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

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 Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time

Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We solve the longstanding open problem of finding a complete axiom system for basic quantifier-free propositional ITL (PITL) with infinite time for analysing nonterminating computational systems. Our completeness proof uses a reduction to completeness for PITL with finite time and conventional propositional linear-time temporal logic. Unlike completeness proofs of equally expressive logics with nonelementary computational complexity, our semantic approach does not use tableaux, subformula closures or explicit deductions involving encodings of omega automata and nontrivial techniques for complementing them. We believe that our result also provides evidence of the naturalness of interval-based reasoning

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

Detection of copy number variation from array intensity and sequencing read depth using a stepwise Bayesian model

Abstract Background Copy number variants (CNVs) have been demonstrated to occur at a high frequency and are now widely believed to make a significant contribution to the phenotypic variation in human populations. Array-based comparative genomic hybridization (array-CGH) and newly developed read-depth approach through ultrahigh throughput genomic sequencing both provide rapid, robust, and comprehensive methods to identify CNVs on a whole-genome scale. Results We developed a Bayesian statistical analysis algorithm for the detection of CNVs from both types of genomic data. The algorithm can analyze such data obtained from PCR-based bacterial artificial chromosome arrays, high-density oligonucleotide arrays, and more recently developed high-throughput DNA sequencing. Treating parameters--e.g., the number of CNVs, the position of each CNV, and the data noise level--that define the underlying data generating process as random variables, our approach derives the posterior distribution of the genomic CNV structure given the observed data. Sampling from the posterior distribution using a Markov chain Monte Carlo method, we get not only best estimates for these unknown parameters but also Bayesian credible intervals for the estimates. We illustrate the characteristics of our algorithm by applying it to both synthetic and experimental data sets in comparison to other segmentation algorithms. Conclusions In particular, the synthetic data comparison shows that our method is more sensitive than other approaches at low false positive rates. Furthermore, given its Bayesian origin, our method can also be seen as a technique to refine CNVs identified by fast point-estimate methods and also as a framework to integrate array-CGH and sequencing data with other CNV-related biological knowledge, all through informative priors.</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

A Multi-Sample Based Method for Identifying Common CNVs in Normal Human Genomic Structure Using High-Resolution aCGH Data

BACKGROUND: It is difficult to identify copy number variations (CNV) in normal human genomic data due to noise and non-linear relationships between different genomic regions and signal intensity. A high-resolution array comparative genomic hybridization (aCGH) containing 42 million probes, which is very large compared to previous arrays, was recently published. Most existing CNV detection algorithms do not work well because of noise associated with the large amount of input data and because most of the current methods were not designed to analyze normal human samples. Normal human genome analysis often requires a joint approach across multiple samples. However, the majority of existing methods can only identify CNVs from a single sample. METHODOLOGY AND PRINCIPAL FINDINGS: We developed a multi-sample-based genomic variations detector (MGVD) that uses segmentation to identify common breakpoints across multiple samples and a k-means-based clustering strategy. Unlike previous methods, MGVD simultaneously considers multiple samples with different genomic intensities and identifies CNVs and CNV zones (CNVZs); CNVZ is a more precise measure of the location of a genomic variant than the CNV region (CNVR). CONCLUSIONS AND SIGNIFICANCE: We designed a specialized algorithm to detect common CNVs from extremely high-resolution multi-sample aCGH data. MGVD showed high sensitivity and a low false discovery rate for a simulated data set, and outperformed most current methods when real, high-resolution HapMap datasets were analyzed. MGVD also had the fastest runtime compared to the other algorithms evaluated when actual, high-resolution aCGH data were analyzed. The CNVZs identified by MGVD can be used in association studies for revealing relationships between phenotypes and genomic aberrations. Our algorithm was developed with standard C++ and is available in Linux and MS Windows format in the STL library. It is freely available at: http://embio.yonsei.ac.kr/~Park/mgvd.php

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