A splitting theorem for Kahler manifolds whose Ricci tensors have constant eigenvalues

It is proved that a compact Kahler manifold whose Ricci tensor has two distinct, constant, non-negative eigenvalues is locally the product of two Kahler-Einstein manifolds. A stronger result is established for the case of Kahler surfaces. Irreducible Kahler manifolds with two distinct, constant eigenvalues of the Ricci tensor are shown to exist in various situations: there are homogeneous examples of any complex dimension n > 1, if one eigenvalue is negative and the other positive or zero, and of any complex dimension n > 2, if the both eigenvalues are negative; there are non-homogeneous examples of complex dimension 2, if one of the eigenvalues is zero. The problem of existence of Kahler metrics whose Ricci tensor has two distinct, constant eigenvalues is related to the celebrated (still open) Goldberg conjecture. Consequently, the irreducible homogeneous examples with negative eigenvalues give rise to complete, Einstein, strictly almost Kahler metrics of any even real dimension greater than 4.Comment: 18 pages; final version; accepted for publication in International Journal of Mathematic

Coincidence between transcriptome analyses on different microarray platforms using a parametric framework

A parametric framework for the analysis of transcriptome data is demonstrated to yield coincident results when applied to data acquired using two different microarray platforms. Discrepancies among transcriptome studies are frequently reported, casting doubt on the reliability of collected data. The inconsistency among observations can be largely attributed to differences among the analytical frameworks employed for data analysis. The existing frameworks normalizes data against a standard determined from the data to be analyzed. In the present study, a parametric framework based on a strict model for normalization is applied to data acquired using an in-house printed chip and GeneChip. The framework is based on a common statistical characteristic of microarray data, and each data is normalized on the basis of a linear relationship with this model. In the proposed framework, the expressional changes observed and genes selected are coincident between platforms, achieving superior universality of data compared to other methods

Interpreting microarray experiments via co-expressed gene groups analysis

International audienceMicroarray technology produces vast amounts of data by measuring simultaneously the expression levels of thousands of genes under hundreds of biological conditions. Nowadays, one of the principal challenges in bioinformatics is the interpretation of huge data using different sources of information. We propose a novel data analysis method named CGGA (Co-expressed Gene Groups Analysis) that automatically finds groups of genes that are functionally enriched, i.e. have the same functional annotations, and are co- expressed. CGGA automatically integrates the information of microarrays, i.e. gene expression profiles, with the functional annotations of the genes obtained by the genome-wide information sources such as Gene Ontology (GO)1. By applying CGGA to well-known microarray experiments, we have identified the principal functionally enriched and co-expressed gene groups, and we have shown that this approach enhances and accelerates the interpretation of DNA microarray experiments

The general form of supersymmetric solutions of N=(1,0) U(1) and SU(2) gauged supergravities in six dimensions

We obtain necessary and sufficient conditions for a supersymmetric field configuration in the N=(1,0) U(1) or SU(2) gauged supergravities in six dimensions, and impose the field equations on this general ansatz. It is found that any supersymmetric solution is associated to an $SU(2)\ltimes \mathbb{R}^4$ structure. The structure is characterized by a null Killing vector which induces a natural 2+4 split of the six dimensional spacetime. A suitable combination of the field equations implies that the scalar curvature of the four dimensional Riemannian part, referred to as the base, obeys a second order differential equation. Bosonic fluxes introduce torsion terms that deform the $SU(2)\ltimes\mathbb{R}^4$ structure away from a covariantly constant one. The most general structure can be classified in terms of its intrinsic torsion. For a large class of solutions the gauge field strengths admit a simple geometrical interpretation: in the U(1) theory the base is K\"{a}hler, and the gauge field strength is the Ricci form; in the SU(2) theory, the gauge field strengths are identified with the curvatures of the left hand spin bundle of the base. We employ our general ansatz to construct new supersymmetric solutions; we show that the U(1) theory admits a symmetric Cahen-Wallach$_4\times S^2$ solution together with a compactifying pp-wave. The SU(2) theory admits a black string, whose near horizon limit is $AdS_3\times S_3$. We also obtain the Yang-Mills analogue of the Salam-Sezgin solution of the U(1) theory, namely $R^{1,2}\times S^3$, where the $S^3$ is supported by a sphaleron. Finally we obtain the additional constraints implied by enhanced supersymmetry, and discuss Penrose limits in the theories.Comment: 1+29 pages, late

Supersymmetric AdS_5 solutions of M-theory

We analyse the most general supersymmetric solutions of D=11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M_6, with four-form flux on M_6. We show that M_6 is partly specified by a one-parameter family of four-dimensional Kahler metrics. We find a large family of new explicit regular solutions where M_6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kahler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T^{1,1}/Z_2. Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.Comment: 40 pages. v2: minor changes, eqs. (2.22) and (D.12) correcte

Constitutive gene expression profile segregates toxicity in locally advanced breast cancer patients treated with high-dose hyperfractionated radical radiotherapy

Breast cancer patients show a wide variation in normal tissue reactions after radiotherapy. The individual sensitivity to x-rays limits the efficiency of the therapy. Prediction of individual sensitivity to radiotherapy could help to select the radiation protocol and to improve treatment results. The aim of this study was to assess the relationship between gene expression profiles of ex vivo un-irradiated and irradiated lymphocytes and the development of toxicity due to high-dose hyperfractionated radiotherapy in patients with locally advanced breast cancer. Raw data from microarray experiments were uploaded to the Gene Expression Omnibus Database (GEO accession GSE15341). We obtained a small group of 81 genes significantly regulated by radiotherapy, lumped in 50 relevant pathways. Using ANOVA and t-test statistical tools we found 20 and 26 constitutive genes (0 Gy) that segregate patients with and without acute and late toxicity, respectively. Non-supervised hierarchical clustering was used for the visualization of results. Six and 9 pathways were significantly regulated respectively. Concerning to irradiated lymphocytes (2 Gy), we founded 29 genes that separate patients with acute toxicity and without it. Those genes were gathered in 4 significant pathways. We could not identify a set of genes that segregates patients with and without late toxicity. In conclusion, we have found an association between the constitutive gene expression profile of peripheral blood lymphocytes and the development of acute and late toxicity in consecutive, unselected patients. These observations suggest the possibility of predicting normal tissue response to irradiation in high-dose non-conventional radiation therapy regimens. Prospective studies with higher number of patients are needed to validate these preliminary results

Molecular markers and mechanisms of stroke: RNA studies of blood in animals and humans

Whole genome expression microarrays can be used to study gene expression in blood, which comes in part from leukocytes, immature platelets, and red blood cells. Since these cells are important in the pathogenesis of stroke, RNA provides an index of these cellular responses to stroke. Our studies in rats have shown specific gene expression changes 24 hours after ischemic stroke, hemorrhage, status epilepticus, hypoxia, hypoglycemia, global ischemia, and following brief focal ischemia that simulated transient ischemic attacks in humans. Human studies show gene expression changes following ischemic stroke. These gene profiles predict a second cohort with >90% sensitivity and specificity. Gene profiles for ischemic stroke caused by large-vessel atherosclerosis and cardioembolism have been described that predict a second cohort with >85% sensitivity and specificity. Atherosclerotic genes were associated with clotting, platelets, and monocytes, and cardioembolic genes were associated with inflammation, infection, and neutrophils. These gene profiles predicted the cause of stroke in 58% of cryptogenic patients. These studies will provide diagnostic, prognostic, and therapeutic markers, and will advance our understanding of stroke in humans. New techniques to measure all coding and noncoding RNAs along with alternatively spliced transcripts will markedly advance molecular studies of human stroke

SLEPR: A Sample-Level Enrichment-Based Pathway Ranking Method — Seeking Biological Themes through Pathway-Level Consistency

Analysis of microarray and other high throughput data often involves identification of genes consistently up or down-regulated across samples as the first step in extraction of biological meaning. This gene-level paradigm can be limited as a result of valid sample fluctuations and biological complexities. In this report, we describe a novel method, SLEPR, which eliminates this limitation by relying on pathway-level consistencies. Our method first selects the sample-level differentiated genes from each individual sample, capturing genes missed by other analysis methods, ascertains the enrichment levels of associated pathways from each of those lists, and then ranks annotated pathways based on the consistency of enrichment levels of individual samples from both sample classes. As a proof of concept, we have used this method to analyze three public microarray datasets with a direct comparison with the GSEA method, one of the most popular pathway-level analysis methods in the field. We found that our method was able to reproduce the earlier observations with significant improvements in depth of coverage for validated or expected biological themes, but also produced additional insights that make biological sense. This new method extends existing analyses approaches and facilitates integration of different types of HTP data