Geometric description of lightlike foliations by an observer in general relativity

We introduce new concepts and properties of lightlike distributions and foliations (of dimension and co-dimension 1) in a space-time manifold of dimension $n$, from a purely geometric point of view. Given an observer and a lightlike distribution $\Omega$ of dimension or co-dimension 1, its lightlike direction is broken down into two vector fields: a timelike vector field $U$ representing the observer and a spacelike vector field $S$ representing the relative direction of propagation of $\Omega$ for this observer. A new distribution $\Omega_U^-$ is defined, with the opposite relative direction of propagation for the observer $U$. If both distributions $\Omega$ and $\Omega _U^-$ are integrable, the pair \Omega ,\Omega_U^- $represents the wave fronts of a stationary wave for the observer$U$. However, we show in an example that the integrability of$\Omega $does not imply the integrability of$\Omega_U^-$.Comment: 14 pages, 4 figure

Invariant manifolds of the Bonhoeffer-van der Pol oscillator

The stable and unstable manifolds of a saddle fixed point (SFP) of the Bonhoeffer-van der Pol oscillator are numerically studied. A correspondence between the existence of homoclinic tangencies (whic are related to the creation or destruction of Smale horseshoes) and the chaos observed in the bifurcation diagram is described. It is observed that in the non-chaotic zones of the bifurcation diagram, there may or may not be Smale horseshoes, but there are no homoclinic tangencies.Comment: 14 pages, 15 figure

A probabilistic model for crystal growth applied to protein deposition at the microscale

A probabilistic discrete model for 2D protein crystal growth is presented. This model takes into account the available space and can describe growing processes of different nature due to the versatility of its parameters which gives the model great flexibility. The accuracy of the simulation is tested against a real protein (SbpA) crystallization experiment showing high agreement between the proposed model and the actual images of the nucleation process. Finally, it is also discussed how the regularity of the interface (i.e. the curve that separates the crystal from the substrate) affects to the evolution of the simulation.Comment: 13 pages, 12 figure

Center of mass, spin supplementary conditions, and the momentum of spinning particles

We discuss the problem of defining the center of mass in general relativity and the so-called spin supplementary condition. The different spin conditions in the literature, their physical significance, and the momentum-velocity relation for each of them are analyzed in depth. The reason for the non-parallelism between the velocity and the momentum, and the concept of "hidden momentum", are dissected. It is argued that the different solutions allowed by the different spin conditions are equally valid descriptions for the motion of a given test body, and their equivalence is shown to dipole order in curved spacetime. These different descriptions are compared in simple examples.Comment: 45 pages, 7 figures. Some minor improvements, typos fixed, signs in some expressions corrected. Matches the published version. Published as part of the book "Equations of Motion in Relativistic Gravity", D. Puetzfeld et al. (eds.), Fundamental Theories of Physics 179, Springer, 201

ZEB1 Links p63 and p73 in a Novel Neuronal Survival Pathway Rapidly Induced in Response to Cortical Ischemia

Background: Acute hypoxic/ischemic insults to the forebrain, often resulting in significant cellular loss of the cortical parenchyma, are a major cause of debilitating injury in the industrialized world. A clearer understanding of the pro-death/ pro-survival signaling pathways and their downstream targets is critical to the development of therapeutic interventions to mitigate permanent neurological damage. Methodology/Principal Findings: We demonstrate here that the transcriptional repressor ZEB1, thought to be involved in regulating the timing and spatial boundaries of basic-Helix-Loop-Helix transactivator-mediated neurogenic determination/ differentiation programs, functions to link a pro-survival transcriptional cascade rapidly induced in cortical neurons in response to experimentally induced ischemia. Employing histological, tissue culture, and molecular biological read-outs, we show that this novel pro-survival response, initiated through the rapid induction of p63, is mediated ultimately by the transcriptional repression of a pro-apoptotic isoform of p73 by ZEB1. We show further that this phylogenetically conserved pathway is induced as well in the human cortex subjected to episodes of clinically relevant stroke. Conclusions/Significance: The data presented here provide the first evidence that ZEB1 induction is part of a protective response by neurons to ischemia. The stroke-induced increase in ZEB1 mRNA and protein levels in cortical neurons is both developmentally and phylogenetically conserved and may therefore be part of a fundamental cellular response to thi

Down-Regulation of GEP100 Causes Increase in E-Cadherin Levels and Inhibits Pancreatic Cancer Cell Invasion

AIMS: Invasion and metastasis are major reasons for pancreatic cancer death and identifying signaling molecules that are specifically used in tumor invasion is of great significance. The purpose of this study was to elucidate the role of GEP100 in pancreatic cancer cell invasion and metastasis and the corresponding molecular mechanism. METHODS: Stable cell lines with GEP100 knocked-down were established by transfecting GEP100 shRNA vector into PaTu8988 cells and selected by puromycin. qRT-PCR and Western blot were performed to detect gene expression. Matrigel-invasion assay was used to detect cancer cell invasion in vitro. Liver metastasis in vivo was determined by splenic injection of indicated cell lines followed by spleen resection. Immunofluorescence study was used to detect the intracellular localization of E-cadherin. RESULTS: We found that the expression level of GEP100 protein was closely related to the invasive ability of a panel of 6 different human pancreatic cancer cell lines. Down-regulation of GEP100 in PaTu8988 cells significantly decreased invasive activity by Matrigel invasion assay, without affecting migration, invasion and viability. The inhibited invasive activity was rescued by over-expression of GEP100 cDNA. In vivo study showed that liver metastasis was significantly decreased in the PaTu8988 cells with GEP100 stably knocked-down. In addition, an epithelial-like morphological change, mimicking a mesenchymal to epithelial transition (MET) was induced by GEP100 down-regulation. The expression of E-cadherin protein was increased 2-3 folds accompanied by its redistribution to the cell-cell contacts, while no obvious changes were observed for E-cadherin mRNA. Unexpectedly, the mRNA of Slug was increased by GEP100 knock-down. CONCLUSION: These findings provided important evidence that GEP100 plays a significant role in pancreatic cancer invasion through regulating the expression of E-cadherin and the process of MET, indicating the possibility of it becoming a potential therapeutic target against pancreatic cancer