98,065 research outputs found
Semiparametric curve alignment and shift density estimation for biological data
Assume that we observe a large number of curves, all of them with identical,
although unknown, shape, but with a different random shift. The objective is to
estimate the individual time shifts and their distribution. Such an objective
appears in several biological applications like neuroscience or ECG signal
processing, in which the estimation of the distribution of the elapsed time
between repetitive pulses with a possibly low signal-noise ratio, and without a
knowledge of the pulse shape is of interest. We suggest an M-estimator leading
to a three-stage algorithm: we split our data set in blocks, on which the
estimation of the shifts is done by minimizing a cost criterion based on a
functional of the periodogram; the estimated shifts are then plugged into a
standard density estimator. We show that under mild regularity assumptions the
density estimate converges weakly to the true shift distribution. The theory is
applied both to simulations and to alignment of real ECG signals. The estimator
of the shift distribution performs well, even in the case of low
signal-to-noise ratio, and is shown to outperform the standard methods for
curve alignment.Comment: 30 pages ; v5 : minor changes and correction in the proof of
Proposition 3.
The distribution of word matches between Markovian sequences with periodic boundary conditions
Word match counts have traditionally been proposed as an alignment-free measure of similarity for biological sequences. The D2 statistic, which simply counts the number of exact word matches between two sequences, is a useful test bed for developing rigorous mathematical results, which can then be extended to more biologically useful measures. The distributional properties of the D2 statistic under the null hypothesis of identically and independently distributed letters have been studied extensively, but no comprehensive study of the D2 distribution for biologically more realistic higher-order Markovian sequences exists. Here we derive exact formulas for the mean and variance of the D2 statistic for Markovian sequences of any order, and demonstrate through Monte Carlo simulations that the entire distribution is accurately characterized by a Pólya-Aeppli distribution for sequence lengths of biological interest. The approach is novel in that Markovian dependency is defined for sequences with periodic boundary conditions, and this enables exact analytic formulas for the mean and variance to be derived. We also carry out a preliminary comparison between the approximate D2 distribution computed with the theoretical mean and variance under a Markovian hypothesis and an empirical D2 distribution from the human genome
Galaxy alignments: Observations and impact on cosmology
Galaxy shapes are not randomly oriented, rather they are statistically
aligned in a way that can depend on formation environment, history and galaxy
type. Studying the alignment of galaxies can therefore deliver important
information about the physics of galaxy formation and evolution as well as the
growth of structure in the Universe. In this review paper we summarise key
measurements of galaxy alignments, divided by galaxy type, scale and
environment. We also cover the statistics and formalism necessary to understand
the observations in the literature. With the emergence of weak gravitational
lensing as a precision probe of cosmology, galaxy alignments have taken on an
added importance because they can mimic cosmic shear, the effect of
gravitational lensing by large-scale structure on observed galaxy shapes. This
makes galaxy alignments, commonly referred to as intrinsic alignments, an
important systematic effect in weak lensing studies. We quantify the impact of
intrinsic alignments on cosmic shear surveys and finish by reviewing practical
mitigation techniques which attempt to remove contamination by intrinsic
alignments.Comment: 52 pages excl. references, 16 figures; minor changes to match version
published in Space Science Reviews; part of a topical volume on galaxy
alignments, with companion papers arXiv:1504.05456 and arXiv:1504.0554
Spin alignment of stars in old open clusters
Stellar clusters form by gravitational collapse of turbulent molecular
clouds, with up to several thousand stars per cluster. They are thought to be
the birthplace of most stars and therefore play an important role in our
understanding of star formation, a fundamental problem in astrophysics. The
initial conditions of the molecular cloud establish its dynamical history until
the stellar cluster is born. However, the evolution of the cloud's angular
momentum during cluster formation is not well understood. Current observations
have suggested that turbulence scrambles the angular momentum of the
cluster-forming cloud, preventing spin alignment amongst stars within a
cluster. Here we use asteroseismology to measure the inclination angles of spin
axes in 48 stars from the two old open clusters NGC~6791 and NGC~6819. The
stars within each cluster show strong alignment. Three-dimensional
hydrodynamical simulations of proto-cluster formation show that at least 50 %
of the initial proto-cluster kinetic energy has to be rotational in order to
obtain strong stellar-spin alignment within a cluster. Our result indicates
that the global angular momentum of the cluster-forming clouds was efficiently
transferred to each star and that its imprint has survived after several
gigayears since the clusters formed.Comment: 14 pages, 3 figures, 1 table. Published in Nature Astronom
The WiggleZ Dark Energy Survey: Direct constraints on blue galaxy intrinsic alignments at intermediate redshifts
Correlations between the intrinsic shapes of galaxy pairs, and between the
intrinsic shapes of galaxies and the large-scale density field, may be induced
by tidal fields. These correlations, which have been detected at low redshifts
(z<0.35) for bright red galaxies in the Sloan Digital Sky Survey (SDSS), and
for which upper limits exist for blue galaxies at z~0.1, provide a window into
galaxy formation and evolution, and are also an important contaminant for
current and future weak lensing surveys. Measurements of these alignments at
intermediate redshifts (z~0.6) that are more relevant for cosmic shear
observations are very important for understanding the origin and redshift
evolution of these alignments, and for minimising their impact on weak lensing
measurements. We present the first such intermediate-redshift measurement for
blue galaxies, using galaxy shape measurements from SDSS and spectroscopic
redshifts from the WiggleZ Dark Energy Survey. Our null detection allows us to
place upper limits on the contamination of weak lensing measurements by blue
galaxy intrinsic alignments that, for the first time, do not require
significant model-dependent extrapolation from the z~0.1 SDSS observations.
Also, combining the SDSS and WiggleZ constraints gives us a long redshift
baseline with which to constrain intrinsic alignment models and contamination
of the cosmic shear power spectrum. Assuming that the alignments can be
explained by linear alignment with the smoothed local density field, we find
that a measurement of \sigma_8 in a blue-galaxy dominated, CFHTLS-like survey
would be contaminated by at most +/-0.02 (95% confidence level, SDSS and
WiggleZ) or +/-0.03 (WiggleZ alone) due to intrinsic alignments. [Abridged]Comment: 18 pages, 12 figures, accepted to MNRAS; v2 has correction to one
author's name, NO other changes; v3 has minor changes in explanation and
calculations, no significant difference in results or conclusions; v4 has an
additional footnote about model interpretation, no changes to
data/calculations/result
Scale dependence of galaxy biasing investigated by weak gravitational lensing: An assessment using semi-analytic galaxies and simulated lensing data
Galaxies are biased tracers of the matter density on cosmological scales. For
future tests of galaxy models, we refine and assess a method to measure galaxy
biasing as function of physical scale with weak gravitational lensing. This
method enables us to reconstruct the galaxy bias factor as well as the
galaxy-matter correlation on spatial scales between for redshift-binned lens galaxies below redshift .
In the refinement, we account for an intrinsic alignment of source
ellipticities, and we correct for the magnification bias of the lens galaxies,
relevant for the galaxy-galaxy lensing signal, to improve the accuracy of the
reconstructed . For simulated data, the reconstructions achieve an
accuracy of (68\% confidence level) over the above -range for a
survey area and a typical depth of contemporary ground-based surveys.
Realistically the accuracy is, however, probably reduced to about ,
mainly by systematic uncertainties in the assumed intrinsic source alignment,
the fiducial cosmology, and the redshift distributions of lens and source
galaxies (in that order). Furthermore, our reconstruction technique employs
physical templates for and that elucidate the impact of central
galaxies and the halo-occupation statistics of satellite galaxies on the
scale-dependence of galaxy bias, which we discuss in the paper. In a first
demonstration, we apply this method to previous measurements in the
Garching-Bonn-Deep Survey and give a physical interpretation of the lens
population.Comment: 31 pages, 16 figures; corrected typos in Eqs. (31), (34), and (36
The network of stabilizing contacts in proteins studied by coevolutionary data
The primary structure of proteins, that is their sequence, represents one of
the most abundant set of experimental data concerning biomolecules. The study
of correlations in families of co--evolving proteins by means of an inverse
Ising--model approach allows to obtain information on their native
conformation. Following up on a recent development along this line, we optimize
the algorithm to calculate effective energies between the residues, validating
the approach both back-calculating interaction energies in a model system, and
predicting the free energies associated to mutations in real systems. Making
use of these effective energies, we study the networks of interactions which
stabilizes the native conformation of some well--studied proteins, showing that
it display different properties than the associated contact network
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