Irreducible Killing Tensors from Third Rank Killing-Yano Tensors

We investigate higher rank Killing-Yano tensors showing that third rank Killing-Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric were from two rank Killing-Yano tensors we obtain a reducible Killing tensor and from third rank Killing-Yano tensors we obtain three Killing tensors, one reducible and two irreducible.Comment: 10 page

Microglial morphology in the somatosensory cortex across lifespan. A quantitative study

Background: Microglia are long-lived cells that constantly monitor their microenvironment. To accomplish this task, they constantly change their morphology both in the short and long term under physiological conditions. This makes the process of quantifying physiological microglial morphology difficult. Results: By using a semi-manual and a semi-automatic method to assess fine changes in cortical microglia morphology, we were able to quantify microglia changes in number, surveillance and branch tree starting from the fifth postnatal day to 2 years of life. We were able to identify a fluctuating behavior of most analyzed parameters characterized by a rapid cellular maturation, followed by a long period of relative stable morphology during the adult life with a final convergence to an aged phenotype. Detailed cellular arborization analysis revealed age-induced differences in microglia morphology, with mean branch length and the number of terminal processes changing constantly over time. Conclusions: Our study provides insight into microglia morphology changes across lifespan under physiological conditions. We were able to highlight, that due to the dynamic nature of microglia several morphological parameters are needed to establish the physiological state of these cells

Dirac Spinor Waves and Solitons in Anisotropic Taub-NUT Spaces

We apply a new general method of anholonomic frames with associated nonlinear connection structure to construct new classes of exact solutions of Einstein-Dirac equations in five dimensional (5D)gravity. Such solutions are parametrized by off-diagonal metrics in coordinate (holonomic) bases, or, equivalently, by diagonal metrics given with respect to some anholonomic frames (pentads, or funfbiends, satisfing corresponding constraint relations). We consider two possibilities of generalization of the Taub NUT metric in order to obtain vacuum solutions of 5D Einsitein equations with effective renormalization of constants having distinguished anisotropies on an angular parameter or on extra dimension coordinate. The constructions are extended to solutions describing self-consistent propagations of 3D Dirac wave packets in 5D anisotropic Taub NUT spacetimes. We show that such anisotropic configurations of spinor matter can induce gravitational 3D solitons being solutions of Kadomtsev-Petviashvili or of sine-Gordon equations.Comment: revtex, 16 pages, version 4, affiliation changed, accepted to CQ