Measuring reproducibility of high-throughput experiments

Reproducibility is essential to reliable scientific discovery in high-throughput experiments. In this work we propose a unified approach to measure the reproducibility of findings identified from replicate experiments and identify putative discoveries using reproducibility. Unlike the usual scalar measures of reproducibility, our approach creates a curve, which quantitatively assesses when the findings are no longer consistent across replicates. Our curve is fitted by a copula mixture model, from which we derive a quantitative reproducibility score, which we call the "irreproducible discovery rate" (IDR) analogous to the FDR. This score can be computed at each set of paired replicate ranks and permits the principled setting of thresholds both for assessing reproducibility and combining replicates. Since our approach permits an arbitrary scale for each replicate, it provides useful descriptive measures in a wide variety of situations to be explored. We study the performance of the algorithm using simulations and give a heuristic analysis of its theoretical properties. We demonstrate the effectiveness of our method in a ChIP-seq experiment.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS466 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A logarithmic generalization of tensor product theory for modules for a vertex operator algebra

We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. The corresponding intertwining operators contain logarithms of the variables.Comment: 39 pages. Misprints corrected. Final versio

Spectral Energy Distributions of Gamma Ray Bursts Energized by External Shocks

Sari, Piran, and Narayan have derived analytic formulas to model the spectra from gamma-ray burst blast waves that are energized by sweeping up material from the surrounding medium. We extend these expressions to apply to general radiative regimes and to include the effects of synchrotron self-absorption. Electron energy losses due to the synchrotron self-Compton process are also treated in a very approximate way. The calculated spectra are compared with detailed numerical simulation results. We find that the spectral and temporal breaks from the detailed numerical simulation are much smoother than the analytic formulas imply, and that the discrepancies between the analytic and numerical results are greatest near the breaks and endpoints of the synchrotron spectra. The expressions are most accurate (within a factor of ~ 3) in the optical/X-ray regime during the afterglow phase, and are more accurate when epsilon_e, the fraction of swept-up particle energy that is transferred to the electrons, is <~ 0.1. The analytic results provide at best order-of-magnitude accuracy in the self-absorbed radio/infrared regime, and give poor fits to the self-Compton spectra due to complications from Klein-Nishina effects and photon-photon opacity.Comment: 16 pages, 7 figures, ApJ, in press, 537, July 1, 2000. Minor changes in response to referee report, corrected figure

The measurement and analysis of age-related changes in Caenorhabditis elegans

Aging is characterized by progressive degenerative changes in tissue organization and function that increase the probability of mortality. Major goals of aging research include elucidating the series of events that cause degenerative changes and analyzing environmental and genetic factors that modulate these changes. The basis for mechanistic studies of aging are accurate and precise descriptions of age-related changes, since these descriptions define the aging phenotype. Here we review studies that describe age-related changes in C. elegans including measurements of integrated functions such as behavior, microscopic analyses of tissue organization, and biochemical studies of macromolecules. Genetic and environmental factors that influence these changes are described, and studies that analyze the relationships between different age-related changes are discussed. Together these studies provide fundamental insights into aging in C. elegans that may be relevant to aging in other animals

Differential gene expression associated with postnatal equine articular cartilage maturation

<p>Abstract</p> <p>Background</p> <p>Articular cartilage undergoes an important maturation process from neonate to adult that is reflected by alterations in matrix protein organization and increased heterogeneity of chondrocyte morphology. In the horse, these changes are influenced by exercise during the first five months of postnatal life. Transcriptional profiling was used to evaluate changes in articular chondrocyte gene expression during postnatal growth and development.</p> <p>Methods</p> <p>Total RNA was isolated from the articular cartilage of neonatal (0–10 days) and adult (4–5 years) horses, subjected to one round of linear RNA amplification, and then applied to a 9,367-element equine-specific cDNA microarray. Comparisons were made with a dye-swap experimental design. Microarray results for selected genes (COL2A1, COMP, P4HA1, TGFB1, TGFBR3, TNC) were validated by quantitative polymerase chain reaction (qPCR).</p> <p>Results</p> <p>Fifty-six probe sets, which represent 45 gene products, were up-regulated (p < 0.01) in chondrocytes of neonatal articular cartilage relative to chondrocytes of adult articular cartilage. Conversely, 586 probe sets, which represent 499 gene products, were up-regulated (p < 0.01) in chondrocytes of adult articular cartilage relative to chondrocytes of neonatal articular cartilage. Collagens, matrix-modifying enzymes, and provisional matrix non-collagenous proteins were expressed at higher levels in the articular cartilage of newborn foals. Those genes with increased mRNA abundance in adult chondrocytes included leucine-rich small proteoglycans, matrix assembly, and cartilage maintenance proteins.</p> <p>Conclusion</p> <p>Differential expression of genes encoding matrix proteins and matrix-modifying enzymes between neonates and adults reflect a cellular maturation process in articular chondrocytes. Up-regulated transcripts in neonatal cartilage are consistent with growth and expansion of the articular surface. Expression patterns in mature articular cartilage indicate a transition from growth to homeostasis, and tissue function related to withstanding shear and weight-bearing stresses.</p

Poisson valuations

We study Poisson valuations and provide their applications in solving problems related to rigidity, automorphisms, Dixmier property, isomorphisms, and embeddings of Poisson algebras and fields.Comment: 47 page

Weighted Poisson polynomial rings

We discuss Poisson structures on a weighted polynomial algebra $A:=\Bbbk[x, y, z]$ defined by a homogeneous element $\Omega\in A$, called a potential. We start with classifying potentials $\Omega$ of degree deg$(x)+$deg$(y)+$deg$(z)$ with any positive weight (deg$(x)$, deg$(y)$, deg$(z)$) and list all with isolated singularity. Based on the classification, we study the rigidity of $A$ in terms of graded twistings and classify Poisson fraction fields of $A/(\Omega)$ for irreducible potentials. Using Poisson valuations, we characterize the Poisson automorphism group of $A$ when $\Omega$ has an isolated singularity extending a nice result of Makar-Limanov-Turusbekova-Umirbaev. Finally, Poisson cohomology groups are computed for new classes of Poisson polynomial algebras.Comment: 37 page

Robust Quantitative Susceptibility Mapping via Approximate Message Passing

Purpose: It is challenging to recover magnetic susceptibility in the presence of phase errors, which may be caused by noise or strong local-susceptibility shifts in cases of brain hemorrhage and calcification. We propose a Bayesian formulation for quantitative susceptibility mapping (QSM) where a customized Gaussian-mixture distribution is used to model the long-tailed noise distribution. Theory: Complex exponential functions of the phase are used as nonlinear measurements. Wavelet coefficients of the susceptibility map are modeled by the Laplace distribution. Measurement noise is modeled by a two-component Gaussian-mixture distribution, where the second component is reserved to model the noise outliers. The susceptibility map and distribution parameters are jointly recovered using approximate message passing (AMP). Methods: The proposed AMP with built-in parameter estimation (AMP-PE) is compared with the state-of-the-art nonlinear L1-QSM and MEDI approaches that adopt the L1-norm and L2-norm data-fidelity terms respectively. They are tested on the simulated and in vivo datasets. Results: On the simulated Sim2Snr1 dataset, AMP-PE achieved the lowest NRMSE and SSIM, MEDI achieved the lowest HFEN. On the in vivo datasets, AMP-PE is more robust and better at preserving structural details and removing streaking artifacts in the hemorrhage cases than L1-QSM and MEDI. Conclusion: By leveraging a customized Gaussian-mixture noise prior, AMP-PE achieves better performance in challenging cases of brain hemorrhage and calcification. It is equipped with built-in parameter estimation, which avoids subjective bias from the usual visual-tuning step of in vivo reconstruction.Comment: Keywords: Approximate message passing, Compressive sensing, Parameter estimation, QS