Existence uniqueness and ratio decomposition for Gibbs states via duality

We give an elementary proof of existence and uniqueness of Gibbs states for Hölder weight systems on subshifts of finite type. This uses a notion of duality for such subshifts. The approach of Paterson [2] is used to construct a measure with a prescribed Jacobian and the duality is used to produce an invariant measure from this

Smoothness of holonomies for codimension 1 hyperbolic dynamics

Hyperbolic invariant sets {Lambda} of C1+{gamma} diffeomorphisms where either the stable or unstable leaves are 1-dimensional are considered in this paper. Under the assumption that the {Lambda} has local product structure, the authors prove that the holonomies between the 1-dimensional leaves are C1+{alpha} for some 0 < {alpha} < 1

Rigidity of hyperbolic sets on surfaces

Given a hyperbolic invariant set of a diffeomorphism on a surface, it is proved that, if the holonomies are sufficiently smooth, then the diffeomorphism on the hyperbolic invariant set is rigid in the sense that it is C1+ conjugate to a hyperbolic affine model

Teichmüller spaces and HR structures for hyperbolic surface dynamics

We construct a Teichmüller space for the C^{1+}-conjugacy classes of hyperbolic dynamical systems on surfaces. After introducing the notion of an HR structure which associates an affine structure with each of the stable and unstable laminations, we show that there is a one-to-one correspondence between these HR structures and the C^{1+}-conjugacy classes. As part of the proof we construct a canonical representative dynamical system for each HR structure. This has the smoothest holonomies of any representative of the corresponding C^{1+}-conjugacy class. Finally, we introduce solenoid functions and show that they provide a good Teichmüller space

A temporal switch model for estimating transcriptional activity in gene expression

Motivation: The analysis and mechanistic modelling of time series gene expression data provided by techniques such as microarrays, NanoString, reverse transcription–polymerase chain reaction and advanced sequencing are invaluable for developing an understanding of the variation in key biological processes. We address this by proposing the estimation of a flexible dynamic model, which decouples temporal synthesis and degradation of mRNA and, hence, allows for transcriptional activity to switch between different states. Results: The model is flexible enough to capture a variety of observed transcriptional dynamics, including oscillatory behaviour, in a way that is compatible with the demands imposed by the quality, time-resolution and quantity of the data. We show that the timing and number of switch events in transcriptional activity can be estimated alongside individual gene mRNA stability with the help of a Bayesian reversible jump Markov chain Monte Carlo algorithm. To demonstrate the methodology, we focus on modelling the wild-type behaviour of a selection of 200 circadian genes of the model plant Arabidopsis thaliana. The results support the idea that using a mechanistic model to identify transcriptional switch points is likely to strongly contribute to efforts in elucidating and understanding key biological processes, such as transcription and degradation

Infrared Spectroscopy of the Diffuse Ionized Halo of NGC 891

We present infrared spectroscopy from the Spitzer Space Telescope at one disk position and two positions at a height of 1 kpc from the disk in the edge-on spiral NGC 891, with the primary goal of studying halo ionization. Our main result is that the [Ne III]/[Ne II] ratio, which provides a measure of the hardness of the ionizing spectrum free from the major problems plaguing optical line ratios, is enhanced in the extraplanar pointings relative to the disk pointing. Using a 2D Monte Carlo-based photo-ionization code which accounts for the effects of radiation field hardening, we find that this trend cannot be reproduced by any plausible photo-ionization model, and that a secondary source of ionization must therefore operate in gaseous halos. We also present the first spectroscopic detections of extraplanar PAH features in an external normal galaxy. If they are in an exponential layer, very rough emission scale-heights of 330-530 pc are implied for the various features. Extinction may be non-negligible in the midplane and reduce these scale-heights significantly. There is little significant variation in the relative emission from the various features between disk and extraplanar environment. Only the 17.4 micron feature is significantly enhanced in the extraplanar gas compared to the other features, possibly indicating a preference for larger PAHs in the halo.Comment: 35 pages in ApJ preprint format, 8 figures, accepted for publication in ApJ. Minor change to Introduction to give appropriate credit to earlier, related wor