Probabilities of spurious connections in gene networks: Application to expression time series

Motivation: The reconstruction of gene networks from gene expression microarrays is gaining popularity as methods improve and as more data become available. The reliability of such networks could be judged by the probability that a connection between genes is spurious, resulting from chance fluctuations rather than from a true biological relationship. Results: Unlike the false discovery rate and positive false discovery rate, the decisive false discovery rate (dFDR) is exactly equal to a conditional probability without assuming independence or the randomness of hypothesis truth values. This property is useful not only in the common application to the detection of differential gene expression, but also in determining the probability of a spurious connection in a reconstructed gene network. Estimators of the dFDR can estimate each of three probabilities: 1. The probability that two genes that appear to be associated with each other lack such association. 2. The probability that a time ordering observed for two associated genes is misleading. 3. The probability that a time ordering observed for two genes is misleading, either because they are not associated or because they are associated without a lag in time. The first probability applies to both static and dynamic gene networks, and the other two only apply to dynamic gene networks. Availability: Cross-platform software for network reconstruction, probability estimation, and plotting is free from http://www.davidbickel.com as R functions and a Java application.Comment: Like q-bio.GN/0404032, this was rejected in March 2004 because it was submitted to the math archive. The only modification is a corrected reference to q-bio.GN/0404032, which was not modified at al

A Study of the Matrix Carleson Embedding Theorem with Applications to Sparse Operators

In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions and $H^1$-BMO duality. Along the way, we establish boundedness results about new maximal functions associated to matrix $A_2$ weights and duality results concerning $H^1$ and BMO sequence spaces in the matrix setting. As an application, we then use this Carleson Embedding Theorem to show that if $S$ is a sparse operator, then the operator norm of $S$ on $L^2(W)$ satisfies: $$\| S\|_{L^2(W) \rightarrow L^2(W)} \lesssim [W]_{A_2}^{\frac{3}{2}},$$ for every matrix $A_2$ weight $W$.Comment: 14 page

Development of flight check-out system Final report

Flight checkout system breadboard design, construction and testin

Depletion forces near a soft surface

We investigate excluded-volume effects in a bidisperse colloidal suspension near a flexible interface. Inspired by a recent experiment by Dinsmore et al. (Phys. Rev, Lett. 80, 409 (1998)), we study the adsorption of a mesoscopic bead on the surface and show that depletion forces could in principle lead to particle encapsulation. We then consider the effect of surface fluctuations on the depletion potential itself and construct the density profile of a polymer solution near a soft interface. Surprisingly we find that the chains accumulate at the wall, whereas the density displays a deficit of particles at distances larger than the surface roughness. This non-monotonic behavior demonstrates that surface fluctuations can have major repercusions on the properties of a colloidal solution. On average, the additional contribution to the Gibbs adsorbance is negative. The amplitude of the depletion potential between a mesoscopic bead and the surface increases accordingly.Comment: 10 pages, 5 figure

Composite Effects of Polymorphisms near Multiple Regulatory Elements Create a Major-Effect QTL

Many agriculturally, evolutionarily, and medically important characters vary in a quantitative fashion. Unfortunately, the genes and sequence variants accounting for this variation remain largely unknown due to a variety of biological and technical challenges. Drosophila melanogaster contains high levels of sequence variation and low linkage disequilibrium, allowing us to dissect the effects of many causative variants within a single locus. Here, we take advantage of these features to identify and characterize the sequence polymorphisms that comprise major effect QTL alleles segregating at the bric-a-brac locus. We show that natural bric-a-brac alleles with large effects on cuticular pigmentation reflect a cumulative impact of polymorphisms that affect three functional regions: a promoter, a tissue-specific enhancer, and a Polycomb response element. Analysis of allele-specific expression at the bric-a-brac locus confirms that these polymorphisms modulate transcription at the cis-regulatory level. Our results establish that a single QTL can act through a confluence of multiple molecular mechanisms and that sequence variation in regions flanking experimentally validated functional elements can have significant quantitative effects on transcriptional activity and phenotype. These findings have important design and conceptual implications for basic and medical genomics