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

Why Ni3_3Al is an itinerant ferromagnet but Ni3_3Ga is not

Ni$_3$Al and Ni$_3$Ga are closely related materials on opposite sides of a ferromagnetic quantum critical point. The Stoner factor of Ni is virtually the same in both compounds and the density of states is larger in Ni$_3$Ga. So, according to the Stoner theory, it should be more magnetic, and, in LDA calculations, it is. However, experimentally, it is a paramagnet, while Ni$_3$Al is an itinerant ferromagnet. We show that the critical spin fluctuations are stronger than in Ni$_3$Ga, due to a weaker q-dependence of the susceptibility, and this effect is strong enough to reverse the trend. The approach combines LDA calculations with the Landau theory and the fluctuation-dissipation theorem using the same momentum cut-off for both materials. The calculations provide evidence for strong, beyond LDA, spin fluctuations associated with the critical point in both materials, but stronger in Ni$_3$Ga than in Ni$_3$Al.Comment: replaced (incorrect version submitted

Randomized Benchmarking of Quantum Gates

A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography. However, standard process tomography is limited by errors in state preparation, measurement and one-qubit gates. It suffers from inefficient scaling with number of qubits and does not detect adverse error-compounding when gates are composed in long sequences. An additional problem is due to the fact that desirable error probabilities for scalable quantum computing are of the order of 0.0001 or lower. Experimentally proving such low errors is challenging. We describe a randomized benchmarking method that yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. We implemented randomized benchmarking on trapped atomic ion qubits, establishing a one-qubit error probability per randomized pi/2 pulse of 0.00482(17) in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.Comment: 13 page

Slip-velocity of large neutrally-buoyant particles in turbulent flows

We discuss possible definitions for a stochastic slip velocity that describes the relative motion between large particles and a turbulent flow. This definition is necessary because the slip velocity used in the standard drag model fails when particle size falls within the inertial subrange of ambient turbulence. We propose two definitions, selected in part due to their simplicity: they do not require filtration of the fluid phase velocity field, nor do they require the construction of conditional averages on particle locations. A key benefit of this simplicity is that the stochastic slip velocity proposed here can be calculated equally well for laboratory, field, and numerical experiments. The stochastic slip velocity allows the definition of a Reynolds number that should indicate whether large particles in turbulent flow behave (a) as passive tracers; (b) as a linear filter of the velocity field; or (c) as a nonlinear filter to the velocity field. We calculate the value of stochastic slip for ellipsoidal and spherical particles (the size of the Taylor microscale) measured in laboratory homogeneous isotropic turbulence. The resulting Reynolds number is significantly higher than 1 for both particle shapes, and velocity statistics show that particle motion is a complex non-linear function of the fluid velocity. We further investigate the nonlinear relationship by comparing the probability distribution of fluctuating velocities for particle and fluid phases

Multicanonical Study of Coarse-Grained Off-Lattice Models for Folding Heteropolymers

We have performed multicanonical simulations of hydrophobic-hydrophilic heteropolymers with two simple effective, coarse-grained off-lattice models to study the influence of specific interactions in the models on conformational transitions of selected sequences with 20 monomers. Another aspect of the investigation was the comparison with the purely hydrophobic homopolymer and the study of general conformational properties induced by the "disorder" in the sequence of a heteropolymer. Furthermore, we applied an optimization algorithm to sequences with up to 55 monomers and compared the global-energy minimum found with lowest-energy states identified within the multicanonical simulation. This was used to find out how reliable the multicanonical method samples the free-energy landscape, in particular for low temperatures.Comment: 11 pages, RevTeX, 10 Postscript figures, Author Information under http://www.physik.uni-leipzig.de/index.php?id=2

A Nonparametric Method for the Derivation of α/β Ratios from the Effect of Fractionated Irradiations

Multifractionation isoeffect data are commonly analysed under the assumption that cell survival determines the observed tissue or tumour response, and that it follows a linear-quadratic dose dependence. The analysis is employed to derive the α/β ratios of the linear-quadratic dose dependence, and different methods have been developed for this purpose. A common method uses the so-called Fe plot. A more complex but also more rigorous method has been introduced by Lam et al. (1979). Their method, which is based on numerical optimization procedures, is generalized and somewhat simplified in the present study. Tumour-regrowth data are used to explain the nonparametric procedure which provides α/β ratios without the need to postulate analytical expressions for the relationship between cell survival and regrowth delay

Transcriptional adaptation of Mycobacterium tuberculosis within macrophages: Insights into the phagosomal environment

Little is known about the biochemical environment in phagosomes harboring an infectious agent. To assess the state of this organelle we captured the transcriptional responses of Mycobacterium tuberculosis (MTB) in macrophages from wild-type and nitric oxide (NO) synthase 2–deficient mice before and after immunologic activation. The intraphagosomal transcriptome was compared with the transcriptome of MTB in standard broth culture and during growth in diverse conditions designed to simulate features of the phagosomal environment. Genes expressed differentially as a consequence of intraphagosomal residence included an interferon � – and NO-induced response that intensifies an iron-scavenging program, converts the microbe from aerobic to anaerobic respiration, and induces a dormancy regulon. Induction of genes involved in the activation and �-oxidation of fatty acids indicated that fatty acids furnish carbon and energy. Induction of �E-dependent, sodium dodecyl sulfate–regulated genes and genes involved in mycolic acid modification pointed to damage and repair of the cell envelope. Sentinel genes within the intraphagosomal transcriptome were induced similarly by MTB in the lungs of mice. The microbial transcriptome thus served as a bioprobe of the MTB phagosomal environment

The Abelian Manna model on two fractal lattices

We analyze the avalanche size distribution of the Abelian Manna model on two different fractal lattices with the same dimension d_g=ln(3)/ln(2), with the aim to probe for scaling behavior and to study the systematic dependence of the critical exponents on the dimension and structure of the lattices. We show that the scaling law D(2-tau)=d_w generalizes the corresponding scaling law on regular lattices, in particular hypercubes, where d_w=2. Furthermore, we observe that the lattice dimension d_g, the fractal dimension of the random walk on the lattice d_w, and the critical exponent D, form a plane in 3D parameter space, i.e. they obey the linear relationship D=0.632(3) d_g + 0.98(1) d_w - 0.49(3).Comment: 4 pages, 3 figures, 3 tables, submitted to PRE as a Brief Repor

Spectral Density on the Lattice

Spectral density in the pseudoscalar and vector channels is extracted from the SU(2) lattice quenched data. It is shown to consist of three sharp poles within the energy range accessible on the lattice.Comment: 38 pages, uuencoded tar-compressed ps-fil