On the local existence of maximal slicings in spherically symmetric spacetimes

In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.Comment: 4 pages. Accepted for publication in Journal of Physics: Conference Series, Proceedings of the Spanish Relativity Meeting ERE200

Upregulation of the microRNA cluster at the Dlk1-Dio3 locus in lung adenocarcinoma.

Mice in which lung epithelial cells can be induced to express an oncogenic Kras(G12D) develop lung adenocarcinomas in a manner analogous to humans. A myriad of genetic changes accompany lung adenocarcinomas, many of which are poorly understood. To get a comprehensive understanding of both the transcriptional and post-transcriptional changes that accompany lung adenocarcinomas, we took an omics approach in profiling both the coding genes and the non-coding small RNAs in an induced mouse model of lung adenocarcinoma. RNAseq transcriptome analysis of Kras(G12D) tumors from F1 hybrid mice revealed features specific to tumor samples. This includes the repression of a network of GTPase-related genes (Prkg1, Gnao1 and Rgs9) in tumor samples and an enrichment of Apobec1-mediated cytosine to uridine RNA editing. Furthermore, analysis of known single-nucleotide polymorphisms revealed not only a change in expression of Cd22 but also that its expression became allele specific in tumors. The most salient finding, however, came from small RNA sequencing of the tumor samples, which revealed that a cluster of ∼53 microRNAs and mRNAs at the Dlk1-Dio3 locus on mouse chromosome 12qF1 was markedly and consistently increased in tumors. Activation of this locus occurred specifically in sorted tumor-originating cancer cells. Interestingly, the 12qF1 RNAs were repressed in cultured Kras(G12D) tumor cells but reactivated when transplanted in vivo. These microRNAs have been implicated in stem cell pleuripotency and proteins targeted by these microRNAs are involved in key pathways in cancer as well as embryogenesis. Taken together, our results strongly imply that these microRNAs represent key targets in unraveling the mechanism of lung oncogenesis

Effect of Structural Parameters on Superconductivity in Fluorine-Free LnFeAsO1-y (Ln=La,Nd)

The crystal structure of LnFeAsO$_{1-y}$ (Ln = La, Nd) has been studied by the powder neutron diffraction technique. The superconducting phase diagram of NdFeAsO$_{1-y}$ is established as a function of oxygen content which is determined by Rietveld refinement. The small As-Fe bond length suggests that As and Fe atoms are connected covalently. FeAs$_4$-tetrahedrons transform toward a regular shape with increasing oxygen deficiency. Superconducting transition temperatures seem to attain maximum values for regular FeAs$_4$-tetrahedrons

The Degenerate Parametric Oscillator and Ince's Equation

We construct Green's function for the quantum degenerate parametric oscillator in terms of standard solutions of Ince's equation in a framework of a general approach to harmonic oscillators. Exact time-dependent wave functions and their connections with dynamical invariants and SU(1,1) group are also discussed.Comment: 10 pages, no figure

The global wave front set of tempered oscillatory integrals with inhomogeneous phase functions

We study certain families of oscillatory integrals $I_\varphi(a)$, parametrised by phase functions $\varphi$ and amplitude functions $a$ globally defined on $\mathbb{R}^d$, which give rise to tempered distributions, avoiding the standard homogeneity requirement on the phase function. The singularities of $I_\varphi(a)$ are described both from the point of view of the lack of smoothness as well as with respect to the decay at infinity. In particular, the latter will depend on a version of the set of stationary points of $\varphi$, including elements lying at the boundary of the radial compactification of $\mathbb{R}^d$. As applications, we consider some properties of the two-point function of a free, massive, scalar relativistic field and of classes of global Fourier integral operators on $\mathbb{R}^d$, with the latter defined in terms of kernels of the form $I_\varphi(a)$.Comment: 30 pages, 2 figures, mistakes and typos correctio

A mutate-and-map protocol for inferring base pairs in structured RNA

Chemical mapping is a widespread technique for structural analysis of nucleic acids in which a molecule's reactivity to different probes is quantified at single-nucleotide resolution and used to constrain structural modeling. This experimental framework has been extensively revisited in the past decade with new strategies for high-throughput read-outs, chemical modification, and rapid data analysis. Recently, we have coupled the technique to high-throughput mutagenesis. Point mutations of a base-paired nucleotide can lead to exposure of not only that nucleotide but also its interaction partner. Carrying out the mutation and mapping for the entire system gives an experimental approximation of the molecules contact map. Here, we give our in-house protocol for this mutate-and-map strategy, based on 96-well capillary electrophoresis, and we provide practical tips on interpreting the data to infer nucleic acid structure.Comment: 22 pages, 5 figure

A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.Comment: 32 page

A Facile Nanoparticle Immunoassay for Cancer Biomarker Discovery

<p>Abstract</p> <p>Background</p> <p>Gold nanoparticles (AuNPs) scatter light intensely at or near their surface plasmon wavelength region. Using AuNPs coupled with dynamic light scattering (DLS) detection, we developed a facile nanoparticle immunoassay for serum protein biomarker detection and analysis. A serum sample was first mixed with a citrate-protected AuNP solution. Proteins from the serum were adsorbed to the AuNPs to form a protein corona on the nanoparticle surface. An antibody solution was then added to the assay solution to analyze the target proteins of interest that are present in the protein corona. The protein corona formation and the subsequent binding of antibody to the target proteins in the protein corona were detected by DLS.</p> <p>Results</p> <p>Using this simple assay, we discovered multiple molecular aberrations associated with prostate cancer from both mice and human blood serum samples. From the mice serum study, we observed difference in the size of the protein corona and mouse IgG level between different mice groups (i.e., mice with aggressive or less aggressive prostate cancer, and normal healthy controls). Furthermore, it was found from both the mice model and the human serum sample study that the level of vascular endothelial growth factor (VEGF, a protein that is associated with tumor angiogenesis) adsorbed to the AuNPs is decreased in cancer samples compared to non-cancerous or less malignant cancer samples.</p> <p>Conclusion</p> <p>The molecular aberrations observed from this study may become new biomarkers for prostate cancer detection. The nanoparticle immunoassay reported here can be used as a convenient and general tool to screen and analyze serum proteins and to discover new biomarkers associated with cancer and other human diseases.</p