 4, and 7 days after proconvulsive agent administration were analyzed. The obtained results confirmed the utility of X-ray fluorescence microscopy in the research of mechanisms involved in the pathogenesis and progress of epilepsy. The topographic and quantitative elemental analysis of hippocampal formations from different periods of epileptogenesis showed that excitotoxicity, mossy fibers sprouting, and iron-induced oxidative stress may be the processes responsible for seizure-induced neurodegenerative changes and spontaneous recurrent seizures occurring in the chronic phase of the pilocarpine model. The analysis of correlations between the recorded elemental anomalies and quantitative parameters describing animal behavior in the acute period of pilocarpine-induced status epilepticus showed that the areal densities of selected elements measured in the latent period strongly depend on the progress of the acute phase. Especially important seem to be the observations done for Ca and Zn levels which suggest that the intensity of the pathological processes such as excitotoxicity and mossy fibers sprouting depend on the total time of seizure activity. These results as well as dependencies found between the levels of S, K, and Cu and the intensity of maximal seizures clearly confirm how important it is to control the duration and intensity of seizures in clinical practice