178 research outputs found
Stability and aggregation of ranked gene lists
Ranked gene lists are highly instable in the sense that similar measures of differential gene expression may yield very different rankings, and that a small change of the data set usually affects the obtained gene list considerably. Stability issues have long been under-considered in the literature, but they have grown to a hot topic in the last few years, perhaps as a consequence of the increasing skepticism on the reproducibility and clinical applicability of molecular research findings. In this article, we review existing approaches for the assessment of stability of ranked gene lists and the related problem of aggregation, give some practical recommendations, and warn against potential misuse of these methods. This overview is illustrated through an application to a recent leukemia data set using the freely available Bioconductor package GeneSelector
Passive Scalar: Scaling Exponents and Realizability
An isotropic passive scalar field advected by a rapidly-varying velocity
field is studied. The tail of the probability distribution for
the difference in across an inertial-range distance is found
to be Gaussian. Scaling exponents of moments of increase as
or faster at large order , if a mean dissipation conditioned on is
a nondecreasing function of . The computed numerically
under the so-called linear ansatz is found to be realizable. Some classes of
gentle modifications of the linear ansatz are not realizable.Comment: Substantially revised to conform with published version. Revtex (4
pages) with 2 postscript figures. Send email to [email protected]
Universal statistics of non-linear energy transfer in turbulent models
A class of shell models for turbulent energy transfer at varying the
inter-shell separation, , is investigated. Intermittent corrections in
the continuous limit of infinitely close shells () have
been measured. Although the model becomes, in this limit, non-intermittent, we
found universal aspects of the velocity statistics which can be interpreted in
the framework of log-poisson distributions, as proposed by She and Waymire
(1995, Phys. Rev. Lett. 74, 262). We suggest that non-universal aspects of
intermittency can be adsorbed in the parameters describing statistics and
properties of the most singular structure. On the other hand, universal aspects
can be found by looking at corrections to the monofractal scaling of the most
singular structure. Connections with similar results reported in other shell
models investigations and in real turbulent flows are discussed.Comment: 4 pages, 2 figures available upon request to [email protected]
Lognormal scale invariant random measures
In this article, we consider the continuous analog of the celebrated
Mandelbrot star equation with lognormal weights. Mandelbrot introduced this
equation to characterize the law of multiplicative cascades. We show existence
and uniqueness of measures satisfying the aforementioned continuous equation;
these measures fall under the scope of the Gaussian multiplicative chaos theory
developed by J.P. Kahane in 1985 (or possibly extensions of this theory). As a
by product, we also obtain an explicit characterization of the covariance
structure of these measures. We also prove that qualitative properties such as
long-range independence or isotropy can be read off the equation.Comment: 31 pages; Probability Theory and Related Fields (2012) electronic
versio
Periodically kicked turbulence
Periodically kicked turbulence is theoretically analyzed within a mean field
theory. For large enough kicking strength A and kicking frequency f the
Reynolds number grows exponentially and then runs into some saturation. The
saturation level can be calculated analytically; different regimes can be
observed. For large enough Re we find the saturation level to be proportional
to A*f, but intermittency can modify this scaling law. We suggest an
experimental realization of periodically kicked turbulence to study the
different regimes we theoretically predict and thus to better understand the
effect of forcing on fully developed turbulence.Comment: 4 pages, 3 figures. Phys. Rev. E., in pres
Generalized scaling in fully developed turbulence
In this paper we report numerical and experimental results on the scaling
properties of the velocity turbulent fields in several flows. The limits of a
new form of scaling, named Extended Self Similarity(ESS), are discussed. We
show that, when a mean shear is absent, the self scaling exponents are
universal and they do not depend on the specific flow (3D homogeneous
turbulence, thermal convection , MHD). In contrast, ESS is not observed when a
strong shear is present. We propose a generalized version of self scaling which
extends down to the smallest resolvable scales even in cases where ESS is not
present. This new scaling is checked in several laboratory and numerical
experiment. A possible theoretical interpretation is also proposed. A synthetic
turbulent signal having most of the properties of a real one has been
generated.Comment: 25 pages, plain Latex, figures are available upon request to the
authors ([email protected], [email protected]
A new scaling property of turbulent flows
We discuss a possible theoretical interpretation of the self scaling property
of turbulent flows (Extended Self Similarity). Our interpretation predicts
that, even in cases when ESS is not observed, a generalized self scaling, must
be observed. This prediction is checked on a number of laboratory experiments
and direct numerical simulations.Comment: Plain Latex, 1 figure available upon request to
[email protected]
Longitudinal Structure Functions in Decaying and Forced Turbulence
In order to reliably compute the longitudinal structure functions in decaying
and forced turbulence, local isotropy is examined with the aid of the isotropic
expression of the incompressible conditions for the second and third order
structure functions. Furthermore, the Karman-Howarth-Kolmogorov relation is
investigated to examine the effects of external forcing and temporally
decreasing of the second order structure function. On the basis of these
investigations, the scaling range and exponents of the longitudinal
structure functions are determined for decaying and forced turbulence with the
aid of the extended-self-similarity (ESS) method. We find that 's are
smaller, for , in decaying turbulence than in forced turbulence. The
reasons for this discrepancy are discussed. Analysis of the local slopes of the
structure functions is used to justify the ESS method.Comment: 15 pages, 16 figure
Exact Resummations in the Theory of Hydrodynamic Turbulence: I The Ball of Locality and Normal Scaling
This paper is the first in a series of three papers that aim at understanding
the scaling behaviour of hydrodynamic turbulence. We present in this paper a
perturbative theory for the structure functions and the response functions of
the hydrodynamic velocity field in real space and time. Starting from the
Navier-Stokes equations (at high Reynolds number Re) we show that the standard
perturbative expansions that suffer from infra-red divergences can be exactly
resummed using the Belinicher-L'vov transformation. After this exact (partial)
resummation it is proven that the resulting perturbation theory is free of
divergences, both in large and in small spatial separations. The hydrodynamic
response and the correlations have contributions that arise from mediated
interactions which take place at some space- time coordinates. It is shown that
the main contribution arises when these coordinates lie within a shell of a
"ball of locality" that is defined and discussed. We argue that the real
space-time formalism developed here offers a clear and intuitive understanding
of every diagram in the theory, and of every element in the diagrams. One major
consequence of this theory is that none of the familiar perturbative mechanisms
may ruin the classical Kolmogorov (K41) scaling solution for the structure
functions. Accordingly, corrections to the K41 solutions should be sought in
nonperturbative effects. These effects are the subjects of papers II and III in
this series, that will propose a mechanism for anomalous scaling in turbulence,
which in particular allows multiscaling of the structure functions.Comment: PRE in press, 18 pages + 6 figures, REVTeX. The Eps files of figures
will be FTPed by request to [email protected]
Variational bound on energy dissipation in plane Couette flow
We present numerical solutions to the extended Doering-Constantin variational
principle for upper bounds on the energy dissipation rate in turbulent plane
Couette flow. Using the compound matrix technique in order to reformulate this
principle's spectral constraint, we derive a system of equations that is
amenable to numerical treatment in the entire range from low to asymptotically
high Reynolds numbers. Our variational bound exhibits a minimum at intermediate
Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a
consequence of a bifurcation of the minimizing wavenumbers, there exist two
length scales that determine the optimal upper bound: the effective width of
the variational profile's boundary segments, and the extension of their flat
interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one
uuencoded .tar.gz file from [email protected]
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