4,200 research outputs found
Finite mixtures of matrix-variate Poisson-log normal distributions for three-way count data
Three-way data structures, characterized by three entities, the units, the
variables and the occasions, are frequent in biological studies. In RNA
sequencing, three-way data structures are obtained when high-throughput
transcriptome sequencing data are collected for n genes across p conditions at
r occasions. Matrix-variate distributions offer a natural way to model
three-way data and mixtures of matrix-variate distributions can be used to
cluster three-way data. Clustering of gene expression data is carried out as
means to discovering gene co-expression networks. In this work, a mixture of
matrix-variate Poisson-log normal distributions is proposed for clustering read
counts from RNA sequencing. By considering the matrix-variate structure, full
information on the conditions and occasions of the RNA sequencing dataset is
simultaneously considered, and the number of covariance parameters to be
estimated is reduced. A Markov chain Monte Carlo expectation-maximization
algorithm is used for parameter estimation and information criteria are used
for model selection. The models are applied to both real and simulated data,
giving favourable clustering results
Non-Relativistic Gravitation: From Newton to Einstein and Back
We present an improvement to the Classical Effective Theory approach to the
non-relativistic or Post-Newtonian approximation of General Relativity. The
"potential metric field" is decomposed through a temporal Kaluza-Klein ansatz
into three NRG-fields: a scalar identified with the Newtonian potential, a
3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor.
The derivation of the Einstein-Infeld-Hoffmann Lagrangian simplifies such that
each term corresponds to a single Feynman diagram providing a clear physical
interpretation. Spin interactions are dominated by the exchange of the
gravito-magnetic field. Leading correction diagrams corresponding to the 3PN
correction to the spin-spin interaction and the 2.5PN correction to the
spin-orbit interaction are presented.Comment: 10 pages, 3 figures. v2: published version. v3: Added a computation
of Einstein-Infeld-Hoffmann in higher dimensions within our improved ClEFT
which partially confirms and partially corrects a previous computation. See
notes added at end of introductio
Gene expression during preimplantation mouse development
To develop a resource for the identification and isolation of genes expressed in the early mammalian embryo, large and representative cDNA libraries were constructed from unfertilized eggs, and two-cell, eight-cell, and blastocyst-stage mouse embryos. Using these libraries, we now report the first stages at which the cytokines interleukin (IL)-6, IL-1 beta, and interferon (IFN)-gamma are transcribed in the developing embryo and the presence of IL-7 transcripts in the unfertilized egg. Transcripts for IL-1 alpha, -2, -3, -4, or -5 were not detected at these stages. To identify novel genes expressed on activation of the embryonic genome, the egg and eight-cell stage-specific cDNA libraries were subtracted from the two-cell library, yielding a specialized cDNA library enriched for transcripts expressed at the two-cell stage. Sequence and Southern blot analysis of several of these cDNAs expressed predominantly at the two-cell stage of embryogenesis revealed them to be from novel genes, thereby providing the first molecular tools with which to approach the study of gene expression in the early mammalian embryo
High Energy Field Theory in Truncated AdS Backgrounds
In this letter we show that, in five-dimensional anti-deSitter space (AdS)
truncated by boundary branes, effective field theory techniques are reliable at
high energy (much higher than the scale suggested by the Kaluza-Klein mass
gap), provided one computes suitable observables. We argue that in the model of
Randall and Sundrum for generating the weak scale from the AdS warp factor, the
high energy behavior of gauge fields can be calculated in a {\em cutoff
independent manner}, provided one restricts Green's functions to external
points on the Planck brane. Using the AdS/CFT correspondence, we calculate the
one-loop correction to the Planck brane gauge propagator due to charged bulk
fields. These effects give rise to non-universal logarithmic energy dependence
for a range of scales above the Kaluza-Klein gap.Comment: LaTeX, 7 pages; minor typos fixe
Finite Mixtures of Multivariate Poisson-Log Normal Factor Analyzers for Clustering Count Data
A mixture of multivariate Poisson-log normal factor analyzers is introduced
by imposing constraints on the covariance matrix, which resulted in flexible
models for clustering purposes. In particular, a class of eight parsimonious
mixture models based on the mixtures of factor analyzers model are introduced.
Variational Gaussian approximation is used for parameter estimation, and
information criteria are used for model selection. The proposed models are
explored in the context of clustering discrete data arising from RNA sequencing
studies. Using real and simulated data, the models are shown to give favourable
clustering performance. The GitHub R package for this work is available at
https://github.com/anjalisilva/mixMPLNFA and is released under the open-source
MIT license.Comment: 29 pages, 2 figure
Next to leading order spin-orbit effects in the motion of inspiralling compact binaries
Using effective field theory (EFT) techniques we calculate the
next-to-leading order (NLO) spin-orbit contributions to the gravitational
potential of inspiralling compact binaries. We use the covariant spin
supplementarity condition (SSC), and explicitly prove the equivalence with
previous results by Faye et al. in arXiv:gr-qc/0605139. We also show that the
direct application of the Newton-Wigner SSC at the level of the action leads to
the correct dynamics using a canonical (Dirac) algebra. This paper then
completes the calculation of the necessary spin dynamics within the EFT
formalism that will be used in a separate paper to compute the spin
contributions to the energy flux and phase evolution to NLO.Comment: 25 pages, 4 figures, revtex4. v2: minor changes, refs. added. To
appear in Class. Quant. Gra
Finite size corrections to the radiation reaction force in classical electrodynamics
We introduce an effective field theory approach that describes the motion of
finite size objects under the influence of electromagnetic fields. We prove
that leading order effects due to the finite radius of a spherically
symmetric charge is order rather than order in any physical model, as
widely claimed in the literature. This scaling arises as a consequence of
Poincar\'e and gauge symmetries, which can be shown to exclude linear
corrections. We use the formalism to calculate the leading order finite size
correction to the Abraham-Lorentz-Dirac force.Comment: 4 pages, 2 figure
Precision Measurements of Stretching and Compression in Fluid Mixing
The mixing of an impurity into a flowing fluid is an important process in
many areas of science, including geophysical processes, chemical reactors, and
microfluidic devices. In some cases, for example periodic flows, the concepts
of nonlinear dynamics provide a deep theoretical basis for understanding
mixing. Unfortunately, the building blocks of this theory, i.e. the fixed
points and invariant manifolds of the associated Poincare map, have remained
inaccessible to direct experimental study, thus limiting the insight that could
be obtained. Using precision measurements of tracer particle trajectories in a
two-dimensional fluid flow producing chaotic mixing, we directly measure the
time-dependent stretching and compression fields. These quantities, previously
available only numerically, attain local maxima along lines coinciding with the
stable and unstable manifolds, thus revealing the dynamical structures that
control mixing. Contours or level sets of a passive impurity field are found to
be aligned parallel to the lines of large compression (unstable manifolds) at
each instant. This connection appears to persist as the onset of turbulence is
approached.Comment: 5 pages, 5 figure
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