Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, like Brans-Dicke or higher-dimensional theories.Comment: 41 pages, REVTEX/LaTeX 2.09 file (don't use LaTeX2e !!!) Accepted for publication in Phys. Rev.

Closed cosmologies with a perfect fluid and a scalar field

Closed, spatially homogeneous cosmological models with a perfect fluid and a scalar field with exponential potential are investigated, using dynamical systems methods. First, we consider the closed Friedmann-Robertson-Walker models, discussing the global dynamics in detail. Next, we investigate Kantowski-Sachs models, for which the future and past attractors are determined. The global asymptotic behaviour of both the Friedmann-Robertson-Walker and the Kantowski-Sachs models is that they either expand from an initial singularity, reach a maximum expansion and thereafter recollapse to a final singularity (for all values of the potential parameter kappa), or else they expand forever towards a flat power-law inflationary solution (when kappa^2<2). As an illustration of the intermediate dynamical behaviour of the Kantowski-Sachs models, we examine the cases of no barotropic fluid, and of a massless scalar field in detail. We also briefly discuss Bianchi type IX models.Comment: 15 pages, 10 figure

No Chaos in Brane-World Cosmology

We discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models close to the initial singularity. We find that generically the cosmological singularity is isotropic in Bianchi type IX brane-world models and consequently these models do not exhibit Mixmaster or chaotic-like behaviour close to the initial singularity. We argue that this is typical of more general cosmological models in the brane-world scenario. In particular, we show that an isotropic singularity is a past-attractor in all orthogonal Bianchi models and is a local past-attractor in a class of inhomogeneous brane-world models.Comment: Updated Refs. Final version to appear in Class. Quantum Gra

Isotropic singularity in inhomogeneous brane cosmological models

We discuss the asymptotic dynamical evolution of spatially inhomogeneous brane-world cosmological models close to the initial singularity. By introducing suitable scale-invariant dependent variables and a suitable gauge, we write the evolution equations of the spatially inhomogeneous $G_{2}$ brane cosmological models with one spatial degree of freedom as a system of autonomous first-order partial differential equations. We study the system numerically, and we find that there always exists an initial singularity, which is characterized by the fact that spatial derivatives are dynamically negligible. More importantly, from the numerical analysis we conclude that there is an initial isotropic singularity in all of these spatially inhomogeneous brane cosmologies for a range of parameter values which include the physically important cases of radiation and a scalar field source. The numerical results are supported by a qualitative dynamical analysis and a calculation of the past asymptotic decay rates. Although the analysis is local in nature, the numerics indicates that the singularity is isotropic for all relevant initial conditions. Therefore this analysis, and a preliminary investigation of general inhomogeneous ($G_0$) models, indicates that it is plausible that the initial singularity is isotropic in spatially inhomogeneous brane-world cosmological models and consequently that brane cosmology naturally gives rise to a set of initial data that provide the conditions for inflation to subsequently take place.Comment: 32 pages with 8 pictures. submitted to Class. Quant. Gra

Spacelike Singularities and Hidden Symmetries of Gravity

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added. Published versio

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Prognostic DNA methylation patterns in cytogenetically normal acute myeloid leukemia are predefined by stem cell chromatin marks

Cytogenetically normal acute myeloid leukemia (CN-AML) compose between 40% and 50% of all adult acute myeloid leukemia (AML) cases. In this clinically diverse group, molecular aberrations, such as FLT3-ITD, NPM1, and CEBPA mutations, recently have added to the prognostic accuracy. Aberrant DNA methylation is a hallmark of cancer, including AML. We investigated in total 118 CN-AML samples in a test and a validation cohort for genome-wide promoter DNA methylation with Illumina Methylation Bead arrays and compared them with normal myeloid precursors and global gene expression. IDH and NPM1 mutations were associated with different methylation patterns (P = .0004 and .04, respectively). Genome-wide methylation levels were elevated in IDH-mutated samples (P = .006). We observed a negative impact of DNA methylation on transcription. Genes targeted by Polycomb group (PcG) proteins and genes associated with bivalent histone marks in stem cells showed increased aberrant methylation in AML (P &lt; .0001). Furthermore, high methylation levels of PcG target genes were independently associated with better progression-free survival (odds ratio = 0.47, P = .01) and overall survival (odds ratio = 0.36, P = .001). In summary, genome-wide methylation patterns show preferential methylation of PcG targets with prognostic impact in CN-AML

Self-Similarity in General Relativity \endtitle

The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ``first'' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of self-similar solutions to Einstein's field equations and the different mathematical approaches used in studying them. We focus mainly on spatially homogenous and spherically symmetric self-similar solutions, emphasizing their possible roles as asymptotic states for more general models. Perfect fluid spherically symmetric similarity solutions have recently been completely classified, and we discuss various astrophysical and cosmological applications of such solutions. Finally we consider more general types of self-similar models.Comment: TeX document, 53 page

Seroprevalence of Toxoplasma gondii and Neospora spp. Infections in Arab Horses, Southwest of Iran

Background: Because of the economic importance of the Arab race horses and also the role of Toxoplasma gondii and Neospora spp. in abortion and reproductive failure of these animals, we decided to perform this study. Objectives: We designed this study to investigate the seroprevalence of anti-Toxoplasma gondii and anti-Neospora spp. antibodies in Arab horses from 12 cities of Khuzestan province in southwest of Iran. Materials and Methods: From October 2009 to March 2011, a total of 235 blood samples were collected from jugular veins of Arab horses of different ages and genders from 12 cities of Khuzestan province. All the sera were tested for anti-Toxoplasma antibodies using the modified agglutination test (MAT) and the existence of anti-Neospora antibodies were tested using N-MAT for Neospora spp. Results: According to the MAT results, antibodies to T. gondii were found in 114 (48.5%) of 235 sera with titers of 1:20 in 84, 1:40 in 19, 1:80 in four, 1:160 in four, and 1:320 in three horses. According to the N-MAT results, antibodies to Neospora spp. were found in 47 (20%) of 235 sera with titers of 1:40 in 39, 1:80 in five, and 1:160 in three horses. We did not observe any statistically significant differences regarding age groups and genders between seropositive and seronegative horses for Neospora spp. using chi-square (chi(2)) test, but it seemed that anti-Toxoplasma antibodies were more prevalent in older horses ( >= 10 years old). Conclusions: The results indicated that Arab horses are exposed to these parasites in southwest of Iran. Further research is required to determine the genomic structures of these parasites in Arab horses in southwest of Iran

Resistance to chemotherapy: new treatments and novel insights into an old problem

Resistance to cancer chemotherapeutic treatment is a common phenomenon, especially in progressive disease. The generation of cellular models of drug resistance has been pivotal in unravelling the main effectors of resistance to traditional chemotherapy at the molecular level (i.e. intracellular drug inactivation, detoxifying systems, defects in DNA repair, apoptosis evasion, membrane transporters and cell adhesion). The development of targeted therapies has also been followed by resistance, reminiscent of an evolutionary arms race, as exemplified by imatinib and other BCR-ABL inhibitors for the treatment of chronic myelogenous leukaemia. Although traditionally associated with the last stages of the disease, recent findings with minimally transformed pretumorigenic primary human cells indicate that the ability to generate drug resistance arises early during the tumorigenic process, before the full transformation. Novel technologies, such as genome profiling, have in certain cases predicted the outcome of chemotherapy and undoubtedly have tremendous potential for the future. In addition, the novel cancer stem cell paradigm raises the prospect of cell-targeted therapies instead of treatment directed against the whole tumour