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

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

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

Most, but not All, Yeast Strains in the Deletion Library Contain the [PIN+] Prion

The yeast deletion library is a collection of over 5100 single gene deletions that has been widely used by the yeast community. The presence of a non-Mendelian element, such as a prion, within this library could affect the outcome of many large-scale genomic studies. We previously showed that the deletion library parent strain contained the [PIN+] prion. [PIN+] is the misfolded infectious prion form of the Rnq1 protein that displays distinct fluorescent foci in the presence of RNQ1–GFP and exists in different physical conformations, called variants. Here, we show that over 97% of the library deletion strains are [PIN+]. Of the 141 remaining strains that have completely (58) or partially (83) lost [PIN+], 139 deletions were able to efficiently maintain three different [PIN+] variants despite extensive growth and storage at 4 °C. One strain, cue2Δ, displayed an alteration in the RNQ1–GFP fluorescent shape, but the Rnq1p prion aggregate shows no biochemical differences from the wild-type. Only strains containing a deletion of either HSP104 or RNQ1 are unable to maintain [PIN+], indicating that 5153 non-essential genes are not required for [PIN+] propagation. Copyright © 2009 John Wiley & Sons, Ltd

Universality of Decoherence

We consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian $H_{\rm sys}$ of the isolated system. While the golden rule then does not apply we can discard $H_{\rm sys}$. By allowing for simultaneous couplings to different reservoirs, we reveal decoherence as a universal short-time phenomenon independent of the character of the system as well as the bath and of the basis the superimposed states are taken from. We discuss consequences for the classical behavior of the macroworld and quantum measurement: For the decoherence of superpositions of macroscopically distinct states the system Hamiltonian is always negligible.Comment: 4 revtex pages, no figure