On theories of random variables

We study theories of spaces of random variables: first, we consider random variables with values in the interval $[0,1]$, then with values in an arbitrary metric structure, generalising Keisler's randomisation of classical structures. We prove preservation and non-preservation results for model theoretic properties under this construction: i) The randomisation of a stable structure is stable. ii) The randomisation of a simple unstable structure is not simple. We also prove that in the randomised structure, every type is a Lascar type

Randomizations of models as metric structures

The notion of a randomization of a first order structure was introduced by Keisler in the paper Randomizing a Model, Advances in Math. 1999. The idea was to form a new structure whose elements are random elements of the original first order structure. In this paper we treat randomizations as continuous structures in the sense of Ben Yaacov and Usvyatsov. In this setting, the earlier results show that the randomization of a complete first order theory is a complete theory in continuous logic that admits elimination of quantifiers and has a natural set of axioms. We show that the randomization operation preserves the properties of being omega-categorical, omega-stable, and stable

On perturbations of continuous structures

We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are approximately $\aleph_0$-saturated up to arbitrarily small perturbations are isomorphic up to arbitrarily small perturbations (where the notion of perturbation is part of the data). As a corollary, we obtain a Ryll-Nardzewski style characterisation of complete theories all of whose separable models are isomorphic up to arbitrarily small perturbations

Reflexive representability and stable metrics

It is well-known that a topological group can be represented as a group of isometries of a reflexive Banach space if and only if its topology is induced by weakly almost periodic functions (see \cite{Shtern:CompactSemitopologicalSemigroups}, \cite{Megrelishvili:OperatorTopologies} and \cite{Megrelishvili:TopologicalTransformations}). We show that for a metrisable group this is equivalent to the property that its metric is uniformly equivalent to a stable metric in the sense of Krivine and Maurey (see \cite{Krivine-Maurey:EspacesDeBanachStables}). This result is used to give a partial negative answer to a problem of Megrelishvili

A novel SNP analysis method to detect copy number alterations with an unbiased reference signal directly from tumor samples

<p>Abstract</p> <p>Background</p> <p>Genomic instability in cancer leads to abnormal genome copy number alterations (CNA) as a mechanism underlying tumorigenesis. Using microarrays and other technologies, tumor CNA are detected by comparing tumor sample CN to normal reference sample CN. While advances in microarray technology have improved detection of copy number alterations, the increase in the number of measured signals, noise from array probes, variations in signal-to-noise ratio across batches and disparity across laboratories leads to significant limitations for the accurate identification of CNA regions when comparing tumor and normal samples.</p> <p>Methods</p> <p>To address these limitations, we designed a novel "Virtual Normal" algorithm (VN), which allowed for construction of an unbiased reference signal directly from test samples within an experiment using any publicly available normal reference set as a baseline thus eliminating the need for an in-lab normal reference set.</p> <p>Results</p> <p>The algorithm was tested using an optimal, paired tumor/normal data set as well as previously uncharacterized pediatric malignant gliomas for which a normal reference set was not available. Using Affymetrix 250K Sty microarrays, we demonstrated improved signal-to-noise ratio and detected significant copy number alterations using the VN algorithm that were validated by independent PCR analysis of the target CNA regions.</p> <p>Conclusions</p> <p>We developed and validated an algorithm to provide a virtual normal reference signal directly from tumor samples and minimize noise in the derivation of the raw CN signal. The algorithm reduces the variability of assays performed across different reagent and array batches, methods of sample preservation, multiple personnel, and among different laboratories. This approach may be valuable when matched normal samples are unavailable or the paired normal specimens have been subjected to variations in methods of preservation.</p

Wavelet-based identification of DNA focal genomic aberrations from single nucleotide polymorphism arrays

<p>Abstract</p> <p>Background</p> <p>Copy number aberrations (CNAs) are an important molecular signature in cancer initiation, development, and progression. However, these aberrations span a wide range of chromosomes, making it hard to distinguish cancer related genes from other genes that are not closely related to cancer but are located in broadly aberrant regions. With the current availability of high-resolution data sets such as single nucleotide polymorphism (SNP) microarrays, it has become an important issue to develop a computational method to detect driving genes related to cancer development located in the focal regions of CNAs.</p> <p>Results</p> <p>In this study, we introduce a novel method referred to as the wavelet-based identification of focal genomic aberrations (WIFA). The use of the wavelet analysis, because it is a multi-resolution approach, makes it possible to effectively identify focal genomic aberrations in broadly aberrant regions. The proposed method integrates multiple cancer samples so that it enables the detection of the consistent aberrations across multiple samples. We then apply this method to glioblastoma multiforme and lung cancer data sets from the SNP microarray platform. Through this process, we confirm the ability to detect previously known cancer related genes from both cancer types with high accuracy. Also, the application of this approach to a lung cancer data set identifies focal amplification regions that contain known oncogenes, though these regions are not reported using a recent CNAs detecting algorithm GISTIC: SMAD7 (chr18q21.1) and FGF10 (chr5p12).</p> <p>Conclusions</p> <p>Our results suggest that WIFA can be used to reveal cancer related genes in various cancer data sets.</p

Candida albicans AGE3, the Ortholog of the S. cerevisiae ARF-GAP-Encoding Gene GCS1, Is Required for Hyphal Growth and Drug Resistance

BACKGROUND: Hyphal growth and multidrug resistance of C. albicans are important features for virulence and antifungal therapy of this pathogenic fungus. METHODOLOGY/PRINCIPAL FINDINGS: Here we show by phenotypic complementation analysis that the C. albicans gene AGE3 is the functional ortholog of the yeast ARF-GAP-encoding gene GCS1. The finding that the gene is required for efficient endocytosis points to an important functional role of Age3p in endosomal compartments. Most C. albicans age3Delta mutant cells which grew as cell clusters under yeast growth conditions showed defects in filamentation under different hyphal growth conditions and were almost completely disabled for invasive filamentous growth. Under hyphal growth conditions only a fraction of age3Delta cells shows a wild-type-like polarization pattern of the actin cytoskeleton and lipid rafts. Moreover, age3Delta cells were highly susceptible to several unrelated toxic compounds including antifungal azole drugs. Irrespective of the AGE3 genotype, C-terminal fusions of GFP to the drug efflux pumps Cdr1p and Mdr1p were predominantly localized in the plasma membrane. Moreover, the plasma membranes of wild-type and age3Delta mutant cells contained similar amounts of Cdr1p, Cdr2p and Mdr1p. CONCLUSIONS/SIGNIFICANCE: The results indicate that the defect in sustaining filament elongation is probably caused by the failure of age3Delta cells to polarize the actin cytoskeleton and possibly of inefficient endocytosis. The high susceptibility of age3Delta cells to azoles is not caused by inefficient transport of efflux pumps to the cell membrane. A possible role of a vacuolar defect of age3Delta cells in drug susceptibility is proposed and discussed. In conclusion, our study shows that the ARF-GAP Age3p is required for hyphal growth which is an important virulence factor of C. albicans and essential for detoxification of azole drugs which are routinely used for antifungal therapy. Thus, it represents a promising antifungal drug target

Gene profiling of the erythro- and megakaryoblastic leukaemias induced by the Graffi murine retrovirus

<p>Abstract</p> <p>Background</p> <p>Acute erythro- and megakaryoblastic leukaemias are associated with very poor prognoses and the mechanism of blastic transformation is insufficiently elucidated. The murine Graffi leukaemia retrovirus induces erythro- and megakaryoblastic leukaemias when inoculated into NFS mice and represents a good model to study these leukaemias.</p> <p>Methods</p> <p>To expand our understanding of genes specific to these leukaemias, we compared gene expression profiles, measured by microarray and RT-PCR, of all leukaemia types induced by this virus.</p> <p>Results</p> <p>The transcriptome level changes, present between the different leukaemias, led to the identification of specific cancerous signatures. We reported numerous genes that may be potential oncogenes, may have a function related to erythropoiesis or megakaryopoiesis or have a poorly elucidated physiological role. The expression pattern of these genes has been further tested by RT-PCR in different samples, in a Friend erythroleukaemic model and in human leukaemic cell lines.</p> <p>We also screened the megakaryoblastic leukaemias for viral integrations and identified genes targeted by these integrations and potentially implicated in the onset of the disease.</p> <p>Conclusions</p> <p>Taken as a whole, the data obtained from this global gene profiling experiment have provided a detailed characterization of Graffi virus induced erythro- and megakaryoblastic leukaemias with many genes reported specific to the transcriptome of these leukaemias for the first time.</p

Loss of PTB or Negative Regulation of Notch mRNA Reveals Distinct Zones of Notch and Actin Protein Accumulation in Drosophila Embryo

Polypyrimidine Tract Binding (PTB) protein is a regulator of mRNA processing and translation. Genetic screens and studies of wing and bristle development during the post-embryonic stages of Drosophila suggest that it is a negative regulator of the Notch pathway. How PTB regulates the Notch pathway is unknown. Our studies of Drosophila embryogenesis indicate that (1) the Notch mRNA is a potential target of PTB, (2) PTB and Notch functions in the dorso-lateral regions of the Drosophila embryo are linked to actin regulation but not their functions in the ventral region, and (3) the actin-related Notch activity in the dorso-lateral regions might require a Notch activity at or near the cell surface that is different from the nuclear Notch activity involved in cell fate specification in the ventral region. These data raise the possibility that the Drosophila embryo is divided into zones of different PTB and Notch activities based on whether or not they are linked to actin regulation. They also provide clues to the almost forgotten role of Notch in cell adhesion and reveal a role for the Notch pathway in cell fusions