The Effect of Finite Element Discretisation on the Stationary Distribution of SPDEs

This article studies the effect of discretisation error on the stationary distribution of stochastic partial differential equations (SPDEs). We restrict the analysis to the effect of space discretisation, performed by finite element schemes. The main result is that under appropriate assumptions the stationary distribution of the finite element discretisation converges in total variation norm to the stationary distribution of the full SPDE.Comment: 15 pages, 1 figur

A Dynamically Diluted Alignment Model Reveals the Impact of Cell Turnover on the Plasticity of Tissue Polarity Patterns

The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganisation in response to an opposing instructive cue, which we here consider by example of experimentally inducible body axis inversions in planarian flatworms. Our dynamically diluted alignment model represents three processes: entrainment of cell polarity by a global signal, local cell-cell coupling aligning polarity among neighbours and cell turnover inserting initially unpolarised cells. We show that a persistent global orienting signal determines the final mean polarity orientation in this stochastic model. Combining numerical and analytical approaches, we find that neighbour coupling retards polarity pattern reorganisation, whereas cell turnover accelerates it. We derive a formula for an effective neighbour coupling strength integrating both effects and find that the time of polarity reorganisation depends linearly on this effective parameter and no abrupt transitions are observed. This allows to determine neighbour coupling strengths from experimental observations. Our model is related to a dynamic $8$-Potts model with annealed site-dilution and makes testable predictions regarding the polarisation of dynamic systems, such as the planarian epithelium.Comment: Preprint as prior to first submission to Journal of the Royal Society Interface. 25 pages, 6 figures, plus supplement (18 pages, contains 1 table and 7 figures). A supplementary movie is available from https://dx.doi.org/10.6084/m9.figshare.c388781

Interpreting Ambiguous Stimuli: Separating Perceptual and Judgmental Biases

Interpreting ambiguous situations is not a purely data-driven process but can be biased towards positive interpretations by top-down influences. The present study tries to identify the underlying processes of these top-down influences. There are two separable types of processes that can be influenced by motivational biases: A perceptual bias affects information uptake whereas a judgmental bias affects acceptance criteria for positive and negative outcomes. In the present study, motivated influences on perception and judgment were investigated with a simple color discrimination task in which ambiguous stimuli had to be classified according to their dominating color. One of two colors indicated a financial gain or a loss, whereas a third color was neutral. To separate perceptual and judgmental biases, Ratcliff’s (1978) diffusion model was employed. Results revealed motivational influences on perception and judgment

Forests of Stumps

Many numerical studies (Hansen and Salamon (1990), Schapire (1990)) indicate that bagged decision stumps perform more accurately than a single stump. In this work, we will investigate two approaches to create a forest of stumps for classification. The first method is bagging with stumps, that is growing a stump on different bootstrap sample size drawn from the training dataset. The second method is Gini-sampled stumps, where we sample split points with probability proportional to the Gini index. These two methods are combined with two aggregation methods: Majority vote and weighted vote. We use simulation studies to compare the performance and consumed time for these two methods. The computing time of generating split points by Gini-sampled stumps is less than half of the time needed to generate split points from bootstrap samples. Also, weighted vote aggregation results in more accurate performance than majority vote aggregation

Results from the Exoplanet Search Programmes with BEST and TEST

Thueringer Landessternwarte Tautenburg (TLS) has started to operate a small dedicated telescope - the Tautenburg Exoplanet Search Telescope (TEST) - searching for transits of extrasolar planets in photometric time series observations. In a joint effort with the Berlin Exoplanet Search Telescope (BEST) operated by the Institut fuer Planetenforschung of the "Deutsches Zentrum fuer Luft- und Raumfahrt (DLR)" at the Observatoire de Haute-Provence (OHP), France, two observing sites are used to optimise transit search. Here, we give a short overview of these systems and the data analysis. We describe a software pipeline that we have set up to identify transit events of extrasolar planets and variable stars in time series data from these and other telescopes, and report on some first results.Comment: 6 pages, 5 figures, contributed paper to the "Solar and Stellar Physics Through Eclipses" conference, eds. O. Demircan, S.O. Selam, B. Albayrak (Turkey, March 2006

Some Fundamental Properties of a Multivariate von Mises Distribution

In application areas like bioinformatics multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modelling of such situations is to use mixtures of unimodal distributions. In the literature (Mardia et al., 2011), the multivariate von Mises distribution, also known as the multivariate sine distribution, has been suggested for components of such models, but work in the area has been hampered by the fact that no good criteria for the von Mises distribution to be unimodal were available. In this article we study the question about when a multivariate von Mises distribution is unimodal. We give sufficient criteria for this to be the case and show examples of distributions with multiple modes when these criteria are violated. In addition, we propose a method to generate samples from the von Mises distribution in the case of high concentration.Comment: fixed a typo in the article title, minor fixes throughou

MCMC Methods for Diffusion Bridges

We present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The method is based on recent theory concerning stochastic partial differential equations (SPDEs) reversible with respect to the target bridge, derived by applying the Langevin idea on the bridge pathspace. In the process, a Random-Walk Metropolis algorithm and an Independence Sampler are also obtained. The novel algorithmic idea of the paper is that proposed moves for the MCMC algorithm are determined by discretising the SPDEs in the time direction using an implicit scheme, parametrised by θ ∈ [0,1]. We show that the resulting infinite-dimensional MCMC sampler is well-defined only if θ = 1/2, when the MCMC proposals have the correct quadratic variation. Previous Langevin-based MCMC methods used explicit schemes, corresponding to θ = 0. The significance of the choice θ = 1/2 is inherited by the finite-dimensional approximation of the algorithm used in practice. We present numerical results illustrating the phenomenon and the theory that explains it. Diffusion bridges (with additive noise) are representative of the family of laws defined as a change of measure from Gaussian distributions on arbitrary separable Hilbert spaces; the analysis in this paper can be readily extended to target laws from this family and an example from signal processing illustrates this fact

A new quantitative approach to identify reworking in Eocene to Miocene pollen records from offshore Antarctica using red fluorescence and digital imaging

Antarctic palaeoclimate evolution and vegetation history after the formation of a continent-scale cryosphere at the Eocene–Oligocene boundary, 33.9 million years ago, has remained a matter of controversy. In particular, the reconstruction of terrestrial climate and vegetation has been strongly hampered by uncertainties in unambiguously identifying non-reworked as opposed to reworked sporomorphs that have been transported into Antarctic marine sedimentary records by waxing and waning ice sheets. Whereas reworked sporomorph grains over longer non-successive geological timescales are easily identifiable within younger sporomorph assemblages (e.g. Permian sporomorphs in Pliocene sediments), distinguishing non-reworked from reworked material in palynological assemblages over successive geological time periods (e.g. Eocene sporomorphs in Oligocene sediments) has remained problematic. This study presents a new quantitative approach to identifying non-reworked pollen assemblages in marine sediment cores from circum-Antarctic waters. We measured the fluorescence colour signature, including red, green, and blue fluorescence; brightness; intensity; and saturation values of selected pollen and spore taxa from Eocene, Oligocene, and Miocene sediments from the Wilkes Land margin Site U1356 (East Antarctica) recovered during Integrated Ocean Drilling Program (IODP) Expedition 318. Our study identified statistically significant differences in red-fluorescence values of non-reworked sporomorph taxa against age. We conclude that red fluorescence is a reliable parameter for identifying the presence of non-reworked pollen and spores in Antarctic marine sediment records from the circum-Antarctic realm that are influenced by glaciation and extensive reworking. Our study provides a new tool to accurately reconstruct Cenozoic terrestrial climate change on Antarctica using fossil pollen and spores

Development of a GEM-TPC prototype

The use of GEM foils for the amplification stage of a TPC instead of a con- ventional MWPC allows one to bypass the necessity of gating, as the backdrift is suppressed thanks to the asymmetric field configuration. This way, a novel continuously running TPC, which represents one option for the PANDA central tracker, can be realized. A medium sized prototype with a diameter of 300 mm and a length of 600 mm will be tested inside the FOPI spectrometer at GSI using a carbon or lithium beam at intermediate energies (E = 1-3AGeV). This detector test under realistic experimental conditions should allow us to verify the spatial resolution for single tracks and the reconstruction capability for displaced vertexes. A series of physics measurement implying pion beams is scheduled with the FOPI spectrometer together with the GEM-TPC as well.Comment: 5 pages, 4 figures, Proceedings for 11th ICATTP conference in como (italy