Bayesian data assimilation in shape registration

In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions\ud for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterisation in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterisation vector field v, informed by regularity results about the forward model. Having done this, we illustrate how Maximum Likelihood Estimators (MLEs) can be used to find regions of high posterior density, but also how we can apply recently developed MCMC methods on function spaces to characterise the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem

Solving the Poisson equation on small aspect ratio domains using unstructured meshes

We discuss the ill conditioning of the matrix for the discretised Poisson equation in the small aspect ratio limit, and motivate this problem in the context of nonhydrostatic ocean modelling. Efficient iterative solvers for the Poisson equation in small aspect ratio domains are crucial for the successful development of nonhydrostatic ocean models on unstructured meshes. We introduce a new multigrid preconditioner for the Poisson problem which can be used with finite element discretisations on general unstructured meshes; this preconditioner is motivated by the fact that the Poisson problem has a condition number which is independent of aspect ratio when Dirichlet boundary conditions are imposed on the top surface of the domain. This leads to the first level in an algebraic multigrid solver (which can be extended by further conventional algebraic multigrid stages), and an additive smoother. We illustrate the method with numerical tests on unstructured meshes, which show that the preconditioner makes a dramatic improvement on a more standard multigrid preconditioner approach, and also show that the additive smoother produces better results than standard SOR smoothing. This new solver method makes it feasible to run nonhydrostatic unstructured mesh ocean models in small aspect ratio domains.Comment: submitted to Ocean Modellin

A Constrained Approach to Multiscale Stochastic Simulation of\ud Chemically Reacting Systems

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper we introduce a multiscale methodology suitable to address this problem. It is based on the Conditional Stochastic Simulation Algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the Constrained Multiscale Algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems

Variational data assimilation using targetted random walks

The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian\ud posterior distribution on the unknown functions of interest, given observations. Since we are aware that these\ud methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available\ud which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces

The Redshift Distribution of FIRST Radio Sources at 1 mJy

We present spectra for a sample of radio sources from the FIRST survey, and use them to define the form of the redshift distribution of radio sources at mJy levels.We targeted 365 sources and obtained 46 redshifts (13 per cent of the sample). We find that our sample is complete in redshift measurement to R $\sim 18.6$, corresponding to $z\sim 0.2$. Early-type galaxies represent the largest subset (45 per cent) of the sample and have redshifts 0.15\la z \la 0.5 ; late-type galaxies make up 15 per cent of the sample and have redshifts 0.05\la z \la 0.2; starbursting galaxies are a small fraction ($\sim 6$ per cent), and are very nearby (z\la 0.05). Some 9 per cent of the population have Seyfert1/quasar-type spectra, all at z\ga 0.8, and there are 4 per cent are Seyfert2 type galaxies at intermediate redshifts ($z\sim 0.2$). Using our measurements and data from the Phoenix survey, we obtain an estimate for $N(z)$ at $S_{1.4 \rm {GHz}}\ge 1$ mJy and compare this with model predictions. At variance with previous conclusions, we find that the population of starbursting objects makes up \la 5 per cent of the radio population at S $\sim 1$ mJy.Comment: 20 pages, sumbitted to MNRA

Adaptive finite element method assisted by stochastic simulation of chemical systems

Stochastic models of chemical systems are often analysed by solving the corresponding\ud Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability\ud distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with non-negligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the probability density

Optical Spectroscopy of Bright Fermi LAT Blazars

We report on HET and Palomar 5 m spectroscopy of recently identified $\gamma$-ray blazars in the {\it Fermi} LAT Bright Source List. These data provide identifications for 10 newly discovered $\gamma$-ray flat spectrum radio quasars (FSRQ) and six new BL Lacs plus improved spectroscopy for six additional BL Lacs. We substantially improve the identification completeness of the bright LAT blazars and give new redshifts and $z$ constraints, new estimates of the black hole masses and new measurements of the optical SED.Comment: 8 pages, 5 figures, 2 tables. Accepted for publication in Ap

Shotgun Metagenomic Sequencing Revealed the Prebiotic Potential of a Fruit Juice Drink with Fermentable Fibres in Healthy Humans

Fibre-based dietary interventions are at the forefront of gut microbiome modulation research, with a wealth of 16S rRNA information to demonstrate the prebiotic effects of isolated fibres. However, there is a distinct lack of data relating to the effect of a combination of soluble and insoluble fibres in a convenient-to-consume fruit juice food matrix on gut microbiota structure, diversity, and function. Here, we aimed to determine the impact of the MOJU Prebiotic Shot, an apple, lemon, ginger, and raspberry fruit juice drink blend containing chicory inulin, baobab, golden kiwi, and green banana powders, on gut microbiota structure and function. Healthy adults (n = 20) were included in a randomised, double-blind, placebo-controlled, cross-over study, receiving 60 mL MOJU Prebiotic Shot or placebo (without the fibre mix) for 3 weeks with a 3-week washout period between interventions. Shotgun metagenomics revealed significant between-group differences in alpha and beta diversity. In addition, the relative abundance of the phyla Actinobacteria and Desulfobacteria was significantly increased as a result of the prebiotic intervention. Nine species were observed to be differentially abundant (uncorrected p-value of <0.05) as a result of the prebiotic treatment. Of these, Bifidobacterium adolescentis and CAG-81 sp900066785 (Lachnospiraceae) were present at increased abundance relative to baseline. Additionally, KEGG analysis showed an increased abundance in pathways associated with arginine biosynthesis and phenylacetate degradation during the prebiotic treatment. Our results show the effects of the daily consumption of 60 mL MOJU Prebiotic Shot for 3 weeks and provide insight into the functional potential of B. adolescentis

Defences against brood parasites from a social immunity perspective

Parasitic interactions are so ubiquitous that all multicellular organisms have evolved a system of defences to reduce their costs, whether the parasites they encounter are the “classic parasites” that feed on the individual, or “brood parasites” that usurp parental care. Many parallels have been drawn between defences deployed against both types of parasite, but typically, whilst defences against classic parasites have been selected to protect survival, those against brood parasites have been selected to protect the parent’s inclusive fitness, suggesting that the selection pressures they impose are fundamentally different. However, there is another class of defences against classic parasites that have specifically been selected to protect an individual’s inclusive fitness, known as “social immunity”. Social immune responses include the anti-parasite defences typically provided for others in kin-structured groups, such as the antifungal secretions produced by termite workers to protect the brood. Defences against brood parasites, therefore, are more closely aligned with social immune responses. Much like social immunity, host defences against brood parasitism are employed by a donor (a parent) for the benefit of one or more recipients (typically kin), and as with social defences against classic parasites, defences have therefore evolved to protect the donor’s inclusive fitness, not the survival or ultimately the fitness of individual recipients This can lead to severe conflicts between the different parties, whose interests are not always aligned. Here we consider defences against brood parasitism in the light of social immunity, at different stages of parasite encounter, addressing where conflicts occur and how they might be resolved. We finish with considering how this approach could help us to address longstanding questions in our understanding of brood parasitism.Peer reviewe